The Plane Strain Young's Modulus in Cubic Materials

The orientation dependence of the plane strain Young's modulus, , of cubic materials has been analysed as a function of the direction along which a uniaxial stress is applied to a single crystal and the perpendicular direction in the single crystal along which the strain is constrained to be zero. The locus of in the plane perpendicular to the axis of uniaxial stress is shown to be a circle when this stress is applied along . For materials with anisotropy ratios , global minima in occur when the stress is applied along and when the strain along one of the two perpendicular directions is set to zero. Identical global maxima in are found when the stress is applied along two different families of directions and the direction of zero strain is along either a perpendicular or direction. For materials with , the global maxima in occur when the stress is applied along and when the strain along one of the two perpendicular directions is set to zero, and identical global minima are found when the stress is applied along two different families of directions and the direction of zero strain is along either a perpendicular or direction.