加层压电半空间界面裂纹力电联合冲击动态响应

基于线性压电弹性理论,研究电绝缘和电接触两种电边界条件下,任意多个任意排列的压电加层半空间界面裂纹在力电联合冲击作用下的动态响问题。通过引进Laplace变换和 Fourier 变换及位错密度函数,将问题首先转化为Cauchy 奇异积分方程,进而转化为代数方程进行数值求解。数值算例表明,电载荷、加层厚度及材料参数对动能量释放率具有重要的但不同的影响。研究结果对结构设计及结构失效的预防具有理论和应用价值。     

离散多层圆筒在热冲击载荷下的弹性动力响应

离散多层圆筒由薄内筒和倾角错绕的钢带层组成,具有制造简便、成本低等优点。预测筒体在热冲击载荷下的热应力对强度设计和安全操作具有重要的应用价值。该文首次研究了离散多层圆筒在热冲击载荷作用下的热弹性动态响应。将内筒和钢带层的径向位移分别分解为满足给定应力边界条件的准静态解和满足初始条件的动态解,准静态解通过齐次线性方法确定,热弹性动态解通过有限Hankel积分变换和Laplace变换确定。根据内外层界面处位移连续条件,得到层间压力关于时间的第二类Volterra积分方程,利用Hermit二次三项式插值方法可求得该层间应力。最后将离散多层圆筒的热弹性动力响应与单层厚壁圆筒的响应进行了比较,并分析了钢带缠绕倾角和材料参数对热弹性动力响应的影响。     

无限长条板中弹性与粘弹性界面裂纹尖端场

研究无限长条板中粘弹性-弹性界面Griffith裂纹在 Ⅰ 型突加载荷作用下,裂纹尖端动态应力强度因子的时间响应。利用积分变换方法、Fourier和Laplace变换,分别推导出了弹性和粘弹性问题的控制方程组;引入位错密度函数,并结合边界条件,导出了反映裂纹尖端奇异性的Cauchy型奇异积分方程组,运用Chebyshev正交多项式化奇异积分方程组为代数方程组,用配点法进行求解;最后用Laplace积分变换数值反演方法,将拉氏域内的解反演到时间域内,求得动态应力强度因子的时间响应,并对材料参数的影响进行了分析。结果表明,剪切松弛参量对 Ⅰ 型动应力强度因子的影响小于对 Ⅱ 型的影响,而膨胀松弛参量对 Ⅰ 型动应力强度因子的影响大于对 Ⅱ 型的影响。      

加层压电条界面裂纹的稳态扩展

研究当压电条同时与两个不同材料的弹性条粘接在一起,在反平面机械载荷及面内电载荷联合作用下,长度不变的有限Griffith 界面裂纹沿加层压电条界面以常速稳态扩展时裂尖的动态断裂问题。应用Fourier积分变换将问题化为以第二类Fredholm积分方程表示的对偶积分方程,导出了相应的动应力强度因子表达式。给出了动应力强度因子与裂纹传播速度、裂纹长度、压电条及弹性条厚度、电荷载大小及方向的关系曲线。研究结果对结构设计及结构失效的预防具有理论和应用价值。     

多裂纹弹塑性干涉效应及其工程解

本文针对Ｒａｍｂｅｒｇ－Ｏｓｇｏｏｄ关系材料进行弹塑性有限元计算，研究分析了平面应力问题下的近似无限宽板中双共线裂纹弹塑性干涉效应的变化规律，利用双裂纹裂纹Ｊ积分值和等载荷比下单裂纹尖Ｊ积分值之比来确定双裂纹间的弹塑性干涉效应，研究发现，弹塑性干涉效应不同于线弹性干步效应。除了与裂纹几何尺寸有关外，且是载荷比和材料性能的函数，由此证明线弹性分析作为裂纹问题处理的依据有可能出现危险的结果，在此基础上     

考虑温度效应的圆形均布载荷下沥青混凝土场坪的动力响应分析

对黏弹性材料的积分型本构关系进行Laplace积分变换,推导出采用广义Maxwell模型描述的黏弹性算子,并引入“时温等效”原理来反映温度对沥青混凝土力学性能的影响。将直角坐标系下黏弹性问题的动力平衡方程、几何方程以及物理方程进行Laplace变换和二维Fourier变换,建立了多层黏弹性体系的传递关系。在此基础上,根据已知边界条件给出了场坪表面垂向位移的求解方法,并利用Matlab软件编写计算程序。以三层沥青混凝土场坪为例,分析了考虑温度效应的圆形均布动载荷下场坪的动力响应。结果表明,温度越高,场坪下沉量越大,局部弯沉现象越明显,残余变形也愈大。     

压电压磁材料中周期裂纹对SH波的散射

本文用奇异积分方程方法研究了SH波和压电压磁材料中周期裂纹的相互作用.根据电磁弹性材料的控制微分方程,通过傅立叶积分变换,将问题转化为Hilbert核的奇异积分方程组.利用Lobatto-Chebyshev多项式逼近求解积分方程,得到了强度因子的表达式.通过数值算例,说明了SH波的频率、入射角以及材料参数对强度因子的影...     

磁电弹性功能梯度板共线Griffith裂纹断裂行为

该文考察了磁电弹性功能梯度板的反平面问题。该板具有多个垂直于边界的共线裂纹。裂纹表面采用磁电不穿透或可穿透假设。应用积分变换和位错密度函数将问题化为柯西奇异积分方程求解。导出和分析了场强度因子和能量释放率。数值结果表明了载荷组合参数、材料梯度指数及裂纹构形对裂尖断裂行为的影响。     

加层压电层硬币型裂纹断裂分析

研究粘接着弹性层的压电层内硬币型裂纹的断裂问题。压电层与弹性层均为横观各向同性材料,r轴方向无限长,z轴方向有限厚度。压电层沿z轴方向极化。考虑电不导通裂纹表面条件,利用Hankel积分变换将问题化为求解积分方程组,导出了场强度因子与能量释放率的表达式。给出了数值计算结果,并分析了弹性层厚度对场强度因子与能量释放率的影响。     

JBC—300型电子测力冲击试验机研制

简要介绍新近研制成功的ＪＢＣ－３００型电力测力冲击试验机结构原理。它主要由机械主机和以计算机为核心的电控系统组成。该试验机除可获得材料的冲击功Ａｔ，弹性功，Ａｃ，裂纹萌生功Ａｉ，裂纹扩展功Ａｐ，断裂功Ａｆ，以及弹性载荷Ｆｅ，屈服载荷Ｆ，ｙ最大载荷Ｆｍ，断裂点Ｆｆ等动态力不性能参数，还能获得冲击力对变形，冲击力对时间，变形对时间关系曲线。     

Dynamic fracture behavior of an internal interfacial crack between two dissimilar magneto-electro-elastic plates

In this paper, the anti-plane problem for an interfacial crack between two dissimilar magneto-electro-elastic plates subjected to anti-plane mechanical and in-plane magneto-electrical impact loadings is investigated. Four kinds of crack surface conditions are adopted: magneto-electrically impermeable (Case 1), magnetically impermeable and electrically permeable (Case 2), magnetically permeable and electrically impermeable (Case 3), and magneto-electrically permeable (Case 4). The position of the interfacial crack is arbitrary. The Laplace transform and finite Fourier transform techniques are employed to reduce the mixed boundary-value problem to triple trigonometric series equations in the Laplace transform domain. Then the dislocation density functions and proper replacements of the variables are introduced to reduce the series equations to a standard Cauchy singular integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition is approximated as a system of linear algebra equations, which can easily be solved. Field intensity factors and energy release rates are determined and discussed. The effects of loading combination parameters on dynamic energy release rate are plotted for Cases 1-3. On the other hand, since the magneto-electrically permeable condition is perhaps more physically reasonable for type III crack, the effect of the crack configuration on the dynamic fracture behavior of the crack tips is studied in detail for Case 4. The results could be useful for the design of multilayered magneto-electro-elastic structures and devices.     

Impact response of an anti-plane crack in a FGPM bonded to a homogeneous piezoelectric strip

A finite crack under transient anti-plane shear loads in a functionally graded piezoelectric material (FGPM) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential functions along the thickness of the strip, and that the two layered strips is under combined anti-plane shear mechanical and in-plane electrical impact loads. The analysis is conducted on the electrically unified crack boundary condition. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Fredholm integral equations of the second kind in the Laplace transform domain. Then, a numerical Laplace inversion is performed and the dynamic intensities are obtained as functions of time and geometric parameters, which are displayed graphically.     

Scattering of SH waves by an arc-shaped interface crack between a cylindrical magneto-electro-elastic inclusion and matrix with the symmetry of 6 mm

Summary Investigated are the scattered field properties of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material in this paper. The debonding region is modeled as an arc-shaped interface crack with magneto-electrically permeable surfaces. By expressing the scattered fields as the wave function expansions with unknown coefficients, the mixed boundary value problem is first reduced to a set of dual series equations. Then the dislocation density function is introduced as an unknown to transform the dual series equations to a Cauchy singular integral equation of the first type, which can be solved numerically. Finally, the scattered field intensity factor, the scattered far field pattern and scattered cross section are obtained. The effects of incident direction, crack opening angle and material combination on the properties of both near fields and far fields are respectively examined graphically. The solution of this problem is relevant to ultrasonic nondestructive detection of the debonding between two dissimilar magneto-electro-elastic materials and is expected to have applications to the question of how dynamic loading can lead to growth of debonds.     

Dynamic stress intensity factors studied by boundary integro-differential equations

The boundary integro-differential equation method is illustrated by two numerical examples concerning the study of the dynamic stress intensity factor around a penny-shaped crack in an infinite elastic body. Harmonic and impact load on the crack surface has been considered. Applying the Laplace transform with respect to time to the governing equations of motion the problem is solved in the transformed domain by the boundary integro-differential equations. The Laplace transformed general transient problem can be used to solve the steady-state problem as a special case where no numerical inversion is involved.     

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

The elastodynamic response of an infinite non-homogeneous orthotropic material with an interfacial finite crack under distributed normal and shear impact loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some materials are obtained. Interfacial cracks between two different materials and between two pieces of the same material but different fiber orientation are considered. Bimaterial formulation of a crack problem is shown to converge to the mono-material formulation, derived independently, in the limiting case when both materials are the same.     

Random dynamic response and reliability of a crack in a functionally graded material layer between two dissimilar elastic half-planes

An analytical approach is presented for the random dynamic analysis of a functionally graded material (FGM) layer between two dissimilar elastic half-planes. This FGM layer contains a crack and its material properties vary randomly in the thickness direction, while their mean values are exponential functions of field position. The transient loadings applied on the crack faces are assumed to be stochastic processes of time. In order to obtain the solution, the FGM layer is divided into several sub-layers, and the material properties of each layer are reduced to random variables by an average method. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. Both stress intensity factor history with its statistics and dynamic reliability are analytically derived. Numerical calculations are provided to show the effects of related parameters.     

An indirect boundary element method for three-dimensional dynamic fracture mechanics

Indirect boundary element methods (fictitious load and displacement discontinuity) have been developed for the analysis of three-dimensional elastostatic and elastodynamic fracture mechanics problems. A set of boundary integral equations for fictitious loads and displacement discontinuities have been derived. The stress intensity factors were obtained by the stress equivalent method for static loading. For dynamic loading the problem was studied in Laplace transform space where the numerical calculation procedure, for the stress intensity factor K_I(p), is the same: as that for the static problem. The Durbin inversion method for Laplace transforms was used to obtain the stress intensity factors in the time domain K_I(t). Results of this analysis are presented for a square bar, with either a rectangular or a circular crack, under static and dynamic loads.     

Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface - Part II: Transient problem

In Part I of this paper, the static problem of a functionally graded coating-substrate system with an internal or edge crack perpendicular to the interface has been studied. In this part, the transient response of the structure is considered under an in-plane impact. Laplace and Fourier transforms are applied to reduce the mixed boundary value problem to a singular integral equation which is solved in the Laplace domain numerically. The dynamic stress intensity factors (DSIFs) are obtained by numerical Laplace inversion technique. The influences of material constants and geometry parameters on the dynamic stress intensity factors are studied. It is found that the DSIFs for an internal crack rise rapidly to a peak and then tend to the steady value without obvious oscillations, but the DSIFs for an edge crack have more obvious oscillations after rising to a peak with the increasing of the nonhomogeneity constant.