A dislocation density based material model to simulate the anisotropic creep behavior of single-phase and two-phase single crystals

The primary and secondary creep behavior of single crystals is observed by a material model using evolution equations for dislocation densities on individual slip systems. An interaction matrix defines the mutual influence of dislocation densities on different glide systems. Face-centered cubic (fcc), body-centered cubic (bcc) and hexagonal closed packed (hcp) lattice structures have been investigated. The material model is implemented in a finite element method to analyze the orientation dependent creep behavior of two-phase single crystals. Three finite element models are introduced to simulate creep of a γ′ strengthened nickel base superalloy in 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 directions. This approach allows to examine the influence of crystal slip and cuboidal microstructure on the deformation process.     

Synthesis of highly convergent 2D and 3D finite elements for short acoustic wave simulation

New higher-order finite elements of enhanced convergence properties for acoustic wave simulation are presented in the paper. The element matrices are obtained by combining modal synthesis and optimization techniques in order to achieve minimum errors of higher modes of the computational domain. As a result, simulation models of propagating wave pulses require a smaller number of finite element divisions per wavelength compared to the conventional element model thus significantly reducing computational costs. Though finite element matrices are obtained in optimization, the resulting patterns of the matrices are versatile and further can be used in any wave propagation model. The mass matrices of the elements are diagonal, so explicit time integration schemes are applicable. The usage of new elements is especially efficient in situations where wavelengths of the simulated signal are much shorter than the dimensions of the computational domain. This is referred to as short wave propagation analysis. The results of wave propagation simulation for ultrasonic measurements are presented as application examples. The B-scans and computed dispersion curves are provided for visual interpretation of the results.     

Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification

The elastic/crystalline viscoplastic constitutive equation, based on a newly proposed hardening-softening evolution equation, is introduced into the dynamic-explicit finite element code “Itas-Dynamic.” In the softening evolution equation, the effective distance and the angle between each slip system of a crystal are introduced to elucidate the interaction between the slip systems, which causes a decrease of dislocation density. The polycrystal sheet is modeled by Voronoi polygons, which correspond to the crystal grains; and by the selected orientations, which can relate to the texture, they are assigned to the integration points of the finite elements. We propose a direct crystal orientation assignment method, which means that each integration point of finite element has an assigned orientation, and its orientation can be rotated independently. Therefore, this inhomogeneous polycrystal model can consider the plastic induced texture development and subsequent anisotropy evolution. The parameters of the constitutive equation are identified by uni-axial tension tests carried out on single crystal sheets. Numerical results obtained for sheet tensions are compared with experimental ones to confirm the validity of our finite element code. Further, we investigate the following subjects: (1) how the initial orientation of single crystal affects slip band formation and strain localization; (2) how the grain size and particular orientations of the grain affect the strain localization in case of a polycrystal sheet. It is confirmed that the orientation of a single crystal can be related to the primary slip system and the deformation induced activation of that system, which in turn can be related to the slip band formation of the single crystal sheet. Further, in case of a polycrystal sheet, the larger the grain size, the more the strain localizes at a specific crystal, which has the particular orientation. It is confirmed through comparisons with experiments that our finite element code can predict the localization of strain in sheets and consequently can estimate the formability of sheet metals.     

Finite element modeling of tube hydroforming of polycrystalline aluminum alloy extrusions

Finite element modeling of tube hydroforming requires information about the anisotropy of the extruded aluminum tube. Unlike sheet metals, the complex geometry of extruded tubes makes it difficult, except in extrusion direction, to directly measure material properties. Therefore, polycrystalline models provide a good alternative for calculating the anisotropy of the tube in all directions and under various loading conditions. Using a rate-independent single crystal yield surface and rigid plasticity, a Taylor-type polycrystalline model was developed and implemented into ABAQUS/Explicit finite element (FE) code using VUMAT. The constitutive model was then used to calculate the crystallographic texture evolution during the hydroforming of an extruded aluminum tube. Initial crystallographic texture measured using orientation imaging microscopy (OIM) and uniaxial tensile test data obtained along the extrusion direction were input to this FEA model. In order to efficiently and practically simulate the tube hydroforming process using the polycrystalline model, sensitivity to the number of grain orientation, total simulation time, and number of finite elements were studied. Predicted results agreed very well with experimentally measured strain obtained from tube hydroforming process.     

An energy-based microstructure model to account for fatigue scatter in polycrystals

Scatter observed in the fatigue response of a nickel-based superalloy, U720, is linked to the variability in the microstructure. Our approach is to model the energy of a persistent slip band (PSB) structure and use its stability with respect to dislocation motion as our failure criterion for fatigue crack initiation. The components that contribute to the energy of the PSB are identified, namely, the stress field resulting from the applied external forces, dislocation pile-ups, and work-hardening of the material is calculated at the continuum scale. Further, energies for dislocations creating slip in the matrix/precipitates, interacting with the GBs, and nucleating/agglomerating within the PSB are computed via molecular dynamics simulations. Through this methodology, fatigue life is predicted based on the energy of the PSB, which inherently accounts for the microstructure of the material. The present approach circumvents the introduction of uncertainty principles in material properties. It builds a framework based on mechanics of microstructure, and from this framework, we construct simulated microstructures based on the measured distributions of grain size, orientation, neighbor information, and grain boundary character, which allows us to calculate fatigue scatter using a deterministic approach. The uniqueness of the approach is that it avoids the large number of parameters prevalent in previous fatigue models. The predicted lives are in excellent agreement with the experimental data validating the model capabilities.     

延性单晶非均匀变形的三维有限元模拟

对延性单晶在拉伸载荷作用下的应变局域化和颈缩等非均匀变形过程进行了三维有限元数值模拟。将相关晶体塑性本构模型及一种新的数值积分方法补充到ABAQUS6.1商用有限元软件中。该方法的特点是，利用晶体塑性的动力学方程，获得一个关于晶体弹性变形梯度的演化方程，采用半隐式积分方案进行求解。本文推导出一种新的应力变本构矩阵。按此方式更新本构矩阵，计算速度和计算稳定性大大提高。加载方式，边界条件和变形程度等因素影响着滑移系的启动状况，这是平面模型所不能预测的。本文利用三维有限元方法模拟了不同取向下滑移系的启动状况，全面地考虑了FCC单晶材料12个可能滑移系在变形过程中的启动状况，合理地模拟了FCC面心立方单晶沿不同取向加载时晶轴旋转导致的应变局域化和颈缩等非均匀变形过程。     

3-D numerical simulation of fracture processes in heterogeneous brittle materials

By using the lattice model combined with finite element methods and statistical techniques, a numerical approach is developed to establish mechanical models of three-dimensional heterogeneous brittle materials. A special numerical code is introduced, in which a lattice model and statistical approaches are used to simulate the initial heterogeneity of material properties. The size of displacement-load step is adaptively determined so that only few elements would fail in each load step. When the tensile principal strain in an element exceeds the ultimate strain of this element, the element is considered broken and its Young's modulus is set to be very low. Some important behaviors of heterogeneous brittle materials are indicated using this code. Load-displacement curves and figures of three-dimensional fracture patterns are also numerically obtained, which are similar to those observed in laboratory tests.     

Prediction of plane strain fracture of AHSS sheets with post-initiation softening

In this investigation, the three-parameter Modified Mohr–Coulomb (MMC) fracture model and the determination of the material parameters are briefly described. The formulation of the post-initiation behavior is proposed by defining both the explicit softening law and the incremental damage evolution law. As opposed to the existing attempts to simulate slant fracture with material weakening before crack formation, softening is assumed to occur only in the post-initiation range. The justification of this assumption can be provided by the interrupted fracture tests, for example, Spencer et al. (2002).Element deletion with a gradual loss of strength is used to simulate crack propagation after fracture initiation. The main emphasis of the paper is the numerical prediction of slant fracture which is almost always observed in thin sheets. For that purpose, VUMAT subroutines of ABAQUS are coded with post-initiation behavior for both shell elements and plane strain elements. Fracture of flat-grooved tensile specimens cut from advanced high strength steel (AHSS) sheets are simulated by 2D plane strain element and shell element models.     

Study of work hardening models for single crystals using three dimensional finite element analysis

A comparative study of some hardening models that have been proposed for single crystals is presented in this paper. These models are compared by simulating the deformation of FCC single crystals under uniaxial tension using the finite element method. During large deformation of single crystals, multiple-slip systems can be activated resulting in a three-dimensional deformation. Therefore, three-dimensional finite element models have been used for the simulation. A rate dependent constitutive model was implemented into a non-linear large deformation finite element program to simulate the deformation of single crystals. The hardening laws are compared in order to study their ability to predict the three stages of hardening observed experimentally in FCC single crystals.     

On the transverse compression response of Kevlar KM2 using fiber-level finite element model

Flexible textile composites like woven Kevlar fabrics are widely used in high velocity impact (HVI) applications. Upon HVI they are subjected to both longitudinal tensile and transverse compressive loads. To understand the role of transverse properties, the single fiber and tow transverse compression response (SFTCR and TTCR) of Kevlar KM2 fibers are numerically analyzed using plane strain finite element (FE) models. A finite strain formulation with a minimum number of 84 finite elements is determined to be required for the fiber cross section to capture the finite strain SFTCR through a mesh convergence study. Comparison of converged numerical solution to the experimental results indicates the dominant role of geometric stiffening at finite strains due to growth in contact width. The TTCR is studied using a fiber length scale FE model of a single tow comprised of 400 fibers transversely loaded between rigid platens. This study along with micrographs of yarn after mechanical compaction illustrates fiber spreading and fiber–fiber contact friction interactions are important deformation mechanisms at finite strains. The TTCR is also studied using homogenized yarn level models with properties from the literature. Comparison of TTCR between fiber length scale and homogenized yarn length scale models indicate the need for a nonlinear material model for homogenized approaches to accurately predict the transverse compression response of the fabrics.     

砂井地基的一个简化计算模型

基于三维有限元方法,提出了一个预测和评价砂井地基的简化计算模型。该计算模型采用块体单元模拟砂井周围的土体,用砂井单元模拟砂井的竖向排水和水平排水过程,并且推导了反映土体单元和砂井单元之间排水过程的连续性方程。克服了以往有限元法计算砂井地基时,需要将砂井和周围土体作均质化等价的缺点,并可用弹塑性模型反映砂井周围土体的非线性变形和强度特性。计算了单个砂井地基固结排水过程。通过和理论解的比较表明,用本文简化计算模型得到的结果和理论解比较接近。同时,还计算了日本某高速公路路基用砂井 堆载预压法处理的过程,通过分析表明,该简化模型能反映砂井地基的固结排水过程,可以应用于实际工程。     

Investigation of stress-strain behavior of single walled carbon nanotube/rubber composites by a multi-scale finite element method

The excellent properties of carbon nanotubes have generated technological interests in the development of nanotube/rubber composites. This paper describes a finite element formulation that is appropriate for the numerical prediction of the mechanical behavior of rubber-like materials which are reinforced with single walled carbon nanotubes. The considered composite material consists of continuous aligned single walled carbon nanotubes which are uniformly distributed within the rubber material. It is assumed that the carbon nanotubes are imperfectly bonded with the matrix. Based on the micromechanical theory, the mechanical behavior of the composite may be predicted by utilizing a representative volume element. Within the representative volume element, the reinforcement is modeled according to its atomistic microstructure. Therefore, non-linear spring-based line elements are employed to simulate the discrete geometrical structure and behavior of the single-walled carbon nanotube. On the other hand, the matrix is modeled as a continuum medium by utilizing solid elements. In order to describe its behavior an appropriate constitutive material model is adopted. Finally, the interfacial region is simulated via the use of special joint elements of variable stiffness which interconnect the two materials in a discrete manner. Using the proposed multi-scale model, the stress-strain behavior for various values of reinforcement volume fraction and interfacial stiffness is extracted. The influence of the single walled carbon nanotube addition within the rubber is clearly illustrated and discussed.     

用于准脆性材料破坏过程数值模拟的虚拟连接单元法

将有限变形单元与虚拟连接单元相结合,用于模拟准脆性材料破坏过程.首先基于精确的有限变形理论,采用第二类Piola-Kirchhoff应力与Green-Lagrange应变作为能量共轭的应力、应变对,推导出虚拟连接单元的单元刚度矩阵;通过数值算例,验证该单元的正确性与合理性,给出虚拟连接单元高度的取值范围,并与无此单元时...     

用于多种夹层板等效的有限元分析法

针对夹层板力学性能解析法难于计算复杂结构的夹层板且通用性差的问题,本文采用有限元分析法研究了夹层板性能的等效方法。对夹层板的代表体单元模型施加位移约束,模拟弯曲变形时线性独立的应变分量和弯曲内力;根据夹层板内力与应变的本构关系,求出刚度矩阵;最后由刚度矩阵得出宏观等效弹性常数,从而把夹层板等效成连续材料的单层板单元。将该方法与解析法计算结果进行比较得到的夹层板单元四个主要弹性常数误差在0.2%以内,验证了该方法的有效性;另外采用该方法等效三种典型结构夹层板,比较实际模型和等效模型的弯曲响应,得到的误差均在1.4%以内,表明该方法在不考虑复杂多变的夹芯结构时具有通用性。     

复合材料层合板低速冲击响应和损伤分析

通过在有限元软件Abaqus/Explicit中编写用户材料子程序VUMAT,建立了一种基于能量演化的复合材料低速冲击渐进损伤模型．该模型以三维Hashin准则来预测层内损伤的起始,以一种简化的损伤变量来模拟层内损伤的演化,将具有双线性牵引-分离本构的零厚度界面单元插入层间来模拟分层损伤．采用该模型对14.7 J冲击能量下的纤维增强复合材料低速冲击过程进行了仿真分析,计算得到的冲击力-时间曲线、能量-时间曲线和损伤分布与试验结果吻合较好．根据数值模拟结果,分析了纤维、基体和分层损伤的扩展规律,为低速冲击下的复合材料结构设计提供了理论依据．     

沥青混合料三点弯曲断裂的扩展有限元模拟

利用随机骨料生成和投放算法建立沥青混合料两相异质模型,借助ABAQUS软件开展了分别在跨中、偏中20mm和40mm不同位置包含预切口的沥青混合料三点弯曲试件断裂行为的扩展有限元模拟,分析了预切口位置对裂纹扩展路径、载荷位移曲线等的影响规律,并与实验结果进行了比较。结果表明,预切口偏离跨中越远,裂纹扩展方向偏离预切口延长线的角度越大,试件的峰值载荷越大,对试件承载能力的削弱越弱。实验和数值模拟结果在定性上的一致性表明,利用扩展有限元方法模拟沥青混合料断裂行为是可行的。     

晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

加筋材料的格形模型和统计数值方法

本文采用格形化方法和统计技术建立加筋复合材料有限元力学模型，使用自动选取载荷步长方法和非平衡迭代技术，对加筋复合材料的宏观等效模量和破坏全过程进行了数值模拟，分析了材料分布的非均匀程度，相对体积比和横截面加筋分布方式对加筋复合材料整体宏观等效模量和承载力的影响。     

等径通道挤压过程三维有限元模拟

利用三维有限元模型对等径通道挤压过程中变形分布的不均匀性进行了模拟,通过对不同摩擦系数下截面等效塑性应变分布比较发现:沿三个方向截面上的变形分布都不是均匀的,这说明二维有限元模型不能真实模拟等径通道挤压过程中试样中的变形分布。此外,摩擦对等效塑性应变分布及挤压力的影响较大,截面变形不均匀参数和最大等效塑性应变出现的位置随摩擦系数的增大而变化。压力-位移曲线的变化可以结合试样的变形过程来解释。