Evaluation of the VDA 238–100 Tight Radius Bend Test for Plane Strain Fracture Characterization of Automotive Sheet Metals

Accurate characterization of the fracture limit in plane strain tension of automotive sheet metals is critical for the design and crash performance of structural components. Plane strain bending using the VDA 238–100 V-bend test has potential for proportional fracture characterization by avoiding a tensile instability. The VDA 238–100 V-bend test was evaluated using DIC strain measurement to characterize the plane strain fracture limit under proportional plane stress loading and to evaluate the effect of the VDA pre-straining methodology for ductile alloys upon the material response. The load-based failure criterion of the V-bend test was evaluated with DIC to monitor the development of surface cracking. The influence of the non-linear strain path imposed by the pre-straining procedure for ductile materials was then evaluated for three automotive alloys: an advanced high strength dual phase steel, DP1180, a rare-earth magnesium, ZEK100, and an AA5182 aluminum. A fracture criterion based on the load threshold was reasonable for the three alloys considered. Pre-straining in uniaxial tension prior to plane strain bending affected each alloy differently. The DP1180 was not affected by the non-linear strain path whereas the cumulative equivalent strain for the AA5182 and ZEK100 increased by strains of 0.07 and 0.05 strain, respectively. The non-linear strain path within the VDA pre-straining methodology creates ambiguity in comparing the fracture limits of different materials. The plane strain fracture limit for proportional loading can be readily obtained in the V-bend test with DIC strain measurement.

     

激光选区熔化增材制造GP1不锈钢动态拉伸力学响应与层裂破坏

采用选择性激光熔化增材制造技术,制备了GP1不锈钢单轴拉伸板条试样和层裂圆片试样,并对材料微观结构进行了表征。借助Zwick-HTM5020高速拉伸试验机,并结合数字图像相关性全场应变测量技术,开展了增材制造GP1不锈钢材料的轴向拉伸力学性能实验研究,得到了不同应变率下材料的拉伸应力-应变曲线,结果显示:(1)GP1不锈钢流动应力具有比较显著的应变强化效应;(2)通过回收试样的电子背散射衍射表征,发现GP1不锈钢在拉伸变形过程中会发生奥氏体与马氏体之间的相变;(3)GP1不锈钢的屈服应力随着应变率呈幂指数增大,断裂应变在中低应变率下保持不变,但在高应变率下则显著减小。采用一级轻气炮实验装置和激光干涉粒子速度测量技术,开展了增材制造GP1不锈钢的层裂实验,发现GP1不锈钢的层裂强度随着飞片撞击速度增大而减小。单轴拉伸试样断口和层裂试样断口的显微分析结果表明:随着应变率增大,单轴拉伸断裂模式和断裂机理都发生了转变;层裂损伤易成核于激光熔池边界线的交汇处,断口韧窝形貌明显区别于单向拉伸断口。     

Prediction of the initial thickness of shear band localization based on a reduced strain gradient theory

Plastic flow localization in ductile materials subjected to pure shear loading and uniaxial tension is investigated respectively in this paper using a reduced strain gradient theory, which consists of the couple-stress (CS) strain gradient theory proposed by Fleck and Hutchinson (1993) and the strain gradient hardening (softening) law (C–W) proposed by Chen and Wang (2000). Unlike the classical plasticity framework, the initial thickness of the shear band and the strain rate distribution in both cases are predicted analytically using a bifurcation analysis. It shows that the strain rate is obviously non-uniform inside the shear band and reaches a maximum at the center of the shear band. The initial thickness of the shear band depends on not only the material intrinsic length l_cs but also the material constants, such as the yield strength, ultimate tension strength, the linear hardening and softening shear moduli. Specially, in the uniaxial tension case, the most possible tilt angle of shear band localization is consistent qualitatively with the existing experimental observations. The results in this paper should be useful for engineers to predict the details of material failures due to plastic flow localization.     

Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels

Abstract

In this article, we investigated the effect of martensite morphology on the mechanical properties and formability of dual phase steels. At first, three heat treatment cycles were subjected to a low-carbon steel to produce ferrite–martensite microstructure with martensite morphology of blocky-shaped, continuous, and fibrous. Tensile tests were then carried out so as to study mechanical properties, particularly the strength and strain hardening behavior of dual phase steels. In order to study the formability of dual phase samples, Forming Limit Diagram was obtained experimentally and numerically. Experimental forming limit diagram was obtained using Nakazima forming test, while Finite Element Method was utilized to numerically predict the forming limit diagram. The results indicated that the dual phase samples with fibrous martensite morphology had the highest tensile properties and strain rate hardening out of the three different microstructures. Blocky-shaped martensite morphology, on the other hand, had the worst mechanical properties. The study of the strain hardening behavior of dual phase sample by Kocks–Mecking-type plots, evinced two stages of strain hardening for all specimens with different microstructures: stages III and IV. The forming limit diagram of dual phase steels also proved that samples with fibrous martensite morphology had the best formability compared to other two microstructures. The simulated forming limit diagram manifested that there is a good agreement between experimental results and those obtained by FEM.     

Effects of the strain-hardening exponent on two-parameter characterizations of surface-cracks under large-scale yielding

The influence of strain hardening exponent on two-parameter J-Q near tip opening stress field characterization with modified boundary layer formulation and the corresponding validity limits are explored in detail. Finite element simulations of surface cracked plates under uniaxial tension are implemented for loads exceeding net-section yield. The results from this study provide numerical methodology for limit analysis and demonstrate the strong material dependencies of fracture parameterization under large scale yielding. Sufficient strain hardening is shown to be necessary to maintain J-Q predicted fields when plastic flow progresses through the remaining ligament. Lower strain hardening amplifies constraint loss due to stress redistribution in the plastic zone and increases the ratio of tip deformation to J. The onset of plastic collapse is marked by shape change and/or rapid relaxation of tip fields compared to those predicted by MBL solutions and thus defining the limits of J-Q dominance. A radially independent Q-parameter cannot be evaluated for the low strain hardening material at larger deformations within a range where both cleavage and ductile fracture mechanisms are present. The geometric deformation limit of near tip stress field characterization is shown to be directly proportional to the level of stress the material is capable of carrying within the plastic zone. Accounting for the strain hardening of a material provides a more adjusted and less conservative limit methodology compared to those generalized by the yield strength alone. Results from this study are of relevance to establishing testing standards for surface cracked tensile geometries.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下,以Ohno-Abdel-Karim非线性随动硬化模型为基础,建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应,并在塑性应变记忆项中加入恢复系数,提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中,模拟不同平均应力、应力幅值下的棘轮应变,均与实验数据吻合较好,证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

Analysis of Damage and Failure in Anisotropic Ductile Metals Based on Biaxial Experiments with the H-Specimen

Background

Dependence of strength and failure behavior of anisotropic ductile metals on loading direction and on stress state has been indicated by many experiments. To realistically predict safety and lifetime of structures these effects must be taken into account in material models and numerical analysis.

Objective

The influence of stress state and loading direction on damage and failure behavior of the anisotropic aluminum alloy EN AW-2017A is investigated.

Methods

New biaxial experiments and numerical simulations have been performed with the H-specimen under different load ratios. Digital image correlation shows evolution of strain fields and scanning electron microscopy is used to visualize failure modes on fracture surfaces. Corresponding numerical studies predict stress states to explain damage and fracture processes on the micro-scale.

Results

The stress state, the load ratio and the loading direction with respect to the principal axes of anisotropy affect the width and orientation of localized strain fields and the formation of damage mechanisms and fracture modes at the micro-level.

Conclusions

The enhanced experimental program with biaxial tests considering different loading directions and load ratios is suggested for characterization of anisotropic metals.

     

复杂加载下混凝土的弹塑性本构模型

混凝土材料在不同应力路径下或复杂加载条件下会表现出差异性显著的应力应变关系,在小幅循环加载条件下,其应力应变关系会表现出类似于弹性变形的滞回曲线.在不同应力水平下,混凝土的应力应变关系以及破坏特性都具有静水压力相关特点,即随着静水压力增大,各向异性强度特性弱化.此外,混凝土受压及受拉破坏机理不同,因而对应于混凝土硬化损伤亦有不同,即可分为受压硬化损伤,受拉硬化损伤及两者的混合硬化损伤类型.基于Hsieh模型,对该模型进行了三点改进.（1）针对小幅循环加载下混凝土无塑性变形的试验规律,而模型中在应力水平较低的循环加载条件下始终存在塑性变形的预测问题,采用在边界面模型框架下,设置了应力空间的弹性域,初始屈服面与后续临界状态屈服面几何相似的假定.（2）基于广义非线性强度准则将原模型采用变换应力方法将其推广为三维弹塑性本构模型,采用变换后模型可合理的考虑不同应力路径对于子午面以及偏平面上静水压力效应形成的影响,并避免了边界面应力点奇异问题.（3）分别对拉压两种加载损伤模式建议了相应的硬化参数表达式,可分别用于描述上述加载中产生的应变软化及强度退化行为.基于多种加载路径模拟表明:所建立的三维弹塑性本构模型可合理地用于描述混凝土的一般应力应变关系特性.      

Experimental investigation and modeling of the tension behavior of polycarbonate with temperature effects from low to high strain rates

The effects of strain rate and temperature on the tension stress–strain responses of polycarbonate are experimentally investigated over a wide range of strain rates (0.001–1700 s⁻¹) and temperatures (0–120 °C). A modified split Hopkinson tension bar is used for high-rate uniaxial tension tests. Experimental results indicate that the stress–strain responses of polycarbonate at high strain rates exhibit the nonlinear characteristics including the obvious yielding and strain softening. The tension behavior is strongly dependent on the strain rate and temperature. The values of yield stress and strain at yield present a dramatic increase at higher strain rates and decrease with the increase in temperature. Moreover, there exists a significant rate-sensitivity transition in the polycarbonate tension yield behavior. Based on the experimental investigation, a physically based three-dimensional elastoplastic constitutive model for the finite deformation of glassy polymers is used to characterize the rate-temperature dependent yield and post-yield behavior of polycarbonate when subjected to tension loading. The model results are shown close to the experimental data within the investigated strain-rate and temperature ranges.     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

Nano-Indentation Hardness and Strain Hardening of Silicon,Sodium Chloride and Tungsten Crystals

Background

A previous review of micro- and nano-indentation hardness tests and their analyses gave emphasis to obtaining measurements of continuous nano-indentation load, P, versus, depth, h, recordings that monitor the full elastic–plastic deformation behavior of a localized crystal volume [1].

Objective

Attention is given to determining the complete, indentation-based, elastic–plastic deformation properties of the local volume, including the initial crystal elastic deformation behavior and, especially to evaluation of post pop-in plastic strain hardening.

Method

Stress–strain calculations are presented for an initial Hertzian elastic loading and follow-on crystal micro- and nano-scale plastic deformation responses [2].

Results

Applied load, P, dependencies on contact diameters, d_i, of silicon crystals are compiled on the basis of elastic, plastic and cracking predictions, giving indication at the lowest P values of an indentation size effect (ISE) for the crystal hardness. Elastic–plastic stress–strain curves are presented for sodium chloride and tungsten crystals. The hardness and strain hardening calculations also demonstrate an influence of the ISE.

Conclusions

The exceptional plastic strain hardening behaviors scale dimensionally with corresponding dislocation interactions and sessile reactions within the very localized plastic indentation zones. There is usefulness in determining elastic modulus values from the initial loading record. Micro- and nano-scale dislocation interactions/reactions account for the high stress and strain hardening levels as well as the occurrence of an ISE.

     

Modelling of the plastic flow of trip-aided multiphase steel based on an incremental mean-field approach

An incremental mean-field model is developed for the prediction of transformation induced plasticity (TRIP) in multiphase steel. The partitioning of strain between softer and harder constituents is computed based on an elastic-plastic Mori–Tanaka approach that accounts for the progressive transformation of austenite into martensite. The latter transformation is predicted using an energy-balance criterion that is formulated at the level of individual austenite grains. The model has been tested against experimental data. Macroscopic stress-strain curves and rate of martensite formation have been measured on sheet samples subjected to various loading modes: uniaxial tension, simple shear, and (in-plane) uniaxial compression. These experiments were performed at 20 °C and the uniaxial tensile test was repeated at ?30 °C. The mean-field model produces fair predictions of the macroscopic hardening resulting from TRIP on the condition that a sufficient proportion of the load is carried by the very hard martensite inclusions. Such prediction implies that one accounts for the stress heterogeneity across the ferrite-based matrix. At the same time, the model reproduces the elastic lattice strains and the plastic elongation which are measured within the phases by neutron diffraction and by image correlation in a scanning electron microscope, respectively. The model can be used in finite element simulations of forming processes which is illustrated in a study of necking of a cylindrical bar under uniaxial tension.     

Multi-Axial Deformation Setup for Microscopic Testing of Sheet Metal to Fracture

While the industrial interest in sheet metal with improved specific-properties led to the design of new alloys with complex microstructures, predicting their safe forming limits and understanding their microstructural deformation mechanisms remain as significant challenges largely due to the inadequacy of the existing experimental tools. The investigation of the strain-path dependent failure mechanisms requires miniaturized testing equipment, which can be placed in a scanning electron microscope for in situ experiments. So far, such tests could only be carried out for a single strain path (uniaxial tension). In this work, in order to fill this gap, a miniaturized Marciniak test setup is designed, built and tested. With this setup real-time, multi-axial tests of industrial sheet metal can be carried out to the point of fracture within a scanning electron microscope. Proof-of-principle experiments demonstrate that a realm of information can be obtained, crucial for the understanding of the mechanical behavior of new alloys.     

岩石拉压蠕变试验仪研制及应用

为了探索岩石在周期性恒定拉伸、压缩荷载作用下的蠕变行为,结合杠杆原理,设计研制了一种岩石杠杆式拉伸、压缩蠕变试验仪。该仪器具有挂重质量小、可方便切换拉、压荷载等特点。首先,通过标定好的数显式拉压荷重传感器对该试验仪拉伸、压缩荷载进行了校正,得出试验仪压缩、拉伸荷载杠杆扩力比分别为81.29倍与59.46倍,挂重质量与施加在岩样荷载呈线性关系(压缩作用下线性关系相关系数R2=0.99975,拉伸作用下R2=0.9991),荷载施加稳定。最后,采用该试验仪对红砂岩进行了单轴恒定拉、压循环荷载下的蠕变试验,探讨了受荷岩样拉压蠕变规律。上述成果丰富了岩石蠕变测试与研究内容,有助于岩石力学试验测试的发展。     

Visco-plastic constitutive modeling on Ohno-Wang kinematic hardening rule for uniaxial ratcheting behavior of Z2CND18.12N steel

Experimental results of monotonic uniaxial tensile tests at different strain rates and the reversed strain cycling test showed the characteristics of rate-dependence and cyclic hardening of Z2CND18.12N austenitic stainless steel at room temperature, respectively. Based on the Ohno-Wang kinematic hardening rule, a visco-plastic constitutive model incorporated with isotropic hardening was developed to describe the uniaxial ratcheting behavior of Z2CND18.12N steel under various stress-controlled loading conditions. Predicted results of the developed model agreed better with experimental results when the ratcheting strain level became higher, but the developed model overestimated the ratcheting deformation in other cases. A modified model was proposed to improve the prediction accuracy. In the modified model, the parameter m_i of the Ohno-Wang kinematic hardening rule was developed to evolve with the accumulated plastic strain. Simulation results of the modified model proved much better agreement with experiments.     

An experimental and numerical study on the formability of textured AlZnMg alloys

The influence of texture and grain structure on strain localisation and formability is investigated experimentally and numerically for two AlZnMg alloys. The considered alloys have recrystallised or non-recrystallised grain structure and strong or nearly random texture. The textured materials have rotated cube texture or β-fibre texture of high intensity. A comprehensive test programme, including uniaxial tension tests in three directions, through-thickness compression tests, plane-strain tension tests and double-plate formability tests, is completed to determine the work hardening, plastic anisotropy and formability of the materials. Strain localisation and failure are examined by optical microscopy. Using parts of the test data, an anisotropic plasticity model is calibrated and applied in calculation of forming limit curves, using the Marciniak–Kuczynski (M-K) analysis for anisotropic materials. The formability tests show that the materials with nearly random texture exhibit superior formability. This is mainly attributed to enhanced work hardening for these materials. For the material exhibiting strong β-fibre texture significantly lower formability is found in equibiaxial stretching than in plane strain, while this characteristic is not seen for the material with strong cube texture. The M-K analysis is capable of predicting the major trends of the experiments, and captures the low formability of the alloy with strong β-fibre texture under equibiaxial straining. A numerical study is performed to evaluate the sensitivity of the predicted forming limit curves to parameters not determined experimentally.     

Stretching Graphene to 3.3% Strain Using Formvar-Reinforced Flexible Substrate

Background

As a one-atom-thick material, the mechanical loading of graphene in large scale remains a challenge, and the maximum tensile strain that can be realized is through a flexible substrate, but only with a value of 1.8% due to the weak interfacial stress transfer.

Objective

Aims to illustrate the interface reinforcement brought by formvar resins as a buffering layer between graphene and substrates.

Methods

Single crystal graphene transferred to different substrates, applied with uniaxial stretching to compare the interface strength, and finite element analysis was performed to simulate tensile process for studying the influence of Poisson’s ratio of the buffering layer for interface reinforcement.

Results

In this work we use formvar resins as a buffering layer to achieve a maximum uniaxial tensile strain of 3.3% in graphene, close to the theoretical limit (3.7%) that graphene can achieve by flexible substrate stretching. The interface reinforcement by formvar is significantly higher than that by other polymers, which is attributed to the liquid–solid phase transition of formvar for more conformal interfacial contact and its suitable Poisson’s ratio with graphene to avoid its buckling along the transverse direction.

Conclusions

We believe that these results can provide guidance for the design of substrates and interfaces for graphene loading, as well as the support for mechanics analysis of graphene-based flexible electronic devices.