Analysis of the extended stress-based forming limit curve considering the effects of strain path and through-thickness normal stress

In this study, an approach based on the modified Marciniak–Kuczynski (M–K) method for computation of an extended stress-based forming limit curve (FLC) is presented. The extended stress-based FLC is built based on equivalent plastic stress versus mean stress. This curve has some advantages in comparison with the conventional FLC. This new criterion is much more strain path independent than the conventional FLC. The effect of strain path on the predicted extended stress-based FLC is reexamined. For this purpose, two types of pre-straining on the sheet metal have been loaded. Moreover, the plane stress state assumption is not adopted in the current study. The influence of a through-thickness compressive normal stress is also investigated theoretically. The verifications of the theoretical FLCs are performed by using some available published experimental data.     

600 MPa级相变诱导塑性钢的动态力学性能

目的研究相变诱导塑性钢不同应变速率下的力学性能,尤其是动态力学性能。方法对600 MPa级相变诱导塑性钢进行了准静态至动态6种不同应变速率下的力学性能测试,并对各试样断口处残余奥氏体含量进行了测试比对。0.001~0.01 s~(-1)准静态测试在ZWICK Z050万能试验机上完成,0.1,1,10,100 s~(-1)动态测试在ZWICK HTM5020液压伺服高速拉伸试验机上完成。结果力学测试结果表明,TRIP600具有明显的应变速率效应。在较高速率下,随应变速率的升高材料屈服强度、抗拉强度及伸长率都有一定程度的提高。结论断口处残余奥氏体含量在较高速率下无明显差别,表明较动态条件下应变速率对残余奥氏体转变影响不明显。     

Influences of simple strain path changes on mechanical behaviours of pearlitic steel wire

The mechanical behaviours of the pearlitic steel wires under simple strain path changes (SSPCs) are investigated, including monotonic, cross and reversal loadings. Both the cross and reversal loadings lead to an apparent softening. Especially during the whole reversal loading, the stress is much lower than before unloading. And it is a function of the pre-strain. Additionally, it is found that the maximum strain increases significantly in reversal loading. The microstructures under different SSPCs are investigated using scanning electron microscopy (SEM) and transmission electron microscopy (TEM), with an aim to reveal the micro-mechanisms of the SSPC effects on the mechanical behaviours.     

Stress–strain curves of metallic materials and post‐necking strain hardening characterization: A review

For metallic materials, standard uniaxial tensile tests with round bar specimens or flat specimens only provide accurate equivalent stress–strain curve before diffuse necking. However, for numerical modelling of problems where very large strains occur, such as plastic forming and ductile damage and fracture, understanding the post‐necking strain hardening behaviour is necessary. Also, welding is a highly complex metallurgical process, and therefore, weldments are susceptible to material discontinuities, flaws, and residual stresses. It becomes even more important to characterize the equivalent stress–strain curve in large strains of each material zone in weldments properly for structural integrity assessment. The aim of this paper is to provide a state‐of‐the‐art review on quasi‐static standard tensile test for stress–strain curves measurement of metallic materials. Meanwhile, methods available in literature for characterization of the equivalent stress–strain curve in the post‐necking regime are introduced. Novel methods with axisymmetric notched round bar specimens for accurately capturing the equivalent stress–strain curve of each material zone in weldment are presented as well. Advantages and limitations of these methods are briefly discussed.     

Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛ_p) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area A_PEEQ surrounded by the ɛ_p isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area A_PEEQ, a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_IC/J_ref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛ_p isolines. The unified J_IC/J_ref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_IC/J_ref−reference line for materials with ductile fracture.     

Effects of hydrogen on the mechanical response of X80 pipeline steel subject to high strain rate tensile tests

Hydrogen‐induced degradation of X80 pipeline steel was investigated through a high strain rate tensile test (2 × 10^?4/s) with interposed unloading, reloading, aging at 30°C, or annealing at 200°C with or without hydrogen charging. The results indicated that plasticity degradation does not occur in the hydrogen‐precharged specimens; however, hydrogen embrittlement occurs in the reloading stage when the specimens are charged with hydrogen in the unloading stage after applying a prestrain. Interposed aging at 30°C or annealing at 200°C can also increase the degradation. It indicates that the hydrogen traps caused by the strain along with hydrogen charging are the major source of dislocations. The formation of a hydrogen atmosphere around mobile dislocations, which is related to the rates of hydrogen diffusion and dislocation movement, plays an important role in the degradation process. Both pinning and depinning of dislocations affect plasticity degradation.     

连续碳纤维单丝的应变电阻效应

碳纤维是一种十分重要的新型材料,是先进复合材料中最重要的增强材料之一,同时又是一种功能材料. 研究了连续碳纤维单丝的应变电阻效应,分析了在拉应力作用下其电阻率的变化规律.结果表明:连续碳纤维单丝的电阻应变灵敏系数为1.38,比常用电阻应变片的要低,原因是碳纤维的电阻率在拉应力作用下是减小的.另外连续碳纤维受拉时,其电阻的变化由纤维几何尺寸及电阻率的变化引起,但主要是由几何尺寸的变化而引起的.同时,测试了连续碳纤维单丝的力学性能.     

Influence of stress triaxiality and strain rate on the failure behavior of a dual-phase DP780 steel

To better understand the in-service mechanical behavior of advanced high-strength steels, the influence of stress triaxiality and strain rate on the failure behavior of a dual-phase (DP) 780 steel sheet was investigated. Three flat, notched mini-tensile geometries with varying notch severities and initial stress triaxialities of 0.36, 0.45, and 0.74 were considered in the experiments. Miniature specimens were adopted to facilitate high strain rate testing in addition to quasi-static experiments. Tensile tests were conducted at strain rates of 0.001, 0.01, 0.1, 1, 10, and 100 s⁻¹ for all three notched geometries and compared to mini-tensile uniaxial samples. Additional tests at a strain rate of 1500 s⁻¹ were performed using a tensile split Hopkinson bar apparatus. The results showed that the stress–strain response of the DP780 steel exhibited mainly positive strain rate sensitivity for all geometries, with mild negative strain rate sensitivity up to 0.1 s⁻¹ for the uniaxial specimens. The strain at failure was observed to decrease with strain rate at low strain rates of 0.001–0.1 s⁻¹; however, it increased by 26% for an increase in strain rate from 0.1 to 1500 s⁻¹ for the uniaxial condition. Initial triaxiality was found to have a significant negative impact on true failure strain with a decrease of 32% at the highest triaxiality compared to the uniaxial condition at a strain rate of 0.001 s⁻¹. High resolution scanning electron microscopy images of the failure surfaces revealed a dimpled surface while optical micrographs revealed shearing through the thickness indicating failure occurred via ductile-shear. Finite element simulations of the tests were used to predict the effective plastic strain versus triaxiality history within the deforming specimens. These predictions were combined with the measured conditions at the onset of failure in order to construct limit strain versus triaxiality failure criteria.     

Effect of strain path on recrystallisation kinetics during hot rolling of Al–Mn

Abstract

Hot rolling of an aluminium–1% manganese alloy has been carried out. Wedge shaped specimens were rolled in two pass schedules, of either two forward passes or a forward and a reverse pass to the same overall net strain. Through thickness marker pins were inserted to allow the investigation of plastic flow during the different rolling schedules. The reversed rolling technique allowed the determination of the effect of a strain path change on the recrystallisation kinetics during hot rolling. Following subsequent annealing, quantitative metallography indicated that the forward–forward specimens showed faster recrystallisation kinetics than the forward–reverse specimens, and produced a finer recrystallised grain size following equivalent thermomechanical treatments differing only in strain path. A through thickness microstructural gradient was found in all materials.     

平面应变模具尺寸差对金属流变及其力能的影响

采用MARC/Superform有限元软件对平面应变压缩过程进行了二维有限元分析,分析了上下模具尺寸不相等时,对金属流变规律及其力能参数的影响.同时应用滑移线场理论对端部的滑移线场进行了分析,分析了金属的流动情况,进一步验证了有限元模拟结果的可靠性.研究结果显示:模具尺寸相等时,金属流动呈现对称分布;当上下两个模具尺寸不等时,金属流动呈现非对称分布,有剪切变形产生.而且随着模具尺寸差的增大,其交叉剪切变形越严重,总压力也增大,平均压力相对降低,这与异步轧制过程类似.所研究结果为异步轧制过程提供了一种新的物理模拟方法.     

Effect of prestrain with a path change on the strain rate sensitivity of AA5754 sheet

The effect of prestrain with a path change on the strain rate sensitivity of AA5754 sheet was investigated. Prestrain magnitudes between 0% and 12% were applied in plane strain in either the transverse or longitudinal (rolling) material direction. Samples were then loaded in uniaxial tension in the longitudinal direction at strain rates of 0.001/s and 0.1/s. Results show that when a path change is involved between prestrain and subsequent uniaxial loading, the strain rate sensitivity of the hardening rate at 0.1/s compared to 0.001/s is reduced. The rate sensitivity of the yield stress remains constant with increasing magnitudes of prestrain, while the rate sensitivity of the elongation to failure decreases with increasing prestrain. A permanent softening of the flow stress is also observed, which is greater when the path change is combined with a change in orientation.     

Effect of cooling rate on the high strain rate properties of boron steel

In this work, the effect of cooling rate on the high strain rate behavior of hardened boron steel was investigated. A furnace was used to austenize boron sheet metal blanks which were then quenched in various media. The four measured cooling rates during the solid state transformation were: 25 (compressed air quench), 45 (compressed air quench), 250 (oil quench) and 2200 °C/s (water quench). Micro-hardness measurements and optical microscopy verified the expected as-quenched microstructure for the various cooling rates. Miniature dog-bone specimens were machined from the quenched blanks and tested in tension at a quasi-static rate, 0.003 s⁻¹ (Instron) and a high rate, 960 s⁻¹ (split Hopkinson tensile bar). The resulting stress vs. strain curves showed that the UTS increased from 1270 MPa to 1430 MPa as strain rate increased for the specimens cooled at 25 °C/s, while the UTS increased from 1615 MPa to 1635 MPa for the specimens cooled at 2200 °C/s. The high rate tests showed increased ductility for the 25, 45 and 250 °C/s specimens, while the specimens cooled at 2200 °C/s showed a slight decrease. The Hollomon hardening curve was fit to the true stress vs. true strain curves and showed that the mechanical response of the high rate tests exhibited a greater rate of hardening prior to fracture than the quasi-static tests. The hardening rate also increased for the specimens quenched at higher cooling rates. Optical micrographs of the fractured specimens showed that the failure mechanism transformed from a ductile-shear mode at the lower cooling rates to a shear mode at the high cooling rates.     

A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis

A mathematical programming formulation of strain‐driven path‐following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in an FEM context is presented. From the optimization point of view, standard arc‐length strain‐driven elastoplastic analyses, recently extended to shakedown, are identified as particular decomposition strategies used to solve a proximal point algorithm applied to the static shakedown theorem that is then solved by means of a convergent sequence of safe states. The mathematical programming approach allows: a direct comparison with other non‐linear programming methods, simpler convergence proofs and duality to be exploited. Owing to the unified approach in terms of total stresses, the strain‐driven algorithms become more effective and less non‐linear with respect to a self‐equilibrated stress formulation and easier to implement in the existing codes performing elastoplastic analysis. The elastic domain is represented avoiding any linearization of the yield function so improving both the accuracy and the performance. Better results are obtained using two different finite elements, one with a good behavior in the elastic range and the other suitable for performing elastoplastic analysis. The proposed formulation is compared with a specialized implementation of the primal–dual interior point method suitable to solve the problems at hand. Copyright © 2011 John Wiley & Sons, Ltd.     

Mesh objective modeling of cracks using continuous linear strain and displacement interpolations

The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is deemed as the main difficulty to be overcome in the discrete problem, a (stabilized) mixed formulation with continuous linear strain and displacement interpolations is used. The necessary convergence rate can be proved for such a formulation, at least in the linear problem. Two standard local isotropic Rankine damage models with strain‐softening, differing in the definition of the damage criteria, are used as discrete constitutive model. Numerical examples demonstrate the application of the proposed formulation using linear triangular P1P1 and bilinear quadrilateral Q1Q1 mixed elements. The results obtained do not suffer from spurious mesh‐bias dependence without the use of auxiliary tracking techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions

A new four‐node quadrilateral membrane finite element with drilling rotational degree of freedom based on the enhanced assumed strain formulation is presented. A simple formulation is achieved by five incompatible modes that are added to the Allman‐type interpolation. Furthermore, modified shape functions are used to improve the behaviour of distorted elements. Numerical results show that the proposed new element exhibits good numerical accuracy and improved performance, and in many cases, superior to existing elements. In particular, Poisson's locking in nearly incompressible elasticity fades and the element performs well when it becomes considerably distorted even when it takes almost triangular shape. Copyright © 2016 John Wiley & Sons, Ltd.     

试样加工对金属材料拉伸性能的影响

通过对大量拉伸试验数据进行分析比较,从样坯切取和试样制备两大方面分析了试样加工对金属材料拉伸性能的影响。结果表明:取样方向、取样位置、取样方法、试样形状、试样尺寸以及试样制备方法等都不同程度地影响着金属材料的拉伸性能,在实际检测工作中应正确认识这些因素对拉伸试验结果的影响,拉伸试验前应选择正确的取样部位和取样方向,加工成规定横截面和形状的试样,并避免试样在加工过程中受到热影响和加工硬化影响,同时还应尽可能提高试样的加工精度。     

真空热循环对空间级缩合型硅橡胶拉伸性能的影响

对空间级缩合型硅橡胶KH－X－B进行了真空热循环试验（123－403K，10^-5Pa），测试了热循环前后材料的质损率，拉伸性能，热膨胀性能，讨论了循环过程中的应变滞后效应和附加残余应变以及它们对材料的强化作用，结果表明，材料质损率随循环次数增加而提高后趋于平缓，室温及高温拉伸强度随循环次数的增加是先增强而后下降，循环过程中发生应变滞后现象，且第一次循环后产生附加残余应变，206次循环后残余应变消失，材料强化，400次循环后重新产生残余应变，材料强度下降。     

黄麻纤维束力学性能的尺寸和应变率效应

为了探究黄麻纤维束的尺寸效应和应变率敏感性,利用C43电子式万能试验机和CEAST 9340落锤试验冲击系统分别在静动载条件下对黄麻纤维束进行测试,获得了杨氏模量、强度、峰值应变和韧性随标距和应变率的变化关系静载试验在1/600s-1应变率条件下进行,测试了6组不同标距(25、50、100、150、200和300mm)的试件;动载试验以应变率为变量,在4组不同的应变率(40、80、120和160s-1)条件下进行了测试,试件标距均为25mm。测试结果表明:随着试件标距增大,杨氏模量初始增大,当标距大于100mm时趋于稳定;强度、峰值应变和韧性均减小。随着应变率增大,杨氏模量和强度均增大;峰值应变初始减小后趋于稳定;韧性先减小后增大。鉴于植物纤维束材料较大的性能离散性,采用Weibull分布对试验数据进行拟合,获得了黄麻纤维束强度在不同试验条件(标距和应变率)下的分布规律。