材料参数对板材胀形过程综合影响的数值研究

本文将Hosford 与Hill 各向异性屈服函数应用于刚粘塑性有限元方法,分析了圆形薄板液压胀形过程.研究了材料性能参数:硬化指数n、速率敏感指数m、厚向各向异性参数R、屈服函数非多项式指数M 对液压胀形过程的综合影响.并通过数值分析,找出了临界厚向断裂应变-ε_3~(ov·)与材料参数关系的经验方程式.屈服表面形状对极限厚度应变的影响,可以用Barlat 提出的包含了R 和M 影响的p 值表示出来.     

Hill（1979）屈服准则的展开及在金属薄板成形极限图中的应用

本文对于Hill(1979)屈服准则在平面应力条件下进行了展开,给出了五种特定条件下的等效应力和等效应变速率表达式,对这些特例的凸条件检验表明,其中的四种可做为合理的屈服函数,将这些屈服函数应用于金属薄板在拉伸范围内的成形极限图的M—K理论预测,获得了较为理想的结果。     

梯度增强Cosserat连续体的广义Hill定理

基于经典Cauchy连续体的Hill定理,在平均场理论的框架下导出了梯度增强Cosserat连续体细、宏观均匀化方法的广义Hill定理。在梯度增强Cosserat连续体中,不仅宏观样条点上的应变和应力张量,而且它们的梯度均作用于与该样条点相关联的细观表征元（RVE）。依据此广义Hill定理,对梯度增强Cosserat连...     

各向异性屈服准则的发展及实验验证综述

鉴于材料的屈服行为对板料成形的重要性, 人们对各向异性屈服准则进行了长期研究. 本文对各向异性屈服准则的发展进行了较为全面的回顾, 对Hill系列、Hosford系列和Drucker系列3类屈服准则分别进行归纳. 重点介绍不同类型屈服准则的适用范围及缺陷, 总结目前国内外所采用的不同的实验验证方法, 最后指出各向异性屈服准则在数值模拟中应用的难点及今后的研究方向.      

汽车薄钢板应力应变曲线及屈服轨迹的研究

采用十字形双向拉伸的实验方法对两种汽车用薄钢板BH220和SPEN进行了不同 加载路径下的双向拉伸试验，得到了不同应力状态下的应力应变关系曲线，同时，根据单位 体积塑性功相等的原则，确定了两种钢板等效塑性应变从0.2\%$\sim$2\%的实验屈服轨迹. 结果分析表明：不同加载路径下板料的应力应变关系不同，随着加载比例由单拉到等双拉状 态，板料的硬化指数逐步增大；实验屈服轨迹呈外凸性，且以等双拉为界的上下部分屈服轨 迹不对称，随着变形程度的增加，屈服轨迹向外扩大，但单拉时强化程度最小，而等双拉 时最大. 对BH220和SPEN钢板的实验屈服轨迹与几种常用理论屈服轨迹的比较发现，Hosford各向 异性屈服准则的理论轨迹与实验结果最为接近，Hill48准则与实验结果相差最大，此外一 向被视为只适用于各向同性材料的Mises准则与实验结果也较为接近，其他几个屈服准则的 理论屈服轨迹与实验点相差较大.     

金属的后继屈服面研究—单试样与多试样测试

采用退火45号钢薄壁试样进行拉扭组合试验,测试材料经历预拉伸后的系列后继屈服面。试验采用偏移应变法定义屈服应力,讨论了不同的偏移应变、预变形程度对后继屈服面测试结果的影响;试验分别用单试样法和多试样法进行,分析讨论了两种方法的合理性与局限性。试验研究得到以下结果：（1）单试样法和多试样法确定的初始屈服面的形状与Mises圆很接近;（2）单试样法屈服点的测试顺序对所测得的屈服面的形状有很大影响,第一测试点与预加载方向相反时,所得屈服面会出现“内凹”现象,而若改变测试顺序,可不再出现“内凹”;（3）单试样法测得的后继屈服面与测试的屈服点数密切相关,当测试的屈服点数较多时,所得结果因累积塑性应变引起的应变强化作用而出现较大的偏离;（4）单试样法与多试样法测得的后继屈服面形状和大小有较明显的差异,测试过程中塑性变形的积累对单试样法的测试结果有明显影响,采用多试样法研究屈服面演化更为合理;（5）多试样法若采用较小目标偏移应变定义屈服,测得的后继屈服面也出现轻微内凹。     

不同后继屈服函数在弹塑性有限元中的应用评估

构造了一种在π平面上为椭圆的后续屈服函数,将该屈服函数、“Tresca”及“Misses型”后继屈服函数分别应用于干涉孔及冷胀孔问题的弹塑性有限元分析,并对这三种屈服函数在弹塑性有限元中的应用进行了评估。本文三种屈服函数在弹塑性问题中的应用评估对更有效地解决工程中的弹塑性问题有着实际的应用价值。     

冻土屈服面与屈服准则的研究

基于广义塑性力学,分析了理想塑性冻土屈服面的一些具体特性,对冻土的体积屈服面进行了比较详尽的探讨.通过对已有屈服函数Matsuoka-Nakai屈服准则的修改,提出了一个冻土屈服函数,并对此函数进行了具体研究.通过和试验数据的对比,验证了所提出屈服函数的正确性,所提出的函数含有三个参数,随着温度的不同对冻土屈服面的形状和大小都有重要的影响.     

广义双剪粘弹塑性本构模型在渤海海冰动力学中的应用

在连续介质力学基础上建立了一个广义双剪粘弹塑性海冰动力学本构模型。该模型在海冰屈服前采用Kelvin-Vogit粘弹性模型,考虑中间主应力和静水压力对海冰屈服的影响选用广义双剪应力屈服准则作为海冰屈服判据,屈服后采用相关联的正则流动法则。采用该本构模型对渤海海冰动力过程进行了48小时数值模拟,讨论了辽东湾海冰的厚度、密集度、冰速和主应力的分布规律,其中海冰厚度分布与卫星遥感资料符合良好,从而有效地验证了该广义双剪粘弹塑性本构模型在海冰动力学中的可靠性。     

立方晶体单晶材料屈服面的研究

将Hill屈服准则用于DD3镍基单晶合金屈服应力的预测，通过与试验结果比较发现，在760℃时的误差较大，根据立方单晶材料的屈服特点，用正应力偏张量平方与剪应力偏张量平方乘积项构成的应力不变量考虑单晶合金偏轴受载时存在的拉、剪应力耦合效应，提出了一个在工程上实用的新屈服准则．在新屈服准则中出现的参数可以通过单向拉伸试验确定，给出了确定这些参数的方法，并重新定义了适合新屈服准则的等效应力和等效应变，对各向同性材料，新屈服准则退化为Von Mises屈服准则，新定义的等效应力和等效应变退化为Von，Mises等效应力和等效应变，用新屈服准则对国产DD3单晶合金的屈服应力进行预测，能很好地符合试验结果；与Hill屈服准则比较，在760℃时的预测精度显提高。     

General Hosford yield functions of orthorhombic materials

Although the Hosford yield function is more suitable for describing both the yielding and the plastic deformation of orthorhombic materials than the Hill quadratic yield function, the Hosford yield function suffers from the restriction that the loading has to be coaxial with the orthotropy of the materials. To relax this restriction, herein we present a new general Hosford yield function for the orthorhombic materials. The new general Hosford yield function is suitable to any stress state of the orthorhombic materials. When η = 2, the new general Hosford yield function becomes the Hill quadratic yield function. The new general Hosford yield function is more general than the general Hosford yield function of Huang and Man (Int J Plast 41:97–123, 2013), which covers only weakly-textured sheets of cubic metals. Two examples show that the new general Horsford yield function with suitable η value gives much better fits than those of the Hill quadratic yield function (η = 2).     

A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming

In this paper an anisotropic material model based on non-associated flow rule and mixed isotropic–kinematic hardening was developed and implemented into a user-defined material (UMAT) subroutine for the commercial finite element code ABAQUS. Both yield function and plastic potential were defined in the form of Hill’s [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. Lond. A 193, 281–297] quadratic anisotropic function, where the coefficients for the yield function were determined from the yield stresses in different material orientations, and those of the plastic potential were determined from the r-values in different directions. Isotropic hardening follows a nonlinear behavior, generally in the power law form for most grades of steel and the exponential law form for aluminum alloys. Also, a kinematic hardening law was implemented to account for cyclic loading effects. The evolution of the backstress tensor was modeled based on the nonlinear kinematic hardening theory (Armstrong–Frederick formulation). Computational plasticity equations were then formulated by using a return-mapping algorithm to integrate the stress over each time increment. Either explicit or implicit time integration schemes can be used for this model. Finally, the implemented material model was utilized to simulate two sheet metal forming processes: the cup drawing of AA2090-T3, and the springback of the channel drawing of two sheet materials (DP600 and AA6022-T43). Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior and the Bauschinger ratio. The in-plane anisotropy (r-value and yield stress directionalities) of these sheet materials was also compared with the results of numerical simulations using the non-associated model. These results showed that this non-associated, mixed hardening model significantly improves the prediction of earing in the cup drawing process and the prediction of springback in the sidewall of drawn channel sections, even when a simple quadratic constitutive model is used.     

Prediction of forming limit curves using an anisotropic yield function with prestrain induced backstress

The Forming Limit Diagram (FLD), a plot of the maximum major principal strains that can be sustained by sheet materials prior to the onset of localized necking, is a useful concept for characterizing the formability of sheet metal. Both experimental and numerical results in the literature have shown that the level of the FLD is strongly strain path dependent and the prediction of FLD depends on the shape of the initial yield function and its evolution. In this work, to improve the accuracy of FLD prediction under nonlinear strain paths for a given material, the evolution of the yield function is proposed in terms of the changes of its center and its curvature. The center of the subsequent yield surface after preloading and unloading will be determined via a backstress tensor, and the curvature change will be reflected by changing the exponent in the yield function. Both parameters are functions of the effective plastic strain and will be determined using the forming limit strains obtained from two nonlinear tests. Using this approach, a combination of Marciniak–Kuczynski (M–K) analysis (Marciniak, Z., Kuczynski, K. 1967. Limit strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609.) and a general anisotropic yield criterion developed by Karafillis and Boyce (Karafillis, A.P., Boyce, M.C. 1993. A general anisotropic yield criterion using bounds and transformation weighting tensor, J. Mech. Phys. Solids, 41, 1859) is used to predict nonlinear FLDs of both Al2008-T4 and Al6111-T4. Excellent agreements were obtained between computed FLDs with the experimental data of Graf and Hosford (Graf, A., Hosford, W.F. 1993a. Calculations of forming limit diagrams for changing strain paths. Metall. Trans. A. 24, 2497; Graf, A., Hosford, W.F. 1993b. Effect of changing strain paths on forming limit diagrams of Al 2008-T4. Metall. Trans. A. 24, 2503; Graf, A., Hosford, W.F. 1994. The influence of strain path changes on forming limit diagrams of Al 6111-T4. Int. J. Mech. Sci. 36, 897). This prediction capability provides a powerful tool in the design and optimization process of 3D sheet metal forming where strain path changes are inevitable.     

Numerical study for influences of material parameters on hydrostatic bulging of metal sheet

In this paper, the influences of various material parameters, the hardening exponent (n), the rate sensitivity (m). the thickness anisotropy parameter (R) and the index M in the Hosford and Hill yield function, on the hydrostatic bulging of a circular clamped sheet of ductile metal materials are analysed by introducting a rigid-viscoplastic finite element method. By numerical studies, an empirical relationship within the average limit thickness strain – ₃ ^* and the material parameters (n andm) is obtained. Besides, it has been found that the influences of surface shapes of the yield function on the average limit thickness strain can be reflected by the Barlat'sP value which represents the effects ofR andM values.This work is supported by the National Natural Science Foundation and Natural Science Foundation of the Youth of China.     

Prediction of localized thinning in sheet metal using a general anisotropic yield criterion

The forming limit diagram (FLD) is a useful concept for characterizing the formability of sheet metal. The ability to accurately predict the FLD for a given material has been shown to depend on the shape of the selected yield function. In addition, both experimental and numerical results have shown that the level of the FLD is strongly strain path dependent. In this work, a combination of Marciniak–Kuczynski (M–K) analysis and a general anisotropic yield criterion developed by Karafillis and Boyce (Karafillis, A.P., Boyce, M.C., 1993. A general anisotropic yield criterion using bounds and transformation weighting tensor. J. Mech. Phys. Solids 41, 1859) is used to predict localized thinning of sheet metal alloys for linear and nonlinear strain paths. A new method for determining the constants in the yield criterion is proposed. The optimal values are obtained by fitting the initial yield stresses and calculated FLD under linear strain paths with the experimental measurement. Using this approach, accurate yield functions can be defined for both Al2008-T4 and Al6111-T4. Comparisons of computed FLDs with the experimental data of Graf and Hosford (Graf, A., Hosford, W.F., 1993b. Effect of changing strain paths on forming limit diagrams of Al 2008-T4. Metall. Trans. A. 24, 2503; Graf, A., Hosford, W.F., 1994. The influence of strain path changes on forming limit diagrams of Al 6111-T4. Int. J. Mech. Sci. 36, 897) show good agreements.     

Anisotropic work hardening of steel sheets under plane stress

This work is a follow-up of the previous report by Kim and Yin [Kim, K.H., Yin, J.J., 1997. Evolution of anisotropy under plane stress. J. Mech. Phys. Solids 45, 841–851] regarding the anisotropic work hardening of cold rolled steel sheets. Tensile prestrain has been applied at angles to the rolling direction and then tensile uniaxial yield stress and R-value distributions are measured. As reported earlier, the orientations of local maxima and minima in the yield stress are altered when the prestrain axis is not in the rolling direction. This led Kim and Yin [Kim and Yin (1997)] to suggest that the orientations of orthotropy axes are altered by the tensile prestrain at angles to the rolling direction. However, R-value distribution is found to be hardly affected by the prestrain. The unchanging R-value distribution shows that the material remembers the rolling direction even after the prestrain. An attempt is made to approximate the observed yield and flow behavior based upon isotropic-kinematic hardening with the quadratic yield function (Hill, 1948). The degree of approximation raises the issues of yield point definition, flexibility of yield function, non-associated flow rules, distortional hardening and others.