Sixth GAMM Seminar on Microstructures - Abstract

Stein, Erwin

Shape memory effect of cyclic martensitic phase transformation in monocrystals with finite strains: theoretical and computational aspects

Modeling of solid-solid martensitic phase transformation of multi-variant mono-crystals leads to a nonconvex multi-well free energy functional. The effective microscopic behavior at linearized strains in case of mono-crystals was characterized by quasi-convexification of energy wells for n phase variants given by Govindjee, Mielke and Hall, citeGoMielke. For linearized strains a generalized variational formulation, including quasi-convexification of energy wells, was developed in citeGoMiehe and computationally extended in citeEsOz. This lecture presents the generalization of this work for finite strain kinematics for quasiplastic phase transformation including quasi-convexification of energy wells with monotonous hyperelastic stress-strain functions in order to account for large transformation strains, citeEsGs. This includes the step-wise linearization of stress-strain functions for Neo-Hookean material and yields the generalized lower Reuss bound for mixing energy in case of $nleq2$ phase variants, citeEsGs. Iterative time-integration of the phase transformation evolution equation was programmed in C++ and implemented into Abaqus via UMAT-interface which requires Jaumann rate of Cauchy stresses. Computations are done using 3D-hexahedral B-bar elements. Numerical validation of the used micro-macro material model is presented by comparing numerical results with experimental data for $Cu_82Al_14Ni_4$ monocrystals, citeXiQuSh, at quasiplastic phase transformation. The zigzag type experimental stress-strain curve, called 'yield tooth', within the loading process of a uniaxial tension specimen is numerically approximated sufficiently good by the computationally obtained averaged curve which could not be achieved with linearized kinematics, citeEsOz.
smallskip Co-authored by Gautam Sagar, Institute of Mechanics and Computational Mechanics (IBNM), Leibniz University of Hanover.
bibliographystyleunsrt beginthebibliography1 bibitemGoMielke S. Govindjee, A. Mielke, and G. J. Hall. newblock The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis. newblock em J. Mechanic. and phys. of Solids.51(4): I-XXVI, 2003. bibitemGoMiehe S. Govindjee and C. Miehe. newblock A multi-variant martensitic phase transformation model: formulation and numerical implementation. newblock em Comput. Methods Appl. Mech. Engng.,191: 215-238, 2001. bibitemEsOz E. Stein and O. Zwickert. newblock Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strain. newblock em Int. J. Comp. Mech., in print: 17 pages, 2006. bibitemEsGs E. Stein and G. Sagar. newblock Theory and finite element computation of cyclic martensitic phase transformation with finite strain using umat. newblock em Int. J. Num. Meth. Engng., in review process: 28 pages, 2006. bibitemXiQuSh Z. Xiangyang, S. Quingping, and Y. Shouwen. newblock A non-invariant plane model for the interface in cualni single crystal shape memory alloys. newblock em J. Mech. Phys. Solids, 48:2163-2182, 2000. endthebibliography