Application of optical field analysis of tensile tests for calibration of the Rusinek–Klepaczko constitutive relation of Ti6Al4V titanium alloy

In this paper, the application of the Rusinek–Klepaczko relation to describe the constitutive behaviour of Ti6Al4V titanium alloy with an HCP crystalline structure was proposed. The calibration of model coefficients was carried out on the basis of tensile tests. To obtain true stress–strain curves at quasi-static and dynamic loading conditions, the optical field measurement method was applied to determine the history of specimen cross-sections at the necking point. The outline of the specimen was tracked by virtual strain gauges implemented in TEMA Motion software. Adiabatic characteristics obtained at high strain rates using a pre-tension Hopkinson bar were corrected into quasi-isothermal using an analytical approach. Subsequently, a visco-plastic model calibrated using introduced methodology was validated using the finite element method. Engineering stress–strain curves, calculated using ABAQUS software incorporating the Rusinek–Klepaczko model, showed good agreement with experimental data at both quasi-static and dynamic deformation regimes. Moreover, numerical analysis of tensile tests shows that the strain, temperature and stress triaxiality distribution is non-homogenous in specimen cross-sections perpendicular to the loading direction. The value of the strain, temperature and stress triaxiality also depends on the strain rate.     

A novel constitutive model for Ti–6Al–4V alloy based on dislocation pile-up theory

The mechanical properties of the titanium alloy Ti–6Al–4V, which vary with the specimen size under different temperatures, are studied through the Split Hopkinson Pressure Bar (SHPB) test and the quasi-static tensile test to determine the parameters for the classical Johnson-Cook (JC) constitutive model. Based on the dislocation pile-up theory, the classical JC constitutive model is modified by adding a grain strain term Δσ to consider the influence of grain size. The SHPB and tensile tests are analysed using a finite element method simulation. Compared with the experimental results, the simulation results based on the modified JC model exhibit a much higher calculation accuracy than that of the classical JC model.     

Dynamic strain-rate effect on uniaxial tension deformation of Ti5Al2.5Sn α-titanium alloy at various temperatures

The uniaxial tensile experiments for Ti5Al2.5Sn alloy were performed at strain rates ranging from 10^?3–10⁺³ s^?1 and test temperatures of 153–873 K. Experimentally measured stress-strain responses indicate the yield strength exhibits positive strain-rate dependency, while the yield strength increases as the test temperature is decreased. To understand the thermomechanical coupling of dynamic plastic deformation, a specially developed single-tensile-pulse loading technique was used, and the isothermal stress-strain curves for the rates of 180 and 450 s^?1 were obtained at temperatures of 203, 298 and 573 K. The plastic strain hardening measurements obtained here are essentially athermal and largely independent of strain rate, consistent with titanium and its alloys being bcc-structure-like in mechanical behaviour. Based on the experimentally obtained plastic deformation features of the alloy, the physically based Voyiadjis-Abed constitutive relationship was modified to model the dynamic tensile deformation of the Ti5Al2.5Sn alloy at low and high temperatures.     

Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500 °C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.     

Finite element implementation of a kinetic model of dynamic strain aging in aluminum–magnesium alloys

Soare and Curtin (Acta Mater. 2008; 56 :4091–4101, 4046–4061) have recently developed a model of dynamic strain aging in solute‐strengthened alloys. Their constitutive law describes time‐dependent solute strengthening using rate equations that can be calibrated using atomistic simulations. In this paper, their material model is incorporated into a continuum finite element simulation, with a view to completing a multi‐scale method for predicting the formability of solute‐strengthened alloys. The Soare–Curtin model is first re‐formulated as a state‐variable constitutive law, which is suitable for finite element computations. An efficient numerical procedure is then developed to track the strength distribution of aging mobile and forest dislocations in the solid during deformation. The method is tested by simulating the behavior of a 3D aluminum–magnesium alloy tensile specimen subjected to uniaxial loading at constant nominal strain rate. The model predicts the influence of strain rate on the steady‐state flow stress of Al–Mg alloys, but no Portevin–Le Châtelier bands or serrated flow were observed in any of our simulations, and the influence of strain rate on tensile ductility is not predicted correctly. The reasons for this behavior and possible resolutions are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite Element Analysis and Experimental Measurement of Deformation Behavior for NiTi Plate With Stress Concentration Part Under Uniaxial Tensile Loading

Abstract: The aim of this study is to verify the effectiveness of ordinary phenomenological constitutive relation of NiTi shape memory alloy under mechanical loading at a constant temperature, sufficiently. First, finite element analysis is performed by using ordinary phenomenological constitutive relation for rectangular plate with double notch under tensile loading at a constant temperature. Next, uniaxial tensile loading is carried out for 50.5Ni49.5Ti rectangular plate with double notch. At the same time, macroscopic stress–strain curve and local strain distribution are measured by using in‐house measurement system on the basis of digital image correlation. As a result, it is found that the stress–strain curve obtained from finite element analysis is much different from those obtained experimental measurement, especially during stress‐induced martensite transformation. The result can be derived from the phenomena of local strain band behavior arising in NiTi under mechanical loading. The phenomenological constitutive model used in present finite element analysis is constructed under assumptions that the material has isotropic characteristics and shows homogeneous deformation. However, this experimental result suggests that the material itself has anisotropy microscopically. Furthermore, material shows unique inhomogeneous deformation. Also, there is possibility that these anisotropic characteristic and inhomogeneous deformation behaviour may derive from its microstructure. In future, to sufficiently describe the macroscopic stress–strain curve of NiTi we should take into consideration the material microstructure.     

聚乙烯拉伸应变速率的本构方程改进及运用

目的 对等密度、恒温条件下聚乙烯（PE）在不同应变率下的力学性能进行研究,改进原有本构方程的应变率项。方法 使用万能材料试验机,测量不同拉伸速率下PE的应力-应变曲线,并研究随着应变速率的增加,最大拉伸强度和断裂伸长率的变化趋势;基于Sherwood-Frost本构模型,对经典的热激活机制Seeger模型添加幂函数项,实现应变率与应变的耦合;基于最小二乘法,采用Matlab软件拟合本构模型参数,并将本构方程拟合结果与300,400,500 mm/min速率下的试验数据进行对比。结果 改进后的本构模型拟合数据与试验结果具有更高的吻合度,最大误差为8.12%,出现在300 mm/min的速度条件下。结论 随着拉伸速率的增加,PE材料的最大拉伸强度逐渐增加,断裂伸长率逐渐降低;改进应变率项后,本构模型具有更高的拟合精度,能够为有限元分析提供准确的材料参数。     

2.5D C/SiC复合材料连续损伤本构模型

基于连续损伤力学建立了一种包含拉伸与剪切损伤变量的2.5D C/SiC复合材料连续损伤本构模型。分别开展了拉伸和剪切试验,获得应力-应变曲线,并通过拟合试验曲线获得各损伤变量的演化参数。采用子程序技术将本构模型嵌入商用有限元软件ANSYS,应用有限元法计算了材料的应力-应变曲线。考虑了拉剪损伤耦合效应,计算了偏轴拉伸情况下的应力-应变曲线。结果表明:沿经纱拉伸、沿纬纱拉伸以及面内剪切的应力-应变曲线与试验结果吻合,最大偏差依次为4.30%、3.09%及3.73%;偏轴拉伸计算与试验应力-应变曲线也吻合较好。      

Hyper-elastic constitutive equations of conjugate stresses and strain tensors for the Seth-Hill strain measures

The use of hypo-elastic constitutive equations for large strains in nonlinear finite element applications usually requires special considerations. For example, the strain does not tend to zero upon unloading in some elastic loading-unloading closed cycles. Furthermore, these equations are based on objective material time rate tensors, which require incrementally objective algorithms for numerical applications and integration. Hyper-elastic constitutive equations on the other hand do not require such considerations. However, their behaviour for large elastic strains is important and may differ in tension and compression. In the present work, Hyper-elastic constitutive equations for the Seth-Hill strains and their conjugate stresses are explored as a natural generalisation of Hook’s law for finite elastic deformations. Based on the uniaxial and simple shear tests, the response of the material for different constitutive equations is examined. Together with an objective rate model, the effect of different constitutive laws on Cauchy stress components is compared. It is shown that the constitutive equation based on logarithmic strain and its conjugate stress gives results closer to that of the rate model. In addition, the use of Biot stress-strain pairs for a bar element results in an elastic spring which obeys the Hook’s law even for large deformations and has the same behaviour in both tension and compression. The effect of the constitutive equation on the volume change of the material has also been considered here.     

Application of activated barrier hopping theory to viscoplastic modeling of glassy polymers

An established statistical mechanical theory of amorphous polymer deformation has been incorporated as a plastic mechanism into a constitutive model and applied to a range of polymer mechanical deformations. The temperature and rate dependence of the tensile yield of PVC, as reported in early studies, has been modeled to high levels of accuracy. Tensile experiments on PET reported here are analyzed similarly and good accuracy is also achieved. The frequently observed increase in the gradient of the plot of yield stress against logarithm of strain rate is an inherent feature of the constitutive model. The form of temperature dependence of the yield that is predicted by the model is found to give an accurate representation. The constitutive model is developed in two-dimensional form and implemented as a user-defined subroutine in the finite element package ABAQUS. This analysis is applied to the tensile experiments on PET, in some of which strain is localized in the form of shear bands and necks. These deformations are modeled with partial success, though adiabatic heating of the instability causes inaccuracies for this isothermal implementation of the model. The plastic mechanism has advantages over the Eyring process, is equally tractable, and presents no particular difficulties in implementation with finite elements.     

Predictive modelling of the properties and toughness of polymeric materials Part III Simultaneous prediction of micro- and macrostructural deformation of rubber-modified polymers

The deformation behaviour of heterogeneous tensile bars is investigated by using the recently developed multi-level finite element method (MLFEM) that allows for a numerical coupling between the microscopic and macroscopic stress-strain behaviour, combined with an accurate elasto-viscoplastic constitutive model (single-mode compressible Leonov model) and a detailed finite element model of the microstructure. The method is used to predict the influence of the microstructure on localisation phenomena in plane strain notched and hour-glass-shaped polycarbonate and polystyrene tensile specimen with different volume fractions of non-adhering or adhering rubbery particles. In Part I and II of this series it was already suggested that elimination of the unstable post-yield strain softening behaviour of a polymeric material by appropriate microstructural modifications may be essential for toughening. The results of the multi-level analyses presented in this paper confirm this statement. It is shown that a stable post-yield response, resulting from microstructural adaptations, is indeed a prerequisite for the distribution of plastic strains over the whole macro- and microstructure: massive shearing is promoted by the introduction of voids in the polycarbonate or load bearing pre-cavitated rubbery particles in the polystyrene. Furthermore, it is shown that the voids indeed reduce the macroscopic dilative stresses to safe values. The results suggest that localisations of strain and stress will always occur on a macro and/or micro level. Catastrophic failure, however, can be postponed by stabilisation of the post-yield behaviour of the material and reduction of the macroscopic dilative stresses through appropriate microstructural adjustments.     

基于Sherwood–Frost模型构建聚乙烯泡沫拉伸本构

目的 研究聚乙烯泡沫的拉伸力学性能,并构建聚乙烯泡沫的拉伸本构模型。方法 利用万能材料试验机对不同密度的聚乙烯泡沫进行不同拉伸速率的单轴拉伸实验,得到聚乙烯泡沫的拉伸应力–应变曲线;在Sherwood–Frost唯象本构模型框架的基础上,构建将密度和应变耦合的密度项,以及将应变率、应变和密度耦合的应变率项的拉伸本构模型。结果 聚乙烯泡沫在断裂前的拉伸力学特性为非线性弹性,表现出明显的应变率强化效应,现有的密度项和应变率项与实验数据的拟合精度较低,最大平均误差分别可达11.76%、7.90%。新构建的密度项和应变率项与实验数据拟合精度较好,最大平均误差分别为1.17%、1.92%。结论 新构建的拉伸本构模型能够更精确地描述聚乙烯泡沫单轴拉伸的应力应变关系,为聚乙烯泡沫的综合力学性能的进一步研究提供参考。     

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。     

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.     

Constitutive equation of a non-simple elastic plastic material

Summary The mechanical response predicted by the constitutive equation of a non-simple elastic material is considered in relation to the total strain behaviour of an elastic-plastic solid extensively deformed in the range of plastic strain. Both loading and unloading are considered in relation to the range of total elastic-plastic strain. In the absence of appropriate experimental studies, comparison of the predictions of the proposed constitutive equation of a non-simple elastic material, when applied to the work-hardening behaviour of the material, has been restricted to a study of the characteristic stress-strain behaviour of a strain hardening material. This has centred on the correlation of stress-strain curves characteristic of the mechanical response of a material tested in simple compression, simple torsion and pure shear with the object of obtaining a universal stress-strain curve.With 1 Figure     

长径比对TiB/Ti6Al4V网状复合材料力学行为的影响

目的 针对高性能钛基复合材料开发过程中所面临的强韧性倒置问题,对网状构型钛基复合材料拉伸行为进行仿真,以揭示增强体长径比对材料强度与韧性的影响机理。方法 针对TiB/Ti6Al4V网状构型复合材料体系,构建增强相长径比不同的复合材料有限元模型,分别进行拉伸行为仿真,并对其应力-应变曲线、应力集中系数、应力云图和应变云图等进行预测与分析。结果 随着增强相TiB长径比的增大,复合材料的断裂伸长率单调递增,弹性模量与抗拉强度则呈先下降后上升的趋势。结论 增强相长径比是影响复合材料力学性能的重要参数。增强相的长径比和局部体积分数的共同作用导致复合材料模量和强度随长径比的增大先降低后升高。此外,随着TiB长径比的增大,断口更加曲折,主裂纹多次偏转扩展方向,并沿着TiBw/Ti6Al4V-Ti6Al4V“限域”界面扩展,进而消耗了大量的体系能量,这对材料韧化有积极影响。     

A mixed finite element for the nonlinear analysis of in-plane loaded masonry walls

A mixed membrane eight-node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history-dependent 2D stress-strain constitutive law is used to model masonry material, the element derivation is based on a Hu-Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral-type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement-based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.     

A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

Determination of mechanical properties of PVC foam using a modified Arcan fixture

The design and development of a modified Arcan fixture (MAF) is described. The purpose of the fixture is to characterise polymer foam materials with respect to their tensile, compressive, shear and bidirectional mechanical properties. The MAF enables the application of pure compression or high compression to shear bidirectional loading conditions that is not possible with conventional Arcan fixtures. The tensile and shear behaviour to failure of a cross-linked Divinycell H100 PVC foam core material are studied using Digital Image Correlation (DIC). A detailed investigation of the parasitic effects of the fixture and misalignment of the fixture and loading machine are discussed. Thermoelastic Stress Analysis (TSA) is used to directly examine and validate the uniformity and symmetry of the stress fields obtained for both tensile and shear specimens. To account for the inhomogeneity of the strain field across the specimen cross sections, a “correction factor” for the measured “gauge section” surface strains has been determined using nonlinear finite element analysis (FEA). The outcome is a set of validated mechanical properties that are in excellent agreement with material property measurements conducted using conventional test tensile and shear test fixtures.     

二维编织C/SiC复合材料非线性损伤本构模型与应用

基于二维编织C/SiC复合材料的基本力学性能试验, 建立了该材料的宏观正交各向异性非线性损伤本构模型。模型中以可检测的应变作为变量, 采用形式简单的函数分别描述了单轴拉伸和剪切加载下的材料损伤演变下的应力-应变关系, 以及卸载状态的刚度变化规律。同时, 考虑了材料的单边效应以及拉压应力状态转换时的损伤钝化行为。将此本构模型编写成UMAT子程序并引入ABAQUS有限元软件, 可以完整描述该材料的加载非线性和卸载线性的应力-应变关系特征, 及其加卸载历史。通过对带孔板的拉伸模拟, 孔边应变分布与试验结果吻合较好, 验证了本构模型的有效性。