Experimental investigation of the effects of artificial wedges on fatigue crack growth and crack closing behavior in annealed SAE1045 steel

International Journalof Fatigue

International Journal of Fatigue 29 (2007) 962–976

www.elsevier.com/locate/ijfatigue

Experimental investigation of the effects of artificial wedges on fatigue crack growth and crack closing behavior in annealed SAE1045 steel Mitsuhiro Okayasu, Zhirui Wang

*

Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, Ont., Canada M5S 3E4 Received 25 October 2005; received in revised form 3 June 2006; accepted 17 July 2006 Available online 20 October 2006

Abstract To better understand the effect of asperity on the crack closure and fatigue crack growth behavior, the load–CMOD relations and crack propagation rate were examined through the addition of artificial wedges into pre-cracks. Experimental results revealed that the unloading phase of the load vs. CMOD curve exhibited always a concave shape, signifying the acceleration in the CMOD decrease. This was related to the plastic deformation in the wedge as well as in the specimen material surrounding the wedge. With the addition of an artificial wedge, reduced fatigue crack growth rate was found. The crack growth rate was then correlated with the effective load intensity factor range, DPeff = Pmax  Pmin,real, which itself was correlated also to the deformation severity in the asperity as well as in the specimen material. Furthermore, the DPeff value was found to change with increasing the crack length. In a short crack range, approximately 0.1 mm crack length, the value of DPeff decreased due to the asperity- and plasticity-induced crack closing behavior. As the crack length increased, the DPeff value increased as well due to the reduction in the closing behavior until just prior to the final fracture. Based upon the DPeff variation as a function of crack length, details of the crack closing behavior were further discussed.  2006 Elsevier Ltd. All rights reserved. Keywords: Artificial asperity; Crack closure; Crack driving force; Crack growth rate; Crack opening displacement

1. Introduction Since Christensen recognized the fatigue crack closure effect as a major problem in his crack propagation study in 1963 [1] and Elber observed the actual behavior experimentally in 1970 [2], this phenomenon has been one of the most intensively studied parameters associated with fatigue crack growth behavior. Up to date, there have been more than 3000 searchable ‘‘crack closure’’ papers published. The concept of crack closure has been widely applied to rationalize various aspects of fatigue crack propagation phenomena, such as the effects of material property, microstructure, loading condition and environment. In particular, it has been stated that fatigue crack growth behavior in the near-threshold regime cannot be explained if crack closure effect is not taken into account [3]. Although *

Corresponding author. Fax: +1 416 978 4155. E-mail address: [email protected] (Z. Wang).

0142-1123/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2006.07.019

numerous research papers have been published involving crack closure characteristics and closure models to understand the related crack growth behavior, in recent years discussions on the validity of the crack closure concept has been reported in the literature [2,4–10]. For instance, the roughness-induced crack closure model (zig-zag model), proposed by Suresh and Ritchie [4], has been questioned by Wang et al. [5] and Wase´n and Karlsson [6] due to its oversimplification. In Wang et al.’s study [5], the model of fracture surface mismatch has been extended using dislocation theory; the crack closing stress intensity factor, predicted with the dislocation model, was in good agreement with the experimental data. The fundamental mechanism of plasticity-induced crack closure [2] has also been challenged by Vasudevan et al. [7–9]. Vasudevan and his colleagues reported that there is no significant contribution to crack closure by the plasticity behind the crack tip. However, such a claim was countered by the work of Pippan and Riemelmoser [10], who proposed a mathemat-

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

ical model based upon dislocation configuration in front of crack tip for the fracture surface contact mechanism. To understand clearly the effect of crack closure on fatigue crack growth behavior, several researchers [11–16] have made attempts to use artificial wedge/asperity. Kitagawa et al. [11] used adhesive material injected into the crack surfaces as the artificial wedge, and the crack growth rate was then examined at various loading conditions. One of their conclusions is that the lower part of the load range, i.e., the load portion below Kop (see Fig. 1 for definition), also affects the fatigue crack growth rate in addition to the conventional effective DK (DKeff,conv), where DKeff,conv = Kmax  Kop. This conclusion is different from the Elber’s model [2,17]. Vecchio et al. [12] measured the crack growth rate influenced by a needle tip positioned adjacent to the crack tip in a 2024 aluminum alloy sample, and the crack growth rate was found to change marginally despite the dramatic increase in the DKeff,conv value. In a similar approach, Hertzberg et al. [13] employed shims of different sizes as the artificial asperity in their investigation on the relationship between the crack growth rate and the DKeff,conv value. They concluded that the value of DKeff,conv measured with the crack mouth compliance gage underes-

a

K (or P)

ΔKeff (or ΔPeff ) ΔKeff,conv (or ΔPeff,conv )

Kmax (or Pmax )

Kop (or Pop )

No contact

Kmin,real (or Pmin,real)

o

b

σmin

K (or P) Kmax (or Pmax )

Contact region

σmax

σop

σ

ΔKeff (or ΔPeff ) ΔKeff,conv (or ΔPeff,conv )

Kop (or Pop )

No contact

Kmin,real (or Pmin,real)

COD CODmin

CODop

timated the crack growth rate. In still another different study, epoxy with 0.2 and 0.5 lm alumina particles were employed to assess the effect of infiltration-induced crack closure on crack growth retardation by Sheu et al. [15], who then reported that ‘‘even though the crack growth increment is affected by the size of reinforcing particles, no distinct trend was detected in the crack growth rate at the maximum retardation’’. In addition, Sheu et al.’s work also indicates that the crack growth rates for some specimens could not be clearly related to DKeff,conv value. From the above statements, it may be considered that the conventional crack closure concept, i.e., the DKeff,conv consideration, seems questionable in explaining the fatigue crack growth behavior. Up to now, several researchers have modified the DKeff,conv value [11,18–23] to reconsider the crack closing concept using various crack closure models. A good example is Kitagawa et al.’s extensive study, in which they proposed a new form of the effective crack driving force, DKeff = Kmax  Kmin,real as shown in Fig. 1a, where the influence of deformation in the wedge as well as the specimen arising from their contact action is considered [11]. A similar concept of crack closing behavior was also reported by Chen et al. [18], who suggested that since the load vs. COD curve (Fig. 1b) below the Kop level is highly affected by the fracture surface roughness, the DKeff approach may be a more realistic one than the DKeff,conv method to account for the crack growth behavior. Although their crack closure models [11,18] are considered valid for particular reasons, there is apparently a lack of experimental data for the validation. Further to the above, there have been reports of still different models on the crack closing concept [19–23], but the fundamental aspects of closure characteristics have not been clearly verified experimentally, such as direct experimental observation. The aim of this work is therefore (i) to verify the effect of the DKeff value on the crack growth behavior and (ii) to clarify the crack closing characteristics experimentally. Artificial asperities are used in this study, and they are designed in accordance with the crack closure phenomena reported on various ‘‘nature’’ wedges, such as Al2O, SiC and SiO2 ceramic particles [24–26] and MnS, MgO and CaO non-metallic inclusions [27–29]. It should be pointed out that, compared to aforementioned particles and inclusions, the size of artificial wedges selected in the present study is larger; however, to facilitate a more pronounced and accurate examination of the crack closing behavior, the selection of the larger artificial wedge could be appropriate. 2. Material and experimental procedures

Contact region

o

963

2.1. Specimens and fatigue test

CODmax

Fig. 1. Schematic illustration of typical crack closure models, showing the conventional effective stress intensity factor range (DKeff,conv) and modified effective stress intensity factor range (DKeff): (a) K vs. r relations [11]; (b) K vs. COD relations [18].

The material selected in this investigation is the commercial hot rolled medium carbon steel, SAE1045, supplied in the form of 12.7 mm thick flat bars. The chemical composition of the steel is (wt%): 0.45 C, 0.76 Mn, <0.01 P, <0.01

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Fig. 2. Optical micrograph showing the microstructure of the annealed SAE1045 steel.

S and balanced with Fe. The material was first annealed at 650 C for 2 h, and air cooled to remove the residual stresses. Fig. 2 shows the microstructure of the material after annealing consisting of regular ferrite and pearlite, where the mean grain size is approximately 25 lm. After the

annealing, the material was machined into three point bending (TPB) specimens (W = 12 mm and B = 8 mm), Fig. 3. In the mid-section of the TPB specimen, a through-thickness-slit (2 mm in length with a V-notch root angle of 45) was machined. The mechanical properties of

a1= 3 mm

a1= 3 mm

a

ai = 5 mm

ai = 5 mm Pre-crack

Pre-crack

Semi-circular hole

Rectangular hole

Notch tip

Notch tip

W =12 mm B = 8 mm TPB specimen

b

Round wedge

S = 48 mm

Rectangular wedge

0.1 mm (COD at asperity) φ 0.75 mm

w = 0.75 mm 0.1 mm (COD at asperity) h = 0.55 mm

Fig. 3. Dimensions of three point bending specimen, asperities, and the location of semi-circular and rectangular holes used to facilitate inserting the asperities.

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

Rectangular-shaped asperity

Fatigue crack

Notch tip Pre-crack 200μm Fig. 4. Macrograph of the specimen with the hard rectangular asperity, showing the fatigue crack extended from the pre-crack.

the specimen material tested at room temperature are: tensile strength rUTS = 538 MPa, yield strength rys = 290 MPa, elongation to fracture c = 15%, and the average Vickers hardness = 185 HV. The surfaces of the specimens were polished with 600 emery papers in the direction perpendicular to the expected crack path to facilitate the crack length monitoring. A pre-crack of approximately 3 mm (ai/ W = 0.42) in the specimen was produced through fatigue test using an electro-servo-hydraulic testing system with 100 kN capacity under a load control mode. The pre-cracking fatigue test was conducted with a sinusoidal waveform at a frequency of 10 Hz and load ratio of R (Pmin/ Pmax) = 0.05. The value of Pmax is chosen to be about 50% of the bending yield load (BYL) of this specimen material. In this case, the BYL is defined as the specific load level, at which a 0.01 mm proof-CMOD (crack mouth opening displacement) value is measured. The crack length during the cyclic loading was monitored using a traveling light microscope with a resolution of 0.01 mm. Following the pre-cracking test, a small hole on the crack path was introduced by electro-discharge machining (EDM) to facilitate the insert of an artificial asperity. To insert the artificial asperity, the specimen was slowly loaded to about P = 3000 N, corresponding to about 60% of BYL. After the artificial wedge was inserted, the load was removed; the fatigue test was then carried out continuously under the same condition for the pre-cracking creation until the final fracture, and the fatigue crack was detected to propagate almost linearly from the pre-crack, as shown in Fig. 4. To obtain the different trends of crack growth and crack closing behavior, various artificial asperities, having different shapes and different mechanical properties [30–32], as

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shown in Table 1, were used. There are three series of specimen tested: Series A (A-1) specimen without any artificial asperities; Series B specimens with a round (B0.75 mm · l = 8 mm) shaped wedge; Series C specimens with a rectangular shaped wedge (h = 0.55 mm · w = 0.75 mm · l = 8 mm). In addition, the artificial wedges were made of three materials: (i) aluminum alloy, 5052, (Al), (ii) medium carbon steel, C: 0.3 wt%, (MCS), and (iii) high carbon steel, C: 1.2 wt%, (HCS). It should be noted that in this study the above asperities were designed based upon the following four major factors: (i) The asperities made of Al and HCS are softer and harder than the TPB specimen, respectively, and the hardness of MCS is close to the specimen. (ii) The contacting status between the wedge and specimen is different, i.e., point contact in Series B and surface contact in Series C. (iii) The crack opening displacement (COD) value at the asperity in all cases is pre-determined to be the same, i.e., 0.1 mm, as shown in Fig. 3b. (iv) The two different asperity configurations, i.e., the round and the rectangular, are designed to have almost same cross-section area (0.44 mm2 vs. 0.41 mm2) so as to compare their deformation status during crack closing process. 2.2. Load–CMOD examination To investigate the crack closing behavior, the load vs. CMOD was examined at several stages during the fatigue test. The load–CMOD curves, measured by a standard load cell and an extensometer, were obtained using a data acquisition system in conjunction with a computer through the electro-servo-hydraulic system. To obtain clear load– CMOD curves, the load–CMOD relations were measured by a slow loading and unloading with a frequency of 0.05 Hz between the Pmin and Pmax. Details of this technique can be found in Ref. [18]. 2.3. Finite element analysis (FEA) Finite element analysis was performed to analyze the deformation pattern in the asperity and the specimen material. In this analysis, two-dimensional finite element simulation with 8-noded quad elements was employed. The FE

Table 1 Profiles and mechanical properties of the artificial asperities Specimen No.

Asperity profile

Material

Tensile strength (MPa)

Yield strength (MPa)

Hardness (HV)

Elastic constant (GPa)

Series A

A-1

–

–

–

–

–

–

Series B

B-1 B-2 B-3

Round Round Round

Al MCS HCS

191 515 1950

88 285 1470

73 175 600

71 206 206

Series C

C-1 C-2 C-3

Rectangular Rectangular Rectangular

Al MCS HCS

191 515 1950

88 285 1470

73 175 600

71 206 206

Specimen

–

–

SAE1045

(538)

(290)

(185)

(206)

Al, aluminium alloy (5052); MCS, medium carbon steel (C: 0.3 wt%); HCS, high carbon steel (C: 1.2 wt%).

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models were designed based upon the geometry of the TPB specimen and the wedges, where the mesh size of asperity and specimen adjacent to the wedge and crack tip was 0.01 mm. In this calculation, the case of bilinear kinematics hardening was selected, where the initial slope of the stress– strain curve was taken to be the elastic constant of the material, and after yielding the curve continues along the second slope defined by the tangent modulus. In this case, tangent modulus was defined to be equal 10% of the material’s elastic constant [33]. Details of the mechanical properties for the wedges and specimen are shown in Table 1. 3. Results 3.1. Crack growth behavior The relationship between the crack length (al) and the number of fatigue cycles (N) for all specimens is given in Fig. 5. It should be mentioned first that the thick solid line at the lower left corner of the plot indicates the crack growth behavior in the pre-cracking test; the arrow indicates the point at which the wedge is inserted into the specimen. The al vs. N relations in Fig. 5 can be divided into two major groups: that for specimen A-1 and those for specimens in Series B and Series C. For the specimen A1, a linear relation of al vs. N is obtained until the final fracture. On the other hand, for those specimens in Series B and C, the relations can be divided into two stages: in the first stage, i.e., Stage I, the crack growth rate is sharply decreased to a very low level immediately after the wedge insertion, and in the second stage, i.e., Stage II, the crack growth rate increases rapidly till the final fracture. As a matter of fact, as indicated in the figure as Stage L-II, before the final fracture, the crack growth rate of specimens in Series B and C becomes extremely high and is similar to that of specimen A-1 in the same stage.

An important observation from Fig. 5 is that once any wedge is inserted, the specimen’s fatigue life would be extended. Furthermore, depending on the wedge shape and the strength of the wedge material, the fatigue life extension would be different. In the actual results shown in Fig. 5, at the identical strength level, the rectangular cross-sectioned wedge, i.e., Series C, yielded longer fatigue life than that of the circular cross-sectioned wedge, i.e., Series B, see, for example, al vs. N relations for specimens C-3 and B-3. On the other hand, with an identical wedge shape, the harder the material, the longer the fatigue life, see, for example, relations for C-3 and C-2. A similar effect of the wedge on fatigue life is also previously reported [12,14–16]. For instance, Sharp et al. [14] examined the effect of an artificial asperity of two epoxy materials on the fatigue behavior of 7050 aluminum alloy. The asperities filled in the pre-crack fully while keeping the crack open at three load levels: 0%, 50% and 80% of the peak cyclic load. Infiltration at 0% peak load produced negligible retardation, whereas the infiltration at the 80% peak load produced about a 300% increase in fatigue life for one adhesive and 3000% for the other adhesive. 3.2. Crack closure behavior To investigate the influence of artificial asperity on the crack closing behavior, the load vs. CMOD relations and the effective crack driving force (DPeff) value were examined. Fig. 6 shows the load–CMOD curves obtained at the first cycle for A-1, B-1, B-3, and C-3, respectively. It is seen that the load–CMOD relation exhibits a hysteresis loop if the artificial asperity is inserted into the crack surfaces, Figs. 6b–d. However, even without the asperity, a small amount of hysteresis loop can also be seen, Fig. 6a. This might be caused by the rough crack surface contact and/or plastic deformation around the crack tip [34,35].

5.5 Crack length from notch tip (al). mm

A-1

Series B

A-1 B-1 B-2 B-3 C-1 C-2 C-3

Series C

5.0 4.5 4.0

Stage II

3.5

Stage L-II (Final fracture stage)

3.0

Stage I Pre-cracking

2.5 2.0 0

50.000

100.000 150.000 Number of cycles (N)

200.000

250.000

Fig. 5. Fatigue crack propagation data obtained as a function of the number of cycles for A-1 and for Series B and C. The solid line represents the crack growth in the pre-cracking test and the arrow shows the wedge insertion point.

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

a

c

2,500

967

2,500 B-3 Pmax

Pmax 2,000

2,000

1,500

1,500

Load, N

Load, N

A-1

ΔPeff

1,000

ΔPeff Linear portion

1,000

Linear portion

500

500 Pmin,real

Pmin,real Pmin 0

Pmin 0 .2

6

CMODmin

b

2,500 B-1

d

1

CMOD

2,500 C-3 Pmax

2,000

2,000

1,500

Load, N

Load, N

0 1.

CMODmin

Pmax

ΔPeff

1,000

1,500

ΔPeff Linear portion

1,000

Linear portion

500

500 Pmin,real Pmin

Pmin,real Pmin 0

0

CMOD

0

0 0. 8

CMODmin

CMOD

0 .1

CMODmin

CMOD

Fig. 6. Load–CMOD relations showing the effective crack driving force, DPeff, [18]: (a) for A-1, (b) for B-1, (c) for B-3, (d) for C-3.

2,100

A-1

Series B

Series C

2,000 1,900 Δ P eff , N

The unloading phases for specimens B-1, B-3 and C-3 show a clear concave shape, signifying an acceleration in the reduction of the measured CMOD value at Pmin (CMODmin). In our previous study [20], it was found that such a concave curve as well as CMODmin value could be associated with the plastic deformation, arising from the contact action, in the asperity and the specimen material. Based upon the load–CMOD curves in Fig. 6, the DPeff value, defined as DPeff = Pmax  Pmin,real in Fig. 1b, was examined. In this case, the Pmin,real value was determined from the intersection between the linear loading portion and the vertical line based on the point of the actual CMODmin value. Such an approach is in accordance with the study of Chen et al. [18], who reported that the DPeff is strongly associated with the deformation in the wedge during the unloading process. The obtained DPeff values for all specimens are now plotted in Fig. 7. It is clear that the all DPeff values of Series B specimen are higher than those of Series C, but lower than that of A-1. On the other hand, for the same wedge series, the softer wedge specimen makes the DPeff value higher. It should be noted that, in this case, the effects of wedge configuration on the DPeff

1,800

1,700

No artificial wedge Al: Aluminum alloy wedge

1,600

MCS: Medium carbon steel wedge HCS: High carbon steel wedge

1,500

A-1

B-1

B-2

B-3 C-1 Specimens

C-2

C-3

Fig. 7. Effective crack driving force, DPeff, at the first cycle for all specimens.

values (or severity of crack closure) are stronger than those of wedge materials strength (or wedge hardness). Such a DPeff variation may be explained from an assumption that a different level of plastic deformation in the wedge and

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specimen surrounding the asperity occurred during the unloading process [11,20]. To reveal the role of the plastic deformation in the DPeff change, the plastic deformation in the wedge and specimen was examined both experimentally and theoretically. Fig. 8 shows the macrographs of the mid-section of the wedges after the load–CMOD tests (Fig. 6): (a) for Series B and (b) for Series C. In the soft and medium–hard wedges (B1, B-2, C-1 and C-2), the plastic deformation can be clearly observed around the top of the round asperities and the

corner of the rectangular ones, as marked by the dotted circle. The soft wedges are seen to have been deformed more severely compared to the medium ones. On the other hand, no apparent plastic deformation is detected in B-3 and C-3. To verify their deformation patterns in terms of stress– strain distribution, FE analysis was further executed. Fig. 9 illustrates the plastic strain distribution calculated with von-Mises criterion for the six different testing conditions, as illustrated in Fig. 8. Similar to the experimental results shown in Fig. 8, the FEA results also show that

Fig. 8. Macrographs of the central cross-section of asperities after the load–CMOD test: (a) Series B, (b) Series C.

Fig. 9. von-Mises plastic strain distribution in the asperities and specimen materials: (a) Series B, (b) Series C.

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

Maximum plastic strain (ε max)

0.16 in Asperity in Specimen

0.12

0.08

0.04

0

B-1

B-2

B-3 C-1 Specimens

C-2

C-3

Fig. 10. Maximum plastic strain values in the asperity and the specimen for the six testing conditions.

2.100 2.000

B-1 B-3

1.900 Δ Peff , N

plastic strains occurred only in the soft (B-1 and C-1) and medium–hard (B-2 and C-2) asperities, but not in the hard (B-3 and C-3) wedges. Also confirmed is the important fact that the matrix material (TPB specimen) is also plastically strained at a different level depending on its relative strength to the wedge material as well as on the contact condition with the wedge (point or surface contact). As a typical example, the specimens B-2 and C-2 are compared. In the former, i.e., with a medium–hard round wedge, the specimen matrix is severely plastically deformed, but there is almost no apparent plastic strain in the matrix of C-2. On the basis of the FEA results shown in Fig. 9, an attempt was made to relate the value of plastic strain in both the wedge and the specimen with the DPeff value. In this approach, quantitative strain values, such as the maximal plastic strain, were employed as the strain parameter. This approach was performed based upon a previous study by Srivastava and Garg [36], who demonstrated that the crack growth rate is almost linearly correlated with the plastic strain range (or the maximum plastic strain value) in the specimen material adjacent to the fatigue crack. The obtained strain results are shown in Fig. 10. Since the plastic strain is found both in the wedge and in the matrix material, the sum of the two maximum plastic strain values, emax, is then employed as the ordinate of the plot in Fig. 10. It should be mentioned that the maximum strain value in the wedge and in the matrix material have always been found immediately adjacent to the strong contact region. However, as the two materials, the wedge and the specimen, have different strength and different geometrical configuration, the actual value of the maximum strain in each material is different. Under the same wedge series, the emax value for soft asperities, B-1 and C-1, is higher than that for the medium and hard ones. In addition, the overall emax of Series B is higher than Series C. Such a difference in emax value between Series B and C can be easily understood from the contacting status between the asperity and the specimen material: point contact (Series B) and

969

C-1 B-2

1.800 1.700

C-2 C-3

1.600 1.500 0

0.05 0.1 Maximum plastic strain. ε max

0.15

Fig. 11. Maximum plastic strain vs. DPeff.

surface contact (Series C). The plastic deformation occurs severely in Series B due to the higher degree of stress concentration arising from the point contact. Using the result of maximum plastic strain in Fig. 10, the relationship between the emax and DPeff is now established, Fig. 11. Obviously, the DPeff value increases with the emax increase, and there is an almost linear correlation between the two factors. Thus, it can be considered that the plastic strain in the wedge as well as the specimen played important roles in the effective crack driving force. 4. Discussion 4.1. Relationship between crack driving force and crack growth behavior To provide an explanation for the different trend of crack growth behavior under different testing conditions in Fig. 5, the DPeff variation as a function of cyclic number (N) was examined. Fig. 12 displays the DPeff vs.N relations for A-1, B-1, B-3, C-1 and C-3. Similar to Fig. 5, the arrow at the higher left corner of the plot represents the asperity insertion point, and the hatched area and dashed lines indicate the approximate location of Stages I and II (Fig. 5), respectively. From Fig. 12, the different trends of DPeff vs. N relations were obtained depending on the specimen material. The DPeff value increases gradually prior to the final fracture for A-1. On the other hand, for Series B and C, the DPeff values initially decrease drastically, and then increase gradually until fracture. This gives a concave curve with a minimum effective load range, DPeff,min, for these conditions, B-1, B-3, C-1 and C-3, respectively. As seen, the lower the DPeff,min, the longer the fatigue life. It must be pointed out that such a difference in DPeff,min value for different testing conditions as well as degree of the concavity of the DPeff  N curves would be influenced by the severity of crack closing behavior, which will be discussed later in this paper.

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M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976 2,100

A-1

Series B

Series C

Stage I Stage II

1,900

Δ P eff , N

1,800 1,700 1,600

A-1 B-1 B-3 C-1 C-3

1,500 1,400

ΔPeff,min

1,300 1,200 0

50,000

100,000

150,000

200,000

250,000

Number of cycles

at 1st cycle after the wedge insertion

Fig. 12. DPeff variation as a function of number of cycles for A-1, B-1, B3, C-1, and C-3. The arrow shows the wedge insertion point.

From Fig. 12, it is also clear that the DPeff values for Stage I of all testing conditions are always below 1800 N. Note that the crack growth rate in Stage I is subdued considerably. Based on the observation of the low crack growth rate or no crack propagation at DPeff< 1800 N, it may be suggested that the DPeff value of 1800 N might be related to the effective threshold DK value, i.e., DKeff,th. To confirm this, the following approach was conducted: (i) DKeff value of our specimen material at DPeff = 1800 N was calculated. (ii) The obtained DKeff was compared with the actual DKeff,th value for SAE1045. In this approach, the value of DKeff was estimated using the following equations [37]: DK eff ¼

DP eff S f ðai =W Þ BW 3=2

for three point bending specimen ð1Þ

with f ðai =W Þ ¼

related with the actual threshold for no fatigue crack propagation. To further understand the effect of DPeff on crack growth behavior, the relationship between fatigue life (N) and DPeff value was examined. The obtained results for B-1, B-3, C-1 and C-3 are shown in Fig. 13. It should be noted that, because DPeff values vary with increasing cyclic number, which gives concave curves as shown in Fig. 12, two specific values of DPeff, i.e., (a) DPeff at 1st cycle (DPeff,1st) and (b) minimal DPeff (DPeff,min), were employed in this approach. As can be seen in Fig. 13, there are linear correlations between N and DPeff with a correlation factor of more than 0.96 in both cases, i.e., N =  662.3DPeff,1st + 131 · 104 and N =  617.3DPeff,min + 115 · 104. It is, therefore, the effective crack driving force, defined as DPeff = Pmax  Pmin,real, that may be used to predict the approximate fatigue life. Similar results were also obtained in a study by Khalil and Topper [39]. In their study, the crack opening stress vs. fatigue life relations are almost linearly correlated especially for soft metals, such as 2024T351 aluminum alloy and annealed 1045 steel. They concluded that ‘‘the crack opening stress level could give a conservative estimate of fatigue life’’. 4.2. Crack closing behavior during the fatigue 4.2.1. In the early crack growth stage As shown in Fig. 12, the DPeff vs. N relations are shown by the concave curves for Series B and C. In this case, at the first cycle after the wedge insertion as indicated in Fig. 12, the DPeff value decreases with different rate depending on the wedge characteristics. This is due to the different severity of artificial wedge-induced crack closure as mentioned earlier. In the early fatigue stage, the DPeff value for Series B and C further decreases with increasing the number of cycle until acquiring the DPeff,min value. However, this further reduction in DPeff value seems to

3ðai =W Þ1=2 3=2

2.000

2ð1 þ 2ai =W Þð1  ai =W Þ  ½1:990  ðai =W Þð1  ai =W Þ2:15  3:93ðai =W Þ þ 2:7a2i =W 2 ;

B-1

1.900

ð1aÞ

where S is a supporting span, and B and W are specimen thickness and width, respectively; ai is the crack length from the bottom edge of specimen to the crack tip; f(ai/ W) is the geometric correction factor. In this case, ai/W is taken as 0.42, and then f(ai/W) becomes a constant, i.e., f(ai/W) = 1.07, according to Eq. (1a). As shown in Fig. 3, S = 48 mm, W = 12 mm and B = 8 mm, DKeff value pffiffiffiffi calculated in terms of Eq. (1) is DKeff = 8.2 MPa m. McDowell [38] examined the da/dN vs. DKeff relations for the annealed SAE1045 steel. In his da/dN vs. DKeff relation [38], the threshold level for pffiffiffiffia non-propagating fatigue crack was at DKeff = 6.5 MPa m (R = 0), and that is close to the pffiffiffiffi calculated DKeff of 8.2 MPa m. Thus, the value of DPeff = 1800 N in this study might be considered to be

B-3

1.800 Δ Peff . N

2,000

C-1 C-3

1.700

(a)

1.600 (a) N = - 662.3 ΔPeff.1st + 131 x 10

1.500

4

(b) N = - 617.3 ΔPeff.min + 115 x 10

(b)

4

1.400 0

50.000

100.000

150.000

200.000

250.000

Fatigue life (Number of cycles)

Fig. 13. Relationship between the fatigue life and effective crack driving force, DPeff: (a) for DPeff at the first cycle (DPeff,1st), (b) for minimal DPeff (DPeff,min).

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976 2.100 2.000 1.900 1.800 Δ P eff . N

be conflict because of the following reason. From the results of plastic deformation examination shown in Fig. 11, it could be considered that the DPeff value increases with increasing the number of cycle without any reduction of DPeff value, since the plastic deformation level in the asperity as well as in the specimen material, created by their contact action, should always increase during fatigue. Such a discrepancy may be attributed to the other possible factors of crack closure. Interestingly, similar concave relation of DPeff vs. N is also observed in related publications [40,41], in which the reduction of DPeff in the early crack growth stage is found to be influenced by the plasticityinduced crack closure, produced by the overload. In our experiment, to insert the artificial wedge into the crack surfaces, the specimen material was slowly loaded to 3000 N, corresponding to about 60% of the BYL as described earlier. Because of the slow loading and relatively high applied load, plastic strain (or monotonic plastic strain) in the vicinity of the crack tip may have occurred strongly, which might induce crack closure in addition to the artificial wedge-induced crack closure. To verify this, the plastic strain pattern and its size were examined using FE analysis. The von-Mises plastic strain distribution, calculated with plane strain condition criterion, is shown in Fig. 14. From this result, the typical form of plastic strain around the crack tip can be observed. Moreover, high plastic strain of more than 0.1 is obtained around the crack tip; the depth of this high strain ahead of the crack tip is approximately 0.2 mm as indicated in Fig. 14. Due to the high plastic strain, the plasticity-induced crack closure may have occurred, and that implies a reduction in DPeff value at the crack extension of less than 0.2 mm (3.0 mm < al < 3.2 mm) is related to the size (or depth) of the high strain zone. To confirm this, the examination of the relationship between the DPeff and crack length was attempted, and the obtained result is shown in Fig. 15. As can be seen, the DPeff value increases slowly with increasing crack length until just prior to the fracture for A-1. On the contrary, for sample Series B and C, the DPeff values decrease sharply before a minimal DPeff, and then it

971

1.700

ΔPeff.min

1.600

A-1 B-1 B-3 C-1 C-3

1.500 1.400 1.300 1.200 3.0

3.5

3.1

4.0

4.5

5.0

Crack lengteh from notch tip (a l ). mm

Fig. 15. DPeff variation as a function of the crack length for A-1, B-1, B-3, C-1, and C-3.

increases gradually until the final fracture. It also appears that the minimum DPeff values for all cases are measured between the crack length (al) 3.05 and 3.1 mm, which is positioned in the high plastic strain region ahead of the crack tip according to the strain distribution, Fig. 14. Hence, it is considered that in the early crack growth stage the plasticity-induced crack closure would occur and lead to the accelerated reduction in the DPeff value. 4.2.2. In the final fracture stage As described in Fig. 5, in Stage L-II the crack growth rates of specimens in Series B and C are similar to that for A-1, where their crack growth rates are considerably high. Due to the high crack growth rate, a weak crack closure might have occurred. To substantiate this, the load– CMOD relations were examined at different crack lengths. Figs. 16a–c show the obtained load vs. CMOD for the specimens in A-1, B-1 and C-3, respectively. The first point to note in Fig. 16 is that the thick dashed line represents the DPeff variation, obtained with connecting the load value of Pmin,real in all load–CMOD curves. Three crack growth

Fig. 14. von-Mises plastic strain distribution in the specimen around the crack tip.

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M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

A-1

a

q˚

Linear potion

B-1

b

2,500

2,500

q˚’

Pmax

2,000

θ ˚’

2,000

1,500

Load, N

Load, N

θ˚

Pmax

ΔPeff

1,000

1,500 ΔPeff

1,000 Δ δmax

Δd max

500

Δδ max’

Δδmax’

500 Pmin,real

Pmin,real Pmin

Pmin

0

0 ΔPeff variation0.05 line Stage I

0.1

0.15 Stage L-II

Stage II

0.2 CMOD COD, mm

c

0.25

0.03 mm

ΔPeff variation 0.05 line

0.3

Stage I

0.1

Stage 0.15 L-II 0.2 CMOD Stage II COD, mm

0.25

0.03 mm

C-3

2,500 θ˚

Pmax

θ ˚’

2,000

Load, N

1,500

ΔPeff

1,000

Δδ max

Δδ max’

Pmin,real

500 Pmin

0 0.05 Stage I

0.1

Stage L-II 0.15 Stage II COD,

CMOD 0.2

0.250.03 mm

mm

ΔPeff variation line

Fig. 16. Load vs. CMOD relations at several stages: (a) for A-1, (b) for B-1, (c) for C-3.

stages, Stage I, II and L-II determined in Fig. 5, are also indicated. From Fig. 16, the DPeff value and the shape of load–CMOD curve are changed with the increment of crack length. With increasing the crack length, the DPeff value increases nonlinearly for both B-1 and C-3, while that value is almost constant at a higher level for A-1. In Stage I and early Stage II, the overall DPeff value for B-1 is greater than that for C-3; smaller than that for A-1. On the contrary, in Stage L-II, the DPeff level is observed to be similar for all specimens. Since the specimen, A-1, did not have any artificial wedge, the DPeff level for B-1 and C-3 in Stage L-II should imply little or no asperity wedging [14]. This closing behavior can also be understood from the shape of load–CMOD curve. From Fig. 16, although different trends of load vs. CMOD relations are obtained depending on the actual specimen status in Stage I and early Stage II, the shape of load vs. CMOD is similar for all cases in Stage L-II, i.e., including both the lower slope of the loading stage, h 0 , and the wider hysteresis loop width, Dd0max . Such

a load vs. CMOD curve shape in Stage L-II may be related to the following three major factors: (i) weakened stiffness in the specimen ahead of crack tip [42–44], (ii) severely deformed wedge and specimen material arising from the contact action, and (iii) plastic deformation in the specimen around the crack tip [34,35]. Of course, the above three factors signify the acceleration in the reduction of crack closing behavior. It can be, hence, concluded that in Stage L-II the inserted asperities for B-1 and C-3 (or Series B and C) would no longer affect the crack closing behavior. 4.3. The crack closing behavior during fatigue The experimental results and associated FE analysis described above have provided a clear relationship between DPeff and the crack closure behavior during cyclic loading. Based upon these results, the following mechanisms for the crack closure are proposed (Fig. 17). During the pre-cracking cyclic loading test, the DPeff value is almost constant, in

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

which a weak closure occurs, Fig. 17a. On application of a static load for the wedge insertion, a monotonic plastic strain is produced in the specimen surrounding the crack tip; after removing the static load, the asperity wedging immediately occurs, resulting in the reduction in DPeff value shown in Fig. 17b. The crack growth is retarded as the crack penetrates the monotonic plastic strain region due to the plasticity-induced crack closure, which leads to further reduction of DPeff. After the fatigue crack passed through the region of monotonic plastic strain, the DPeff value increases slowly prior to the final fracture, Fig. 17c, where the severity of artificial asperity-induced crack closure is decreasing. The artificial asperity selected in this work could be correlated directly to the possible wedges encountered in practice, such as particles and inclusions, as described earlier. In previous studies, several researchers [45–48] have examined the effect of asperities, such as Al2O3 and SiC particles, on the crack closing behaviors. Wang and Zhang [46] examined the relationship between crack growth rate (da/dN) and crack length (al) for Al alloy (2014) reinforced with 10% Al2O3 particles (Fig. 18a). As shown in Fig. 18a, the crack growth rate, affected by the reinforcing particles, can be divided into three regimes: an initial fast development, followed by a deceleration of the crack growth until an arrest is reached and, finally, an increasing growth rate. These authors interpreted the reasons for the deceleration and acceleration of crack growth rate using the crack closure characteristics [47,48]. The deceleration is especially influenced by the two closing behaviors: first due to the particle bridging function and second due to the particle

a

ΔPeff

cracking-roughened fracture surface. On the other hand, the acceleration of crack growth rate occurred by the reduction in the crack closure because of the failure in the particles. Interestingly, the basic concept of their closing characteristics during the cyclic loading is similar to our proposed crack closure model as shown in Fig. 17, e.g., a crack closure occurs due to the asperity wedging, and the reduction of crack closure is associated with the failure of the wedge arising from the contact action. To compare the results of Wang and Zhang, Fig. 18a, with our samples, the da/dN vs. al relations for B-3 and C-3 are shown in Fig. 18b. It should be pointed out that in this work the samples of B-3 and C-3 were selected, as their material combination – soft specimen material (annealed SAE1045) and hard wedge material (high carbon steel, HCS) – is similar to that used in Ref. [46], i.e., Al alloy and Al2O3 particles. As can be seen in Fig. 18b, the crack growth rate decreases sharply in the early crack growth stage; afterward the growth rate increases until the final fracture. It is obvious that the trend of the da/ dN vs. al relations is similar to the aforementioned Al alloy with Al2O3 particles, Fig. 18a. From this result, it is considered that the present investigation, achieved using simple asperities, could present a similar situation of the crack closing and crack growth behavior occurring in the particulate reinforced materials. Note that, for B-3 and C-3, the reduction of crack growth rate in the early crack growth stage, D(da/dN) as shown in Fig. 18, is approximately 1.5 times greater than that for Al alloy reinforced with Al2O3 particles; this might be attributed to the strong severity of artificial wedge- and plasticity-induced crack closure for

Cyclic plastic zone

Pre-crack Crack length (a) Monotonic plastic zone

b

ΔPeff Overload Crack growth into the plastic zone

a

Wedge insertion

c

Plastic zone produced by contact action

ΔPeff

973

a

Fig. 17. Schematic illustration of the crack closure mechanism associated with artificial asperity during the cyclic loading.

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M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

a

1.E-04 Al (2014) reinforced with Al2O3

da/dN , m/cycle

1.E-05

Δ( da

dN )

1.E-06 1.E-07 1.E-08 1.E-09 1.E-10

b

0

0.2

0.4 0.6 0.8 Crack length fromnotch tip,mm

1.E-03 B-3

1.E-04 da/dN , m/cycle

1

1.E-05

Δ(da

C-3 dN)

1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 3

3.1

3.5

4 4.5 5 Crack length from notch tip (al),mm

5.5

Fig. 18. Fatigue crack growth behavior, da/dN vs. crack length: (a) A1(2014) alloy reinforced with 10% Al2O3 particulate [46], (b) for the present samples, B-3 and C-3.

B-3 and C-3, produced by the over loading for the wedge insertion as mentioned earlier. It must be pointed out that such a reduction in crack growth rate in the early stage of crack growth may also be related to the behavior of short fatigue crack growth. As well known, the short crack is considered to be embedded in several grains, and the reduction of crack growth rate for the short crack occurs due to crack closing behavior, arising from the localized plastic strain and rough crack surface contact [49,50]. In the present work, the rate of da/dN is reduced during the crack growth of less than 0.1 mm, as shown in Figs. 15 and 18b, and this crack length corresponds to several grain diameters of our specimen material SAE1045 which has an average grain size of about 25 lm, in Fig. 2. Thus, in this case, the reduction of crack growth rate in the early crack growth stage might also be associated with the short crack growth behavior. 5. Conclusions With the insertion of specific wedges into cracks, the effects of asperities on crack closure and fatigue crack

growth behavior in annealed SAE1045 carbon steel have been systematically investigated. Results obtained have yielded the following conclusions. 1. The fatigue crack length for the specimen without any artificial wedge almost linearly increases with increasing the cyclic number, whereas for the specimens with the artificial wedge, the crack length increases non-linearly. Due to the wedging effect of asperity, the crack growth rate is clearly reduced to a low level initially, Stage I, and then gradually increases till the final fracture, Stage II. 2. The fatigue life of specimens with artificial asperity is found to depend not only on the strength of the wedge material but also on the configuration of the wedge. The overall fatigue life for the specimen with rectangular wedge is found to be longer than that for the round one. In addition, under the same wedge configuration, the harder the wedge material, the longer the fatigue life. Such a trend in the fatigue life change is attributed to the different severity of crack closing behavior.

M. Okayasu, Z. Wang / International Journal of Fatigue 29 (2007) 962–976

3. On the macroscopic side, the fatigue life is related to the effective crack driving force (DPeff), and a linear correlation between the DPeff value and the number of cycles to the fracture is obtained. The DPeff value is also found dependent on the deformation level in the wedge as well as in the specimen material arising from their contact. The more severe the plastic deformation, the bigger the DPeff value; and the bigger the DPeff value, the shorter the fatigue life. 4. The DPeff value changes with increasing the number of cycles. It decreases initially and then increases non-linearly prior to the final fracture. In the early stage of crack growth, the reduction in DPeff value is attributed to the artificial asperity- and plasticity-induced crack closure. After acquiring the minimal effective load range, DPeff,min, the DPeff value increases gradually due to the weakening of crack closing behavior. In the final fracture stage and with the crack opened, the DPeff value increases rapidly as the inserted asperities no longer exert apparent effect on the crack closure behavior. 5. Based upon the experimental results and FE analysis, a crack closing mechanism is proposed, which could be utilized to explain the crack closing behavior in a particulate reinforced metal matrix composite, i.e., A2O3 particle reinforced Al (2014) alloy.

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