Numerical implementation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers

Due to their high deformation capabilities, polymeric materials are widely used in several industries. However, polymers exhibit a complex behaviour with strain rate, temperature and pressure dependencies. Numerous constitutive models were developed in order to take into account their specific behaviour. Among these models, the ones proposed by Richeton et al Polymer 46:6035–6043 (2005a), Polymer 46:8194–8201 (2005b) seem to be particularly suitable. They proposed expressions for the Young modulus and the yield stress with strain rate and temperature dependence. Moreover, these models were also implemented in a finite elastic-viscoplastic deformation approach using a flow rule based on thermally activated process. The increase of computational capabilities allowed simulating polymer forming processes using finite element (FE) codes. The aim of the study is to implement the proposed constitutive model in a commercial FE code via a user material subroutine. The implementation of the model was verified using compressive tests over a wide range of strain rates. Next, FE simulations of an impact test and of a plane strain forging process were carried out. The FE predictions are in good agreement with the experimental results taken from the literature.     

An iterative method for coupling of deformation and failure mechanisms on different length scales

An iterative method for coupling of numerical simulations on two length scales is presented. The computations on the microscale and on the macroscale are linked via a suitable macroscopic constitutive law. The parameters of this material law depend on the deformation history and are obtained from simulations using microstructurally representative volume elements (RVEs) subjected to strain paths derived from the associated material points in the macroscopic structure. Thus, different constitutive parameter sets are assigned to different regions of the macrostructure. The microscopic and macroscopic simulations are performed iteratively and interact mutually via the strain paths and the constitutive parameters, respectively. As an example, the strip tension test for a porous material is modelled using the finite element (FE) method. The coupling procedure, the material law and its numerical implementation are described. The method is shown to allow for a detailed simulation of the deformation mechanisms both on the micro‐ and the macroscale as well as for an assessment of their interactions while keeping the computational efforts reasonably low. Copyright © 2000 John Wiley & Sons, Ltd.     

增量成形内凸螺旋波纹管研究

目的 研究增量成形螺旋波纹管过程中,工具头的单次压下量与摩擦因数对成形质量和极限的影响规律,优化成形工艺参数。方法 通过ABAQUS有限元模拟和实验相结合,对各个成形工艺参数进行有限元模拟;使用前端直径为8 mm的成形工具头对外径40 mm、壁厚0.8 mm的304不锈钢进行增量成形螺旋波纹管实验研究。结果 不同摩擦因数对成形极限影响较小,对成形质量有较大影响。单次进给量为0.1 mm,摩擦因数为0.02时,螺纹深度极限可以提高10.5%。模拟和实验都验证了工艺参数的合理性。结论 摩擦因数一定的情况下,单次压下量越小,成形力越小,螺纹深度极限越大。     

Prediction of transverse and angular distortions of gas tungsten arc bead-on-plate welding using artificial neural network

The angular distortion and transverse shrinkage are often generated in gas tungsten arc (GTA) bead-on-plate welding process, which leads to additional costs of rework. Therefore, it is beneficial to estimate the welding deformations prior to bead-on-plate welding in terms of several process parameters. This paper presents the development of a back propagation neural (BPN) network model for the prediction of angular distortion and transverse shrinkage generated in GTA bead-on-plate welding process. The model is based on the results from finite element (FE) simulations. The GTA bead-on-plate welding for S304L stainless steel was simulated using finite element method, and experiments were conducted to verify the accuracy of the FE model. The experimental results were also used as testing samples for the BPN model. Welding speed, current and voltage were considered as the input parameters and the angular distortion and transverse shrinkage were the output parameters in the development of the BPN model. The correlation coefficients and percentage errors for all the samples were calculated to evaluate the prediction accuracy of BPN model. The results show that the BPN model developed in this study can predict the angular distortion and transverse shrinkage with reasonable accuracy.     

Substructuring in the implicit simulation of single point incremental sheet forming

This paper presents a direct substructuring method to reduce the computing time of implicit simulations of single point incremental forming (SPIF). Substructuring is used to divide the finite element (FE) mesh into several non-overlapping parts. Based on the hypothesis that plastic deformation is localized, the substructures are categorized into two groups: the plastic—nonlinear—substructures and the elastic—pseudo-linear—substructures. The plastic substructures assemble a part of the FE mesh that is in contact with the forming tool; they are iteratively updated respecting all nonlinearities. The elastic substructures model the elastic deformation of the rest of the FE mesh. For these substructures, the geometrical and the material behaviour are assumed linear within the increment. The stiffness matrices and the internal force vectors are calculated at the beginning of each increment then they are statically condensed to eliminate the internal degrees of freedom (DOF). In the iteration process the condensed stiffness matrices for the elastic substructures are kept constant. The condensed internal force vectors are updated by the multiplication of the condensed stiffness matrices and the displacement increments. After convergence, any geometrical and material nonlinearity for the elastic substructures are nonlinearly updated. The categorization of substructures in plastic and elastic domains is adapted during the simulation to capture the tool motion. The resulting, plastic and condensed elastic, set of equations is solved on a single processor. In an example with 1600 shell elements, the presented substructuring of the SPIF implicit simulation is 2.4 times faster than the classical implicit simulation.     

板料渐进成形数值模拟与实验研究

为提高渐进成形的成形效率和成形质量,了解板料渐进成形的变形规律及工艺参数对成形的影响,采用有限元方法对板料渐进成形过程进行了数值模拟研究,分析了斜壁盒形件渐进成形过程应力分布和厚度变化趋势,通过对不同进给量和不同成形路径进行数值模拟,分析了工艺参数对成形的影响.结果表明,斜壁盒形件最大应力和最大厚度减薄发生在底面拐角处;成形过程中工具头运动轨迹应尽量采用走螺旋线的方式,可以提高成形件的成形能力和成形质量.渐进成形实验表明,数值模拟结果与实验结果基本吻合.     

单点渐进成形工艺参数对正五边锥形件壁厚的影响

目的 利用数值模拟方法研究单点渐进成形工艺参数对制件成形区最小壁厚的影响规律,得出最优工艺参数组合,提高制件的成形质量。方法 在对2024铝合金正五边锥形件建立有模单点渐进成形数值仿真模型的基础上,对进给率、层间距、成形工具头直径和摩擦因数对制件成形区最小壁厚的影响进行单因素和正交试验分析,并通过物理试验对仿真优化后的工艺参数组合进行验证。结果 正五边锥形件单点渐进成形加工过程中,最小壁厚与进给率、层间距成反比,与成形工具头直径成正比,而摩擦因数对最小壁厚的影响较小;各工艺参数对最小壁厚的影响程度为进给率＞层间距＞成形工具头直径＞摩擦因数;最佳工艺参数为成形头直径9 mm、进给率200 mm/min、加工层间距0.2 mm和摩擦因数0.1。结论 通过有限元仿真得出了单点渐进有模成形工艺对制件最小壁厚的影响规律,通过正交试验分析得出了正五边锥形件单点渐进有模成形最佳工艺参数组合,利用该参数组合可以得到壁厚较为均匀的正五边锥形件。     

Models for ductile damage and fracture prediction in cold bulk metal forming processes: a review

Ductile damage and fracture prediction in real size structures subjected to complex loading conditions has been of utmost interest in the scientific and engineering community in the past century. Numerical simulations with nonlinear finite element (FE) codes allow investigating various complicated problems for damage and fracture prediction in real scale models, which is an important topic in many industries, including metal forming industry. For all industrial cold forming processes, the ability of numerical modeling to predict ductile fracture is crucial. However, this ability is still limited because of the complex loading paths (multi-axial and non-proportional loadings) and important shear effects in several forming processes. The development robust damage and fracture prediction models is essential to obtain realistic results for both geometry precision and mechanical properties. The present article reviews the models in three approaches of ductile damage, namely: uncoupled phenomenological model (or fracture criteria), coupled phenomenological models, and micromechanics-based models, which have been developed to predict ductile fracture in metal forming processes. The objective is to supply to engineers and scientists an overview on a “top-down” procedure to be able to construct predictive tools for metal forming processes.     

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.     

Mixed-Mode Delamination – Experimental and Numerical Studies

Abstract: A fracture energy approach for modelling mixed-mode delamination of composite materials and other bonded structures is introduced. The model is incorporated within an explicit finite element (FE) code and ties layered shell elements together via a stiffness condition, a failure criterion and post-failure damage law. The procedure for predictive modelling of delamination using the approach is described and the set of required input parameters is presented. A benchmark test comparing experimental results for a continuous filament random E-glass/polyester composite and explicit FE simulations for standard fracture toughness tests for a range of mode mixities is included.     

An approach to modeling time-dependent creep and residual stress relaxation around cold worked holes in aluminium alloys at room temperature

Creep behaviour of aluminium alloys is also observed at room temperature. As a result, a relaxation occurs of deliberately introduced beneficial residual stresses around fastener holes, before the relevant structural component is subjected to exploitation. Therefore, to adequately asses the life-time of the component with cold worked holes, it is necessary to quantify this relaxation. In this paper a combined iterative approach for building a time-dependent creep constitutive model of aluminium alloys at room temperature has been developed in order to be used in finite element (FE) simulations of the cold hole working process. The approach is based on an experimental study of the change in diameters of cold worked holes through mandrel cold working method and a subsequent series of FE simulations of the cold working process and of the following creep behaviour to determine the necessary equivalent stresses in the constitutive model. The obtained creep constitutive model has been founded on the power-law model. The model parameters A, n and m have been determined on the basis of a developed by the authors algorithm. The approach has been illustrated on D16T aluminium alloy widely used in the airspace industry. The material behaviour in the plastic field has been described by the nonlinear kinematic hardening model, obtained through a uniaxial tensile test. Both constitutive models have been used in FE simulations of the cold working processes and of subsequent residual stress relaxation around the cold worked open holes due to creep at room temperature. On the base of the FE results, mathematical models describing the residual stress relaxation have been obtained. Thus, the residual stresses are adequately evaluated immediately before introducing the structural component in operation.     

Industrial challenges for finite element and multiscale methods for material modeling

The automotive industry promotes lightweight design to reduce the CO2-emission and enhances the passenger’s safety using high strength steel grades. One limiting factor to the accuracy of modern stamping simulation are the empirical constitutive models. In particular for high strength multiphase steels the modelling techniques like multi-scale methods are becoming more interesting. However they should meet the industrial needs. Not only the accuracy but also features like time, costs and complexity are rapidly increasing. The challenge is the development of finite element technologies and multi-scale methods in an appropriate framework for industrial projects. The crystal plasticity finite element method bridges the gap between the micro level and macroscopic mechanical properties that opens the way for more profound consideration of metal anisotropy in stamping process simulation. Nevertheless new empirical constitutive models are favourable for spring back prediction in forming simulations, even if the number of material parameters and the amount of tests for their identification increases. In this paper the application of crystal plasticity FEM within the concept of virtual material testing with a representative volume element (RVE) is demonstrated.     

Strain evolution in the single point incremental forming process: digital image correlation measurement and finite element prediction

Incremental Sheet Forming (ISF) is a relatively new class of sheet forming processes that allow the manufacture of complex geometries based on computer-controlled forming tools in replacement (at least partially) of dedicated tooling. This paper studies the straining behaviour in the Single Point Incremental Forming (SPIF) variant (in which no dedicated tooling at all is required), both on experimental basis using Digital Image Correlation (DIC) and on numerical basis by the Finite Element (FE) method. The aim of the paper is to increase understanding of the deformation mechanisms inherent to SPIF, which is an important issue for the understanding of the high formability observed in this process and also for future strategies to improve the geometrical accuracy. Two distinct large-strain FE formulations, based on shell and first-order reduced integration brick elements, are used to model the sheet during the SPIF processing into the form of a truncated cone. The prediction of the surface strains on the outer surface of the cone is compared to experimentally obtained strains using the DIC technique. It is emphasised that the strain history as calculated from the DIC displacement field depends on the scale of the strain definition. On the modelling side, it is shown that the mesh density in the FE models plays a similar role on the surface strain predictions. A good qualitative agreement has been obtained for the surface strain components. One significant exception has however been found, which concerns the circumferential strain evolution directly under the forming tool. The qualitative discrepancy is explained through a mechanism of through-thickness shear in the experiment, which is not fully captured by the present FE modelling since it shows a bending-dominant accommodation mechanism. The effect of different material constitutive behaviours on strain prediction has also been investigated, the parameters of which were determined by inverse modelling using a specially designed sheet forming test. Isotropic and anisotropic yield criteria are considered, combined with either isotropic or kinematic hardening. The adopted constitutive law has only a limited influence on the surface strains. Finally, the experimental surface strain evolution is compared between two cones with different forming parameters. It is concluded that the way the plastic zone under the forming tool accommodates the moving tool (i.e. by through-thickness shear or rather by bending) depends on the process parameters. The identification of the most determining forming parameter that controls the relative importance of either mechanism is an interesting topic for future research.     

Research on deformation characteristics of JCOE forming in large diameter welding pipe

In the present work, the JCOE forming is investigated using the finite element (FE) method. A twodimensional FE model is established for the plane strain condition by FE code ABAQUS, and the FE model is validated by experiments. The aim of this research is to investigate forming quality states in the JCOE forming process; in particular, the effects of technological parameters on forming quality are evaluated. Taking the JCOE forming process of X80 steel φ1 219 mm×22 mm×12 000 mm welding pipe for instance, the deformation characteristics of JCOE forming are analyzed, in which the geometry of the formed pipe, residual stress distributions and effects of process parameters on JCOE forming quality can be obtained. Thus, the presented results of this research provide an effective approach to improve welding pipe forming quality.     

Prediction of Process-Induced Distortions in L-Shaped Composite Profiles Using Path-Dependent Constitutive Law

In this paper, the corner spring-in angles of AS4/8552 L-shaped composite profiles with different thicknesses are predicted using path-dependent constitutive law with the consideration of material properties variation due to phase change during curing. The prediction accuracy mainly depends on the properties in the rubbery and glassy states obtained by homogenization method rather than experimental measurements. Both analytical and finite element (FE) homogenization methods are applied to predict the overall properties of AS4/8552 composite. The effect of fiber volume fraction on the properties is investigated for both rubbery and glassy states using both methods. And the predicted results are compared with experimental measurements for the glassy state. Good agreement is achieved between the predicted results and available experimental data, showing the reliability of the homogenization method. Furthermore, the corner spring-in angles of L-shaped composite profiles are measured experimentally and the reliability of path-dependent constitutive law is validated as well as the properties prediction by FE homogenization method.     

Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites

This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.     

Simulation of 3D interlock composite preforming

The ply to ply interlock fabric preform enables to manufacture, by R.T.M. process, thick composite parts that are resistant to delamination and cracking. Numerical simulation of interlock reinforcement forming allows to determine conditions for feasibility of the process and above all to know the position of fibres in the final composite part. For this forming simulation, specific hexahedral finite elements made of segment yarns are proposed. Position of each yarn segment within the element is taken into account. This avoids determination of a homogenized equivalent continuous law that would be very difficult considering the complexity of the weaving. Transverse properties of fabric are taken into account within a hypoelastic constitutive law. A set of 3D interlock fabric forming simulations shows the efficiency of the proposed approach.     

Fast simulation of incremental sheet metal forming by adaptive remeshing and subcycling

In order to use incremental sheet forming (ISF) in an industrial context, it is necessary to provide fast and accurate simulation methods for virtual process design. Without reliable process simulations, first-time right production seams infeasible and the process loses its advantage of offering a short lead time. Previous work indicates that implicit finite element (FE) methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires a very small time step. Finite element methods based on explicit time integration can be sped up using mass or time scaling to enable the simulation of large-scale sheet metal forming problems. However, AISF still requires dedicated adaptive meshing methods to further reduce the calculation times. In this paper, an adaptive remeshing strategy based on a multi-mesh method is developed and applied to the simulation of AISF. It is combined with subcycling to further reduce the calculation times. For the forming of a cone shape, it is shown that savings in CPU time of up to 80 % are possible with acceptable loss of accuracy, and that the simulation time scales more moderately when the part size is increased, so that larger, industrially relevant parts become feasible.     

基于神经网络遗传算法的深腔型零件拉深工艺参数优化

目的 解决冲压成形中工艺参数优化难的问题.方法 以一种深腔型零件的冲压成形为例.首先,借助灰度关联分析法对有限元中的工艺参数进行分析,获取该零件冲压成形中影响成形质量的2个主要因素——冲压速度和压边力.其次,借助拉丁超立方抽样法对上述2个因素进行随机取样,并借助DYNAFORM软件对其进行逐一模拟.再次,将冲压速度和压边力作为输入,最大减薄作为输出,训练在MATLAB中建立的BP神经网络,并借助遗传算法对其进行寻优.结果 最优成形压边力为1.372 MN,最优加载速度为1.5366 m/s.结论 与神经网络遗传算法预测相比,有限元结果的相对误差小于2％,零件试制结果的相对误差小于6％,该方法有较高的预测精度.