A Finite Element Analysis of a Viscoplastic Plate Subjected to Rapid Heating

Abstract

This paper models the response of a thin metallic plate that is subjected to a rapid heat input. In order to accurately model plate response, both the dynamic mechanical and transient heat transfer problems must be solved. The solution is complicated by nonlinearities due to radiation boundary conditions and material inelasticity. Furthermore, the viscoplastic constitutive equations that model the mechanical material behavior are numerically stiff. Nonlinear finite element algorithms are developed for both heat transfer and mechanical analyses. The algorithms are both stable and efficient for solving the problems considered herein. Example problems presented in the paper demonstrate the importance of including material nonlinearity in the model     

An Experimental Rig to Investigate Fatigue Crack Growth Under Dynamic Loading

A novel experimental rig capable of generating a versatile dynamic loading has been designed and tested to overcome the shortcomings of conventional fatigue testing machines such as the difficulty in providing zero crossing aperiodic loading. The main principle of this new design is based on two, single degree of freedom based excited oscillators, where inertial forces act on a specially designed specimen. By changing the natural frequency of the oscillator, the extent of the preloads and pattern of the excitation signal on the shaker, the rig provides a new and robust means of fatigue testing, particularly for aperiodic loading.     

一种裂纹扩展的有限元仿真分析方法及其实现

为分析含多裂纹体在任意载荷下的断裂过程问题,给出了一种基于有限元的仿真方法及程序.基于商业有限元软件的应力分析结果和合适的断裂力学准则,判断裂纹的扩展以及扩展角;通过对每一个裂纹尖端扩展影响区域进行单元重划分,实现了多裂纹任意扩展的几何描述有限元模型更新.由于只对裂纹扩展区局部进行有限单元更新,网格划分和前期网格结果到新网格的映射的工作量相对较小,典型的裂纹扩展分析实例表明本文方法和程序的有效性.     

受弯脱层层板后屈曲有限元分析

脱层是复合材料层板结构中主要的缺陷形式之一。当脱层层板受到压力载荷的作用会造成脱层的局部屈曲和扩展,从而使结构的强度和刚度大为降低。含脱层层板的弯曲问题包含了脱层的压缩问题,却比压缩问题更加复杂。本文对含穿透脱层层板在纯弯载荷作用下的后屈曲问题进行了基于一阶剪切层板理论的几何非线性有限元分析,运用虚裂纹闭合技术求解了纯弯载荷作用下的脱层尖端的能量释放率各型分量,并用脱层扩展判据求解了脱层起始扩展载荷。     

弯曲疲劳短裂纹扩展规律研究

本文对３５ＣｒＭｏ钢和４２ＣｒＭｏ钢带穿透短裂纹（初始裂纹长度ａ＝０．１～０．５ｍｍ）的试件进行了弯曲疲劳试验研究，得到了在弯曲疲劳加载下短裂纹扩展速率的计算表达式以及应力比，试件厚度对短裂纹扩展的影响。     

疲劳裂纹扩展门槛值试验的可靠性分析

本文用30块30CrMnSiA合金铜的CCT试件所测得的ΔK_(th)试验数据检验了随机变量ΔK_(th)的分布特性,确认材料与厚度相同的试件在相同应力比下所测得的ΔK_(th)值基本遵循正态分布。在此基础上对ΔK_(th)试验进行了如下可靠性分析:具有指定可靠度与置信度的ΔK_(th)值,不同材料ΔK_(th)的统计对比,最少试件数。     

循环J积分作为疲劳裂纹扩展驱动力的研究

对循环Ｊ积分ΔＪ可否作为应力强度因子幅ΔＫ不再适用的场合的裂纹扩展驱动力进行了研究。用Ｄ－Ｂ法估计了中心裂纹板（ＣＣＰ）和单边裂纹板（ＳＥＣＰ）试件受单调加载作用的Ｊ积分的塑性部分Ｊｐ，并与有限元结果进行了比较。本文还对Ｖ型和半圆切口根部萌生的短裂纹在循环载荷下进行了弹塑性大应变有限元分析。结果表明ΔＪ有一定的路径相关性，即由较靠近裂尖的积分路径得的ΔＪ值小于较远路径上获得的，两者又都小于Ｄ－Ｂ法估计得ΔＪ值，切口根部短裂纹扩展实验和表面裂纹远场大应变控制下低周疲劳实验表明，由Ｄ－Ｂ法估计的ΔＪ在一定条件下可以作为疲劳裂纹扩展驱动力，深度方向和表面长度方面的裂纹扩展率皆可由线性似合线来表示。考虑闭合效应后，ｄａ／ｄＮ－ΔＪｅｆｆ也是Ｐａｒｉｓ型关系，而且可在切口根部萌生出的裂纹很短的条件下使用     

航空导管弯曲试验的疲劳裂纹萌生寿命

飞行器液压导管受接头和卡箍等约束,在使用的振动环境中,会因弯曲应力而导致破裂,影响到飞行安全.本文对飞行器液压系统通用的不锈钢导管的裂纹萌生寿命进行了试验研究.首先在对8 mm、12 mm无缺陷导管和含U型缺口8 mm导管的疲劳试验和有限元分析的基础上,得到了导管的最大拉应变-裂纹萌生寿命数据.然后采用基于强度极限和弹性模量估算法的Manson-Coffin公式来预测导管裂纹萌生寿命.最后引入加载类型修正系数、表面质量修正系数、试样尺寸修正系数、应力集中敏感系数和有效应力集中系数,使修正后的公式对三种类型的导管均有较好的裂纹萌生寿命预测精度.     

基于精化高阶理论的层合板热-力问题有限元分析

基于精化高阶理论,建立了层合板有限元模型,编制了相应的MATLAB程序。分析了三层四边简支层合板在力荷载作用下的响应,与解析解吻合良好。分析了热-力共同作用下层合板的响应,与基于ABAQUS软件建立的精细有限元模型计算结果相对比,验证了模型的高效性。研究了跨厚比和铺设方式对层合板层间应力的影响,结果表明:跨厚比对层间应力影响显著,两者之间大致呈反比例函数关系;对称铺设方式可以有效降低层合板中的层间应力。     

功能梯度材料纯弯曲梁的弹塑性分析

假设功能梯度材料为一理想弹塑性材料,其弹性模量和屈服强度沿梁高度方向按照幂函数变化,在小变形及平截面假设下研究功能梯度材料纯弯曲梁的弹塑性性能.根据Mises屈服准则导出了纯弯曲梁的弹性极限弯矩的解析表达式,建立了梁在弹塑性状态时截面弯矩与截面弹、塑性区分布之间的关系式,给出了梁进入塑性极限状态时中性轴的位置以及塑性极限弯矩的解析计算公式.数值算例的结果表明,功能梯度材料梁的弹塑性性能与均匀材料梁不同,其屈服不一定首先产生于截面最大应力点,而可能有多种不同的屈服模态及相应的塑性扩展.弹性模量及屈服强度的梯度变化对功能梯度材料纯弯曲梁的中性轴位置、截面弹塑性应力分布以及塑性极限弯矩均有较大影响.研究结果可为功能梯度材料梁的弹塑性分析提供一定的参考.     

Fatigue Growth Analysis of a Surface Crack in a Solid Cylinder under Combined Cyclic Axial-Torsion Loading

Experimental Techniques - In this paper, fatigue growth analyses of a surface crack in a solid cylinder under combined cyclic axial-torsion loadings through experimentation and numerical simulation...     

The General Solution for a Finite Thermopiezoelectric Plate Containing a Hole and a Crack

By application of complex variables and conformal transformation, the general solution to multiply connected domains of two dimensions is constructed in terms of multiple Laurent series for thermopiezoelectric materials. Three typical boundaries, i.e., a rectangular contour, a curvilinear hole, and a line crack are considered in the paper. Though the Green’s function of an arbitrarily shaped hole still remains unknown for anisotropic materials, the approximate solutions both for thermal and electro-mechanical fields are obtained in explicit form by the least square method. The accuracy of the approximation are investigated upon each boundary contours. It is found that the local error on the crack surface diminishes below 10⁻⁷% by adopting only 20 terms of related power series. For a rectangular plate, the precision is enhanced up to the level of 99.99% on its boundary contour by adding the supplementary function, due to the rectangular corners, into the complex solution. Considering that the singular character of a crack is retained in the solution, the stress and electric displacement intensity factors influenced by the hole width and plate size are exhibited herein.     

Finite Element Analysis of Elasto-plastic Plate Bending Problems using Transition Rectangular Plate Elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.The English text was polished by Keren Wang.     

三维有限变形线性光弹性材料研究

制成了１５％应变量的三维有限变形线性光弹性材料，可供对橡胶类零件的应力分析之用；在该材料中，以尼龙６作内含体，可以制作初应力很小的三维有限变形复合光弹性模型。     

求解含钝裂纹体应力场的扩展单元方法

本文基于钝裂纹端部位移场的渐近解和等参元构造方法,开发了一种新的适合钝裂纹端部应力场计算的扩展单元法,为了消除不同单元间的位移不协调又在扩展单元的基础上提出过渡单元.和常规的等参元相比,扩展单元除了以节点位移为待求未知量外,它们额外增加了Ⅰ型和Ⅱ型广义应力强度因子作为未知量.根据这个理论我们编制了有限元的程序并计算了算例,算例表明,在网格较大的情况下,与常规等参元计算方案相比,扩展单元和过渡单元法更好地接近理论值,它具有计算精度高、减少缺陷附近的单元数量和计算时间等优点.     

40Cr钢疲劳裂纹萌生寿命的测量

用系统分析的方法，通过三点弯曲疲劳试验，分别跟踪监测了40Cr钢及它的两种表面处理试样疲劳损伤过程，得出了40Cr钢经过两种表面处理对其疲劳裂纹萌生寿命有显著影响的结果，提出了对疲劳裂纹萌生寿命测量的一种新方法。     

疲劳荷载与氯盐耦合作用下混凝土中氯离子扩散行为的试验研究

混凝土桥梁在服役过程中经常同时承受疲劳荷载和氯离子侵蚀,但现有研究多未考虑疲劳和氯离子侵蚀的耦合作用。本文研究了疲劳荷载与氯盐侵蚀耦合作用下混凝土中氯离子的扩散行为,并运用超声检测表征混凝土的疲劳损伤,以建立疲劳损伤与氯离子扩散性能之间的关系。研究结果表明:随着疲劳压应力水平提高,超声参数表征的混凝土损伤值也逐渐增大;应力水平低于0.4时,不同疲劳应力水平对混凝土中氯离子浓度分布没有明显影响,氯离子扩散系数甚至略有减小,这应是应力水平较低时混凝土中微孔隙和裂缝被压缩而降低了氯离子的扩散能力;应力水平为0.5及0.6时,混凝土中氯离子浓度显著提高,扩散系数明显增大,并且与应力水平呈正相关;超声参数表征的混凝土损伤与氯离子渗透性的发展趋势不一致,表明由于混凝土内部缺陷分布的不均匀性使得超声技术难以定量表征荷载引起的混凝土损伤。     

单元类型和尺寸对裂尖疲劳塑性数值模拟的影响研究

本文采用Jiang-Sehitoglu循环塑性模型和多轴疲劳准则对紧凑拉伸式样裂尖的循环塑性变形、裂纹扩展速率和残余应力进行了有限元数值模拟,着重考察了单元的类型和最小单元尺寸对裂尖循环塑性和裂纹扩展速率的影响.紧凑拉伸试样的材料为1070钢,数值模拟采用了线性单元(四节点)和二次单元(八节点)两种单元,裂尖附近有限元单元的最小尺寸从0.007mm到0.24mm不等.文中将裂纹扩展速率的预测值与实验值进行了比较,通过对裂纹扩展速率的比较,确定在疲劳塑性分析时对单元类型和尺寸进行合理选取.     

扭力轴三维裂纹扩展寿命仿真研究

对疲劳载荷谱作用下三维表面裂纹,采用双重边界元理论求解裂纹前沿的应力应变场,运用Forman理论、最小应变能密度法和Elber模型,计算裂纹前沿各点的扩展长度、扩展方向和应力强度因子等特征量.根据增量步下裂纹几何形状的改变,对裂纹面进行网格重划分和迭代计算,模拟三维裂纹的扩展,预测裂纹扩展寿命.扭力轴表面裂纹扩展的仿真结果表明该方法合理可行.     

Some Remarks on Finite Element Approximations of Crack Problems and an Analysis of Hybrid Methods

Abstract

We discuss here several results on the convergence of finite element methods for problems with corners and cracks. We also derive some a priori estimates for a certain class of hybrid finite elements.