基于试验与有限元耦合技术的延性材料全程单轴本构关系获取方法

摘 要: 材料拉伸直至断裂的全程单轴本构关系对材料大变形和断裂机理研究具有重要意义。传统拉伸试验获取的材料真应力-真应变曲线在试样颈缩后不可测。借助可以精确测量三维变形的DIC(Digital image correlate) 技术和有限元分析技术(Finite element analysis),本文提出了基于漏斗试样拉伸试验获取材料全程单轴本构关系的新方法,即TF(Test and FEA)方法。该方法将TF方法获取的材料全程单轴应力应变关系曲线作为有限元软件中的材料本构关系对漏斗试样拉伸变形过程进行模拟,其模拟载荷-位移曲线、漏斗根部直径-位移曲线和漏斗变形轮廓线等均与试验结果吻合良好,试样表面模拟应变也与DIC测试结果吻合, 根据不同半径漏斗试样模拟获得的全程真应力-真应变曲线保持良好一致性。最后,还对试样颈缩断面的力学行为进行了讨论,并给出了304不锈钢、汽轮机叶片材料2Cr12Ni4Mo3VNBN和 1Gr12Ni3Mo2VN、汽轮机转子材料30Cr2Ni4MoV的全程单轴本构关系模型参数、破断应力和破断应变。     

基于应力三轴度和罗德参数的6061和7075铝合金材料断裂失效分析

分别对6061铝合金和7075铝合金材料的缺口圆棒试件和凹槽平板试件进行准静态拉伸试验,并采用ABAQUS软件对拉伸过程进行数值模拟。模拟结果与试验测试结果吻合很好,验证了有限元模型的合理性和可靠性。通过有限元模拟,分别给出了不同试件的应力三轴度和罗德参数随等效塑性应变的变化曲线以及两种材料的失效轨迹,并对它们进行了分析讨论。结果表明:形状相同、材料性质不同的试件,应力三轴度的演化规律不同;材料的失效应变受应力三轴度和罗德参数的影响,并且不同性质的材料对罗德参数的敏感性不同。     

Multi-cycle deformation of silicone elastomer: observations and constitutive modeling with finite strains

Observations are reported on a medical grade of silicone elastomer in uniaxial tensile tests up to breakage of specimens, short-term relaxation tests, and cyclic tests with monotonically increasing maximum elongation ratios. Experimental data in cyclic tests demonstrate the fading memory phenomenon: stress–strain diagrams for two specimens with different deformation histories along the first n?1 cycles and coinciding loading programs for the other cycles become identical starting from the nth cycle. A constitutive model is developed in cyclic viscoplasticity of elastomers with finite strains, and its adjustable parameters are found by fitting the experimental data. Ability of the stress–strain relations to predict the mechanical response in cyclic tests with various deformation programs is confirmed by numerical simulation.     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

应力三轴度的有限元计算修正

对某高强度钢制成的光滑圆棒和缺口圆棒进行了系列准静态拉伸实验,采用ABAQUS对每个试 件进行了数值模拟,得到了该材料的真实应力应变曲线,拟合出了J-C本构模型和失效模型的部分材料常数。 最后,对该高强度钢制成的平板进行了撞击实验,并用得到的J-C模型对平板撞击实验进行了数值模拟,计算 结果与实验结果吻合很好,证明利用数值模拟并修正应力三轴度的方法是可行的。     

Experimental and numerical investigations of the deformation of soft materials under tangential loading

The surface ‘tensile test’, in which tangential loads are applied through surface mounted adhesive tapes, is a viable method for the assessment of mechanical properties of soft materials, particularly biological soft materials in vivo. In the present work the deformation pattern and force–displacement relationship in the surface tensile test were experimentally investigated using surface displacement analysis (SDA) and numerically simulated using finite element modelling. The experimental and FE results showed close agreement using silicone rubber as a model material. The force–displacement relationship was found to be dependent on the tape separations. SDA measurements and FE simulation showed that the displacement and strain fields were not uniform and the distribution pattern varies with tape separation. A combined experimental–numerical approach to inversely extract material properties using multiple tests with different length scales is proposed and assessed using a model material.     

On the application of FEM to deformation of high-density polyethylene

This paper presents a study that uses finite element method (FEM) to simulate deformation behaviour of high-density polyethylene (HDPE) when subjected to tensile loading, either without or with the presence of pre-cracks. For the former, dog-bone-shaped model of HDPE was deformed under uni-axial tensile (UT) loading beyond the initial yielding, to generate stable necking in the gauge section. The paper proposes a simple correction factor to determine the equivalent von Mises stress that is needed for the input to the FEM model, in order to generate the same loading level as that observed experimentally for neck propagation. The paper points out that such consistency in the loading level could not be generated in the past mainly because of a misconception that axial stress in the neck was regarded as the equivalent of the von Mises stress. The study also explored the consideration of crack growth in double-edge-notched tensile (DENT) specimen, and showed that the conventional von Mises yield function, with the assumption of isotropic work hardening, cannot be directly applied to simulate the deformation behaviour of DENT specimen. Instead, empirical parameters were employed to reflect the polymer orientation during the necking process. The paper shows that FEM models for both UT and DENT tests can reproduce the experimental load–displacement curves quite accurately, and concludes that with a proper yield function to reflect the deformation involved in the mechanical tests, the deformation behaviour observed experimentally can be accurately mimicked using the FEM simulation.     

扭转塑性变形对6063铝合金拉伸力学性能的影响机理研究

扭转是一种常用的冷作硬化方法。本文通过实心圆轴扭转实验和预扭试件的单向拉伸实验,研究了扭转塑性变形程度对6063铝合金拉伸力学性能的影响。通过理论研究和硬度分析探究了造成这一影响的内在机理。结果表明,试件扭转后其内部形成的以屈服强度为特征参数的梯度结构,是造成预扭试件力学性能得到改善的根本原因。并且,扭转不同的角度,材料内部产生的梯度结构也是不同的。而不同的梯度结构对试件力学性能的影响则表现为后继拉伸屈服强度随预扭角度的增大而增大。为了预测预扭试件的后继拉伸力学行为,验证前述结论的正确性,建立了由内到外屈服强度逐渐变化的有限元模型。此模型代表了预扭转变形试件,对其施加位移载荷,模拟后继单向拉伸加载过程。模拟所得材料力学性能随扭转角的变化趋势与实验结果基本吻合,从而验证了扭转冷作硬化后,圆轴试件内部产生了以屈服强度为特征参数的梯度结构这一结论。同时,也提供了一种有效的预测材料扭转后拉伸力学性能的数值模拟方法。     

Constitutive modeling of ice in the high strain rate regime

The objective of the present work is to propose a constitutive model for ice by considering the influence of important parameters such as strain rate dependence and pressure sensitivity on the response of the material. In this regard, the constitutive model proposed by Carney et al. (2006) is considered as a starting basis and subsequently modified to incorporate the effect of brittle cracking within a continuum damage mechanics framework. The damage is taken to occur in the form of distributed cracking within the material during impact which is consistent with experimental observations. At the point of failure, the material is assumed to be fluid-like with deviatoric stress almost dropping down to zero. The constitutive model is implemented in a general purpose finite element code using an explicit formulation. Several single element tests under uniaxial tension and compression, as well as biaxial loading are conducted in order to understand the performance of the model. Few large size simulations are also performed to understand the capability of the model to predict brittle damage evolution in un-notched and notched three point bend specimens. The proposed model predicts lower strength under tensile loading as compared to compressive loading which is in tune with experimental observations. Further the model also asserts the strain rate dependency of the strength behavior under both compressive as well as tensile loading, which also corroborates well with experimental results.     

A computational model of viscoplasticity and ductile damage for impact and penetration

A coupled constitutive model of viscoplasticity and ductile damage for penetration and impact related problems has been formulated and implemented in the explicit finite element code LS-DYNA. The model, which is based on the constitutive model and fracture strain model of Johnson and Cook, and on continuum damage mechanics as proposed by Lemaitre, includes linear thermoelasticity, the von Mises yield criterion, the associated flow rule, non-linear isotropic strain hardening, strain-rate hardening, temperature softening due to adiabatic heating, isotropic ductile damage and failure. For each of the physical phenomena included in the model, one or several material constants are required. However, all material constants can be identified from relatively simple uniaxial tensile tests without the use of numerical simulations. In this paper the constitutive model is described in detail. Then material tests for Weldox 460 E steel and the calibration procedure are presented and discussed. The calibrated model is finally verified and validated through numerical simulations of material and plate perforation tests investigated experimentally.     

Membrane Curvatures and Stress-strain Full Fields of Axisymmetric Bulge Tests from 3D-DIC Measurements. Theory and Validation on Virtual and Experimental results

The bulge test is mostly used to analyze equibiaxial tensile stress state at the pole of inflated isotropic membranes. Three-dimensional digital image correlation (3D-DIC) technique allows the determination of three-dimensional surface displacements and strain fields. In this paper, a method is proposed to determine also the membrane stress tensor fields for in-plane isotropic materials, independently of any constitutive equation. Stress-strain state is then known at any surface point which enriches greatly experimental data deduced from the axisymmetric bulge tests. Our method consists, first in calculating from the 3D-DIC experimental data the membrane curvature tensor at each surface point of the bulge specimen. Then, curvature tensor fields are used to investigate axisymmetry of the test. Finally in the axisymmetric case, membrane stress tensor fields are determined from meridional and circumferential curvatures combined with the measurement of the inflating pressure. Our method is first validated for virtual 3D-DIC data, obtained by numerical simulation of a bulge test using a hyperelastic material model. Afterward, the method is applied to an experimental bulge test performed using as material a silicone elastomer. The stress-strain fields which are obtained using the proposed method are compared with results of the finite element simulation of this overall bulge test using a neo-Hookean model fitted on uniaxial and equibiaxial tensile tests.     

Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.     

Experiments and Material Parameter Identification Using Finite Elements. Uniaxial Tests and Validation Using Instrumented Indentation Tests

In this article, we focus our attention on the relation between instrumented indentation tests and the prediction by means of finite element calculations. To this end, a finite strain viscoplasticity model of Perzyna-type with non-linear isotropic and kinematic hardening is calibrated at experimental data of steel S690QL. A particular concept for conducting uniaxial tensile and compression tests is taken up in order to represent the basic rate-dependent material behavior. In this respect, an algorithmic framework of material parameter identification using finite elements is proposed leading to a two-stage procedure in the case of the underlying rate-dependent constitutive model. On the basis of the termination points of relaxation the rate-independent equilibrium stress state can be identified and all viscous parts of the model are obtained using rate-dependent loading paths. Finally, use is made of finite elements for predicting indentation experiments, which results in a critical view on modeling and parameter identification on the basis of experimental results occurring in instrumented indentation tests.     

岩石紧凑拉伸断裂过程及其尺寸效应的三维数值模拟

采用最近开发的三维岩石破裂过程分析软件RFPA3D模拟单边裂纹紧凑拉伸断裂过程。试验中五个不同尺寸的岩样具有相同的力学性质参数分布,模拟结果得到了裂纹扩展中的应力场、位移场和声发射的空间分布以及单边裂纹扩展贯通的过程。单边裂纹拉伸断裂的路径是一个复杂的空间三维曲面,三维裂纹比二维裂纹更为复杂。分析了岩石试样的峰值强度和试样尺寸之间的关系。随着岩样尺寸的增加,峰值强度逐渐减小,并且延性破坏特征更加明显,模拟结果满足岩石的尺寸效应规律。最后模拟了三组不同均匀性的试样拉伸破坏过程,结果表明细观上的非均匀性对岩石尺寸效应有很大影响,随着非均匀性的增加,岩石宏观强度随之提高,即使在均匀材料中一样存在尺寸效应。     

Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

Fatigue Life Estimation for an NBR Rubber and an Expanded Polyurethane

In this paper, we deal with the mechanical behavior of elastomeric materials subjected to high cyclic loading in cases of high strain. First, a methodology for material parameter identification is used for a constitutive visco-hyperelastic law with discontinuous damage, modeling the Mullins effect. Then a fatigue model characterized by a strain energy density-based criterion is proposed and implemented in the finite element code, Code-Aster [1]. Two kinds of elastomer are considered, an incompressible rubber and an expanded compressible polyurethane. Cyclic tensile tests were performed to identify material fatigue parameters. Finally, a numerical application using a finite element model is presented. This model is a plate perforated by a ?6 mm hole for the first sample and a ?10 mm hole for the second one. The results obtained from the finite element model are compared to experimental results.     

Finite viscoplasticity of semicrystalline polymers

Summary  A series of uniaxial tensile tests is performed on isotactic polypropylene at room temperature with cross-head speeds ranging from 5 to 100 mm/min. Prior to mechanical testing, injection-molded samples are annealed for 24 h at the temperature 160 ^°C that ensures that the specimens can be drawn up to the Hencky strain of 0.6 without necking. A constitutive model is derived for the viscoplastic behavior of a semicrystalline polymer at finite strains. The stress–strain relations are determined by five adjustable parameters that are found by matching the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. It is shown that the material parameters in the constitutive equations are strongly affected by the strain rate. Received 9 July 2002; accepted for publication 12 November 2002     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为，本文建立了基于微结构演化的塑性本构模型。首先，采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验，并对其在不同应变程度下的微结构演化特征进行了分析。研究发现，影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程，并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响，进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后，根据隐式应力更新算法对新模型进行了有限元实现，并与实验结果进行比较，验证了新模型的合理性和预测精度。     

Experimental and numerical investigation of fracture in a cast aluminium alloy

This paper describes an experimental and numerical investigation on the fracture behaviour of a cast AlSi9MgMn aluminium alloy. In the experiments, a modified Arcan test set-up was used to study mixed-mode fracture. During testing, the tension load and the displacement of the actuator of the test machine were recorded, simultaneously as a high-resolution digital camera was used to record a speckle-patterned surface of the specimen. The recorded images were post-processed using an in-house digital image correlation (DIC) software to obtain information of the displacement and strain fields in the specimen during the test. In addition, some newly implemented features in the DIC software allowed us to detect and follow the crack propagation in the material. The numerical calculations were carried out with a user-defined material model implemented in an explicit finite element code. In the model, the material behaviour is described by the classical J₂ flow theory, while fracture was modelled by the Cockcroft–Latham criterion, assuming the fracture parameter to follow a modified weakest-link Weibull distribution. With the proposed probabilistic fracture modelling approach, the fracture parameter can be introduced as a random variable in the finite element simulations. Crack propagation was modelled by element erosion, and a non-local damage formulation was used to reduce mesh-size sensitivity. To reveal the effect of mesh density and meshing technique on the force–displacement curves and the crack propagation, several different meshes were used in the numerical simulations of the modified Arcan tests. The numerical results were finally compared to the experimental data and the agreement between the measured and predicted response was evaluated.