Elsevier

International Journal of Fatigue

Volume 67, October 2014, Pages 103-116
International Journal of Fatigue

Multiaxial effects on LCF behaviour and fatigue failure of AZ31B magnesium extrusion

https://doi.org/10.1016/j.ijfatigue.2014.01.025Get rights and content

Abstract

Multiaxial cyclic tests were performed on wrought AZ31B magnesium extrusion. Axial, torsional and multiaxial cyclic behaviours of the material are presented. Effects of phase angle on stress–strain response, cyclic hardening and fatigue life are discussed. It was found that the material exhibits additional cyclic hardening due to non-proportional loading. However, the phase angle has no pronounced effect on fatigue life. Fatigue cracking behaviour was examined and two characteristics of crack geometry, i.e., size and orientation, are presented. Multiaxial fatigue lives using the Fatemi–Socie and the Smith–Watson–Topper models were predicted. In addition, the Jahed–Varvani energy model was used for fatigue life prediction and was shown to have a potential to be evaluated at plane of maximum axial strain energy density. Reverse analysis for predicting fatigue life by pre-defined critical plane as the observed plane is discussed in details.

Introduction

Lightweight materials are demanded by many industries. The motives in automobile industry are fuel economy and air pollution reduction. The use of aluminium instead of steel was one of the first steps taken in automotive vehicle for weight reduction. Aluminium was successfully used for both structural and non-structural parts. Although magnesium alloys, which have one fourth the density of steel and two third that of aluminium, have also been used in automobiles, however, their applications were limited to non-structural parts [1], [2], [3], [4]. The recent interest is to use magnesium alloys as structural materials for automotive load bearing components. However, an understanding of cyclic multiaxial behaviour of magnesium alloys is necessary because of two reasons. First, fatigue is considered to be a significant cause of ground vehicle component failure. Second, load-bearing components in automobiles are usually subjected to multiaxial cyclic loading.

Uniaxial cyclic behaviour of several magnesium alloys has been investigated at both mechanistic [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] and material [18], [19], [20], [21], [22], [23], [24] levels. On the contrary, limited investigations have been conducted to analyse multiaxial cyclic behaviour of magnesium alloys. Zhang et al. [25] performed multiaxial experiment on AZ61A extrusions. They observed mechanical twinning at large shear strain amplitudes. However, they found that the existence of twins has no influence on the symmetry of the shear hysteresis. Zhang et al. [25] attributed this to the existence of some grains that are in a favourable orientation for twinning. The cyclic shear behaviour of AZ31B extrusion was also found to be symmetric. Yu et al. [26] investigated multiaxial behaviour of AZ61A extrusion under strain-controlled axial–torsional loading condition. The authors defined equivalent strain amplitude as the radius of the minimum circle circumscribing the loading path shown in the ε-3/γ strain space. Using this definition, Yu et al. found that the highest and the lowest fatigue lives were obtained from in phase and 90° out of phase loading, respectively. Fatigue lives from pure axial and torsional loading were found to fall in between. According to Jiang’s [27] cracking definition, the authors examined the cracking behaviour of AZ61A extrusion and concluded that the material exhibits mixed or shear cracking when the equivalent strain is less than or greater than 0.5%, respectively. Yu et al. successfully estimated the multiaxial fatigue life using modified Smith–Watson–Topper [28], [29], that was proposed by Jiang and Sehitoglu [30], and Fatemi–Socie [31] parameters, especially for the low cycle regime. Albinmousa et al. [32] investigated the cyclic behaviour of AZ31B magnesium extrusion under multiaxial loading. This study was focused on the effect of twinning deformation on the cyclic behaviour and fatigue life prediction using strain and energy approaches. Later, Xiong et al. [33] investigated multiaxial fatigue behaviour of AZ31B extrusion. Using this equivalent strain by Yu et al. [26] they compared fatigue lives for different multiaxial loading paths and found that 90° out of phase loading is the most detrimental. They were able to predict multiaxial fatigue lives using modified Smith–Watson–Topper [28], [29], [30] and Jiang’s models [27].

Experimental observations on fatigue failure indicate that fatigue crack nucleation occurs at the persistent slip bands (planes). The critical plane approach was originated on the bases of these observations [34], [35]. As a result, components of stress or strain are evaluated at specific planes for fatigue damage calculation. The fact that critical plane models can predicts both fatigue life as well as fatigue cracking plane gives these model an advantage over other models that provide predictions for only fatigue life. It is known that fatigue life analysis marks the end of initiation life and the beginning of propagation life, which is governed by fracture mechanics. Fracture mechanics-based analysis requires knowledge about the geometry, such as size and orientation, of the initial flaw. If the flaw is a crack resulting from any type of loading both the crack length and the crack angle are needed for crack propagation analysis [36], [37], [38], [39], [40], [41]. Therefore, a better understanding of the fatigue cracking behaviour may help the development of generalized multistage fatigue model [42], [43] and crack path analysis [44]. Critical plane models became popular in recent years because of their success in predicting fatigue life for various engineering materials and under different loading conditions. Models such as Fatemi–Socie [31], Smith–Watson–Topper [28], [29] and Jiang [27] have been used to analyse various multiaxial loading paths, different materials on both specimen’s and component’s levels [25], [26], [32], [45], [46], [47], [48], [49], [50]. However, there are studies indicating that the predictions of cracking orientations may not necessarily be in agreement with the critical plane predicted by the models even though fatigue predictions are considered reasonable, generally between ±2× scatter bands. Reis et al. [51] performed multiaxial fatigue experiments and examined fatigue crack path under six multiaxial loading paths for AISI 303 stainless steel and 42CrMo4 steel. Six criteria were used for critical plane predictions: Brown–Miller [52], [53], Findley [54], Wang–Brown [55], Fatemi–Socie [31], Smith–Watson–Topper [29] and Liu [56]. In general, they found that crack orientation predictions of 42CrMo4 steel were better than those of AISI 303 stainless steel. The authors reported that the measured crack size was around 1 mm. Jiang et al. [47] performed multiaxial cyclic experimental analysis on fine grain structural steel S460N and evaluated two strain-based criteria: Fatemi–Socie [31], Jiang [27] and one short crack criterion by Doring et al. [57]. Total of 56 tubular specimens were tested under thirteen different multiaxial loading paths. In general, the predictions of fatigue life using the aforementioned criterion mostly falls between ±2× scatter bands especially for lives under 105 cycles. Conversely, by examining physical cracks Jiang el al. [47] found that predictions of critical plane models are not in agreement with the experimental observations. Later, Zhao and Jiang [58] investigated the multiaxial fatigue behaviour of 7075-T651 aluminium alloys. The authors examined the SWT [28], [29] and the modified SWT [30] models for both fatigue life and fatigue crack orientation predictions. Zhao and Jiang found that while SWT parameter can provide good predictions of fatigue lives its predictions of fatigue crack orientation are not in agreement with the experimental observations. They found that an improvement in the estimation of the fatigue crack orientation could be achieved using the modified SWT model. It should be noted that no measurements of crack sizes were reported in these studies.

This study focuses on the effect of multiaxial loading on the cyclic behaviour of AZ31B magnesium extrusion. A careful experimental program had been designed to reveal influence of axial and shear modes on one another and influence of phase angle on stress–strain response, cyclic hardening and fatigue life. In addition, the idea of predicting fatigue crack orientation using critical plane concept is examined and discussed.

Section snippets

Material

The investigated material is AZ31B magnesium extrusion. The air-quenched section of AZ31B extrusion was manufactured by Timminco. This section was extruded from a 177.8 mm diameter, 406.4 mm long billet, with an extrusion ratio of 6. The extrusion temperature was between 360 and 382 °C, with an extrusion exit speed of 50.8 mm/s. The geometry and sizes of this section are shown in Fig. 1a and b. The crystals orientations as well as the definition of the extrusion, transverse and normal directions

Background

SWT [29] is an energy parameter that is evaluated at the plane of maximum axial strain. SWT was originally developed to account for mean-stress effects in uniaxial fatigue. Later, Socie [62] proposed a modified form of this parameter for multiaxial fatigueσn,maxΔε12=σf2E(2Nf)2b+σfεf(2Nf)b+cwhere σn,max and Δɛ1 are the maximum normal stress and maximum normal strain range at the critical plane, σf and εf are the axial fatigue strength and axial fatigue ductility coefficients, respectively,

Cyclic behaviour

Detailed summary of uniaxial, torsional and multiaxial fatigue tests results is presented in Table 2. These include applied strain amplitudes, axial and shear stress responses, strain energy densities, crack size and fatigue life. The middle number in the specimen ID of multiaxial tests stands for the phase angle. Material constants for strain- and energy-life equations were obtained from strain- and energy-life curves, respectively, for both axial and shear modes. However, it should be noted

Discussion

AZ31B extrusion has a strong texture, with the majority of the basal planes parallel to the extrusion direction [23], [66], [67]. Only loading that causes extension along the c-axis can activate tension twinning [21], [23], [65], [68], [69]. Therefore, twinning is the dominant plastic deformation mechanism in compression. The reflection of this on the cyclic behaviour can be seen from three characteristics: load asymmetry with high tensile and low compressive stresses, larger plastic strain in

Conclusion

Multiaxial cyclic fatigue of wrought AZ31B magnesium extrusion was investigated. Careful testing program was design to examine the effect of phase angle on stress–strain response, cyclic hardening and fatigue life. As far as LCF, it was found that phase angle causes additional hardening with phase angle of 90° resulting in the highest hardening compared with 0° and 45°. Interestingly, this additional hardening was shown to have no noticeable effect on fatigue life. Fatigue life predictions were

Acknowledgments

The first author would like to acknowledge the supported of King Fahd University of Petroleum & Minerals (KFUPM) for supporting part of this work under SABIC Fast Track, an internally funded project from DSR (Project No. SB121003). The authors acknowledge the financial support of AUTO21 Network Center of Excellence, the Natural Science and Engineering Research Council of Canada (NSERC), CANMET-Material Testing Laboratory, and the Canada foundation for Innovation (CFI). General Motors Research &

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