Virtual material testing for stamping simulations based on polycrystal plasticity

In the modern practice of stamping simulation of complex industrial parts the prediction of springback still lacks accuracy. In commercial software packages various empirical constitutive laws for stamping are available. Limited to simple empirical models for material anisotropy they do not take into account in a full manner the effects of microstructure and its evolution during the deformation process. The crystal plasticity finite element method bridges the gap between the polycrystalline texture and macroscopic mechanical properties that opens the way for more profound consideration of metal anisotropy in the stamping process simulation. In this paper the application of crystal plasticity FEM within the concept of virtual material testing with a representative volume element (RVE) is demonstrated. Using virtual tests it becomes possible, for example, to determine the actual shape of the yield locus and Lankford parameters and to use this information to calibrate empirical constitutive models. Along with standard uniaxial tensile tests other strain paths can be investigated like biaxial tensile, compressive or shear tests. The application of the crystal plasticity FEM for the virtual testing is demonstrated for DC04 and H320LA steel grades. The parameters of the Vegter yield locus are calibrated and the use case demonstration is completed by simulation of a typical industrial part in PAMSTAMP 2G.     

Concepts for Integrating Plastic Anisotropy into Metal Forming Simulations

Modern metal forming and crash simulations are usually based on the finite element method. Aims of such simulations are typically the prediction of the material shape, failure, and mechanical properties during deformation. Further goals lie in the computer assisted lay‐out of manufacturing tools used for intricate processing steps. Any such simulation requires that the material under investigation is specified in terms of its respective constitutive behavior. Modern finite element simulations typically use three sets of material input data, covering hardening, forming limits, and anisotropy. The current article is about the latter aspect. It reviews different empirical and physically based concepts for the integration of the elastic‐plastic anisotropy into metal forming finite element simulations. Particular pronunciation is placed on the discussion of the crystallographic anisotropy of polycrystalline material rather than on aspects associated with topological or morphological microstructure anisotropy. The reviewed anisotropy concepts are empirical yield surface approximations, yield surface formulations based on crystallographic homogenization theory, combinations of finite element and homogenization approaches, the crystal plasticity finite element method, and the recently introduced texture component crystal plasticity finite element method. The paper presents the basic physical approaches behind the different methods and discusses engineering aspects such as scalability, flexibility, and texture update in the course of a forming simulation.     

基于Yoshida-Uemori材料模型的汽车结构件冲压回弹分析

Yoshida-Uemori随动硬化材料模型能够准确描述应变路径发生变化时材料性能的改变,从而较好地反映复杂加载情况下材料的各向异性.本文基于JSTAMP件分别采用Yoshida-Uemori随动硬化材料模型和各向同性硬化材料模型对汽车高强钢结构件的冲压成形进行了仿真分析与回弹预测,研究了不同材料硬化模型对回弹预测精度...     

Elastic crack propagation model for crystalline solids using a self-consistent coupled atomistic–continuum framework

Deformation and failure processes of crystalline materials are governed by complex phenomena at multiple scales. It is necessary to couple these scales for physics-based modeling of these phenomena, while overcoming limitations of modeling at individual scales. To address this issue, this paper develops self-consistent elastic constitutive and crack propagation relations of crystalline materials containing atomic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The concurrent multi-scale model incorporates a finite temperature atomistic region containing the crack, a continuum region represented by a self-consistent crystal elasticity constitutive model, and a handshaking interphase region. Atomistic modeling is done by the molecular dynamics code LAMMPS, while continuum modeling is conducted by the finite element method. For single crystal nickel a nonlinear and nonlocal crystal elasticity constitutive relation is derived, consistent with the atomic potential function. An efficient, staggered solution scheme with parallel implementation is designed for the coupled problem. The atomistic–continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in the interphase region. Quantitative analyses of the crack propagation process focuses on size dependence, strain energy release rate, crack propagation rate and degradation of the local stiffness. The self-consistent constitutive and crack propagation relations, derived from the concurrent model simulation results are validated by comparing results from the concurrent and full FE models. Excellent accuracy and enhanced efficiency are observed in comparison with pure MD and concurrent model results.     

汽车用先进高强钢本构模型与韧性断裂模型研究进展

轻量化是当前汽车行业全产业链共同面对的课题,提高先进高强钢使用比例是实现汽车轻量化的有效手段。对先进高强钢本构模型与韧性断裂模型的充分研究有助于提高先进高强钢开裂分析和预测的准确性,从而推动先进高强钢工程的应用进程。目前,在先进高强钢的研究过程中,学者们通常通过多种应变强化模型的线性组合,或结合微观结构与宏观力学行为进行多尺度分析来建立本构模型;通过多种应力状态下的准静态拉伸实验以及使用仿真与实验混合的方法来标定韧性断裂模型的参数。以第三代先进高强钢中的淬火配分（QP）钢为重点讨论对象,介绍了制备工艺与材料特性及其相关研究进展,并介绍了QP钢本构模型的研究现状、新近发展的非耦合韧性断裂模型以及考虑了应力三轴度和罗德角参数影响的韧性断裂模型在先进高强钢上的应用现状,最后指出了先进高强钢本构模型和韧性断裂模型未来的研究方向。     

Dual-time scale crystal plasticity FE model for cyclic deformation of Ti alloys

A dual-time scale finite element model is developed in this paper for simulating cyclic deformation in a Titanium alloy Ti-6242. The material is characterized by crystal plasticity constitutive relations. Modeling cyclic deformation using conventional time integration algorithms in a single time scale can be prohibitive for crystal plasticity computations. Typically 3D crystal plasticity based fatigue simulations found in the literature are in the range of 100 cycles. Results are subsequently extrapolated to thousands of cycles, which can lead to considerable error in fatigue predictions. However, the dual-time scale model enables simulations up to a significantly high number of cycles to reach local states of damage initiation leading to fatigue crack growth. This formulation decomposes the governing equations into two sets of problems, corresponding to a coarse time scale (low frequency) cycle-averaged problem and a fine time scale (high frequency) oscillatory problem. A statistically equivalent 3D polycrystalline model of Ti-6242 is simulated by the crystal plasticity finite element model to study the evolution of local stresses and strains in the microstructure with cyclic loading. The comparison with the single time scale reference solution shows excellent accuracy while the efficiency gained through time-scale compression can be enormous.     

ATENA — A tool for engineering analysis of fracture in concrete

Advanced constitutive models implemented in the finite element system ATENA serve as rational tools to explain the behaviour of connection between steel and concrete. Three nonlinear material models available in ATENA are described: crack band model based on fracture energy, fracture-plastic model with non-associated plasticity and microplane material model. Nonlinear simulation using these advanced constitutive models can be efficiently used to support and extend experimental investigations and to predict behaviour of structures and structural details.     

Void growth simulations in single crystals

The growth and coalescence of microvoids leading to ductile failure in single crystals is simulated using the finite element method. Finite deformation, rate dependent, crystal plasticity theory is used in the context of 2D plane strain models. The details of material failure at the microscale and macroscale are investigated under variation in a range of parameters including void volume fraction, loading state and lattice structure and orientation. Remeshing is used to improve accuracy of results. Results are compared with those produced by models based on other constitutive theories and experimental observation.     

Integration of multi‐step stamping effects in the bending fatigue analysis of a steel wheel

Bending fatigue prediction accuracy of steel wheel can hardly be guaranteed without clearly understanding the influence of stamping process on fatigue. In this research, multi‐step stamping processes of spoke were analysed by different finite element simulation techniques. Major influences of stamping process on fatigue property were distinguished. Data‐mapping technique was used to transfer information between stamping and fatigue analysis models. Difference material experiments were carried out to research the influence of prestrain on material properties. Modified E‐N function was established according to the theoretical analysis and material experiment results. Bending fatigue finite element simulation was carried out, and result matched experiment well both in position and cycle life.     

Rate dependent modelling of the forming behaviour of viscous textile composites

A predictive approach to modelling the forming of viscous textile composites has been implemented in two finite element codes; Abaqus Standard™ and Abaqus Explicit™. A multi-scale energy model is used to predict the shear force–shear angle–shear rate behaviour of viscous textile composites, at specified temperatures, using parameters supplied readily by material manufacturers, such as fibre volume fraction, weave architecture and matrix rheology. The predictions of the energy model are fed into finite element simulations to provide the in-plane shear properties of two different macro-scale constitutive models implemented in the finite element codes. The manner of coupling predictions of the multi-scale energy model with the macro-scale models is shown to affect the rate-dependent material response in the simulations. These coupling methods are evaluated using picture frame test simulations.     

Mesoscale Modeling of Microstructure and Texture Evolution During Deformation Processing of Metals

The application of the finite element method to model the deformation of metals at the mesoscale to study the microstructure and texture evolution is described. The finite element discretization is applied directly to the various grains, and crystal plasticity is used as the constitutive basis to model the plastic deformation by crystallographic slip, and to evolve the slip system strength and crystal lattice orientation of the material. Applications of the methodology to detailed studies of the non‐uniform deformations of individual grains, and effects of grain interactions on the distributions of deformation and stress in the microstructure are discussed.     

Quantitative re-examination of Taylor model for FCC polycrystals

The quantitative adequacy of the Taylor model for representing the behaviors of FCC polycrystals is discussed through comparison with crystal plasticity analysis using the homogenization-based finite method. The key element of the crystal plasticity theory is the constitutive relation for single crystals. The most classical way to apply it to polycrystals is the Taylor model. This model assumes that all crystal grains in a crystal aggregate are subjected to the same strain under macroscopically uniform deformation. This assumption provides a solution satisfying the continuity of displacement between crystal grains. The effect and evolution of the crystallographic texture can easily be taken into account. However, the assumption of uniform strain, the main idea in the Taylor model, has never been validated quantitatively. On the other hand, the homogenization-based finite element method can represent arbitrary microscopic deformations, i.e., each crystal grain may have nonuniform deformation, and can provide a material response under more realistic boundary conditions. In this paper, we first determine the appropriate size for the representative volume element (RVE) in the homogenization-based finite element method that can represent the macroscopic polycrystalline behavior of FCC. After that, the polycrystalline behaviors obtained using the Taylor model are compared with those obtained using the homogenization-based finite element method. Finally, the quantitative adequacy of the Taylor model is discussed. It is clarified that the Taylor model is qualitatively consistent with the homogenization-based finite element method and can be used as a practical model of polycrystalline FCC metals for a first-order approximation, although it is not quantitatively reasonable even for FCC metals.     

考虑接头作用的全复合材料桁架结构多尺度分析

为提高全复合材料桁架分析的精度和效率,引入结构多尺度有限元思想,对接头进行精细化建模,通过建立两点位移约束实现不同尺度模型连接,从而将接头模型嵌入宏观桁架模型,并针对具体制备工艺赋予桁架材料属性。为验证多尺度模型的优势,同时进行全复合材料桁架实验,以及分别基于全部梁单元模型和全部实体单元模型的有限元分析。对比相关模型的计算精度与效率,结果表明多尺度模型能够较好地兼顾计算精度与效率。该文针对全复合材料桁架的结构多尺度有限元建模方法,可精确分析全复合材料桁架承载性能,并且能够提供有效的局部信息,可用于分析其他包含复杂细节构造的大尺度复合材料结构。     

Multiscale prediction of mechanical behavior of ferrite–pearlite steel with numerical material testing

Multiscale mechanical behaviors of ferrite–pearlite steel were predicted using numerical material testing (NMT) based on the finite element method. The microstructure of ferrite–pearlite steel is regarded as a two‐component aggregate of ferrite crystal grains and pearlite colonies. In NMT, the macroscopic stress–strain curve and the deformation state of the microstructure were examined by means of a two‐scale finite element analysis method based on the framework of the mathematical homogenization theory. The microstructure of ferrite–pearlite steel was modeled with finite elements, and constitutive models for ferrite crystal grains and pearlite colonies were prepared to describe their anisotropic mechanical behavior at the microscale level. While the anisotropic linear elasticity and the single crystal plasticity based on representative characteristic length have been employed for the ferrite crystal grains, the constitutive model of a pearlite colony was newly developed in this study. For that reason, the constitutive behavior of the pearlite colony was investigated using NMT on a smaller scale than the scale of the ferrite–pearlite microstructure, with the microstructure of the pearlite colony modeled as a lamellar structure of ferrite and cementite phases with finite elements. On the basis of the numerical results, the anisotropic constitutive model of the pearlite colony was formulated based on the normal vector of the lamella. The components of the anisotropic elasticity were estimated with NMT based on the finite element method, where the elasticity of the cementite phase was numerically evaluated with a first‐principles calculation. Also, an anisotropic plastic constitutive model for the pearlite colony was formulated with two‐surface plasticity consisting of yield functions for the interlamellar shear mode and yielding of the overall lamellar structure. After addressing the microscopic modeling of ferrite–pearlite steel, NMT was performed with the finite element models of the ferrite–pearlite microstructure and with the microscopic constitutive models for each of the components. Finally, the results were compared with the corresponding experimental results on both the macroscopic response and the microscopic deformation state to ascertain the validity of the numerical modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical implementation of a neural network based material model in finite element analysis

Neural network (NN) based constitutive models can capture non‐linear material behaviour. These models are versatile and have the capacity to continuously learn as additional material response data becomes available. NN constitutive models are increasingly used within the finite element (FE) method for the solution of boundary value problems. NN constitutive models, unlike commonly used plasticity models, do not require special integration procedures for implementation in FE analysis. NN constitutive model formulation does not use a material stiffness matrix concept in contrast to the elasto‐plastic matrix central to conventional plasticity based models. This paper addresses numerical implementation issues related to the use of NN constitutive models in FE analysis. A consistent material stiffness matrix is derived for the NN constitutive model that leads to efficient convergence of the FE Newton iterations. The proposed stiffness matrix is general and valid regardless of the material behaviour represented by the NN constitutive model. Two examples demonstrate the performance of the proposed NN constitutive model implementation. Copyright © 2004 John Wiley & Sons, Ltd.     

Nonlinear fracture mechanics and plasticity of the split cylinder test

The split cylinder test is subjected to an analysis combining nonlinear fracture mechanics and plasticity. The fictitious crack model is applied for the analysis of splitting tensile fracture, and the Mohr-Coulomb yield criterion is adopted for modelling the compressive crushing/sliding failure. Two models are presented, a simple semi-analytical model based on analytical solutions for the crack propagation in a rectangular prismatic body, and a finite element model including plasticity in bulk material as well as crack propagation in interface elements. A numerical study applying these models demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive properties. This implies that the linear elastic interpretation of the ultimate splitting force in term of the uniaxial tensile strength of the material is only valid for special situations, e.g. for very large cylinders. Furthermore, the numerical analysis suggests that the split cylinder test is not well suited for determining the tensile strength of early age or fibre reinforced concrete.     

A computational multi-scale approach for the stochastic mechanical response of foam-filled honeycomb cores

This paper investigates the uncertainty in the mechanical response of foam-filled honeycomb cores by means of a computational multi-scale approach. A finite element procedure is adopted within a purely kinematical multi-scale constitutive modelling framework to determine the response of a periodic arrangement of aluminium honeycomb core filled with PVC foam. By considering uncertainty in the geometric properties of the microstructure, a significant computational cost is added to the solution of a large set of microscopic equilibrium problems. In order to tackle this high cost, we combine two strategies. Firstly, we make use of symmetry conditions present in a representative volume element of material. Secondly, we build a statistical approximation to the output of the computer model, known as a Gaussian process emulator. Following this double approach, we are able to reduce the cost of performing uncertainty analysis of the mechanical response. In particular, we are able to estimate the 5th, 50th, and 95th percentile of the mechanical response without resorting to more computationally expensive methods such as Monte Carlo simulation. We validate our results by applying a statistical adequacy test to the emulator.     

Touran轿车天窗框架冲压成形的数值模拟

应用LS-DYNA有限元软件,对Touran轿车天窗框架冲压成形过程进行了数值仿真,研究了框架易于失效沟槽处材料的变形行为,并预测了开裂产生的原因,同时对其成形后的厚度变化、变形安全裕度及天窗框架的材料选择进行了分析.仿真结果与实际冲压结果取得了较好的一致,证明了所建立的天窗框架仿真模型的合理性及计算结果的准确性,同时也进一步说明了材料性能对成形化具有显著的影响,为天窗框架冲压材料的选择提供了科学依据.     

Analysis of the mechanical performance of a cardiovascular stent design based on micromechanical modelling

Stents are very commonly used in the treatment of coronary heart disease. They are permanent vascular support structures that offer a preferred alternative to bypass surgery in certain situations. The purpose of this work is to examine the mechanical behaviour of a stainless steel balloon expandable stent design using computational micromechanics in the context of the finite element method. Deployment and cardiac pulsing loading conditions are considered. Classical phenomenological plasticity theory (J₂ flow theory) and physically based crystal plasticity theory are used to describe the stent material behaviour. Parametric studies are carried out using both constitutive theories with a view to determining important stent deployment characteristics such as recoil and foreshortening. Comparisons of the results obtained using both theories illustrate differences, with the crystal plasticity theory models showing closer agreement to published performance data. The implications of this for stent design are discussed.     

A robust and efficient substepping scheme for the explicit numerical integration of a rate‐dependent crystal plasticity model

This paper describes the development of efficient and robust numerical integration schemes for rate‐dependent crystal plasticity models. A forward Euler integration algorithm is first formulated. An integration algorithm based on the modified Euler method with an adaptive substepping scheme is then proposed, where the substepping is mainly controlled by the local error of the stress predictions within the time step. Both integration algorithms are implemented in a stand‐alone code with the Taylor aggregate assumption and in an explicit finite element code. The robustness, accuracy and efficiency of the substepping scheme are extensively evaluated for large time steps, extremely low strain‐rate sensitivity, high deformation rates and strain‐path changes using the stand‐alone code. The results show that the substepping scheme is robust and in some cases one order of magnitude faster than the forward Euler algorithm. The use of mass scaling to reduce computation time in crystal plasticity finite element simulations for quasi‐static problems is also discussed. Finally, simulation of Taylor bar impact test is carried out to show the applicability and robustness of the proposed integration algorithm for the modelling of dynamic problems with contact. Copyright © 2014 John Wiley & Sons, Ltd.