Conference Agenda

Studying the evolution of alloy polycrystalline microstructures under the action of thermomechanical loads such as those occurring during metal additive manufacturing (AM), quenching, welding, laser rescanning, etc., can help identify the impact of different process parameters on the origin of residual stresses, plastic deformations, the eventual mechanical response. This information can be used to guide the aforementioned processes to design microstructures with a desired response.

To that end, a polycrystal thermo-elasto-viscoplastic finite element (T-EVP-FE) model has been developed. It takes into account the strong coupling between evolving temperatures and stresses under thermomechanical boundary conditions. The constitutive laws of the model include the generalised 3D Hooke’s law, a viscoplastic power law that accounts for the shear rate from each slip system, a Voce-type hardening law, and the generalised Fourier law of heat conduction.

Recently, a series of laser scanning experiments have been performed using a novel laser-SEM (scanning electron microscope) experimental setup; this device is a coupling between a continuous wave fibre laser and an environmental SEM. In these experiments, electron backscattered diffraction was performed before and after laser scanning to study the role of laser scanning on an AM 316L stainless steel microstructure. The experiment revealed the formation of misorientation bands, and hence, geometrically necessary dislocations, that vary as a function of the laser scanning velocity. The T-EVP-FE model has been applied to simulate these laser scanning experiments.

In this talk, the model will be presented, the microstructure state will be compared with experimental observations and the role of laser scan velocity on the evolution of intergranular residual stresses, plastic deformation, stress concentrations, geometrically necessary dislocation formation, etc. will be discussed.

The solution of multi-field problems and the numerical implementation by means of the finite element method constitute a sophisticated part of the characterisation of complex material behaviour. Particularly the implementation into commercial finite element codes is of major importance for practical and industrial applications. Although the wide range of available finite element codes (e.g. Abaqus) provides the opportunity for multiphysical modelling, those implementations are rather restricted to the solution of two coupled field equations. In [1, 2] an Abaqus UMAT framework was introduced to use the balance of linear momentum and the heat equation for the solution of two arbitrary coupled field equations of Laplace-type. An extension of the framework to the solution of three coupled Laplace equations is presented in this contribution.

A comprehensive implementation framework for such a three-field problem into the finite element software Abaqus is provided. The procedure is derived for a micromorphic approach in thermomechanics. Although the provided framework contributes to a particular three-field problem, it is not limited to a particular application or a specific number of coupled field equations from a conceptual point of view. The solution of the considered system of equations is separated onto two coupled domains and is based on a two-instance formulation.

To assess the framework for a particular constitutive model, a gradient-enhanced damage model in a thermo-mechanical setting is adopted and representative simulation results are discussed on a local and a global level. Since the framework is not limited to the solution of three coupled field equations, the extension to arbitrary multi-field problems is discussed.

[1] Ostwald R., Kuhl E., Menzel A. (2019) On the implementation of finite deformation gradient-enhanced damage models. Computational Mechanics 64(847-877). https://doi.org/10.1007/s00466-019-01684-5.

[2] Seupel A., Hütter G., Kuna M. (2018) An efficient FE-implementation of implicit gradient-enhanced damage models to simulate ductile failure. Engineering Fracture Mechanics 199:41-60. https://doi.org/10.1016/j.engfracmech.2018.01.022.

High concentrations of vacancies in crystals may be the result of large plastic deformations or irradiation. Void formation and subsequent growth are well-known to be involved in swelling of irradiated materials and seem to play an important role for the nucleation and evolution of porosity in the early stages of ductile failure as recent experiments suggest [1]. Vacancy diffusion and void formation have been modelled using spatially resolved approaches like the phase-field method. Taking into account that vacancies induce an eigenstrain field, which emerges from the relaxation of the surrounding crystal lattice if a single atom is removed, indicates that the evolution of vacancy concentration needs to be properly coupled to the elastic stress field.

In our recent work [2], we proposed a model for coupling elastically driven vacancy diffusion with a phase-field model of void surfaces, which overcomes the short-comings of former models and closely reproduces the sharp interface solution for small-strain elasticity. This is achieved by making the vacancy eigenstrain a function of the non-conserved order parameter used to distinguish the void and crystal phase. With the recent findings and aiming at being able to numerically analyze the early stages of ductile failure as implied by the mentioned experiments, we present the extension of our model to finite strains. Using a multiplicative split for the deformation gradient, a proper coupling of kinematics and the kinetics of vacancy–void interactions is emphasized. A thermodynamically consistent definition of the energy contributions and the derivation of the resulting driving forces based on the underlying phase-field description are outlined. The model is verified with benchmark problems and the influence of the chemo-mechanical coupling is discussed. The implementation of the governing equations in the multi-physics software tool DAMASK [3] allows a coupling to different plasticity laws, like e.g. continuum dislocation dynamics theory for modelling creep or ductile failure.

[1] P. J. Noell et al. Nanoscale conditions for ductile void nucleation in copper: Vacancy condensation and the growth-limited microstructural state. Acta Materialia, 184:211–224

[2] K. A. Pendl and T. Hochrainer. Coupling stress fields and vacancy diffusion in phase-field models of voids as vacancy phase. [Accepted for publication in Computational Materials Science]

[3] F. Roters et al. DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science, 158:420–478

In the present work, a variational formulation for coupled chemo-mechanical problems in elastic and dissipative solids at infinitesimal strains is outlined. In doing so, it is seen that the gradient of the primary fields additionally enter the energetic and dissipative potential functions, resulting in additional balance equations. The governing balance equations of the coupled problem are derived as Euler equations of the incremental variational principles, formulated in a continuous-and discrete-time setting. Furthermore, the variables governing the inelastic process are locally condensed which yields a reduced global problem that is solved in a discrete-space-time setting. The symmetric structure of the proposed framework with respect to the primary and state variables is an advantage, and this is exploited in the numerical treatment within the finite element paradigm. The framework is applied to Cahn-Hilliard- type diffusion and Allen-Cahn-type phase transformation in elastic and dissipative solids. The applicability of the proposed framework is demonstrated by means of two- and three-dimensional representative numerical simulations.