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裂尖前方塑性区内的局部弹性场 总被引:2,自引:0,他引:2
该文给出了平面应变下,不同材料HRR场对应的能量分布图,在裂尖前方扇形域内,静水拉应力很高,约为3σ0-7σ0,而等效效应力却很小,接近屈服应力σ0,使此区内仅能产生弹性体变能。 相似文献
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幂硬化材料中准静态定常扩展裂纹的研究 总被引:2,自引:0,他引:2
本研究根据问题的支配方程组以及高-黄假设对幂硬化材料中裂纹的准静态定常扩展作了渐近分析,文中从扩展裂纹尖端附近的弹性变形与塑性变形必须保持平衡的观点对反平面应变、平面应变和平面应力三类裂纹作了统一的考察与分析,裂尖附近应力场确定为(1n r)~(2/(n-1))阶奇性,并对前两类裂纹问题作了渐近分析,指出:根据本文分析结果及文献中习用的组装渐近场的方法,可以获得无强间断的,Ⅲ型裂纹和平面应变I型裂纹的最低阶渐近解。按本文所用本构关系,硬化指数n及无因次材料常数(σ_y/E)/ασ_y~n或(σ_y/G)/ασ_y~n对渐近场的角分布都有影响。 相似文献
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考虑了I型裂纹尖端损伤区域内三种不同的约束应力分布形式,即右三角分布形式(情况A)、均匀分布形式(情况B)、左三角分布形式(情况C),并采用复变函数方法求得了应力强度因子与裂纹张开位移的解析解;在此基础上,通过数值计算得到了应力强度因子和裂纹张开位移随约束应力区长度、约束应力大小以及分布形式的变化规律。研究结果表明:随裂尖材料损伤程度的增加,裂尖损伤区内约束应力减小,应力强度因子和裂纹张开位移增大;约束应力的分布形式对应力强度因子和裂纹张开位移有显著影响;相对于其他区域,约束应力对裂纹尖端区域裂纹张开位移的影响较大。然而,对于裂尖损伤区域的形成与作用荷载、材料性质、构件几何尺寸之间的关系,还需要进行更为深入的研究。 相似文献
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采用复变函数法研究了在远场承受均布声子场机械载荷作用下十次对称二维准晶中穿透周期轴的一个圆弧形裂纹;报导了表征声子场和相位子场的4个复应力函数的解析表达式,并由复应力函数获得了两个裂尖处声子场和相位子场应力强度因子、裂面张开位移以及能量释放率的表达式. 相似文献
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基于新型裂尖杂交元的压电材料断裂力学研究 总被引:2,自引:1,他引:2
提出了一种裂尖邻域杂交元模型,将其与标准杂交应力元结合来求解压电材料裂纹尖
端的奇性电弹场和断裂参数的数值解.裂纹尖端杂交元的建立步骤为:1)
利用高次内插有限元特征法求解特征问题,得到反映裂尖奇异性电弹场状况的特
征值和特征角分布函数;2)
利用广义Hellinger-Reissner变分泛函以及特征问题的解来建立裂尖邻域杂交元模型.该
方法求解电弹场时,摒弃了传统有限元方法中裂尖奇异性场需要借助解析解的做法,也避免
了单纯有限元方法中需要在裂尖端部进行高密度单元划分.采用PZT5板中心裂纹问题
作为考核例,数值结果显示了良好的精确性.作为进一步应用,求解了含中心界面裂纹
的PZT4-PZT5两相压电材料的应力强度因子和电位移强度因子.所有的算例都考虑
了3种裂纹面电边界条件. 相似文献
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压剪载荷作用下界面裂纹尖端场的研究 总被引:2,自引:2,他引:2
建立了弹性-幂律蠕变双材料界面裂纹准静态扩展的力学模型,求得了裂纹尖端应力、应变和位移场分离变量形式的解及其数值结果;讨论了材料性能参数对裂纹尖端场的影响;计算和分析了界面裂纹的摩擦效应,并且得出了给定条件下裂尖场的轮廓图形. 相似文献
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进行了Ⅰ/Ⅱ复合型载荷作用下航空结构铝合金CTS试样线弹性的全场三维有限元计算,分析了复合型离面应力约束因子Tz和面内约束T应力的分布特性,研究了厚度和载荷条件对应力各分量及应力三轴性水平Rσ、应变能密度U0的影响以及这些量在实验中观察到的裂纹起裂方向上的特点。结果表明:(1)平面内约束T应力在此种试样形式下为零;(2... 相似文献
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双压电体界面上的电偶极子和裂纹5 总被引:1,自引:0,他引:1
求得了压电体双材料界面上的孤立二维电偶极子的解析解,结果表明某点电偶极子激发的应力-电位移场与该点到电偶极子的距离的平方成反比。研究了压电体双材料界面上的电偶极子对裂纹的作用,得到了问题的闭合解。在电偶极子的作用下,界面裂纹裂尖近区应力-电位移仍具有r^-1/2 iεα的振荡奇异性,文中求得裂尖应力强度因子,当电偶极子距裂尖距离ρ很近时,裂尖应力强度因子与ρ^-3/2-iεα成比例。 相似文献
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大多数已有的拓扑优化研究为系统刚度最大化设计,尤其以体积比约束下的静态柔顺度最小化问题为典型.从工程角度出发,结构强度设计至关重要.以往的应力研究表明,应力约束拓扑优化存在着奇异性、约束数目庞大、高度非线性特性等诸多数值困难.为了实现应力约束下的拓扑优化设计,采用归一化p范数应力指标以减少单元应力约束数目.遵循独立连续映射建模方式,引入密度变量的倒变量函数作为设计变量.推导了应力约束函数和体积目标函数对设计变量的敏度,并基于一阶和二阶泰勒近似得到各自的显式表达式.通过构造的系列二次规划子问题,原拓扑优化问题采用序列二次规划算法高效求解.二维数值算例考察了结构刚度和强度设计结果的异同,以及不同应力约束上限值对应力约束拓扑优化结果的影响.通过提出方法与传统变密度法结果的比较,说明提出的独立连续映射方法在应力约束下具有可行性和有效性.优化结果也表明了考虑应力约束的连续体拓扑优化具有必要性. 相似文献
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《International Journal of Plasticity》2004,20(1):1-18
The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed. 相似文献
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Peishi Yu Chongmin She Wanlin Guo 《International Journal of Solids and Structures》2010,47(16):2123-2130
Thickness dependence of the one-parameter-based fracture toughness has been well recognized and widely studied. However, it is still a challenge to predict the fracture of structures with curved cracks from the fracture toughness data obtained from the standard through-the-thickness cracked specimens. The complicated three-dimensional (3D) stress fields near the crack front play a vital role in the fracture strength of materials. Based on a systematical numerical study of the 3D stress fields near the crack tip of quarter elliptic corner cracks and comparison with that of ideal through-the-thickness cracks, an equivalent thickness conception for curved cracks is proposed from the viewpoint of out-of-plane constraint, and a semi-analytical solution for the equivalent thickness of corner cracks is obtained. With the evaluated equivalent thickness, the fracture toughness of corner cracked specimens is predicted efficiently by the plane-strain toughness value of the material obtained from the standard through-the-thickness specimen. 相似文献
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动力应变局部化传播及尺寸效应数值模拟 总被引:11,自引:0,他引:11
采用 FLAC-3 D模拟了应变软化岩土材料局部化剪切带的发展、扩容对剪切带倾角的影响及试件的宽度效应。随着加载时步的增加 ,彼此孤立的两个应变场逐渐靠近、叠加 ,最终形成了剪切带网络。无论端面约束强或弱 ,剪切带的倾角的数值模拟结果都与罗斯科倾角比较接近。增加试样宽度 ,剪切带的宽度增加 ,剪切带变得不平直 ;宽度越大 ,岩样上端面中点的压应力 -加载时步曲线的峰值强度越大 ,宽度对弹性阶段没有大的影响 相似文献
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G.Z. Wang X.L. Liu F.Z. Xuan S.T. Tu 《International Journal of Solids and Structures》2010,47(1):51-57
In this paper, the effect of constraint induced by the crack depth on creep crack-tip stress field in compact tension (CT) specimens is examined by finite element analysis, and the effect of creep deformation and damage on the Hutchinson–Rice–Rosengren (HRR) singularity stress field are discussed. The results show the constraint induced by crack depth causes the difference in crack-tip opening stress distributions between the specimens with different crack depth at the same C*. The maximum opening stress appears at a distance from crack tips, and the stress singularity near the crack tips does not exist due to the crack-tip blunting caused by the large creep deformation in the vicinity of the crack tips. The actual stress calculated by the finite element method (FEM) in front of crack tip is significantly lower than that predicted by the HRR field. Based on the reference stress field in the deep crack CT specimen with high constraint, a new constraint parameter R is defined and the constraint effect in the shallow crack specimen is examined at different distances ahead of the crack tip from transient to steady-state creep conditions. During the early stages of creep constraint increases with time, and then approaches a steady state value as time increases. With increasing the distance from crack tips and applied load, the negative R increases and the constraint decreases. 相似文献
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Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions 总被引:1,自引:0,他引:1
The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions
is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests
of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to
cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with
the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion
to show that this variation can be interpreted using the critical stress intensity factorK
Cand a second parameterT orA
3,whereT andA
3are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this
constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release
rateG
Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving
or instability under mode I loading conditions. Experimental data are presented and compared with the theory. 相似文献
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《International Journal of Solids and Structures》2003,40(23):6267-6284
Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A2 three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A2 approach. 相似文献