Green’s function for T-stress of semi-infinite plane crack

Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Gre...     

半无限平面裂纹构型横向应力的Green函数

针对各向同性弹性无限大板中半无限裂纹,用解析函数方法求解了裂尖处横向应力的Green函数.加载情况为一任意集中力作用于任意一内点处.用叠加法求解了复势,它给出该平面问题的弹性解.通过渐近分析抽取复势的非奇异部分.基于该非奇异部分,用一种直接方法求解了横向应力的Green函数.进一步,用叠加法得到了一对对称和反对称集中力加载时的Green函数.然后,用得到的Green函数来预测铁电材料双悬臂梁试验中畴变引起的横向应力.用力电联合加载引起的横向应力来判断试验中所观察到的稳定和不稳定裂纹扩展行为.预测结果和试验数据基本吻合.     

干涉问题中T应力与各向异性的作用

采用离散模型（包括半无限主裂纹和近尖微裂纹）研究了各向异性材料主微裂纹干涉问题中T应力对主裂尖参数的影响,并且与相同情况下各向同性材料的结果进行了比较,比较结果列于文中各图。研究结果表明,在各向异性材料和各向同性材料中T应力对主裂尖应力强度因子的影响趋势是相似的,但是由于T应力与材料各向异性性质的共同作用,使两种情况下T应力对主裂尖参数的影响结果存在着明显的偏差。     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

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.     

Effect of T-Stress on Crack Growth Along an Interface Between Ductile and Elastic Solids

For crack growth along an interface joining an elastic-plastic solid to an elastic substrate the effect of a non-singular stress component in the crack growth direction in the elastic-plastic solid is investigated. Conditions of small scale yielding are assumed, and due to the mismatch of elastic properties across the interface the corresponding oscillating stress singularity fields are applied as boundary conditions on the outer edge of the region analysed. The fracture process is represented in terms of a cohesive zone model. It is shown that the interface fracture toughness is significantly increased by a negative T-stress in the elastic-plastic solid, while a positive T-stress in the elastic-plastic solid leads to a reduced fracture toughness.     

周期裂纹削弱的无限长板条的应力分析

作出了周期裂纹削弱的无限长板条的应力分析．假设这些裂纹均在水平位置,又板条承受 y方向的拉伸力p．此时边值问题归结为一个复杂混合边值问题．发现,对此问题言,特征展开变分原理方法 ( eigenfunction expansion variational method,简称为EEVM)是非常有效的．研究了裂纹端的应力强度因子和T-应力．从拉伸力作用下的弹性变形考虑,开裂板条可等价于一不开裂的正交异性板条．还分析了等价正交异性板条的弹性性质．最后给出了算例和数值结果．     

The solution of deflection of elastic thin plate by the joint action of dynamical lateral pressure,force in central surface and external field on the elastic base

In this paper the Euler equation of the deflection of clastic thin plate is reduced to the equation with schrödinger form by the principle of quantum electro-dynamics. Then we can obtain the general solution of deflection of eleastic thin bending plate by the joint action of dynamical lateral pressure, force in central surface and external field on the elastic base.     

T应力对光弹性条纹影响的理论分析

以裂尖弹性应力场的多参数模型为基础,研究I型、II型以及I/II混合型裂纹参数对光弹性条纹的影响. T应力的存在和符号影响着等色线条纹环的半径大小和旋转方向,对于纯I型或II型裂纹而言,条纹环的旋转角度只与T应力有关;而对于I/II混合型裂纹,条纹环旋转角度与K_{\rm I}, K_{\rm II}和T应力有关. T应力的存在使得I型裂纹在裂尖±π/3方向上出现2个各向同性点(T应力为正时),使得II型裂纹在裂尖后的裂纹面上出现1个各向同性点. 对于I/II混合型裂纹而言,当T应力为正时等倾线出现距裂尖半径不等的3个各向同性点;反之, T应力为负时在裂尖后只存在1个各向同性点,这些各向同性点分别与I型和II型裂纹情况具有相同的规律.      

基于数值流形方法和交互积分法的平面裂纹T应力求解

发展了用于计算含裂纹平面各向同性线弹性材料T应力的数值流形方法(NMM)。利用修正变分原理导出了分析二维裂纹问题的NMM离散方程,给出了围域型交互积分法提取T应力的主要公式;对单边裂纹问题、倾斜裂纹问题、孔边多裂纹问题三个算例进行了模拟,证实了本文方法的收敛性和精度,并进一步探讨了裂纹构型(如裂纹的长度和倾角)对T应力的影响规律。     

广义平均形状改变能密度断裂准则及应用

基于形状改变能为材料起裂扩展控制参量的物理事实及裂纹尖端断裂控制区能量平均概念,提出了计及裂纹尖端应力场特征级数展开奇异项和常数项的广义平均形状改变能密度(GADSED)准则,建立了I-II-III 混合型裂纹断裂判据计算式,为工程结构疲劳断裂评估提供了新选择．基于提出的GADSED 准则,系统分析了T应力对裂纹断裂判据的影响,结果表明：当参数|Ba|数值相同时：负值T应力的I-II 混合型裂纹更易起裂扩展,正值T应力的KΙf值高于负值T应力的KΙf值,正负T应力的KIIf值相同;T应力在区间0 < Bα < 0.45 时增大了KΙf值（3 %以内）,T应力降低了KIIf值．根据GADSED 准则完成了双轴疲劳载荷平板表面I 型裂纹扩展寿命预报,结果表明：基于GADSED 准则的裂纹扩展寿命预报值约为传统方法预报值的40.7 %,可为工程实际评估提供借鉴．