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An engineering high cycle fatigue strength prediction model for low plasticity burnished samples
Accepted Manuscript An engineering high cycle fatigue strength prediction model for low plasticity burnished samples Xilin Yuan, Yuwen Sun, Chunyan Li PII: DOI: Reference:
S0142-1123(17)30263-3 http://dx.doi.org/10.1016/j.ijfatigue.2017.06.013 JIJF 4369
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
13 March 2017 6 June 2017 7 June 2017
Please cite this article as: Yuan, X., Sun, Y., Li, C., An engineering high cycle fatigue strength prediction model for low plasticity burnished samples, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/ j.ijfatigue.2017.06.013
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An engineering high cycle fatigue strength prediction model for low plasticity burnished samples Xilin Yuan1,Yuwen Sun1*, Chunyan Li2 1.Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, Dalian University of Technology, Dalian, 116024, China 2. School of Material Science and Engineering, Dalian University of Technology, Dalian, 116024, China
Abstract: High cycle fatigue performance is significantly affected by the surface conditions of mechanical components. Traditionally, one major effect of low plasticity burnishing process in promotion fatigue resistance has been ascribed to the generation of compressive residual stresses and the formation of gradient structure in the top-treated surface layer. However, the prediction model of fatigue performance considering the effects of roughness, microhardness and residual stress has not been well established. Thus, the aim of this work is to develop a model predicting the fatigue strength of high cycle fatigue for burnished metallic components. First, the main parameters affecting the fatigue performance of burnished components are investigated by dimension analysis method. Then, by introducing the influence factors of stress gradient and microhardness gradient, a fatigue strength prediction model is proposed to correlate the fatigue strength of untreated and treated samples. This model considers the effects of residual stress, microhardness, roughness, gradient and size. In order to verify the validity of the model, double faces low plasticity burnishing and tension-tension fatigue tests are carried out on TA2 alloy samples with center hole. In addition, to investigate the effect of low plasticity burnishing on the fatigue performance when the direction of crack propagation is perpendicular to the burnished surface, one face burnishing and three-point bending fatigue tests are also performed. The tension-tension fatigue strength and bending fatigue strength after low plasticity burnishing are 144 MPa and 329 MPa, respectively. The predicted tension-tension fatigue strength and bending fatigue strength after low plasticity burnishing are 133 MPa and 313 MPa, respectively. The error between the measured value and the predicted value is less than 15%. At last, fatigue comparison tests using new burnishing process parameters are carried out. The fatigue strength after treatment is 309MPa. The predicted fatigue strength after treatment is 322MPa. The prediction error is less than 10%. This demonstrates that the proposed model is effective in the high cycle fatigue strength prediction model for low plasticity burnished samples. Keywords: fatigue strength, low plasticity burnishing, residual stress, microhardness;
1 Introduction Engineering structures and components due to serving under cyclic loading, prone to fatigue damage. Fatigue cracks generally initiate at the stress concentration of the components surface. The subsequent fatigue crack growth determine the fatigue life of the components. Therefore, techniques that improve the fatigue resistance of the components are significant. Existing studies have shown that surface modification or treatment technologies are effective for improving the fatigue performance, such as shot peening, deep rolling, laser shock peening(or laser peening), ultrasonic surface rolling, machine hammer peening. Shot peening is a surface treatment method, which uses the plastic deformation layer on the surface of the material to improve the performance of the material. After shot peening process, the introduced residual compressive stress field in the surface layer can effectively restrain the cracks initiation and propagation, and then improve the fatigue strength and fatigue life. Such method is widely used in the manufacture of aviation, spaceflight, automobile, electric power station and so on. The advantage of shot peening is that the cost is low. Moreover, it can be used to the surface strengthening treatment of large parts. However, in addition to the properties of the component materials, the effects of shot peening are related to many process parameters, such as the size of the shot, shape, hardness, shot peening *[email protected]
velocity and peening flow. Therefore, it is difficult to accurately predict the effect of shot peening. In addition, the surface roughness of the shot peened component is not as good as that produced by ball burnishing. In contrast, laser peening is a new surface modification technology. During the process of laser peening, a deep layer of compressive residual stresses can be introduced by high energy and short pulsed laser [1]. Compared to shot peening, there is a sacrificial layer known as protective coating or ablative material on the surface of the workpiece. This coating can reduce the thermal effects of the laser beam on the part. After operating more three times, the protective coating must be removed. Thus, laser shock peening is costly. In contrast, low plasticity burnishing (also called ball burnishing or deep rolling) is a competitive and effective surface finishing process. This process produces surface plastic deformation by a free rolling ball. This ball is pressed on the surface of the component. In the burnishing process, the applied burnishing load force the surface material spread and flow from the peaks to the valleys on the component surface. This plastic deformation can improve the component surface roughness. At the same time, a hard layer on the finishing surface can be formed. Previous works paid attention to the burnishing process parameters on the surface integrity, including surface roughness, hardness, distribution of residual stress and sub-surface characteristics of burnished components. In literature [2] the influence of process parameters (force, speed and feed) on the surface
roughness and hardness was studied in detail. For advanced materials such as biomedical Nitinol, non-uniform martensitic transformation could be observed on the cross-sectional surface after ball burnishing process [3]. As for the residual stress, M. Beghini et al. found that the process parameter that affected mostly the residual stress distribution was force, followed by the feed rate. In addition, the depth of the maximum compressive residual stress location increased with the rolling force. At high rolling force, the feed parameter did not significantly affect the distribution of the residual stress [4]. Finite element simulation results also showed that the amplitude and magnitude of residual stress increased with the burnishing force [5-6]. These research results will be beneficial to guide the production of rolling process. By means of ball burnishing process, gradient structure of the top-treated surface can be obtained. In this gradient layer, coarse grains in the surface layer can be refined. In addition, the grain size increases with the increase of depth. Meanwhile, the residual compressive stress of the top-treated surface is characteristic of the gradient distribution along the depth direction due to the uneven strain. The compressive residual stress induced by ball burnishing can enhance the crack closure forces and the crack closure effects, thus, the propagation of fatigue crack is suppressed [7-11].However, only quantitatively studying the effect of residual stress on fatigue properties can be beneficial for the practical design. At present, superposition method is usually utilized to study the effect of residual stress on fatigue performance [12].The effective stress is the superposition of the mean residual stress and the stress introduced by external load. However, there are still some differences between the residual stress and the mean residual stress. The method of converting residual stress into mean stress ignores the effect of stress gradient. At present, the most representative fatigue strength or fatigue life prediction method, which considering the effects of stress gradient, is stress field intensity method and advanced volumetric method [13-18]. According to the stress field intensity method, fatigue is a local damage phenomenon. Under cyclic loading, the fatigue crack is initiated at the notch root. The performance of the material in a certain area of the notch, the maximum stress at the notch root, the stress gradient near the notch and the stress and strain field distribution play a decisive role in the fatigue performance of the specimen. The advanced volumetric method is developed on the basis of the stress field intensity method. The failure region is defined as the critical volume in the advanced volumetric method. Then, the stress field intensity in the volume method can be obtained by simplifying the weight function in the stress field intensity method. In general, a circular region centered at the root of the notch is regarded as the failure region in the stress field intensity method. The radius of this circle is called the field diameter. The difficulty of the stress field intensity method is the determination of the field diameter. For the actual component, the determination of the field diameter is more complex and difficult. The advanced volumetric method requires accurate calculation of the stress gradient at the root of the notch. Further, it is more
difficult to accurately calculate the stress gradient for the notched specimen with higher stress concentration. In order to consider the effect of residual stress, stress gradient, roughness and hardness on the fatigue performance of burnished components, a new fatigue strength prediction model is proposed. First, the key factors affecting the fatigue performance of ball burnished sample based on the dimensional analysis.an analytical approach is proposed. The effects of residual stress, hardness are taken into account. Then, with a view to the complexity of the gradient calculation, the modified fatigue strength prediction model for ball burnished samples is proposed. And the influence of surface roughness and size effect are also considered in the modified model. In order to verify the rationality of the proposed model, the tension-tension fatigue strength and the bending fatigue strength of the ball burnished samples are predicted respectively. Finally, the proposed model is used to predict the bending fatigue strength of the specimens burnished with new process parameters.
2 Dimensional analysis of fatigue properties of gradient structure materials The fatigue properties of the material are affected by many factors, such as the size and distribution of inclusions, load conditions and environmental factors. In addition, the fatigue properties of gradient materials are also affected by the size and distribution of the grain, the residual stress and the gradient changes of material properties. Table1 lists the main factors affecting the fatigue limit of the gradient materials. At present, there is not a unified mathematical equation to describe the effect of these factors on fatigue performance. Dimensional analysis method can be used to reveal the essence of the problem by designing a suitable model. Table1 Parameters affecting fatigue life
h
The depth of the gradient layer
E
The elastic
E0
modulus of the original material
µ
Poisson's ratio of
µ0
the original material
σ 0.2( local )
Strain hardening
n0
exponent of the original material
of the original material
σ load
Stress produced by external load
l
Characteristic length of the
surface-treated material Poisson's ratio of the surface-treated material
The yield strength of the surface-treated material Strain hardening exponent
n
of the surface-treated material
∂E ∂h
Gradient of elastic modulus
The yield strength
σ 0.2
The elastic modulus of the
∂σ 0.2( local ) ∂h
σ mr
of the surface-treated layer
Gradient of yield strength of the surface-treated layer
Mean residual stress in the
specimen
surface-treated layer
In engineering applications, the gradient distribution of
To simplify the analysis, the fatigue life of the specimen can be expressed as the following equation:
hardness is easier to obtain. A large number of experiments show that there is a linear relationship between hardness and
∂E ∂σ 0.2(local ) N f = f h, E0 , µ0 ,σ 0.2 , n0 , E, µ,σ 0.2(local ) , n, , ,σ load , l ∂h ∂h (1) and are assumed as the dimensionally independent variables. The rest of the variables can be represented as: h l
π1 =
π2 =
(2)
E0
(4)
σ load
(5)
E0
Substituting π1 ∼π7 to Eq.(1) , one can have
gradient of yield strength of the surface-treated layer
∂σ 0.2 (local ) ∂h is replaced with the gradient of hardness
b2
b
b3
(6) Using Buckingham’s Π Theorem, Eq. (6) can be derived as a
2 3 a1 h σ E σ 0.2( local ) N f = A 0.2 l E0 E0 E0
a7
a4
l ∂E E0 ∂h
a8
σ n µ load E0 n0 µ0
a9
a5
(7)
where A and ai ( i = 1 ~ 9 ) are constants. The material of the specimen can be treated as homogeneous material, if the specimen is not subjected to any surface strengthening treatment. Then E0 , µ0 , n0 and σ 0.2 are material constants. Consequently, the above Eq.(7) can be rewriting as the following equation, which is a typical Basquin formula.
b4
1 h H E H l ∂E N f = A0 0 l E0 E0 H 0 E0 ∂h
b7
b8
l ∂H σ load n µ H 0 ∂h E0 n0 µ0
b5
(9)
b9
where A0 and bi ( i = 1 ~ 9 ) are constants. For strain hardening materials, the strain hardening index has little change, and the elastic modulus and Poisson's ratio have no change. Consequently, the above Eq. (9) can be simplified as: d2
d3
1 h H l ∂H σ load N f = A1 l H 0 H 0 ∂h E0
d
h σ E σ 0.2(local ) l ∂E l ∂σ0.2(local ) σload n µ N f = f , 0.2 , , , , , , , l E E E0 E0 ∂h E0 ∂h E0 n0 µ0 0 0
l ∂σ 0.2(local ) ∂h E0
yield strength of the gradient surface layer σ 0.2( local ) . And the
b6
……
a6
respectively replace the original yield strength σ 0.2 and the
rewritten as: (3)
E π3 = E0
a
the hardness of the gradient surface layer H are used to
of the surface-treated layer ∂H ∂h .Then Eq. (7) can be
σ 0.2
π7 =
strength [19-21]. Consequently, the original hardness H 0 and
d4
(10)
where A1 and d i ( i = 1 ~ 4 ) are constants. Taking into account the residual stress in the surface after the surface treatment process, the average residual stress can be superimposed on the external load stress [22]. Then the above Eq. (10) can be written as: 1 h H N f = A2 l H0
aa
aa2
l ∂H H 0 ∂h
aa3
σ mr E0
aa4
σ load E0
aa5
(11)
where A2 and aai ( i = 1 ~ 5) are constants. Under the same fatigue life, the relationship between the fatigue strength of the treated and untreated parts can be expressed as the following equation: bb2
bb3
bb4
h H l ∂H σ mr σ treated = A3 σ untreated l H 0 H 0 ∂h E0 bb1
(12) a
σ N f = C load = σ f σ b E0
(8)
where A3 and bbi ( i = 1 ~ 4 ) are constants. σ treated and σ untreated represents respectively the fatigue strength of the treated and untreated parts.
It can be inferred from Eq. (12) that the fatigue strength of the surface-treated specimen could be predicted as the distribution of hardness and residual stress was obtained. Likewise, considering the influence of residual stress gradient, the above Eq. (12) can be rewritten as: dd2
dd3
dd4
dd5
dd h H l ∂H σr l ∂σr σtreated = A4 σuntreated l H0 H0 ∂h E0 H0 ∂h 1
Define
Yσ ′ = r
1
(19)
2 Sσ ′ 0.5 r
where represents residual stress gradient factor, Sσ ′ 0.5 r
represents the area of the normalized curve of residual stress (13) where A4 and ddi ( i = 1 ~ 5) are constants. σ r is the residual stress in the surface-treated layer. Equation(13) can be simplified as: σ treated = C0 CH Csσ untreated (14)
H where CH = H0
dd2
l ∂H H 0 ∂h
dd3
σ , Cs = r E0
dd4
l ∂σ r H 0 ∂h
and the coordinate axis in the 0 ≤ x ≤ 0.5 interval. The normalization of residual stress is carried out according to the following equation. σ ′ (h′) =
dd5
and C0 is a correction factor used to eliminate the error caused by the integral interval. CH is a parameter that is related to the hardness of the burnished component. Cs is a parameter that is related to the residual stress of the burnished component.
hr′ =
(20)
h hrmax
(21)
where σ ( h ) is the residual stress of the surface-treated layer, σ max is the maximum residual in the stress affected layer, hrmax is the maximum depth of residual stress affected layer. The stress gradient index is defined as follows:
β=
3 Modeling an engineering fatigue model for low plasticity burnished specimens If the residual stress and hardness gradient are not large, then it is very convenient to predict the fatigue strength of strengthened components by utilization the Equation (13). However, application derivation method to calculate the gradient will be difficult when the stress or hardness gradient are large. In order to avoid these defects, the integral method is used to redefine the gradient factor [23].
σ (h ) σ max
hrmax l/2
(22)
Considering the improvement of the surface roughness of the specimens caused by low plasticity burnishing, the fatigue strength of burnished specimen can be expressed as: α
( ) 1+ K K− K σ
σtreated = C0 (YH′ ) Yσ ′ r
0
β
1
t
t
0
untreated
t
(23)
Define (15)
where Kt0 is the stress concentration factor caused by surface roughness before low plasticity burnishing process,
wher YH ′ represents hardness gradient factor, S H ′0.5 represents the area of the normalized curve of hardness in the interval
K t1 is the stress concentration factor caused by surface roughness after low plasticity burnishing process. The above
x ∈ [ 0,0.5] . The normalization of hardness is carried out
fatigue strength prediction model is not suitable for the prediction of low cycle fatigue strength because the depth of
YH ′ =
1 2 S H ′ 0.5
according to the following equation. H ( h ′) =
h ′=
H (h ) hmax
h hmax
(16) (17)
where H ( h ) is the hardness of the surface-treated layer, and hmax is the maximum depth of hardness-increased layer. The hardness gradient index is defined as follows:
α=
hmax l/2
(18)
the influence layer is relatively small. The stress concentration factor caused by surface roughness can be calculated by the following equation:
Kt =1+2 Rz / ρ
(24)
where Rz and are the 10-point surface height and notch root radius, respectively[24-26]. According to micro-meso-process theory of fatigue source initiation, the formation of the fatigue source consists of the following four microscopic processes: (1) under cyclic
loading, the slip systems in the grain are activated. Then, the dislocations move along the slip surfaces. The pile-up of dislocations will be formed when the dislocations meet with the grain boundaries and sub grain boundaries, inclusions, secondary phase. These pile-up of dislocations result in a rise of stress concentration. When the stress reaches or exceeds the meso-scopical yield strength of some adjacent grains, the concentrated stresses are relaxed. The dislocations continue to slide. With the progress of the process, pre-yield regions involving a considerable number of grains are formed. However, at this time, the stress produced by external load does not reach the yield strength of the whole material. That is to say, the material in the other parts except the pre-yield regions is still in the elastic deformation stage. In general, the outside of the grains on the surface of the part are free. Due to the restriction of the inner grains, the dislocation motion of the grains on the surface is relatively small. Hence, pre-yield regions are easily formed on the surface of the parts. As a consequence, most of the fatigue cracks are initiated on the surface of the part. However, for the surface treated parts, the surface layer is strengthened or the residual compressive stress is formed. As a result, the formation of pre-yield regions requires larger stress. Moreover, under the strengthened layer, the residual tensile stress or low strength may be beneficial for the formation of pre-yield regions. This is the initial stage of fatigue crack initiation. (2) Consideration of the probability of the structure distribution of the material, there may be some micro region in the pre-yield regions. In these micro regions, the grains are well coordinated with each other. The plastic deformation resistance in these regions is relatively small. Under the same load, these micro regions firstly formed strain-concentrated micro region. (3) The material properties of pre-yield regions, strain-concentrated micro regions and the matrix are different. The yield strength of material in strain-concentrated micro regions is relatively low. As a consequence, strain-concentrated micro regions are easy to reversely yield in unloading or reverse loading stage. (4) Under the suitable cyclic load, alternating plastic deformation will be formed in strain-concentrated micro regions. The initial fatigue cracks initiate in a few strain-concentrated micro regions. As the initial crack continues to propagate, macroscopic cracks are formed and eventually lead to fatigue fracture. The fatigue limit of the material can be considered as the critical stress for the meso-scopic yielding. In fact, the formation of strain-concentrated micro regions around the weak grains is the key process of fatigue cracks initiation. Moreover, the surrounding grains restrict the formation of the microstructural yield region near the inner grains. This constraint increases as the distance of the weak grains from the surface increases. When the distance reaches a certain depth, the constraint gradually reaches saturation due to the interdependence between grains. It can be inferred that this critical depth is closely related to the microstructure of the material, especially the grain size. For the notched specimen, this critical depth highly affect the fatigue limit. Although the stress at the root of the notch reaches the fatigue limit of the material, it is far from satisfying the coordination and
probabilistic condition of the fatigue crack initiation because of the stress gradient near the root of the notch. The meaning of this critical depth is illustrated in Fig.1. It can be seen that the stress decreases with the increase of the distance from the notch root. When the nominal stress σ is equal to the fatigue limit of the material σ f , the distance from the root of the notch is the critical distance d c .The results from literature [27-28] show that the critical distance d c is highly related with 10d is the average grain diameter of the surface layer).Actually, the burnished surface of the part is covered with grooves. These grooves are distributed in different positions. However, they are not at the center of the maximum stress. Consequently, they have little effect on fatigue failure. Therefore, it can be considered that the rest of the burnished surface of the part is flat except for the notch at the center of the maximum stress (Fig.2) [29-31]. For burnished specimens, it is reasonable that the critical depth of the strain-concentrated micro regions 10d .This depth is approximately half the depth of the affected layer. This is the reason why the half of the influence layer depth is defined as the integral interval.
Fig.1. Local stress distribution of notched specimen
Fig.2. Notch model for ball burnished surfaces
Fig.3. Dimensions and burnished region of fatigue specimens:(Up) Tension-tension fatigue specimen, (Down) Bending fatigue specimen
4.Verification of the model 4.1 Sample preparation and experimental procedures To assess the prediction accuracy of the engineering model, in this section five serials fatigue tests are performed. And, four serials fatigue tests are firstly carried out to determine the effect of ball burnishing on the tension-tension fatigue strength and bending fatigue strength at the 1 10 cycles.In these four serials fatigue tests, the up and down method is employed. Samples, used for determining the fatigue strength at the 1×106cycles after burnishing process, are treated with the same ball burnishing process parameters. The fifth serials fatigue testes are used to compare the fatigue strength (at the 1 10 cycles) before and after treatment. A new set of burnishing process parameters is utilized in theses burnished samples. The material of the specimens is TA2 alloy. The mechanical properties of TA2 are shown in Table.2. Dimensions and burnished region of the specimens are illustrated in Fig.3. In order to reduce axial abrasion and burrs generated at the edge of the hole, chamfering is performed at the edge of the hole. The specimens are firstly machined on a Haas machining center (VF-5/40XT). The machining conditions are spindle speed of 1000rpm, feed of 300mm/min, and depth of cut of 0.05mm. Taking into account the
friction damage is relatively large if the initial rough surface is ball burnished, the fatigue specimens are firstly smoothed with roller burnishing tool. After the roller burnishing process, the surface modification is Fig.4 shows the roller burnishing tool (SFP20-S20, Sugino Machine Limited) and low plasticity burnishing tool (HG6-19E90°-ZS20X, Ecoroll Corporation). The roller burnishing parameters are referenced from the results of literature [29].The detailed roller burnishing process parameters are: spindle speed = 1500 r/min, feed =148 mm/min, depth = 0.05 mm. The parameters of group (a) are used to determine fatigue strength at the 1×106cycles. The parameters of group (b) are used to compare the fatigue strength at the 1×105cycles. The details of the burnishing process parameters are shown in Table 3. The description of the process parameters has been described in literature [32]. Tensile fatigue samples are double face burnished. Bending fatigue samples are single face burnished. Table2 The mechanical properties of TA2
Density (g/cm3 )
Tensile strength(MPa)
Yield strength(MPa)
Modulus of elasticity
Hardness (HV)
(GPa) 4.5
510
460
107.8
190
Table3 Ball burnishing process parameters
a b
Fig.4. Burnishing tools:(L) Roller burnishing tool(R)low plasticity burnishing tool
In order to detect the microhardness distribution and the residual stress distribution of the surface layer after burnishing, a square plate using the aforementioned processing parameters is machined. The surface roughness is measured by Zygo New View 5022 scanning white light interferometer (SWLI). The average surface roughness value is obtained from the mean value of five different positions on the surface. The surface microhardness was measured with an HXD- 1000TM microhardness tester under a load of 98g with a dwelling time of 15s. The average microhardness value is obtained from the mean value of five different positions on the surface.Only one sample of each group is selected for microhardness measurement. Residual stress is examined by X-ray diffractometry (XRD, PANAlytical Empyrean, CuKα radiation). Similarly, only one sample of each group is selected for residual stress measurement. In order to detect the residual stress distribution along the depth direction, electrolytic polishing is used to remove excess material before each stress measurement. The 5% perchloric acid and 95% glacial acetic acid solution was employed to remove the surface material layer-by-layer. Electrolytic polishing is performed using a custom electrolytic cell. Electrolytic polishing voltage is 50 volts. Every time the sample was polished for 65 minutes, and then the remaining sample thickness was measured by a screw micrometer to calculate the thickness of the removed layer. The thickness of the removal layer is controlled at about 50µm. As the material is removed, the residual stress in the specimen will be redistributed. The stress value measured after the removal of the material is not the true stress of the measured point. Therefore, the following formula Eq.(25) is used to modify the measured stress value of the material after material removal, so as to obtain the true stress value of the measured point (the burnished surface is used as the starting point of integration). σ z = σ z′ +
Pressure
Feed rate
Number of
Speed
(Mpa)
(mm)
passes
(mm/min)
14 10
0.15 0.05
9 5
150 150
1 h−z
∫
z 0
σ ′ ( ξ )d ξ −
6
∫ (h − z ) 2
z 0
1 ( h − ξ ) σ ′ (ξ ) d ξ 2
(25)
where σ z the modified stress value, σ z ′ is the measured stress value, h is the thickness of the specimen, z is the thickness of the removed material, σ ′ (ξ ) is the distribution function of residual stress. According to the results of literature [33], the residual stress varies little in the direction perpendicular to the ball burnishing velocity and in parallel with the ball burnishing velocity. Hence, only the residual stress perpendicular to the burnishing speed direction is measured. Tension-tension fatigue tests and bending fatigue tests have been performed at room temperature using servo-hydraulic MTS810 test system with a load cell capacity of 250 kN. A stress-controlled mode is selected to provide cyclic stress. The stress waveform is a sine wave. The load frequency is 15 Hz. The load ratio is 0.1. The span of the bending fatigue test is 70 mm. In order to select the appropriate initial stress and stress difference, six untreated tension-tension fatigue samples and six untreated bending fatigue samples are used for tentative fatigue tests. According to the results of tentative fatigue tests, the stress step is 5MPa for tension-tension fatigue samples. For bending fatigue tests, the stress step is 5MPa for unburnished samples and 10MPa for burnished samples.
4.2 Results and discussion The initial surface roughness are Ra0.484µm.After treatment with parameters (a), the surface roughness is Ra0.363µm. For parameters(b), the surface roughness is Ra0.07µm.Fig.5 shows the microhardness varies with the depth. The results of residual stress distribution are shown in Fig.6.
Fig.6. The residual stress distribution along the depth of the ball burnished specimens
Fig.7. Up-down graph of tension-tension fatigue samples:(a) unburnished samples, (b)burnished samples Fig.5. The hardness distribution along the depth of the ball burnished specimens:(Up)paramters of group (a),(Down)paramters of group (b)
Eq.(15)~Eq.(22). Table 4 shows the results of related parameters. For parameters (a),the predicted tension-tension fatigue strength and bending fatigue strength are 133MPa and 313MPa,repectively. The error between the predicted value and the measured value are 13% and 11%, respectively. For burnishing process parameters (b), the predicted bending fatigue strength is 322MPa. The predicted value is close to the measured value. In sum, when the direction of crack propagation is perpendicular to the burnished surface, the error between the predicted value and the actual measured value is relatively small. After double face burnishing process, the crack propagation may be greatly influenced by the microstructure of the material. Moreover, Eq. (23) can also be used to predict the fatigue strength of laser shock peening or shot peening.Fig.10 depicts the comparison results of the predicted and measured fatigue strength in literature [34-37]. The error between the predicted value and the measured value is less than 20%. It can be seen from Fig.10 that the error in the prediction of fatigue strength in literature[34]and literature[37]is relatively large. This may concern with the selection of the critical depth of the strain-concentrated micro regions.
Fig.8. Up-down graph of tension-tension fatigue samples:(a) unburnished samples, (b)burnished samples
Fig.7 and Fig.8 illustrate the results of conditional fatigue tests. According to the fatigue results, the average fatigue strength of the sample of unburnished tensile samples is 118MPa and 144MPa for burnished tensile samples. There is nearly 27% increase in the tension-tension fatigue strength as compared to that of the unburnished sample. The average fatigue strength of the sample of unburnished bending samples is 282MPa and 329MPa for burnished samples. The bending fatigue strength is improved as much as 17%. The bending fatigue strength(at 5 105cycles) is 295MPa. After burnished with process parameters (b), the fatigue strength is 309Mpa. The bending fatigue strength is improved as much as 5%. The fatigue strength of unburnished and burnished samples is shown in Fig.9.
Fig.9. Fatigue strength comparison for unburnished and burnished samples
According to the distribution of microhardness and residual stress(Fig.5,Fig.6), the hardness gradient factor and the residual stress gradient factor can be obtained by means of
Fig.10. Application of the proposed model in other surface treatments :(a) laser shock peening TC11 [34], (b)shot peening C70 steel [35], (b)shot peening Cr–Mo steel [36], (d)shot peening TC4[37]
Table4 Parameters related to fatigue strength prediction of burnished samples Parameters
SH0.5′
YH0.5′
Sσr′ 0.5
0 t
1 t
Initial
Predicted
fatigue
fatigue
α
β
K
0.112
0.1146
1.7714
1.6652
1.03
118
133
0.0612
0.0789
1.831
1.7211
1.03
282
313
0.029
0.0349
1.8232
1.7467
1.03
295
322
Yσ r′
K
σ untreated σ treated
C0
(a) Tensile fatigue 0.4358
1.147
0.4468
1.119
(a) Bending fatigue (b) 0.3793
1.318
0.382
1.309
Bending fatigue
5 Conclusions In this work, after analyzing the main factors affecting the fatigue life of burnished components, a new fatigue strength prediction method considering the effects of residual stress, surface roughness, gradient and size effect is developed. With the model, tension-tension fatigue tests and three-point bending fatigue tests are carried out on TA2 alloy components. The results show that the predicted and actual results have good agreement. The tension-tension fatigue strength(at1 106cycles) of the unburnished sample is 118MPa and 282MPa for bending fatigue strength. After ball burnishing process, the tension-tension fatigue strength(at1×106cycles) is 144MPa and 329MPa for bending fatigue strength. The tension-tension fatigue strength is increased by an amount of 27%. The bending fatigue strength is improved as much as 17%.The predicted tension-tension fatigue strength is 133MPa. The error between the predicted value and the measured value is 13%. The predicted bending fatigue strength is 313MPa. The error between the predicted value and the measured value is 11%.The bending fatigue strength(at5 105cycles) is 295MPa. After burnished with parameters(b), the fatigue strength increased to 309MPa. The predicted fatigue strength is 322MPa. The error between the predicted value and the measured value is less than 10%. The improvement of fatigue effect of burnished components is mainly attributed to the residual compressive stress introduced after burnishing process, the gradient structure formed on the top-treated surface due to the plastic deformation and the improvement of surface roughness. The proposed model can also be used for the prediction of high cycle fatigue strength of surface hardened components due to gradient plastic deformation. The model has important significance in engineering practice.
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Highlights
1.A high cycle fatigue strength prediction model for low plasticity burnished samples has been developed.
2.Impact of residual stress,surface roughness,microhardness,gradient and size should be considered.
3.The proposed model is not only applicable to the prediction of the high cycle fatigue strength of rolling specimens, but also to the prediction of the high cycle fatigue strength of surface strengthening samples such as shot peening and laser peening.
S0142-1123(17)30263-3 http://dx.doi.org/10.1016/j.ijfatigue.2017.06.013 JIJF 4369
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
13 March 2017 6 June 2017 7 June 2017
Please cite this article as: Yuan, X., Sun, Y., Li, C., An engineering high cycle fatigue strength prediction model for low plasticity burnished samples, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/ j.ijfatigue.2017.06.013
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An engineering high cycle fatigue strength prediction model for low plasticity burnished samples Xilin Yuan1,Yuwen Sun1*, Chunyan Li2 1.Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, Dalian University of Technology, Dalian, 116024, China 2. School of Material Science and Engineering, Dalian University of Technology, Dalian, 116024, China
Abstract: High cycle fatigue performance is significantly affected by the surface conditions of mechanical components. Traditionally, one major effect of low plasticity burnishing process in promotion fatigue resistance has been ascribed to the generation of compressive residual stresses and the formation of gradient structure in the top-treated surface layer. However, the prediction model of fatigue performance considering the effects of roughness, microhardness and residual stress has not been well established. Thus, the aim of this work is to develop a model predicting the fatigue strength of high cycle fatigue for burnished metallic components. First, the main parameters affecting the fatigue performance of burnished components are investigated by dimension analysis method. Then, by introducing the influence factors of stress gradient and microhardness gradient, a fatigue strength prediction model is proposed to correlate the fatigue strength of untreated and treated samples. This model considers the effects of residual stress, microhardness, roughness, gradient and size. In order to verify the validity of the model, double faces low plasticity burnishing and tension-tension fatigue tests are carried out on TA2 alloy samples with center hole. In addition, to investigate the effect of low plasticity burnishing on the fatigue performance when the direction of crack propagation is perpendicular to the burnished surface, one face burnishing and three-point bending fatigue tests are also performed. The tension-tension fatigue strength and bending fatigue strength after low plasticity burnishing are 144 MPa and 329 MPa, respectively. The predicted tension-tension fatigue strength and bending fatigue strength after low plasticity burnishing are 133 MPa and 313 MPa, respectively. The error between the measured value and the predicted value is less than 15%. At last, fatigue comparison tests using new burnishing process parameters are carried out. The fatigue strength after treatment is 309MPa. The predicted fatigue strength after treatment is 322MPa. The prediction error is less than 10%. This demonstrates that the proposed model is effective in the high cycle fatigue strength prediction model for low plasticity burnished samples. Keywords: fatigue strength, low plasticity burnishing, residual stress, microhardness;
1 Introduction Engineering structures and components due to serving under cyclic loading, prone to fatigue damage. Fatigue cracks generally initiate at the stress concentration of the components surface. The subsequent fatigue crack growth determine the fatigue life of the components. Therefore, techniques that improve the fatigue resistance of the components are significant. Existing studies have shown that surface modification or treatment technologies are effective for improving the fatigue performance, such as shot peening, deep rolling, laser shock peening(or laser peening), ultrasonic surface rolling, machine hammer peening. Shot peening is a surface treatment method, which uses the plastic deformation layer on the surface of the material to improve the performance of the material. After shot peening process, the introduced residual compressive stress field in the surface layer can effectively restrain the cracks initiation and propagation, and then improve the fatigue strength and fatigue life. Such method is widely used in the manufacture of aviation, spaceflight, automobile, electric power station and so on. The advantage of shot peening is that the cost is low. Moreover, it can be used to the surface strengthening treatment of large parts. However, in addition to the properties of the component materials, the effects of shot peening are related to many process parameters, such as the size of the shot, shape, hardness, shot peening *[email protected]
velocity and peening flow. Therefore, it is difficult to accurately predict the effect of shot peening. In addition, the surface roughness of the shot peened component is not as good as that produced by ball burnishing. In contrast, laser peening is a new surface modification technology. During the process of laser peening, a deep layer of compressive residual stresses can be introduced by high energy and short pulsed laser [1]. Compared to shot peening, there is a sacrificial layer known as protective coating or ablative material on the surface of the workpiece. This coating can reduce the thermal effects of the laser beam on the part. After operating more three times, the protective coating must be removed. Thus, laser shock peening is costly. In contrast, low plasticity burnishing (also called ball burnishing or deep rolling) is a competitive and effective surface finishing process. This process produces surface plastic deformation by a free rolling ball. This ball is pressed on the surface of the component. In the burnishing process, the applied burnishing load force the surface material spread and flow from the peaks to the valleys on the component surface. This plastic deformation can improve the component surface roughness. At the same time, a hard layer on the finishing surface can be formed. Previous works paid attention to the burnishing process parameters on the surface integrity, including surface roughness, hardness, distribution of residual stress and sub-surface characteristics of burnished components. In literature [2] the influence of process parameters (force, speed and feed) on the surface
roughness and hardness was studied in detail. For advanced materials such as biomedical Nitinol, non-uniform martensitic transformation could be observed on the cross-sectional surface after ball burnishing process [3]. As for the residual stress, M. Beghini et al. found that the process parameter that affected mostly the residual stress distribution was force, followed by the feed rate. In addition, the depth of the maximum compressive residual stress location increased with the rolling force. At high rolling force, the feed parameter did not significantly affect the distribution of the residual stress [4]. Finite element simulation results also showed that the amplitude and magnitude of residual stress increased with the burnishing force [5-6]. These research results will be beneficial to guide the production of rolling process. By means of ball burnishing process, gradient structure of the top-treated surface can be obtained. In this gradient layer, coarse grains in the surface layer can be refined. In addition, the grain size increases with the increase of depth. Meanwhile, the residual compressive stress of the top-treated surface is characteristic of the gradient distribution along the depth direction due to the uneven strain. The compressive residual stress induced by ball burnishing can enhance the crack closure forces and the crack closure effects, thus, the propagation of fatigue crack is suppressed [7-11].However, only quantitatively studying the effect of residual stress on fatigue properties can be beneficial for the practical design. At present, superposition method is usually utilized to study the effect of residual stress on fatigue performance [12].The effective stress is the superposition of the mean residual stress and the stress introduced by external load. However, there are still some differences between the residual stress and the mean residual stress. The method of converting residual stress into mean stress ignores the effect of stress gradient. At present, the most representative fatigue strength or fatigue life prediction method, which considering the effects of stress gradient, is stress field intensity method and advanced volumetric method [13-18]. According to the stress field intensity method, fatigue is a local damage phenomenon. Under cyclic loading, the fatigue crack is initiated at the notch root. The performance of the material in a certain area of the notch, the maximum stress at the notch root, the stress gradient near the notch and the stress and strain field distribution play a decisive role in the fatigue performance of the specimen. The advanced volumetric method is developed on the basis of the stress field intensity method. The failure region is defined as the critical volume in the advanced volumetric method. Then, the stress field intensity in the volume method can be obtained by simplifying the weight function in the stress field intensity method. In general, a circular region centered at the root of the notch is regarded as the failure region in the stress field intensity method. The radius of this circle is called the field diameter. The difficulty of the stress field intensity method is the determination of the field diameter. For the actual component, the determination of the field diameter is more complex and difficult. The advanced volumetric method requires accurate calculation of the stress gradient at the root of the notch. Further, it is more
difficult to accurately calculate the stress gradient for the notched specimen with higher stress concentration. In order to consider the effect of residual stress, stress gradient, roughness and hardness on the fatigue performance of burnished components, a new fatigue strength prediction model is proposed. First, the key factors affecting the fatigue performance of ball burnished sample based on the dimensional analysis.an analytical approach is proposed. The effects of residual stress, hardness are taken into account. Then, with a view to the complexity of the gradient calculation, the modified fatigue strength prediction model for ball burnished samples is proposed. And the influence of surface roughness and size effect are also considered in the modified model. In order to verify the rationality of the proposed model, the tension-tension fatigue strength and the bending fatigue strength of the ball burnished samples are predicted respectively. Finally, the proposed model is used to predict the bending fatigue strength of the specimens burnished with new process parameters.
2 Dimensional analysis of fatigue properties of gradient structure materials The fatigue properties of the material are affected by many factors, such as the size and distribution of inclusions, load conditions and environmental factors. In addition, the fatigue properties of gradient materials are also affected by the size and distribution of the grain, the residual stress and the gradient changes of material properties. Table1 lists the main factors affecting the fatigue limit of the gradient materials. At present, there is not a unified mathematical equation to describe the effect of these factors on fatigue performance. Dimensional analysis method can be used to reveal the essence of the problem by designing a suitable model. Table1 Parameters affecting fatigue life
h
The depth of the gradient layer
E
The elastic
E0
modulus of the original material
µ
Poisson's ratio of
µ0
the original material
σ 0.2( local )
Strain hardening
n0
exponent of the original material
of the original material
σ load
Stress produced by external load
l
Characteristic length of the
surface-treated material Poisson's ratio of the surface-treated material
The yield strength of the surface-treated material Strain hardening exponent
n
of the surface-treated material
∂E ∂h
Gradient of elastic modulus
The yield strength
σ 0.2
The elastic modulus of the
∂σ 0.2( local ) ∂h
σ mr
of the surface-treated layer
Gradient of yield strength of the surface-treated layer
Mean residual stress in the
specimen
surface-treated layer
In engineering applications, the gradient distribution of
To simplify the analysis, the fatigue life of the specimen can be expressed as the following equation:
hardness is easier to obtain. A large number of experiments show that there is a linear relationship between hardness and
∂E ∂σ 0.2(local ) N f = f h, E0 , µ0 ,σ 0.2 , n0 , E, µ,σ 0.2(local ) , n, , ,σ load , l ∂h ∂h (1) and are assumed as the dimensionally independent variables. The rest of the variables can be represented as: h l
π1 =
π2 =
(2)
E0
(4)
σ load
(5)
E0
Substituting π1 ∼π7 to Eq.(1) , one can have
gradient of yield strength of the surface-treated layer
∂σ 0.2 (local ) ∂h is replaced with the gradient of hardness
b2
b
b3
(6) Using Buckingham’s Π Theorem, Eq. (6) can be derived as a
2 3 a1 h σ E σ 0.2( local ) N f = A 0.2 l E0 E0 E0
a7
a4
l ∂E E0 ∂h
a8
σ n µ load E0 n0 µ0
a9
a5
(7)
where A and ai ( i = 1 ~ 9 ) are constants. The material of the specimen can be treated as homogeneous material, if the specimen is not subjected to any surface strengthening treatment. Then E0 , µ0 , n0 and σ 0.2 are material constants. Consequently, the above Eq.(7) can be rewriting as the following equation, which is a typical Basquin formula.
b4
1 h H E H l ∂E N f = A0 0 l E0 E0 H 0 E0 ∂h
b7
b8
l ∂H σ load n µ H 0 ∂h E0 n0 µ0
b5
(9)
b9
where A0 and bi ( i = 1 ~ 9 ) are constants. For strain hardening materials, the strain hardening index has little change, and the elastic modulus and Poisson's ratio have no change. Consequently, the above Eq. (9) can be simplified as: d2
d3
1 h H l ∂H σ load N f = A1 l H 0 H 0 ∂h E0
d
h σ E σ 0.2(local ) l ∂E l ∂σ0.2(local ) σload n µ N f = f , 0.2 , , , , , , , l E E E0 E0 ∂h E0 ∂h E0 n0 µ0 0 0
l ∂σ 0.2(local ) ∂h E0
yield strength of the gradient surface layer σ 0.2( local ) . And the
b6
……
a6
respectively replace the original yield strength σ 0.2 and the
rewritten as: (3)
E π3 = E0
a
the hardness of the gradient surface layer H are used to
of the surface-treated layer ∂H ∂h .Then Eq. (7) can be
σ 0.2
π7 =
strength [19-21]. Consequently, the original hardness H 0 and
d4
(10)
where A1 and d i ( i = 1 ~ 4 ) are constants. Taking into account the residual stress in the surface after the surface treatment process, the average residual stress can be superimposed on the external load stress [22]. Then the above Eq. (10) can be written as: 1 h H N f = A2 l H0
aa
aa2
l ∂H H 0 ∂h
aa3
σ mr E0
aa4
σ load E0
aa5
(11)
where A2 and aai ( i = 1 ~ 5) are constants. Under the same fatigue life, the relationship between the fatigue strength of the treated and untreated parts can be expressed as the following equation: bb2
bb3
bb4
h H l ∂H σ mr σ treated = A3 σ untreated l H 0 H 0 ∂h E0 bb1
(12) a
σ N f = C load = σ f σ b E0
(8)
where A3 and bbi ( i = 1 ~ 4 ) are constants. σ treated and σ untreated represents respectively the fatigue strength of the treated and untreated parts.
It can be inferred from Eq. (12) that the fatigue strength of the surface-treated specimen could be predicted as the distribution of hardness and residual stress was obtained. Likewise, considering the influence of residual stress gradient, the above Eq. (12) can be rewritten as: dd2
dd3
dd4
dd5
dd h H l ∂H σr l ∂σr σtreated = A4 σuntreated l H0 H0 ∂h E0 H0 ∂h 1
Define
Yσ ′ = r
1
(19)
2 Sσ ′ 0.5 r
where represents residual stress gradient factor, Sσ ′ 0.5 r
represents the area of the normalized curve of residual stress (13) where A4 and ddi ( i = 1 ~ 5) are constants. σ r is the residual stress in the surface-treated layer. Equation(13) can be simplified as: σ treated = C0 CH Csσ untreated (14)
H where CH = H0
dd2
l ∂H H 0 ∂h
dd3
σ , Cs = r E0
dd4
l ∂σ r H 0 ∂h
and the coordinate axis in the 0 ≤ x ≤ 0.5 interval. The normalization of residual stress is carried out according to the following equation. σ ′ (h′) =
dd5
and C0 is a correction factor used to eliminate the error caused by the integral interval. CH is a parameter that is related to the hardness of the burnished component. Cs is a parameter that is related to the residual stress of the burnished component.
hr′ =
(20)
h hrmax
(21)
where σ ( h ) is the residual stress of the surface-treated layer, σ max is the maximum residual in the stress affected layer, hrmax is the maximum depth of residual stress affected layer. The stress gradient index is defined as follows:
β=
3 Modeling an engineering fatigue model for low plasticity burnished specimens If the residual stress and hardness gradient are not large, then it is very convenient to predict the fatigue strength of strengthened components by utilization the Equation (13). However, application derivation method to calculate the gradient will be difficult when the stress or hardness gradient are large. In order to avoid these defects, the integral method is used to redefine the gradient factor [23].
σ (h ) σ max
hrmax l/2
(22)
Considering the improvement of the surface roughness of the specimens caused by low plasticity burnishing, the fatigue strength of burnished specimen can be expressed as: α
( ) 1+ K K− K σ
σtreated = C0 (YH′ ) Yσ ′ r
0
β
1
t
t
0
untreated
t
(23)
Define (15)
where Kt0 is the stress concentration factor caused by surface roughness before low plasticity burnishing process,
wher YH ′ represents hardness gradient factor, S H ′0.5 represents the area of the normalized curve of hardness in the interval
K t1 is the stress concentration factor caused by surface roughness after low plasticity burnishing process. The above
x ∈ [ 0,0.5] . The normalization of hardness is carried out
fatigue strength prediction model is not suitable for the prediction of low cycle fatigue strength because the depth of
YH ′ =
1 2 S H ′ 0.5
according to the following equation. H ( h ′) =
h ′=
H (h ) hmax
h hmax
(16) (17)
where H ( h ) is the hardness of the surface-treated layer, and hmax is the maximum depth of hardness-increased layer. The hardness gradient index is defined as follows:
α=
hmax l/2
(18)
the influence layer is relatively small. The stress concentration factor caused by surface roughness can be calculated by the following equation:
Kt =1+2 Rz / ρ
(24)
where Rz and are the 10-point surface height and notch root radius, respectively[24-26]. According to micro-meso-process theory of fatigue source initiation, the formation of the fatigue source consists of the following four microscopic processes: (1) under cyclic
loading, the slip systems in the grain are activated. Then, the dislocations move along the slip surfaces. The pile-up of dislocations will be formed when the dislocations meet with the grain boundaries and sub grain boundaries, inclusions, secondary phase. These pile-up of dislocations result in a rise of stress concentration. When the stress reaches or exceeds the meso-scopical yield strength of some adjacent grains, the concentrated stresses are relaxed. The dislocations continue to slide. With the progress of the process, pre-yield regions involving a considerable number of grains are formed. However, at this time, the stress produced by external load does not reach the yield strength of the whole material. That is to say, the material in the other parts except the pre-yield regions is still in the elastic deformation stage. In general, the outside of the grains on the surface of the part are free. Due to the restriction of the inner grains, the dislocation motion of the grains on the surface is relatively small. Hence, pre-yield regions are easily formed on the surface of the parts. As a consequence, most of the fatigue cracks are initiated on the surface of the part. However, for the surface treated parts, the surface layer is strengthened or the residual compressive stress is formed. As a result, the formation of pre-yield regions requires larger stress. Moreover, under the strengthened layer, the residual tensile stress or low strength may be beneficial for the formation of pre-yield regions. This is the initial stage of fatigue crack initiation. (2) Consideration of the probability of the structure distribution of the material, there may be some micro region in the pre-yield regions. In these micro regions, the grains are well coordinated with each other. The plastic deformation resistance in these regions is relatively small. Under the same load, these micro regions firstly formed strain-concentrated micro region. (3) The material properties of pre-yield regions, strain-concentrated micro regions and the matrix are different. The yield strength of material in strain-concentrated micro regions is relatively low. As a consequence, strain-concentrated micro regions are easy to reversely yield in unloading or reverse loading stage. (4) Under the suitable cyclic load, alternating plastic deformation will be formed in strain-concentrated micro regions. The initial fatigue cracks initiate in a few strain-concentrated micro regions. As the initial crack continues to propagate, macroscopic cracks are formed and eventually lead to fatigue fracture. The fatigue limit of the material can be considered as the critical stress for the meso-scopic yielding. In fact, the formation of strain-concentrated micro regions around the weak grains is the key process of fatigue cracks initiation. Moreover, the surrounding grains restrict the formation of the microstructural yield region near the inner grains. This constraint increases as the distance of the weak grains from the surface increases. When the distance reaches a certain depth, the constraint gradually reaches saturation due to the interdependence between grains. It can be inferred that this critical depth is closely related to the microstructure of the material, especially the grain size. For the notched specimen, this critical depth highly affect the fatigue limit. Although the stress at the root of the notch reaches the fatigue limit of the material, it is far from satisfying the coordination and
probabilistic condition of the fatigue crack initiation because of the stress gradient near the root of the notch. The meaning of this critical depth is illustrated in Fig.1. It can be seen that the stress decreases with the increase of the distance from the notch root. When the nominal stress σ is equal to the fatigue limit of the material σ f , the distance from the root of the notch is the critical distance d c .The results from literature [27-28] show that the critical distance d c is highly related with 10d is the average grain diameter of the surface layer).Actually, the burnished surface of the part is covered with grooves. These grooves are distributed in different positions. However, they are not at the center of the maximum stress. Consequently, they have little effect on fatigue failure. Therefore, it can be considered that the rest of the burnished surface of the part is flat except for the notch at the center of the maximum stress (Fig.2) [29-31]. For burnished specimens, it is reasonable that the critical depth of the strain-concentrated micro regions 10d .This depth is approximately half the depth of the affected layer. This is the reason why the half of the influence layer depth is defined as the integral interval.
Fig.1. Local stress distribution of notched specimen
Fig.2. Notch model for ball burnished surfaces
Fig.3. Dimensions and burnished region of fatigue specimens:(Up) Tension-tension fatigue specimen, (Down) Bending fatigue specimen
4.Verification of the model 4.1 Sample preparation and experimental procedures To assess the prediction accuracy of the engineering model, in this section five serials fatigue tests are performed. And, four serials fatigue tests are firstly carried out to determine the effect of ball burnishing on the tension-tension fatigue strength and bending fatigue strength at the 1 10 cycles.In these four serials fatigue tests, the up and down method is employed. Samples, used for determining the fatigue strength at the 1×106cycles after burnishing process, are treated with the same ball burnishing process parameters. The fifth serials fatigue testes are used to compare the fatigue strength (at the 1 10 cycles) before and after treatment. A new set of burnishing process parameters is utilized in theses burnished samples. The material of the specimens is TA2 alloy. The mechanical properties of TA2 are shown in Table.2. Dimensions and burnished region of the specimens are illustrated in Fig.3. In order to reduce axial abrasion and burrs generated at the edge of the hole, chamfering is performed at the edge of the hole. The specimens are firstly machined on a Haas machining center (VF-5/40XT). The machining conditions are spindle speed of 1000rpm, feed of 300mm/min, and depth of cut of 0.05mm. Taking into account the
friction damage is relatively large if the initial rough surface is ball burnished, the fatigue specimens are firstly smoothed with roller burnishing tool. After the roller burnishing process, the surface modification is Fig.4 shows the roller burnishing tool (SFP20-S20, Sugino Machine Limited) and low plasticity burnishing tool (HG6-19E90°-ZS20X, Ecoroll Corporation). The roller burnishing parameters are referenced from the results of literature [29].The detailed roller burnishing process parameters are: spindle speed = 1500 r/min, feed =148 mm/min, depth = 0.05 mm. The parameters of group (a) are used to determine fatigue strength at the 1×106cycles. The parameters of group (b) are used to compare the fatigue strength at the 1×105cycles. The details of the burnishing process parameters are shown in Table 3. The description of the process parameters has been described in literature [32]. Tensile fatigue samples are double face burnished. Bending fatigue samples are single face burnished. Table2 The mechanical properties of TA2
Density (g/cm3 )
Tensile strength(MPa)
Yield strength(MPa)
Modulus of elasticity
Hardness (HV)
(GPa) 4.5
510
460
107.8
190
Table3 Ball burnishing process parameters
a b
Fig.4. Burnishing tools:(L) Roller burnishing tool(R)low plasticity burnishing tool
In order to detect the microhardness distribution and the residual stress distribution of the surface layer after burnishing, a square plate using the aforementioned processing parameters is machined. The surface roughness is measured by Zygo New View 5022 scanning white light interferometer (SWLI). The average surface roughness value is obtained from the mean value of five different positions on the surface. The surface microhardness was measured with an HXD- 1000TM microhardness tester under a load of 98g with a dwelling time of 15s. The average microhardness value is obtained from the mean value of five different positions on the surface.Only one sample of each group is selected for microhardness measurement. Residual stress is examined by X-ray diffractometry (XRD, PANAlytical Empyrean, CuKα radiation). Similarly, only one sample of each group is selected for residual stress measurement. In order to detect the residual stress distribution along the depth direction, electrolytic polishing is used to remove excess material before each stress measurement. The 5% perchloric acid and 95% glacial acetic acid solution was employed to remove the surface material layer-by-layer. Electrolytic polishing is performed using a custom electrolytic cell. Electrolytic polishing voltage is 50 volts. Every time the sample was polished for 65 minutes, and then the remaining sample thickness was measured by a screw micrometer to calculate the thickness of the removed layer. The thickness of the removal layer is controlled at about 50µm. As the material is removed, the residual stress in the specimen will be redistributed. The stress value measured after the removal of the material is not the true stress of the measured point. Therefore, the following formula Eq.(25) is used to modify the measured stress value of the material after material removal, so as to obtain the true stress value of the measured point (the burnished surface is used as the starting point of integration). σ z = σ z′ +
Pressure
Feed rate
Number of
Speed
(Mpa)
(mm)
passes
(mm/min)
14 10
0.15 0.05
9 5
150 150
1 h−z
∫
z 0
σ ′ ( ξ )d ξ −
6
∫ (h − z ) 2
z 0
1 ( h − ξ ) σ ′ (ξ ) d ξ 2
(25)
where σ z the modified stress value, σ z ′ is the measured stress value, h is the thickness of the specimen, z is the thickness of the removed material, σ ′ (ξ ) is the distribution function of residual stress. According to the results of literature [33], the residual stress varies little in the direction perpendicular to the ball burnishing velocity and in parallel with the ball burnishing velocity. Hence, only the residual stress perpendicular to the burnishing speed direction is measured. Tension-tension fatigue tests and bending fatigue tests have been performed at room temperature using servo-hydraulic MTS810 test system with a load cell capacity of 250 kN. A stress-controlled mode is selected to provide cyclic stress. The stress waveform is a sine wave. The load frequency is 15 Hz. The load ratio is 0.1. The span of the bending fatigue test is 70 mm. In order to select the appropriate initial stress and stress difference, six untreated tension-tension fatigue samples and six untreated bending fatigue samples are used for tentative fatigue tests. According to the results of tentative fatigue tests, the stress step is 5MPa for tension-tension fatigue samples. For bending fatigue tests, the stress step is 5MPa for unburnished samples and 10MPa for burnished samples.
4.2 Results and discussion The initial surface roughness are Ra0.484µm.After treatment with parameters (a), the surface roughness is Ra0.363µm. For parameters(b), the surface roughness is Ra0.07µm.Fig.5 shows the microhardness varies with the depth. The results of residual stress distribution are shown in Fig.6.
Fig.6. The residual stress distribution along the depth of the ball burnished specimens
Fig.7. Up-down graph of tension-tension fatigue samples:(a) unburnished samples, (b)burnished samples Fig.5. The hardness distribution along the depth of the ball burnished specimens:(Up)paramters of group (a),(Down)paramters of group (b)
Eq.(15)~Eq.(22). Table 4 shows the results of related parameters. For parameters (a),the predicted tension-tension fatigue strength and bending fatigue strength are 133MPa and 313MPa,repectively. The error between the predicted value and the measured value are 13% and 11%, respectively. For burnishing process parameters (b), the predicted bending fatigue strength is 322MPa. The predicted value is close to the measured value. In sum, when the direction of crack propagation is perpendicular to the burnished surface, the error between the predicted value and the actual measured value is relatively small. After double face burnishing process, the crack propagation may be greatly influenced by the microstructure of the material. Moreover, Eq. (23) can also be used to predict the fatigue strength of laser shock peening or shot peening.Fig.10 depicts the comparison results of the predicted and measured fatigue strength in literature [34-37]. The error between the predicted value and the measured value is less than 20%. It can be seen from Fig.10 that the error in the prediction of fatigue strength in literature[34]and literature[37]is relatively large. This may concern with the selection of the critical depth of the strain-concentrated micro regions.
Fig.8. Up-down graph of tension-tension fatigue samples:(a) unburnished samples, (b)burnished samples
Fig.7 and Fig.8 illustrate the results of conditional fatigue tests. According to the fatigue results, the average fatigue strength of the sample of unburnished tensile samples is 118MPa and 144MPa for burnished tensile samples. There is nearly 27% increase in the tension-tension fatigue strength as compared to that of the unburnished sample. The average fatigue strength of the sample of unburnished bending samples is 282MPa and 329MPa for burnished samples. The bending fatigue strength is improved as much as 17%. The bending fatigue strength(at 5 105cycles) is 295MPa. After burnished with process parameters (b), the fatigue strength is 309Mpa. The bending fatigue strength is improved as much as 5%. The fatigue strength of unburnished and burnished samples is shown in Fig.9.
Fig.9. Fatigue strength comparison for unburnished and burnished samples
According to the distribution of microhardness and residual stress(Fig.5,Fig.6), the hardness gradient factor and the residual stress gradient factor can be obtained by means of
Fig.10. Application of the proposed model in other surface treatments :(a) laser shock peening TC11 [34], (b)shot peening C70 steel [35], (b)shot peening Cr–Mo steel [36], (d)shot peening TC4[37]
Table4 Parameters related to fatigue strength prediction of burnished samples Parameters
SH0.5′
YH0.5′
Sσr′ 0.5
0 t
1 t
Initial
Predicted
fatigue
fatigue
α
β
K
0.112
0.1146
1.7714
1.6652
1.03
118
133
0.0612
0.0789
1.831
1.7211
1.03
282
313
0.029
0.0349
1.8232
1.7467
1.03
295
322
Yσ r′
K
σ untreated σ treated
C0
(a) Tensile fatigue 0.4358
1.147
0.4468
1.119
(a) Bending fatigue (b) 0.3793
1.318
0.382
1.309
Bending fatigue
5 Conclusions In this work, after analyzing the main factors affecting the fatigue life of burnished components, a new fatigue strength prediction method considering the effects of residual stress, surface roughness, gradient and size effect is developed. With the model, tension-tension fatigue tests and three-point bending fatigue tests are carried out on TA2 alloy components. The results show that the predicted and actual results have good agreement. The tension-tension fatigue strength(at1 106cycles) of the unburnished sample is 118MPa and 282MPa for bending fatigue strength. After ball burnishing process, the tension-tension fatigue strength(at1×106cycles) is 144MPa and 329MPa for bending fatigue strength. The tension-tension fatigue strength is increased by an amount of 27%. The bending fatigue strength is improved as much as 17%.The predicted tension-tension fatigue strength is 133MPa. The error between the predicted value and the measured value is 13%. The predicted bending fatigue strength is 313MPa. The error between the predicted value and the measured value is 11%.The bending fatigue strength(at5 105cycles) is 295MPa. After burnished with parameters(b), the fatigue strength increased to 309MPa. The predicted fatigue strength is 322MPa. The error between the predicted value and the measured value is less than 10%. The improvement of fatigue effect of burnished components is mainly attributed to the residual compressive stress introduced after burnishing process, the gradient structure formed on the top-treated surface due to the plastic deformation and the improvement of surface roughness. The proposed model can also be used for the prediction of high cycle fatigue strength of surface hardened components due to gradient plastic deformation. The model has important significance in engineering practice.
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Highlights
1.A high cycle fatigue strength prediction model for low plasticity burnished samples has been developed.
2.Impact of residual stress,surface roughness,microhardness,gradient and size should be considered.
3.The proposed model is not only applicable to the prediction of the high cycle fatigue strength of rolling specimens, but also to the prediction of the high cycle fatigue strength of surface strengthening samples such as shot peening and laser peening.