固体材料不稳定性的特征

基于分析势函数的二次变分,从理论上证明了固体材料不稳定性主要取决于材质不断退化的重要特征。另一特征是：材料往往会由基本变形路径漂移为一个轴向应变被限定的模态以至的失稳。文中以有限元方法计算模拟受周期性分布孔洞损伤的平面板材模型,结果显示,孔周边的应变局部化使变形路径转移到一个轴向应变被限定的失效模态。此类现象与金属板材拉胀实验中所观测到的结果相符合。     

高分子材料平面应变拉伸变形局部化

将基于应变软化玻璃状高分子材料微观特征建立的ＢＰＡ８－链分子网络模型引入ＵｐｄａｔｉｎｇＬａｇｒａｎｇｅ有限元方法，建立了适于变形局部化分析的大变形弹塑性有限元驱动应力法．在此基础上，数值模拟了初始各向同性高分子材料平面应变拉伸变形局部化的传播过程．探讨了ＢＰＡ模型对具有加工硬化特性的结晶性高分子材料变形分析的适应性；分析了局部化传播过程中颈缩截面的非均匀应力三轴效应；最后，讨论了网格尺寸以及初始几何不均匀性对颈缩扩散以及应力三轴效应的影响     

光滑拉伸试件中不同初始形状孔洞长大的有限元模拟

本文对具有不同硬化指数（ｎ＝０．０５，ｎ＝０．１，ｎ＝０．２）的幂硬化材料的光滑拉伸试样的拉伸变形过程进行了有限元模拟，通过有限元计算和经Ｂｒｉｄｇｍａｎ修正分别得到了试样变形过程中心部应力三维度随应变的变化情况；在此基础上运用控制体胞宏观应力三维度的方法，对含不同初始形状孔洞的体胞模型进行了有限元分析，计算结果表明：（１）孔洞初始形状和材料硬化特性对试样的拉伸破坏过程有重要影响；（２）Ｂｒｉｄｇ     

冲压板材拉伸筋阻力的一种有效数值计算方法

将弹塑性有限变形的拟流动角点本构理论和厚向各向异性屈服函数引入弹塑性动力显式有限元列式,对板材通过拉伸筋的变形过程及拉伸筋阻力进行了数值模拟,并与有关实验结果进行了比较很好的一致性,表明了该计算方法的有效性。进而,数值研究了拉伸筋形状、界面摩擦状况以及材料的厚向各向异性对拉伸筋阻力的影响,为实际覆盖件冲压成形中拉伸筋的设置提供了重要的定量依据。     

应用数字图像相关方法测量含缺陷试样的全场变形

利用数字图像相关方法测量表面带孔洞、裂纹、缺口等缺陷试样的全场变形是许多实际测量任务中经常遇到的问题。就此问题，本文阐述了一种先对要避免计算的缺陷区域进行标记，在随后进行的相关计算中直接避免这些标记区域的方法。在已计算得到全场位移的情况下，文中提出了基于局部位移场最小二乘拟合的方法来计算区域边界、孔洞、裂纹或缺口附近等区域应变。最后对单侧边带半圆缺口试样的单向疲劳拉伸实验的计算结果充分显示本文方法的有效性和可靠性。     

粗晶超塑性单轴拉伸颈缩模拟

利用粘塑性本构模型模拟粗晶超塑性单轴拉伸。数值结果表明，颈缩的位置及发展过程受拉伸应变速率的影响。不只一处分散不均匀变形相互牵制与协调，使材料得以在接近均匀的状态下经受大的变形，模拟得到的局部应变速率演化曲线，可以预测变形局部化发展的情况。     

方板对角拉伸分叉、鼓动与起皱

以Ｈｉｌ关于弹塑性材料唯一性的充分性条件为理论基础，采用虚功率增率型原理和Ｍｉｎｄｌｉｎ曲壳单元的弹塑性大变形有限元模型成功地模拟了方板对角拉伸（ＹＢＴ）分叉后继变形的鼓动与起皱过程，并与同类实验结果进行了比较最后还讨论了板厚ｔ和端面拉伸宽度Ｂ对分叉模式和起皱模式的影响为板材成形过程中发生的分叉、鼓动与起皱现象提供一种有效的有限元数学模型     

海洋结构薄板弹性屈曲的群孔效应

针对含孔洞板结构,重点考虑非均匀孔洞分布,采用有限元方法对小变形结构的极限承载能力进行计算,得到孔洞数量、面积、位置、分布等因素对屈曲临界应力的影响规律。结果表明:孔洞分布不仅会改变有效承载面积并使承载能力变化,局部结构还会进入不同承载状态,使板结构承载性能产生非单调变化,即孔洞对板结构屈曲应力的影响具有一定的"群孔"效应。     

预延伸非晶聚合物材料各向异性变形局部化

给出一种可描述预延伸各向异性特性的背应力张量三维表达式，引入大变形弹塑性有限元驱动应力法，结合ＢＰＡ８ 链细观分子网络模型，模拟了预延伸各向异性非晶聚合物材料平面应变拉伸变形局部化力学行为．详细讨论了预延伸比（ＩｎｉｔｉａｌＤｒａｗｉｎｇＲａｔｉｏ；ＩＤＲ）和预延伸方向（ＩｎｉｔｉａｌＤｒａｗｉｎｇＤｉｒｅｃｔｉｏｎ；ＩＤＤ）对变形抗力、颈缩规律、剪切带方向以及试件中心部位链延伸比的影响．     

冲击载荷下炸药装药动态响应的有限元分析及热点形成机理的数值模拟

对稳态温度场中受冲击载荷作用的炸药药柱进行了弹粘塑性分析。在Ｐｅｒｚｙｎａ本 构模型的基础上，作了适当的补充和修正，将流动参数γ、弹性模量Ｅ均视为温度的函数，动态 有限元计算结果表明，计算曲线和实验曲线有很好的近似。为模拟材料中不均匀性的影响，在 药柱中心引入一孔洞，有限元计算结果给出含孔洞药柱的粘塑性动态响应、药柱网格变形图以 及药柱等温线，可以清楚看出在孔洞附近区域有局部高温产生。本文的本构模型和计算方法对 于研究冲击载荷下炸药装药的力学响应以及炸药装药中热点形成机理的数值模拟提供了良好 的基础。     

Effects of void band orientation and crystallographic anisotropy on void growth and coalescence

The effects of void band orientation and crystallographic anisotropy on void growth and linkage have been investigated. 2D model materials were fabricated by laser drilling a band of holes into the gage section of sheet tensile samples using various orientation angles with respect to the tensile axis normal. Both copper and magnesium sheets have been studied in order to examine the role of crystallographic anisotropy on the void growth and linkage processes. The samples were pulled in uniaxial tension inside the chamber of an SEM, enabling a quantitative assessment of the growth and linkage processes. The void band orientation angle has a significant impact on the growth and linkage of the holes in copper. As the void band orientation angle is increased from 0° to 45°, the processes of coalescence and linkage are delayed to higher strain values. Furthermore, the mechanism of linkage changes from internal necking to one dominated by shear localization. In contrast, the void band orientation does not have a significant impact on the void growth and linkage processes in magnesium. Void growth in these materials occurs non-uniformly due to interactions between the holes and the microstructure. The heterogeneous nature of deformation in magnesium makes it difficult to apply a coalescence criterion based on the void dimensions. Furthermore, the strain at failure does not show a relationship with the void band orientation angle. Failure associated with twin and grain boundaries interrupts the plastic growth of the holes and causes rapid fracture. Therefore, the impact of the local microstructure outweighs the effects of the void band orientation angle in this material.     

Applications of planar anisotropic yield criteria to porous sheet metal forming simulations

Planar anisotropic yield functions, with rounded vertexes especially near the equal-biaxial direction of the corresponding yield loci, appropriate for some structure metals are employed for the matrix surrounding voids in the present study. The widely adopted Hill anisotropic yield functions are also implemented into the matrix for comparisons. Mechanisms of the void growth, void nucleation, and void coalescence are simultaneously considered here. Effects of the yield function of the corresponding matrix on the sheet metal under two typical sheet forming operations, a hemispherical punch stretching operation and a cup drawing operation, are investigated via a finite element analysis. Thickness strains in various orientations of the sheet are then evaluated. Simulation results show that the yield function of the corresponding matrix plays important roles on the strain distribution and the strain localization as well. Early localization would be found for the sheet with relatively small initial void volume fraction in two operations. Yield functions of the matrix rather influence the earing phenomenon under the cup drawing procedure even similar displacement profiles of the outer boundary could be observed.     

Experimental investigation into plastic damage of microvoids with interaction

A mechanism of plastic flow localization in ductile matter near microvoids is studied. The voids with the size-scale of micromillimeter exist in sheet specimens under tensile loading, and the plastic strain field around voids is obtained by digital image processing of deformed grids. The size growth of the microvoids, the spacing change of the neighboring voids, and the development of shear bands in the ligament between the voids, are presented by experimental results accompanied with the plastic strain distribution, that gives good interpretation to the process of void growth and coalescence with the flow localization in the ligaments. The project supported by the National Natural Science Foundation of China     

A perturbation analysis of the unstable plastic flow pattern evolution in an aluminum alloy

In the tensile loading of sheet metals made from some polycrystalline aluminum alloys, a single deformation band appears inclined to the elongation axis in the early stage of deformation, and symmetric double bands are observed in the later stage. This evolution of spatial characteristics of such an unstable plastic flow pattern in a polycrystalline aluminum alloy has been analyzed by a perturbation method. A small number of slip modes are taken to describe the tensile strain. A rate-dependent constitutive equation is used for each slip mode to account for the interaction between dislocations and solute atoms in dynamic strain aging. Unconstrained and constrained models are used to impose appropriate loading conditions at the early and later deformation stages, respectively. Both plane-strain and plane-stress cases are considered. It is found out that the change of boundary conditions and material inhomogeneity during the course of plastic deformation are closely related to the evolution of spatial characteristics of shear band (the Portevin–Le Chatelier band) patterns observed in experiments.     

Failure prediction in anisotropic sheet metals under forming operations with consideration of rotating principal stretch directions

An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted to develop a failure prediction methodology that can be used to investigate the failure of sheet metals under forming operations. Hill's quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The approximate macroscopic anisotropic yield criterion is a function of the anisotropy parameter R, defined as the ratio of the transverse plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial loading conditions. The Marciniak–Kuczynski approach is employed here to predict failure/plastic localization by assuming a slightly higher void volume fraction inside randomly oriented imperfection bands in a material element of interest. The effects of the anisotropy parameter R, the material/geometric inhomogeneities, and the potential surface curvature on failure/plastic localization are first investigated. Then, a non-proportional deformation history including relative rotation of principal stretch directions is identified in a critical element of a mild steel sheet under a fender forming operation given as a benchmark problem in the 1993 NUMISHEET conference. Based on the failure prediction methodology, the failure of the critical sheet element is investigated under the non-proportional deformation history. The results show that the gradual rotation of principal stretch directions lowers the failure strains of the critical element under the given non-proportional deformation history.     

Influence of void nucleation on ductile shear fracture at a free surface

An approximate continuum model of a ductile, porous material is used to study the influence of the nucleation and growth of micro-voids on the formation of shear bands and the occurrence of surface shear fracture in a solid subject to plane strain tension. Bifurcation into diffuse modes is analysed for a plane strain tensile specimen described by these constitutive relations, which account for a considerable plastic dilatancy due to void growth and for the possibility of non-normality of the plastic flow law. In particular, bifurcation into surface wave modes and the possible influence of such modes triggering shear bands is investigated. For solids with initial imperfactions such as a surface undulation, a local material inhomogeneity on an inclusion colony, the inception and growth of plastic flow localization is analysed numerically. Both the formation of void-sheets and the final growth of cracks in the shear bands is described numerically. Some special features of shear band development in the solid obeying non-normality are studied by a simple model problem.     

On the propagation and pulsation of Portevin-Le Chatelier deformation bands: An experimental study with digital speckle pattern metrology

The Portevin-Le Chatelier (PLC) effect is closely associated with inhomogeneous deformation, which is characterized by the band of strain localization. In this work, the spatio-temporal dynamics of the Portevin-Le Chatelier deformation bands are investigated by a novel digital speckle pattern metrology technique consisting of digital speckle pattern interferometry (DSPI) and digital speckle correlation (DSC). A series of tension process of a commercial aluminum alloy (A2017) under different imposed strain rates in a range from 10⁻⁶ to 10⁻³ s⁻¹ are monitored in real time with this technique. The formation of the PLC band, the evolution of the band structure and the propagation of the band are visualized and followed by fringe patterns. The distribution of the deformation in the specimen containing the band is measured precisely. It is shown that even for a tensile test, an elastic shrinkage deformation, which is caused by the avalanche-like shearing deformation within the band, occurs outside the band.     

Evolving internal length scales in plastic strain localization for granular materials

A numerical model in the Cosserat continuum for strain localization phenomena in granular materials is developed and proposed in this paper. The model assumes a constant internal length scale that is used to describe the shear band thickness. However, it is observed that the internal length scales need to change to accommodate the possible change in the contact surface between the particles, damage of the particles or/and any change in the local void ratio within the domain, which will change the shear band thickness. The mathematical formulations used in the present numerical model were equipped with evolution equations for the length scales through the Micropolar theory, those formulations are proposed and discussed in this paper. The evolution equations of the internal length scales describe any possible change in the contact surface between the particles, damage of the particles if exists and/or any change in the local void ratio within the domain. Hence, the strain localization described by the enhanced model with evolving internal length scales is more accurate and closer to the real solution. The solution for the shear bands thickness shows more accurate correlation with the experimental results and less dependency on the mesh size when such evolution equations are used. Moreover, the shear band thickness and inclination evolve during the deformation process.     

Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification

The elastic/crystalline viscoplastic constitutive equation, based on a newly proposed hardening-softening evolution equation, is introduced into the dynamic-explicit finite element code “Itas-Dynamic.” In the softening evolution equation, the effective distance and the angle between each slip system of a crystal are introduced to elucidate the interaction between the slip systems, which causes a decrease of dislocation density. The polycrystal sheet is modeled by Voronoi polygons, which correspond to the crystal grains; and by the selected orientations, which can relate to the texture, they are assigned to the integration points of the finite elements. We propose a direct crystal orientation assignment method, which means that each integration point of finite element has an assigned orientation, and its orientation can be rotated independently. Therefore, this inhomogeneous polycrystal model can consider the plastic induced texture development and subsequent anisotropy evolution. The parameters of the constitutive equation are identified by uni-axial tension tests carried out on single crystal sheets. Numerical results obtained for sheet tensions are compared with experimental ones to confirm the validity of our finite element code. Further, we investigate the following subjects: (1) how the initial orientation of single crystal affects slip band formation and strain localization; (2) how the grain size and particular orientations of the grain affect the strain localization in case of a polycrystal sheet. It is confirmed that the orientation of a single crystal can be related to the primary slip system and the deformation induced activation of that system, which in turn can be related to the slip band formation of the single crystal sheet. Further, in case of a polycrystal sheet, the larger the grain size, the more the strain localizes at a specific crystal, which has the particular orientation. It is confirmed through comparisons with experiments that our finite element code can predict the localization of strain in sheets and consequently can estimate the formability of sheet metals.