Convexity of internal energy of cubic crystal deformed to orthorhombic structure |
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Authors: | K P Thakur R K Jha O P Thakur |
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Affiliation: | (1) Department of Physics, Asmara University, P.O. Box 1220, Asmara, Ethiopia;(2) Department of Physics, TNB College Bhagalpur University, 812 007 Bhagalpur, India;(3) Department of Physics, Delhi Institute of Technology, 110 006 Kashmere Gate, Delhi, India |
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Abstract: | A generalized set of strain variablesq r N , has been defined to develop the expression for a generalized set of second order and third-order elastic moduliC rs N andC rst N for a cubic crystal deformed to orthorhombic structure. The HessainC rs N δqrδqs andC rst N δqrδqsδqt (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. |
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Keywords: | Material strength elastic constants |
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