Cyclic deformation behavior of a super-vacuum die cast magnesium alloy

Materials Science and Engineering A 546 (2012) 72–81

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Cyclic deformation behavior of a super-vacuum die cast magnesium alloy H.A. Patel a , N. Rashidi a , D.L. Chen a,∗ , S.D. Bhole a , A.A. Luo b a b

Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario M5B 2K3, Canada General Motors Global Research and Development Center, Warren, MI 48090, USA

a r t i c l e

i n f o

Article history: Received 14 December 2011 Received in revised form 2 March 2012 Accepted 8 March 2012 Available online 21 March 2012 Keywords: Magnesium alloy Super-vacuum die cast Low cycle fatigue Pseudoelasticity Strain ratio Twinning

a b s t r a c t Magnesium alloy as a lightweight structural material has recently kindled considerable interest in the automotive and aerospace industries, since lightweighting is considered as one of the salient strategies in reducing fuel consumption and anthropogenic greenhouse gas emissions. The structural applications of magnesium alloys inevitably involve fatigue resistance. This study was aimed at evaluating cyclic deformation behavior and fatigue life of a super-vacuum die cast (SVDC) AM60B alloy using straincontrolled low cycle fatigue tests at two strain ratios of Rs = −1 and Rs = 0.1. The SVDC AM60B alloy exhibited a superior fatigue resistance to the conventional die cast AM60 alloy especially in the high-cycle fatigue region. Fatigue life was longer at Rs = −1 than at Rs = 0.1 at lower strain amplitudes. With increasing total strain amplitude, cyclic stress amplitudes increased, hysteresis loops exhibited a clockwise rotation despite the symmetry in tension and compression at Rs = −1, and fatigue life and psuedoelastic modulus decreased at both strain ratios. Cyclic hardening increased with increasing strain amplitude and strain ratio due to the formation of more twins and their interaction with dislocations. Two types of twins (wider lenticular extension twins and narrower banded contraction twins) were observed in some favorably oriented large ␣-Mg cells near the fracture surface. Mean stress relaxation occurred mainly within the initial 10–30% of fatigue life. Cyclic hardening exponent was higher than monotonic hardening exponent. Fatigue crack initiation occurred from the specimen surface or near-surface defects, and crack propagation was mainly characterized by fatigue striations coupled with some secondary cracks and tear ridges. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Weight reduction is considered as a primary design metric for increasing fuel efficiency and improving performance of the automotive and aircraft systems [1–5]. The low density of magnesium (Mg) alloys combined with their reasonable strength, excellent machinability and castability makes them attractive for structural applications [1,6]. Most Mg components are produced by casting processes. Die cast AM50 and AM60 Mg alloys are rapidly growing in the automotive applications such as door inners and instrument panel beams [7]. Previous studies involved monotonic [8–11] and creep [12–14] properties of die cast Mg alloys. The applications of Mg alloys in the transportation vehicles involve unavoidably the fatigue and cyclic deformation due to the fact that they are subjected to cyclic stresses and strains. Hence, it is necessary to evaluate the cyclic deformation resistance of these Mg alloys. A lot of investigations have been conducted on fatigue behavior of Mg alloys in the last decade or so, including pure polycrystalline magnesium [15], wrought alloys AZ31 [16–28], AZ61A [29,30], AM30 [31,32] and ZK60 [33–35], and cast alloys AZ91 [36–41],

∗ Corresponding author. Tel.: +1 416 979 5000x6487; fax: +1 416 979 5265. E-mail address: [email protected] (D.L. Chen). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.03.028

AM60 [5,6,41–43], AM50 [44–46]. Most previous work on the fatigue of cast AM60 alloy was focused on the load-controlled S–N curves [42,43,47,48]. Kulyasova et al. [42] and Islamgaliev et al. [43] reported the microstructures and fatigue properties of an ultrafine-grained AM60 Mg alloy processed by equal-channel angular pressing (ECAP) tested at constant stress amplitudes at R = 0.1 and various temperatures. Renner and Zenner [49] investigated the effect of different rib thicknesses and notch radii on the fatigue strength of die cast AZ91 and AM60 alloy under constant amplitude bending stresses at a stress ratio of R = 0. Gall et al. [50–52] examined the growth of microstructurally small fatigue crack in die cast AM60B alloy cycled under both high vacuum and water vapour environments. Zeng et al. [53,54] studied constant load amplitude fatigue crack propagation of extruded and rolled AM60 alloy at a load ratio of R = 0. The effect of two different HPDC manufacturing processes on microstructure, tensile and fatigue properties of AM60 Mg alloy were investigated by Kang and Ostrom [7]. Mayer et al. [55] evaluated the influence of porosity on stress-controlled high cycle fatigue properties of HPDC Mg alloys AZ91, AM60, AE42, AS21 and Al alloy AlSi9 Cu3 using ultrasonic fatigue tests at a stress ratio of R = −1 and a frequency of 20 kHz. Some limited strain-controlled low cycle fatigue (LCF) tests on the conventional die cast AM60 alloy have also been reported. El Kadiri et al. [5] and Horstemeyer et al. [6] conducted fully reversed

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(Rs = −1) strain-controlled fatigue tests of die cast AM60B Mg alloy, with focus on the micro-mechanisms of fatigue crack nucleation and growth. Lee et al. [56,57] performed fatigue tests at total strain amplitudes ranging between 0.1% and 0.6% with Rs = −1 on a HPDC AM60 alloy produced with different processing parameters to study the effects of macro-segregation on the fatigue behavior. Xu et al. [58] studied the cyclic stress–strain behavior using straincontrolled fatigue testing, where different R-ratios ranged from 0.1 to 0.7 at a strain amplitude of 0.3% was applied in order to examine the effect of R-ratio on the mean stress relaxation. While there were lots of reports on the stress-controlled S–N curves and some reports on the strain-controlled LCF behavior of cast AM60 alloy [5,6,56–58], they were basically limited to pressure die castings. Recently, super-vacuum die casting (SVDC), a special high integrity die casting process, has been developed to produce high integrity parts with less porosity by removing trapped gas cavities using vacuum and improve monotonic mechanical properties as reported for AZ91 Mg alloy [59,60]. Some studies on the thermal fatigue behavior of vacuum die cast AZ91 Mg alloy have also been reported [61,62]. However, to the authors’ knowledge, no reports have been seen on the low cycle fatigue behavior of SVDC AM60B alloy. In most Mg alloys some non-linear elastic behavior, also referred to as pseudoelasticity [16–19,31,33,34,63], was observed that led to hysteresis loops in the die cast Mg alloys [39,45] being different from the typical hysteresis loops in most metals. Furthermore, the tension–compression asymmetry reflected directly by the hysteresis loops of wrought Mg alloys was associated with the presence of strong crystallographic texture and the resultant twinning–detwinning [16–19,31–33]. Currently more and more efforts are being made to reduce such asymmetry and understand the deformation mechanisms so as to expand the structural applications of Mg alloys. However, in the SVDC AM60B alloy, it remains unclear if the psuedoelastic behavior and twinning would still occur during cyclic deformation, how the hysteresis loops are influenced by the strain ratio, and what the effects of the applied strain ratio on fatigue parameters are. The objective of the present investigation was, therefore, to evaluate the cyclic deformation characteristics under two different strain ratios and to identify the role of twinning in a SVDC AM60B alloy. 2. Materials and experimental procedure The SVDC AM60B alloy in the present investigation, with a nominal composition of 6.0% Al, 0.13% Mn and the balance Mg, was supplied by General Motors (GM) and had a thickness of 2 mm. Metallographic samples were cut and cold-mounted with LECO 7007 resin powder. The mount was ground with SiC sand papers with a grit number of 320, 600, 800, and 1200, respectively. Water was used as lubricant in each grinding steps. Polishing was carried out with 6 ␮m and 1 ␮m diamond paste using diamond extender as lubricant. The polished samples were ultrasonically cleaned in ethanol, followed by drying with compressed air. After the final polishing with 0.05 ␮m alumina paste, the samples were etched with Acetic-Picral solution (10 ml acetic acid, 4.2 g picric acid, 10 ml distilled water, and 70 ml ethanol) to reveal the microstructure. The microstructure and fracture surfaces were examined using a scanning electron microscope (SEM) equipped with energy dispersive X-ray spectroscopy (EDS). Sub-sized specimens following ASTM E8 standards were machined with dimensions of 140 mm (L) × 9.5 mm (W) × 2 mm (T) for both tensile and fatigue tests. The tensile samples had a gauge length of 25 mm and a cross section of 6 mm × 2 mm in the gauge area, while the fatigue samples had a gauge length of 12.5 mm and a cross section of 2 mm × 2 mm in the gauge area. The gauge area was ground with SiC papers up to a grit number of 600 to prevent surface irregularities.

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Fig. 1. Typical SEM micrograph with EDS line scan of the SVDC AM60B alloy, (a) overall view, and (b) magnified view of the compositional variation.

Tensile tests were conducted using a computerized United tensile testing machine at a strain rate of 1 × 10−2 s−1 . LCF tests were performed under total strain control using computerized Instron 8801 servo-hydraulic testing system at a constant strain rate of 1 × 10−2 s−1 and room temperature of 25 ◦ C. A triangular strain waveform was applied during the tests. Two different strain ratios of Rs = −1 and 0.1 were applied at total strain amplitudes ranging from 0.1% to 0.8% and two samples were tested at each level. The strain-controlled tests at lower total strain amplitude levels were continued up to 104 cycles, and then changed to load control with a frequency of 50 Hz, using sine waveform and maintaining the same stress amplitude and mean stress at 104 cycles. The fracture surfaces of fatigued specimens were examined using SEM to identify fatigue crack initiation sites and propagation mechanisms. 3. Experimental results 3.1. Microstructure and tensile properties Fig. 1(a) and (b) shows a typical SEM image of the SVDC AM60B alloy and EDS line scan across the microstructural features. The microstructure consisted of ␣ (Mg) cell surrounded by the Al-rich eutectic layer at the boundary where ␤ (Mg17 Al12 ) precipitated. The EDS line scan revealed depletion of Al content from the cell boundary towards the cell center and some Al peaks found across the eutectic layer, where Mn was below the detention level. Across the

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Table 1 Monotonic tensile properties of the SVDC AM60B alloy tested at a strain rate of 1 × 10−2 s−1 . YS (MPa)

UTS (MPa)

%El

E (GPa)

n

K (MPa)

137

260

12.2

42.8

0.24

473

relatively large white particle in Fig. 1(a) both Al and Mn concentrations increased, while Mg concentration decreased, indicating that this particle was an Al–Mn containing inclusion. These Al–Mn rich particles were present in the form of Al8 Mn5 . Similar particles were reported in AM series Mg alloys [5,6,42,44,64,65], irrespective of the processing route of either casting or extrusion. The tensile properties determined at a strain rate of 1 × 10−2 s−1 are listed in Table 1. It should be mentioned that for the die cast AM60B alloy, ASTM standard (B94-07) specifies an ultimate tensile strength (UTS) of 220 MPa, yield strength (YS) of 130 MPa, and elongation of 8%. It is seen from Table 1 that both the strength (YS and UTS) and ductility of the SVDC AM60B alloy exceeded the data specified in the ASTM standard. The obtained tensile properties were also in agreement with those reported in [59,60] for vacuum die cast AZ91 alloy, suggesting that the improved tensile properties were due to less porosity in this process compared to non-vacuum or conventional die cast processes. 3.2. Cyclic stress response behavior Fig. 2(a) and (b) shows the variation of stress amplitude with respect to the number of cycles for different total strain amplitudes at strain ratio of Rs = −1 and Rs = 0.1, respectively. It is seen that as the total strain amplitude increased, the stress amplitude and the amount of strain hardening increased, while fatigue life decreased at both strain ratios. As shown in Fig. 2(a), for Rs = −1 at a higher total strain amplitude of 0.8%, the alloy showed cyclic hardening characteristics throughout the fatigue life. For other total strain amplitudes (from 0.6% to 0.2%) the alloy showed slightly initial cyclic softening followed by cyclic hardening for the remaining life, and the amount of cyclic softening and their effect on fatigue life reduced with increasing strain amplitudes in that range. It is seen from Fig. 2(b) that no cyclic softening occurred in the Rs = 0.1 tests at all total strain amplitudes applied from 0.1% to 0.8%. The stress amplitude remained basically constant at a low strain amplitude of 0.1%. At intermediate strain amplitudes of 0.2–0.4%, the increase of the initial stress amplitude appeared slightly slower as cyclic deformation progressed, followed by stronger cyclic hardening (steeper slope) before failure. At higher strain amplitudes (0.6% and 0.8%) the alloy showed stronger initial cyclic hardening which slowed slightly and then increased again until failure. Similar cyclic hardening behavior has been documented for die cast AZ91 alloy in as-cast and heat-treated conditions [38,39], and some extruded AZ31 [17,18] and AM30 [31] alloys under strain-controlled low cycle fatigue tests. Xu et al. [66] observed hardening effect in the fine-grained HPDC AM50, AE44, AJ62A Mg alloys and softening effect in the coarse-grained LPDC AM50 alloy. This study also indicated that twinning was the main cause for both the hardening and softening behavior, which will be discussed later. The change in the mean stress at different strain ratios is shown in Fig. 3 at a total strain amplitude of 0.6%, where the mean stress was plotted as a function of a normalized number of cycles (or cycle ratio, N/Nf ). The value of mean stress was higher at Rs = 0.1 while the value of mean stress at Rs = −1 was nearly zero which corresponded to mean strain that was zero for completely reversed (Rs = −1) strain tests. However, the variation trend at both strain ratios was the same, where the main part of the mean stress relaxation occurred in the initial 10–30% of fatigue life, then the mean stress almost linearly decreased, and finally decreased drastically again prior to

Fig. 2. Variation of stress amplitude vs. number of cycles at different total strain amplitudes at a strain ratio of (a) Rs = −1, and (b) Rs = 0.1.

failure. The results are in good agreement with those reported in die cast AZ91E-T4 [67] and AM50 [45] Mg alloys. Xu et al. [58] also studied the cyclic relaxation of die cast AM60 alloy with a R-ratio ranging from 0.1 to 0.7 at a strain amplitude of 0.3% and showed

Fig. 3. Mean stress vs. normalized number of cycles (N/Nf ) at a total strain amplitude of 0.6% for different strain ratios of Rs = −1 and Rs = 0.1.

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Fig. 4. Change in the 1st, 2nd and mid-life hysteresis loops at a total strain amplitude of 0.8% and strain ratio of (a) Rs = −1 and (b) Rs = 0.1.

that the mean stress relaxation increased with increasing R-ratio, which is in agreement with the result shown in Fig. 3. 3.3. Hysteresis loops The hysteresis loops for the 1st, 2nd and mid-life cycles at a total strain amplitude of 0.8% are shown in Fig. 4(a) and (b) at strain ratios of Rs = −1 and Rs = 0.1, respectively. Compared with the 1st or 2nd hysteresis loop, the mid-life loop at Rs = −1 showed slightly cyclic hardening, which was in agreement with Fig. 2(a). At Rs = −1 the loops were fairly symmetrical with respect to X-axis, corresponding to the small or nearly zero mean stress (Fig. 3). On the other hand, at Rs = 0.1 the 1st hysteresis loop was asymmetric with a large amount of plastic deformation in the tensile phase, as seen from Fig. 4(b). While the maximum peak stress for the 2nd cycle remained nearly the same as that for the 1st cycle, the minimum peak stress became lower. This implied that cyclic hardening occurred (Fig. 2) and also that the mean stress decreased (Fig. 3). Indeed this is seen from the mid-life loop where it shifted downwards and the stress amplitude (or range) became larger, and corresponded well to the cyclic hardening shown in Fig. 2. Such a shift of hysteresis loops at Rs = 0.1 was related to the mean stress relaxation. With increasing number of cycles from the 1st cycle to mid-life, the maximum stress decreased from ∼200 MPa to ∼175 MPa, but the minimum stress also increased (in the sense of absolute values) from ∼−110 MPa to ∼−160 MPa. Thus a difference of 25 MPa between the decrease in the maximum stress and the increase in the minimum stress

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Fig. 5. Typical mid-life hysteresis loops at different total strain amplitudes at strain ratios of (a) Rs = −1 and (b) Rs = 0.1.

appeared, indicating the presence of cyclic hardening as seen in Fig. 2(b). Fig. 5(a) and (b) shows the effect of total strain amplitudes on the shape of mid-life hysteresis loops at strain ratios of Rs = −1 and Rs = 0.1, respectively. It is seen that the hysteresis loops became larger in both height and width with increasing total strain amplitude, and tended to exhibit a clockwise rotation at both strain ratios, which were not present in the common fcc metals such as copper, nickel and aluminum. However, unlike the asymmetric hysteresis loops in extruded Mg alloys [16–18,31], all hysteresis loops in the SVDC AM60B alloy tested at Rs = −1 were almost symmetrical during tension and compression. The majority of non-linear change of the descending half loop at the mid-life might be described by different modulus (E1 , E2 , E3 , . . ., Ex ), as indicated in Fig. 4(a), and such a non-linear variation was indeed very different from the typical hysteresis loops of fcc metals. 3.4. Change of elastic modulus during cyclic deformation The non-linear response of hysteresis loops posed a complex issue to engineers who try to design structural components on the assumption of a constant value of elastic modulus. To study this non-linear response in relation to the total strain amplitude applied, the variation of elastic modulus during cyclic deformation of SVDC AM60B alloy was evaluated. Fig. 6(a) and (b) shows the change in elastic modulus over the fatigue life in loading and

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Fig. 6. Effect of total strain amplitudes on (a) loading modulus and (b) unloading modulus during cyclic deformation at a strain ratio of Rs = −1.

unloading phases (i.e., E1 in both ascending and descending phases as shown in Fig. 4(a)) at a strain ratio of Rs = −1, respectively. It is seen that both loading and unloading moduli decreased with increasing total strain amplitude, corresponding to the clockwise rotation shown in Fig. 5. The similarity in the loading and unloading moduli reflected the symmetrical hysteresis loops in tension and compression, as shown in Figs. 4(a) and 5(a). A similar tendency of decreasing modulus with increasing strain amplitude was observed at Rs = 0.1 as well. At lower total strain amplitudes (0.2–0.4%) both loading and unloading moduli remained nearly constant within the experimental scatter throughout the fatigue life, while at higher total strain amplitudes (0.6% and 0.8%) both moduli increased in the entire fatigue life until failure, and the rate (or slope) increased with increasing total strain amplitude in the semi-log scale. This could be understood by the stronger cyclic hardening that occurred at higher total strain amplitudes (Fig. 2(a)). Similar observations of the decrease in the elastic moduli with increasing strain amplitude were also reported for HPDC AZ91 [63] and extruded Mg alloys [17,18,31]. 3.5. Fatigue life and LCF parameters The fatigue life (i.e., the number of cycles to failure, Nf ) as a function of the applied total strain amplitude (εt /2) for the SVDC AM60B alloy tested at both strain ratios (Rs = −1 and 0.1) is presented in Fig. 7(a). Run-outs were indicated by arrows pointing

Fig. 7. (a) Fatigue lifetime and (b) specific strain amplitudes at the mid-life cycles as a function of the number of reversals to failure at a strain ratio of Rs = −1 and Rs = 0.1 for the SVDC AM60B alloy.

diagonally upward at or more than 107 cycles. The alloy showed a similar trend of increasing fatigue life with decreasing total strain amplitudes at both strain ratios. Though both tests showed an equivalent fatigue life within the experimental scatter at higher total strain amplitudes (≥0.4%), fully reversed strain ratio (Rs = −1) tests gave a longer fatigue life at lower total strain amplitudes (<0.4%). For instance, at a total strain amplitude of 0.2% three samples did not fail up to 107 cycles out of four samples tested at Rs = −1, while only one sample reached 107 cycles without failure and other three samples failed well before 107 cycles at Rs = 0.1. The tests at Rs = 0.1 were continued at a further lower level of strain amplitude of 0.1%, where the two run-out samples were seen. The results of fully reversed strain-controlled tests at Rs = −1 in the present investigation were in good agreement with the data reported in the literature of die cast AM60 alloy with similar test conditions [5,6]. It is well known that tensile mean stress had a detrimental effect on the fatigue resistance by the mechanisms of accelerating the crack initiation and propagation, while the reverse was true for compressive mean stress [68]. This is true since Rs = −1 showed nearly zero to compressive mean stress, thus giving rise to a longer fatigue life compared to Rs = 0.1 with high tensile mean stress (Fig. 3). The total stain amplitude (εt /2), plastic stain amplitude (εp /2), and elastic stain amplitude (εe /2) vs. the number of reversals (2Nf ) in the present SVDC AM60B alloy are plotted in Fig. 7(b), where the values of individual strain amplitudes were

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taken from the relevant mid-life stress–strain hysteresis loops. As described in [69,70], the total strain amplitude could be obtained by the superposition of elastic strain component known as the Basquin relation and plastic strain component known as Coffin–Manson relation, i.e., f

εp εt εe = + = (2Nf )b + εf (2Nf )c , 2 2 2 E

(1)

where f is the fatigue strength coefficient, b is the fatigue strength exponent, εf is the fatigue ductility coefficient, c is the fatigue ductility exponent, and E is the elastic modulus. As seen from Fig. 7(b), the tests at both strain ratios followed the Coffin–Manson and Basquin relationships well, and the pertinent fatigue life parameters evaluated following Eq. (1) are listed in Table 2. 3.6. Fracture surface analysis Fatigue fracture surfaces were examined using SEM. Fig. 8(a)–(e) shows typical fracture surfaces of a specimen tested at a total strain amplitude of 0.4% at Rs = −1. Fig. 8(a) presents a low-magnification

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Table 2 Fatigue parameters obtained for estimating fatigue life of the SVDC AM60B alloy in the present investigation at strain ratios of Rs = −1 and Rs = 0.1. Low cycle fatigue parameters

R = −1

R = 0.1

Fatigue strength coefficient, f (MPa)

389

408

Fatigue strength exponent, b Fatigue ductility coefficient, εf (%) Fatigue ductility exponent, c Cyclic strain hardening exponent, n Cyclic strength coefficient, K (MPa)

−0.11 1.6

−0.12 2.2

−0.28 0.30 904

−0.34 0.29 867

full image showing three different zones corresponding to three fatigue stages of crack initiation, propagation, and final rapid fracture. It is seen from Fig. 8(b) that the fatigue crack initiated from the surface or near-surface defects (shrinkage pores). The propagation zone near the initiation site was characterized by fatigue striation-like features that were more randomly oriented (due to random grain orientation) with each other in conjunction with some secondary cracks marked by arrows in Fig. 8(c). The crack propagation zone away from the initiation site was characterized

Fig. 8. SEM images of fatigue fracture surfaces of a specimen tested at a total strain amplitude of 0.4% and strain ratio of Rs = −1: (a) overall view of the fracture surface, (b) magnified view of the crack initiation site, (c) propagation region near the initiation site, (d) propagation region far from the initiation site, and (e) final rapid fracture region.

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Fig. 9. SEM images of fatigue fracture surface of a specimen tested at a total strain amplitude of 0.6% and strain ratio of Rs = 0.1: (a) overall view of the fracture surface, (b) magnified view of the propagation region.

mainly by fatigue striations that were perpendicular to the crack propagation direction (Fig. 8(d)). Once the cracks reached a sufficient length beyond which the remaining cross section could not support the applied cyclic load, the remaining portion/ligament failed like tensile fracture with dimple-like features as shown in Fig. 8(e). Fig. 9(a) and (b) shows typical fracture surfaces at a total strain amplitude of 0.6% at Rs = 0.1. At this higher total strain amplitude multiple crack initiation sites from either the surface or the corners (intersection of two surfaces of the specimen) were observed (Fig. 9(a)), and the fatigue striations observed were relatively large in conjunction with tear ridges (Fig. 9(b)). SEM examinations revealed that the area of fatigue crack propagation zone decreased and the spacing of fatigue striations increased with increasing total strain amplitudes. Similar observations were reported in the extruded Mg alloys [12,13,16–18,31,56]. The fatigue striation could be considered to represent the successive position of an advancing crack front that was normal to the greatest tensile stress. Then each fatigue striation would represent a single stress cycle [69], and the spacing of fatigue striations could reflect the fatigue crack propagation rate. As a result, the larger spacing of fatigue striations observed at higher total strain amplitudes (and also higher strain ratio) corresponded to faster crack propagation, and thus a shorter fatigue life, as shown in Fig. 7(a).

lives especially at higher strain amplitudes and positive strain ratio tests. For example, Fig. 2(a) and (b) shows basically cyclic hardening at a higher total strain amplitude of 0.8%, where the initial stress amplitude was ∼145–155 MPa and the final stress amplitude was ∼165–175 MPa. This type of cyclic hardening was typical of materials which deformed by twinning, including other hcp Mg alloys [16–18,31,33,39,71]. It is believed that cyclic hardening was mainly attributed to the interaction or impediment of the residual twins to the dislocation slip during cyclic deformation. The cyclic stress–strain curve may be represented by a power curve [17,18,31,69],  = K 2



εp 2

n ,

(2)

4. Discussion

where n is the cyclic strain hardening exponent and K is the cyclic strength coefficient. Eq. (2) describes the relationship between flow stress and plastic strain amplitude under cyclic loading, and is a useful aid in understanding strain hardening behavior. The cyclic strain hardening exponent was obtained to be n = 0.30 (Table 2), which was about 1.25 times higher than the monotonic strain hardening exponent (n = 0.24). This means that the SVDC AM60B alloy could be hardened more in the cyclic loading condition than in the monotonic loading condition. Extruded Mg alloys also showed cyclic hardening behavior as reported in [16–18,31]. Indeed the extent of cyclic hardening appeared to be more in the extruded Mg alloys than in the cast Mg alloys.

4.1. Cyclic hardening/softening behavior

4.2. Twinning during cyclic deformation

The variation of cyclic stress response with the number of fatigue cycles is an important characteristic of low cycle fatigue process. Such a cyclic stress response depends mainly on the mechanical and/or cyclic stability of the intrinsic processes between the hardening from the multiplication of dislocations and the twin boundaries as barriers to dislocation slip, and the softening due to the annihilation and rearrangement of dislocations [33]. Xu et al. [66] reported that the hardening effect by mechanical twinning in the fine-grained samples may be caused by the reduction of the free slip distance and by the transformation of glissile dislocations to sessile dislocations inside the twins, while the twinning softening occurred by facilitating deformation in the coarse-grained samples. The slight cyclic softening observed at lower strain amplitudes in the early part of cyclic deformation in the Rs = −1 tests (Fig. 2(a)) could be understood by the above mechanisms. That is, the initial cyclic softening would start from some relatively large grains due to the less constraint of grain boundaries. However, cyclic hardening behavior was dominated in most of the fatigue

Mg has a hexagonal closed-packed (hcp) crystal structure. The basic slip systems in Mg and Mg alloys are of the {0 0 0 1} 1 1 2¯ 0 type and are not enough for the requirement of 5 independent slip systems. In supplement to the simple slip deformation, Mg and its alloys exhibited other deformation mechanisms such as twinning and grain boundary sliding with mechanical twinning being the second most important deformation mechanism [33,66]. For Mg √ alloys with c/a = 1.624 < 3, the {1 0 1¯ 2} twinning mode could accommodate extensions along the c-axis of the hexagonal lattice [33,72,73]. Koike [74] also reported {1 0 1¯ 2} twins were expected when a grain was in tension along its c-axis, and {1 0 1¯ 1} twins were expected when a grain was in compression along its c-axis. Thus it was not surprising to observe some twinning after fatigue, where both tension and compression phases were applied for a large number of times during cyclic deformation. Twinning plays an important role in the plastic deformation of Mg alloys [16–18,31,42,71,75–77]. Fig. 10(a)–(d) shows typical SEM images for the formation of twins, mainly narrower banded type

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Fig. 10. Typical SEM images showing the formation of twins near the fracture surface of the SVDC AM60B alloy tested at strain ratio of Rs = −1 and total strain amplitude of 0.4%: (a) overall view of narrower banded twins, (b) magnified view of the boxed region in (a), (c) overall view of wider lenticular shaped twin, and (d) magnified view of the boxed region in (c).

(Fig. 10(b)) and wider lenticular type (Fig. 10(d)), near the fracture surface in the fatigue tested sample at a total strain amplitude of 0.4%. The wider lenticular twins were {1 0 1¯ 2} extension twins, while the narrower banded type twins were {1 0 1¯ 1} contraction twins as reported in [74,78]. It can be seen from Fig. 10 that the twinning occurred in some favorably oriented ␣-Mg grain, especially in some larger grains and the area without the ␤-phase. The occurrence of twins in areas where the Al alloying element was in solid solution could be explained by the decreasing stacking fault energy in these areas, offering better conditions for twinning during the fatigue tests [43]. The small grains surrounded by the eutectic near boundaries were difficult to deform by twinning. The relative contribution of twinning to the overall deformation depended on the strain rate, temperature, and microstructure (grain size and precipitates), i.e., high strain rate, low temperature and coarse grain size would promote mechanical twinning [66]. As a result, the twins can be formed easily on the larger favorably oriented grains, as shown in Fig. 10(b) and (d).

state was not stable, and a driving force could cause them to return back upon unloading [80]. Caceres et al. [63] developed the idea that twinning rather than dislocation plasticity was mainly responsible for the shape of hysteresis loops and also showed that the pseudoelastic effect developed gradually to a maximum and the elastic modulus decreased drastically up to 70%, with increasing plastic strain up to about 1–2% for their HPDC AZ91 alloy. This was attributed to the partial reversal of twins upon unloading which was observed in situ in that study [63]. The fact that twinning and detwinning alternated with cyclic loading was confirmed using in situ neutron scattering [33] as well, i.e., most twins formed during compression were removed via detwinning when the load was reversed, but some residual twins remained. The twins observed in Fig. 10 were the direct proof for the residual twins. It follows that the occurrence of twining–detwinning during cyclic deformation would be responsible for such non-linear pseudoelastic behavior observed in Figs. 4–6. 4.4. Comparison of cast and extruded Mg alloys

4.3. Psuedoelastic behavior The hysteresis loops in the present study (Figs. 4 and 5) were different from the typical hysteresis loops in the fcc metals, where the loading and unloading moduli kept on changing at various portions of hysteresis loops, as shown in Fig. 4(a). Also, the modulus (e.g., E1 in both unloading/descending and loading/ascending phases in Fig. 4(a)) was observed to be dependent on the applied total strain amplitude (Fig. 6). Any non-linearity in the unloading curve could be referred to as pseudoelasticity, which might be related to several origins such as reversible movement of dislocations [79], twinning, and stress-induced phase transformation [80,81]. Twinning pseudoelasticity was caused by the reversible movement of twin boundaries, or detwinning. The position of twins in the deformed

In magnesium single crystal basic mechanical twinning occurred when the basal plane is in compression or the prism plane is in tension. The twinning process started in the compressive loading phase and detwinning (or dissolution of twins) occurred in the tensile loading phase for the wrought Mg alloys when cycling along the rolling or extrusion direction [16–19,31,33]. The asymmetry of deformation was associated with (i) the presence of strong crystallographic texture in the wrought material, which stemmed from the deformation process (e.g., rolling and extrusion), and (ii) the difference in the twinning initiation stress under tensile and compressive stresses [82]. Extruded Mg alloys were strongly textured with the preferred orientation placing the c-axis in most grains perpendicular to the loading axis favorable to twinning under

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fatigue life. Fatigue striations normally occurred via a repeated plastic blunting–sharpening process via the slip of dislocations at the fatigue crack tip in fcc materials [69,83]. It was expected that the generation of twins in the plastic zone ahead of the crack tip (Fig. 10) would participate in the formation of fatigue striations in Mg alloys, which has also been pointed out in [16–18,31,32]. As shown in Fig. 10, two types of twins could occur. The narrow banded contraction twins were reported to be more detrimental since voids were observed to form largely at this type of narrow contraction twins that were arrested by grain boundaries [78]. This was considered to be due to the fact that the narrow contraction twins led to a reduction in cross-sectional area, thus increasing stress concentration and premature transgranular failure in the extruded AM30 Mg alloy [78]. More studies in this aspect are needed to further identify the relationship between the formation of fatigue striations and twinning in Mg alloys.

Fig. 11. Fatigue lifetime of the SVDC AM60B alloy in comparison with that of the conventional die cast AM60B alloy reported in the literature.

compressive loading [16–19,31,33], while general cast Mg alloys (such as SVDC AM60B alloy in the present study) had relatively more randomly oriented grains with respect to the loading axis, leading to less extensive twinning. However, some larger grains favorably oriented relative to the loading axis still twinned (Fig. 10(a)–(d)), resulting in the non-linear variation of hysteresis loops despite a less degree of asymmetry (Figs. 4(a) and 5(a)) in comparison with that of wrought Mg alloys [16–21,31,33]. Wu et al. [33] carried out LCF testing of a wrought magnesium alloy ZK60A in the extrusion direction and observed the asymmetric hysteresis loops due to the fact that more favorably oriented grains could undergo twinning, which were distinct from the relatively symmetrical loops present in the ZK60A alloy cycled in the transverse direction. This suggested that Mg alloys fatigued in a direction nonfavorable for excessive twinning should generate more symmetric loops such as in the present SVDC AM60B alloy (Figs. 4(a) and 5(a)). 4.5. Fatigue life and fracture characteristics Fig. 11 shows the fatigue lifetime of the present SVDC AM60B alloy tested at Rs = −1 in comparison with the experimental data available in the literature with similar test conditions for the die cast AM60 alloy [5,6]. Horstemeyer et al. [6] reported longer fatigue life compared to other two alloys at a higher total strain amplitude of 0.8%. Below that level the SVDC alloy showed approximately the same fatigue life as that of Horstemeyer et al. [6] within the experimental scatter, but a longer fatigue life than that of El Kadiri et al. [5]. At lower total strain amplitudes (≤0.3%) the fatigue life of the SVDC AM60B alloy was comparatively longer. For instance, all the conventional die cast samples tested failed much earlier than 107 cycles (run-out samples were only seen at total strain amplitudes of 0.15% and 0.1%) in [5]. In [6] one sample reached 107 cycles without failure at total strain amplitudes of 0.2% and 0.1%, while premature failure occurred in one sample at 0.2% and both samples at 0.15% total strain amplitudes. In the present SVDC AM60B alloy though one premature failure occurred prior to 107 cycles, three samples remained unfailed at or after 107 cycles at a total strain amplitude of 0.2%. Therefore, the SVDC AM60B alloy exhibited in general a better fatigue resistance than the conventional die cast AM60 alloy, especially in the high-cycle fatigue region. This was likely due to the reduced porosity in the SVDC samples compared with the conventional die castings [59,60]. As mentioned earlier, the spacing of fatigue striations (Fig. 8(d)) could reflect the fatigue crack propagation rate and the related

5. Conclusions Strain-controlled low cycle fatigue tests were conducted at two strain ratios (Rs = −1 and Rs = 0.1) on a SVDC AM60B alloy, and fatigue life, fatigue parameters, fatigue deformation mechanisms and fracture characteristics of the alloy along with role of twinning were studied. The following conclusions could be drawn: 1. The SVDC AM60B alloy exhibited in general a better fatigue resistance than the conventional die cast AM60 alloy especially in the high-cycle fatigue region. 2. At low strain amplitudes, the slight cyclic softening occurred at Rs = −1 in the initial cycles. Cyclic hardening was observed to increase with increasing total strain amplitude and strain ratio, which could be due to the formation of more twins and their interaction with dislocations. 3. The value of mean stress was higher at Rs = 0.1 and nearly constant and close to zero at Rs = −1. However, the variation trend at both strain ratios was the similar, where the main part of the mean stress relaxation occurred in the initial 10–30% of fatigue life, then the mean stress linearly decreased, and finally decreased drastically again prior to failure. 4. The mid-life hysteresis loops in the alloy were basically symmetrical in tension and compression at Rs = −1, and exhibited slight asymmetry at Rs = 0.1. However, there existed a strong non-linear stress–strain variation throughout the loop in both the tensile and compressive phases especially at higher total strain amplitudes. 5. The elastic moduli in both loading and unloading phases were observed to decrease with increasing strain amplitude arising from the strong non-linear or pseudoelastic cyclic deformation behavior due to the occurrence of twinning–detwinning. Two types of twins (wider lenticular extension twins and narrower banded contraction twins) were observed in some favorably oriented large ␣-Mg cells near the fracture surface. 6. The fatigue life of the alloy was observed to be equivalent at total strain amplitudes higher than 0.4% at both strain ratios, while at lower total strain amplitudes the fatigue life was longer at Rs = −1 than at Rs = 0.1 mainly because of the lower mean stress (near zero) observed at Rs = −1. 7. Compared with the monotonic tensile tests, the alloy exhibited stronger cyclic hardening capacity at both strain ratios at the same strain rate of 1 × 10−2 s−1 , mainly due to the stronger interaction of residual twins with dislocations during cyclic deformation. 8. SEM examinations revealed that fatigue cracks initiated from the specimen surface or near-surface defects, regardless of the strain amplitudes applied. Multiple initiation sites at the specimen

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surface were observed at higher total strain amplitudes. Fatigue crack propagation was mainly characterized by fatigue striationlike features with larger striation spacing observed at higher total strain amplitudes and higher strain ratio, corresponding to faster crack propagation and shorter fatigue life. Acknowledgments The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and AUTO21 Network of Centers of Excellence for providing financial support. This investigation involves part of Canada–China–USA Collaborative Research Project on the Magnesium Front End Research and Development (MFERD). One of the authors (D.L. Chen) is grateful for the financial support by the Premier’s Research Excellence Award (PREA), NSERC-Discovery Accelerator Supplement (DAS) Award, Canada Foundation for Innovation (CFI), and Ryerson Research Chair (RRC) program. Dr. S. Xu, K. Sadayappan, Dr. M.S. Kozdras, and Dr. J. Jackman (CANMET-MTL) are gratefully acknowledged for the helpful discussion and continuous encouragement while performing this investigation. The authors would also like to thank Q. Li, A. Machin, J. Amankrah, D. Ostrom and R. Churaman for their assistance in the experiments. The authors also thank Professor N. Atalla, Professor N. Zhou, Professor D. Weckman, Professor S. Lambert, Professor H. Jahed, Professor Y.S. Yang, Professor J. Allison, Professor M.F. Horstemeyer, Professor B. Jordon, Mr. R. Osborne, Mr. J.F. Quinn, Dr. X.M. Su, and Mr. L. Zhang for the helpful discussion. References [1] T.M. Pollock, Science 328 (2010) 986–987. [2] M. Wise, K. Calvin, A. Thomson, L. Clarke, B. Bond-Lamberty, R. Sands, S.J. Smith, A. Janetos, J. Edmonds, Science 324 (2009) 1183–1186. [3] L.R. Kump, Nature 419 (2002) 188–190. [4] J.A. Patz, D. Campbell-Lendrum, T. Holloway, J.A. Foley, Nature 438 (2005) 310–317. [5] H. El Kadiri, M.F. Horstemeyer, J.B. Jordon, Y. Xue, Metall. Mater. Trans. A 39 (2008) 190–205. [6] M.F. Horstemeyer, N. Yang, K. Gall, D. McDowell, J. Fan, P. Gullett, Fatigue Fract. Eng. Mater. Struct. 25 (2002) 1045–1056. [7] H.T. Kang, T. Ostrom, Mater. Sci. Eng. A 490 (2008) 52–56. [8] G. Chadha, J.E. Allison, J.W. Jones, Metall. Mater. Trans. A 38 (2007) 286–297. [9] C.D. Lee, Mater. Sci. Eng. A 454–455 (2007) 575–580. [10] K. Mathis, Z. Trojanova, P. Lukac, C.H. Caceres, J. Lendvai, J. Alloys Compd. 378 (2004) 176–179. [11] D.G. Leo Prakash, D. Regener, W.J.J. Vorster, J. Alloys Compd. 470 (2009) 111–116. [12] W. Blum, P. Zhang, B. Watzinger, B.V. Grossmann, H.G. Haldenwanger, Mater. Sci. Eng. A 319–321 (2001) 735–740. [13] J. Bai, Y. Sun, F. Xue, S. Xue, J. Qiang, T. Zhu, J. Alloys Compd. 437 (2007) 247–253. [14] H. Liu, Y. Chen, Y. Tang, S. Wei, G. Niu, J. Alloys Compd. 440 (2007) 122–126. [15] Q. Yu, J.X. Zhang, Y.Y. Jiang, Mater. Sci. Eng. A 528 (2011) 7816–7826. [16] S. Begum, D.L. Chen, S. Xu, A.A. Luo, Mater. Sci. Eng. A 517 (2009) 334–343. [17] S. Begum, D.L. Chen, S. Xu, A.A. Luo, Int. J. Fatigue 31 (2009) 726–735. [18] X.Z. Lin, D.L. Chen, Mater. Sci. Eng. A 496 (2008) 106–113. [19] D.W. Brown, A. Jain, S.R. Agnew, B. Clausen, Mater. Sci. Forum 539–543 (2007) 3407–3413. [20] U. Noster, B. Scholtes, Mater. Res. Adv. Tech. (Z. Metallkd.) 94 (2003) 559–563. [21] S. Hasegawa, Y. Tsuchida, H. Yano, M. Matsui, Int. J. Fatigue 29 (2007) 1839–1845. [22] F. Lv, F. Yang, Q.Q. Duan, Y.S. Yang, S.D. Wu, S.X. Li, Z.F. Zhang, Int. J. Fatigue 33 (2011) 672–682. [23] M. Huppmann, M. Lentz, S. Chedid, W. Reimers, J. Mater. Sci. 46 (2011) 938–950. [24] S.H. Park, S.G. Hong, B.H. Lee, W. Bang, C.S. Lee, Int. J. Fatigue 32 (2010) 1835–1842. [25] J. Koike, N. Fujiyama, D. Ando, Y. Sutou, Scripta Mater. 63 (2010) 747–750. [26] M. Huppmann, M. Lentz, K. Brömmelhoff, W. Reimers, Mater. Sci. Eng. A 527 (2010) 5514–5521. [27] S. Kwon, K. Song, K.S. Shin, S.I. Kwun, Trans. Nonferr. Metals Soc. China 20 (Suppl. 2) (2010) s533–s539. [28] S.H. Park, S.G. Hong, W. Bang, C.S. Lee, Mater. Sci. Eng. A 527 (2010) 417–423. [29] Q.Z. Li, Q. Yu, J.X. Zhang, Y.Y. Jiang, Scripta Mater. 62 (2010) 778–781. [30] Q. Yu, J.X. Zhang, Y.Y. Jiang, Q.Z. Li, Int. J. Fatigue 33 (2011) 437–447. [31] S. Begum, D.L. Chen, S. Xu, A.A. Luo, Metall. Mater. Trans. A 39 (2008) 3014–3026. [32] C.L. Fan, D.L. Chen, A.A. Luo, Mater. Sci. Eng. A 519 (2009) 38–45.

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