Elastic interaction stresses: Part II. The influence of orientation on stresses generated in iso-axial bicrystals
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I.
INTRODUCTION
T H E R E is a body of evidence in the literature indicating that elastic interactions play an important role in initiating slip. 1~-7] In one instance, it was possible to predict, on essentially a 100 pct basis, which slip system would operate in polycrystalline 70-30 as-cast alpha brass when elastic interaction stresses were taken into account, t61 Subsequently, the role of elastic interactions on yield strength was incorporated into a model for yielding, t81 This model proposed that elastic interactions were highest at the grain boundaries and decayed into the grains. It also proposed that the interactions would pass through a maximum over a range of grain sizes. Outside of this range, at large and small grain sizes, it was proposed that the elastic interaction stresses would effectively vanish. rSj This behavior would result in a volume fraction, Vgb, of enhanced grain boundary resolved shear stress zone, which would follow the same pattern. In a study which preceded the present w o r k ] 9j this proposed behavior for Vgb was examined for a [213] 7030 alpha brass iso-axial bicrystal, in which dimensions normal and parallel to the bicrystal boundary were altered, and various strains parallel and normal to the bicrystal boundary were imposed. It was found that the largest enhanced stresses at the bicrystal boundary were produced by shear and normal strains parallel to the boundary and that the volume fraction of the enhanced grain boundary resolved shear stress zone did, indeed, pass through a maximum, approaching zero at large and small bicrystal widths. In the present study, we have examined the effect of bicrystal orientation on stresses induced in 70-30 alpha brass iso-axial bicrystals as a result of elastic incompatibility.
II. P R O C E D U R E FOR D E T E R M I N I N G STRESSES To determine the stresses, finite element method (FEM) calculations were carried out with the STRUDL II program. I~~ The mesh consisted of three-dimensional isoparametric elements, each of which contained 20 nodes. There were six elements in the x direction and three each in the y and z directions. Both ends of the mesh were held fixed in the x and y directions, and the ends moved as a unit in the tensile or z direction. Away from the ends, the nodes moved freely in the x, y, and z directions. The data provided at each node were the six stresses, six strains, and three displacements. The stresses were resolved onto the 12 possible slip systems along two levels at the front and rear surfaces and two levels at the interior. On the front and rear surfaces, stresses were resolved along lines 1/3 up from the base and 2 / 3 up from the base. At these same levels, stresses were also calculated at positions 1/3 the thickness in from the front surface and 2 / 3 in from the front surface. Thus, stresses along four surface lines and four interior lines were determined. These are illustrated in Figure 1 as lettered dashed lines. The elastic constants used were obtained from Reference 11. III. ORIENTATION AND SIZE OF ISO-AXIAL
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