Non-uniform deformation after prestrain

The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.     

A parameter for measuring the magnitude of a change of strain path: Validation and comparison with experiments on low carbon steel

Various tension-tension and tension-shear strain sequential experiments have been performed on low carbon steel sheet along different material axes. Owing to the rapid plastic instability that occurs during the reloading in uniaxial tension of prestrained samples, the results are focussed on the evolution of the macroscopic reloading yield stress (back extrapolated stress). For a given prestrain amount, the reloading stress is a function of the magnitude of the strain path change. A parameter is proposed, which allows the comparison of different sequential loading tests: the scalar product of the unit tensors corresponding to the prestrain and to the subsequent strain modes, respectively. For low carbon steel, a single curve is obtained when the reloading stress, normalized by the stress along the monotonic strain path is plotted against this parameter whatever the combination of loading sequences and the material direction of the prestrain.     

DP钢板应变路径多步演变下的弹塑性力学行为

针对DP高强双相钢板在复杂载荷作用下的弹塑性力学特征,提出利用三步拉伸力学实验,对比分析单轴循环加载和非等轴加载下材料的各向异性硬化、永久软化和弹性模量衰减特性等力学行为,揭示应变路径多步演变下的弹塑性力学特性.研究结果表明:材料再加载初期的瞬态行为与应变路径有关,在初期瞬态阶段显示出明显的各向异性,且再加载角度、预应...     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.     

Plane strain pure bending of sheets with damage evolution at large strains

An analysis of plane-strain bending at large strains for the rigid/plastic incompressible material model including arbitrary strain-hardening and damage evolution laws is performed. The fracture criterion is based on a critical value of the damage parameter. Numerical treatment is reduced to the system of two partial differential equations written in characteristic coordinates. The through-thickness distribution of the principal stresses and damage parameter as well as the variation of the bending moment with the radius of curvature of the concave surface are found for Swift’s hardening law and one specific damage evolution law. General tendencies in solution behaviour are in agreement with physical expectations.     

A unified plasticity model for cyclic behaviour of clay and sand

This paper presents the development and an experimental evaluation of a simple unified bounding surface plasticity theory for modelling the stress–strain behaviour of sand and clay under both drained and undrained cyclic loading conditions. The model concerned is called CASM-c, which is based on the unified critical state model CASM developed by Yu [Yu, H.S., 1995. A unified critical state model for clay and sand. Civil Engineering Research Report No. 112.08.1995. University of Newcastle, NSW 2308, Australia; Yu, H.S., 1998. CASM: a unified state parameter model for clay and sand. International Journal of Numerical and Analytical Methods in Geomechanics 22, 621–653]. CASM is a relatively simple model as it only requires seven model constants, five of which are the same as those used in the modified Cam-clay model. All these constants have clear physical meanings and may be easily determined from the results of triaxial tests. A key advantage of CASM over many other existing critical state models lies on its simplicity and unified nature as it can model the behaviour of both clay and sand.The extension of the model CASM presented in this paper consists of adopting the bounding surface plasticity theory and treating the reloading and unloading processes differently when calculating the hardening modulus. As a result, a smooth transition of stiffness and gradual accumulation of permanent strain and/or pore pressure in unload–reload cycles as well as the hysteretic behaviour can be reproduced. The results of model simulations show an encouraging agreement with experimental data from triaxial tests subjected to both one-way and two-way cyclic loading conditions.     

A new view on transformation induced plasticity (TRIP)

The phenomenon of transformation induced plasticity (TRIP) in steel is reinvestigated both experimentally and theoretically. The irreversible length change (TRIP strain) consists not only of a plastic contribution (“Greenwood–Johnson” effect) but also of a contribution due to the length change caused by the transformation shear component of the martensitic variants (orientation effect or “Magee” effect). This orientation effect, which is fully accepted for shape memory alloys, is explained for steels. Micromechanical investigations help to quantify the orientation effect. Finally a proposal for a modified constitutive law for elastic plastic phase changing materials is presented.     

Computational modelling of the stress-softening phenomenon of rubber-like materials under cyclic loading

When a rubber specimen is subjected to cyclic loading, not only non-linear behaviour but also damage-induced stress-softening phenomena (the Mullins effect) have been observed. Applications of a continuum damage mechanics model and Ogden and Roxburgh's pseudo-elastic model to describe the Mullins effect in elastomers have been considered. Both models together with Gao's elastic law were implemented to describe the mechanical behaviour of rubber-like materials including the stress-softening phenomenon. Two sets of experimental data (a simple tension test and a simple tension and pure shear test) are used to validate the constitutive models. Model parameters are estimated via an inverse technique. Computational results show that both constitutive models together with Gao's elastic law can describe the typical Mullins effect. From engineering point of view, the pseudo-elastic model has the advantages that (i) the model is simple and practical, since it considers that the stress-softening function is only activated on unloading or reloading paths, (ii) the model with a slight modification of the damage variable is very stable in finite element calculations, and (iii) the numerical results agree very well with experimental data in both simple tension and pure shear deformation. Two applications illustrate the capability of combining the pseudo-elastic model with Gao's elastic law in describing the Mullins effect. It is emphasized that both models are applicable to multiaxial states of stress and strain because both models are energy-based and not strain-based.     

A viscoplasticity theory applied to proportional and non-proportional cyclic loading at small strains

The small strain, isotropic, Viscoplasticity theory Based on Overstress (VBO) is modified so that the experimentally observed, complex cyclic hardening behavior under proportional and non-proportional loading with fixed as well as variable strain amplitude can be reproduced. This is accomplished by formulating a growth law for the isotropic, rate independent stress, a scalar valued state variable of VBO. The non-proportionality measure employed for modeling the effects of loading path, amplitude and prior history is Tanaka's fourth order tensor [Eur. J. Mech. Solids 13 (1994) 155]. Numerical experiments show the responses in step-up and down two amplitude tests and include further hardening after an increase in the strain amplitude. The differences in the responses to proportional and non-proportional loading including circular, square, one step and two steps are demonstrated. History dependence of the hardening is depicted. The cross hardening behavior, sudden increase in the stress level which is followed by softening after the path change are modeled well.     

A model of thermoelectroplasticity of variations in the mechanical properties of metals based on defect structure reorganization under the action of pulse electric current

We consider variations in the mechanical properties of prestrained samples made of metallic materials with defects like microcracks and micropores under the action of pulse high-energy electric currents of certain intensity and duration. It was experimentally shown [1–5] that the treatment with a high-energy electromagnetic field of a prestretched sample with defects like microcracks that are located normally to the sample tension axis increases the sample limit plastic strain, which simplifies the treatment of hard-to-deform alloys in various technological processes. We consider a slow quasi-stationary process of thermal-electric treatment of samples, which permits obtaining materials with desired mechanical properties including samples with a high limit plastic strain.     

Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

A generic stress-strain model for metallic materials with two-stage strain hardening behaviour

Constitutive equations are often used to describe the stress-strain behaviour of metallic materials. This allows the execution of parametric studies for various purposes. Despite the large number of developed stress-strain equations, all frequently applied ones fail to accurately describe a strain hardening behaviour in two distinct stages, which many metallic materials tend to show. For this purpose, the authors developed a new stress-strain model, based on the well-known Ramberg-Osgood equation, which focuses on this two-stage strain hardening behaviour. This article describes the model and its analytical background, along with a graphical method to derive suited model parameters. To validate the proposed methodology, it is applied on stress-strain curves of two high-strength steels, an aluminium alloy and a duplex stainless-steel alloy. Whereas a good correspondence for the stainless-steel alloy is confined to limited plastic strains, excellent agreements are observed for the steels and the aluminium alloy. Following the proposed method, it was possible to obtain model parameter values that give a good correspondence within a detectable strain range.     

A microscopic damage model considering the change of void shape and application in the void closing

A microscopic damage model of ellipsoidal body containing ellipsoidal void for nonlinear matrix materials is developed under a particular coordinate. The change of void shape is considered in this model. The viscous restrained equation obtained from the model is affected by stress ∑_(ij), void volume fraction f, material strain rate exponent m as well as the void shape. Gurson's equation is modified from the numerical solution. The modified equation is suitable for the case of nonlinear matrix materials and changeable voids. Lastly, the model is used to analyze the closing process of voids.     

一种考虑非比例附加损伤的多轴低周疲劳模型

在实际工作环境中,机械结构往往承受着多轴非比例循环载荷.相比多轴比例循环加载,多轴非比例循环加载由于产生了附加强化现象,造成机械结构疲劳寿命下降.通过分析薄壁圆筒管件在非比例加载工况下应力应变变化规律和发生破坏位置,本文基于临界面法提出一种考虑多轴非比例附加损伤的疲劳模型.该模型将最大剪切应变幅平面作为临界面,提出一个新的附加强化因子,结合临界面上切应变幅和正应变幅组成新的多轴疲劳损伤参量.此参量不仅考虑了非比例加载下临界面上正应变幅和切应变幅对材料造成的疲劳损伤,还考虑到应变路径的变化和材料非比例加载敏感特性对材料疲劳寿命的影响.考虑到实际情况下模型所需材料附加强化系数有时难以获得的情况,给出了材料附加强化系数的有关近似计算公式.只需要材料基本力学参数便可得到材料附加强化系数,方便工程实际应用.采用8种材料的多轴疲劳寿命数据对提出的新模型进行检验,结果表明所提出的新模型与传统多轴疲劳模型相比预测寿命精度更高.      

Effects of deformed volume, volume fraction and particle size on the deformation behaviour of W/Cu composites

Tungsten/copper (W/Cu) particle reinforced composites were used to investigate the scaling effects on the deformation and fracture behaviour. The effects of the volume fraction and the particle size of the reinforcement (tungsten particles) were studied. W/Cu-80/20, 70/30 and 60/40 wt.% each with tungsten particle size of 10 μm and 30 μm were tested under compression and shear loading. Cylindrical compression specimens with different volumes (D_S = H) were investigated with strain rates between 0.001 s⁻¹ and about 5750 s⁻¹ at temperatures from 20 °C to 800 °C. Axis-symmetric hat-shaped shear specimens with different shear zone widths were examined at different strain rates as well. A clear dependence of the flow stress on the deformed volume and the particle size was found under compression and shear loading. Metallographic investigation was carried out to show a relation between the deformation of the tungsten particles and the global deformation of the specimens. The size of the deformed zone under either compression or shear loading has shown a clear size effect on the fracture of the hat-shaped specimens.The quasi-static flow curves were described with the material law from Swift. The parameters of the material law were presented as a function of the temperature and the specimen size. The mechanical behaviour of the composite materials were numerically computed for an idealized axis-symmetric hat-shaped specimen to verify the determined material law.     

固体跨尺度压痕标度律的研究与展望

压痕标度律是对通过压痕试验方法测定固体材料力学性能参量问题所给出的一般性结论, 具有重要的理论意义, 是探寻材料力学性能潜在规律的方法论研究. 本综述论文系统而简要地介绍如下主要内容: 采用传统理论对传统固体材料压痕标度律的研究回顾; 采用跨尺度力学理论对先进固体材料的跨尺度压痕标度律的研究回顾. 总结并得到了如下主要结论: 传统固体材料压痕标度律可由一空间曲面完整描绘, 若进一步已知某类无量纲独立参量的取值范围, 则该空间曲面可退化为系列平面曲线族; 先进固体材料(新材料)的跨尺度压痕标度律可由一个三维函数关系完整描绘, 若存在某类独立无量纲参量取值范围已知, 则该三维函数关系将退化为系列空间曲面族. 压痕标度律的未来研究发展仍将重点集中在建立新材料的跨尺度压痕标度律上, 以试图从根本上解决新材料力学性能标准规范难以建立的理论问题. 除此之外也将重点关注建立各类功能新材料的多尺度及跨尺度压痕标度律规律.      

Experimental and numerical investigation of combined isotropic-kinematic hardening behavior of sheet metals

To prevent a sheet specimen from buckling subjected to a tension-compression cyclic loading, a new fixture has been developed to use with a regular tensile-compression machine. The novelty of this device lies in 4-block wedge design with pre-loaded springs. This design allows blocks to freely move in the vertical direction while providing the normal support to the entire length of the specimen during the tension-compression cycle. The entire test is easy to setup, which is another advantage of this design. In order to measure the strain accurately, the transmission type laser extensometer was utilized together with the implementation of double-side fins in the specimen. Experimental results of tension-compression tests are presented followed by a review of existing testing methods. In order to describe the accurate cyclic tension-compression behavior, the combined isotropic-kinematic hardening law based on the modified Chaboche model and the practical two-surface model based on Dafalias-Popov and Krieg models have been modified in this work, considering the permanent softening behavior during reverse loading and the non-symmetric behavior during reloading. Through tension-compression tests, the material characterization has been performed for three base materials, BH180, DP600 steels and AA6111-T4 sheets.