Multiscale thermomechanical analysis of multiphase materials

The thermomechanical simulation of materials with evolving, multiphase microstructures poses various modeling and numerical challenges. For example, the separate phases in a multiphase microstructure can interact with each other during thermal and/or mechanical loading, the effect of which is significantly more complicated than the individual behavior of the phases. The interactive behavior also depends on the specific volume fractions and spatial distribution of the individual phases. An accurate modeling of the phases requires a thermodynamically consistent formulation and a robust numerical implementation of the evolution of the corresponding observable and internal variables. The complex nonlinear characteristics of these micromechanical models introduce substantial challenges with respect to their upscaling towards higher levels of observation, as necessary for analyzing large-scale engineering problems in a computationally efficient way. The work presented in this thesis addresses these aspects in detail by focusing on a class of multiphase steels, which are the so-called transformation-induced plasticity (TRIP) steels. This class of structural steels shows an excellent combination of strength and ductility. The transformation-induced plasticity effect can be ascribed to the presence of grains of metastable austenite that are surrounded by ferritic grains. The austenite can undergo a phase transformation when subjected to thermal and/or mechanical loading, thereby introducing an increase in the effective material strength. In addition, both the austenite and the ferritic matrix may deform plastically, which increases the overall ductility of the material. In order to explore the complex micromechanical characteristics and the practical application of this material in more detail, three main research questions were identified, of which the first one is: (1) How can a TRIP steel microstructure be modelled in a fully thermodynamically consistent way? The thermomechanical coupling is particularly relevant since in TRIP steels the phase transformation occurring during mechanical loading is accompanied by the release of a substantial amount of energy (latent heat) that, in turn, affects the mechanical response of the material. The second research question formulated is: (2) How does the response of a TRIP steel microstructure depend on the spatial distribution of the austenitic phase within the ferritic matrix? From the viewpoint of practical applications, the attention here is focused on comparing the response of a TRIP steel sample with a banded austenitic microstructure to that of a sample with randomly distributed austenitic grains. Considering the large number of degrees of freedom of these and other engineering problems, a computationally efficient implementation of the micromechanical model is necessary. This issue is reflected by the third research question, which reads: (3) Is it possible to include the micromechanical constitutive behavior and geometry of the individual phases within an computationally efficient multiscale formulation? For answering the three research questions above, the thermomechanical behavior of the TRIP steel phases is modelled in a fully coupled way, where the generation of heat associated to the martensitic phase transformation and the plastic deformation are accounted for explicitly in the thermodynamic formulation. In analogy with the decomposition of the deformation, the entropy density is separated in a reversible contribution, a transformation contribution, a plasticity contribution and a thermal-mechanical coupling contribution. The last term follows from combining mechanical and thermal constitutive information of the individual phases with basic thermodynamical requirements. One of the observations resulting from this approach is that for a single crystal of austenite the increase in temperature associated with the latent heat of transformation reduces the transformation rate and significantly reduces the transformation-induced plasticity effect. However, for an aggregate of austenitic and ferritic grains, which is representative of a TRIP steel, the delay in the transformation-induced plasticity effect due to latent heat is relatively small, since the ferric matrix absorbs the latent heat generated in the austenite and thus effectively acts as a thermal sink. To evaluate the influence of the spatial distribution of the austenitic (secondary) phase within the ferritic matrix, the effective responses for banded and dispersed austenitic microstructures are computed by means of numerical homogenization. A comparison of these microstructures shows that banded microstructures may allow for plastic localization in the ferritic matrix, which, in comparison to dispersed microstructures, diminishes the strengthening effect provided by the austenitic phase. For the performance of more demanding computational simulations at higher (macroscopic) scales of observation, an efficient multiscale approach termed the generalized grain cluster method (GGCM) was developed. The method is suitable for the prediction of the effective macroscopic behavior of an aggregate of single-crystal grains composing a multiphase steel. The GGCM is based on the minimization of a functional that depends on the microscopic deformation gradients in the grains through the equilibrium requirements of the grains as well as kinematic compatibility between grains. By means of the specification of weighting factors it is possible to mimic responses falling between the Taylor and Sachs bounds. The numerical computation is carried out with an incremental-iterative algorithm based on a constrained gradient descent method. For a multiscale analysis, the GCCM can be included at integration points of a standard finite element code to simulate macroscopic problems. A comparison with FEM direct numerical simulations illustrates that the computational time of the GGCM may be up to about an order of magnitude lower. In large-scale FEM models for structural applications, the responses at material point level thus may either follow from the GGCM alone, or from combining this method with fully-resolved FEM modeling at the level of individual grains (i.e., a combined GGCM - FE2 approach), depending on the required resolution.