Anti-Plane Fracture Analysis of a Functionally Gradient Material Infinite Strip With Finite Width
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摘要: 研究了功能梯度材料有限宽板中与板边平行的III型裂纹问题.假设材料的剪切模量沿板宽度方向呈指数规律变化,利用Fourier变换将问题描述为奇异积分方程,并进一步将未知的位错密度函数表示为Chebyshev多项式的级数式,从而将奇异积分方程化为线性代数方程组进行配点数值求解.基于数值结果,讨论了材料非均匀性参数、板和裂纹的几何参数等对应力强度因子(SIF)的影响.研究表明,SIF随裂纹长度的增大而增大,随裂纹所在区域材料刚度的增大而减小;板越窄,SIF对非均匀性参数的变化越敏感,且变化规律也越复杂.随着非均匀性参数的增大,SIF既可能增大也可能减小还可能基本保持不变,这主要取决于板的相对宽度和裂纹的相对位置.当裂纹位于板的中央或当板较宽时,SIF对非均匀性参数的变化都不太敏感.Abstract: The special case of a crack under mode conditions was treated,lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges.By using Fourier transforms the problem was formulate dinterms of a singular integral equation.It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations.The stress intensity factor (SIF)results were discussed with respect to the influences of different geometric parameter sand the strength of the non-homogeneity.It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack.The SIF of narrow strip is very sensitive to the change of the non-homog eneity parameter and its variation is complicated.With the increase of the non-homogeneity parameter,the stress intensity factor may increase,decrease or keep constant,which is mainly determined by the strip width and the relative crack location.If the crack is located at the midline of the strip or if the strip is wide,the stress intensity factor is not sensitive to the material non-homogeneity parameter.
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