Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip
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摘要: 研究非均匀条中硬币型裂纹的扭转冲击问题．材料的剪切模量假定按特定的梯度变化．采用Laplace 和Hankel 变换将问题化为求解Fredholm积分方程，通过将Bessel函数渐进展开获得裂纹尖端动态应力场．考查非均匀参数和功能梯度条高度对裂尖动态断裂行为的影响．动应力强度因子和能量密度因子的清晰表达式表明，作为裂纹扩展力，对于这里所研究的问题，二者是等价的．动应力强度因子的数值结果显示，增加剪切模量的非均匀参数可以抑制动应力强度因子的幅度，而条形域的高度对动态断裂特性的影响较小．Abstract: The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered.The shear modulus is assumed to be functionally graded such that the mathematics is tractable.Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation.The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function.Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that,as crack driving force,they are equivalent for the present crack problem.Investigated are the effects of material nonhomogeneity and strip's highness on the dynamic fracture behavior.Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus,and that the dynamic behavior varies little with the adjusting of the strip's highness.
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