Modeling the temperature dependent effect of twinning on the behavior of magnesium alloy AZ31B sheet

Abstract

Uniaxial compression test data were obtained from magnesium alloy AZ31B sheet material tested along three sample directions (rolling, transverse and normal direction) over the temperature range T = 22–250 °C. The yield point during in-plane compression is insensitive to temperature, up to 200 °C, suggesting that athermal mechanisms are responsible for yielding. The in-plane compression samples exhibit very low r-values, which provides another signature of significant twinning activity in magnesium sheet, in addition to the characteristic sigmoidal strain hardening curve. By varying the critical resolved shear strengths (CRSS) and hardening behaviors of the deformation mechanisms, it is possible to model the changes in the flow stress profile, the strain anisotropy, and texture evolution using a viscoplastic self-consistent polycrystal model. Notably, the CRSS values for basal slip were observed to be constant, while that of twinning increased slightly, and the CRSS values of thermally activated slip modes, i.e., prismatic and pyramidal 〈c + a〉 slip, decrease over the temperature range investigated. Because deformation twinning is observed to be significantly active over the entire temperature range, and the ductility improves markedly as the temperature is increased, it is concluded that twinning is not intrinsically detrimental to the ductility. However, the poor ductility during in-plane compression at the lower temperatures appears to be connected with the twinning reorientation since there is a very limited ability to accommodate c-axis compression.

Introduction

Stress conditions during sheet metal forming operations are complex and can invoke responses that are not adequately characterized by common in-plane tension testing. In other words, a simple yield criterion such as Von Mises J₂ flow rule, even when coupled with a strain hardening description, is inadequate for predicting the forming behavior of sheet metals that exhibit significant anisotropy and/or asymmetry. Rolled magnesium alloy sheets typically display strong in-plane tension–compression asymmetry, i.e., the material yields at a significantly lower stress in compression than in tension [1]. This behavior has been connected with mechanical twinning on the $\left\{10\overline{1}2\right\}$ planes in the $〈10\overline{1}\overline{1}〉$ directions during compression but not during tension, due to the strong textures that are present in magnesium alloy sheets (e.g., [2]) and the polar nature of twinning [3]. (For hexagonal crystals with $c/a<\sqrt{3}$, the $\left\{10\overline{1}2\right\}$ twinning mode produces tensile strains along the c-axis of the lattice, but not compressive [3].) After a low stress plateau in the flow curve, the material hardens rapidly resulting in a sigmoidal (S-shaped) compressive flow curve, and this has been connected with the radical texture evolution that attends extensive mechanical twinning (e.g., [4]). Both of these phenomena (asymmetry and sigmoidal hardening) are similar to those observed in the case of tension and compression along the axis of magnesium alloy extrusions [5]. Thus, in order to perform accurate secondary deformation process modeling for magnesium, it is important to develop constitutive models which can account for these effects of twinning under complex loading conditions. Different approaches for modeling the effect of twinning have been proposed, including polycrystal models [6], [7] such as the predominant twin reorientation [6] scheme employed in the present work as well as the recently developed analytical model which accounts for the aforementioned tension–compression asymmetry [8].

In addition to the need for improved modeling capability, there is also a need to develop efficient experimental approaches to characterize the constitutive response. It is noted that the dominant stress condition within the flange during deep drawing involves in-plane compression (actually in-plane pure shear) [9]. Additionally, through-thickness compression enforces the same strain path as biaxial tension, the dominant stress condition during sheet stretching operations. While some metals exhibit significantly higher strains to failure during compression than during tension, magnesium alloys can have the same or lower strains to failure in compression, as compared to those obtained in tension. Similarly, while most deep drawing failures occur in tension within the cup wall, magnesium alloys often fail in the flange. Thus, developing a better understanding of the compressive deformation of magnesium alloys sheet material could yield important insights regarding the poor overall sheet formability at low temperatures.

Historically, the poor cold forming properties of magnesium alloys have been attributed to the inadequate number of independent slip systems [10]. For instance, extensive studies involving slip trace analysis of single crystals, established that pure magnesium crystals possess only two independent slip systems at room temperature, both involving the slip of dislocations with type 〈a〉 Burgers vectors on the basal plane [10]. However, recent experimental and modeling investigations have called this understanding into question, because the significant activity of so-called hard deformation mechanisms, i.e., non-basal slip of 〈a〉 and 〈c + a〉 dislocations, has been established [11], [12], [13].

At mildly elevated temperatures, the ductility and formability of Mg alloys improve drastically [14]. It has been suggested that mechanical twinning is athermal, i.e., the stress to activate twinning is relatively insensitive to temperature or strain rate [15]. If so, thermally activated deformation mechanisms will be increasingly competitive with mechanical twinning at elevated temperatures. This raises fundamental questions about the role of twinning in determining the ductility and formability of magnesium alloys since, on the one hand, twinning may help fulfill the requirement for an increased number of independent deformation mechanisms [16], while on the other hand, there is the observation that conditions leading to improved ductility (i.e., higher temperatures or slower rates) also lead to less mechanical twinning. The present investigation focuses on measuring and modeling the temperature dependent role of mechanical twinning in determining the deformation response of the most common wrought magnesium alloy.