【作者】 蔡艳红；

【导师】 唐立强；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2002， 硕士

【摘要】 材料损伤是工程设计中需要考虑的重要因素之一，而裂纹尖端场的研究为断裂破坏准则提供理论依据。本文研究的是无限大板中的半无限长的Ⅲ型裂纹问题。在Kachanov描述的一维应力状态下的脆性材料的损伤演化模型的基础上，文中给出非线性损伤材料的本构方程，唯象地假设损伤变量与应变成幂次关系，D~*=(Gγ/K)~n，其中G为剪切模量，K为损伤模量，γ为有效应变因子，D为损伤变量，n为硬化指数。当n=1时，材料的损伤形式为线性应变损伤模型。当应力达到临界值时，材料迅速软化而失稳破坏。文中给出了损伤变量临界值D_c的表达式，随着n的增加，D_c增加，即对于韧性材料，它的临界损伤值要大于脆性材料的临界损伤。 通过坐标变换，将物理平面中Ⅲ型裂纹问题变换到应变(应力)平面中加以研究，推导出用(γ_x，，γ_y)为未知变量表示(x，y)的平衡方程和协调方程。引入应变函数Ψ，应用几何方程、协调方程和本构方程推导出Ⅲ型裂纹问题中Ψ满足的基本方程，对不同的n值，通过计算可以得出Ψ的小范围屈服解。 利用相应的公式推导出损伤区形状的表达式，得出损伤区是一族圆，它们的圆心和半径随D和n值而变化。由物理平面与应变平面坐标间的关系，得出了极坐标中损伤区应力、应变场的分布。当n=1时，所得结论与C．H．Popelar给出的相同。当n≥2时，n影响着裂纹尖端场的性质。如果取损伤刚度和屈服强度相同，当n→∞时，材料为弹性材料，那么损伤区的半径与理想弹塑性材料的塑性区的半径相同。以上工作为材料建立破坏准则提供理论依据。更多还原

【Abstract】 Material failure is an important consideration in the design of engineering structure. The near tip field solution provides insight into the selection of the failure criterion. This paper is concerned with an infinite slab containing a semi-infinite crack, which is subjected to the anti-plane shear loading condition. Based on the damage evolution formation depicted by Kachanov of brittle materials in unitary stress state, In this dissertation, the constitutive equation of nonlinear damage material is given, macroscopically, on the assumption thatdamage variable is exponential relation to strain, D = (Gy I K)" , where G is theshear module, K is the damage module and the y is the effective strain, D is damage variable and n is hardening exponent. When n=l, damage form of materials is linear strain damage model. When stress approach to critical, materials soften rapidly, unstable and destroyed. Formation of damage variable critical Dc is given by. this dissertation, Dc increasing with the increase of n, that is to say, the damage critical of tough materials is greater than that of brittle materials.Via the transform of coordinate, mode III crack problem in physical plane is inversed to stress plane to be investigated. Equilibrium equation and compatibility equation are deducted, in which (x, y) is expressed by unknownvariable 7^,7^,. Introducing strain function y/ , applying geometry equation ,compatibility equation and constitutive equation to deduct the basis equation satisfied by i// in mode III crack problem, for different n, small area damage solution of \i/ is obtained by means of calculation.Applying relevant formulae to deduct the formulation about shape of damage area, the shape of which being a series of circle is obtained, the center of circle and radius vary with D and n. In terms of the relation of coordinate of physical plane and strain plane, stress and strain field distribution curve expressed by polar coordinates in damage area is derived, when n=l,the result is same as that given by C.H.Popelar. When n>2, n influences the properties of the near tip crack field. If damage hardness equals to damage intensity, when n - , materials is elastic,then the radius of damage area is the same as the radius of ideal elastic-plasticitymaterials. The above provides theory bases for the establishment of failurecriterion.更多还原