Explicit incremental-update algorithm for modeling crystal elasto-viscoplastic response in finite element simulation

Computational stability and efficiency are the key problems for numerical modeling of crystal plasticity, which will limit its development and application in finite element (FE) simulation evidently. Since implicit iterative algorithms are inefficient and have difficulty to determine initial values, an explicit incremental-update algorithm for the elasto-viscoplastic constitutive relation was developed in the intermediate frame by using the second Piola-Kirchoff (P-K) stress and Green stain. The increment of stress and slip resistance were solved by a calculation loop of linear equations sets. The reorientation of the crystal as well as the elastic strain can be obtained from a polar decomposition of the elastic deformation gradient. User material subroutine VUMAT was developed to combine crystal elasto-viscoplastic constitutive model with ABAQUS/Explicit. Numerical studies were performed on a cubic upset model with OFHC material (FCC crystal). The comparison of the numerical results with those obtained by implicit iterative algorithm and those from experiments demonstrates that the explicit algorithm is reliable. Furthermore, the effect rules of material anisotropy, rate sensitivity coefficient (RSC) and loading speeds on the deformation were studied. The numerical studies indicate that the explicit algorithm is suitable and efficient for large deformation analyses where anisotropy due to texture is important.

Computational stability and efficiency are the key problems for numerical modeling of crystal plasticity, which will limit its development and application in finite element （FE） simulation evidently. Since implicit iterative algorithms are inefficient and have difficulty to determine initial values, an explicit incremental-update algorithm for the elasto-viscoplastic constitutive relation was developed in the intermediate flame by using the second Piola-Kirchoff（P-K） stress and Green stain. The increment of stress and slip resistance were solved by a calculation loop of linear equations sets. The reorientation of the crystal as well as the elastic strain can be obtained from a polar decomposition of the elastic deformation gradient. User material subroutine VUMAT was developed to combine crystal elasto-viscoplastic constitutive model with ABAQUS/Explicit. Numerical studies were performed on a cubic upset model with OFHC material （FCC crystal）. The comparison of the numerical results with those obtained by implicit iterative algorithm and those from experiments demonstrates that the explicit algorithm is reliable. Furthermore, the effect rules of material anisotropy, rate sensitivity coefficient （RSC） and loading speeds on the deformation were studied. The numerical studies indicate that the explicit algorithm is suitable and efficient for large deformation analyses where anisotropy due to texture is important.