Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multi-scale homogenization

Evolution of properties during processing of materials depends on the underlying material microstructure. A finite element homogenization approach is presented for calculating the evolution of macro-scale properties during processing of microstructures. A mathematically rigorous sensitivity analysis of homogenization is presented that is used to identify optimal forging rates in processes that would lead to a desired microstructure response. Macro-scale parameters such as forging rates are linked with microstructure deformation using boundary conditions drawn from the theory of multi-scale homogenization. Homogenized stresses at the macro-scale are obtained through volume-averaging laws. A constitutive framework for thermo-elastic–viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modelling microstructure evolution. The continuum sensitivity method (CSM) used for designing processes involves differentiation of the governing field equations of homogenization with respect to the processing parameters and development of the weak forms for the corresponding sensitivity equations that are solved using finite element analysis. The sensitivity of the deformation field within the microstructure is exactly defined and an averaging principle is developed to compute the sensitivity of homogenized stresses at the macro-scale due to perturbations in the process parameters. Computed sensitivities are used within a gradient-based optimization framework for controlling the response of the microstructure. Development of texture and stress–strain response in 2D and 3D FCC aluminum polycrystalline aggregates using the homogenization algorithm is compared with both Taylor-based simulations and published experimental results. Processing parameters that would lead to a desired equivalent stress–strain curve in a sample poly-crystalline microstructure are identified for single and two-stage loading using the design algorithm.     

Investigation of microstructure evolution during self-annealing in thin Cu films by combining mesoscale level set and ab initio modeling

Microstructure evolution in thin Cu films during room temperature self-annealing is investigated by means of a mesoscale level set model. The model is formulated such that the relative, or collective, influence of anisotropic grain boundary energy, mobility and heterogeneously distributed stored energy can be investigated. Density functional theory (DFT) calculations are performed in the present work to provide the variation of grain boundary energy for different grain boundary configurations. The stability of the predominant (111) fiber texture in the as-deposited state is studied as well as the stability of some special low-Σ grain boundaries. Further, the numerical model allows tracing of the grain size distribution and occurrence of abnormal grain growth during self-annealing. It is found that abnormal grain growth depends mainly on the presence of stored energy variations, whereas anisotropic grain boundary energy or mobility is insufficient to trigger any abnormal growth in the model. However, texture dependent grain boundary properties, mobility in particular, contribute to an increased content of low-Σ boundaries in the annealed microstructure. The increased presence of such boundaries is also promoted by stored energy variations. In addition, if the stored energy variations are sufficient the coexisting (111) and (001) texture components in the as-deposited state will evolve into a (001) dominated texture during annealing. Further, it is found that whereas stored energy variations promote the stability of the (001) texture component, anisotropic grain boundary energy and mobility tend to work the other way and stabilize the (111) component at the expense of (001) grains.     

Assessment of crystal plasticity based calculation of the lattice spin of polycrystalline metals for FE implementation

When texture is incorporated in the finite element simulation of a metal forming process, much computer time can be saved by replacing continuous texture and corresponding yield locus updates by intermittent updates after strain intervals of e.g. 20%. The hypothesis that the evolution of the anisotropic properties of a polycrystalline material during such finite interval of plastic deformation can be modelled by just rotating the initial texture instead of continuously updating it by means of a polycrystal deformation model is tested in this work. Two spins for rotating the frame have been assessed: the classical rigid body spin and a crystal plasticity based “Mandel spin” (calculated from the rotated initial texture) which is the average of the spins of all the crystal lattices of the polycrystal. Each of these methods was used to study the evolution of the yield locus and the r-value distribution during the 20% strain interval. The results were compared to those obtained by simulating the texture evolution continuously using a polycrystal deformation model. When the texture was not updated during deformation, it was found that for most initial textures the Mandel spin does not perform better than the rigid body spin, except for some special initial textures for which the Mandel spin is much better. The latter ones are textures which are almost stable for the corresponding strain mode. When the texture was updated after each strain interval of e.g. 20% the Mandel spin performed much better than the rigid body spin.     

Fast texture updates in fcc polycrystal plasticity based on a linear active-set-estimate of the lattice spin

The paper presents a framework for a fast computational estimate of the texture evolution in fcc polycrystals. The underlying basis is a Taylor-type approach of rigid-plasticity for fcc crystals, where the decision of slip activity is based on a purely geometric argument in terms of the rate of total deformation. This approach allows a purely kinematic estimate of the texture evolution completely independent of the hardening response of the single crystal grains. We show that such a geometric estimate of the orientation microstructure provides very good approximations when compared with Taylor-type models of rigid viscoplasticity or elasto-plasticity of fcc crystals. It is shown for several deformation modes of polycrystalline aggregates that the geometric approach predicts the texture evolution very well in the range of large strains. In contrast to standard approaches for the analysis of texture, the proposed new method is extremely robust and very fast even for a high number of discrete grain orientations. As a consequence, such an approach provides a perfect base for large scale computations of anisotropy development in polycrystals.     

Evolution of properties in hydration of cements—A numerical study

The present work develops a numerical method for analysis of the microstructure and property evolution in the hydration of the cement. A time-dependent micro-mechanical model is established to investigate the microstructure development and the effective property evolution of the cement paste, while the input parameters of the model are based on experimental data. It is assumed that the cement paste composite consists of the anhydrous cement particles, cement gel and pores. The cement particles have a periodically spatial array and are wrapped by the cement gel. The Young’s modulus and Poisson’s ratio of the cement paste are calculated by direct average method and two-scale expansion method. The comparisons between the numerical results and experimental data show that this model can simulate the evolution of the microstructure and properties during the hydration of the cements quite satisfactorily.     

A new computational algorithm for contact friction modeling of large plastic deformation in powder compaction processes

In this paper, the large deformation frictional contact of powder forming process is modeled based on a new computational algorithm by imposing the contact constraints and modifying the contact properties of frictional slip. A simple and efficient numerical algorithm is presented for imposing the contact constraints and frictional contact properties based on the node-to-surface contact technique to simulate the large deformation contact problem in the compaction process of powder. The Coulomb friction law is used to simulate the friction between the rigid punch and the workpiece by the use of penalty approach. A double-surface cap plasticity model is employed together with the nonlinear contact friction algorithm within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die-pressing. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.     

考虑磁头表面高度不连续性气膜润滑的数值模拟与有效算法

随着磁头滑块的飞行高度不断降低,给气体润滑方程的数值求解带来了诸如计算时间过长、甚至计算发散等方面的问题。为了获得1Tbit/in2的存储密度,磁头滑块尾部的最小飞行高度接近1.5nm。本文基于作者提出的修正气膜润滑方程的线性流率(LFR)模型,考虑磁头滑块表面高度的不连续性,建立了基于有限体积法的气膜润滑方程离散格式,并把网格自适应技术与多重网格法应用到离散方程的迭代算法中,发展了可模拟最小飞行高度为0.5nm时磁头滑块压力分布的数值模拟方法与有效算法。文中以一个具有复杂表面形状的磁头滑块为例,检验了计算方法与算法的有效性。数值结果表明:在磁头滑块最小飞行高度较低时,必须要考虑滑块表面高度的不连续性,否则就得不到收敛的数值计算结果;与FK-Boltzmann模型相比,LFR模型具有较高的计算效率,采用网格自适应技术与多重网格法能有效地提高求解气膜润滑方程的计算效率。     

Variational asymptotic micromechanics modeling of heterogeneous porous materials

This paper presents a numerical technique to predict the effective elastic properties of heterogeneous fluid-filled porous media where the heterogeneity may result from dissimilar solid and fluid phase properties or due to mismatch in porous microstructure. The technique is based on the variational asymptotic method of homogenization where finite element method is employed for discretization. Biot’s theory of poroelasticity is used to describe porous media where both solid and fluid phase motions (u ? U formulation) are considered with associated strain measures. The method estimates the poroelastic constitutive law in single analysis which makes it very efficient compared to other finite element based homogenization techniques. The method is also general enough to compute all 28 elements of an anisotropic constitutive matrix. Other than estimating the effective properties the micro-stress/strain distribution is also obtained at no additional cost.The method is successfully applied for homogenization of porous media, fluid-filled cavity and finally for effective property estimation of bone lamella. In absence of any other direct method of porous media homogenization, the present technique is compared with classical homogenization methods with fluid approximated as solid of very high Poisson’s ratio. The suitability of this approximation and various other alternatives are also discussed. It is shown that the present homogenization method can be an efficient tool for bone property estimation where fluid-filled porous hierarchical micro-/nanostructure must be respected at all steps.     

纳米多晶NiTi形状记忆合金超弹性的晶粒取向依赖性相场研究

本文基于Ginzburg-Landau理论,建立了一个反映纳米多晶NiTi形状记忆合金取向依赖性的二维多晶相场模型,研究了晶粒取向对其超弹性性能的影响。结果表明,纳米多晶NiTi形状记忆合金的超弹性行为依赖于晶粒取向分布,即：多晶模型中在所研究的参数变化范围内,晶粒取向分布范围越广、晶粒间取向差越大（无明显织构）,超弹性性能越差;而晶粒取向分布范围越窄、晶粒间取向差越小（织构越强）,超弹性性能越好。该晶粒取向依赖性可解释为：由于晶粒取向的不同,马氏体相变过程中相邻晶粒间的变形不匹配程度不同,因此,多晶模型中在所研究的参数变化范围内,晶粒间取向差异越大,晶界处的变形失配越严重,由此而产生的局部内应力将阻碍其附近马氏体相变的扩展,进而导致纳米多晶NiTi形状记忆合金超弹性性能下降。     

基于显微CT图像的近场动力学建模与复合材料微结构破坏模拟

随着纤维增强复合材料应用领域的不断扩展且用量激增,亟需理清复合材料微观结构损伤对宏观力学性能影响的内在机制。因此,发展针对纤维增强复合材料微结构破坏过程的建模与高效模拟方法就显得十分重要。本文借助显微CT(Micro-computed Tomography)扫描技术,提出了一种基于显微CT图像中像素点离散的近场动力学建模与模拟方法。一方面,近场动力学作为一种由积分方程建模的非局部理论,便于采用基于空间点离散的数值计算方法,相比传统的连续介质力学能够更有效地模拟材料从连续变形到裂纹萌生与扩展(非连续变形)的全过程。另一方面,对显微CT图像使用像素点灰度阈值分割处理技术,能够快速建立含有复合材料原位微结构信息的空间点离散模型。该离散模型可以直接用于微结构破坏过程的近场动力学模拟,从而避免了传统的数值模拟技术需要依据像素点先建立光滑的几何模型、再划分成有限单元网格的复杂前处理过程,并且极大地保留了复合材料的原位组分分布信息。数值模拟结果表明,基于显微CT图像的近场动力学建模方法能够精确捕捉到复合材料微结构信息,并能准确模拟纤维增强复合材料的微结构破坏过程。     

Medical image-based simulation of abdominal aortic aneurysm growth

Advances in theoretical modeling of biological tissue growth and remodeling (G&R) and computational biomechanics have been helpful to capture salient features of vascular remodeling during the progression of vascular diseases. Nevertheless, application of such advances to individualized diagnosis and clinical treatment of diseases such as abdominal aortic aneurysm (AAA) remains challenging. As a step toward that goal, in this paper, we present a computational framework necessary towards patient-specific modeling of AAA growth. Prior to AAA simulations, using an inverse optimization method, initial material parameters are identified for a healthy aorta such that a homeostatic condition is satisfied for the given medical image-based geometrical model under physiological conditions. Various shapes of AAAs are then computationally created by inducing elastin degradation with different spatio-temporal distributions. The simulation results emphasize the role of extent of elastin damage, geometric complexity of an enlarged AAA, and sensitivity of stress-mediated collagen turnover on the wall stress distribution and the rate of expansion. The results also show that the distributions of stress and local expansion initially correspond to the extent of elastin damage, but change via stress-mediated tissue G&R depending on the aneurysm shape. Finally, we suggest that the current framework can be utilized along with medical images from an individual patient to predict the AAA shape and mechanical properties in the near future via an inverse scheme.     

A texture evolution model in cubic-orthotropic polycrystalline system

A new methodology based on a conservation principle in the orientation space is developed to simulate the texture evolution in a cubic-orthotropic polycrystalline system. A least squares error method was used to improve the accuracy of the simulation results obtained from the texture evolution function. The model is applied to uniaxial tension, compression and rolling for a large deformation of more than 50% using a single evolution parameter. The validity and application range of this new model are discussed by simulating and predicting texture evolution during different loading conditions. The new methodology provides a family of texture evolution paths and streamlines which empowers the materials designer to optimize the desired microstructure.     

A multi-scale modeling framework for instabilities of film/substrate systems

Spatial pattern formation in stiff thin films on soft substrates is investigated from a multi-scale point of view based on a technique of slowly varying Fourier coefficients. A general macroscopic modeling framework is developed and then a simplified macroscopic model is derived. The model incorporates Asymptotic Numerical Method (ANM) as a robust path-following technique to trace the post-buckling evolution path and to predict secondary bifurcations. The proposed multi-scale finite element framework allows sinusoidal and square checkerboard patterns as well as their bifurcation portraits to be described from a quantitative standpoint. Moreover, it provides an efficient way to compute large-scale instability problems with a significant reduction of computational cost compared to full models.     

Influence of particle shape on the microstructure evolution and the mechanical properties of granular materials

In order to study the influence of particle shape on the microstructure evolution and the mechanical properties of granular materials, a two-dimensional DEM analysis of samples with three particle shapes, including circular particles, triangular particles, and elongated particles, is proposed here to simulate the direct shear tests of coarse-grained soils. For the numerical test results, analyses are conducted in terms of particle rotations, fabric evolution, and average path length evolution. A modified Rowe's stress–dilatancy equation is also proposed and successfully fitted onto simulation data.     

Microstructural effects on yield surface evolution in cubic metals using the viscoplastic ?-model

Polycrystalline yield surfaces of metals are a good way to characterize the anisotropy of plastic deformation. The evolution of these surfaces is impossible to accurately reproduce without taking into account the evolution of the material microstructure such as texture development. In this paper, a numerical computation of yield surfaces using the viscoplastic ?-model is proposed. Results concerning face-centered cubic metals subjected to a plane strain compression test are presented. The influence of several mechanical parameters (strain hardening, strain rate sensitivity coefficient and accumulated deformation) on subsequent yield surfaces evolution is studied. The analysis of the change in the shape and size of the yield surfaces shows that the results depend strongly on the parameter ? which controls the strength of the interactions in the polycrystal. In addition, the predictions are compared to the widely used viscoplastic self-consistent model as well as to experimental yield loci taken from the literature for various aluminum alloy sheets. A fairly good qualitative agreement between our ?-model results and the experimental ones is found. The probable links between the parameter ? and the microstructural features such as the stacking fault energy and the grain size of the polycrystal are also briefly discussed.     

增材制造微结构演化及疲劳分散性计算

为了预测增材制造中工艺参数?微结构?力学性能之间的关联规律, 提出了集成离散元、相场模拟、晶体塑性有限元和极值概率理论的计算方法, 揭示了激光扫描速度对微结构演化、屈服应力和疲劳分散性的影响. 首先, 采用离散元实现了重力作用下粉床在已凝固层表面上的逐层铺设; 其次, 通过热?熔体?微结构耦合的非等温相场模拟, 获得了熔体、气孔、晶界、晶粒取向等的时空演化以及最终形成的多晶微结构; 然后, 应用晶体塑性有限元计算了增材制造多晶微结构的宏观力学响应, 并得到表征疲劳裂纹萌生驱动力的疲劳指示参数(FIP); 最后, 采用极值概率理论分析了增材制造多晶微结构的FIP极值分布规律及疲劳分散性. 以316L不锈钢选区激光熔化增材制造为例的计算结果表明: 增材制造微结构的宏观屈服强度随激光扫描速度的增加而降低, 且呈各向异性; FIP极值符合Gumbel极值分布规律, 激光扫描速度增加可降低增材制造微结构疲劳分散性, 但会导致FIP极值升高, 使得疲劳裂纹萌生驱动力增加, 疲劳寿命降低.