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Effect of microstructure on fatigue behavior of AZ31 magnesium alloy
Materials Science and Engineering A 468–470 (2007) 214–222
Effect of microstructure on fatigue behavior of AZ31 magnesium alloy Sotomi Ishihara ∗ , Zhenyu Nan, Takahito Goshima Department of Mechanical Engineering, University of Toyama, 3190 Gofuku, Toyama City 930-8555, Japan Received 22 March 2006; received in revised form 7 May 2006; accepted 6 September 2006
Abstract Fatigue experiments were carried out in laboratory air using an extruded magnesium alloy, AZ31. In the alloy (designated as material E), a lamellar structure which is parallel to the extruded direction exists. This type of lamellar structure of the extruded material is not common for the AZ31 magnesium alloy. In the present study, two kinds of specimens, with axial directions parallel (designated as EP specimen) or vertical (designated as EV specimen) to the lamellar structure, were used for comparison. By comparing the S–N curves and crack generation and propagation characteristics of both specimens, effects of the lamellar-structure of the AZ31 magnesium alloy on the fatigue characteristics were studied. In the EP specimens, fatigue cracks initiated at a very early stage of the fatigue process, so the greater part of the fatigue life was occupied with fatigue propagation. Crack retardations or arrests due to the lamellar structure were observed. Accordingly, a sharp bend in the S–N curve was observed. In the EV specimens, fatigue cracks also initiated at an early stage of the fatigue process. However, in the EV specimens, many cracks were generated and propagated as compared to the EV specimens. Accordingly, the effect of crack coalescence is reflected in the propagation behavior of the EV specimens. The rate of fatigue crack growth in the EV specimens was more rapid than in the EP specimens, and this led to a reduction in fatigue lives for the former as compared with the latter. In addition, a rolled magnesium alloy without the lamellar structure (designated as material R) was also tested. This type of microstructure is common for the AZ31 magnesium alloy. Two specimens with two different axial directions, parallel (RP specimen) or vertical (RV specimen) to the rolling direction, were prepared for testing. However, no differences in the fatigue behavior between the RP and RV specimens were observed. This result differs from that of the extruded materials, EP and EV. The rate of fatigue crack growth in the rolled specimen was more rapid than that of the EP specimens and led to a reduction in the fatigue lives as compared with the EP specimens. © 2007 Elsevier B.V. All rights reserved. Keywords: Magnesium alloy; Fatigue short crack; Crack initiation; Crack propagation; Microstructure
1. Introduction Magnesium alloys are very attractive as structural materials, because they are extremely light, possessing excellent specific tensile strength, good stiffness, and good vibrational absorption [1]. Due to their energy and weight saving characteristics, magnesium alloy are considered to be good candidates for material in, for example, auto parts, portable personal computers, and telephones. The demand for magnesium alloys in such applications has increased rapidly in recent years. Understanding the fatigue characteristics of magnesium alloys is vital when they are used as structural members. There are many studies on fatigue properties of magnesium alloy. For example, Goodenberger and Stephens [2] studied the fatigue behavior of a cast magnesium alloy, AZ91E-T6, in lab-
∗
Corresponding author. Tel.: +81 76 445 6771; fax: +81 76 445 6771. E-mail address: [email protected] (S. Ishihara).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.09.124
oratory air. Hilpert and Wagner [3] also studied the corrosion fatigue behavior of AZ80 magnesium alloys that had received various surface treatments, such as electro-polishing, grinding, machining, and shot-peening. They showed that the corrosion fatigue lives of the treated specimens were shorter compared to specimens in laboratory air. Eisenmeier et al. [4] studied the fatigue behavior of AZ91 magnesium alloy, which was processed using the vacuum die casting method. They reported that the fatigue cracks initiated from casting defects in the material, and that crack growth behavior was influenced by the microstructure of the material. Shih et al. [5] performed rotating bending fatigue experiments on the extruded magnesium alloy AZ61A. They reported that cracks initiated from inclusions, which existed on the specimen surface, or the vicinity of the surface, and that the initial crack growth behavior was affected by the specimen microstructure. The present authors investigated crack initiation and propagation behaviors during fatigue of the extruded magnesium alloy AZ31 in detail and discussed their relationship to fatigue lives [6,7].
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extruded direction. In addition, other crystals exist in both the A phase and B phase. They are designated D phase and C phase, respectively. In the alloy, a lamellar structure which is parallel to the extruded direction exists. This lamellar structure of the extruded material is not common for the AZ31 magnesium alloy. In the present study, the material will be designated as material E. 2.2. Rolled magnesium alloy A plate of rolled magnesium alloy AZ31 with a thickness of 15.8 mm was used for the present study. Its chemical composition is listed in Table 1(b). Fig. 1(b) shows the microstructure of the rolled magnesium alloy where the rolling direction is indicated. As seen from the figure, inclusions with an average diameter of 16 m are scattered in the matrix, which has an average crystal grain size of 20 m. The rolled magnesium alloy shown in Fig. 1(b) does not have the banded microstructures of the extruded magnesium alloy in Fig. 1(a). It is interesting to observe the ways in which S–N characteristic, crack initiation, and crack propagation behaviors of the rolled alloy differ from those of the extruded material. This type of microstructure is common for the AZ31 magnesium alloy. In the present study, the material will be designated as material R. Fig. 1. Microstructure of the AZ31 magnesium alloy.
2.3. EPMA analysis and X-ray diffraction As reviewed above, the fatigue characteristics of magnesium alloys produced by various techniques, such as rolling, casting and extrusion, have been the subject of numerous studies. However, their fatigue mechanisms have not been studied in detail. In the present study, fatigue experiments were carried out on both extruded and rolled magnesium alloy AZ31 to supplement information about the effect of microstructure on the fatigue behavior, specifically, the S–N characteristic, crack initiation, and crack propagation behavior. 2. Materials 2.1. Extruded magnesium alloy The AZ31 magnesium alloy used in the present study was prepared by extruding a round bar of diameter 88.9 mm into one of 19 mm diameter. Its chemical composition is listed in Table 1(a). Fig. 1(a) shows a photograph of the microstructure of the plane which is parallel to the extrusion direction. At the right side of the figure, a schematic illustration is attached as an explanation. As seen from this figure, a white layer (A phase) and a black layer (B phase) accumulate alternately parallel to the
Analysis of the chemical compositions of the microstructure and inclusions in the materials E and R was done using EPMA (Shimadzu, EPMA-1500) and X-ray diffraction equipment (Rigaku, RINT2200/PC/K). Hardness of the matrix and inclusions was measured using a Vickers micro-hardness tester (Akashi: HM-102). Widths of the A and B phases, and grain diameters of the C and D phases, were measured using an optical microscope. Table 2(a) shows identifications of the microstructures of the extruded and rolled magnesium alloys by EPMA analysis and X-ray diffraction. In the table, the sizes and hardnesses of the phases are also listed. As seen from the table, the white layer (A phase) and the black layer (B phase) observed in the material E (extruded alloy) of Fig. 1(a) are pure Mg and Mg32 (Al + Zn)49 , respectively. The C phase and D phases are Mg17 Al12 and Al81 Mn19 , respectively. The hardness for the D, B, and C phases are HV = 95, 91, and 81 kgf/mm2 , respectively. These hardnesses are clearly higher than those for the A phase, HV = 60 kgf/mm2 . Average dimensions of the phases, WA , WB , dC , and dD are 40, 24, 20, and 15 m, respectively, where WA and WB are width of the A and B phase, and dC and dD are grain diameters of the C phase and D phase, respectively.
Table 1 Chemical compositions of the material (wt%) Al
Zn
Mn
Fe
Ni
Cu
Si
Ca
Mg
(a) Material E (extruded magnesium alloy) 2.98 0.97 0.004
0.007
0.005
0.002
0.02
0.05
Balance
(b) Material R (rolled magnesium alloy) 2.5–3.5 0.7–1.3
0.005
0.005
0.002
0.05
0.04
Balance
0.2
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Table 2 Compositions and Vickers hardness of the phases Structure
Composition
Vickers hardness (kgf/mm2 )
Typical size (m)
(a) Material E (extruded magnesium alloy) A Mg 60 B Mg32 (Al + Zn)49 91 81 C Mg17 Al12 95 D Al81 Mn19 Structure
Composition
(b) Material R (rolled magnesium alloy) A Mg D Al81 Mn19
WA = 40 WB = 24 dC = 20 dD = 15 Vickers hardness (kgf/mm2 ) 57 93
The EPMA analysis of the material R (rolled magnesium alloy) revealed that the inclusions are the intermetallic compound (Al81 Mn19 system), and that Zn and Si particles distribute uniformly in the magnesium matrix. The inclusions designated as D are the same as in the extruded alloy. The hardness measurements show clearly that the inclusions (HV = 95) are harder than the matrix (HV = 58). 3. Specimens and experimental methods 3.1. Shapes of the specimens To study the influence of the rod-like structure which appeared in the material E (extruded magnesium alloy) of Fig. 1(a) on the fatigue behavior, two types of specimens were machined so that their axial directions were parallel and vertical to the rod-like structure. They were designated specimens EP and EV, respectively. Rotating bending fatigue tests were performed using the above specimens. The shape of the EP specimen is shown in Fig. 2(a). Its stress concentration factor is 1.04. Fig. 2(b) shows the shape of the EV specimen. Its stress concentration factor is 1.15. The fatigue experiments were performed by attaching a grip to both ends of the specimen as shown in Fig. 2(b). Two types of specimens were prepared, namely, the RP and RV specimens. In the former, the axial direction of the specimen is parallel, while in the latter it is vertical, to the rolled direction. The specimens were machined into the ASTM standard hourglass shape as shown in Fig. 2(c). Its stress concentration factor KT is 1.04.
Fig. 2. Shapes and dimensions of specimens.
3.2. Mechanical properties of the specimens Table 3 shows the mechanical properties of the specimens. In the table, the data for both the material E and material R are listed. Tensile tests were performed using specimens with gauge length of 3 mm and gauge diameter of 4 mm for the EP and EV specimens. For the RP and RV specimens, specimens with gauge length of 60 mm and gauge diameter of 12.5 mm were used. As seen in this table, tensile strength and yield strength of the EP specimens are about 17% greater than those of the EV specimen. This result indicates that the static strength is greater when the load is applied parallel to the extrusion direction than when it is applied vertical to the extrusion direction. On the other hand, for the material R (rolled material), a difference in the mechanical properties for the RP and RV specimens was
Table 3 Mechanical properties of the material Material
Yield strength (MPa)
Tensile strength (MPa)
Elongation (%)
Young’s modulus (GPa)
(a) Material E (extruded magnesium alloy) EP 200 EV 170
275 235
11 16
45 45
(b) Material R (rolled magnesium alloy) RP 140 RV 165
257 256
26 28
45 45
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not observed. Moreover, it is interesting that the mechanical properties of the material E (extruded material) were superior to those of the material R (rolling material). 3.3. Experimental methods The fatigue experiments were carried out in laboratory air with a humidity of 63–73% at room temperature using a cantilever rotating bending fatigue machine. Its cyclic speed was 30 Hz. During the fatigue tests, the temperature and humidity of the atmosphere was not strictly controlled. Some experiments were interrupted at fixed numbers of cycles to collect replicas of the specimen surface. The cyclic speed employed for these experiments, was 10 Hz. The crack initiation and propagation behavior during the fatigue process were investigated by observing these replicas with an optical microscope (OLYMPUS: BX51) at 400× magnification. To facilitate specimen surface observations, the smallest cross sections of all specimens were polished prior to testing into a mirror-like finish using emery paper and diamond paste. 4. Experimental results 4.1. S–N curves Fig. 3(a) shows the S–N curves for the EP and the EV specimens in laboratory air at a stress ratio of −1 and frequency of 30 Hz. As seen from this figure, in the EP specimen, a clear horizontal part can be observed from N = 105 –107 cycles at stress amplitude of 120 MPa. On the other hand, in the EV specimen, the horizontal part is observed at a stress amplitude of 95 MPa. So the fatigue limit decreased by about 20% in the EV specimen as compared with the EP specimens. Further, in the high stress amplitude region, the fatigue life of EV specimens was shortened to about 1/10 of that of EP specimens. So, it is clear that the EP specimen possesses a superior fatigue resistance in both fatigue limit and fatigue lives. Fig. 3(b) shows S–N curves for the RP and RV specimens (rolled magnesium alloy) in laboratory air. In this figure, for comparison purposes, the S–N curves of the EP and EV specimens (extruded magnesium alloy) are shown by solid and broken lines, respectively. As seen from the figure, the fatigue life of the rolled magnesium alloy is relatively shorter than that of the EP specimen, but almost the same as the EV specimen. The extent
Fig. 3. S–N curves of the AZ31 magnesium alloys.
of bending in the S–N curve is gentler in the rolled and EV specimens than in the EP specimen. Next let us compare the S–N characteristics of the RP and RV specimens. There are no great differences in the fatigue lives and in the fatigue limits, except that at the higher stress amplitudes, there are some differences in the fatigue lives. 4.2. Successive observations of the fatigue process The fatigue process was investigated in detail for the purpose of illustrating the fatigue characteristics of the extruded
Fig. 4. Successive observations on the specimen surface during the fatigue process (EP specimen, σ a = 122.5 MPa).
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Fig. 5. Successive observations of the specimen surface during the fatigue process (EV specimen, σ a = 120 MPa). (a) Nf = 27,000 cycles and (b) Nf = 36,000 cycles.
and rolled magnesium alloys. Accordingly, successive observations of the specimen surface were conducted at several stress levels to study the effect of the material microstructure on the fatigue lives. In order to distinguish the reasons for differences in the fatigue lives of the EP specimen and EV specimen, the fatigue processes of both specimens were continuously observed for the range of stress amplitudes 95–122.5 MPa. Fig. 4 shows the result of successive observations of the specimen surface during the fatigue process for an EP specimen at a stress amplitude of 122.5 MPa. In order to examine the interaction between crack initiation and propagation behavior and the microstructure of the specimen, the fatigue experiment included pre-revealing the microstructure by etching. In the figure, the crack tips are shown by arrows. As seen from the figure, a crack initiated at the C phase, Fig. 4(b), joined with another crack, Fig. 4(c), and then propagated into the next phase, Fig. 4(d). The crack propagation rate decreased and the direction of crack propagation turned to the side when the crack crossed into the B phase, Fig. 4(e).
Fig. 5 shows the result of successive observations of the specimen surface during the fatigue process of an EV specimen at a stress amplitude of 120 MPa. As seen from Fig. 5(a), multiple cracks, 1, 2, 3, that initiated in the A phase propagated when short in isolation, with no interaction between them. However, as shown in Fig. 5(b), the multiple cracks coalesced with each other when they propagated farther. Such crack coalescence was observed at other stress amplitudes also. When compared to EP specimens, we see that more cracks occur during the fatigue process in EV specimens. For the rolled material, successive observations during the fatigue process were conducted for only RP specimens, since there were no significant differences in the S–N curves for RP and the RV specimens. Fig. 6(a) and (b) shows the results of successive observations at stress amplitudes 105 and 110 MPa, respectively. As seen from the figures, fatigue cracks initiated from the interface between Al–Mn inclusions and the Mg matrix at an early stage of the fatigue life. This result was commonly observed for stress amplitudes 105 and 110 MPa. Therefore, the fatigue life of this magnesium alloy is predominately the crack propagation life. The fatigue crack propagated almost linearly and not in a zigzag manner. This fatigue crack morphology observed in this magnesium alloy is different from that in aluminum alloys [8]. 4.3. Crack propagation behavior 4.3.1. 2a versus (N/Nf ) relations Fig. 7(a)–(c) shows the variations of crack length, 2a, measured from successive observations as a function of fatigue life ratio N/Nf for the EP, EV and RP specimens, respectively. As seen in Fig. 7(a) for the EP specimen, a stress amplitude dependency was not clearly observed in the 2a versus N/Nf relation. Also, a crack with a length of about 20 m initiated at 5–6% of the fatigue life at stress amplitudes 122.5 and 140 MPa. On the
Fig. 6. Successive observations on a specimen surface during the fatigue process (RP specimen).
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3 coalesced at 35% of the fatigue life, and afterwards the joined crack coalesced with Crack 1 at 45% of the fatigue life. Cracks 5 and 6 coalesced at 65% of the fatigue life, and afterwards the joined crack coalesced with Crack 4 at 75% of the fatigue life. Moreover, Crack 7 propagated as a single crack without coalescing with other cracks. As mentioned above, the crack initiation and propagation behavior in the EV specimen was different from that of the EP specimen in the following ways: cracks initiated at C phase inclusions within the B phase in EP specimens, while in EV specimens, cracks initiated from D phase inclusions within the A phase. Moreover, crack coalescence was caused by many cracks initiating during the fatigue process in EV specimens, while in EP specimens, crack coalescence did not readily occur, since crack initiation was limited. Fig. 7(c) shows the variation of the main crack length determined by successive observations as a function of fatigue life ratio N/Nf , the main crack being the crack that propagated to cause final failure of the specimen. In this figure, the data for three different stress amplitudes are plotted. As seen from the figure, the fatigue crack initiated at an early stage of fatigue life regardless of the stress amplitude. Therefore, the total fatigue life can be considered as equal to the crack propagation life. Also, the effect of stress amplitude on the relation 2a–N/Nf was not readily evident for stress amplitudes over the range 105–120 MPa. These observed trends in the rolled material are similar to those in the extruded material. 4.3.2. Relations of da/dN versus K Fig. 8(a)–(c) show the relationships between the rate of crack propagation, da/dN, and stress intensity factor range, K, for EP, EV and RP specimens, respectively. For the calculation of K for the EP and RP specimen, the following expression was used. √ K = 1.04Yσa πa
(1)
where the value 1.04 is a stress concentration factor due to the notch from the specimen radius of 20 mm. Further, Y = 0.73 is a correction factor for a surface crack with a semicircular shape, and a is the half crack length. For the EV specimen, the following expression was used for the calculation of K. Fig. 7. Variations of crack lengths as a function of fatigue life ratio N/Nf .
other hand, at stress amplitude 130 MPa, a crack with a length of about 20 m initiated at 30% of the fatigue life. However, it is possible that more detailed observations would show that cracks initiated earlier than was observed. From the above experimental result, it is concluded that the total fatigue life is almost the same as the crack propagation life. Fig. 7(b) shows variations of crack length, 2a as a function of the fatigue life ratio N/Nf in the EV specimen. The data at stress amplitude 120 MPa are plotted in the figure. As seen from the figure, a crack with a length of about 10–30 m initiated at 5–6% of the fatigue life. At stress amplitude 120 MPa, a number was assigned to each of the cracks, since multiple cracks were observed during the fatigue process. Coalescence of cracks occur at positions C in the figure. Cracks 2 and
√ K = 1.15Yσ πa
(2)
where the value 1.15 is a stress concentration factor due to the notch from the 4 mm radius. As seen from Fig. 8, threshold behavior is not clearly seen in the da/dN versus K relations. However, we observed experimentally existences of non-propagating cracks with a length of about 15 m or so at the fatigue limits of the EP, EV and RP specimens. After measuring the non-propagating crack lengths, we evaluated the threshold stress intensity factors Kth for each of the specimens by substituting both the non-propagating crack length and fatigue limit into Eq. (1) for the EP and RP specimens, and Eq. (2) for the EV specimen. As seen in Fig. 8(a), stress amplitude dependency in the da/dN versus K relation of the EP specimen was not clearly evident within the range of stress amplitudes 122.5–160 MPa.
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EV specimen. The solid line in the figure is the approximated curve represented by the next expression. √ da 2 = A(1.15Yσa πa − Kth ) dN
(4)
where A = 9 × 10−9 MPa−2 cycle−1 and Kth = 0.35 MPa m1/2 are material constants of the EV specimen. As seen from the figure, the relation da/dN versus K for the EV specimen can be approximated by expression (4). For comparison purposes, the da/dN versus K relation for the EP specimen is also shown by the broken line in the figure. As seen from the figure, the crack growth rate for the EV specimen is faster than that for the EP specimen at a constant K level. And the threshold level for the crack propagation Kth for the EV specimen (0.35 MPa m1/2 ) is lower than that for the EP specimen (0.44 MPa m1/2 ). Fig. 8(c) shows a log–log plot of the relationship between stress intensity factor range K and crack growth rate da/dN for the RP specimen. The relation for the EP specimen is also shown by a solid line in the figure for comparison purposes. At the low stress intensity factors, the crack growth rate for the rolled magnesium alloy was more rapid than for the EP specimen. In the figure, the same relation for long through cracks in the rolled magnesium alloy AZ31 is shown by the broken line. The data was investigated by Tokaji et al. [9] at stress ratio, R = 0.05. There is an effect of the stress amplitude in the da/dN–K relation. The crack growth rates at the higher stress amplitude were more rapid than at the lower stress amplitudes. This was due to the low yield stress of the rolled material. The plastic zone size ahead of the crack tip increased and could not be neglected when compared to the total crack length. Such a deviation from the small scale yielding condition is often observed in low strength materials. 5. Discussion 5.1. Effect of microstructure on the crack initiation behavior
Fig. 8. Fatigue crack growth rate as a function of K.
The relation can be approximated by the following expression which is indicated by the solid line. √ da 2 = A(1.04Yσa πa − Kth ) dN
(3)
where A = 7 × 10−9 MPa−2 cycle−1 and Kth = 0.44 MPa m1/2 are material constants for the EP specimens. Fig. 8(b) shows the relationship between the rate of crack propagation, da/dN and stress intensity factor range, K for the
Fatigue cracks initiated at the top and bottom edges of C phase inclusions within the B phase in EP specimens. On the other hand, the crack was observed as initiating from D phase inclusions within the A phase in EV specimens. Discussion of crack initiation phenomena at an arbitrary point should include consideration of both the stress and the crack initiation strength at that point. Crack initiation occurs when the stress is greater than the crack initiation strength, and the reverse is true. Here we assume that crack initiation strength for the A, B, C, and D phases are equal, since they are not known at present. In the following, we will consider only the amount of stress. Microstructures of the EP and the EV specimens can be simply modeled by parallel and series springs, respectively, as shown in Fig. 9(a) and (b). These models are composed of a soft spring (the A phase, spring constant = kA ) and a hard spring (the B phase, spring constant = kB ), where kB > kA . In the parallel spring model for EP specimens of Fig. 9(a), we assume that the model is pulled to the right and left under
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and D phase by the stress concentration due to the displacement. As a result, flaking off or breaking of the D phase may occur, leading to crack initiation at the interface between the A and D phases. In the case of the RP specimen (rolled magnesium alloy), fatigue cracks were observed as initiating from the D phase inclusions within the A phase. In the RP specimen, the D phase (hard) exists within the soft matrix (A phase). When an external force is applied to this material system, it is expected that intense stress will be induced at the interface between the A and D phases by local stress concentration. As a result, flaking off or breaking of the D phase inclusions may occur and lead to crack initiation at the interface between the A and D phases, as in the case of the EV specimen.
Fig. 9. Microstructure model for EP and EV specimens that contain the rod-like structure.
constant displacement. In this case, the load applied to the B phase (hard) becomes obviously greater than that applied to the A phase (soft). In EP specimens, there is a softer phase named C that is surrounded by the harder phase B, as shown in Fig. 1(a). When an external force is applied to this system, a large stress is generated by the stress concentration at the interface between the C and B phases. As a result, a fatigue crack may initiate at the top and bottom edges of the C phase inclusions within the B phase. In the case of the EV specimen modeled in Fig. 9(b), let us consider that a series spring model is pulled under a constant load condition. In this case, the displacement occurring at the A phase (soft) becomes greater than that at the B phase (hard). In the EV specimen, the D phase (hard) exists within the A phase (soft) as shown in Fig. 1(b). It is expected that a large amount of stress will be induced at the interface between the A phase
5.2. Effect of microstructure on the crack propagation behavior It was observed that resistance to crack propagation in EP specimens was clearly higher than in EV specimens, and it was observed that resistance in EV specimens was almost equal to that in RP specimens. In EP specimens (material E), there is a rod-like structure parallel to the extrusion direction as shown in Fig. 1(a). This structure is harder than the matrix (A phase) and therefore possesses higher crack propagation resistance. As shown in the schematic illustration of Fig. 10(a), in EP specimens, cracks propagated and crossed the hard rod-like structure. However, in EV specimens (Fig. 10(b)), cracks propagated within the A phase without crossing the rod-like structure. In EP specimens, the rod-like structure acted as a barrier to crack propagation and provided higher resistance to crack propagation than in EV specimens. In RP specimens (material R), the rodlike structure does not exist as shown in Fig. 1(c). So, the crack propagation resistance for this material is almost equal to that of EV specimens.
Fig. 10. Schematic illustration of crack initiation and propagation behavior in the EP, EV and RP specimens.
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6. Conclusions Completely reversed fatigue experiments were conducted on smooth specimens of two kinds of AZ31 magnesium alloys, to study the effect of microstructure on crack initiation and propagation behavior during the fatigue process. The conclusions obtained can be summarized as follows: (i) Fatigue lives and the fatigue limit of EP specimens were higher than those of EV specimens and RP specimens. There was a sharp bend in the S–N curve for EP specimens as compared to EV and RP specimens. (ii) In both materials E and R of AZ31 magnesium alloy, cracks initiated at an early stage of the fatigue process. Therefore, fatigue life and crack propagation life can be considered as equal in length. In EP specimens, fatigue cracks initiated at the top and bottom edges of the C phase within the B phase; however in EV and R specimens, cracks were observed to initiate from the D phase within the A phase. (iii) Crack propagation resistance of EP specimens was superior to that of EV and RP specimens. Crack propagation resistance for EV and RP specimens was almost equal. (iv) In EP specimens, cracks propagated with crossing the rodlike structure, On the other hand, in EV and RP specimens, cracks propagated without crossing the rod-like structure. This rod-like structure acted as a barrier to crack propaga-
tion and provided superior crack propagation resistance in EP specimens. Acknowledgements The authors express their thanks to Prof. Arthur J. McEvily at The University of Connecticut for valuable discussions during the course of the present study. Thanks go also to Prof. Hiroshi Shibata and Dr. Masayoshi Shimizu for their valuable advice during the study. References [1] Y. Kojima, Handbook of Advanced Magnesium Technology, Kallos Publishing C., L., Tokyo, Japan, 2000. [2] D.L. Goodenberger, R.I. Stephens, J. Eng. Mater. Techn. 115 (1993) 391–397. [3] M. Hilpert, L. Wagner, J. Mater. Eng. Perform. 9 (2000) 402–407. [4] G. Eisenmeier, B. Holzwarth, H.W. H¨oppel, H. Mughrabi, Mater. Sci. Eng. A 319 (2001) 578–582. [5] T.S. Shih, W.S. Liu, Y.J. Chen, Mater. Sci. Eng. A 325 (2002) 152–162. [6] Z.Y. Nan, S. Ishihara, T. Goshima, R. Nakanishi, Scripta Mater. 50 (4) (2004) 429–434. [7] Z.Y. Nan, S. Ishihara, T. Goshima, R. Nakanishi, F. Nilsson (Eds.), Proceedings of the 15th European Conference of Fracture (CD-ROM), Stockholm, Sweden, August 11–13, ESIS, Torino, Italy, 2004. [8] H. Nisitani, Fatigue Strength, Ohmsha, Tokyo, Japan, 1985. [9] K. Tokaji, M. Kamakura, N. Hasegawa, Y. Tsuboi, J. Soc. Mater. Sci. Jpn. 52 (2003) 821–826.
Effect of microstructure on fatigue behavior of AZ31 magnesium alloy Sotomi Ishihara ∗ , Zhenyu Nan, Takahito Goshima Department of Mechanical Engineering, University of Toyama, 3190 Gofuku, Toyama City 930-8555, Japan Received 22 March 2006; received in revised form 7 May 2006; accepted 6 September 2006
Abstract Fatigue experiments were carried out in laboratory air using an extruded magnesium alloy, AZ31. In the alloy (designated as material E), a lamellar structure which is parallel to the extruded direction exists. This type of lamellar structure of the extruded material is not common for the AZ31 magnesium alloy. In the present study, two kinds of specimens, with axial directions parallel (designated as EP specimen) or vertical (designated as EV specimen) to the lamellar structure, were used for comparison. By comparing the S–N curves and crack generation and propagation characteristics of both specimens, effects of the lamellar-structure of the AZ31 magnesium alloy on the fatigue characteristics were studied. In the EP specimens, fatigue cracks initiated at a very early stage of the fatigue process, so the greater part of the fatigue life was occupied with fatigue propagation. Crack retardations or arrests due to the lamellar structure were observed. Accordingly, a sharp bend in the S–N curve was observed. In the EV specimens, fatigue cracks also initiated at an early stage of the fatigue process. However, in the EV specimens, many cracks were generated and propagated as compared to the EV specimens. Accordingly, the effect of crack coalescence is reflected in the propagation behavior of the EV specimens. The rate of fatigue crack growth in the EV specimens was more rapid than in the EP specimens, and this led to a reduction in fatigue lives for the former as compared with the latter. In addition, a rolled magnesium alloy without the lamellar structure (designated as material R) was also tested. This type of microstructure is common for the AZ31 magnesium alloy. Two specimens with two different axial directions, parallel (RP specimen) or vertical (RV specimen) to the rolling direction, were prepared for testing. However, no differences in the fatigue behavior between the RP and RV specimens were observed. This result differs from that of the extruded materials, EP and EV. The rate of fatigue crack growth in the rolled specimen was more rapid than that of the EP specimens and led to a reduction in the fatigue lives as compared with the EP specimens. © 2007 Elsevier B.V. All rights reserved. Keywords: Magnesium alloy; Fatigue short crack; Crack initiation; Crack propagation; Microstructure
1. Introduction Magnesium alloys are very attractive as structural materials, because they are extremely light, possessing excellent specific tensile strength, good stiffness, and good vibrational absorption [1]. Due to their energy and weight saving characteristics, magnesium alloy are considered to be good candidates for material in, for example, auto parts, portable personal computers, and telephones. The demand for magnesium alloys in such applications has increased rapidly in recent years. Understanding the fatigue characteristics of magnesium alloys is vital when they are used as structural members. There are many studies on fatigue properties of magnesium alloy. For example, Goodenberger and Stephens [2] studied the fatigue behavior of a cast magnesium alloy, AZ91E-T6, in lab-
∗
Corresponding author. Tel.: +81 76 445 6771; fax: +81 76 445 6771. E-mail address: [email protected] (S. Ishihara).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.09.124
oratory air. Hilpert and Wagner [3] also studied the corrosion fatigue behavior of AZ80 magnesium alloys that had received various surface treatments, such as electro-polishing, grinding, machining, and shot-peening. They showed that the corrosion fatigue lives of the treated specimens were shorter compared to specimens in laboratory air. Eisenmeier et al. [4] studied the fatigue behavior of AZ91 magnesium alloy, which was processed using the vacuum die casting method. They reported that the fatigue cracks initiated from casting defects in the material, and that crack growth behavior was influenced by the microstructure of the material. Shih et al. [5] performed rotating bending fatigue experiments on the extruded magnesium alloy AZ61A. They reported that cracks initiated from inclusions, which existed on the specimen surface, or the vicinity of the surface, and that the initial crack growth behavior was affected by the specimen microstructure. The present authors investigated crack initiation and propagation behaviors during fatigue of the extruded magnesium alloy AZ31 in detail and discussed their relationship to fatigue lives [6,7].
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extruded direction. In addition, other crystals exist in both the A phase and B phase. They are designated D phase and C phase, respectively. In the alloy, a lamellar structure which is parallel to the extruded direction exists. This lamellar structure of the extruded material is not common for the AZ31 magnesium alloy. In the present study, the material will be designated as material E. 2.2. Rolled magnesium alloy A plate of rolled magnesium alloy AZ31 with a thickness of 15.8 mm was used for the present study. Its chemical composition is listed in Table 1(b). Fig. 1(b) shows the microstructure of the rolled magnesium alloy where the rolling direction is indicated. As seen from the figure, inclusions with an average diameter of 16 m are scattered in the matrix, which has an average crystal grain size of 20 m. The rolled magnesium alloy shown in Fig. 1(b) does not have the banded microstructures of the extruded magnesium alloy in Fig. 1(a). It is interesting to observe the ways in which S–N characteristic, crack initiation, and crack propagation behaviors of the rolled alloy differ from those of the extruded material. This type of microstructure is common for the AZ31 magnesium alloy. In the present study, the material will be designated as material R. Fig. 1. Microstructure of the AZ31 magnesium alloy.
2.3. EPMA analysis and X-ray diffraction As reviewed above, the fatigue characteristics of magnesium alloys produced by various techniques, such as rolling, casting and extrusion, have been the subject of numerous studies. However, their fatigue mechanisms have not been studied in detail. In the present study, fatigue experiments were carried out on both extruded and rolled magnesium alloy AZ31 to supplement information about the effect of microstructure on the fatigue behavior, specifically, the S–N characteristic, crack initiation, and crack propagation behavior. 2. Materials 2.1. Extruded magnesium alloy The AZ31 magnesium alloy used in the present study was prepared by extruding a round bar of diameter 88.9 mm into one of 19 mm diameter. Its chemical composition is listed in Table 1(a). Fig. 1(a) shows a photograph of the microstructure of the plane which is parallel to the extrusion direction. At the right side of the figure, a schematic illustration is attached as an explanation. As seen from this figure, a white layer (A phase) and a black layer (B phase) accumulate alternately parallel to the
Analysis of the chemical compositions of the microstructure and inclusions in the materials E and R was done using EPMA (Shimadzu, EPMA-1500) and X-ray diffraction equipment (Rigaku, RINT2200/PC/K). Hardness of the matrix and inclusions was measured using a Vickers micro-hardness tester (Akashi: HM-102). Widths of the A and B phases, and grain diameters of the C and D phases, were measured using an optical microscope. Table 2(a) shows identifications of the microstructures of the extruded and rolled magnesium alloys by EPMA analysis and X-ray diffraction. In the table, the sizes and hardnesses of the phases are also listed. As seen from the table, the white layer (A phase) and the black layer (B phase) observed in the material E (extruded alloy) of Fig. 1(a) are pure Mg and Mg32 (Al + Zn)49 , respectively. The C phase and D phases are Mg17 Al12 and Al81 Mn19 , respectively. The hardness for the D, B, and C phases are HV = 95, 91, and 81 kgf/mm2 , respectively. These hardnesses are clearly higher than those for the A phase, HV = 60 kgf/mm2 . Average dimensions of the phases, WA , WB , dC , and dD are 40, 24, 20, and 15 m, respectively, where WA and WB are width of the A and B phase, and dC and dD are grain diameters of the C phase and D phase, respectively.
Table 1 Chemical compositions of the material (wt%) Al
Zn
Mn
Fe
Ni
Cu
Si
Ca
Mg
(a) Material E (extruded magnesium alloy) 2.98 0.97 0.004
0.007
0.005
0.002
0.02
0.05
Balance
(b) Material R (rolled magnesium alloy) 2.5–3.5 0.7–1.3
0.005
0.005
0.002
0.05
0.04
Balance
0.2
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Table 2 Compositions and Vickers hardness of the phases Structure
Composition
Vickers hardness (kgf/mm2 )
Typical size (m)
(a) Material E (extruded magnesium alloy) A Mg 60 B Mg32 (Al + Zn)49 91 81 C Mg17 Al12 95 D Al81 Mn19 Structure
Composition
(b) Material R (rolled magnesium alloy) A Mg D Al81 Mn19
WA = 40 WB = 24 dC = 20 dD = 15 Vickers hardness (kgf/mm2 ) 57 93
The EPMA analysis of the material R (rolled magnesium alloy) revealed that the inclusions are the intermetallic compound (Al81 Mn19 system), and that Zn and Si particles distribute uniformly in the magnesium matrix. The inclusions designated as D are the same as in the extruded alloy. The hardness measurements show clearly that the inclusions (HV = 95) are harder than the matrix (HV = 58). 3. Specimens and experimental methods 3.1. Shapes of the specimens To study the influence of the rod-like structure which appeared in the material E (extruded magnesium alloy) of Fig. 1(a) on the fatigue behavior, two types of specimens were machined so that their axial directions were parallel and vertical to the rod-like structure. They were designated specimens EP and EV, respectively. Rotating bending fatigue tests were performed using the above specimens. The shape of the EP specimen is shown in Fig. 2(a). Its stress concentration factor is 1.04. Fig. 2(b) shows the shape of the EV specimen. Its stress concentration factor is 1.15. The fatigue experiments were performed by attaching a grip to both ends of the specimen as shown in Fig. 2(b). Two types of specimens were prepared, namely, the RP and RV specimens. In the former, the axial direction of the specimen is parallel, while in the latter it is vertical, to the rolled direction. The specimens were machined into the ASTM standard hourglass shape as shown in Fig. 2(c). Its stress concentration factor KT is 1.04.
Fig. 2. Shapes and dimensions of specimens.
3.2. Mechanical properties of the specimens Table 3 shows the mechanical properties of the specimens. In the table, the data for both the material E and material R are listed. Tensile tests were performed using specimens with gauge length of 3 mm and gauge diameter of 4 mm for the EP and EV specimens. For the RP and RV specimens, specimens with gauge length of 60 mm and gauge diameter of 12.5 mm were used. As seen in this table, tensile strength and yield strength of the EP specimens are about 17% greater than those of the EV specimen. This result indicates that the static strength is greater when the load is applied parallel to the extrusion direction than when it is applied vertical to the extrusion direction. On the other hand, for the material R (rolled material), a difference in the mechanical properties for the RP and RV specimens was
Table 3 Mechanical properties of the material Material
Yield strength (MPa)
Tensile strength (MPa)
Elongation (%)
Young’s modulus (GPa)
(a) Material E (extruded magnesium alloy) EP 200 EV 170
275 235
11 16
45 45
(b) Material R (rolled magnesium alloy) RP 140 RV 165
257 256
26 28
45 45
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not observed. Moreover, it is interesting that the mechanical properties of the material E (extruded material) were superior to those of the material R (rolling material). 3.3. Experimental methods The fatigue experiments were carried out in laboratory air with a humidity of 63–73% at room temperature using a cantilever rotating bending fatigue machine. Its cyclic speed was 30 Hz. During the fatigue tests, the temperature and humidity of the atmosphere was not strictly controlled. Some experiments were interrupted at fixed numbers of cycles to collect replicas of the specimen surface. The cyclic speed employed for these experiments, was 10 Hz. The crack initiation and propagation behavior during the fatigue process were investigated by observing these replicas with an optical microscope (OLYMPUS: BX51) at 400× magnification. To facilitate specimen surface observations, the smallest cross sections of all specimens were polished prior to testing into a mirror-like finish using emery paper and diamond paste. 4. Experimental results 4.1. S–N curves Fig. 3(a) shows the S–N curves for the EP and the EV specimens in laboratory air at a stress ratio of −1 and frequency of 30 Hz. As seen from this figure, in the EP specimen, a clear horizontal part can be observed from N = 105 –107 cycles at stress amplitude of 120 MPa. On the other hand, in the EV specimen, the horizontal part is observed at a stress amplitude of 95 MPa. So the fatigue limit decreased by about 20% in the EV specimen as compared with the EP specimens. Further, in the high stress amplitude region, the fatigue life of EV specimens was shortened to about 1/10 of that of EP specimens. So, it is clear that the EP specimen possesses a superior fatigue resistance in both fatigue limit and fatigue lives. Fig. 3(b) shows S–N curves for the RP and RV specimens (rolled magnesium alloy) in laboratory air. In this figure, for comparison purposes, the S–N curves of the EP and EV specimens (extruded magnesium alloy) are shown by solid and broken lines, respectively. As seen from the figure, the fatigue life of the rolled magnesium alloy is relatively shorter than that of the EP specimen, but almost the same as the EV specimen. The extent
Fig. 3. S–N curves of the AZ31 magnesium alloys.
of bending in the S–N curve is gentler in the rolled and EV specimens than in the EP specimen. Next let us compare the S–N characteristics of the RP and RV specimens. There are no great differences in the fatigue lives and in the fatigue limits, except that at the higher stress amplitudes, there are some differences in the fatigue lives. 4.2. Successive observations of the fatigue process The fatigue process was investigated in detail for the purpose of illustrating the fatigue characteristics of the extruded
Fig. 4. Successive observations on the specimen surface during the fatigue process (EP specimen, σ a = 122.5 MPa).
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Fig. 5. Successive observations of the specimen surface during the fatigue process (EV specimen, σ a = 120 MPa). (a) Nf = 27,000 cycles and (b) Nf = 36,000 cycles.
and rolled magnesium alloys. Accordingly, successive observations of the specimen surface were conducted at several stress levels to study the effect of the material microstructure on the fatigue lives. In order to distinguish the reasons for differences in the fatigue lives of the EP specimen and EV specimen, the fatigue processes of both specimens were continuously observed for the range of stress amplitudes 95–122.5 MPa. Fig. 4 shows the result of successive observations of the specimen surface during the fatigue process for an EP specimen at a stress amplitude of 122.5 MPa. In order to examine the interaction between crack initiation and propagation behavior and the microstructure of the specimen, the fatigue experiment included pre-revealing the microstructure by etching. In the figure, the crack tips are shown by arrows. As seen from the figure, a crack initiated at the C phase, Fig. 4(b), joined with another crack, Fig. 4(c), and then propagated into the next phase, Fig. 4(d). The crack propagation rate decreased and the direction of crack propagation turned to the side when the crack crossed into the B phase, Fig. 4(e).
Fig. 5 shows the result of successive observations of the specimen surface during the fatigue process of an EV specimen at a stress amplitude of 120 MPa. As seen from Fig. 5(a), multiple cracks, 1, 2, 3, that initiated in the A phase propagated when short in isolation, with no interaction between them. However, as shown in Fig. 5(b), the multiple cracks coalesced with each other when they propagated farther. Such crack coalescence was observed at other stress amplitudes also. When compared to EP specimens, we see that more cracks occur during the fatigue process in EV specimens. For the rolled material, successive observations during the fatigue process were conducted for only RP specimens, since there were no significant differences in the S–N curves for RP and the RV specimens. Fig. 6(a) and (b) shows the results of successive observations at stress amplitudes 105 and 110 MPa, respectively. As seen from the figures, fatigue cracks initiated from the interface between Al–Mn inclusions and the Mg matrix at an early stage of the fatigue life. This result was commonly observed for stress amplitudes 105 and 110 MPa. Therefore, the fatigue life of this magnesium alloy is predominately the crack propagation life. The fatigue crack propagated almost linearly and not in a zigzag manner. This fatigue crack morphology observed in this magnesium alloy is different from that in aluminum alloys [8]. 4.3. Crack propagation behavior 4.3.1. 2a versus (N/Nf ) relations Fig. 7(a)–(c) shows the variations of crack length, 2a, measured from successive observations as a function of fatigue life ratio N/Nf for the EP, EV and RP specimens, respectively. As seen in Fig. 7(a) for the EP specimen, a stress amplitude dependency was not clearly observed in the 2a versus N/Nf relation. Also, a crack with a length of about 20 m initiated at 5–6% of the fatigue life at stress amplitudes 122.5 and 140 MPa. On the
Fig. 6. Successive observations on a specimen surface during the fatigue process (RP specimen).
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3 coalesced at 35% of the fatigue life, and afterwards the joined crack coalesced with Crack 1 at 45% of the fatigue life. Cracks 5 and 6 coalesced at 65% of the fatigue life, and afterwards the joined crack coalesced with Crack 4 at 75% of the fatigue life. Moreover, Crack 7 propagated as a single crack without coalescing with other cracks. As mentioned above, the crack initiation and propagation behavior in the EV specimen was different from that of the EP specimen in the following ways: cracks initiated at C phase inclusions within the B phase in EP specimens, while in EV specimens, cracks initiated from D phase inclusions within the A phase. Moreover, crack coalescence was caused by many cracks initiating during the fatigue process in EV specimens, while in EP specimens, crack coalescence did not readily occur, since crack initiation was limited. Fig. 7(c) shows the variation of the main crack length determined by successive observations as a function of fatigue life ratio N/Nf , the main crack being the crack that propagated to cause final failure of the specimen. In this figure, the data for three different stress amplitudes are plotted. As seen from the figure, the fatigue crack initiated at an early stage of fatigue life regardless of the stress amplitude. Therefore, the total fatigue life can be considered as equal to the crack propagation life. Also, the effect of stress amplitude on the relation 2a–N/Nf was not readily evident for stress amplitudes over the range 105–120 MPa. These observed trends in the rolled material are similar to those in the extruded material. 4.3.2. Relations of da/dN versus K Fig. 8(a)–(c) show the relationships between the rate of crack propagation, da/dN, and stress intensity factor range, K, for EP, EV and RP specimens, respectively. For the calculation of K for the EP and RP specimen, the following expression was used. √ K = 1.04Yσa πa
(1)
where the value 1.04 is a stress concentration factor due to the notch from the specimen radius of 20 mm. Further, Y = 0.73 is a correction factor for a surface crack with a semicircular shape, and a is the half crack length. For the EV specimen, the following expression was used for the calculation of K. Fig. 7. Variations of crack lengths as a function of fatigue life ratio N/Nf .
other hand, at stress amplitude 130 MPa, a crack with a length of about 20 m initiated at 30% of the fatigue life. However, it is possible that more detailed observations would show that cracks initiated earlier than was observed. From the above experimental result, it is concluded that the total fatigue life is almost the same as the crack propagation life. Fig. 7(b) shows variations of crack length, 2a as a function of the fatigue life ratio N/Nf in the EV specimen. The data at stress amplitude 120 MPa are plotted in the figure. As seen from the figure, a crack with a length of about 10–30 m initiated at 5–6% of the fatigue life. At stress amplitude 120 MPa, a number was assigned to each of the cracks, since multiple cracks were observed during the fatigue process. Coalescence of cracks occur at positions C in the figure. Cracks 2 and
√ K = 1.15Yσ πa
(2)
where the value 1.15 is a stress concentration factor due to the notch from the 4 mm radius. As seen from Fig. 8, threshold behavior is not clearly seen in the da/dN versus K relations. However, we observed experimentally existences of non-propagating cracks with a length of about 15 m or so at the fatigue limits of the EP, EV and RP specimens. After measuring the non-propagating crack lengths, we evaluated the threshold stress intensity factors Kth for each of the specimens by substituting both the non-propagating crack length and fatigue limit into Eq. (1) for the EP and RP specimens, and Eq. (2) for the EV specimen. As seen in Fig. 8(a), stress amplitude dependency in the da/dN versus K relation of the EP specimen was not clearly evident within the range of stress amplitudes 122.5–160 MPa.
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EV specimen. The solid line in the figure is the approximated curve represented by the next expression. √ da 2 = A(1.15Yσa πa − Kth ) dN
(4)
where A = 9 × 10−9 MPa−2 cycle−1 and Kth = 0.35 MPa m1/2 are material constants of the EV specimen. As seen from the figure, the relation da/dN versus K for the EV specimen can be approximated by expression (4). For comparison purposes, the da/dN versus K relation for the EP specimen is also shown by the broken line in the figure. As seen from the figure, the crack growth rate for the EV specimen is faster than that for the EP specimen at a constant K level. And the threshold level for the crack propagation Kth for the EV specimen (0.35 MPa m1/2 ) is lower than that for the EP specimen (0.44 MPa m1/2 ). Fig. 8(c) shows a log–log plot of the relationship between stress intensity factor range K and crack growth rate da/dN for the RP specimen. The relation for the EP specimen is also shown by a solid line in the figure for comparison purposes. At the low stress intensity factors, the crack growth rate for the rolled magnesium alloy was more rapid than for the EP specimen. In the figure, the same relation for long through cracks in the rolled magnesium alloy AZ31 is shown by the broken line. The data was investigated by Tokaji et al. [9] at stress ratio, R = 0.05. There is an effect of the stress amplitude in the da/dN–K relation. The crack growth rates at the higher stress amplitude were more rapid than at the lower stress amplitudes. This was due to the low yield stress of the rolled material. The plastic zone size ahead of the crack tip increased and could not be neglected when compared to the total crack length. Such a deviation from the small scale yielding condition is often observed in low strength materials. 5. Discussion 5.1. Effect of microstructure on the crack initiation behavior
Fig. 8. Fatigue crack growth rate as a function of K.
The relation can be approximated by the following expression which is indicated by the solid line. √ da 2 = A(1.04Yσa πa − Kth ) dN
(3)
where A = 7 × 10−9 MPa−2 cycle−1 and Kth = 0.44 MPa m1/2 are material constants for the EP specimens. Fig. 8(b) shows the relationship between the rate of crack propagation, da/dN and stress intensity factor range, K for the
Fatigue cracks initiated at the top and bottom edges of C phase inclusions within the B phase in EP specimens. On the other hand, the crack was observed as initiating from D phase inclusions within the A phase in EV specimens. Discussion of crack initiation phenomena at an arbitrary point should include consideration of both the stress and the crack initiation strength at that point. Crack initiation occurs when the stress is greater than the crack initiation strength, and the reverse is true. Here we assume that crack initiation strength for the A, B, C, and D phases are equal, since they are not known at present. In the following, we will consider only the amount of stress. Microstructures of the EP and the EV specimens can be simply modeled by parallel and series springs, respectively, as shown in Fig. 9(a) and (b). These models are composed of a soft spring (the A phase, spring constant = kA ) and a hard spring (the B phase, spring constant = kB ), where kB > kA . In the parallel spring model for EP specimens of Fig. 9(a), we assume that the model is pulled to the right and left under
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and D phase by the stress concentration due to the displacement. As a result, flaking off or breaking of the D phase may occur, leading to crack initiation at the interface between the A and D phases. In the case of the RP specimen (rolled magnesium alloy), fatigue cracks were observed as initiating from the D phase inclusions within the A phase. In the RP specimen, the D phase (hard) exists within the soft matrix (A phase). When an external force is applied to this material system, it is expected that intense stress will be induced at the interface between the A and D phases by local stress concentration. As a result, flaking off or breaking of the D phase inclusions may occur and lead to crack initiation at the interface between the A and D phases, as in the case of the EV specimen.
Fig. 9. Microstructure model for EP and EV specimens that contain the rod-like structure.
constant displacement. In this case, the load applied to the B phase (hard) becomes obviously greater than that applied to the A phase (soft). In EP specimens, there is a softer phase named C that is surrounded by the harder phase B, as shown in Fig. 1(a). When an external force is applied to this system, a large stress is generated by the stress concentration at the interface between the C and B phases. As a result, a fatigue crack may initiate at the top and bottom edges of the C phase inclusions within the B phase. In the case of the EV specimen modeled in Fig. 9(b), let us consider that a series spring model is pulled under a constant load condition. In this case, the displacement occurring at the A phase (soft) becomes greater than that at the B phase (hard). In the EV specimen, the D phase (hard) exists within the A phase (soft) as shown in Fig. 1(b). It is expected that a large amount of stress will be induced at the interface between the A phase
5.2. Effect of microstructure on the crack propagation behavior It was observed that resistance to crack propagation in EP specimens was clearly higher than in EV specimens, and it was observed that resistance in EV specimens was almost equal to that in RP specimens. In EP specimens (material E), there is a rod-like structure parallel to the extrusion direction as shown in Fig. 1(a). This structure is harder than the matrix (A phase) and therefore possesses higher crack propagation resistance. As shown in the schematic illustration of Fig. 10(a), in EP specimens, cracks propagated and crossed the hard rod-like structure. However, in EV specimens (Fig. 10(b)), cracks propagated within the A phase without crossing the rod-like structure. In EP specimens, the rod-like structure acted as a barrier to crack propagation and provided higher resistance to crack propagation than in EV specimens. In RP specimens (material R), the rodlike structure does not exist as shown in Fig. 1(c). So, the crack propagation resistance for this material is almost equal to that of EV specimens.
Fig. 10. Schematic illustration of crack initiation and propagation behavior in the EP, EV and RP specimens.
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6. Conclusions Completely reversed fatigue experiments were conducted on smooth specimens of two kinds of AZ31 magnesium alloys, to study the effect of microstructure on crack initiation and propagation behavior during the fatigue process. The conclusions obtained can be summarized as follows: (i) Fatigue lives and the fatigue limit of EP specimens were higher than those of EV specimens and RP specimens. There was a sharp bend in the S–N curve for EP specimens as compared to EV and RP specimens. (ii) In both materials E and R of AZ31 magnesium alloy, cracks initiated at an early stage of the fatigue process. Therefore, fatigue life and crack propagation life can be considered as equal in length. In EP specimens, fatigue cracks initiated at the top and bottom edges of the C phase within the B phase; however in EV and R specimens, cracks were observed to initiate from the D phase within the A phase. (iii) Crack propagation resistance of EP specimens was superior to that of EV and RP specimens. Crack propagation resistance for EV and RP specimens was almost equal. (iv) In EP specimens, cracks propagated with crossing the rodlike structure, On the other hand, in EV and RP specimens, cracks propagated without crossing the rod-like structure. This rod-like structure acted as a barrier to crack propaga-
tion and provided superior crack propagation resistance in EP specimens. Acknowledgements The authors express their thanks to Prof. Arthur J. McEvily at The University of Connecticut for valuable discussions during the course of the present study. Thanks go also to Prof. Hiroshi Shibata and Dr. Masayoshi Shimizu for their valuable advice during the study. References [1] Y. Kojima, Handbook of Advanced Magnesium Technology, Kallos Publishing C., L., Tokyo, Japan, 2000. [2] D.L. Goodenberger, R.I. Stephens, J. Eng. Mater. Techn. 115 (1993) 391–397. [3] M. Hilpert, L. Wagner, J. Mater. Eng. Perform. 9 (2000) 402–407. [4] G. Eisenmeier, B. Holzwarth, H.W. H¨oppel, H. Mughrabi, Mater. Sci. Eng. A 319 (2001) 578–582. [5] T.S. Shih, W.S. Liu, Y.J. Chen, Mater. Sci. Eng. A 325 (2002) 152–162. [6] Z.Y. Nan, S. Ishihara, T. Goshima, R. Nakanishi, Scripta Mater. 50 (4) (2004) 429–434. [7] Z.Y. Nan, S. Ishihara, T. Goshima, R. Nakanishi, F. Nilsson (Eds.), Proceedings of the 15th European Conference of Fracture (CD-ROM), Stockholm, Sweden, August 11–13, ESIS, Torino, Italy, 2004. [8] H. Nisitani, Fatigue Strength, Ohmsha, Tokyo, Japan, 1985. [9] K. Tokaji, M. Kamakura, N. Hasegawa, Y. Tsuboi, J. Soc. Mater. Sci. Jpn. 52 (2003) 821–826.