Surface energies in microstructure of martensite

A continuum model for laminate geometry in microstructure of martensite, employing energy minimization, is presented. Ansatzes for twin interface energies as well as grain boundary energy are proposed. The model is applied to predict scale properties and geometrical characteristics of refinement and accommodation of microstructure. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigations on autogenous shrinkage of cement paste and mortar

Autogenous shrinkage of cement paste and concrete is defined as the macroscopic length change occurring with no moisture transferred to the exterior surrounding environment. It is a result of chemical shrinkage affiliated with the hydration of cement particles and the ongoing process of self-desiccation. The process of self-desiccation can be modeled starting from the formation of the capillary pore space during hydration in the cement paste. In this proposal a working model will be introduced explaining the difficulties to obtain the autogenous shrinkage strains directly from a simulated or measured microstructure of cement paste. In a second step the autogenous shrinkage of a hardening cement mortar was described on a mesoscopic level. It based on measurements on cement paste. The mortar simply consists of cement paste and a defined fraction of spherical aggregates with a known modulus of elasticity. Furthermore the influence of the interfacial transition zone (ITZ) is studied in numerical simulations. The results of these finite-element-calculations are introduced and compared with testing results of the autogenous shrinkage of hardening mortar samples. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

利用内聚力模型(CZM)模拟弹粘塑性多晶体的裂纹扩展

采用内聚力模型（CZM）,模拟多晶体中起裂于晶界的二维平面应变裂纹扩展．结果表明,弹粘塑性体中,初始裂纹尖端不会最先开裂．晶体本构的率敏感指数表征了塑性变形和内聚力区耗散两种机制的相互竞争．率敏感指数越大,塑性耗散能越大,内聚力区粘着能越小,使材料的塑性变形越容易,内聚力区诱发的破坏越不易;率敏感指数越小,材料响应越接近弹塑性性质,塑性耗散能减小,粘着能增大,外力功易转化为内聚力区的粘着能,使内聚力单元更易分离．增大内聚力区结合强度或临界张开位移使晶内和晶界的三轴应力度减小,即提高内聚力区韧性也使基体材料抗孔洞损伤能力提高．     

Finite-element modeling of the particle clustering effect in a powder-metallurgy-processed ceramic-particle-reinforced metal matrix composite on its mechanical properties

A new numerical method is proposed to predict the effect of particle clustering on grain boundaries in a ceramic- particle-reinforced metal matrix composite on its mechanical properties, and micromechanical finite-element simulation of stress–strain responses in composites with random and clustered arrangements of ceramic particles are carried out. A particular material modeled and analyzed is a TiC-particle-reinforced Al matrix composite processed by powder metallurgy. A representative volume element of a composite microstructure with 5 vol.% TiC is reconstructed based on the tetrakaidecahedral grain boundary structure by using a modified random sequential adsorption. The model proposed in this study accurately represents the stress concentrations and particle-particle interactions during deformation of the powder-metallurgy-processed composite. A comparison with the random-arrangement model shows that the present numerical approach is more accurate in simulating the behavior of the composite material.     

A 2D level set finite element grain coarsening study with heterogeneous grain boundary energies

In a previous article (Fausty et al., 2018) a new level-set finite element formulation for pure grain growth with heterogeneous grain boundary energies (i.e. one energy per grain interface) was developed and validated for simple configurations. In this work, the authors apply this new tool to the simulation of two dimensional grain growth of polycrystals using different disorientation dependent grain boundary energy functions. The results of these full-field calculations are assessed using the time dependent evolution of the following criteria: grain size, grain number, total interface energy, grain boundary disorientation distribution, grain boundary energy distribution and number of neighboring grains distribution. Of particular interest is the relationship between the grain boundary energy function and the evolution of the grain boundary network in the sense of both its morphology and its constitution. Some notable results are that the disorientation distribution evolution is inversely correlated to the grain boundary energy function itself and that the kinetics of grain growth are heavily effected by the heterogeneity of the system.     

Numerical modelling of solidification of castings made of two‐component alloys

The paper deals with a numerical modelling of equiaxed microstructure formation during the solidification of two‐component alloys. The basic enthalpy formulation was applied to model the solidification. The equiaxed grain size was dependent on the average cooling velocity at the moment when the liquid metal reaches the liquidus temperature. The experimentally determined dependence between grain radius and cooling velocity was used in the calculation of average grain radii distribution.     

Delamination of Grain-Interfaces in Silicon Nitride

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A constitutive model for the flow stress behavior and microstructure evolution in aluminum alloys under hot working conditions – with application to AA6099

A constitutive model for aluminum alloys under hot working conditions is proposed. The elastic-viscoplastic model is implemented in a finite strain continuum mechanical framework. The model accounts for the interplay between dynamic recovery and recrystallization during hot working of aluminum alloys and central aspects of microstructure evolution such as grain/subgrain size and dislocation density. The proposed model is generic in the sense that it can be used for arbitrary aluminum alloys, but in order to demonstrate its capabilities, the model is calibrated to a newly developed AA6099 alloy in the present study. The model is thoroughly discussed and details on the numerical implementation as well as on the calibration of the model against experimental data are provided.     

A higher gradient theory for solid mixtures

During use the microstructure of solders will change over time. To enable us to determine the lifetime and reliability of these materials, a theory to predict such changes is needed. In this paper two kinds of changes are considered: The forming of intermetallic compounds due to chemical reactions of two components and spinodal decomposition of a binary alloy followed by coarsening. A theoretical approach is presented and evaluated numerically. For this purpose, an extended diffusion equation is needed and derived within the framework of undisputed concepts of the entropy principle. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient energy-stable schemes for the hydrodynamics coupled phase-field model

In this article, several efficient and energy-stable semi–implicit schemes are presented for the Cahn–Hilliard phase-field model of two-phase incompressible flows. A scalar auxiliary variable (SAV) approach is implemented to solve the Cahn–Hilliard equation, while a splitting method based on pressure stabilization is used to solve the Navier–Stokes equation. At each time step, the schemes involve solving only a sequence of linear elliptic equations, and computations of the phase-field variable, velocity, and pressure are totally decoupled. A finite-difference method on staggered grids is adopted to spatially discretize the proposed time-marching schemes. We rigorously prove the unconditional energy stability for the semi-implicit schemes and the fully discrete scheme. Numerical results in both two and three dimensions are obtained, which demonstrate the accuracy and effectiveness of the proposed schemes. Using our numerical schemes, we compare the SAV, invariant energy quadratization (IEQ), and stabilization approaches. Bubble rising dynamics and coarsening dynamics are also investigated in detail. The results demonstrate that the SAV approach is more accurate than the IEQ approach and that the stabilization approach is the least accurate among the three approaches. The energy stability of the SAV approach appears to be better than that of the other approaches at large time steps.     

Creep damage modeling of a polycrystalline material

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermodynamic equilibrium studies of nanocrystallite SrTiO3 grain boundaries by high temperature photoelectron spectroscopy

Nanostructured strontium titanate (SrTiO3) thin films are studied by high temperature photoelectron spectroscopy and thermal gravimetric analysis. The results indicate that ion migration and redistribution as well as transformation between lattice oxygen and gas phase oxygen take place near the grain boundaries during thermodynamic equilibrium process, which lead to obvious variation of the surface composition with temperature. The lattice oxygen ions migrate from bulk to grain surface with temperature rising up; meanwhile Ti ions also migrate to grain surface and combine with oxygen ions forming Ti-O complex. An opposite process takes place during temperature falling down, but the latter process is much slower than the former one. A primary model is proposed to explain this phenomenon.     

A Variational Approach to Dynamic Recrystallization Using Probability Distributions

We investigate a model of dynamic recrystallization in polycrystalline materials. A probability distribution function is introduced to characterize the state of individual grains by grain size and dislocation density. Specifying free energy and dissipation within the polycrystalline aggregate we are able to derive an evolution equation for the probability density function via a thermodynamic extremum principle. Once the distribution function is known macroscopic quantities like average strain and stress can be calculated. For distribution functions which are constant in time, describing a state of dynamic equilibrium, we obtain a partial differential equation in parameter space which we solve using a marching algorithm. Numerical results are presented and their physical interpretation is given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermodynamic equilibrium studies of nanocrystallite SrTiO3 grain boundaries by high temperature photoelectron spectroscopy

Nanostructured strontium titanate (SrTiO₃) thin films are studied by high temperature photoelectron spectroscopy and thermal gravimetric analysis. The results indicate that ion migration and redistribution as well as transformation between lattice oxygen and gas phase oxygen take place near the grain boundaries during thermodynamic equilibrium process, which lead to obvious variation of the surface composition with temperature. The lattice oxygen ions migrate from bulk to grain surface with temperature rising up; meanwhile Ti ions also migrate to grain surface and combine with oxygen ions forming Ti-0 complex. An opposite process takes place during temperature falling down, but the latter process is much slower than the former one. A primary model is proposed to explain this phenomenon.     

A Phase Field Model for Martensitic Transformations

The martensitic transformation is described using a phase field model which is in mathematical terms the regularization of a sharp interface approach. In this work, up to two martensitic orientation variants are considered. The evolution of microstructure is assumed to follow a time dependent Ginzburg-Landau equation. The coupled problem of the mechanical balance equation and the evolution equations is solved using finite elements and an implicit time integration scheme. In this work, the global energy evolution during the martensitic transformation and the influence of external loads on the formation of the different martensitic phases are studied in 2d. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling Dynamic Recrystallization in Polycrystalline Materials via Probability Distribution Functions

A model of dynamic recrystallization in polycrystalline materials is investigated in this work. Within this model a probability distribution function representing a polycrystalline aggregate is introduced. This function characterizes the state of individual grains by grain size and dislocation density. By specifying free energy and dissipation within the polycrystalline aggregate an evolution equation for the probability density function is derived via a thermodynamic extremum principle. For distribution functions describing a state of dynamic equilibrium we obtain a partial differential equation in parameter space. To facilitate numerical treatment of this equation, the equation is further modified by introducing an appropriately rescaled variable. In this the source term is considered to account for nucleation of grains. Then the differential equation is solved by an implicit time-integration scheme based on a marching algorithm [2]. From the obtained distribution function macroscopic quantities like average strain and stress can be calculated. Numerical results of the theory are subsequently presented. The model is compared to an existing implementation in Abaqus as well. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)