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Damage accumulation and crack initiation detection based on the evolution of surface roughness parameters
Accepted Manuscript Damage Accumulation and Crack Initiation Detection Based on the Evolution of Surface Roughness Parameters Ali Haghshenas, M.M. Khonsari PII: DOI: Reference:
S0142-1123(17)30402-4 https://doi.org/10.1016/j.ijfatigue.2017.10.009 JIJF 4483
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
15 August 2017 15 October 2017 17 October 2017
Please cite this article as: Haghshenas, A., Khonsari, M.M., Damage Accumulation and Crack Initiation Detection Based on the Evolution of Surface Roughness Parameters, International Journal of Fatigue (2017), doi: https:// doi.org/10.1016/j.ijfatigue.2017.10.009
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Damage Accumulation and Crack Initiation Detection Based on the Evolution of Surface Roughness Parameters Ali Haghshenas, M. M. Khonsari1 Department of Mechanical and Industrial Engineering, 3283 Patrick Taylor Hall, Louisiana State University, Baton Rouge, LA 70803, USA Abstract Cyclic strain localization generates sharp surface slip markings in the form of depressions and elevations on the surface of materials. The process gives rise to the formation of persistent slip bands and results in immanent changes that manifest themselves in the form of surface roughening. The heights and depths of these extrusions and intrusions grow during cyclic loading up to a critical value leading to crack initiation. In this study, we investigate the evolution of the surface roughness parameters starting from pristine specimens and ending in final fracture in fully-reversed cyclic bending tests. Results are presented for both low-and high-cycle fatigue that covers a wide range of surface finish. Two types of contacting (via a stylus) and no-contacting (optical) profilometers were used in this investigation. The most sensitive and useful surface roughness parameter for the assessment of fatigue growth in low-and high-cycle fatigue is identified, and it shown that results can be utilized to detect the onset of fatigue crack nucleation. For this purpose, a surface roughness criterion for detecting crack initiation at different applied loads is introduced. Keywords: Fatigue; surface roughness parameters; persistent slip bands; extrusions and intrusions; onset of fatigue crack
1. Introduction Fatigue is the most common type of failure in many structures and components subjected to cyclic loading. One of the most concerning issues in fatigue analysis is the difficulty in detection of crack initiation in the material. While progress has been made, a reliable methodology for the determination of the onset of crack still remains elusive. Cracks initiate on the surface, grow and coalesce due to the localization of plastic deformation and the corresponding dissipated energy that eventually leads to final fracture. Thus, naturally, the consideration of energy dissipation and the associated degradation of microstructural parameters in materials has driven many scientists to investigate the fatigue phenomenon using the energy-based approaches [1-9]. The existing methods are generally considered to be satisfactory for low-cycle fatigue (LCF) applications in which the strain energy and macroscopic plastic strain are simpler to evaluate [10]. Recently researchers suggest new methods and techniques to develop the energy approaches to the high-cycle fatigue (HCF) applications [11-13], wherein the onset of crack remains to be a major problem. During fatigue loading, defects in the form of dislocations produce and accumulate within the material. These accumulations gradually increase the dislocation density produced by strain localization, and manifest themselves in the form of slip bands [14]. Slip bands are the main form of surface damage, often referred to as the persistent slip marking (PSMs). The word ‘’persistent’’ indicates the reappearance of PSBs on the surface of the material on the same location, even after polishing the surface [15]. Studies have shown that this reappearance is responsible for the roughening of the surface during fatigue loading. PSMs include extrusions and intrusions created at the advent of PSBs. Encroachments or macro-PSBs are large clusters of extrusions and intrusions in the form of hills and valleys. These macro-PSMs are 1
Corresponding author, [email protected], V: 225.578.9192, F:225.578.5924
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precursors of crack initiation [15-21]. Evolution of the height and depth of the extrusions (hills) and intrusions (valleys) results in roughening of the surface experiencing fatigue. While the importance of the initial surface roughness on the crack initiation and its influence on fatigue life is well recognized, the evolution of surface roughness parameters during the cyclic loading has not been reported. In this article, we report the results of a series of experiments aimed at the understanding of the evaluation of the surface roughness, the determination of the key parameters involved, and the utilization of the approach in determining a viable method for detecting the onset of crack by means of monitoring the surface roughness parameters. The outline of the paper is as follows. Section 2 presents the relevant background. Section 3 describes the materials and the apparatus used for fatigue tests followed by the presentation of the results and the discussion of a series of fully-reversed bending tests and surface roughness measurements in Section 4. Damping response, based on the authors’ previous work [22] is also measured to verify the results reported in Section 4. The utility of the approach to detect the onset of crack in metals using a profilometer is presented in Section 5. The limitations of the technique are presented in Section 6. The concluding remarks are given in Section 7.
2. Background Figure 1 illustrates a bending specimen with its 3-D surface profile, when in its pristine stage, as well as a schematic of the PSMs consisting of extrusions and intrusions that grow on the surface after a certain number of cyclic testing. Research shows that surface fatigue cracks nucleate in the locations with the highest number of PSMs and tend to grow toward the interior of the material [23, 24]. According to Risbet and Feaugas [25], the number of cycles required for the initiation of crack is related to a critical value of the average extrusions height hc for single-phase metals and under-aged alloys. They used the atomic force microscopy (AFM) to correlate the critical value of the plastic strain irreversibility with fatigue crack initiation. Their results established the existence of a critical irreversible plastic strain responsible for local crack initiation. This value is defined as the ratio between the critical height of the extrusion hc and the grain size D [25]: (1) If D is considered to be a constant, then the plastic strain energy only depends on hc. Therefore, it follows that for each grain size there exists a critical extrusion height, which if exceeded causes the crack to nucleate in the grain. Similarly, there exists a critical value for the intrusion’s depth. The literature contains a number of studies that primarily concentrate on the effect of extrusions [26-29] or intrusions [30-32] on the fatigue crack initiation in different materials. In their pioneering work in this field, Ewing and Humfrey [15] showed that slip lines on the surface of crystals tend to increase with the increasing number of stress reversals. After a considerable number of reversals, they found that some of the crystals were cracked along the broadened slip bands and eventually turned into a long continuous crack across the surface of the specimen. As expected, their observations revealed that the lower the stress, the fewer the slip-lines. They pointed out that the applied plastic strain tends to relax the compression stresses that emerge in the material due to the presence of defects in the form of vacancies. As a result, the cyclic plastic strain is localized into PSBs and extrusions grow statically. Therefore, with a higher applied strain, the extrusions grow at a faster rate. A historical review of the experimental and theoretical studies of surface relief in the form of persistent slip bands (PSBs) in metals is presented by Man et al. [33]. They presented several models showing the evolution of extrusions and intrusions on the surface of metals during fatigue tests. They contend that in spite of the 2
existence of many theories and experimental results, the determination of the crack nucleation remains elusive.
Figure 1. Schematic of evolution of extrusions and intrusions during cyclic load
2.1. Surface roughness parameters In this section, we begin by providing experimental results that illustrate the changes in the surface topography of a specimen undergoing cyclic fatigue. Figures 2-4 illustrate how extrusions and intrusions grow and eventually form a crack. These figures show the surface topography of a pristine carbon steel 1018 specimen (Fig. 2) undergoing fully reversed bending after 10,000 and 74,000 of cycles (Figs. 3 and 4, respectively). These figures are obtained using both an optical profilometer and a scanning electron microscope (SEM). They demonstrate that the surface of the specimen changes tremendously with the number of cycles. SEM images clearly show that the number of peaks and valleys increase with the number of cycles of fatigue load. Similarly, the images captured by the optical profilometer show the growth in the heights and depths of the peaks and valleys as the number of cycles increases. Therefore, both the heights and depths as well as the density of the peaks and valleys are indicative of the damage growth in the materials. Figure 2b shows the free surface of the material with no indication of peaks or valleys. However, after 10,000 cycles (Fig. 3) the elevations and depressions appear on the surface, representing the movement of dislocation to the free surface of the material to minimize the total energy of the system. Figure 4b shows that after 74,000 cycles the elevations and depressions finally develop into a crack. Similar observations have been reported by the others [15, 23 and 25-33].
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(a)
(b)
Figure 2. (a) 3D surface roughness profile of a pristine specimen captured by an optical profilometer. (b) Surface image of a pristine specimen captured by SEM
Extrusions and Intrusions emerge on the surface
(a)
(b)
Figure 3. (a) 3D surface roughness profile of a specimen fatigued up to 10,000 cycles captured by an optical profilometer. (b) Surface image of a specimen fatigued up to 10,000 cycles captured by SEM 500 μm
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Micro Crack
Micro Crack
(a)
(b)
Figure 4. (a) 3D surface roughness profile of a specimen fatigued up to 74,000 cycles captured by an optical profilometer. (b) Surface image of a specimen fatigued up to 74,000 cycles captured by SEM
To quantify the change in the surface features, the following standard 2-D and 3-D parameters are measured (Table 1). The Ra and Rq are the centerline average and the rms of the surface roughness in 2-D, respectively and the Rp and Rv represent the maximum peak height and the maximum valley depth. These parameters are conveniently measured using a contacting stylus. The analogue of these parameters in 3-D is denoted by the surface parameters Sa, Sq, Sp and Sv. Table 1. 2-D and 3-D surface roughness parameters 2-D 3-D
where , and N are the height of each point at coordinates relative to the mean plane, a number of data points, and the number of data points in X and Y directions, respectively. 2.2. Material damping In this section, a brief account of the evolution of material damping is presented and utilized to verify the results presented in Section 3. Damping is a material property that varies with the number of reversals of fatigue load. It represents the dissipation of mechanical energy under the cyclic stress and is referred to as the material damping, structural damping, and the fluid damping [34, 35]. In the authors’ previous work, the damping value was measured experimentally and related to the number of cycles of fatigue load for carbon steel 1018 [22]. This procedure is capable of detecting fatigue crack initiation by examining the point at which the measured value of damping experiences an abrupt increase [36].
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The value of the damping parameter is obtained using the vibration theory for a free vibrational damped system based on the following equation: (2) where A1 and A2 are the two consecutive peaks of the log decrement of the transient response of the free vibration. Nowick [37] shows that damping is proportional to the dissipated energy due to the plastic strain during cyclic loading according to the following equation: (3) where Wp and W are the energy dissipated in a cycle per unit volume and the maximum stored energy per unit volume, respectively. Therefore, the change in damping value, similar to surface roughening, can be related to the evolution of plastic strain energy during the fatigue test.
3. Experimental apparatus and procedure 3.1. Fatigue Test Figure 5 presents the experimental setup for a cyclic bending fatigue apparatus. The rig is a compact, bench-mounted unit with a variable speed motor that actuates a crank connected to the reciprocating platen. The strain level is adjusted by selecting a constant strain value on the crank that converts it into a bending force. The frequency of applied load is adjustable via a control box that provides a counter for the number of cycles and an automatic shut off control.
Figure 5. Schematic of experimental setup for the rotating bending fatigue test 3.2. Material, specimen preparation, and experimental procedure All tests were conducted with flat dog-bone specimens made of carbon steel 1018 with dimensions shown in Figure 6. The red region shown on Figure 6 is a critical region wherein stress is maximum; therefore, a crack is most likely to initiate in this region. The material properties and compositions are shown in Table 2. The dimensions of the flat specimens used in the present study are recommended by the manufacturer of the apparatus (Manufactured by Fatigue Dynamics, Michigan, United States). These specimens are designed and manufactured according to the ASTM STP 566 so that each side of the reduced section is formed by a single circular arc. 6
Table 2. Properties and compositions of CS 1018 Carbon
CS 1018
0.130.20%
Manganese
Silicon
0.30-0.90%
0.150.30%
Phosphorus
Sulfur
Iron
Density
Yield Strength
Modulus of Elasticity
0.04% Max
0.50% Max
98.06 99.42 %
7.86 g/cc
360 MPa
202 GPa
3.2.1. Specimens Preparation Four series of specimens with different surface finishes were tested. They were: I. Both faces polished to mirror finished ( ); II. Both faces polished up to P3000 ( ), III. One side mirror finished and the other up to P3000 and IV. Specimen unpolished on both sides. Sandpapers with the following grit sizes are used to polish the specimens respectively: P180, P320, P400, P800, P1200, P1500, P2000, P2500 and P3000. Mirror finishing is done using a rotation polishing and grinding machine. 3.3. Experimental Procedures First, the specimen is mounted on the testing apparatus and fatigued up to a certain number of cycles. Then, it is removed from the fatigue tester and its damping value is measured using a resonance frequency and damping analyser (RFDA) instrument (IMCE, Genk, Belgium). This device is a non-destructive test rig capable of measuring the free-free vibration mode of the specimen by analyzing its acoustic response signature when tapped lightly with a miniature impact hammer. More details on the testing procedure are available in reference [22]. Next, the surface roughness parameters are measured using a stylus profilometer on three different paths in the critical area on the specimen. According to the standard design of the specimen, a region of the specimen with the least cross-sectional area represents the critical region (Figure 6) wherein the stress is maximum and where a crack is most likely to initiate. Surface roughness parameters are measured in this region on three different paths which are three different lines on the left, middle and right side of the critical region. The lines are called representative line elements (RLEs) meaning that by measuring the surface roughness parameters on these three lines crack initiation moment can be detected. And simultaneously, 3D surface roughness parameters are obtained using an optical profilometer. This procedure is repeated several times throughout the life of the specimen and data are recorded for future analysis.
5.0
10. 0
Fig. 6. Schematic illustration of a dog-bone specimen (red area is the critical region in which stress is maximum). All dimensions are in millimeter.
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4. Results and discussions In this section, we begin by first presenting the results of damping value measurements as they evolve during the fatigue tests followed by the evolution of surface roughness parameters as function of the number of cycles for specimens with four different surface finishes as presented in Table 3. Table 3. Rq (rms) for CS 1018 specimens at different surface finishes
Case I Case II
Rq (for pristine specimens) 0.026 0.044
Case III
0.057
Case IV Case V
1.020 0.060
Comments Both faces mirror finish (LCF) Both faces polished up to P3000 (LCF) One face mirror finish and the other polished up to P3000 (LCF) Unpolished specimen (LCF) Both faces polished up to P3000 (HCF)
4.1. Case . Both faces mirror finish 4.1.1. Damping value measurements Figure 7 presents the growth of damping value with the number of cycles. The damping value is obtained using a time-windowed analysis on the exponentially decaying vibrational function of the specimen with an impact excitation technique. It shows that damping exhibits a repeatable three-stage trend. In the first stage, the specimen initially experiences a rapid increase in damping [22] due to the creation of defects (mostly dislocations) in the material. In the second stage, damping reaches to a steady state level, representing the movement of dislocation and defects rather than enlargement. Damage occurs in this stage due to the formation of sub-microcracks that are created in the sites of dislocations with high density, where stresses are concentrated [37]. In the final stage, the onset of fatigue cracks is marked by an abrupt increase in damping associated with the accumulation of dislocations and consequently initiation of micro cracks [36]. It is interesting to note that temperature rise measured on the surface of a specimen undergoes cyclic load also shows a similar three-stage behavior [9,38,39]. Under the conditions tested, there is no significant change in the damping value until 80,000 cycles when an abrupt increase in the damping value (Stage III) is recorded. The last damping measurement at 100,000 cycles was roughly 2.5 times greater than that of the pristine specimen, which reached its final fracture shortly thereafter. These results are consistent with those reported by Mortazavi et al. [22] and can be used for the detection of the onset of crack initiation.
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0.0014 Final Fracture 0.0012 0.001
Damping
Stage III 0.0008 Stage II
Stage I
0.0006 0.0004 0.0002
Crack Initiation
0 0
20000
40000
60000
80000
100000
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Number of Cycles
Figure 7. Damping value versus number of cycles
4.1.2. 2D surface roughness parameters Figures 8a, 8b, 8c and 8d present the two-dimensional roughness parameters for a specimen with mirror surface finish in its pristine state. The results show three different paths on the specimen measured by a stylus profilometer at a different number of cycles. These figures show an increasing trend in all the surface roughness parameters as the number of cycles increases up to the end of the fatigue test. Similar to the trend of the damping values, the evolution of the surface roughness parameters can be divided into three distinct stages. The first and final stages show the same trend as damping values. However, in the second stage, unlike the damping values, the surface roughness parameters exhibit a roughly linear increase. This trend can be attributed to the damage accumulation in the material. In the second stage, defects tend to dislocate rather than enlarge and damping value is not sensitive enough to the movement of dislocations; therefore, no major change in damping value is seen at this stage [22]. However, surface roughness parameters continue to grow because dislocations continue to move toward the free surface due to cyclic straining and contribute further to increase the surface roughness. It is worthwhile to mention that research shows that the evolution of the surface temperature during fatigue test also tends to reach a plateau during the second stage [38]. Because the area under the temperature-time curve represents dissipated plastic energy and although the temperature is constant at this stage, the accumulated dissipated plastic energy increases during the second stage [40-45]. At the end of the second stage (after 80,000 cycles), the roughness parameters undergo an abrupt increase. This is an indication of crack initiation in the specimen, exactly the same as the results obtained via the damping tests. Figures 8c and 8d, show that Rv, which represents the maximum depth of intrusions, shows more sensitivity to the onset of crack initiation than Rp. This can be attributed to the fact that microcracks are in the form of intrusions.
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(C) (d) Figure 8. Evolution of 2D surface roughness parameters as function of number of cycles with mirror finish surfaces at the pristine state. (a) Ra versus number of cycles. (b) Rq versus number of cycles. (c) Rp versus number of cycles. (d) Rv versus number of cycles
4.1.3. Three-dimensional surface roughness parameters Figures 9a and 9b show growth of the 3D surface roughness parameters of a pristine specimen with both surfaces polished to a mirror finish as measured by an optical profilometer at a different number of cycles during a fatigue test. The field of view for optical profilometer is shown is mainly on the critical region (as shown in Figure 6). However, the size of the field of view does not appreciably affect the results as long as it includes the critical region. The results reveal the familiar three-stages roughness evolution, similar to those exhibited by the two-dimensional surface roughness parameters. Clearly Sv and Sp are more sensitive parameters to damage accumulation in the specimen compared to Sa, Sq, since they (Sa, Sq) represent the average of peaks and valleys over the measured region of the specimen. According to Sangid [14] the maximum peaks and valleys on the surface correspond to critical regions that contain more defects in the form of dislocations. Therefore, critical regions are expected to represent more roughening —extrusions and intrusions grow faster— than other locations on the surface. Therefore, Sp 10
and Sv show more sensitivity when plotted against a number of cycles. In the second stage, there is a linear increase in the value of each parameter, due to the constant growth in height and depth of the extrusions and intrusions during the cycling loading. The specimens surface profiles at its pristine condition and after 50,000 and 80,000 cycles are shown in Figures 10a,b, and c, respectively. The dimensions of the images are 1.1 mm by 0.85 mm. These were obtained using the optical profilometer. The area of interest consists of many grains (approximately 1000) that are both favorably and not favorably oriented to slip. That is why statistical parameters that use average parameter (Sa, Sq, Ra and Rq) and maximum parameters (Sp, Sv, Rp and Rv) are selected to represent both types of grains. The first set of parameters (Sa, Sq, Ra and Rq) represent the average values of all grains while maximum values (Sp, Sv, Rp and Rv) represent grains that are favorably oriented to slip and tend to experience more deformation. The measurements reported in this section pertain to the entire area of the critical region called RSE (representative surface element), rather than the three lines in the RLEs shown in Fig. 8. Surprisingly, the 3D parameters show an abrupt increase —signifying the onset of the crack initiation— exactly at the same time that 2D parameters. However, the magnitude of the values for 3D parameters are about three fold greater than those of the 2D parameters, implying that 3D parameters are more sensitive than the 2D parameters. Thus, measuring the surface roughness parameters on an RSE is more useful than RLE. 5
18 Final Fracture
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14 12
3
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
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Crack Initiation
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80000 100000 120000
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Figure 9. Evolution of Sa, Sq, Sp and Sv as function of number of cycle number of cycles
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1.3 mm 0.9 mm
(a)
(b)
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(c) Figure 10. Surface profile of the specimen at different number of cycles (a. pristine, b. 50,000 cycles and c. 80,000 cycles)
4.2. Case . Both faces polished up to P3000 4.2.1. Damping value Figure 11 shows the evolution of the Damping value with fatigue cycles for a specimen polished up to P3000 on both faces. The crack initiation occurs sooner, at 50,000 cycles, and the specimen’s fatigue life is shorter (approximately 75,000 cycles) than the case I where both surfaces were polished to mirror finish.
0.0014
Final Fracture
0.0012
Damping
0.001 0.0008 0.0006 0.0004 0.0002 0 0
10000
20000
30000
40000
50000
60000
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Figure 11. Damping value versus number of cycles of the specimen polished up to P3000 on both faces
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4.2.2. Two dimensional surface roughness parameters The 2D surface roughness parameters plotted as a function of a number of cycles are presented in Figures 12a, 12b, 12c, and 12d. All parameters show the same overall trend; however, parameters measured on the left RLE show more sensitivity to not only the onset of crack nucleation but also the cyclic loading. The reason is that the macro-crack initiates on the left side of the specimen at the final stage (Stage III). Therefore, the parameters on the left RLE show an abrupt increase (which indicates the crack initiation moment) prior to those measured elsewhere. The experiments show that the critical region is on the left side of the specimen and the parameters belong to the left RLE represent the crack initiation at 50,000 — identically the same as the result of the damping tests shown in Fig. 11. At 60,000 cycles when the crack moves to the right, the parameters measured on the middle RLE and right RLE of the specimen detect the initiation of the crack and show the familiar abrupt increase as well. The results also reveal that the surface finish of the pristine specimen does not affect the trend of surface roughness parameters and that the onset of crack initiation can be detected by monitoring the appropriate surface roughness parameters regardless of the pristine specimen’s surface finish. This is further illustrated in Section 4.4 that deals with an unpolished specimen. 0.9
1.2 Final Fracture
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Figure 12. Evolution of Ra, Rq, Rp and Rv as function of number of cycles at different locations (left, middle and right) of the specimen polished up to P3000 on both faces
In Figures 13a, 13b and 13c the behavior of the surface roughness parameters measured on different RLEs are presented separately to show the discrimination between the parameters measured on the crack growth side of the specimen and parameters in the regions away from where the crack is likely to initiate. This representation is chosen to highlight the influence of the crack site on the surface roughness parameters. The extrusions and intrusions on the surface are representative of the local plastic deformation which depends on the dislocation density in that location. The regions with greater dislocation density produce more plastic deformation and, as a result, create more elevation and depression on the surface. Therefore, a crack is expected to initiate on the regions where the surface roughness parameters grow faster and show more sensitivity to the number of cycles. 6
5
Surface Roughness Parameters on the Middle of the Specimen (μm)
Surface Roughness Parameters on the Left Side of the Specimen (μm)
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4 P3000 (front and back)
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Rp 2
Ra
Rq
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1
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20000 40000 60000 Surface Roughness Parameters
80000
(c) Figure 13. Evolution of Ra, Rq, Rp and Rv as function of number of cycles on left side of the specimen (a), middle of the specimen (b) and right sides of the specimen (c), polished up to P3000 on both faces
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4.2.3. Three dimensional surface roughness parameters Figures 14a and 14b show the 3D surface roughness parameters measured by the optical profilometer for four different specimens polished up to P3000 on both faces. As the figures indicate, the crack initiated after 60,000 cycles. For this case, all four parameters show an abrupt increase (representing the onset of the crack initiation) at the same time. This experiment also verifies the previous observation that the surface finish of the pristine conditions does not affect the evolution of surface roughness parameters. The corresponding surface profiles for the specimen at its pristine condition as well after 30,000 and 60,000 cycles are shown in Figure 15.
2 1.8
12
1.6 1.4
10 Sp and Sv (𝜇𝑚)
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Figure 14. Evolution of Sa and Sq and Sp and Sv as function of number of cycles for a specimen polished up to P3000 on both faces
1.3 mm
0.9 mm (a)
(b)
(c)
Figure 15. Surface profile of the specimen at different number of cycles (a. pristine, b. 30,000 cycles and c. 60,000 cycles)
4.3. Case
. One face mirror finish and the other polished up to P3000 16
Figures 16a, 16b, 16c and 16d show two-dimensional surface roughness parameters measured on the three RLEs on the specimen with one surface mirror finish and the other polished up to P3000. Here, the RLEs correspond to the mirror finish face of the specimen where the crack is not expected to initiate. Accordingly, the curves belonging to the left side and middle side of the specimen are not showing any sudden increase in value. However, there is an indication of crack initiation on the right RLE, examination of the surfaces revealed that, indeed, the crack leads to final fracture was initiated on the surface polished up to P3000. As discussed in the previous section, crack initiates on the critical regions, and in this case, the rougher face of the specimen favors crack initiation. Figure 17 shows the surface roughness parameters belonging to the left RLE versus number of cycles. These results indicate that the rate of growth of Rv and Rp is more than Ra and Rq , which make them more promising for both representing the damage in the material and detecting the crack initiation moment. The difference is due to the fact that Rv and Rp represent the extreme values, however, Ra and Rq are averages of some values measured over a RLE (according to Table 1).
1
0.9 Final Fracture 0.8
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Figure 16. Evolution of Ra, Rq, Rp and Rv versus number of cycles at different locations (left, middle and right) measured on the mirror finish face of the specimen
5 Final Fracture
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Figure 17. Evolution of surface roughness parameters (measured at the left RLE) as function of number of cycles measured on the mirror finished face of the specimen
4.4. Case IV. Unpolished specimen The purpose of this section is to investigate the applicability of the results to an unpolished specimen. Figure 18 shows the 3D surface roughness parameters plotted versus the number of cycles for a specimen as received from a hot rolled production process. As shown in the Figure 18, Sa and Sq undergo an abrupt increase after 40,000 cycles while Sp and Sv show the sudden increase shortly after 50,000 cycles. Since Sp and Sv represent maximum values, and for a rough surface their initial value is close to the critical value at which crack initiates, they cannot be a good candidate to represent damage accumulation in the material. However, if their value is below the critical value, it is possible to detect the crack initiation by monitoring their evolution. That is why the abrupt increase in the Figure 18 (b) occurs roughly after 10,000 cycles longer than that of Figure 18 (a). Also, according to Table 1, Sa and Sq represent an average value of the height and depth of all peaks and valleys in the field of view of the profilometer. Thus, the roughening due to cyclic load can be detected more accurately by monitoring Sa and Sq. Therefore, for an unpolished material, Sa and Sq are better candidates to detect damage accumulation and crack initiation. The Surface profiles of the specimen at its pristine condition as after different stages of its fatigue life are shown in Figure 19.
18
1.6
9
1.4
Sa
Sq
8 7
Sv
6
1
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
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5 4 3
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Unpolished (Front and back)
Unpolished (Front and back)
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10000 20000 30000 40000 50000 60000 70000 Number of Cycles
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10000 20000 30000 40000 50000 60000 70000 Number of Cycles
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Figure 18. Evolution of Sa, Sq, Sp and Sv as function of number of cycles for an unpolished specimen
1. 3 m m
0.9 mm (a)
(b)
(d)
Figure 19. Surface profile of the specimen at different number of cycles (a. pristine, b. 40,000 cycles and c. 60,000 cycles)
4.5. Case V. Both faces polished up to P3000 (High-Cycle Test) In this section we explore the applicability of the method to a high-cycle fatigue test, which demonstrates a typical in-service application. The result of a fatigue test on a specimen both faces polished to P3000 and subjected to HCF is presented in Figure 20. Results show the familiar three-stages for all the surface roughness parameters, albeit the change in values is considerably smaller for each parameter compared to the corresponding parameter in LCF tests. This is because of the fact that the material experiences much less plastic deformation. Results show that in HCF test, unlike LCF, Sp plays more important role. While other roughness parameters show an abrupt increase after 900,000 cycles, the Sp parameter detect it at 800,000 cycles. Also the change in Sp value is more distinguishable compare to the other parameters. There are two main reasons why in HCF the growth of intrusions is less than that of extrusions. According to Polak and Sauzay [43] intrusions are formed by vacancies produced by annihilation as a result of dislocation interactions in the walls of PSBs and that they are diffused to or absorbed by the interface of PSBs and matrix on the free surfaces of the material. Therefore, dislocation density and movement of dislocations directly affect the formation of intrusions. In general, formation of dislocations in HCF is considerably less pronounced compared to a LCF due to the smaller applied load. Also, the temperature rise during the LCF test eases the movement of dislocations while the temperature rise in 19
HCF tests is infinitesimal. Thus, it is expected that less changes occur in growth of intrusions compare to that of extrusions in HCF tests. The images captured by the optical profilometer is shown in Figure 20 at three different number stages, pristine, after 800,000 cycles and after one million cycles. Figure 21c shows a visible crack on the surface of the material. The red regions in this figure indicate the highest peaks located in the vicinity of the lowest valleys (blue regions). This observation is in accordance to the theory of fatigue crack initiation which asserts that a crack initiates due to the intrusions in the vicinity of the highest extrusions. 0.3
4.5 4 Stage III
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Figure 20. Evolution of Sa and Sq and Sp and Sv as function of number of cycles for a specimen polished up to P3000 on both faces
1.3 mm
0.9 mm
(a)
(b)
(c)
Figure 21. Surface profile of the specimen at different number of cycles (a. pristine, b. 800,000 cycles and c. 1000,000 cycles)
4.6. Surface roughness parameters at different stress levels Figure 22 shows the so-called S-N curve for the CS 1018 with the corresponding displacement values which is applied at the actuated end of the specimen. The S-N curve is obtained for specimens polished up to P3000. In addition, two different data points are shown on the figure to compare the effect of surface finish on the fatigue life of the specimens. Results show an extended fatigue life for specimens with a better surface finish.
20
Figure 23 presents the 2D surface roughness parameters at various number of cycles for fatigue tests at three different stress levels. δ represents the displacement of the specimen at the actuated end of the specimen in millimeters. These figures show that the higher the strain amplitude, the greater is the rate of increase of all the surface roughness parameters. Applied stress is directly proportional to the number of dislocations created in the material so that the higher the applied stress, the greater is the dislocations density and the resulting plastic deformation. Therefore, for specimens undergoing higher stress (strain) level, a higher rate of growth in surface roughness parameters are expected leading to an eventually shorter life as shown in Figure 23. This finding agrees with the observations of Ewing and Humfrey [15] who investigated the relationship between the applied strain amplitude and the growth size and numbers of extrusions and intrusions on the surface of the specimen. They stated that as the level of the applied strain increases, the observed size of the PSBs and the number of them tend to increase. Polak and Suazay [46] also studied the effect of stress on the emergence of PSBs and reported a similar behavior. 11
480 N=65,000 (Unpolished Specimen)
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8 330
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9
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380
6 230
5 4
180 0
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Number of Cycles to Failure
Figure 22. Relationship between stress and displacement in fully-reversed bending fatigue 1.4
2.5
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Rq (𝜇𝑚)
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(a)
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100000 150000 Number of Cycles
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Figure 23. (a), (b), (c) and (d) represent evolution of Ra, Rq, Rp and Rv as function of cycles for a specimen polished up to P3000 on both faces at three different stress levels
5. A relationship for crack initiation detection Evolution of the surface roughness for low carbon steel samples under cyclic loading is studied by de Lacerda et al. [49]. They investigated the relationship between the evolution of extrusions and intrusions as a function of fatigue load and number of cycles. They found that as the stress decreases the ratio of extrusions height to that of intrusions decreases. In this section, a relationship capable of detecting the onset of crack initiation at different strain levels is developed here based on the evolution of the height of the extrusions (Sp). Table 4 shows ratio of critical of each different roughness parameter over its initial value (i.e., pristine) for a specimen. Table 4. The ratio of critical value of a surface roughness parameter over its initial value for different strain levels
Strain Level (mm)
5 6.35 7.62 10.16
1.3 2 19 51
1.3 2 19 51
1.5 6 21 64
1.2 4.5 25 67
Sv is the most sensitive parameter to the onset of crack in the tested material at LCF but it is less effective in HCF. In contrast, Sp is capable of detecting the onset of crack in both LCF and HCF tests; hence, it is more appropriate for generalization purpose. The relationship is defined between the ratio of the critical Sp over initial value of Sp and applied load level and is presented in Figure 24. The critical Sp is considered to be the value of Sp at which crack initiates. To be conservative, the lowest value of critical Sp from extensive set of experiments is considered. Equation 4 is derived based on a curve fitting (see the red dots) on Figure 24. (4) where is the displacement applied on the actuated end of the specimen. The value for this curve fitting equals 1 which indicates that the regression line perfectly fits the data. The figure shows that, for 22
example, the onset of crack initiation at the displacement level of 8 mm (corresponding to the stress level of 350 MPa), is 21-fold greater than its initial pristine value.
0
100
0
2
200
Stress (MPa) 300
400
500
70 60
Critical Sp / Initial Sp
50 40 30 20 10 0
4
6
8
10
12
Displacement (mm)
Figure 24. A relationship for obtaining
at which crack initiates for different applied displacements
6. Limitations of the technique Risbet et al. [48] used the atomic force microscopy (AFM) to experimentally study the evolution of surface deformation of nickel-base superalloy specimens under cyclic loading. By investigating the height of the extrusions quantitatively, they formulated a microscopic crack initiation law, and obtained a critical value for the height of the extrusions at which crack initiates. High-resolution analysis using the AFM is useful to establish the work in details. However, the use of a profilometer provides a feasible approach for engineering applications especially with potential for in situ measurements. Since the height and depth of the extrusions and intrusions play a significant role here, the vertical resolution of the devices is important. The vertical resolution of the stylus and the optical profilometer is sensitive enough to detect the height and depth of the extrusions and intrusions within slip bands when surface roughness is below a certain value. For some cases (after crack initiates), both stylus and optical profilometer have some limitations to measure high surface slopes. They tend to show the high ratio trenches as graphical shapes with missing data in some small segments. However, the software uses curve fitting to fill the missing data of the trenches. The aim of our study is to detect the onset of crack initiation, and examination of our results reveals that there are very few or no missing data for the depth of intrusions before the crack initiation. Thus, the measurements are accurate enough to detect the crack initiation moment. Another limitation is that this technique can be used for materials and loading conditions in which crack initiates on the surface. For materials in which crack initiates from subsurface, the surface roughness parameters are expected to show a linear growth when plotted versus the number of cycles.
23
7. Conclusions The extrusions and intrusions are the manifestation of PSBs and widely recognized as the source of crack initiation. While the contribution of initial surface roughness on the fatigue life of the materials has been studied by many researchers, the crack initiation detection using the evolution of surface roughness parameters has not been investigated so far. In this paper, an approach for detecting the initiation of crack by means of 2D and 3D surface roughness parameters using both a stylus and an optical profilometer is presented. The approach is based on the monitoring the 2D surface roughness parameters Ra, Rq, Rp and Rv and 3D surface roughness parameters Sa, Sq, Sv and Sp during cyclic loading. Rp, Rv, Sv and Sp represents height of the extrusions and depth of the intrusions on the surface of the specimen. It is shown that the evolution of the surface roughness parameters occurs in three distinct stages and the higher the applied stress, the higher is the growth rate. These parameters can represent damage accumulation in the material, because when damping value shows a plateau in the second stage the surface roughness parameters show a linear increase in value. Furthermore, Rp and Rv, show the same trend as Sv and Sp, respectively. However, interestingly in LCF, Rv and Sv show more sensitivity to both damage accumulation and onset of crack in the material while in HCF Sp plays more important role. The results are verified monitoring damping value during fatigue test. To show the applicability of the method, an experiment is performed on an unpolished specimen. Results show that Sa and Sq are better candidates to detect the crack initiation moment in an unpolished specimen. Finally, a relationship between and load level is presented to detect the onset of the crack initiation. This relationship is useful for determining the safe operation of a specimen before a crack initiates.
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[8] Meneghetti, G. "Analysis of the fatigue strength of a stainless steel based on the energy dissipation." International journal of fatigue 29, no. 1 (2007): 81-94. [9] Naderi, M., M. Amiri, and M. M. Khonsari. "On the thermodynamic entropy of fatigue fracture." In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 466, no. 2114, pp. 423-438. The Royal Society, 2010. [10] Wang, X. G., V. Crupi, C. Jiang, and E. Guglielmino. "Quantitative thermographic methodology for fatigue life assessment in a multiscale energy dissipation framework." International Journal of Fatigue 81 (2015): 249-256. [11] Crupi, V. "An unifying approach to assess the structural strength. "International Journal of Fatigue 30, no. 7 (2008): 1150-1159. [12] Liakat, M., and M. M. Khonsari. "On the anelasticity and fatigue fracture entropy in high-cycle metal fatigue." Materials & Design 82 (2015): 18-27. [13] Meneghetti, G., M. Ricotta, and B. Atzori. "Experimental evaluation of fatigue damage in two-stage loading tests based on the energy dissipation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 7 (2015): 1280-1291. [14] Sangid, M. D., Hans J. Maier, and H. Sehitoglu. "A physically based fatigue model for prediction of crack initiation from persistent slip bands in polycrystals." Acta Materialia 59, no. 1 (2011): 328-341. [15] Ewing, J. A., and J. C. W. Humfrey. "The fracture of metals under repeated alternations of stress." Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 200 (1903): 241-250. [16] Cretegny, L., and A. Saxena. "Evolution of surface deformation during fatigue of PH 13‐8 Mo stainless steel using atomic force microscopy." Fatigue & Fracture of Engineering Materials & Structures 25, no. 3 (2002): 305-314. [17] Thompson, N., N. Wadsworth, and N. Louat. "The origin of fatigue fracture in copper." Philosophical Magazine 1, no. 2 (1956): 113-126. [18] Cretegny, L., and A. Saxena. "AFM characterization of the evolution of surface deformation during fatigue in polycrystalline copper." Acta materialia 49, no. 18 (2001): 3755-3765. [19] Risbet, M., and X. Feaugas. "Some comments about fatigue crack initiation in relation to cyclic slip irreversibility." Engineering Fracture Mechanics 75, no. 11 (2008): 3511-3519. [20] Ho, H. S., M. Risbet, X. Feaugas, and G. Moulin. "The effect of grain size on the localization of plastic deformation in shear bands." Scripta Materialia 65, no. 11 (2011): 998-1001. [21] Risbet, M., X. Feaugas, C. Guillemer-Neel, and Michel Clavel. "Damage in nickel base superalloy: influence of local parameters measured by electron backscattered diffraction and atomic force microscopy." Scripta Materialia 60, no. 5 (2009): 269-272. [22] Mortezavi, V., A. Haghshenas, M. M. Khonsari, and B. Bollen. "Fatigue analysis of metals using damping parameter." International Journal of Fatigue 91 (2016): 124-135. [23] Polák, J., V. Mazánová, I. Kuběna, M. Heczko, and J. Man. "Surface relief and internal Structure in fatigued stainless sanicro 25 steel." Metallurgical and Materials Transactions A 47, no. 5 (2016): 19071911. [24] Suresh S. Fatigue of materials. Cambridge University Press 1998. 25
[25] Risbet, M., X. Feaugas, C. Guillemer-Neel, and M. Clavel. "Use of atomic force microscopy to quantify slip irreversibility in a nickel-base superalloy." Scripta Materialia 49, no. 6 (2003): 533-538. [26] Mughrabi, H., R.Wang, K. Differt, and Uwe Essmann. "Fatigue crack initiation by cyclic slip irreversibilities in high-cycle fatigue." In Fatigue mechanisms: Advances in quantitative measurement of physical damage. ASTM International, 1983. [27] Mughrabi, H.. "Cyclic slip irreversibilities and the evolution of fatigue damage." Metallurgical and materials Transactions A 40, no. 6 (2009): 1257-1279. [28] Schwaiger, R., G. Dehm, and O. Kraft. "Cyclic deformation of polycrystalline Cu films." Philosophical Magazine 83, no. 6 (2003): 693-710. [29] Brown, L. M. "Cracks and extrusions caused by persistent slip bands." Philosophical Magazine 93, no. 28-30 (2013): 3809-3820. [30] Polák, J. "On the role of point defects in fatigue crack initiation." Materials Science and Engineering 92 (1987): 71-80. [31] Polák, J., and J. Man. "Mechanisms of extrusion and intrusion formation in fatigued crystalline materials." Materials Science and Engineering: A 596 (2014): 15-24. [32] Nakai, Yoshikazu, T. Kusukawa, and N. Hayashi. "Scanning atomic-force microscopy on initiation and growth behavior of fatigue slip-bands in α-brass." In Fatigue and Fracture Mechanics: 32nd Volume. ASTM International, 2002. [33] Man, J., K. Obrtlik, and J. Polak. "Extrusions and intrusions in fatigued metals. Part 1. State of the art and history." Philosophical Magazine 89, no. 16 (2009): 1295-1336. [34] De Silva, Clarence W. “Dynamic testing and seismic qualification practice.” D.C. Heath and Co., Lexington, MA, 1983. [35] Zener, Clarence. "Internal friction in solids." Proceedings of the Physical Society 52, no. 1 (1940): 152. [36] Jones, R. L., "A constitutive relationship between crack propagation and specific damping capacity in steel." No. NCEL-N-1817. Naval Civil Engineering Lab Port Hueneme CA, 1990. [37] Nowick, Arthur S. "Anelastic relaxation in crystalline solids." Vol. 1. Elsevier, 2012. [38] Amiri, M., M. Naderi, and M. M. Khonsari. "An experimental approach to evaluate the critical damage." International Journal of Damage Mechanics 20, no. 1 (2011): 89-112. [39] Amiri, M., and M. M. Khonsari. "Life prediction of metals undergoing fatigue load based on temperature evolution." Materials Science and Engineering: A 527, no. 6 (2010): 1555-1559. [40] Liakat, M., and M. M. Khonsari. "Rapid estimation of fatigue entropy and toughness in metals." Materials & Design (1980-2015) 62 (2014): 149-157. [41] Amiri, M., and M. M. Khonsari. "Rapid determination of fatigue failure based on temperature evolution: Fully reversed bending load." International Journal of Fatigue 32, no. 2 (2010): 382-389. [42] Amiri, M., and M. M. Khonsari. "Nondestructive estimation of remaining fatigue life: thermography technique." Journal of failure analysis and prevention 12, no. 6 (2012): 683-688. [43] Amiri, M., and M. M. Khonsari. "On the role of entropy generation in processes involving fatigue." Entropy 14, no. 1 (2011): 24-31. 26
[44] Naderi, M., and M. M. Khonsari. "An experimental approach to low-cycle fatigue damage based on thermodynamic entropy." International Journal of Solids and Structures 47, no. 6 (2010): 875-880. [45] Naderi, M., A. Kahirdeh, and M. M. Khonsari. "Dissipated thermal energy and damage evolution of glass/epoxy using infrared thermography and acoustic emission." Composites Part B: Engineering 43, no. 3 (2012): 1613-1620. [46] Polák, J., and M. Sauzay. "Growth of extrusions in localized cyclic plastic straining." Materials Science and Engineering: A 500, no. 1 (2009): 122-129. [47] Basinski, Z. S., R. Pascual, and S. J. Basinski. "Low amplitude fatigue of copper single crystals I. The role of the surface in fatigue failure." Acta Metallurgica 31, no. 4 (1983): 591-602.I [48] Risbet, M., X. Feaugas, C. Guillemer-Neel, and M. Clavel. "Use of atomic force microscopy to quantify slip irreversibility in a nickel-base superalloy." Scripta Materialia 49, no. 6 (2003): 533-538. [49] de Lacerda, J. C., G. D. Martins, V. T. Signoretti, and R. L. P. Teixeira. "Evolution of the surface roughness of a low carbon steel subjected to fatigue." International Journal of Fatigue 102 (2017): 143148.
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Highlights
Evolution of surface roughness in low-and high-cycle fatigue is investigated. Appropriate surface roughness parameters for monitoring purposes are identified. Roughness parameters undergo three distinct stages from pristine to fracture An approach for detecting the initiation of crack is presented.
.
28
0.3
4.5 4
0.25 3.5 3
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
0.2
Stage II 0.15
0.1
2.5 2 1.5 1
0.05 0.5 0
0 0
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( Pristine,
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1000,000 cycles
S0142-1123(17)30402-4 https://doi.org/10.1016/j.ijfatigue.2017.10.009 JIJF 4483
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
15 August 2017 15 October 2017 17 October 2017
Please cite this article as: Haghshenas, A., Khonsari, M.M., Damage Accumulation and Crack Initiation Detection Based on the Evolution of Surface Roughness Parameters, International Journal of Fatigue (2017), doi: https:// doi.org/10.1016/j.ijfatigue.2017.10.009
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Damage Accumulation and Crack Initiation Detection Based on the Evolution of Surface Roughness Parameters Ali Haghshenas, M. M. Khonsari1 Department of Mechanical and Industrial Engineering, 3283 Patrick Taylor Hall, Louisiana State University, Baton Rouge, LA 70803, USA Abstract Cyclic strain localization generates sharp surface slip markings in the form of depressions and elevations on the surface of materials. The process gives rise to the formation of persistent slip bands and results in immanent changes that manifest themselves in the form of surface roughening. The heights and depths of these extrusions and intrusions grow during cyclic loading up to a critical value leading to crack initiation. In this study, we investigate the evolution of the surface roughness parameters starting from pristine specimens and ending in final fracture in fully-reversed cyclic bending tests. Results are presented for both low-and high-cycle fatigue that covers a wide range of surface finish. Two types of contacting (via a stylus) and no-contacting (optical) profilometers were used in this investigation. The most sensitive and useful surface roughness parameter for the assessment of fatigue growth in low-and high-cycle fatigue is identified, and it shown that results can be utilized to detect the onset of fatigue crack nucleation. For this purpose, a surface roughness criterion for detecting crack initiation at different applied loads is introduced. Keywords: Fatigue; surface roughness parameters; persistent slip bands; extrusions and intrusions; onset of fatigue crack
1. Introduction Fatigue is the most common type of failure in many structures and components subjected to cyclic loading. One of the most concerning issues in fatigue analysis is the difficulty in detection of crack initiation in the material. While progress has been made, a reliable methodology for the determination of the onset of crack still remains elusive. Cracks initiate on the surface, grow and coalesce due to the localization of plastic deformation and the corresponding dissipated energy that eventually leads to final fracture. Thus, naturally, the consideration of energy dissipation and the associated degradation of microstructural parameters in materials has driven many scientists to investigate the fatigue phenomenon using the energy-based approaches [1-9]. The existing methods are generally considered to be satisfactory for low-cycle fatigue (LCF) applications in which the strain energy and macroscopic plastic strain are simpler to evaluate [10]. Recently researchers suggest new methods and techniques to develop the energy approaches to the high-cycle fatigue (HCF) applications [11-13], wherein the onset of crack remains to be a major problem. During fatigue loading, defects in the form of dislocations produce and accumulate within the material. These accumulations gradually increase the dislocation density produced by strain localization, and manifest themselves in the form of slip bands [14]. Slip bands are the main form of surface damage, often referred to as the persistent slip marking (PSMs). The word ‘’persistent’’ indicates the reappearance of PSBs on the surface of the material on the same location, even after polishing the surface [15]. Studies have shown that this reappearance is responsible for the roughening of the surface during fatigue loading. PSMs include extrusions and intrusions created at the advent of PSBs. Encroachments or macro-PSBs are large clusters of extrusions and intrusions in the form of hills and valleys. These macro-PSMs are 1
Corresponding author, [email protected], V: 225.578.9192, F:225.578.5924
1
precursors of crack initiation [15-21]. Evolution of the height and depth of the extrusions (hills) and intrusions (valleys) results in roughening of the surface experiencing fatigue. While the importance of the initial surface roughness on the crack initiation and its influence on fatigue life is well recognized, the evolution of surface roughness parameters during the cyclic loading has not been reported. In this article, we report the results of a series of experiments aimed at the understanding of the evaluation of the surface roughness, the determination of the key parameters involved, and the utilization of the approach in determining a viable method for detecting the onset of crack by means of monitoring the surface roughness parameters. The outline of the paper is as follows. Section 2 presents the relevant background. Section 3 describes the materials and the apparatus used for fatigue tests followed by the presentation of the results and the discussion of a series of fully-reversed bending tests and surface roughness measurements in Section 4. Damping response, based on the authors’ previous work [22] is also measured to verify the results reported in Section 4. The utility of the approach to detect the onset of crack in metals using a profilometer is presented in Section 5. The limitations of the technique are presented in Section 6. The concluding remarks are given in Section 7.
2. Background Figure 1 illustrates a bending specimen with its 3-D surface profile, when in its pristine stage, as well as a schematic of the PSMs consisting of extrusions and intrusions that grow on the surface after a certain number of cyclic testing. Research shows that surface fatigue cracks nucleate in the locations with the highest number of PSMs and tend to grow toward the interior of the material [23, 24]. According to Risbet and Feaugas [25], the number of cycles required for the initiation of crack is related to a critical value of the average extrusions height hc for single-phase metals and under-aged alloys. They used the atomic force microscopy (AFM) to correlate the critical value of the plastic strain irreversibility with fatigue crack initiation. Their results established the existence of a critical irreversible plastic strain responsible for local crack initiation. This value is defined as the ratio between the critical height of the extrusion hc and the grain size D [25]: (1) If D is considered to be a constant, then the plastic strain energy only depends on hc. Therefore, it follows that for each grain size there exists a critical extrusion height, which if exceeded causes the crack to nucleate in the grain. Similarly, there exists a critical value for the intrusion’s depth. The literature contains a number of studies that primarily concentrate on the effect of extrusions [26-29] or intrusions [30-32] on the fatigue crack initiation in different materials. In their pioneering work in this field, Ewing and Humfrey [15] showed that slip lines on the surface of crystals tend to increase with the increasing number of stress reversals. After a considerable number of reversals, they found that some of the crystals were cracked along the broadened slip bands and eventually turned into a long continuous crack across the surface of the specimen. As expected, their observations revealed that the lower the stress, the fewer the slip-lines. They pointed out that the applied plastic strain tends to relax the compression stresses that emerge in the material due to the presence of defects in the form of vacancies. As a result, the cyclic plastic strain is localized into PSBs and extrusions grow statically. Therefore, with a higher applied strain, the extrusions grow at a faster rate. A historical review of the experimental and theoretical studies of surface relief in the form of persistent slip bands (PSBs) in metals is presented by Man et al. [33]. They presented several models showing the evolution of extrusions and intrusions on the surface of metals during fatigue tests. They contend that in spite of the 2
existence of many theories and experimental results, the determination of the crack nucleation remains elusive.
Figure 1. Schematic of evolution of extrusions and intrusions during cyclic load
2.1. Surface roughness parameters In this section, we begin by providing experimental results that illustrate the changes in the surface topography of a specimen undergoing cyclic fatigue. Figures 2-4 illustrate how extrusions and intrusions grow and eventually form a crack. These figures show the surface topography of a pristine carbon steel 1018 specimen (Fig. 2) undergoing fully reversed bending after 10,000 and 74,000 of cycles (Figs. 3 and 4, respectively). These figures are obtained using both an optical profilometer and a scanning electron microscope (SEM). They demonstrate that the surface of the specimen changes tremendously with the number of cycles. SEM images clearly show that the number of peaks and valleys increase with the number of cycles of fatigue load. Similarly, the images captured by the optical profilometer show the growth in the heights and depths of the peaks and valleys as the number of cycles increases. Therefore, both the heights and depths as well as the density of the peaks and valleys are indicative of the damage growth in the materials. Figure 2b shows the free surface of the material with no indication of peaks or valleys. However, after 10,000 cycles (Fig. 3) the elevations and depressions appear on the surface, representing the movement of dislocation to the free surface of the material to minimize the total energy of the system. Figure 4b shows that after 74,000 cycles the elevations and depressions finally develop into a crack. Similar observations have been reported by the others [15, 23 and 25-33].
3
(a)
(b)
Figure 2. (a) 3D surface roughness profile of a pristine specimen captured by an optical profilometer. (b) Surface image of a pristine specimen captured by SEM
Extrusions and Intrusions emerge on the surface
(a)
(b)
Figure 3. (a) 3D surface roughness profile of a specimen fatigued up to 10,000 cycles captured by an optical profilometer. (b) Surface image of a specimen fatigued up to 10,000 cycles captured by SEM 500 μm
4
Micro Crack
Micro Crack
(a)
(b)
Figure 4. (a) 3D surface roughness profile of a specimen fatigued up to 74,000 cycles captured by an optical profilometer. (b) Surface image of a specimen fatigued up to 74,000 cycles captured by SEM
To quantify the change in the surface features, the following standard 2-D and 3-D parameters are measured (Table 1). The Ra and Rq are the centerline average and the rms of the surface roughness in 2-D, respectively and the Rp and Rv represent the maximum peak height and the maximum valley depth. These parameters are conveniently measured using a contacting stylus. The analogue of these parameters in 3-D is denoted by the surface parameters Sa, Sq, Sp and Sv. Table 1. 2-D and 3-D surface roughness parameters 2-D 3-D
where , and N are the height of each point at coordinates relative to the mean plane, a number of data points, and the number of data points in X and Y directions, respectively. 2.2. Material damping In this section, a brief account of the evolution of material damping is presented and utilized to verify the results presented in Section 3. Damping is a material property that varies with the number of reversals of fatigue load. It represents the dissipation of mechanical energy under the cyclic stress and is referred to as the material damping, structural damping, and the fluid damping [34, 35]. In the authors’ previous work, the damping value was measured experimentally and related to the number of cycles of fatigue load for carbon steel 1018 [22]. This procedure is capable of detecting fatigue crack initiation by examining the point at which the measured value of damping experiences an abrupt increase [36].
5
The value of the damping parameter is obtained using the vibration theory for a free vibrational damped system based on the following equation: (2) where A1 and A2 are the two consecutive peaks of the log decrement of the transient response of the free vibration. Nowick [37] shows that damping is proportional to the dissipated energy due to the plastic strain during cyclic loading according to the following equation: (3) where Wp and W are the energy dissipated in a cycle per unit volume and the maximum stored energy per unit volume, respectively. Therefore, the change in damping value, similar to surface roughening, can be related to the evolution of plastic strain energy during the fatigue test.
3. Experimental apparatus and procedure 3.1. Fatigue Test Figure 5 presents the experimental setup for a cyclic bending fatigue apparatus. The rig is a compact, bench-mounted unit with a variable speed motor that actuates a crank connected to the reciprocating platen. The strain level is adjusted by selecting a constant strain value on the crank that converts it into a bending force. The frequency of applied load is adjustable via a control box that provides a counter for the number of cycles and an automatic shut off control.
Figure 5. Schematic of experimental setup for the rotating bending fatigue test 3.2. Material, specimen preparation, and experimental procedure All tests were conducted with flat dog-bone specimens made of carbon steel 1018 with dimensions shown in Figure 6. The red region shown on Figure 6 is a critical region wherein stress is maximum; therefore, a crack is most likely to initiate in this region. The material properties and compositions are shown in Table 2. The dimensions of the flat specimens used in the present study are recommended by the manufacturer of the apparatus (Manufactured by Fatigue Dynamics, Michigan, United States). These specimens are designed and manufactured according to the ASTM STP 566 so that each side of the reduced section is formed by a single circular arc. 6
Table 2. Properties and compositions of CS 1018 Carbon
CS 1018
0.130.20%
Manganese
Silicon
0.30-0.90%
0.150.30%
Phosphorus
Sulfur
Iron
Density
Yield Strength
Modulus of Elasticity
0.04% Max
0.50% Max
98.06 99.42 %
7.86 g/cc
360 MPa
202 GPa
3.2.1. Specimens Preparation Four series of specimens with different surface finishes were tested. They were: I. Both faces polished to mirror finished ( ); II. Both faces polished up to P3000 ( ), III. One side mirror finished and the other up to P3000 and IV. Specimen unpolished on both sides. Sandpapers with the following grit sizes are used to polish the specimens respectively: P180, P320, P400, P800, P1200, P1500, P2000, P2500 and P3000. Mirror finishing is done using a rotation polishing and grinding machine. 3.3. Experimental Procedures First, the specimen is mounted on the testing apparatus and fatigued up to a certain number of cycles. Then, it is removed from the fatigue tester and its damping value is measured using a resonance frequency and damping analyser (RFDA) instrument (IMCE, Genk, Belgium). This device is a non-destructive test rig capable of measuring the free-free vibration mode of the specimen by analyzing its acoustic response signature when tapped lightly with a miniature impact hammer. More details on the testing procedure are available in reference [22]. Next, the surface roughness parameters are measured using a stylus profilometer on three different paths in the critical area on the specimen. According to the standard design of the specimen, a region of the specimen with the least cross-sectional area represents the critical region (Figure 6) wherein the stress is maximum and where a crack is most likely to initiate. Surface roughness parameters are measured in this region on three different paths which are three different lines on the left, middle and right side of the critical region. The lines are called representative line elements (RLEs) meaning that by measuring the surface roughness parameters on these three lines crack initiation moment can be detected. And simultaneously, 3D surface roughness parameters are obtained using an optical profilometer. This procedure is repeated several times throughout the life of the specimen and data are recorded for future analysis.
5.0
10. 0
Fig. 6. Schematic illustration of a dog-bone specimen (red area is the critical region in which stress is maximum). All dimensions are in millimeter.
7
4. Results and discussions In this section, we begin by first presenting the results of damping value measurements as they evolve during the fatigue tests followed by the evolution of surface roughness parameters as function of the number of cycles for specimens with four different surface finishes as presented in Table 3. Table 3. Rq (rms) for CS 1018 specimens at different surface finishes
Case I Case II
Rq (for pristine specimens) 0.026 0.044
Case III
0.057
Case IV Case V
1.020 0.060
Comments Both faces mirror finish (LCF) Both faces polished up to P3000 (LCF) One face mirror finish and the other polished up to P3000 (LCF) Unpolished specimen (LCF) Both faces polished up to P3000 (HCF)
4.1. Case . Both faces mirror finish 4.1.1. Damping value measurements Figure 7 presents the growth of damping value with the number of cycles. The damping value is obtained using a time-windowed analysis on the exponentially decaying vibrational function of the specimen with an impact excitation technique. It shows that damping exhibits a repeatable three-stage trend. In the first stage, the specimen initially experiences a rapid increase in damping [22] due to the creation of defects (mostly dislocations) in the material. In the second stage, damping reaches to a steady state level, representing the movement of dislocation and defects rather than enlargement. Damage occurs in this stage due to the formation of sub-microcracks that are created in the sites of dislocations with high density, where stresses are concentrated [37]. In the final stage, the onset of fatigue cracks is marked by an abrupt increase in damping associated with the accumulation of dislocations and consequently initiation of micro cracks [36]. It is interesting to note that temperature rise measured on the surface of a specimen undergoes cyclic load also shows a similar three-stage behavior [9,38,39]. Under the conditions tested, there is no significant change in the damping value until 80,000 cycles when an abrupt increase in the damping value (Stage III) is recorded. The last damping measurement at 100,000 cycles was roughly 2.5 times greater than that of the pristine specimen, which reached its final fracture shortly thereafter. These results are consistent with those reported by Mortazavi et al. [22] and can be used for the detection of the onset of crack initiation.
8
0.0014 Final Fracture 0.0012 0.001
Damping
Stage III 0.0008 Stage II
Stage I
0.0006 0.0004 0.0002
Crack Initiation
0 0
20000
40000
60000
80000
100000
120000
Number of Cycles
Figure 7. Damping value versus number of cycles
4.1.2. 2D surface roughness parameters Figures 8a, 8b, 8c and 8d present the two-dimensional roughness parameters for a specimen with mirror surface finish in its pristine state. The results show three different paths on the specimen measured by a stylus profilometer at a different number of cycles. These figures show an increasing trend in all the surface roughness parameters as the number of cycles increases up to the end of the fatigue test. Similar to the trend of the damping values, the evolution of the surface roughness parameters can be divided into three distinct stages. The first and final stages show the same trend as damping values. However, in the second stage, unlike the damping values, the surface roughness parameters exhibit a roughly linear increase. This trend can be attributed to the damage accumulation in the material. In the second stage, defects tend to dislocate rather than enlarge and damping value is not sensitive enough to the movement of dislocations; therefore, no major change in damping value is seen at this stage [22]. However, surface roughness parameters continue to grow because dislocations continue to move toward the free surface due to cyclic straining and contribute further to increase the surface roughness. It is worthwhile to mention that research shows that the evolution of the surface temperature during fatigue test also tends to reach a plateau during the second stage [38]. Because the area under the temperature-time curve represents dissipated plastic energy and although the temperature is constant at this stage, the accumulated dissipated plastic energy increases during the second stage [40-45]. At the end of the second stage (after 80,000 cycles), the roughness parameters undergo an abrupt increase. This is an indication of crack initiation in the specimen, exactly the same as the results obtained via the damping tests. Figures 8c and 8d, show that Rv, which represents the maximum depth of intrusions, shows more sensitivity to the onset of crack initiation than Rp. This can be attributed to the fact that microcracks are in the form of intrusions.
9
2
2 1.8 1.6
1.4
Rq (𝜇𝑚)
1.2
Mirror Finish Stage II (front and back)
1
0.8
Final Fracture
Rq
1.6 Stage III
1.4
Ra (𝜇𝑚)
1.8
Final Fracture
Ra
Stage I
1.2
Mirror Finish (front and back)
1 0.8 0.6
0.6
0.4
Crack Initiation
0.2
Left Middle Right
0.4
Left Middle Right
Crack Initiation
0.2 0
0
0
20000
40000 60000 80000 Number of Cycles
0
100000 120000
20000
40000
60000
80000
100000 120000
Number of Cycles
(a)
(b)
7
7
Rp
6
Rv
6
Final Fracture
Final Fracture 5
4
Rv (𝜇𝑚)
Rp (𝜇𝑚)
5
Mirror Finish (front and back)
3
4
Mirror Finish (front and back)
3
Crack Initiation
Crack Initiation 2
2 Left
1
Left
Middle
1
Middle
Right
Right
0
0 0
20000
40000 60000 80000 Number of Cycles
100000 120000
0
20000
40000 60000 80000 Number of Cycles
100000 120000
(C) (d) Figure 8. Evolution of 2D surface roughness parameters as function of number of cycles with mirror finish surfaces at the pristine state. (a) Ra versus number of cycles. (b) Rq versus number of cycles. (c) Rp versus number of cycles. (d) Rv versus number of cycles
4.1.3. Three-dimensional surface roughness parameters Figures 9a and 9b show growth of the 3D surface roughness parameters of a pristine specimen with both surfaces polished to a mirror finish as measured by an optical profilometer at a different number of cycles during a fatigue test. The field of view for optical profilometer is shown is mainly on the critical region (as shown in Figure 6). However, the size of the field of view does not appreciably affect the results as long as it includes the critical region. The results reveal the familiar three-stages roughness evolution, similar to those exhibited by the two-dimensional surface roughness parameters. Clearly Sv and Sp are more sensitive parameters to damage accumulation in the specimen compared to Sa, Sq, since they (Sa, Sq) represent the average of peaks and valleys over the measured region of the specimen. According to Sangid [14] the maximum peaks and valleys on the surface correspond to critical regions that contain more defects in the form of dislocations. Therefore, critical regions are expected to represent more roughening —extrusions and intrusions grow faster— than other locations on the surface. Therefore, Sp 10
and Sv show more sensitivity when plotted against a number of cycles. In the second stage, there is a linear increase in the value of each parameter, due to the constant growth in height and depth of the extrusions and intrusions during the cycling loading. The specimens surface profiles at its pristine condition and after 50,000 and 80,000 cycles are shown in Figures 10a,b, and c, respectively. The dimensions of the images are 1.1 mm by 0.85 mm. These were obtained using the optical profilometer. The area of interest consists of many grains (approximately 1000) that are both favorably and not favorably oriented to slip. That is why statistical parameters that use average parameter (Sa, Sq, Ra and Rq) and maximum parameters (Sp, Sv, Rp and Rv) are selected to represent both types of grains. The first set of parameters (Sa, Sq, Ra and Rq) represent the average values of all grains while maximum values (Sp, Sv, Rp and Rv) represent grains that are favorably oriented to slip and tend to experience more deformation. The measurements reported in this section pertain to the entire area of the critical region called RSE (representative surface element), rather than the three lines in the RLEs shown in Fig. 8. Surprisingly, the 3D parameters show an abrupt increase —signifying the onset of the crack initiation— exactly at the same time that 2D parameters. However, the magnitude of the values for 3D parameters are about three fold greater than those of the 2D parameters, implying that 3D parameters are more sensitive than the 2D parameters. Thus, measuring the surface roughness parameters on an RSE is more useful than RLE. 5
18 Final Fracture
4.5
16
Final Fracture
4
14 12
3
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
3.5 Mirror Finish (front and back)
2.5
Crack Initiation
2
Mirror Finish (front and back)
10 8 6
1.5
4
1
2
0.5
0
0 0
20000
40000
60000
0
80000 100000 120000
20000
40000
60000
80000 100000 120000
Number of Cycles
Number of Cycles
(a)
(b)
Figure 9. Evolution of Sa, Sq, Sp and Sv as function of number of cycle number of cycles
11
1.3 mm 0.9 mm
(a)
(b)
12
(c) Figure 10. Surface profile of the specimen at different number of cycles (a. pristine, b. 50,000 cycles and c. 80,000 cycles)
4.2. Case . Both faces polished up to P3000 4.2.1. Damping value Figure 11 shows the evolution of the Damping value with fatigue cycles for a specimen polished up to P3000 on both faces. The crack initiation occurs sooner, at 50,000 cycles, and the specimen’s fatigue life is shorter (approximately 75,000 cycles) than the case I where both surfaces were polished to mirror finish.
0.0014
Final Fracture
0.0012
Damping
0.001 0.0008 0.0006 0.0004 0.0002 0 0
10000
20000
30000
40000
50000
60000
70000
80000
Number of Cycles
Figure 11. Damping value versus number of cycles of the specimen polished up to P3000 on both faces
13
4.2.2. Two dimensional surface roughness parameters The 2D surface roughness parameters plotted as a function of a number of cycles are presented in Figures 12a, 12b, 12c, and 12d. All parameters show the same overall trend; however, parameters measured on the left RLE show more sensitivity to not only the onset of crack nucleation but also the cyclic loading. The reason is that the macro-crack initiates on the left side of the specimen at the final stage (Stage III). Therefore, the parameters on the left RLE show an abrupt increase (which indicates the crack initiation moment) prior to those measured elsewhere. The experiments show that the critical region is on the left side of the specimen and the parameters belong to the left RLE represent the crack initiation at 50,000 — identically the same as the result of the damping tests shown in Fig. 11. At 60,000 cycles when the crack moves to the right, the parameters measured on the middle RLE and right RLE of the specimen detect the initiation of the crack and show the familiar abrupt increase as well. The results also reveal that the surface finish of the pristine specimen does not affect the trend of surface roughness parameters and that the onset of crack initiation can be detected by monitoring the appropriate surface roughness parameters regardless of the pristine specimen’s surface finish. This is further illustrated in Section 4.4 that deals with an unpolished specimen. 0.9
1.2 Final Fracture
0.8
Ra
0.7
Final Fracture
0.8
0.6 0.5
P3000 (front and back)
Rq (𝜇𝑚)
Ra (𝜇𝑚)
Rq
1
0.4
P3000 (front and back)
0.6
0.4
0.3 0.2
Left
0.2
Left Middle Right
Middle
0.1
Right
0
0 0
20000
40000 Number of Cycles
60000
0
80000
20000
80000
(b)
(a) 5
5 Final Fracture
4.5
Final Fracture
4.5
Rp
4
Rv
4
3.5
3.5
3
3 Rv (𝜇𝑚)
Rp (𝜇𝑚)
40000 60000 Number of Cycles
P3000 (front and back)
2.5 2
2
1.5
1.5
1
1
0.5
0.5
0
P3000 (front and back)
2.5
0 0
20000
40000 60000 Number of Cycles
80000
0
20000
40000 60000 Number of Cycles
(d)
(c)
14
80000
Figure 12. Evolution of Ra, Rq, Rp and Rv as function of number of cycles at different locations (left, middle and right) of the specimen polished up to P3000 on both faces
In Figures 13a, 13b and 13c the behavior of the surface roughness parameters measured on different RLEs are presented separately to show the discrimination between the parameters measured on the crack growth side of the specimen and parameters in the regions away from where the crack is likely to initiate. This representation is chosen to highlight the influence of the crack site on the surface roughness parameters. The extrusions and intrusions on the surface are representative of the local plastic deformation which depends on the dislocation density in that location. The regions with greater dislocation density produce more plastic deformation and, as a result, create more elevation and depression on the surface. Therefore, a crack is expected to initiate on the regions where the surface roughness parameters grow faster and show more sensitivity to the number of cycles. 6
5
Surface Roughness Parameters on the Middle of the Specimen (μm)
Surface Roughness Parameters on the Left Side of the Specimen (μm)
6
Rv Rp
4 P3000 (front and back)
3
Rq Ra
2
1
0 0
20000
40000 60000 Number of Cycles
5 Crack Initiation
4
3
P3000 (front and back)
2
Rp
Rq Ra
Rv 1
0
80000
0
20000
40000 60000 Number of Cycles
(a)
80000
(b)
Surface Roughness Parameters on the Right Side of the Specimen (μm)
6
5 Crack Initiation 4 P3000 (front and back) 3
Rp 2
Ra
Rq
Rv
1
0 0
20000 40000 60000 Surface Roughness Parameters
80000
(c) Figure 13. Evolution of Ra, Rq, Rp and Rv as function of number of cycles on left side of the specimen (a), middle of the specimen (b) and right sides of the specimen (c), polished up to P3000 on both faces
15
4.2.3. Three dimensional surface roughness parameters Figures 14a and 14b show the 3D surface roughness parameters measured by the optical profilometer for four different specimens polished up to P3000 on both faces. As the figures indicate, the crack initiated after 60,000 cycles. For this case, all four parameters show an abrupt increase (representing the onset of the crack initiation) at the same time. This experiment also verifies the previous observation that the surface finish of the pristine conditions does not affect the evolution of surface roughness parameters. The corresponding surface profiles for the specimen at its pristine condition as well after 30,000 and 60,000 cycles are shown in Figure 15.
2 1.8
12
1.6 1.4
10 Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
Final Fracture
14
Final Fracture
1.2 P3000 (front and back)
1 0.8
Sq
Sa
0.6
8
P3000 (front and back)
6
Sp
Sv
4
0.4 2 0.2 0
0 0
20000
40000 60000 Number of Cycles
80000
0
20000
(a)
40000 60000 Number of Cycles
80000
(b)
Figure 14. Evolution of Sa and Sq and Sp and Sv as function of number of cycles for a specimen polished up to P3000 on both faces
1.3 mm
0.9 mm (a)
(b)
(c)
Figure 15. Surface profile of the specimen at different number of cycles (a. pristine, b. 30,000 cycles and c. 60,000 cycles)
4.3. Case
. One face mirror finish and the other polished up to P3000 16
Figures 16a, 16b, 16c and 16d show two-dimensional surface roughness parameters measured on the three RLEs on the specimen with one surface mirror finish and the other polished up to P3000. Here, the RLEs correspond to the mirror finish face of the specimen where the crack is not expected to initiate. Accordingly, the curves belonging to the left side and middle side of the specimen are not showing any sudden increase in value. However, there is an indication of crack initiation on the right RLE, examination of the surfaces revealed that, indeed, the crack leads to final fracture was initiated on the surface polished up to P3000. As discussed in the previous section, crack initiates on the critical regions, and in this case, the rougher face of the specimen favors crack initiation. Figure 17 shows the surface roughness parameters belonging to the left RLE versus number of cycles. These results indicate that the rate of growth of Rv and Rp is more than Ra and Rq , which make them more promising for both representing the damage in the material and detecting the crack initiation moment. The difference is due to the fact that Rv and Rp represent the extreme values, however, Ra and Rq are averages of some values measured over a RLE (according to Table 1).
1
0.9 Final Fracture 0.8
Ra
0.7
Rq
0.8
0.7
0.6
0.6
Mirror Finish (front side only)
0.5
Rq (𝜇𝑚)
Ra (𝜇𝑚)
Final Fracture
0.9
0.4
Mirror Finish (front side only)
0.5 0.4
0.3
0.3
0.2
0.2
Left Middle
0.1
Left Middle Right
0.1
Right
0
0 0
20000
40000 60000 80000 Number of Cycles
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100000
20000
40000 60000 80000 Number of Cycles
(a)
100000
(b) 5
4 Final Fracture
Final Fracture
4.5
Rp
3.5
Rv
4
3 3.5 3
Mirror finish (front side only)
Rv (𝜇𝑚)
Rp (𝜇𝑚)
2.5 2
Mirror finish (front side only)
2.5 2
1.5
1.5 1 1 Left Middle Right
0.5
Left Middle Right
0.5 0
0 0
20000
40000 60000 80000 Number of Cycles
0
100000
17
20000
40000 60000 80000 Number of Cycles
100000
(c)
(d)
Surface Roughness Parameters on the Left Side of the Specimen
Figure 16. Evolution of Ra, Rq, Rp and Rv versus number of cycles at different locations (left, middle and right) measured on the mirror finish face of the specimen
5 Final Fracture
Rv
4
Rp
Mirror finish (front side only)
3
2
Ra
1
Rq
0 0
20000
40000
60000
80000
100000
Number of Cycles
Figure 17. Evolution of surface roughness parameters (measured at the left RLE) as function of number of cycles measured on the mirror finished face of the specimen
4.4. Case IV. Unpolished specimen The purpose of this section is to investigate the applicability of the results to an unpolished specimen. Figure 18 shows the 3D surface roughness parameters plotted versus the number of cycles for a specimen as received from a hot rolled production process. As shown in the Figure 18, Sa and Sq undergo an abrupt increase after 40,000 cycles while Sp and Sv show the sudden increase shortly after 50,000 cycles. Since Sp and Sv represent maximum values, and for a rough surface their initial value is close to the critical value at which crack initiates, they cannot be a good candidate to represent damage accumulation in the material. However, if their value is below the critical value, it is possible to detect the crack initiation by monitoring their evolution. That is why the abrupt increase in the Figure 18 (b) occurs roughly after 10,000 cycles longer than that of Figure 18 (a). Also, according to Table 1, Sa and Sq represent an average value of the height and depth of all peaks and valleys in the field of view of the profilometer. Thus, the roughening due to cyclic load can be detected more accurately by monitoring Sa and Sq. Therefore, for an unpolished material, Sa and Sq are better candidates to detect damage accumulation and crack initiation. The Surface profiles of the specimen at its pristine condition as after different stages of its fatigue life are shown in Figure 19.
18
1.6
9
1.4
Sa
Sq
8 7
Sv
6
1
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
1.2
0.8 0.6
5 4 3
0.4
2
0.2
1
Unpolished (Front and back)
Unpolished (Front and back)
0
0 0
0
10000 20000 30000 40000 50000 60000 70000 Number of Cycles
(a)
10000 20000 30000 40000 50000 60000 70000 Number of Cycles
(b)
Figure 18. Evolution of Sa, Sq, Sp and Sv as function of number of cycles for an unpolished specimen
1. 3 m m
0.9 mm (a)
(b)
(d)
Figure 19. Surface profile of the specimen at different number of cycles (a. pristine, b. 40,000 cycles and c. 60,000 cycles)
4.5. Case V. Both faces polished up to P3000 (High-Cycle Test) In this section we explore the applicability of the method to a high-cycle fatigue test, which demonstrates a typical in-service application. The result of a fatigue test on a specimen both faces polished to P3000 and subjected to HCF is presented in Figure 20. Results show the familiar three-stages for all the surface roughness parameters, albeit the change in values is considerably smaller for each parameter compared to the corresponding parameter in LCF tests. This is because of the fact that the material experiences much less plastic deformation. Results show that in HCF test, unlike LCF, Sp plays more important role. While other roughness parameters show an abrupt increase after 900,000 cycles, the Sp parameter detect it at 800,000 cycles. Also the change in Sp value is more distinguishable compare to the other parameters. There are two main reasons why in HCF the growth of intrusions is less than that of extrusions. According to Polak and Sauzay [43] intrusions are formed by vacancies produced by annihilation as a result of dislocation interactions in the walls of PSBs and that they are diffused to or absorbed by the interface of PSBs and matrix on the free surfaces of the material. Therefore, dislocation density and movement of dislocations directly affect the formation of intrusions. In general, formation of dislocations in HCF is considerably less pronounced compared to a LCF due to the smaller applied load. Also, the temperature rise during the LCF test eases the movement of dislocations while the temperature rise in 19
HCF tests is infinitesimal. Thus, it is expected that less changes occur in growth of intrusions compare to that of extrusions in HCF tests. The images captured by the optical profilometer is shown in Figure 20 at three different number stages, pristine, after 800,000 cycles and after one million cycles. Figure 21c shows a visible crack on the surface of the material. The red regions in this figure indicate the highest peaks located in the vicinity of the lowest valleys (blue regions). This observation is in accordance to the theory of fatigue crack initiation which asserts that a crack initiates due to the intrusions in the vicinity of the highest extrusions. 0.3
4.5 4 Stage III
3.5
0.2
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
0.25
Stage II
3
2.5
0.15 Stage I 0.1
2
1.5 1
0.05 0.5 0
0 0
500000
1000000
0
Number of Cycles
200000
400000
600000
800000 1000000
Number of Cycles
Figure 20. Evolution of Sa and Sq and Sp and Sv as function of number of cycles for a specimen polished up to P3000 on both faces
1.3 mm
0.9 mm
(a)
(b)
(c)
Figure 21. Surface profile of the specimen at different number of cycles (a. pristine, b. 800,000 cycles and c. 1000,000 cycles)
4.6. Surface roughness parameters at different stress levels Figure 22 shows the so-called S-N curve for the CS 1018 with the corresponding displacement values which is applied at the actuated end of the specimen. The S-N curve is obtained for specimens polished up to P3000. In addition, two different data points are shown on the figure to compare the effect of surface finish on the fatigue life of the specimens. Results show an extended fatigue life for specimens with a better surface finish.
20
Figure 23 presents the 2D surface roughness parameters at various number of cycles for fatigue tests at three different stress levels. δ represents the displacement of the specimen at the actuated end of the specimen in millimeters. These figures show that the higher the strain amplitude, the greater is the rate of increase of all the surface roughness parameters. Applied stress is directly proportional to the number of dislocations created in the material so that the higher the applied stress, the greater is the dislocations density and the resulting plastic deformation. Therefore, for specimens undergoing higher stress (strain) level, a higher rate of growth in surface roughness parameters are expected leading to an eventually shorter life as shown in Figure 23. This finding agrees with the observations of Ewing and Humfrey [15] who investigated the relationship between the applied strain amplitude and the growth size and numbers of extrusions and intrusions on the surface of the specimen. They stated that as the level of the applied strain increases, the observed size of the PSBs and the number of them tend to increase. Polak and Suazay [46] also studied the effect of stress on the emergence of PSBs and reported a similar behavior. 11
480 N=65,000 (Unpolished Specimen)
10
430 N=74,000 (Polished up to P3000)
8 330
7 280
Displacement (mm)
Stress (MPa)
9
N=105,000 (Mirror Finish)
380
6 230
5 4
180 0
200000
400000
600000
800000
1000000
1200000
Number of Cycles to Failure
Figure 22. Relationship between stress and displacement in fully-reversed bending fatigue 1.4
2.5
Ra
1.2
Rq
2
0.8
Rq (𝜇𝑚)
Ra (𝜇𝑚)
1
0.6
1.5
1
0.4 0.5 0.2 0
0 0
50000
100000 150000 Number of Cycles
0
200000
50000
100000 150000 Number of Cycles
(b)
(a)
21
200000
10
6
9
Rp
8 7
4
6
Rv (𝜇𝑚)
Rp (𝜇𝑚)
Rv
5
5 4
3 2
3 2
1
1 0
0
0
50000
100000 150000 Number of Cycles
200000
0
50000
100000 150000 Number of Cycles
(c)
200000
(d)
Figure 23. (a), (b), (c) and (d) represent evolution of Ra, Rq, Rp and Rv as function of cycles for a specimen polished up to P3000 on both faces at three different stress levels
5. A relationship for crack initiation detection Evolution of the surface roughness for low carbon steel samples under cyclic loading is studied by de Lacerda et al. [49]. They investigated the relationship between the evolution of extrusions and intrusions as a function of fatigue load and number of cycles. They found that as the stress decreases the ratio of extrusions height to that of intrusions decreases. In this section, a relationship capable of detecting the onset of crack initiation at different strain levels is developed here based on the evolution of the height of the extrusions (Sp). Table 4 shows ratio of critical of each different roughness parameter over its initial value (i.e., pristine) for a specimen. Table 4. The ratio of critical value of a surface roughness parameter over its initial value for different strain levels
Strain Level (mm)
5 6.35 7.62 10.16
1.3 2 19 51
1.3 2 19 51
1.5 6 21 64
1.2 4.5 25 67
Sv is the most sensitive parameter to the onset of crack in the tested material at LCF but it is less effective in HCF. In contrast, Sp is capable of detecting the onset of crack in both LCF and HCF tests; hence, it is more appropriate for generalization purpose. The relationship is defined between the ratio of the critical Sp over initial value of Sp and applied load level and is presented in Figure 24. The critical Sp is considered to be the value of Sp at which crack initiates. To be conservative, the lowest value of critical Sp from extensive set of experiments is considered. Equation 4 is derived based on a curve fitting (see the red dots) on Figure 24. (4) where is the displacement applied on the actuated end of the specimen. The value for this curve fitting equals 1 which indicates that the regression line perfectly fits the data. The figure shows that, for 22
example, the onset of crack initiation at the displacement level of 8 mm (corresponding to the stress level of 350 MPa), is 21-fold greater than its initial pristine value.
0
100
0
2
200
Stress (MPa) 300
400
500
70 60
Critical Sp / Initial Sp
50 40 30 20 10 0
4
6
8
10
12
Displacement (mm)
Figure 24. A relationship for obtaining
at which crack initiates for different applied displacements
6. Limitations of the technique Risbet et al. [48] used the atomic force microscopy (AFM) to experimentally study the evolution of surface deformation of nickel-base superalloy specimens under cyclic loading. By investigating the height of the extrusions quantitatively, they formulated a microscopic crack initiation law, and obtained a critical value for the height of the extrusions at which crack initiates. High-resolution analysis using the AFM is useful to establish the work in details. However, the use of a profilometer provides a feasible approach for engineering applications especially with potential for in situ measurements. Since the height and depth of the extrusions and intrusions play a significant role here, the vertical resolution of the devices is important. The vertical resolution of the stylus and the optical profilometer is sensitive enough to detect the height and depth of the extrusions and intrusions within slip bands when surface roughness is below a certain value. For some cases (after crack initiates), both stylus and optical profilometer have some limitations to measure high surface slopes. They tend to show the high ratio trenches as graphical shapes with missing data in some small segments. However, the software uses curve fitting to fill the missing data of the trenches. The aim of our study is to detect the onset of crack initiation, and examination of our results reveals that there are very few or no missing data for the depth of intrusions before the crack initiation. Thus, the measurements are accurate enough to detect the crack initiation moment. Another limitation is that this technique can be used for materials and loading conditions in which crack initiates on the surface. For materials in which crack initiates from subsurface, the surface roughness parameters are expected to show a linear growth when plotted versus the number of cycles.
23
7. Conclusions The extrusions and intrusions are the manifestation of PSBs and widely recognized as the source of crack initiation. While the contribution of initial surface roughness on the fatigue life of the materials has been studied by many researchers, the crack initiation detection using the evolution of surface roughness parameters has not been investigated so far. In this paper, an approach for detecting the initiation of crack by means of 2D and 3D surface roughness parameters using both a stylus and an optical profilometer is presented. The approach is based on the monitoring the 2D surface roughness parameters Ra, Rq, Rp and Rv and 3D surface roughness parameters Sa, Sq, Sv and Sp during cyclic loading. Rp, Rv, Sv and Sp represents height of the extrusions and depth of the intrusions on the surface of the specimen. It is shown that the evolution of the surface roughness parameters occurs in three distinct stages and the higher the applied stress, the higher is the growth rate. These parameters can represent damage accumulation in the material, because when damping value shows a plateau in the second stage the surface roughness parameters show a linear increase in value. Furthermore, Rp and Rv, show the same trend as Sv and Sp, respectively. However, interestingly in LCF, Rv and Sv show more sensitivity to both damage accumulation and onset of crack in the material while in HCF Sp plays more important role. The results are verified monitoring damping value during fatigue test. To show the applicability of the method, an experiment is performed on an unpolished specimen. Results show that Sa and Sq are better candidates to detect the crack initiation moment in an unpolished specimen. Finally, a relationship between and load level is presented to detect the onset of the crack initiation. This relationship is useful for determining the safe operation of a specimen before a crack initiates.
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[8] Meneghetti, G. "Analysis of the fatigue strength of a stainless steel based on the energy dissipation." International journal of fatigue 29, no. 1 (2007): 81-94. [9] Naderi, M., M. Amiri, and M. M. Khonsari. "On the thermodynamic entropy of fatigue fracture." In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 466, no. 2114, pp. 423-438. The Royal Society, 2010. [10] Wang, X. G., V. Crupi, C. Jiang, and E. Guglielmino. "Quantitative thermographic methodology for fatigue life assessment in a multiscale energy dissipation framework." International Journal of Fatigue 81 (2015): 249-256. [11] Crupi, V. "An unifying approach to assess the structural strength. "International Journal of Fatigue 30, no. 7 (2008): 1150-1159. [12] Liakat, M., and M. M. Khonsari. "On the anelasticity and fatigue fracture entropy in high-cycle metal fatigue." Materials & Design 82 (2015): 18-27. [13] Meneghetti, G., M. Ricotta, and B. Atzori. "Experimental evaluation of fatigue damage in two-stage loading tests based on the energy dissipation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 7 (2015): 1280-1291. [14] Sangid, M. D., Hans J. Maier, and H. Sehitoglu. "A physically based fatigue model for prediction of crack initiation from persistent slip bands in polycrystals." Acta Materialia 59, no. 1 (2011): 328-341. [15] Ewing, J. A., and J. C. W. Humfrey. "The fracture of metals under repeated alternations of stress." Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 200 (1903): 241-250. [16] Cretegny, L., and A. Saxena. "Evolution of surface deformation during fatigue of PH 13‐8 Mo stainless steel using atomic force microscopy." Fatigue & Fracture of Engineering Materials & Structures 25, no. 3 (2002): 305-314. [17] Thompson, N., N. Wadsworth, and N. Louat. "The origin of fatigue fracture in copper." Philosophical Magazine 1, no. 2 (1956): 113-126. [18] Cretegny, L., and A. Saxena. "AFM characterization of the evolution of surface deformation during fatigue in polycrystalline copper." Acta materialia 49, no. 18 (2001): 3755-3765. [19] Risbet, M., and X. Feaugas. "Some comments about fatigue crack initiation in relation to cyclic slip irreversibility." Engineering Fracture Mechanics 75, no. 11 (2008): 3511-3519. [20] Ho, H. S., M. Risbet, X. Feaugas, and G. Moulin. "The effect of grain size on the localization of plastic deformation in shear bands." Scripta Materialia 65, no. 11 (2011): 998-1001. [21] Risbet, M., X. Feaugas, C. Guillemer-Neel, and Michel Clavel. "Damage in nickel base superalloy: influence of local parameters measured by electron backscattered diffraction and atomic force microscopy." Scripta Materialia 60, no. 5 (2009): 269-272. [22] Mortezavi, V., A. Haghshenas, M. M. Khonsari, and B. Bollen. "Fatigue analysis of metals using damping parameter." International Journal of Fatigue 91 (2016): 124-135. [23] Polák, J., V. Mazánová, I. Kuběna, M. Heczko, and J. Man. "Surface relief and internal Structure in fatigued stainless sanicro 25 steel." Metallurgical and Materials Transactions A 47, no. 5 (2016): 19071911. [24] Suresh S. Fatigue of materials. Cambridge University Press 1998. 25
[25] Risbet, M., X. Feaugas, C. Guillemer-Neel, and M. Clavel. "Use of atomic force microscopy to quantify slip irreversibility in a nickel-base superalloy." Scripta Materialia 49, no. 6 (2003): 533-538. [26] Mughrabi, H., R.Wang, K. Differt, and Uwe Essmann. "Fatigue crack initiation by cyclic slip irreversibilities in high-cycle fatigue." In Fatigue mechanisms: Advances in quantitative measurement of physical damage. ASTM International, 1983. [27] Mughrabi, H.. "Cyclic slip irreversibilities and the evolution of fatigue damage." Metallurgical and materials Transactions A 40, no. 6 (2009): 1257-1279. [28] Schwaiger, R., G. Dehm, and O. Kraft. "Cyclic deformation of polycrystalline Cu films." Philosophical Magazine 83, no. 6 (2003): 693-710. [29] Brown, L. M. "Cracks and extrusions caused by persistent slip bands." Philosophical Magazine 93, no. 28-30 (2013): 3809-3820. [30] Polák, J. "On the role of point defects in fatigue crack initiation." Materials Science and Engineering 92 (1987): 71-80. [31] Polák, J., and J. Man. "Mechanisms of extrusion and intrusion formation in fatigued crystalline materials." Materials Science and Engineering: A 596 (2014): 15-24. [32] Nakai, Yoshikazu, T. Kusukawa, and N. Hayashi. "Scanning atomic-force microscopy on initiation and growth behavior of fatigue slip-bands in α-brass." In Fatigue and Fracture Mechanics: 32nd Volume. ASTM International, 2002. [33] Man, J., K. Obrtlik, and J. Polak. "Extrusions and intrusions in fatigued metals. Part 1. State of the art and history." Philosophical Magazine 89, no. 16 (2009): 1295-1336. [34] De Silva, Clarence W. “Dynamic testing and seismic qualification practice.” D.C. Heath and Co., Lexington, MA, 1983. [35] Zener, Clarence. "Internal friction in solids." Proceedings of the Physical Society 52, no. 1 (1940): 152. [36] Jones, R. L., "A constitutive relationship between crack propagation and specific damping capacity in steel." No. NCEL-N-1817. Naval Civil Engineering Lab Port Hueneme CA, 1990. [37] Nowick, Arthur S. "Anelastic relaxation in crystalline solids." Vol. 1. Elsevier, 2012. [38] Amiri, M., M. Naderi, and M. M. Khonsari. "An experimental approach to evaluate the critical damage." International Journal of Damage Mechanics 20, no. 1 (2011): 89-112. [39] Amiri, M., and M. M. Khonsari. "Life prediction of metals undergoing fatigue load based on temperature evolution." Materials Science and Engineering: A 527, no. 6 (2010): 1555-1559. [40] Liakat, M., and M. M. Khonsari. "Rapid estimation of fatigue entropy and toughness in metals." Materials & Design (1980-2015) 62 (2014): 149-157. [41] Amiri, M., and M. M. Khonsari. "Rapid determination of fatigue failure based on temperature evolution: Fully reversed bending load." International Journal of Fatigue 32, no. 2 (2010): 382-389. [42] Amiri, M., and M. M. Khonsari. "Nondestructive estimation of remaining fatigue life: thermography technique." Journal of failure analysis and prevention 12, no. 6 (2012): 683-688. [43] Amiri, M., and M. M. Khonsari. "On the role of entropy generation in processes involving fatigue." Entropy 14, no. 1 (2011): 24-31. 26
[44] Naderi, M., and M. M. Khonsari. "An experimental approach to low-cycle fatigue damage based on thermodynamic entropy." International Journal of Solids and Structures 47, no. 6 (2010): 875-880. [45] Naderi, M., A. Kahirdeh, and M. M. Khonsari. "Dissipated thermal energy and damage evolution of glass/epoxy using infrared thermography and acoustic emission." Composites Part B: Engineering 43, no. 3 (2012): 1613-1620. [46] Polák, J., and M. Sauzay. "Growth of extrusions in localized cyclic plastic straining." Materials Science and Engineering: A 500, no. 1 (2009): 122-129. [47] Basinski, Z. S., R. Pascual, and S. J. Basinski. "Low amplitude fatigue of copper single crystals I. The role of the surface in fatigue failure." Acta Metallurgica 31, no. 4 (1983): 591-602.I [48] Risbet, M., X. Feaugas, C. Guillemer-Neel, and M. Clavel. "Use of atomic force microscopy to quantify slip irreversibility in a nickel-base superalloy." Scripta Materialia 49, no. 6 (2003): 533-538. [49] de Lacerda, J. C., G. D. Martins, V. T. Signoretti, and R. L. P. Teixeira. "Evolution of the surface roughness of a low carbon steel subjected to fatigue." International Journal of Fatigue 102 (2017): 143148.
27
Highlights
Evolution of surface roughness in low-and high-cycle fatigue is investigated. Appropriate surface roughness parameters for monitoring purposes are identified. Roughness parameters undergo three distinct stages from pristine to fracture An approach for detecting the initiation of crack is presented.
.
28
0.3
4.5 4
0.25 3.5 3
Sp and Sv (𝜇𝑚)
Sa and Sq (𝜇𝑚)
0.2
Stage II 0.15
0.1
2.5 2 1.5 1
0.05 0.5 0
0 0
200000
400000
600000
800000
1000000
0
Number of Cycles
200000
400000
600000
800000
1000000
Number of Cycles
( Pristine,
800,000 cycles
1000,000 cycles