含梯度渐变残余应力的弹性半无限体的广义Rayleigh波

Generalized Rayleigh wave in an elastic half space with graded residual stress

研究含梯度残余应力的弹性半无限体的平面应变型表面波,即广义Rayleigh波。将该结构等效为含梯度初应力的弹性覆盖层和无初应力的弹性基底构成的半无限体结构。求得覆盖层中位移函数的幂级数解与均质基底位移函数的解析解,并代入边界条件,得到频散方程。针对拉、压残余应力,分别讨论了其随厚度方向均匀分布、线性变化和指数变化情况下广义Rayleigh波的一阶模态频散特性。数值结果表明:随着拉应力增大,广义Rayleigh波波速会增加,反之,压应力的增大会导致波速的降低;残余应力均匀分布时波速的改变量较大,线性变化次之;当残余应力按照指数函数变化时,梯度参数越趋近于零,其结果越趋近于线性变化情况,随着梯度参数的减小,波速改变量也随之减小。当使用广义Rayleigh波频散特性实现残余应力无损检测时,如果采用与实际梯度渐变残余应力不符的均匀残余应力模型将会低估表面残余应力。本文所得结论可为利用广义Rayleigh波实现梯度残余应力无损检测提供理论基础。

Plain strain surface waves,named as generalized Rayleigh waves,in an elastic half space with graded residual stress are investigated.The structure can be considered as an elastic substrate without initial stress coved an elastic layer with graded initial stress.Based on the power series solution of displacement in covered layer,analytical solution of displacement in substrate and the boundary condition,the dispersion equation of generalized Rayleigh waves is obtained.The effects of different types of tensile and compression residual stress on dispersion properties of generalized Rayleigh waves are discussed,including the homogenous residual stress,the residual stress varying linearly and the residual stress varying exponentially.Numerical results show that the phase velocity increases with the increase in the magnitude of the tensile stress,while decreases with the increase in the magnitude of the compression stress.When Rayleigh wave propagates in an elastic half-space,the difference of phase velocity between non-residual stress and homogeneous residual stress is larger than others.The difference decreases if the residual stress varies linearly.If the residual stress is subject to exponential function,the more the gradient parameter approaches to zero,the more the result approaches to linear residual stress,while the variation of the phase velocity decrease with increase of the absolute value of gradient parameter.When the generalized Rayleigh waves are used to realize the residual stress nondestructive testing,the surface residual stress will be underestimated if adopting the uniform residual stress model instead of the more reasonable graded residual stress model.The results obtained can give theoretical guidance for non-destructive evaluation of graded residual stress using generalized Rayleigh wave in the engineering application.