Abstract
• Precipitation strengthening in structural materials. • Precipitate/matrix misfit stress relaxation by power-law creep. • Semi-analytical model for simulation of stress relaxation. • Successful comparison with ABAQUS. • Possibility of implementation of the model in material design systems. The deformation and stress state relaxation induced by the growth of a misfitting spherical precipitate embedded in a creeping matrix is studied. The precipitate and the matrix may have different elastic properties. The misfit eigenstrain in the precipitate may lead to a remarkable stress state which can be relaxed in the matrix by power-law creep. A semi-analytical solution of the problem, accounting for the interaction of the elastic and creep strain state, is provided by combining an analytical solution with a numerical integration of the creep strain rate with respect to time and the radial coordinate. This procedure provides a complete solution of the system kinetics. The approach is compared with finite element calculations utilizing the standard program package ABAQUS. Finally, also the mechanical contribution to the energetics of the precipitate growth is analyzed.
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