A semianalytical sachs model for the flow stress of a magnesium alloy

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NTRODUCTION

THE yield and work-hardening behavior of wrought magnesium alloys are strongly sensitive to test orientation and sense. This arises in consequence of three factors: (1) Only a limited number of ‘‘easy glide’’ independent slip systems (basal slip) are available;[1] (2) the twinning systems (mainly on the f10" 12g planes) only provide shear in one sense (i.e., they are polar);[2] and (3) the textures in wrought magnesium alloys are typically very strong.[3] These observations have been made in investigations that have included examination of single-crystal behavior,[1,4,5] slip line trace analysis in polycrystals,[6,7] transmission electron microscopy (TEM) studies,[8] crystal plasticity modeling,[9,10,11] neutron[12,13] and X-ray[14,15] diffraction, and acoustic emission.[16] In addition to basal slip and f10" 12g twinning, the importance of nonbasal slip systems has also been identified for higher temperatures[17] and particular orientations.[18] Early single-crystal studies emphasized the onset of nonbasal slip with increasing temperature; the initiation of nonbasal systems for T . 225 °C was first identified by Schmid.[1] Later studies upheld this general observation,[19] but also demonstrated the occurrence of nonbasal slip at lower temperatures near the grips in single crystals[20] and near grain boundaries in polycrystals.[6,7,20] Evidence for both pyramidal[1] and prismatic[7] ,a. slip has been published, but there appears to be a greater weight in favor of an important role of prismatic slip,[5] particularly in polycrystals.[7] Indeed, crystal plasticity models have had considerable success in predicting textures and flow curves by including prismatic ,a. slip in the calculations.[10,11] These models have also frequently included ,c 1 a. slip, to allow for compression along the c-axis direction, which is not provided for by any of the aforementioned systems. Experimental support for the activity of ,c 1 a. second-order pyramidal f11" 22g, 11" 23. slip has been found in single-crystal studies,[21,22,23] and the case for its occurrence is strengthM.R. BARNETT, QEII Research Fellow, Z. KESHAVARZ, Ph.D. Student, and X. MA, Postdoctoral Research Fellow, are with the Centre for Material and Fibre Innovation, Deakin University, Geelong, VIC, 3217, Australia. Contact e-mail: [email protected] Manuscript submitted June 6, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A

ened by analogy with other hcp systems such as Zn[24, 25] and Cd.[26] The incorporation of these four modes, basal slip, tension twinning, prismatic slip, and pyramidal ,c 1 a. slip, into crystal plasticity models has permitted the prediction, with reasonable success, of texture signatures, certain twinning effects, r-value variation, sequential system activation, internal stresses, and flow curve shape.[9,12,27–29] However, these models can be quite complex. Indeed, in a generalized form, the problem is complex. However, in light of the dominance of basal slip and f10"12g twinning, it would appear that a simple semianalytical description