压电压磁材料中正n边形孔边裂纹分析

基于电磁复合材料力学,运用Stroh型公式和复变函数方法,针对压电压磁材料中含正n边形孔边裂纹反平面问题进行了研究。利用Schwarz-Christoffel变换技术,结合Cauchy积分公式和留数定理,导出了磁电全非渗透型边界条件下任意正n边形裂纹尖端场强度因子和能量释放率的解析解。当缺失磁场时,所得解退化为已有结果,以此验证方法的有效性。通过数值算例,对比分析了n=3,n=4和n=5三种特殊情形对应的孔口边长、裂纹长度和受到的力、电和磁载荷对等效场强度因子和无量纲能量释放率的影响规律。研究结果发现,正n边形孔洞的尺寸和裂纹长度均会促进裂纹扩展,且前者的影响更显著一些;正n边形边的数量增加会阻止裂纹的扩展;在磁电全非渗透型边界条件下,机械载荷始终促进裂纹的扩展,电位移载荷可以促进或抑制裂纹的扩展,磁载荷对裂纹的扩展贡献较少。本研究结果适用于任意正n边形孔边裂纹求解问题,为压电压磁材料元器件的优化设计和断裂特性分析提供了新思路。     

磁电弹性体中唇形运动裂纹问题分析

本文通过共形映射公式,利用复变函数方法研究了磁电弹性体中的唇形运动裂纹问题.对裂纹面上受反平面剪应力和面内磁电载荷共同作用情况,导出了磁电全非渗透型边界条件下运动裂纹尖端场应力强度因子和机械应变能释放率的解析解.当运动速度为零时这两解都退化成了静止状态下的解.通过算例,与具有相同尺寸的带双裂纹的椭圆孔口问题进行了比较,给出了两种裂纹尖端点处应力强度因子和机械应变能释放率随孔口高度h与裂纹半长a之比h/a的变化规律曲线图,得出了两种孔口裂纹问题在应力强度因子和能量释放率两方面的异同点,结果表明采用唇形孔口裂纹比采用带双裂纹的椭圆孔口能降低裂纹的扩展,这在工程建设及构件的制造上有一些指导作用.     

磁电弹性体中纳米孔边任意位置贯穿裂纹的解析解

本文研究了反平面机械载荷、面内电载荷和面内磁载荷作用下磁电弹材料中含有纳米尺度孔边任意位置贯穿裂纹的Ⅲ型断裂力学性能.基于Gurtin-Murdoch表面弹性理论考虑纳米缺陷(孔洞和裂纹)的表面效应,利用磁电弹理论和复变弹性理论获得了纳米缺陷表面为磁电不可通条件下磁电弹场的精确解,给出了贯穿裂纹两端裂尖的磁电弹场强因子的解析表达.所得结果与已有研究比较说明了本文方法的有效性.讨论了裂纹位置、裂纹相互作用与施加多物理场载荷对无量纲磁电弹场强因子的影响.结果表明：贯穿裂纹裂尖的无量纲磁电弹场强因子尺寸效应显著;缺陷表面效应对裂纹耦合尖端场的影响受裂纹位置的制约;无量纲磁电弹场强因子受贯穿裂纹两端的裂纹长度比与施加力电磁载荷的显著影响.     

压电复合材料中正n边形孔边裂纹的反平面问题研究

本文基于Cauchy积分理论和Schwarz-Christoffel(SC)变换技术,针对压电复合材料中带一条裂纹的正n边形孔口缺陷的反平面断裂力学进行了探究．假设满足电不可通边界条件,利用Cauchy积分公式和留数定理,获得了任意正n边形裂尖处应力和电位移两个场强度因子以及全能量释放率的封闭形式的显式解．当正n边形边数取定时,所得解可退化为已有结果,以此验证方法的有效性．并通过数值算例,对比分析了n=3, n=4, n=5三种特殊情形对应的等效场强度因子和无量纲能量释放率与孔口边长、裂纹长度和受到的力、电载荷之间的曲线图．数值结果显示：正n边形孔洞的尺寸和裂纹长度均会促进裂纹扩展,且前者的影响更显著一些;正n边形边的数量增加会阻止裂纹的扩展;在电不可通边界条件下,机械载荷对裂纹的扩展始终贡献显著,电场对断裂行为的影响取决于机械载荷．本研究结果具有一般性,适用于任意正n边形孔边裂纹问题的求解,为压电复合材料元器件的优化设计和断裂特性分析提供了新思路．     

一维六方压电准晶三角形孔边裂纹反平面问题

通过引入合适的数值保角映射,利用Stroh型公式研究一维六方压电准晶中正三角形孔边裂纹的反平面问题,给出在电非渗透边界条件下三角形孔边裂纹尖端的场强度因子和能量释放率。通过数值算例,讨论场强度因子和能量释放率随缺陷几何尺寸和力电荷载的变化规律。结果表明:随孔边裂纹长度的增加,场强度因子先急剧增加后减小,并趋于定值1,正三角形孔洞的尺寸对其影响可忽略不计;声子场和相位子场机械载荷总是促进裂纹扩展,而电位移对裂纹的扩展极大地依赖于声子场和相位子场载荷的大小。     

压电效应下一维六方准晶双材料孔边裂纹的反平面问题研究

利用复变函数方法和保角变换技术研究了压电效应下一维六方准晶双材料中圆孔边单裂纹的反平面问题．考虑电不可渗透型边界条件,运用保角变换和Stroh公式得到了弹性体受远场剪切力和面内电载荷作用下裂纹尖端应力强度因子和能量释放率的解析解. 数值算例分析了几何参数、远场受力、电位移载荷对能量释放率的影响．结果表明：裂纹长度、耦合系数和远场剪切力的减小可以抑制裂纹的扩展．不考虑电场时,声子场应力对能量释放率的影响较小．本文的研究结果可作为研究一维六方压电准晶双材料孔边裂纹问题的理论基础,同时为压电准晶及其复合材料的设计、制备、优化和性能评估提供理论依据．     

界面裂纹问题中的通用权函数法

热载荷和机械载荷共同作用下复合材料中的裂纹扩展往往发生在界面处.传统求解热冲击及机械载荷共同作用下界面裂纹尖端的应力强度因子的数值方法(如有限元、边界元法等),计算工作量大、效率低.通用权函数与时间无关,运用通用权函数法可以免除对每个时刻的应力分析,计算效率可得到很大提高.本文将通用权函数法推广到求解热载荷和机械载荷共同作用下界面裂纹尖端的应力强度因子过渡过程的问题中,推导出求解平面双材料界面裂纹问题应力强度因子的通用权函数法计算格式.基于此格式,计算热载荷和机械载荷共同作用下界面裂纹尖端的应力强度因子.通过实例计算比较,表明此方法得到的结果可以达到与相互作用积分法相当的工程应用精度.最后,应用此方法研究了热障涂层受热冲击及表面力共同作用时裂纹长度以及涂层厚度对应力强度因子的影响.结果表明:在一定边界条件下,当热障涂层中存在边缘裂纹时,随着涂层厚度的增加,更容易导致裂纹的扩展和涂层的剥落.     

同震断层三维裂纹扩展波动时域超奇异积分法

应用波动时域超奇异积分法将P波、S波和磁电热弹多场耦合作用下同震断层任意形状三维裂纹扩展问题转化为求解以广义位移间断率为未知函数的超奇异积分方程组问题;定义了广义应力强度因子,得到裂纹前沿广义奇异应力增量解析表达式;应用波动时域有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以三维矩形裂纹扩展问题为例,通过典型算例,研究了广义应力强度因子随裂纹位置变化规律;分析了同震断层裂纹扩展中力、磁、电场辐射规律.      

层状柱壳磁电复合材料的非线性磁电效应研究

本文基于超磁致伸缩材料非线性本构,从基本的控制方程出发,对层状柱壳磁电复合材料的非线性磁电响应进行理论研究,讨论了不同边界下磁场频率以及压电材料厚度比对磁电系数的影响,并得到了不同预压力下磁场大小对于磁电系数的影响。数值计算结果显示,对于Tefernol-D/PZT-5层状磁电复合材料,随着预压力值增大,磁电系数最大值减小,取得最大值时对应的磁场值逐渐增大;不同边界条件、磁场频率和磁场大小下,材料厚度比对磁电系数的也有着不同的影响。特别地当外加磁场频率较大时,相应于压电层厚度比,磁电系数呈现多极值现象。     

功能梯度压电压磁材料粘结的Ⅲ型裂纹问题

利用奇异积分方程方法研究两个半无限大的功能梯度压电压磁材料粘结,在渗透和非 渗透边界条件下的III型裂纹问题. 首先通过积分变换构造出原问题的形式解，然 后利用边界条件通过积分变换与留数定理得到一组奇异积分方程， 最后利用Gauss-Chebyshev方法进行数值 求解，讨论材料参数、材料非均匀参数以及裂纹几何形状等对裂纹尖端应力 强度因子的影响. 从结果中可以看出，压电压磁复合材料中反平面问题的应力奇异性 形式与一般弹性材料中的反平面问题应力奇异形式相同，但材料梯度参数对功能梯度压电压 磁复合材料中的应力强度因子和电位移强度因子有很大的影响.     

Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack

Based on the complex potential approach, the two-dimensional problems in a piezoelectric material containing an elliptic hole subjected to uniform remote loads are studied. The explicit, closed-form solutions satisfying the exact electric boundary condition on the hole surface are given both inside and outside the hole. When the elliptic hole degenerates into a crack, the field intensity factors are obtained. It is shown that the stress intensity factors are the same as that of isotropic material, while the electric displacement intensity factor depends on both the material properties and the mechanical loads, but not on the electric loads. In other words, the uniform electric loads have no influence on the field singularities. It is also shown that the impermeable crack assumption used previously to simply the electric condition is not valid to crack problems in piezoelectric materials.     

Transient response of an interfacial crack between dissimilar magnetoelectroelastic layers under magnetoelectromechanical impact loadings: Mode-I problem

The dynamic response of an interfacial crack between two dissimilar magnetoelectroelastic layers is investigated under magnetic, electrical and mechanical impact loadings. Four kinds of ideal crack-face assumptions, i.e., magnetoelectrically impermeable (Case 1), magnetically impermeable and electrically permeable (Case 2), magnetically permeable and electrically impermeable (Case 3) and magnetoelectrically permeable (Case 4), are adopted separately. The dynamic field intensity factors and energy release rates are derived. The effects of loading combinations and crack configurations especially for the former on the dynamic response are examined according to energy release rate criterion. The numerical results show that, among others, a negative magnetic (or electrical) loading is generally prone to inhibit the crack extension rather than a positive one for a magnetically (or electrically) impermeable interfacial crack. Results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.     

Dynamic fracture analysis of an annular interfacial crack between dissimilar magnetoelectroelastic layers

Transient response of an annular interfacial crack between dissimilar magnetoelectroelastic layers under impacts is investigated. On the crack surface, magnetoelectrically impermeable boundary condition is adopted. Using Laplace and Hankel transform techniques, the mixed boundary value problem is reduced to a system of singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The dynamic field intensity factor and dynamic energy release rate are determined. Numerical results reveal the effects of electric or magnetic loadings and material parameters of composite on crack propagation and growth.     

Fracture mechanics for a mode III crack in a magnetoelectroelastic solid

In this paper, we developed a Stroh-type formalism for anti-plane deformation and then investigated the fracture mechanics for an elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-plane electromagnetic and/or anti-plane mechanical loading, which allowed us to take the electromagnetic field inside the cavity into account. Reducing the cavity into a crack, we had explicit solutions in closed forms for a mode III crack, which included the extreme cases for an impermeable crack and a permeable crack. The results were illustrated with plots, showing that in the absence of mechanical loads, an applied electric or magnetic field, positive or negative, always tended to close the crack. On the other hand, in the presence of a mechanical load, a negative electric or magnetic field retarded crack growth, while a positive field could either enhance or retard crack propagation, depending on the strengths of the applied electric/magnetic fields and the level of the mechanical load as well. In other words, the effect of electric/magnetic fields on the fracture behavior is mechanical load-dependent.     

Applicability of the crack-face electromagnetic boundary conditions for fracture of magnetoelectroelastic materials

This paper discusses the different electromagnetic boundary conditions on the crack-faces in magnetoelectroelastic materials, which possess coupled piezoelectric, piezomagnetic and magnetoelectric effects. A notch of finite thickness in these materials containing air (or vacuum) is also addressed. Four ideal crack-face electromagnetic boundary condition assumptions, that is, (a) electrically and magnetically impermeable crack, (b) electrically impermeable and magnetically permeable crack, (c) electrically permeable and magnetically impermeable crack and (d) electrically and magnetically permeable crack, are investigated separately. The influence of notch thickness on the field intensity factors at notch tips and the electromagnetic field inside the notch are obtained in closed-form. The results are compared with the ideal crack solutions. Applicability of crack-face electromagnetic boundary condition assumptions is discussed.     

An exact and explicit treatment of an elliptic hole problem in thermopiezoelectric media

This paper presents an exact solution for the problem of an elliptic hole or a crack in a thermopiezoelectric solid. First, based on the extended version of Eshelby–Stroh's formulation, the generalized 2D problems of an elliptical hole in a thermopiezoelectric medium subject to uniform heat flow and mechanical–electrical loads at infinity are studied according to exact boundary conditions at the rim of the hole. The complex potentials in the medium and the electric field inside the hole are obtained in closed form, respectively. Then, when the hole degenerates into a crack, the explicit solutions for the field intensity factors near the crack tip and the electric field inside the crack are presented. It is shown that the singularities of all the field are dependent on the material constants, the applied heat load and mechanical loads at infinity, but not on the applied electric loads. It is also found that the electric field inside the crack is linearly variable, which is different from the result based on the impermeable crack model.     

Analysis method of planar cracks of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic magnetoelectroelastic medium

The hyper-singular boundary integral equation method of crack analysis in three-dimensional transversely isotropic magnetoelectroelastic media is proposed. Based on the fundamental solutions or Green’s functions of three-dimensional transversely isotropic magnetoelectroelastic media and the corresponding Somigliana identity, the boundary integral equations for a planar crack of arbitrary shape in the plane of isotropy are obtained in terms of the extended displacement discontinuities across crack faces. The extended displacement discontinuities include the displacement discontinuities, the electric potential discontinuity and the magnetic potential discontinuity, and correspondingly the extended tractions on crack face represent the conventional tractions, the electric displacement and the magnetic induction boundary values. The near crack tip fields and the intensity factors in terms of the extended displacement discontinuities are derived by boundary integral equation approach. A solution method is proposed by use of the analogy between the boundary integral equations of the magnetoelectroelastic media and the purely elastic materials. The influence of different electric and magnetic boundary conditions, i.e., electrically and magnetically impermeable and permeable conditions, electrically impermeable and magnetically permeable condition, and electrically permeable and magnetically impermeable condition, on the solutions is studied. The crack opening model is proposed to consider the real crack opening and the electric and magnetic fields in the crack cavity under combined mechanical-electric-magnetic loadings. An iteration approach is presented for the solution of the non-linear model. The exact solution is obtained for the case of uniformly applied loadings on the crack faces. Numerical results for a square crack under different electric and magnetic boundary conditions are displayed to demonstrate the proposed method.     

Dynamic fracture analysis of a penny-shaped crack in a magnetoelectroelastic layer

This paper analyzes the dynamic magnetoelectroelastic behavior induced by a penny-shaped crack in a magnetoelectroelastic layer subjected to prescribed stress or prescribed displacement at the layer surfaces. Two kinds of crack surface conditions, i.e., magnetoelectrically impermeable and permeable cracks, are adopted. The Laplace and Hankel transform techniques are employed to reduce the problem to Fredholm integral equations. Field intensity factors are obtained and discussed. Numerical results of the crack opening displacement (COD) intensity factors are presented and the effects of magnetoelectromechanical loadings, crack surface conditions and crack configuration on crack propagation and growth are examined. The results indicate that among others, the fracture behaviors of magnetoelectroelastic materials are affected by the sizes and directions of the prescribed magnetic and/or electric fields, and the effects are strongly dependent on the elastic boundary conditions.