Multiscale Transient Thermomechanics of Heterogeneous Materials

Abstract

Here, a number of analytic and computational models are utilized to study the transient thermomechanical response of heterogeneous materials. The models account for thermal stresses generated by incompatibilities in thermal strain fields. These incompatibilities may result from heterogeneities in thermoelastic properties or nonlinear transient temperature fields. The findings have significance for thermal stresses in quenched ceramics, residual stresses in additively manufactured parts, and thermal shock in geology and planetary science. Some simple scaling laws are derived to relate thermal stresses to characteristics of the spatiotemporal temperature field. In addition, the models detailed here account for internal temperature rises resulting from the conversion of inelastic mechanical work into heat. Sources of inelastic mechanical work studied here include viscoelastic dissipation in polymers, dislocation motion in crystalline materials, and pore collapse in porous crystals. A homogenized framework is proposed that accounts for the spatiotemporal evolution of dislocation density and porosity in porous crystals subject to dynamic loading.

The homogenized framework is implemented into Abaqus, a commercially available finite element software package. A number of fully coupled thermomechanical initial boundary value problems are solved computationally. In these simulations, the thermal diffusion equation is simultaneously solved along with the balance of linear momentum and balance of energy equations. The framework naturally predicts strain localization and energy localization, which result in hot-spot formations. The sensitivity of this hot-spot formation to material microstructure and material properties is studied extensively. The role of thermal conduction in these situations is also elucidated. The findings have significance for a number of applications, e.g. manufacturing, forming, and high-speed cutting processes; impact and penetration mechanics; as well as the applications involving materials whose behavior is strongly sensitive to temperature, e.g. polymers, shape memory alloys and polymers, metastable materials, and energetic materials.