Multiscale Problems in Solidification Processes

Our objective is to describe solidification phenomena in alloy systems. In the classical approach, balance equations in the phases are coupled to conditions on the phase boundaries which are modelled as moving hypersurfaces. The Gibbs-Thomson condition ensures that the evolution is consistent with thermodynamics. We present a derivation of that condition by defining the motion via a localized gradient flow of the entropy. Another general framework for modelling solidification of alloys with multiple phases and components is based on the phase field approach. The phase boundary motion is then given by a system of Allen-Cahn type equations for order parameters. In the sharp interface limit, i.e., if the smallest length scale ± related to the thickness of the diffuse phase boundaries converges to zero, a model with moving boundaries is recovered. In the case of two phases it can even be shown that the approximation of the sharp interface model by the phase field model is of second order in ±. Nowadays it is not possible to simulate the microstructure evolution in a whole workpiece. We present a two-scale model derived by homogenization methods including a mathematical justification by an estimate of the model error

Hierarchical micro-adaptation of biological structures by mechanical stimuli

Remodeling and other evolving processes such as growth or morphogenesis are key factors in the evolution of biological tissue in response to both external and internal epigenetic stimuli. Based on the description of these processes provided by Taber, 1995 and Humphrey et al., 2002 for three important adaptation processes, remodeling, morphogenesis and growth (positive and negative), we shall consider the latter as the increase/decrease of mass via the increase/decrease of the number or size of cells, leading to a change in the volume of the organ. The work of Rodriguez et al. (1994) used the concept of natural configuration previously introduced by Skalak et al. (1982) to formulate volumetric growth. Later, Humphrey et al. (2002) proposed a constrained-mixture theory where changes in the density and mass of different constituents were taken into account. Many other works about biological growth have been presented in recent years, see e.g. Imatani and Maugin, 2002, Garikipati et al., 2004, Gleason and Humphrey, 2004, Menzel, 2004, Amar et al., 2005, Ganghoffer et al., 2005, Ateshian, 2007, Goriely et al., 2007, Kuhl et al., 2007, Ganghoffer, 2010a, Ganghoffer, 2010b and Goktepe et al., 2010. Morphogenesis is associated to changes in the structure shape (Taber, 1995 and Taber, 2009) while remodeling denotes changes in the tissue microstructure via the reorganization of the existing constituents or the synthesis of new ones with negligible volume change. All these processes involve changes in material properties. Although remodeling and growth can, and usually do, occur simultaneously, there are some cases where these processes develop in a decoupled way. For example, Stopak and Harris (1982) reported some experimental results showing remodeling driven by fibroblasts, with no volume growth. We will assume this scenario in this contribution, focusing exclusively on remodeling processes and on the reorientation of fibered biological structures. It is well known that biological tissue remodels itself when driven by a given stimulus, e.g. mechanical loads such as an increase in blood pressure, or changes in the chemical environment that control the signaling processes and the overall evolution of the tissue. Biological remodeling can occur in any kind of biological tissue. In particular, the study of collagen as the most important substance to be remodeled, in all its types (preferentiallyPeer ReviewedPostprint (author's final draft

Multi-Scale Multi-Physics Modeling of Laser Powder Bed Fusion Additive Manufacturing

Laser Powder Bed Fusion (LPBF) is a fast-developing metal additive manufacturing process offering unique capabilities including geometric freedom, flexibility, and part customization. The process induces complicated thermal histories with high temperature gradients and cooling rates, leading to rapid solidification microstructures with anisotropic properties as different from those produced conventionally. In addition, the LPBF parts exhibit to a large extent of in-sample and sample-to-sample variabilities in the microstructure and consequently part performance. The high variability in the microstructure and properties is considered the major obstacle against the widespread adoption of LPBF as a viable manufacturing technique. Therefore, a more in depth understanding and control of the solidification microstructure is needed to achieve the LPBF fabricated parts with desired properties. Since the solidification microstructure is highly influenced by the thermal input, it is essential to have an accreditable thermal model first. Therefore, a portion of this dissertation was devoted to developing an accurate thermal model through various methods including code-to-code verification and experimental validation. The materials used in this portion include Ti-6Al-4V, NiTi-SMA (Shape Memory Alloy). Next, a multi-scale multi-physics modeling framework which couples a finite element (FE) thermal model to a non-equilibrium phase field (PF) model was developed to investigate the rapid solidification microstructure during LPBF. The framework was utilized to predict the spatial variation in the morphology, size and micro-segregation in the single-track deposition of binary NiNb alloy during LPBF and a very good agreement with the experimental measurements was achieved

Multi-Scale Multi-Physics Modeling of Laser Powder Bed Fusion Additive Manufacturing

Laser Powder Bed Fusion (LPBF) is a fast-developing metal additive manufacturing process offering unique capabilities including geometric freedom, flexibility, and part customization. The process induces complicated thermal histories with high temperature gradients and cooling rates, leading to rapid solidification microstructures with anisotropic properties as different from those produced conventionally. In addition, the LPBF parts exhibit to a large extent of in-sample and sample-to-sample variabilities in the microstructure and consequently part performance. The high variability in the microstructure and properties is considered the major obstacle against the widespread adoption of LPBF as a viable manufacturing technique. Therefore, a more in depth understanding and control of the solidification microstructure is needed to achieve the LPBF fabricated parts with desired properties. Since the solidification microstructure is highly influenced by the thermal input, it is essential to have an accreditable thermal model first. Therefore, a portion of this dissertation was devoted to developing an accurate thermal model through various methods including code-to-code verification and experimental validation. The materials used in this portion include Ti-6Al-4V, NiTi-SMA (Shape Memory Alloy). Next, a multi-scale multi-physics modeling framework which couples a finite element (FE) thermal model to a non-equilibrium phase field (PF) model was developed to investigate the rapid solidification microstructure during LPBF. The framework was utilized to predict the spatial variation in the morphology, size and micro-segregation in the single-track deposition of binary NiNb alloy during LPBF and a very good agreement with the experimental measurements was achieved

Numerical analysis of the hydrodynamic behaviour of immiscible metallic alloys in twin-screw rheomixing process

A numerical analysis by a VOF method is presented for studying the hydrodynamic mechanisms of the rheomixing process by a twin-screw extruder (TSE). The simplified flow field is established based on a systematic analysis of flow features of immiscible alloys in TSE rheomixing process. The studies focus on the fundamental microstructure mechanisms of rheological behaviour in shear-induced turbulent flows. It is noted that the microstructure of immiscible alloys in the mixing process is strongly influenced by the interaction between droplets, which is controlled by shearing forces, viscosity ratio, turbulence, and shearing time. The numerical results show a good qualitative agreement with the experimental results, and are useful for further optimisation design of prototypical rheomixing processes

ρ\rho-CP: Open Source Dislocation Density Based Crystal Plasticity Framework for Simulating Temperature- and Strain Rate-Dependent Deformation

This work presents an open source, dislocation density based crystal plasticity modeling framework, $\rho$-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallographic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the thermo-mechanical deformation of polycrystalline bcc tantanlum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model's ability to predict large deformation and misorientation development during plastic deformation.Comment: 30 pages, 19 figures, 5 tables, v