Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes

The elastic-plastic behaviour of dual-phase, high-strength steel sheets under two-stage strain-path changes has been investigated. Three different loading sequences, namely monotonic, 45° tensile path changes and orthogonal tensile path changes complied by sequences of simple uniaxial tensile tests, were analysed at room temperature. From the experiments, it was found that there is a considerable reduction of the initial flow stress over the strain-path changes. The transient softening phenomenon is observed to be a function of orientation, and the period of the transient behaviour following the strain-path change is lengthened with the amount of pre-strain. A constitutive model is adopted that includes combined isotropic and kinematic hardening and is capable of describing the marked transient softening behaviour after the pre-straining. The experimental stress–strain behaviour subsequent to the strain path change is predicted with reasonable accuracy, while the model fails to accurately describe the transient, deformation-induced anisotropy in the plastic flow.     

Inelastic stress-responses of an aluminium alloy in non-proportional deformations at elevated temperature

Some characteristics of strain-induced anisotropy and effects of strain-rate on them are experimentally investigated under non-proportional loadings at elevated temperature. By applying combined loadings of axial force and internal pressure to thin-walled tubes of an aluminium alloy at 200°C, inelastic stress-responses are observed at several constant strain-rates along bilinear strain trajectories. It is found that a softening of material and a non-coaxiality between stress and inelastic strain-increment deviators occur after the corner of bilinear strain trajectory. These phenomena appear more markedly and then decay more gradually with the increase of corner angle and/or strain-rate. Experimental results are qualitatively discussed in terms of the activation of piled-up dislocations as well as the so-called back stress and drag stress.     

Deformation induced anisotropy and memorized back stress in constitutive model

Plastic-deformation induced anisotropy and memorization of back stress due to pre-loading affect the current loading. These phenomena are examined with tension and/or torsion tests, using SUS 304. Considering both anisotropy, and movement and memorization of back stress, equi-plastic surfaces are predicted. This explains the dependence of current loading on pre-loading well. Simulated strain paths during radial loading after shear straining show good agreement with experiments.     

一种基于电磁霍普金森杆的材料动态包辛格效应测试装置及方法

金属材料在复杂载荷条件下的动态力学行为研究一直备受关注,但受限于实验设备,金属材料的动态包辛格效应响应一直都难以获得。为了探究金属材料的包辛格效应与应变率效应之间的关系,本文中提出一种基于电磁霍普金森杆(electromagnetic split Hopkinson bar,ESHB) 的非同步加载实验技术,为测试金属材料在高应变率加载下的包辛格效应提供了一种有效的实验方法。本文中,首先介绍了非同步加载装置的主要特点,即可以用两列由脉冲发生器产生的应力波对受载试样进行连续的一次动态拉-压循环加载,且加载过程保证了应力波的一致性。分析了应力波对试样加载过程中的波传播历程,确保了加载过程的连续性。随后介绍了动态加载过程,数据处理方法和波形分离手段,并对动态加载过程进行应力平衡性分析,论证了实验装置的可靠性。最后采用该方法测试了5%预应变下6061铝合金动态压缩-动态拉伸的包辛格效应,并与准静态下的实验结果进行对比。实验结果表明,该材料单轴压缩没有明显的应变率效应,但其包辛格效应具有应变率依赖性,高应变率下材料的包辛格应力影响因子由0.07增大至0.17,具有显著的提升,这对传统意义上铝合金材料应变率不敏感的结论提出了挑战。     

Mechanical behavior of metals under tension- compression loading at high strain rate

By using a new technique based on a split Hopkinson pressure bar method, a sequenced reverse test (quasi-static tensile prestress, followed by dynamic compression and then followed by dynamic tension) at high strain rate was performed and tension-compression stress-strain relations were derived by using one-dimensional stress wave analysis. Three materials, 2017 aluminium alloy, 0.45% carbon steel, and pure aluminium, were investigated at low and high strain rates, and the strain rate effect on the reverse loading stress-strain curves was compared to that on the loading stress-strain curves. It was found that reduction of yield stress is always associated with load reversals, and the strain rate effect on the reverse loading (tension) is almost the same as that during loading (compression) at higher values of reverse deformation.     

单轴载荷下X80钢的包申格效应研究

本文通过单轴拉伸和压缩试验研究了X80管线钢的包申格效应(BE)。采用正向与反向加载方法研究材料变形历史特性。测定了X80钢的简单拉伸试验曲线,其应力-应变关系表明,该材料具有理想弹塑性特点。为了得到X80钢的BE,在不同预变形下对几个试件分别进行加载,并当给定的预应变值分别达到0.63%,0.67%,0.95%,1.27%和1.55%时就卸载。随后再进行反向加载实验,并记录应力应变曲线。该钢材反向加载时出现加工硬化,且屈服强度比正向加载时要低。正反向加载之间的屈服强度差值随着预应变增加而增大;当预应变超过0.95%时,反向屈服强度达到恒量。实验表明,X80钢的反向加载特性可用Remberg-Osgood关系拟合。最后给出了屈服强度降和预塑性应变之间的经验公式。     

疲劳过程中的能量耗散和疲劳寿命的预测

试验测量了A3钢和铝合金LY12CZ在疲劳过程中的耗散能密度与应力幅的关系和破坏时的临界累积耗散能密度。通过一系列不同加载频率和应力比的比较试验,结果表明耗散能密度与应力幅的关系和临界累积耗散能密度在不同加载频率下变化不大,但是受应力比的影响较大。本文还建立了临界累积耗散能密度疲劳寿命预测判据,并用此判据进行了带中心孔板条构件的疲劳寿命预测,取得了较好的结果（误差在25％以内）。这种方法对于构件局部的疲劳主要由一个方向应力控制的工程问题,使用简便有效。     

预应变对中子辐照高纯铝拉伸性能的影响

金属材料的中子辐照硬化和脆化一直都是核能安全领域十分关注的重要问题之一. 为了进一步认识预应变对中子辐照金属材料塑性形变和最终断裂特性的影响规律, 及其微观机理, 本文研究了10%拉伸预应变高纯铝的拉伸应力-应变曲线、失稳应力和失稳应变等随辐照剂量的变化规律. 结果表明, 辐照剂量越高, 预应变高纯铝内部孔洞的尺寸和数密度越高, 导致屈服强度和极限拉伸强度越高, 均匀延伸率和失稳应变越小, 表现出典型的辐照硬化和脆化效应, 但失稳应力与辐照剂量几乎无关. 相同辐照剂量条件下, 预应变引入的高密度位错能够显著降低辐照孔洞的尺寸和数密度, 加之辐照退火效应的综合影响, 导致预应变能够降低高纯铝屈服强度的增长率和失稳应变的下降率, 从而表现出一定的抑制辐照硬化和脆化的能力, 预应变还能够提高高纯铝的失稳应力, 但整体而言预应变并不能提高高纯铝的延性. 最后, 基于J-C本构模型的中子辐照退火态金属材料的脆化模型能够直接应用于预应变金属材料, 且模型预测结果与实验结果吻合较好.      

Cyclic stress-strain behaviour of alloy AA6060 T4, part II: Biaxial experiments and modelling

Laboratory tests have been conducted to investigate the inelastic behaviour of aluminium alloy AA6060 T4 subjected to non-proportional cyclic loading. The results of four tests with variable strain path shapes and strain amplitudes are reported in this paper. The tests were carried out by applying combined axial force and torque to thin-walled tubular specimens, using effective strain amplitudes in the range 0.4–0.8%. Major emphasis has been put on the two important material properties: plastic anisotropy and influence of strain range and strain path shapes on cyclic hardening. A constitutive model for cyclic plasticity is used to predict the stress response of the alloy for the non-proportional strain paths applied in the experiments. The model adopts a quadratic yield function and multi-component non-linear isotropic and kinematic hardening rules to describe plastic anisotropy, the shape of the hysteresis loops and the evolution of cyclic hardening. Good agreement is obtained between the physical and correlated stress response of the alloy.     

A crystal plasticity model for strain-path changes in metals

A model is proposed that deals with the transient mechanical anisotropy during strain-path changes in metals. The basic mechanism is assumed to be latent hardening or softening of the slip systems, dependent on if they are active or passive during deformation, reflecting microstructural mechanisms that depend on the deformation mode rather than on the crystallography. The new model captures the experimentally observed behaviour of cross hardening in agreement with experiments for an AA3103 aluminium alloy. Generic results for strain reversals qualitatively agree with two types of behaviour reported in the literature – with or without a plateau on the stress–strain curve. The influence of the model parameters is studied through detailed calculations of the response of three selected parameter combinations, including the evolution of yield surface sections subsequent to 10% pre-strain. The mathematical complexity is kept to a minimum by avoiding explicit predictions related directly to underpinning microstructural changes. The starting point of the model is a combination of conventional texture and work hardening approaches, where an adapted full-constraints Taylor theory and a simple single-crystal work-hardening model for monotonic strain are used. However, the framework of the model is not restricted to these particular models.     

Effect of curvature of the strain trajectory on the plastic behaviour of brass

As a fundamental example of experimental work to examine the plastic behaviour of metals for deformations along curved strain trajectories under complex loadings, an experiment was performed on the deformation of a thin-walled tubular specimen of brass along orthogonal bilinear trajectories with a rounded corner for various constant radii under the combined loadings of axial force and torque. As the result of experiment, the variation of deformation behaviour under complex loading was clarified in the decreasing stage of the curvature of the rounded corner by comparing the behaviour when there is a significant history effect at the point corner to the behaviour along the so-called trajectory with small curvature which is close to that of proportional deformation. The experimental result was expressed as a vector relation of integral type between stress- and strain-increment vectors. The influence functions in this relation were determined according to the features of the experimental data with the use of an intrinsic time-scale in referring to the endochronic theory proposed by Valanis (1971). The stress-strain relation thus obtained was found to approximate the experimental result with high accuracy.     

Computational analysis of stress-based forming limit curves

This article, through computational analyses, examines the validity of using the stress-based and extended stress-based forming limit curves to predict the onset of necking during proportional loading of sheet metal. To this end, a model material consisting of a homogeneous zone and a zone that has voids (material inhomogeneity) is proposed and used to simulate necking under plane strain and uni-axial stress load paths. Results of the in-plane loading computations are used to construct a strain-based formability limit curve for the model material. This limit curve is transformed into principal stress space using the procedure due to Stoughton [Stoughton, T.B., 2000. A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 42, 1–27]. The stress-based limit curve is then transformed into equivalent stress and mean stress space to obtain an Extended Stress-Based Limit Curve (XSFLC). When subjected to three-dimensional loading, the model material is observed to display a variety of responses. From these responses, a criterion for the applicability of the XSFLC to predict the onset of necking in the model material when it is subjected to three-dimensional loading is obtained. In the context of straight tube hydroforming, to provide support for the use of the XSFLC, it is demonstrated that the criterion is satisfied.     

The inelastic behavior of metals subject to loading reversal

One of the consequences of memory effects in the plastic deformation of metals is the Bauschinger effect (Civilingenieur 27 (1881) 289–348), which manifests itself as a difference in the values of the yield stress in tension and compression for a material that has undergone plastic deformation. The Bauschinger effect has been modeled with the kinematic hardening rules e.g., Ziegler (Quart. Appl. Math. 17 (1959) 55) and Chaboche (Int. J. Plasticity 2 (1986) 149). These models, though, are not able to reproduce the stress-strain response accurately at points of loading reversal: it has been observed (Acta Metall. 34 (1986) 1553; Mater. Sci. Engineering A113 (1989) 441) that, for some materials, the stress has a plateau after the loading is reversed. This is not reflected by the kinematic hardening rule nor by its modifications. In this paper we will develop a general three dimensional model that is able to reproduce the stress–strain response at loading reversals and can be applied also to more general changes of loading direction. The central idea of our model is to link the hardening behavior of the material to thermodynamical quantities such as the stored energy due to cold work and the rate of dissipation. The predictions of the theory show good agreement with the stress–strain curve and also with the manner in which the stored energy varies with the inelastic strain, as obtained from experiments (Progress in Materials Science (1973) Vol. 17. Pergamon, Oxford; Trans. Met. Soc. AIME 224 (1962) 719).     

Cyclic stress-strain behaviour of alloy AA6060, part I: Uniaxial experiments and modelling

An experimental and numerical study of the uniaxial cyclic behaviour of the aluminium alloy AA6060 in tempers T4 and T6 is reported. Material characteristics studied through the experimental programme are the monotonic stress-strain curve, the shape of the hysteresis loops, cyclic hardening and softening, mean stress relaxation and memorization of prior strain histories. A model of cyclic plasticity, proposed in the literature, is used to simulate the physical behaviour of the alloy in temper T4. The model utilizes multi-component forms of kinematic and isotropic hardening variables with non-linear evolutionary rules to describe the hysteresis loops and the transient behaviour of the material. The evolution of the Bauschinger effect and the memory of prior strain histories are properly modelled through additional internal variables. Tests and simulations are compared for temper T4, and good agreement is obtained between physical and correlated behaviour.     

Several contributions to soil compactibility induced by cyclic loading test

To investigate the soil compactibility during the cyclic loading, three different kinds of paddy field soils were prepared so as to clarify interrelationships among stress amplitude ratio, bulk density, soil water content and pore water pressure. The presetting values of specimen include the soil water content(percent dry basis) and bulk density of 25% d.b. and 1.1 Mg/m³ respectively. The relation between the number of cyclic loading and axial strain exhibited an asymptotically increasing trend, converging toward a specific value for each experimental condition. Possible effect caused by elastic–plastic characteristics could be recognized, when axial strain for 0.5 Hz excitation becomes greater than the one of 1.0 Hz under same stress amplitude ratio. When the stress amplitude ratio took 0.1, the absolute value of axial strain of 0.5 Hz was greater than the one of 1.0 Hz, whereas its decreasing trend was recognized in the sequence of silt, clay and silty sand. The qualitative relations between pore water pressure and number of cyclic loading were also examined to scrutinize the effect of effective water pressure to the soil compactibility.     

Non-linear creep damage under one-dimensional variable tensile stress

A non-linear damage relation, containing the axial strain history and a time integral over the stress history, is proposed for the case of one-dimensional time dependent tensile stress. Non-linear steady and transient creep terms are included in the axial strain relation, and elastic and creep Poisson's ratios are introduced into the lateral strain relation. Using these relations, complete damage solutions are obtained for the constant stress rate, step stress, relaxation and constant load tests. Observations are made concerning the associated rupture times.     

不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

The effect of the riveting process and aging on the mechanical behaviour of an aluminium self-piercing riveted connection

The joining of two aluminium plates with an aluminium self-piercing rivet, as discussed by Hoang et al. (2010), showed that heating to soften the plates to be joined might be used to avoid plastic compression or fracture in the rivet. In the present paper, the mechanical behaviour of self-piercing riveted connections using an aluminium rivet was investigated. Two U-shaped specimens in alloy AA6063-W, obtained by a solution heat treatment of the alloy in temper T4, were joined using an aluminium self-pierce rivet in alloy AA7278-T6. The mechanical behaviour of these connections was tested after 3 and 30 days of natural aging of the riveted specimens. Test results showed that the strength of the aluminium riveted joints tended to stabilize after three days of natural aging. In order to evaluate the process effect (i.e. the effect of the pre-straining of the plates in W temper as the result of the riveting process, and the subsequent natural age-hardening of the plates) on the mechanical properties of the riveted connection, a comprehensive material test programme was carried out. Test results revealed that there is an interaction between the pre-straining and natural aging which lowers the material properties in terms of the flow stress compared to the ‘virgin’ material, i.e. the curve obtained after heat treatment and aging only. Then, the process effect on the mechanical behaviour of the riveted connections was investigated more closely by using a 3D-model generated in LS-DYNA. The combined effect of the pre-straining and natural aging was accounted for in the numerical analyses by means of a user-defined constitutive model. Numerical analyses revealed that it is necessary to consider the combined effect of plastic deformation and aging in order to predict the mechanical behaviour with a reasonable accuracy.     

Precise measurement of plastic behaviour of mild steel tubular specimens subjected to combined torsion and axial force

In the present paper, as an investigation for obtaining detailed information about the plastic behaviour of real materials, precise measurement of plastic deformation of thin-walled tubular specimens of initially-isotropic mild steel was performed under combined loading of torsion and axial force having trajectories consisting of two straight lines at a constant rate of the effective strain.From the experimental results, it is found that the effect of the third invariant of the strain tensor appeared even for proportional deformation consisting of torsion and axial force. Moreover, it may be seen that the effective stress drops suddenly with increasing effective strain, and coaxiality between the stress deviator and the plastic strain increment tensor is seriously disturbed just after the corner of the strain trajectory. However, these local disturbances are recovered along the second branch of the trajectory.The effect of the third invariant of the strain tensor was eliminated from the experimental results by the introduction of the modified local stress space for isolating the influence of anisotropy due to the deformation history. This permits a systematic evaluation of the influence of anisotropy for various types of combined loading.     

Mechanical response and modeling of fully compacted nanocrystalline iron and copper

A comprehensive study on the response of nanocrystalline iron and copper to quasi-static and dynamic loading is reported. Bulk solid nanocrystalline iron and copper specimens used in static and dynamic loading experiments were made by compaction and hot sintering of the nanocrystalline powders. The powders, with grain size 16–96 nm, were obtained by using high energy ball milling. The stress/strain response of dense nanocrystalline iron is found to be grain size and strain rate dependent. The KHL model is modified by incorporating Hall–Petch relation (i.e. yield stress dependence on grain size) and is used to represent the behavior of fully compacted nanocrystalline material. A good correlation with the experimental results is demonstrated.