Experimental and finite element simulation methods for rate-dependent metal forming processes

An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.     

Enhanced finite element formulations on the numerical simulation of tailor-welded hydroformed products

This work aims to assess the influence of different finite element formulations in the performance and quality of solution obtained by numerical simulation in the analysis of tailor-welded hydroformed tubular parts. Tube hydroforming represents a cost effective forming process for high-strength, low weight products on, as an example, automotive and airspace applications. On the other side, the use of tailor-welding in order to obtain custom-made combinations of thicknesses and materials - leading to a wide variety of user-defined products - can be introduced into conventional tubular hydroforming processes in order to further improve the applicability range of the later process. The main goal of the present work is to describe the state-of-the-art in the field, focusing on distinct finite element formulations and providing guidelines for the simulation of tubular hydroforming process combined with tailor-welded joining techniques. Hexahedral solid and solid-shell enhanced assumed strain elements, either with reduced and full numerical integration procedures, are analyzed in order to infer about the potentialities of the combined forming technology. Material characterization of the heat affected zone is included and the influence of finite element modeling on defects onset and prediction during forming is considered.     

Crash response of advanced high-strength steel tubes: Experiment and model

The performance of non-hydroformed and hydroformed structural steel tubes in component-level crash testing was investigated using both experimental and analytical techniques. In particular, the focus was on high-strength steels that may have potential to enhance crashworthiness of automobiles. Monolithic tubes made from multiple materials and wall thicknesses were considered in this study. The following materials were used: conventional drawing quality (DDQ) steels; high-strength low alloy (HSLA-350) steels; and advanced high-strength steel (AHSS) materials comprising the dual phase alloys DP600 and DP780. The goal of this research was to study the interaction between the forming and crash response of these materials in order to evaluate their potential for use in vehicle design for crashworthiness. The tubes were hydroformed using two methods known as low- and high-pressure processes. Material characterization of all materials was carried out through quasi-static and high strain rate tensile tests in the range of 0.00333–1500 s⁻¹, and rate sensitive constitutive models for all materials were developed. The nonlinear explicit dynamic finite element code LS-DYNA, in conjunction with the validated constitutive models, was used to simulate both the hydroforming processes and the crash tests performed on the tubes. The energy absorption characteristics of the different tubes were calculated and the results from the numerical analyses were compared against the experimental data. This comparison was performed in order to determine whether the interactions between forming and crush could be adequately predicted using finite element analysis. The effects of thickness changes, work hardening, and component geometry, which resulted from hydroforming, on the crash response were also investigated. A study of the significance of strain rate and the importance of performing detailed material characterization on the accuracy of the numerical analysis was performed. Also, a parametric study on the effect of transferring forming history data between simulations on the accuracy of the numerical analysis was performed, and the importance of carrying forward the histories between multiple forming simulations was demonstrated.     

Impact Damage of 3D Orthogonal Woven Composite Circular Plates

The damages of 3D orthogonal woven composite circular plate under quasi-static indentation and transverse impact were tested with Materials Test System (MTS) and modified split Hopkinson bar (SHPB) apparatus. The load vs. displacement curves during quasi-static penetration and impact were obtained to study the energy absorption of the composite plate. The fluctuation of the impact stress waves has been unveiled. Differences of the load-displacement curves between the quasi-static and impact loading are discussed. This work also aims at establishing a unit-cell model to analyze the damage of composites. A user material subroutine which named VUMAT for characterizing the constitutive relationship of the 3-D orthogonal woven composite and the damage evolution is incorporated with a finite element code ABAQUS/Explicit to simulate the impact damage process of the composite plates. From the comparison of the load-displacement curves and energy absorption curves of the composite plate between experimental and FEM simulation, it is shown that the unit-cell model of the 3D woven composite and the VUMAT combined with the ABAQUS/Explicit can calculate the impact responses of the circular plate precisely. Furthermore, the model can also be extended to simulate the impact behavior of the 3D woven composite structures.     

立式瓦楞复合纸板静态压缩试验与有限元分析

目的对立式瓦楞复合纸板的静态压缩过程进行试验研究和有限元分析,研究不同楞型立式瓦楞复合纸板的力学性能。方法制作A楞、AB楞、B楞等3种不同立式瓦楞复合纸板试样,进行静态压缩实验,得到其压缩应力-应变曲线;建立3种楞型的立式瓦楞复合纸板有限元模型,进行静力学分析,得到其压缩应力-应变曲线,并与实验结果进行对比分析。结果试验和有限元分析均显示立式瓦楞复合纸板的静态压缩过程与蜂窝纸板的静态压缩过程类似,包括弹性阶段、屈服阶段、平台阶段、密实化阶段,试验和有限元分析所得到的压缩应力-应变曲线相吻合。纸板的峰值应力和平台应力与楞型有关,且随着楞高的增大而减小。结论通过试验研究和有限元分析方法得到了不同楞型立式瓦楞复合纸板的静态压缩性能,对该新型材料的应用有重要参考价值。     

Analysis of forward–backward-radial extrusion process

This paper presents the analysis of forward–backward-radial extrusion process. Finite element method has been used to investigate the effect of geometrical parameters such as die corner radius and gap height as well as process condition such as friction on the process. ABAQUS software is used for finite element simulations. The finite element results are compared with experimental data in terms of forming load and material flow in different regions. Hardness distribution in longitudinal cross-section of the product is also used to verify strain distribution obtained from finite element analysis. The comparison between the theoretical and the experimental results show good agreement. The relation between hardness and strain value is compatible with previous work.     

Untersuchung des Fließverhaltens der Magnesiumknetlegie‐rung AZ31 mit Hilfe von Schichtstauch‐ und Zugversuchen

Today design of metal forming processes is often supported by numerical simulation. To obtain realistic simulation results, the used material models need accurate material parameters from the material characterization. Magnesium alloys in particular are not yet sufficiently investigated. Therefore, their material parameters are scarce in literature. Especially determination of flow curves at higher degrees of deformation represents a challenge, but is necessary in order to describe the characteristic hardening and softening, as they occur in magnesium materials at elevated temperature of forming process. In this paper, an approach for the determination of a combined hardening curve from a tensile test and a layer compression test is presented. For this purpose, the corresponding values are recorded experimentally and evaluated based on the principle of the plastic work equivalence.     

基于Johnson-cook本构模型的EPE包装跌落冲击模拟

目的将聚乙烯泡沫塑料在动态压缩试验下得到的力学性能引入有限元中,创建材料模型,并应用于跌落冲击仿真分析,以提高仿真的精确度。方法通过聚乙烯泡沫塑料在不同速率下的压缩试验,得到真实的应力-应变曲线,并基于Johnson-cook本构模型在有限元中建立EPE的材料模型。最后用AnsysWorkbench中的LS-DYNA模块对聚乙烯泡沫缓冲包装的跌落过程进行仿真分析,用LS-PREPOST软件进行后处理。在此基础上,对比分析仿真结果和实验结果。结果仿真结果的误差分别为0.85%,1.6%,2.97%,与实验结果基本一致。结论基于Johnson-cook本构模型构建的聚乙烯泡沫塑料有限元材料模型能有效提高低速冲击的仿真精度,为非线性材料和应变率敏感材料的有限元动态冲击分析提供了参考。     

AA5052板材准静态/动态平面应变成形极限试验研究

为建立磁脉冲辅助冲压成形(EMAS)工艺的有效性,采用准静态平面应变预拉伸和动态磁脉冲成形相结合的方法对5052-O铝合金板材的准静态/动态平面应变状态复合成形极限进行了试验研究.结果表明:准静态/动态复合加载过程能显著改善该铝合金板材的室温成形性;准静态/动态平面应变复合成形极限比准静态平面应变成形极限有显著提高,相似或者略高于完全磁脉冲平面应变成形性,且随着准静态预应变水平的增加,准静态/动态复合变形成形极限变化不大.预变形的存在不会削弱复合成形过程的极限变形能力.     

Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.     

On finite element modelling of surface tension: Variational formulation and applications – Part II: Dynamic problems

In Part I, a finite element model of surface tension has been discussed and used to solve some quasi-static problems. The quasi-static analysis is often required to find not only the initial shape of the liquid but also the static equilibrium state of a liquid body before a dynamic analysis can be carried out. In general, natural and industrial processes in which surface tension force is dominant are of dynamic nature. In this second part of this work, the dynamic effects will be included in the finite element model described in Part I.A fully Lagrangian finite element method is used to solve the free surface flow problem and Newtonian constitutive equations describing the fluid behaviour are approximated over a finite time interval. As a result the momentum equations are function of nodal position instead of velocities. The resulting ordinary differential equation is integrated using Newmark algorithm. To avoid overly distorted elements an adaptive remeshing strategy is adopted. The adaptive strategy employs a remeshing indicator based on viscous dissipation functional and incorporates an appropriate transfer operator.The validation of the model is performed by comparing the finite element solutions to available analytical solutions of a droplet oscillations and experimental results pertaining to stretching of a liquid bridge.     

聚氨酯隔振器特性的有限元分析

利用不同的本构模型对聚氨酯材料的实际应力－应变曲线进行拟合,运用ABAQUS软件的超弹性材料评估功能,得出了适合聚氨酯材料的最佳本构模型。基于该本构模型,对一种新型聚氨酯隔振器的静、动态性能进行有限元分析,得到了隔振器的主要性能指标。通过隔振器的试验,验证了有限元分析的有效性,对聚氨酯材料在新型隔振元件设计中的应用具有一定的指导意义。     

On the numerical simulation of sheet metal blanking process

The use of the blanking process has been widely spread in mass production industries. In this technique, the quality of the final product is directly related to the setting parameters of the process and the material response of the sheet. In the present work, a general framework based on the finite element method for the simulation of the sheet metal blanking process is presented. The proposed approach properly addresses all the numerical challenges related to blanking. First, an extension of elasto-viscoplastic constitutive equations for the large strain regime is used to take into account the material strain-rate sensitivity. Then, the inertial effects coming from high velocity operations are considered by means of an implicit time integration scheme. Moreover, the frictional contact interactions are simulated with the classical Coulomb law and an energetically consistent formulation of area regularization. Finally, ductile fracture is modeled thanks to the element deletion method coupled with a fracture criterion. The blanking process is then simulated for different setting parameters. The accuracy of this approach is evaluated by comparing the numerical predictions to experimental results for both quasi-static and dynamic conditions. Good agreement is found between experimental and numerical results for all cases.     

Effect of Molding Material Temperature on Workpiece in FDM

Fused deposition molding is an advanced kind of rapid prototyping technology. On the accuracy of the forming process,the research on the temperature of the molding material is based on the analysis of the forming parameters. The influence of the temperature of the molding material on the specimen is reasonably described by the actual forming part and the finite element analysis model. The experimental results show that the temperature of the molding material is less affected by the temperature of the molding material in a certain range. This will lay the theoretical foundation for the formation of the molding technology in the future.     

Highly nonlinear solitary waves in chains of hollow spherical particles

We study the dynamic response of one- dimensional granular chains composed of uniform hollow spheres excited by an impulse, and we observe the formation and propagation of highly nonlinear solitary waves. We find that the dynamics of these solitary waves are different from the solitary waves forming in chains composed of uniform solid spheres, because of the changes in the contact interaction between particles. We study the quasi-static contact interaction between two hollows spheres using finite element (FE) simulations, and approximate their response as a power-law type function in the range of forces of interest for this work. The experimental data obtained by testing a chain of particles shows good agreement with theoretical predictions obtained using a long wavelength approximation, and with numerical simulations based on discrete particle and FE models. We also investigate the effect of hollow spheres’ wall thickness on the dynamic response of the chains.     

Meso-Scale Damage Simulation of 3D Braided Composites under Quasi-Static Axial Tension

The microstructure of 3D braided composites is composed of three phases: braiding yarn, matrix and interface. In this paper, a representative unit-cell (RUC) model including these three phases is established. Coupling with the periodical boundary condition, the damage behavior of 3D braided composites under quasi-static axial tension is simulated by using finite element method based on this RUC model. An anisotropic damage model based on Murakami damage theory is proposed to predict the damage evolution of yarns and matrix; a damage-friction combination interface constitutive model is adopted to predict the interface debonding behavior. A user material subroutine (VUMAT) involving these damage models is developed and implemented in the finite element software ABAQUS/Explicit. The whole process of damage evolution of 3D braided composites under quasi-static axial tension with typical braiding angles is simulated, and the damage mechanisms are revealed in detail in the simulation process. The tensile strength properties of the braided composites are predicted from the calculated stress-strain curves. Numerical results agree with the available experiment data and thus validates the proposed damage analysis model. The effects of certain material parameters on the predicted stress-strain responses are also discussed by numerical parameter study.     

Modeling of failure mode of laser welds in lap-shear specimens of HSLA steel sheets

Failure mode of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel sheets is investigated in this paper. The experiments for laser welds in lap-shear specimens under quasi-static loading conditions are briefly reviewed first. The experimental results showed that the laser welds failed in a ductile necking/shear failure mode and the ductile failure was initiated at a distance away from the crack tip near the boundary of the base metal and heat affected zone. In order to understand the failure mode of these welds, finite element analyses under plane strain conditions were conducted to identify the effects of the different plastic behaviors of the base metal, heat affected zone, and weld zone as well as the weld geometry on the ductile failure. The results of the reference finite element analysis based on the homogenous material model show that the failure mode is most likely to be a middle surface shear failure mode in the weld. The results of the finite element analysis based on the multi-zone non-homogeneous material models show that the higher effective stress–plastic strain curves of the weld and heat affected zones and the geometry of the weld protrusion result in the necking/shear failure mode in the load carrying sheet. The results of another finite element analysis based on the non-homogeneous material model and the Gurson yield function for porous materials indicate that the consideration of void nucleation and growth is necessary to identify the ductile failure initiation site that matches well with the experimental observations. Finally, the results of this investigation indicate that the failure mode of the welds should be examined carefully and the necking/shear failure mode needs to be considered for development of failure or separation criteria for welds under more complex loading conditions.     

六边形蜂窝芯异面类静态压缩力学行为的仿真分析

目的研究六边形蜂窝芯材异面类静态压缩载荷的数值模拟方法及相关力学行为。方法基于蜂窝单元阵列的方法,构筑了单双壁厚六边形蜂窝芯材异面类静态压缩有限元数值计算模型和分析方法。结果借助于该模拟方法,分析计算了不同结构参数条件下单双壁厚六边形蜂窝芯材的异面变形模式、变形曲线和类静态峰应力值,并绘制了相应的图、压缩力位移曲线和数据表格。结论将计算结果与现有的实验和理论计算结果作对比分析可知,计算结果与已有结果吻合较好,证明了所提出的有限元分析方法的可靠性。     

Characterization of temperature-dependent tensile and flexural rigidities of a cross-ply thermoplastic lamina with implementation into a forming model

This paper discusses the characterization of temperature-dependent tensile and flexural rigidities for Dyneema® HB80, a cross-ply thermoplastic lamina. The low coefficient of friction of this material posed a challenge to securing specimens during tensile testing. Therefore, modification to the standard gripping method was implemented to facilitate the collection of meaningful test data. Furthermore, a long gauge length was selected to moderate the influence of slippage on the measure of the elastic modulus. A new experimental setup is presented to characterize the bending behavior at elevated-temperature conditions based on the vertical cantilever method. The material properties derived from the test data were implemented in a finite element model of the cross-ply lamina. The finite element model is generated using a hybrid discrete mesoscopic approach, and deep-draw forming of the material is simulated to investigate its formability. Simulation results are compared with an experimental forming trial to demonstrate the capabilities of the model to predict the development of out-of-plane waves during preform manufacturing.