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We develop a multiscale thermomechanical model to analyze martensitic phase transformations from a cubic crystalline lattice to a tetragonal crystalline lattice. The model is intended for simulating the thermomechanical response of single-crystal grains of austenite. Based on the geometrically nonlinear theory of martensitic transformations, we incorporate microstructural effects from several subgrain length scales. The effective stiffness tensor at the grain level is obtained through an averaging scheme, and preserves crystallographic information from the lattice scale as well as the influence of volumetric changes due to the transformation. The model further incorporates a transformation criterion that includes a surface energy term, which takes into account the creation of interfaces between martensite and austenite. These effects, which are often neglected in martensitic transformation models, thus appear explicitly in the expression of the transformation driving force that controls the onset and evolution of the transformation. In the derivation of the transformation driving force, we clarify the relations between different combinations of thermodynamic potentials and state variables. The predictions of the model are illustrated by analyzing the response of a phase-changing material subjected to various types of deformations. Although the model is developed for cubic to tetragonal transformations, it can be adapted to simulate martensitic transformations for other crystalline structures.

The microstructure of multiphase steels assisted by transformation-induced plasticity consists of grains of retained austenite embedded in a ferrite-based matrix. Upon mechanical loading, retained austenite may transform into martensite, as a result of which plastic deformations are induced in the surrounding phases, i.e., the ferrite-based matrix and the untransformed austenite. In the present work, a crystallographically based model is developed to describe the elastoplastic transformation process in the austenitic region. The model is formulated within a large-deformation framework where the transformation kinematics is connected to the crystallographic theory of martensitic transformations. The effective elastic stiffness accounts for anisotropy arising from crystallographic orientations as well as for dilation effects due to the transformation. The transformation model is coupled to a single-crystal plasticity model for a face-centered cubic lattice to quantify the plastic deformations in the untransformed austenite. The driving forces for transformation and plasticity are derived from thermodynamical principles and include lower-length-scale contributions from surface and defect energies associated to, respectively, habit planes and dislocations. In order to demonstrate the essential features of the model, simulations are carried out for austenitic single crystals subjected to basic loading modes. To describe the elastoplastic response of the ferritic matrix in a multiphase steel, a crystal plasticity model for a body-centered cubic lattice is adopted. This model includes the effect of nonglide stresses in order to reproduce the asymmetry of slips in the twinning and antitwinning directions that characterizes the behavior of this type of lattices. The models for austenite and ferrite are combined to simulate the microstructural behavior of a multiphase steel. The results of the simulations show the relevance of including plastic deformations in the austenite in order to predict a more realistic evolution of the transformation process.

SUMMARYA time integration scheme is presented for the martensitic phase transformation model developed in recent theoretical work of Turteltaub and Suiker (A multi-scale thermomechanical model for cubic to tetragonal martensitic phase transformations 2005; Transformation-induced plasticity in ferrous alloys 2005). The phase transformation model can be used for analysing transformation-induced plasticity (TRIP) phenomena in ferrous alloys. The microstructural information for the phase transformation model is provided by the crystallographic theory of martensitic transformations. The transformation characteristics depend on the specific transformation systems activated during a loading process. The time integration scheme is formulated within a framework of finite deformations, where the stressupdate algorithm is based on a fully implicit Euler backward discretization. A robust search algorithm is used for detecting the transformation systems activated during loading. The completion of the transformation process is prescribed by a constraint on the total martensitic volume fraction, which is accurately satisfied in the converged state using a sub-stepping algorithm. The computation of the consistent tangent operator is performed through a numerical differentiation method, which avoids the determination of extensive analytical derivatives and allows the model to be easily adapted if necessary. The ability of the algorithm to solve complex transformation-induced plasticity problems is illustrated with the aid of three-dimensional analyses, in which an aggregate of single-crystal grains of retained austenite embedded in a ferrite-based matrix is subjected to uniaxial tension. The response characteristics are in agreement with experimental findings of Jacques et al.

A cohesive-zone approach is used to study the interaction between an approaching crack and a particle embedded in a matrix material as a function of the mismatch in elastic and fracture properties. Crack-particle interaction is a crucial issue governing fracture behavior of particle-dispersed materials. Special attention is given in the present work to the effect of the mismatch in fracture properties, namely fracture strength and energy, which has not been fully-explored in the literature. Based on extensive finite element simulations using cohesive elements, the basic fracture mechanisms governing the crack-particle interaction are identified, namely particle fracture, crack deflection and interface debonding. The details of the cracking sequences are elucidated and the role of secondary cracks is highlighted. The effect of pre-existing flaws on the fracture behavior is analyzed both for flaws inside the particle as well as flaws on the particle/matrix interface. Several flaw configurations in terms of size, orientation and location are considered. In addition, the effect of the mismatch between the matrix and the interface fracture properties is also considered for a wide range of adhesive characteristics. The results of the simulations are summarized in the form of several fracture maps for different configurations, whereby the main fracture mechanisms are identified in regions inside a two-dimensional space of strength and toughness mismatch between the particle and the matrix. It is observed that the mismatch in the fracture properties usually plays a more dominant role on the crack trajectory than the mismatch in elastic properties in a particle-dispersed system. Pre-existing flaws/defects in the particle and the interface are found to be one of the principal controlling factors that alter the crack propagation characteristics. These results can be used as a guideline for designing particulate composite system with a preferred fracture mechanism, namely matrix cracking, interface debonding or particle fracture.