5A06-O aluminium–magnesium alloy sheet warm hydroforming and optimization of process parameters

The uniaxial tensile test of the 5A06-O aluminium–magnesium (Al–Mg) alloy sheet was performed in the temperature range of 20–300 °C to obtain the true stress–true strain curves at different temperatures and strain rates. The constitutive model of 5A06-O Al–Mg alloy sheet with the temperature range from 150 to 300°C was established. Based on the test results, a unique finite element simulation platform for warm hydroforming of 5A06-O Al–Mg alloy was set up using the general finite element software MSC.Marc to simulate warm hydroforming of classic specimen, and a coupled thermo-mechanical finite element model for warm hydroforming of cylindrical cup was built up. Combined with the experiment, the influence of the temperature field distribution and loading conditions on the sheet formability was studied. The results show that the non-isothermal temperature distribution conditions can significantly improve the forming performance of the material. As the temperature increases, the impact of the punching speed on the forming becomes particularly obvious; the optimal values of the fluid pressure and blank holder force required for forming are reduced.     

03Cr18NiMoN节镍双相不锈钢的热变形行为及热加工图

关键词：双相不锈钢； 流变曲线； 本构方程； 热加工图     

A three‐dimensional model describing stress‐temperature induced solid phase transformations: solution algorithm and boundary value problems

An always increasing knowledge on material properties as well as a progressively more sophisticated production technology make shape memory alloys (SMA) extremely interesting for the industrial world. At the same time, SMA devices are typically characterized by complex multi‐axial stress states as well as non‐homogeneous and non‐isothermal conditions both in space and time. This aspect suggests the finite element method as a useful tool to help and improve application design and realization. With this aim, we focus on a three‐dimensional macroscopic thermo‐mechanical model able to reproduce the most significant SMA features (Int. J. Numer. Methods Eng. 2002; 55 : 1255–1264), proposing a simple modification of such a model. However, the suggested modification allows the development of a time‐discrete solution algorithm, which is more effective and robust than the one previously discussed in the literature. We verify the computational tool ability to simulate realistic mechanical boundary value problems with prescribed temperature dependence, studying three SMA applications: a spring actuator, a self‐expanding stent, a coupling device for vacuum tightness. The effectiveness of the model to solve thermo‐mechanical coupled problems will be discussed in a forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd.     

A new ‘Tailor-made’ methodology for the mechanical behaviour analysis of rubber-like materials: II. Application to the hyperelastic behaviour characterization of a carbon-black filled natural rubber vulcanizate

The purpose of this paper is the modelling of the mechanical behaviour of an elastomeric material, through detailed experimental and numerical procedures, specific to large strains. The experimental technique is based on in-plane kinematics measurements using a speckle extensometer, from which the whole two-dimensional field of in-plane displacements is obtained by a digital image processing [Polymer (2002)]. This part of the work concerns the identification of the constitutive equation for a carbon black natural rubber (NR) vulcanizate. We start by quoting some theoretical considerations relative to rubber elasticity and stress-softening effect, which is the counterpart of the filler reinforcement. Then, we describe the experimental procedure and present data for both non-preconditioned and preconditioned samples. Next, the identification of the constitutive law parameters using a minimization algorithm is driven. Finally, we present the validation of the constitutive model, by its implementation into the finite element code SYSTUS and the numerical simulation of the response of a double edge notched tensile (DENT) specimen.     

Application of Galerkin Method to Dynamical Behavior of Viscoelastic Timoshenko Beam with Finite Deformation

The motion equations governing the dynamical behavior of a viscoelasticTimoshenko beam with finite deformation are derived and simplified byGalerkin method. The viscoelastic material is assumed to obey thethree-dimensional fractional derivative constitutive relation. Thedynamical behaviors of the simplified systems with order 1 and order 2are numerically computed and compared by using the computational methodpresented by the authors. The dynamical behaviors of the systems areuniform qualitatively, but there is a little deviation quantitatively.And the truncated system with order 1 is safer than the one of order 2.It is also shown that the lower order system is reasonable. Theinfluences of the load parameter and the fractional derivative parameter(material parameter) on the deflection of the beam are consideredrespectively. The numerical methods in nonlinear dynamics, such as phasediagram, and Poincaré section, are applied to reveal dynamical behaviorsof the nonlinear viscoelastic Timoshenko beam. There are plenty ofdynamical behaviors, such as periodicity, bifurcation, quasi-periodicityand chaos in the dynamical system.     

循环荷载作用下饱和黏性土的弹塑性双面模型

基于作者新近提出的一种混合塑性硬化准则和临界状态土力学理论建立了一个三维形式表述的适于饱和黏性土的弹塑性双面模型,此硬化准则是著名的M asing方法在三维应力空间中的推广。该模型的二维形式已采用饱和黏性土样室内动态三轴不排水剪切试验的结果进行了验证并已在另文发表。本文所建的三维弹塑性动本构模型与一个半经验的孔隙水压力增长模式相结合,通过有限元程序ABAQUS*对一个循环荷载作用下的条形基础下部地基土层内的位移、应力分布和超孔隙水压力随时间的变化进行了分析,计算结果表明模型预测的地基土的力学响应是符合实际的。     

Implicit integration and consistent tangent modulus of a time‐dependent non‐unified constitutive model

This paper describes the implicit integration and consistent tangent modulus of an inelastic constitutive model with transient and steady strain rates, both of which are time‐ and temperature‐dependent; the transient rate is influenced by the evolution of back stress decomposed into parts, while the steady rate depends only on applied stress and temperature. Such a non‐unified model is useful for high‐temperature structural analysis and is practical owing to the ease in determining material constants. The implicit integration is shown to result in two scalar‐valued coupled equations, and the consistent tangent modulus is derived in a quite versatile form by introducing a set of fourth‐rank constitutive parameters into the discretized evolution rule of back stress. The constitutive model is, then, implemented in a finite element program and applied to a lead‐free solder joint analysis. It is demonstrated that the implicit integration is very accurate if the multilinear kinematic hardening model of Ohno and Wang is employed, and that the consistent tangent modulus certainly affords quadratic convergence to the Newton–Raphson iteration in solving nodal force equilibrium equations. Copyright © 2003 John Wiley & Sons, Ltd.     

Temperature–stress–strain trajectory modelling during thermo-mechanical fatigue

The isothermal strain‐life approach is the most commonly used approach for determining fatigue damage, particularly when yielding occurs. Computationally it is extremely fast and generally requires elastic finite element analyses only. Therefore, it has been adapted for variable temperatures. Local temperature—stress–strain behaviour is modelled with an operator of the Prandtl type. The hysteresis loops are supposed to be stabilized and no creep is considered. The consequences of reversal point filtering are analysed. The approach is finally compared to several thermo‐mechanical fatigue tests and the Skelton model.     

Efficient return algorithms for associated plasticity with multiple yield planes

A new return method for implicit integration of linear isotropic yield criteria is presented. The basic idea is to perform all the manipulations in the principal stress space and thereby achieve very simple formulae for calculating the plastic corrector stresses, based on the constant gradient of such criteria. The return formulae are in closed form and no iteration is required. The method accounts for three types of stress return: return to a single yield plane, to a discontinuity line at the intersection of two yield planes and to a discontinuity point at the intersection between three or more yield planes. The infinitesimal and the consistent elastoplastic constitutive matrix are calculated for each type of stress return, as are the conditions to ascertain which type of return is required. The method is exemplified with the Mohr–Coulomb yield criterion. Copyright © 2005 John Wiley & Sons, Ltd.