压电薄膜表面贯穿裂纹的有限元分析

基于有限元软件ANSYS数值模拟,计算了激光作用下的压电薄膜表面贯穿裂纹外场应力强度因子和电位移强度因子,并且研究了90°畴变所诱致的畴变增韧行为。首先,求解无裂纹压电薄膜在激光作用下的热-力-电响应,将求得的应力和电位移场反向作用于裂纹面,求解裂纹尖端处的外场应力和电位移强度因子,然后基于小范围畴变理论求解了90°畴变所致的屏蔽应力强度因子。讨论了薄膜表面裂纹的外场应力强度因子、电位移强度因子及屏蔽应力强度因子随激光作用时间和裂纹位置的变化关系,从而预测压电薄膜体系在加热工作状况下的裂纹扩展和断裂行为。     

A theoretical investigation on the vibrational characteristics and torsional dynamic response of circumferentially cracked turbo-generator shafts

Turbo-generator shafts are often subjected to complex dynamic torsional loadings, resulting in generation and propagation of circumferential cracks. Mode III fatigue crack growth generally results in a fracture surface consisting of peaks and valleys, resembling a factory roof. The fracture surface roughness depends on the material microstructure, the material yield strength, and the applied cyclic torque amplitude. This crack pattern can severely affect the vibration characteristics of the shafts. The accurate evaluation of the torsional dynamic response of the turbo-generator shafts entails considering the local sources of energy loss in the crack vicinity. The two most common sources of the energy loss are the local energy loss due to the plasticity at the crack tip and frictional energy loss due to interaction of mutual crack surfaces. A theoretical procedure for evaluating the values of the system loss factors corresponding to these sources of energy loss is presented. Furthermore, the local flexibility is obtained by evaluating the resistance of the cracked section of the shaft to the rotational displacement. The shaft material is assumed to be elastic perfectly plastic. The effects of the applied Mode III stress intensity factor and the crack surface pattern parameters on the energy loss due to the friction and the energy loss due to the plasticity at the crack tip are investigated. The results show that depending on the amplitude of the applied Mode III stress intensity factor, one of these energy losses may dominate the total energy loss in the circumferentially cracked shaft. The results further indicate that the torsional dynamic response of the turbo-generator shaft is significantly affected by considering these two sources of the local energy loss.     

Dynamic crack propagation in a magneto-electro-elastic solid subjected to mixed loads: Transient Mode-III problem

The transient response of a Mode-III crack propagating in a magneto-electro-elastic solid subjected to mixed loads is investigated through solving the corresponding boundary-initial-value problem in both the cracked solid region and the interior fluid region with treatment of electro-magnetically permeable and impermeable crack face conditions in a unified way. The closed-form results for the dynamic field intensity factors are used to evaluate the dynamic energy release rate through the crack-tip dynamic contour integral. The permeability of the interior fluid region relative to the cracked solid region significantly affects the magneto-electro-mechanical coupling coefficient in the Bleustein–Gulyaev wave function and, consequently, the horizontal shear surface wave speed, the dynamic field intensity factors and the dynamic energy release rate. It is revealed from dynamic fracture mechanics analysis that the dynamic energy release rate thus obtained has an odd dependence on the dynamic electric displacement intensity factor and the dynamic magnetic induction intensity factor. It is also found that the horizontal shear surface wave speed provides the limiting velocity for the propagation of a Mode-III crack in a magneto-electro-elastic solid when there is only applied traction loading.     

Stress intensity factor evaluation by weight function for surface crack in edge notch

The weight function method is applied to obtain the stress intensity factor for a semi-elliptical surface crack in a circular edge notch subjected to polynomial loading on the crack faces. The crack region is considered as two sets of orthogonal slices superimposed such that the boundary conditions are satisfied. Numerical results are presented for different aspects ratios of the semi-elliptical surface crack in a notched semi-infinite region and compared with those found from the method of finite element.     

Investigation on 3D fatigue crack propagation in surface-cracked specimens

In the present work the fatigue crack growth in AISI304 specimens is investigated experimentally. In 3D finite element analysis the virtual crack closure technique is applied to calculate distributions and variations of the stress intensity factor along the surface crack front. It is confirmed that the stress intensity factor along the surface crack front varies non-uniformly with crack growth. Crack growth rate is proportional to the stress intensity factor distribution in the 3D cracked specimen. The fatigue crack growth in surface cracked specimens can be described by the Forman model identified in conventional compact tension specimens. For crack growth in the free specimen surface the arc length seems more suitable to quantify crack progress. Geometry and loading configuration of the surface cracked specimen seem to not affect the fatigue crack growth substantially.     

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.     

Propagating semi-infinite crack in fluid-saturated porous medium of finite height

Derived in this work are the Mode I stress intensity factor results for a constant velocity semi-infinite crack moving in a fluid-saturated porous medium with finite height. Two limiting cases are discussed; they correspond to a low and high speed crack propagation. To be expected is that the crack front stress intensification would increase as the medium height is reduced in relation to the segment length in which mechanical pressure is applied. Moreover, the stress intensity factor for the high speed crack is larger than the low speed crack, the magnification of which depends on the material. Dissatisfaction of the crack surface and tip boundary condition is found in the present solution which calls possibly for the additional consideration of a local boundary layer as discussed by other authors.     

DETERMINATION OF CRACK SURFACE DISPLACEMENTS FOR A RADIAL CRACK EMANATING FROM A SEMI-CIRCULAR NOTCH USING WEIGHT FUNCTION METHOD

A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate.Results are presented for two load conditions: remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the WuCarlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts

Summary  The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that in anti-plane problems. Received 4 September 2001; accepted for publication 23 July 2002 The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation of Tsinghua University, and the Education Ministry of China.     

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.     

Transient response of a cracked piezoelectric strip under arbitrary electro-mechanical impact

By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation of the crack depending on the time elapse since the application of the external electro-mechanical loads. The project supported by the National Natural Science Foundation of China and the Post-Doctor Science Foundation of China     

Transient response of a piezoelectric ceramic strip with an eccentric crack under electromechanical impacts

The transient response of a piezoelectric strip with an eccentric crack normal to the strip boundaries under applied electromechanical impacts is considered. By using the Laplace transform, the mixed initial-boundary-value problem is reduced to triple series equations, then to a singular integral equation of the first kind by introducing an auxiliary function. The Lobatto–Chebyshev collocation technique is adopted to solve numerically the resulting singular integral equation. Dynamic field intensity factors and energy release rate are obtained for both a permeable crack and an impermeable crack. The effects of the crack position and the material properties on the dynamic stress intensity factor are examined and numerical results are presented graphically.     

Crack identification in beams using wavelet analysis

In this paper a simple method for crack identification in beam structures based on wavelet analysis is presented. The fundamental vibration mode of a cracked cantilever beam is analyzed using continuous wavelet transform and both the location and size of the crack are estimated. The position of the crack is located by the sudden change in the spatial variation of the transformed response. To estimate the size of the crack, an intensity factor is defined which relates the size of the crack to the coefficients of the wavelet transform. An intensity factor law is established which allows accurate prediction of crack size. The viability of the proposed method is investigated both analytically and experimentally in case of a cantilever beam containing a transverse surface crack. In the light of the results obtained, the advantages and limitations of the proposed method as well as suggestions for future work are presented and discussed.     

Electromechanical impact of a crack in a functionally graded piezoelectric medium

The Mode-I transient response of a functionally graded piezoelectric medium is solved for a through crack under the in-plane mechanical and electric impact. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. Numerical results display the effects of the loading combination parameter λ and the material parameter βa on the dynamic stress intensity factor and electric displacement intensity factor. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor and the direction of crack initiation.     

考虑表面效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析

基于表面弹性理论和保角映射,研究了远场反平面剪切载荷作用下考虑表面效应时正三角形孔边裂纹问题的断裂性能。给出了孔边应力场解答,获得了裂纹尖端应力强度因子解析解答。数值算例讨论了应力强度因子随三角形孔尺寸、裂纹长度和表面性能的变化规律。结果表明：当三角形孔尺寸在在纳米量级时,无量纲应力强度因子受孔隙尺寸影响显著;随着三角形孔尺寸的增大,本文结果趋近于经典断裂理论解答;无量纲应力强度因子随裂纹长度的增加,数值先增大而后减小;裂纹相对长度较小时,表面效应影响较弱;应力强度因子的尺寸效应受表面性能影响显著。     

Torsion of a cylinder with a shallow external crack

The torsional problem of a finite elastic cylinder with a circumferential edge crack is studied in this paper. An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations. Unlike the Srivastav approach, this regularization transforms dual equations into a Fredholm integral equation of the second kind given on the crack surface. Hence, exact asymptotic expansions of the Fredholm equation solution, the stress intensity factor and the torque are derived for the case of a shallow crack. The asymptotic expansions are certain power-logarithmic series of the normalized crack depth. Coefficients of these series are found from recurrent relations. Calculations for a shallow crack manifest that the stress intensity factor exhibits the rather weak dependence upon the cylinder length when the torque is fixed and the triple length is larger than the diameter.     

Note on arc crack experiencing slip

Under certain loading conditions a crack surface may undergo partial sliding (slip). Such slip may be triggered by non-uniformity of frictional characteristics along the crack surface, variability of applied stresses or curvilinearity of a crack path. In the present work we study the influence of a curvilinear shape of a crack on slip evolution. The analysis is carried out for the case of a two-dimensional circular arc crack. Initiation and propagation of a slip zone is investigated based on the criterion that the shear stress intensity factor vanishes at endpoints of the slip zone. Two case scenarios are studied: first, when slip is attributed to the non-uniform distribution of a coefficient of friction and, second, when slip is initiated by the far field compressive loads. The curvilinear effects are estimated by comparing the obtained solutions with the ones for a straight crack. Analytical expressions for the stress intensity factors (SIFs) derived in this work may also present certain interest of their own.     

基于表面弹性理论的开裂椭圆孔断裂力学研究

研究纳米尺度时开裂椭圆孔的III型断裂性能。基于表面弹性理论和保角映射技术,利用复势函数理论获得了缺陷(裂纹和椭圆孔)周围应力场和裂纹尖端应力强度因子的闭合解答。所得结果具有一般性,许多已有和新的解答可由本文退化的特殊情形得到。利用解析结果讨论了缺陷的绝对尺寸、椭圆孔的形状比以及裂纹的相对尺寸对应力强度因子的影响。结果表明：考虑表面效应且缺陷尺寸在纳米尺度时,应力强度因子具有显著的尺寸依赖效应;应力强度因子随椭圆孔形状比的变化规律受缺陷表面常数的影响;缺陷表面效应的影响取决于椭圆孔的形状比,非常大的形状比屏蔽了表面效应的影响;裂纹相对尺寸非常小时表面效应影响较弱,裂纹相对尺寸较大时表面效应较为明显。     

Small edge crack in a semi-infinite solid subjected to thermal stratification

The mode I stress intensity factor for a small edge crack in an elastic half-space is found when the space is in contact with two stratified fluids of different temperatures, the boundary between the fluids oscillating sinusoidally over the solid surface. The variation in the stress intensity factor, which may lead to thermal fatigue crack growth, is examined as a function of time, crack depth, amplitude and temporal frequency of oscillation, surface heat transfer coefficient and material properties of the half-space. It is shown how this ‘boundary layer’ solution may be applied to problems involving finite geometries.     

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采用有限元方法对表面含有两个不同大小半椭圆裂纹的有限厚矩形板在拉伸载荷作用下 进行参数化求解，得到两裂纹取不同尺寸和位置坐标时附属裂纹(尺寸较小裂纹)对主 导裂纹(尺寸较大裂纹)前沿参考点($\theta= 0, \pi/2, \pi $)处的应力强 度因子的影响系数$\beta$, 然后结合神经网络技术建立了相邻裂纹尺寸和位置参 数到主导裂纹前沿点处$\beta$的多变量非线性映射关系.