A generalized set of strain variablesqrN, has been defined to develop the expression for a generalized set of second order and third-order elastic moduliCrsN andCrstN for a cubic crystal deformed to orthorhombic structure. The HessainCrsNδqrδqs andCrstNδqrδqsδqt (r=1, 2……6; summation convention) are calculated in the new variables and compared withG-strength andS-strength, for both positive and negative loading environment.
The convexity of the internal energy relative to various choice of strain measure is examined considering up to third degree terms in the internal energy expression. The computational results forbcc iron is presented according to the new moduli. The stable ranges thus obtained for iron under hydrostatic compressive and tensile stresses is found to generate the classical stable range, green-stable range and stretch-stable range as the specific cases. However,bcc iron does not seem to follow any conventional stable ranges under hydrostatic compression, where the present generalized stable range is found satisfactory.
Volume 96, 2022
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