轻型板材的塑性行为及离散插值型各向异性塑性本构模型的研究

Multi step tests along uniaxial and varying loading paths, at different temperature, with or without applying electric current, are to be carried out, in which sheet metals of advanced high strength steel, aluminum alloy and magnesium alloy are to be adopted. The dislocation density crystal models of these materials, imbedding polar dislocation density and its evolution rule as well as twining mechanism, are to be established, and applied in the numerical simulation of their deformation under complicated loading condition. By these methods, the microscopic mechanism governing the anisotropic yielding and hardening behaviors of the sheet metals, and the influence of temperature and electric current on the mechanism and behaviors, are to be investigated. Based on the results of tests and numerical simulations using crystal model, the discretized interpolation type anisotropic constitutive model is to be built. The model consists of the anisotropic yield function keeping convexity, the hardening model in which the isotropic, kinematic and distortional hardening are described by evolving the stress vector, as well as the associated flow rule. The computation and visualization software of the discretized interpolation type constitutive model is to be developed. The influences of the physical fields, such as temperature and electric current on yield surface and its evolution are to be investigated. The proposed model is to be verified by sheet metal forming processes, such as deep drawing. The aim of the project is to propose the discretized interpolation type anisotropic constitutive model with more flexibility, clear physical meaning, computational accuracy, and capable of describing complicated anisotropic plastic behaviors of the materials. The model can be used to improve the accuracy and efficiency of numerical simulation of metal forming processes, and provide a useful tool for the development of advanced forming processes for light weight sheet metals.

选取高强钢板、铝合金板和镁合金板，在不同温度下进行通电和不通电的多步加载实验，将极性位错及演化以及孪晶机制引入位错密度晶体塑性模型，模拟材料在复杂加载条件下的响应，采用实验与晶体塑性模型模拟相结合的方法研究轻型板材的屈服和硬化行为的微观机理以及温度和电流的影响。根据实验和晶体塑性模拟结果，采用离散插值方法构造材料的各向异性本构模型，其中包括保持外凸性的离散插值型各向异性屈服函数，通过应力矢量演化描述各向同性硬化、随动硬化和畸变硬化的硬化法则，以及关联流动法则；研发离散插值型各向异性本构模型的计算和显示软件；研究温度和电流等外场作用对屈服面及其演化的影响；通过板材拉深等实验验证所提模型的有效性。本项目的研究目标是提出一种处理简便、物理意义清晰、计算准确、能描述材料复杂塑性行为的离散插值型各向异性本构模型，提高塑性加工过程数值模拟的精度和效率，为轻型板材冲压新技术的研发提供支撑。

高强钢、铝合金、镁合金等轻型板材的塑性屈服和硬化行为在加载条件和微观组织演化的共同作用下呈现出十分复杂的现象。准确地描述轻型板材复杂的塑性行为，是提高冲压成形过程模拟精度的关键。传统的连续函数型各向异性本构模型拟合参数多，应用复杂；现有的插值型屈服准则在插值点能精确满足实验数据，但存在函数分段多、需较多特定插值点数据等问题，它们都不便于准确地描述屈服轨迹的畸变硬化行为。本项目研究中通过DP590高强钢板多步加载实验研究了其各向异性屈服和硬化行为。基于贝塞尔曲线插值方法，建立了平面应变条件下各向异性板材屈服轨迹及其演化模型，通过引入形状参数，改进了贝塞尔插值屈服模型对BCC、FCC和HCP等不同材料的适用性和预测精度；通过引入屈服函数中傅里叶级数的奇函数项，描述了板材的非正交各向异性屈服行为；采用直角梯形控制的三阶贝塞尔曲线或引入贝塞尔屈服轨迹几何特征参数，改进了控制屈服轨迹形状的灵活性；通过追踪标定屈服函数所需实验点或贝塞尔屈服轨迹几何特征参数的演化规律，提出了适用于曲线插值模型的各向异性硬化模型。为了在一般平面应力状态的三个应力分量（σ_xx，σ_yy，σ_xy）构成的坐标系中描述屈服面的形状，直接反映剪应力分量的作用，采用贝塞尔曲面插值方法，通过构造“经纬线”的方法建立了三维应力空间的屈服面模型，并考虑屈服轨迹畸变规律建立了近似的屈服面模型；提出了采用傅里叶级数对直角梯形控制的“经线”进行插值构造屈服应力曲面模型的方法，提出了一种13参数应力主值型各向异性塑性势函数，二者结合可建立描述板材各向异性屈服行为的精度高、参数少的非关联流动法则。将所建立插值型弹塑性本构模型通过用户材料子程序引入ABAQUS有限元软件平台，采用准隐式的应力更新回映算法解决了插值型本构模型的隐式变量推导、等效应力求解和分段函数实时选取等问题；通过实例验证了所提出的插值型本构理论的正确性和适用性。