On the Algorithmic Implementation of a Material Model Accounting for the Effects of Martensitic Transformation

Abstract

The formulation and numerical implementation of a material model with as little phenomenological input as possible requires a thorough investigation of the physical relationships relevant for the material under consideration. In the present case the focus is on the correct description of the TRIP (Transformation Induced Plasticity) effect and its interpretation in terms of a transformation surface concept similar to the well‐known yield surface approach used in classical plasticity. Some general aspects of the thermodynamics of martensitic transformation along with a general idea of the topology of a transformation surface in stress space are presented and cast into equations suitable for the implementation into a finite element program. A normality rule for the transformation strain rate can be derived in analogy to the well established procedures of flow plasticity. The notion of a transformation hardening is introduced, collectively characterizing the mechanisms inhibiting transformation. They can be quantified based on the data from dilatometer tests. In contrast to earlier models of this group of authors [1], the algorithm at hand allows to keep track of the evolution of each single variant thus providing detailed insights into the variant selection mechanisms for various load levels and loading directions.