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Fatigue crack initiation and propagation in an α-iron polycrystal
Materials Science and Engineering A313 (2001) 64 – 68 www.elsevier.com/locate/msea
Fatigue crack initiation and propagation in an a-iron polycrystal R.Q. Chu *, Z. Cai, S.X. Li, Z.G. Wang State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China Received 23 October 2000; received in revised form 3 January 2001
Abstract The cyclic deformation and crack initiation and propagation of a-iron polycrystals have been studied under stress-control with emphasis on the dependence on the stress amplitudes and orientation of grains. The orientations of grains surrounding cracks were determined by the electron backscatter diffraction (EBSD). It was found that cracks did not originate at grain boundaries but along the slip lines intersecting with the free surface at the corner of the specimen. At lower stress amplitude, the crack propagated in a transgranular mode, but at higher stress amplitude the crack propagated in a mixed mode– transgranular mode and intergranular mode. The stress distribution along the loading axis of grains surrounding the crack was calculated using a three-dimensional anisotropic finite element method (FEM). In the present work, it was shown that the crack initiation mainly depends on three factors: higher stress distribution, abundant dislocation sources and less resistance to dislocation motion. © 2001 Elsevier Science B.V. All rights reserved. Keywords: a-Iron polycrystal; Cyclic deformation; Crack initiation and propagation; Finite element analysis; Crystal orientation
1. Introduction The fundamental mechanisms of metal fatigue have been studied in detail mostly on face-centered cubic (fcc) metals, but to a lesser extent on metals of other crystal structures [1]. In the case of body-centered cubic (bcc) metals the glide properties of dislocations are rather complex and depend sensitively on temperature, strain rate, and on the sense of deformation. Thus it is not surprising that a comprehensive understanding of the behavior of bcc metals under cyclic loading is still lacking, especially the mechanism of crack initiation. a-Iron, which is perhaps traditionally the most important bcc metal, has been widely used for investigating the mechanism of fatigue crack initiation [2,3]. It has been reported that the mechanism of fatigue crack initiation in a-iron sensitively depends on the testing frequency, plastic strain amplitude and material purity. Guiu and Dulniak [4] have proposed that the incompatible deformation of surface grains may induce the nucleation of fatigue cracks at the surface grain boundaries. * Corresponding author. E-mail address: [email protected] (R.Q. Chu).
It is known that the mechanical properties of polycrystalline materials depend strongly on the specific properties of grain boundaries, triple junctions and the arrangement of these elements [5,6]. The local microstress field in a polycrystal grain depends not only on the applied stress but also on the orientation of its surrounding grain [7]. It is necessary to investigate the influence of stress distribution and orientation of grains on the crack initiation. In this paper the results of fatigue crack initiation and propagation in pure polycrystalline a-iron are reported and special attention was placed on the influence of stress distribution and orientation of grains on crack initiation.
2. Experimental procedure The observations were performed on specimens of a-iron with a nominal purity of 99.98%. The dimension of the gauge section was 4× 6 × 10 mm3. The gauge section of the specimens was chemically polished in a solution of four parts of HF and 96 parts H2O2, at room temperature, to give a smooth surface. A MTS fatigue testing machine was used for the tests at a
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 0 9 6 6 - 2
R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
65
constant frequency of 25 Hz under load control. Two maximum nominal stresses of 130 and 140 MPa were applied respectively on two specimens, and the stress ratio was − 1. During the tests, the observations of slip patterns and crack initiation were conducted in an optical microscope mounted on the frame of the machine. The tests were terminated when a fatal crack was formed and then the specimens were examined by electron backscatter diffraction (EBSD) technique in SEM. On the surface of the specimen, the orientations of grains near the fatal crack were determined by EBSD and the stress distributions along the loading direction of these grains were obtained using a three-dimensional anisotropic finite element method (FEM). ANSYS soft code was used in the analysis.
3. Results and discussion Two specimens (No. 1 and No. 2) were fatigued to failure at maximum nominal stresses of 130 and 140
Fig. 2. The orientation maps of the grains on the specimen surface around the cracks: (a) specimen No. 1 and (b) specimen No. 2.
Fig. 1. Surface slip features and fatigue cracks of specimens: (a) specimen No. 1 and (b) specimen No. 2.
MPa, respectively. Numbers of cycles to failure were 9.2×105 and 1.4× 105, respectively. The surface appearances of the fatigued specimens are shown in Fig. 1. Most grains on the surface of the specimen appeared featureless even after fatigue failure. Only a few grains showed the slip traces within the grains. It seemed that the slip lines were emitted from the grain boundaries (Fig. 1(a)). For specimen 2, the slip lines were seen in many grains, especially in some grains around the crack, the deformation was larger and multislip had occurred and the slip traces passed through the entire grains (Fig. 1(b)). During fatigue testing, the metallographic observations indicated that crack initiated at slip lines intersecting with free surfaces at the corner of the specimen. During the successive cyclic loading, the crack developed into a fatal crack. At lower stress amplitude the crack propagated in a transgranular mode, but at higher stress amplitude the crack propagated in a mixed mode–transgranular mode and intergranular mode, as shown in Fig. 1. The orientation maps of the surface grains near the cracks are shown in Fig. 2. Mughrabi and Wuthrich [8] suggested that under fatigue loading the incompatible shape change induced by asymmetric slip in neighboring grains on the surface could promote crack initiation at grain boundaries. Guiu and Dulniak [4] reported that fatigue failure in pure iron and iron alloys initiated at grain boundaries rather than slip lines when fatigue tests were performed
R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
66
at room temperature with frequencies higher than 0.1 Hz. Tanaka and coworkers [9] found that cracks originated only at grain boundaries under reversed stress but nucleated along slip bands under alternating tension. In the present study, a testing frequency of 25 Hz and a symmetrical tension– compression – loading mode were used. It was found that cracks nucleated at slip lines, so it was necessary to investigate the crack initiation mechanism. The dependence of the crack initiation on the stress distribution and orientation of grains were mainly investigated. Since the resolved shear stress on the primary slip system in each grain just exceeded the critical resolved shear stress to activate the slip system, the elastic calculation could approximately be used. Based on the experimental results, FEM was then adopted to calculate the elastic stress distribution in each grain of iron polycrystals subjected to tensile loading. In the computation model, no crack was considered. In order to obtain the stress distribution of grains around the crack on the specimen surface, the orientation of each grain should be known. In this paper, the orientations of grains we are interested were determined by EBSD. The orientation matrices of typical grains near the corner of the specimen are as follows: For specimen No.1: Á 0.6949 Ã grain 1 Ã − 0.5203 Ã Ä 0.4964
0.2235 −0.4998 −0.8368
0.6835 Â Ã 0.6924 Ã Ã −0.2311 Å
Á 0.3145 Ã grain 3 Ã 0.6607 Ã Ä −0.6816
− 0.9368 0.3321 − 0.1103
0.1535 Â Ã 0.6732 Ã Ã 0.7233 Å
Á 0.3280 Ã grain 18 Ã 0.6610 Ã Ä −0.6749
− 0.9284 0.3578 − 0.1007
0.1749 Â Ã 0.6595 Ã Ã 0.7310 Å
For specimen No.2: Á0.1954 Ã grain 12 Ã0.8684 Ã Ä0.4557
0.9711 −0.2362 0.0338
−0.1370 Â Ã −0.4359 Ã Ã 0.8895 Å
Á 0.1841 Ã grain 17 Ã 0.9569 Ã Ä −0.2247
0.5251 − 0.2890 − 0.8005
0.8309 Â Ã − 0.0294 Ã Ã 0.5557 Å
Á −0.2752 Ã grain 18 Ã 0.0709 Ã Ä 0.9588
−0.6486 −0.7498 − 0.1308
0.7096 Â Ã − 0.6579 Ã Ã 0.2524 Å
Before carrying out the finite element analysis, the stress–strain relation and the elastic modulus matrix [C] with reference to the global coordinate system of each grain under the global coordinate system must be established. The detailed stress– strain relation and the establishment of the elastic modulus matrix [C] can be found in our previous works [10,11]. For a-iron the elastic modulae are C11 = 242 MPa, C12 = 146.5 MPa, C44 = 112 MPa, 6 =0.291 [12]. After the elastic modulus matrix [C] of each grain has been obtained in combination with the known constraint and load conditions of the multicrystal model, the distribution of stress and strain of each grain in the global coordinate system can be obtained using the three-dimensional anisotropic finite element method. Because we are particularly interested in crack initiation, the existing crack was not considered in the computation model. Fig. 3 showed the stress distribution along the loading axis (|y) of grains around the crack at the front surface. Since there are many slip systems in BCC structure, the higher stress of |y will cause one of the slip systems, which is close to the maximum shear stress plane to operate more easily. In the first approximation, no specific slip system is considered in the present work. Some characteristics about the distribution of |y can be found in Fig. 3. The distribution of stress |y is highly inhomogeneous in each grain. The maximum stress is located at or around the grain boundary parallel to the loading axis (see the grain boundary between grain 3 and grain 4 in Fig. 3(a), the grain boundary between grain 1 and grain 18 in Fig. 3(b)) or at the triple junction (see the triple junction of grains 1, 2 and 3 in Fig. 3(a) and the triple junction of grains 17, 19 and 20 in Fig. 3(b)). The grain boundaries perpendicular to the loading direction usually do not withstand the highest stress and the lowest stress locates at the interior of some grains or at some triple junctions (see grain 9 in Fig. 3(a) and triple junction of grains 9, 10 and 11 in Fig. 3(b)). These results are quite similar to our previous analysis in which an ideal model was used [11,13,14]. After carefully examining these results, one may note that the stress distribution of grains near the corner of the specimen has great influence on the crack initiation. From the stress distribution of grains around the places where the cracks initiated, it can be suggested that the process of fatigue crack initiation possibly took place with the following steps. Firstly, due to the different orientation of grains and different characters of grain boundaries, the stress around the grain boundaries holds high |y, for example the grain boundary between grain 3 and grain 4 in Fig. 3(a). Secondly, the high stress around the grain boundary will activate the slip system of the grain that is right at the corner. Since there are usually many dislocation sources around the grain boundary, the dislocation emitted from the sources in the corner grain glides more
R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
easily than that in the inner grain. Therefore, the activated slip systems will keep operating during cyclic loading, creating intrusions or extrusions at the free surface of the corner grain during the cyclic deformation. Thirdly, the cracks initiated eventually at these intrusions and extrusions. In specimen 2, though the stress around the grain boundary between grains 18 and 1 is not the maximum stress, it is relatively high compared to the stress in the grains 17, 12 and 2 at the free surface near the corner of the specimen. Similar to specimen 1, the higher stress around the grain boundary between grains 18 and 1 and lower resistance to the dislocation motion in the corner grain will cause the crack initiation.
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For these two specimens, some of the maximum stresses are located at the grain boundaries parallel to the loading axis or at triple junctions apart from the corner of the specimens, but cracks did not initiate at these locations. The major reason is probably due to the higher resistance exerted by boundaries to the dislocation motion in an inner grain. During the successive cyclic deformation, the crack propagated in a transgranular mode at lower stress amplitude, but propagated in a mixed mode–transgranular and intergranular mode at higher stress amplitude. Once the crack initiates, the stress field at the crack tip will become more complex. In the present work, the
Fig. 3. The stress distribution along the loading axis (|y): (a) specimen No. 1 and (b) specimen No. 2.
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stress distribution after the crack initiated has not been calculated. However, the variation of the crack propagation mode with stress amplitude may be roughly explained as follows. At lower stress amplitude, only single slip system was activated in a few grains, so the crack will propagate along the slip lines. When the crack reached the grain boundary, it would cross the grain boundary and propagate gradually along the slip lines in another grain. On the other hand, at higher stress amplitude, multiple slip occurred in some grains around the grain boundary. The interaction of secondary slip lines with grain boundary and primary slip lines was very complicated [15]. Obviously, the secondary slip lines may interfere with intergranular cracking process. The impingement of slip lines against grain boundaries perpendicular to the loading axis will cause the initiation of voids at grain boundaries and then the voids may coalesce into an intergranular crack, so at higher stress amplitude, the crack sometimes propagated in a transgranular mode.
4. Conclusions From the results of this investigation on the crack initiation and propagation of h-iron at room temperature, some conclusions may be drawn. At two different nominal stress amplitudes, cracks all initiated at slip lines intersecting with the free surface at the corner of the specimen. At lower stress amplitude, the crack propagated in a transgranular mode, but at higher stress amplitude the crack propagated in a mixed mode –transgranular mode and intergranular mode. The stress distribution of grains on the free surface of the specimen showed that the process of crack initiation probably took place as follows. Due to the different orientations of grains and different characters of grain boundaries, the stress around some grain boundaries holds high stress which will activate the slip system of a
.
grain that is right at the corner. Then it will create the intrusions or extrusions at the free surface of the corner grain during the cyclic deformation. Finally the cracks initiated at these intrusions and extrusions of the slip lines.
Acknowledgements The authors wish to thank Dr S.D. Wu for his help in providing iron polycrystal. This work was financially supported by the key projects of National Fundamental Research of China (G19980615 and G2000671).
References [1] J.C. Grosskreutz, H. Mughrabi, in: A.S. Argon (Ed.), Constitutive Equations in Plasticity, MIT Press, Cambridge, MA, 1977, pp. 251 – 326. [2] H. Mughrabi, Z. Metallk. 66 (1975) 719 – 724. [3] T. Magnin, J.H. Driver, Mater. Sci. Eng. 39 (1979) 175 –185. [4] F. Guiu, R. Dulniak, Fatigue Eng. Mater. Struct. 5 (1982) 311. [5] L. Prister, D.P. Yu, Mater. Sci. Eng. A188 (1994) 113. [6] D. Romero, L. Fionova, Acta Mater. 44 (1996) 391. [7] N.J. Teng, T.H. Lin, J. Eng. Mater. Tech. 117 (1995) 470. [8] H. Mughrabi, C. Wuthrich, Phil. Mag. 33 (1976) 963 –984. [9] T. Tanka, Ritsmueikan University. Fatigue ’87. Vol. 1 [Proc. Conf.], Chariottesville, VA, USA, 28 June – 3 July 1987. Engineering Materials Advisory Services Ltd., 339 Halesowen Rd., Cradley Heath, Warley, UK, 1987 (Met. A., 8809-72-0471) 23 – 42. [10] C.R. Chen, S.X. Li, Z.G. Wang, Mater. Sci. Eng. A247 (1998) 15. [11] C.R. Chen, S.X. Li, Mater. Sci. Eng. A257 (1998) 312 –321. [12] J.P. Hirth, J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968, p. 762. [13] S.X. Li, D.B. Ren, W.P. Jia, C.R. Chen, X.W. Li, Z.G. Wang, Phil. Mag. A80 (2000) 1729. [14] C.R. Chen, S.X. Li, W.P. Jia, J.L. Wen, Mater. Sci. Eng. A282 (2000) 170. [15] Y.M. Hu, Z.G. Wang, Acta Mater. 45 (1997) 2655.
Fatigue crack initiation and propagation in an a-iron polycrystal R.Q. Chu *, Z. Cai, S.X. Li, Z.G. Wang State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China Received 23 October 2000; received in revised form 3 January 2001
Abstract The cyclic deformation and crack initiation and propagation of a-iron polycrystals have been studied under stress-control with emphasis on the dependence on the stress amplitudes and orientation of grains. The orientations of grains surrounding cracks were determined by the electron backscatter diffraction (EBSD). It was found that cracks did not originate at grain boundaries but along the slip lines intersecting with the free surface at the corner of the specimen. At lower stress amplitude, the crack propagated in a transgranular mode, but at higher stress amplitude the crack propagated in a mixed mode– transgranular mode and intergranular mode. The stress distribution along the loading axis of grains surrounding the crack was calculated using a three-dimensional anisotropic finite element method (FEM). In the present work, it was shown that the crack initiation mainly depends on three factors: higher stress distribution, abundant dislocation sources and less resistance to dislocation motion. © 2001 Elsevier Science B.V. All rights reserved. Keywords: a-Iron polycrystal; Cyclic deformation; Crack initiation and propagation; Finite element analysis; Crystal orientation
1. Introduction The fundamental mechanisms of metal fatigue have been studied in detail mostly on face-centered cubic (fcc) metals, but to a lesser extent on metals of other crystal structures [1]. In the case of body-centered cubic (bcc) metals the glide properties of dislocations are rather complex and depend sensitively on temperature, strain rate, and on the sense of deformation. Thus it is not surprising that a comprehensive understanding of the behavior of bcc metals under cyclic loading is still lacking, especially the mechanism of crack initiation. a-Iron, which is perhaps traditionally the most important bcc metal, has been widely used for investigating the mechanism of fatigue crack initiation [2,3]. It has been reported that the mechanism of fatigue crack initiation in a-iron sensitively depends on the testing frequency, plastic strain amplitude and material purity. Guiu and Dulniak [4] have proposed that the incompatible deformation of surface grains may induce the nucleation of fatigue cracks at the surface grain boundaries. * Corresponding author. E-mail address: [email protected] (R.Q. Chu).
It is known that the mechanical properties of polycrystalline materials depend strongly on the specific properties of grain boundaries, triple junctions and the arrangement of these elements [5,6]. The local microstress field in a polycrystal grain depends not only on the applied stress but also on the orientation of its surrounding grain [7]. It is necessary to investigate the influence of stress distribution and orientation of grains on the crack initiation. In this paper the results of fatigue crack initiation and propagation in pure polycrystalline a-iron are reported and special attention was placed on the influence of stress distribution and orientation of grains on crack initiation.
2. Experimental procedure The observations were performed on specimens of a-iron with a nominal purity of 99.98%. The dimension of the gauge section was 4× 6 × 10 mm3. The gauge section of the specimens was chemically polished in a solution of four parts of HF and 96 parts H2O2, at room temperature, to give a smooth surface. A MTS fatigue testing machine was used for the tests at a
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 0 9 6 6 - 2
R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
65
constant frequency of 25 Hz under load control. Two maximum nominal stresses of 130 and 140 MPa were applied respectively on two specimens, and the stress ratio was − 1. During the tests, the observations of slip patterns and crack initiation were conducted in an optical microscope mounted on the frame of the machine. The tests were terminated when a fatal crack was formed and then the specimens were examined by electron backscatter diffraction (EBSD) technique in SEM. On the surface of the specimen, the orientations of grains near the fatal crack were determined by EBSD and the stress distributions along the loading direction of these grains were obtained using a three-dimensional anisotropic finite element method (FEM). ANSYS soft code was used in the analysis.
3. Results and discussion Two specimens (No. 1 and No. 2) were fatigued to failure at maximum nominal stresses of 130 and 140
Fig. 2. The orientation maps of the grains on the specimen surface around the cracks: (a) specimen No. 1 and (b) specimen No. 2.
Fig. 1. Surface slip features and fatigue cracks of specimens: (a) specimen No. 1 and (b) specimen No. 2.
MPa, respectively. Numbers of cycles to failure were 9.2×105 and 1.4× 105, respectively. The surface appearances of the fatigued specimens are shown in Fig. 1. Most grains on the surface of the specimen appeared featureless even after fatigue failure. Only a few grains showed the slip traces within the grains. It seemed that the slip lines were emitted from the grain boundaries (Fig. 1(a)). For specimen 2, the slip lines were seen in many grains, especially in some grains around the crack, the deformation was larger and multislip had occurred and the slip traces passed through the entire grains (Fig. 1(b)). During fatigue testing, the metallographic observations indicated that crack initiated at slip lines intersecting with free surfaces at the corner of the specimen. During the successive cyclic loading, the crack developed into a fatal crack. At lower stress amplitude the crack propagated in a transgranular mode, but at higher stress amplitude the crack propagated in a mixed mode–transgranular mode and intergranular mode, as shown in Fig. 1. The orientation maps of the surface grains near the cracks are shown in Fig. 2. Mughrabi and Wuthrich [8] suggested that under fatigue loading the incompatible shape change induced by asymmetric slip in neighboring grains on the surface could promote crack initiation at grain boundaries. Guiu and Dulniak [4] reported that fatigue failure in pure iron and iron alloys initiated at grain boundaries rather than slip lines when fatigue tests were performed
R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
66
at room temperature with frequencies higher than 0.1 Hz. Tanaka and coworkers [9] found that cracks originated only at grain boundaries under reversed stress but nucleated along slip bands under alternating tension. In the present study, a testing frequency of 25 Hz and a symmetrical tension– compression – loading mode were used. It was found that cracks nucleated at slip lines, so it was necessary to investigate the crack initiation mechanism. The dependence of the crack initiation on the stress distribution and orientation of grains were mainly investigated. Since the resolved shear stress on the primary slip system in each grain just exceeded the critical resolved shear stress to activate the slip system, the elastic calculation could approximately be used. Based on the experimental results, FEM was then adopted to calculate the elastic stress distribution in each grain of iron polycrystals subjected to tensile loading. In the computation model, no crack was considered. In order to obtain the stress distribution of grains around the crack on the specimen surface, the orientation of each grain should be known. In this paper, the orientations of grains we are interested were determined by EBSD. The orientation matrices of typical grains near the corner of the specimen are as follows: For specimen No.1: Á 0.6949 Ã grain 1 Ã − 0.5203 Ã Ä 0.4964
0.2235 −0.4998 −0.8368
0.6835 Â Ã 0.6924 Ã Ã −0.2311 Å
Á 0.3145 Ã grain 3 Ã 0.6607 Ã Ä −0.6816
− 0.9368 0.3321 − 0.1103
0.1535 Â Ã 0.6732 Ã Ã 0.7233 Å
Á 0.3280 Ã grain 18 Ã 0.6610 Ã Ä −0.6749
− 0.9284 0.3578 − 0.1007
0.1749 Â Ã 0.6595 Ã Ã 0.7310 Å
For specimen No.2: Á0.1954 Ã grain 12 Ã0.8684 Ã Ä0.4557
0.9711 −0.2362 0.0338
−0.1370 Â Ã −0.4359 Ã Ã 0.8895 Å
Á 0.1841 Ã grain 17 Ã 0.9569 Ã Ä −0.2247
0.5251 − 0.2890 − 0.8005
0.8309 Â Ã − 0.0294 Ã Ã 0.5557 Å
Á −0.2752 Ã grain 18 Ã 0.0709 Ã Ä 0.9588
−0.6486 −0.7498 − 0.1308
0.7096 Â Ã − 0.6579 Ã Ã 0.2524 Å
Before carrying out the finite element analysis, the stress–strain relation and the elastic modulus matrix [C] with reference to the global coordinate system of each grain under the global coordinate system must be established. The detailed stress– strain relation and the establishment of the elastic modulus matrix [C] can be found in our previous works [10,11]. For a-iron the elastic modulae are C11 = 242 MPa, C12 = 146.5 MPa, C44 = 112 MPa, 6 =0.291 [12]. After the elastic modulus matrix [C] of each grain has been obtained in combination with the known constraint and load conditions of the multicrystal model, the distribution of stress and strain of each grain in the global coordinate system can be obtained using the three-dimensional anisotropic finite element method. Because we are particularly interested in crack initiation, the existing crack was not considered in the computation model. Fig. 3 showed the stress distribution along the loading axis (|y) of grains around the crack at the front surface. Since there are many slip systems in BCC structure, the higher stress of |y will cause one of the slip systems, which is close to the maximum shear stress plane to operate more easily. In the first approximation, no specific slip system is considered in the present work. Some characteristics about the distribution of |y can be found in Fig. 3. The distribution of stress |y is highly inhomogeneous in each grain. The maximum stress is located at or around the grain boundary parallel to the loading axis (see the grain boundary between grain 3 and grain 4 in Fig. 3(a), the grain boundary between grain 1 and grain 18 in Fig. 3(b)) or at the triple junction (see the triple junction of grains 1, 2 and 3 in Fig. 3(a) and the triple junction of grains 17, 19 and 20 in Fig. 3(b)). The grain boundaries perpendicular to the loading direction usually do not withstand the highest stress and the lowest stress locates at the interior of some grains or at some triple junctions (see grain 9 in Fig. 3(a) and triple junction of grains 9, 10 and 11 in Fig. 3(b)). These results are quite similar to our previous analysis in which an ideal model was used [11,13,14]. After carefully examining these results, one may note that the stress distribution of grains near the corner of the specimen has great influence on the crack initiation. From the stress distribution of grains around the places where the cracks initiated, it can be suggested that the process of fatigue crack initiation possibly took place with the following steps. Firstly, due to the different orientation of grains and different characters of grain boundaries, the stress around the grain boundaries holds high |y, for example the grain boundary between grain 3 and grain 4 in Fig. 3(a). Secondly, the high stress around the grain boundary will activate the slip system of the grain that is right at the corner. Since there are usually many dislocation sources around the grain boundary, the dislocation emitted from the sources in the corner grain glides more
R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
easily than that in the inner grain. Therefore, the activated slip systems will keep operating during cyclic loading, creating intrusions or extrusions at the free surface of the corner grain during the cyclic deformation. Thirdly, the cracks initiated eventually at these intrusions and extrusions. In specimen 2, though the stress around the grain boundary between grains 18 and 1 is not the maximum stress, it is relatively high compared to the stress in the grains 17, 12 and 2 at the free surface near the corner of the specimen. Similar to specimen 1, the higher stress around the grain boundary between grains 18 and 1 and lower resistance to the dislocation motion in the corner grain will cause the crack initiation.
67
For these two specimens, some of the maximum stresses are located at the grain boundaries parallel to the loading axis or at triple junctions apart from the corner of the specimens, but cracks did not initiate at these locations. The major reason is probably due to the higher resistance exerted by boundaries to the dislocation motion in an inner grain. During the successive cyclic deformation, the crack propagated in a transgranular mode at lower stress amplitude, but propagated in a mixed mode–transgranular and intergranular mode at higher stress amplitude. Once the crack initiates, the stress field at the crack tip will become more complex. In the present work, the
Fig. 3. The stress distribution along the loading axis (|y): (a) specimen No. 1 and (b) specimen No. 2.
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R.Q. Chu et al. / Materials Science and Engineering A313 (2001) 64–68
stress distribution after the crack initiated has not been calculated. However, the variation of the crack propagation mode with stress amplitude may be roughly explained as follows. At lower stress amplitude, only single slip system was activated in a few grains, so the crack will propagate along the slip lines. When the crack reached the grain boundary, it would cross the grain boundary and propagate gradually along the slip lines in another grain. On the other hand, at higher stress amplitude, multiple slip occurred in some grains around the grain boundary. The interaction of secondary slip lines with grain boundary and primary slip lines was very complicated [15]. Obviously, the secondary slip lines may interfere with intergranular cracking process. The impingement of slip lines against grain boundaries perpendicular to the loading axis will cause the initiation of voids at grain boundaries and then the voids may coalesce into an intergranular crack, so at higher stress amplitude, the crack sometimes propagated in a transgranular mode.
4. Conclusions From the results of this investigation on the crack initiation and propagation of h-iron at room temperature, some conclusions may be drawn. At two different nominal stress amplitudes, cracks all initiated at slip lines intersecting with the free surface at the corner of the specimen. At lower stress amplitude, the crack propagated in a transgranular mode, but at higher stress amplitude the crack propagated in a mixed mode –transgranular mode and intergranular mode. The stress distribution of grains on the free surface of the specimen showed that the process of crack initiation probably took place as follows. Due to the different orientations of grains and different characters of grain boundaries, the stress around some grain boundaries holds high stress which will activate the slip system of a
.
grain that is right at the corner. Then it will create the intrusions or extrusions at the free surface of the corner grain during the cyclic deformation. Finally the cracks initiated at these intrusions and extrusions of the slip lines.
Acknowledgements The authors wish to thank Dr S.D. Wu for his help in providing iron polycrystal. This work was financially supported by the key projects of National Fundamental Research of China (G19980615 and G2000671).
References [1] J.C. Grosskreutz, H. Mughrabi, in: A.S. Argon (Ed.), Constitutive Equations in Plasticity, MIT Press, Cambridge, MA, 1977, pp. 251 – 326. [2] H. Mughrabi, Z. Metallk. 66 (1975) 719 – 724. [3] T. Magnin, J.H. Driver, Mater. Sci. Eng. 39 (1979) 175 –185. [4] F. Guiu, R. Dulniak, Fatigue Eng. Mater. Struct. 5 (1982) 311. [5] L. Prister, D.P. Yu, Mater. Sci. Eng. A188 (1994) 113. [6] D. Romero, L. Fionova, Acta Mater. 44 (1996) 391. [7] N.J. Teng, T.H. Lin, J. Eng. Mater. Tech. 117 (1995) 470. [8] H. Mughrabi, C. Wuthrich, Phil. Mag. 33 (1976) 963 –984. [9] T. Tanka, Ritsmueikan University. Fatigue ’87. Vol. 1 [Proc. Conf.], Chariottesville, VA, USA, 28 June – 3 July 1987. Engineering Materials Advisory Services Ltd., 339 Halesowen Rd., Cradley Heath, Warley, UK, 1987 (Met. A., 8809-72-0471) 23 – 42. [10] C.R. Chen, S.X. Li, Z.G. Wang, Mater. Sci. Eng. A247 (1998) 15. [11] C.R. Chen, S.X. Li, Mater. Sci. Eng. A257 (1998) 312 –321. [12] J.P. Hirth, J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968, p. 762. [13] S.X. Li, D.B. Ren, W.P. Jia, C.R. Chen, X.W. Li, Z.G. Wang, Phil. Mag. A80 (2000) 1729. [14] C.R. Chen, S.X. Li, W.P. Jia, J.L. Wen, Mater. Sci. Eng. A282 (2000) 170. [15] Y.M. Hu, Z.G. Wang, Acta Mater. 45 (1997) 2655.