Crack propagation along the interface of piezoelectric bimaterial

This paper is concerned with the propagation of a crack along the interface of a piezoelectric bimaterial, which can travel at subsonic or intersonic speed. The inertial effects are taken into account while the static approximation is applied to the electric fields. The effect of piezoelectricity on the asymptotic crack-tip field is discussed for an interface crack propagating subsonically and intersonically. An alternative method is used to avoid solving for the eigenvectors. This paper provides a unified method to analyze the crack-tip field of a crack propagating along a piezoelectric bimaterial interface.     

爆炸荷载作用下岩石动态裂纹扩展的数值模拟

运用岩石破裂过程分析软件RFPA-dynamic,就爆炸荷载的加载速率、炮孔到自由边界的距离以及两炮孔中间空孔的大小对动态裂纹扩展方式的影响进行了研究。结果表明:随着加载速率的减小,炮孔周围的破碎区逐渐减少;裂纹开始萌生的位置逐渐由破碎区外边缘向炮孔孔壁转移;萌生的分支小裂纹逐渐减少,主裂纹扩展长度逐渐增大。由于自由边界的影响,炮孔向下扩展的裂纹逐渐弯向水平方向,且炮孔到自由边界的距离越小,这种趋势越明显。由于空孔的导向作用,使靠近空孔的裂纹逐渐弯曲向空孔处扩展,同时在空孔孔壁两端产生一条向炮孔扩展的裂纹;空孔半径大小对裂纹的导向作用,并无明显的影响;材料的非均匀性,对裂纹的扩展方式有显著的影响。     

Further investigation of interaction between interface macrocrack and parallel microcracks in bimaterial anisotropic solids

In this paper, with the aid of superimposing technique and the Pseudo Traction Method (PTM), the interaction problem between an interface macrocrack and parallel microcracks in the process zone in bimaterial anisotropic solids is reduced to a system of integral equations. After the integral equations are solved numerically, a conservation law among three kinds ofJ-integrals is obtained which are induced from the interface macrocrack tip, the microcrack and the remote field, respectively. This conservation law reveals that the microcrack shielding effect in such materials could be considered as the redistribution of the remoteJ-integral. The project supported by the National Natural Science Foundation of China, and the Doctorate Foundation of Xi'an Jiaotong University     

Opening and contact zones of an interface crack in a piezoelectric bimaterial under combined compressive-shear loading

A plane problem for a tunnel electrically permeable interface crack between two semi-infinite piezoelectric spaces is studied. A remote mechanical and electrical loading is applied. Elastic displacements and potential jumps as well as stresses and electrical displacement along the interface are presented using a sectionally holomorphic vector function. It is assumed that the interface crack includes zones of crack opening and frictionless contact. The problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved analytically. From the obtained solution, simple analytical expressions are derived for all mechanical and electrical characteristics at the interface. A quite simple transcendental equation, which determines the point of separation of open and close sections of the crack, is found. For the analysis of the obtained results, the main attention is devoted to the case of compressive-shear loading. The analytical analysis and numerical results show that, even if the applied normal stress is compressive, a certain crack opening zone exists for all considered loading values provided the shear field is present. It is found that the shear stress intensity factor at the closed crack tip and the energy release rates at the both crack tips depend very slightly on the magnitude of compressive loading.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

柱形和球形壳体内爆界面不稳定性数值分析

为了更好地研究柱形和球形构型下果冻界面不稳定性发展,避免内爆聚心反弹前后直角坐标网格计算导致的误差,提高对流场和界面位置的计算精度,通过应用考虑了MVFT程序的网格适应性,使其能够适用于柱形网格和球形网格下的界面不稳定性数值模拟,特别是能够保证内爆聚心反弹前后流场和界面计算的稳定性。应用改进的计算程序对两种构型下的界面不稳定性进行了数值模拟,并对二者界面演化规律进行了详细讨论和归纳。结果表明:对于内外半径相同的柱形和球形果冻,聚心反弹时前者半径较小,而后者反弹时刻早于前者,其向内聚心和向外运动的速度最大值大于前者,对内部气体的压缩强度强于前者。对于外边界带有正弦扰动情况,除遵循上述规律外,计算还给出了峰谷转换现象。该项研究结果为进一步深入进行复杂构型下界面不稳定性高精度数值模拟研究提供了一种分析工具。     

Mode-3 spontaneous crack propagation along functionally graded bimaterial interfaces

The effects of combining functionally graded materials (FGMs) of different inhomogeneous property gradients on the mode-3 propagation characteristics of an interfacial crack are numerically investigated. Spontaneous interfacial crack propagation simulations were performed using the newly developed spectral scheme. The numerical scheme derived and implemented in the present work can efficiently simulate planar crack propagation along functionally graded bimaterial interfaces. The material property inhomogeneity was assumed to be in the direction normal to the interface. Various bimaterial combinations were simulated by varying the material property inhomogeneity length scale. Our parametric study showed that the inclusion of a softening type FGM in the bimaterial system leads to a reduction in the fracture resistance indicated by the increase in crack propagation velocity and power absorbed. An opposite trend of increased fracture resistance was predicted when a hardening material was included in the bimaterial system. The cohesive tractions and crack opening displacements were altered due to the material property inhomogeneity, but the stresses ahead of the cohesive zone remained unaffected.     

Shock propagation along a two-layer interface in confined geometry

The paper presents direct numerical simulations of the propagation of a strong planar shock wave along a two-layer interface confined between two walls. Transient stage and steady state of the propagation are described. In the steady state regime, a stationary irregular refraction of the shock and a vorticity sheet are characterized. Physics of the stationary irregular refraction state is explained. Shock velocity is studied. Quantities are shown to verify a set of generalized Rankine–Hugoniot relations. The unknown coupling mechanism between shear layer and pressure step is predicted by a neural network which leads to a predictive, gray-box type model.     

A general solution method for an anti-plane shear crack dynamically accelerating along a bimaterial interface

We develop a general solution method for a dynamically accelerating crack under anti-plane shear conditions along the interface between two different homogeneous isotropic elastic materials. The crack is initially at rest, and after loading is applied the crack-tip speed which may accelerate up to the shear wave speed of the more compliant material. The analysis includes an exact, closed-form expression for the stress intensity factor for an arbitrary time-dependent crack-face traction, as well as expressions for computing the crack-face displacements and the stress in front of the crack. We also present some numerical examples for fixed loads and for loads moving with the crack tip, using a stress intensity factor fracture criterion, in order to examine the predicted effect of material mismatch on interfacial fracture.     

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.     

Interface crack with a contact zone in an isotropic bimaterial under thermomechanical loading

A plane problem for a thermally insulated interface crack with a contact zone in an isotropic bimaterial under tension–shear mechanical loading and a temperature flux is considered. The expressions for the stresses and the electrical flux as well as for the derivatives of the displacement and the temperature jumps at the material interfaces via sectionally holomorphic mechanical and thermal potential functions are given. After the solution of the thermal problem the inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved exactly. The stresses at the interface and the stress intensity factors at the singular points are presented in a clear analytical form. Special attention is devoted to the case of a small contact zone when the stress intensity factors can be presented in form similar to the associated presentation for an “open” crack model. A transcendental equation and an asymptotic analytic formula for the determination of the real contact zone length are derived. It is shown that for a certain bimaterial this length as well as the correspondent stress intensity factor are defined by a single parameter which depends on the normal-shear loading and the heat flux.     

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

The problem of a mode-II crack close to and perpendicular to an imperfect interface of two bonded dissimilar materials is investigated.The imperfect interface is modelled by a linear spring with the vanishing thickness.The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel.The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation.Several special cases of the mode-II crack problem with an imperfect interface are studied in detail.The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically.The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.     

Numerical simulation of interlaminar damage propagation in CFRP cross-ply laminates under transverse loading

This paper proposes a numerical simulation of interlaminar damage propagation in FRP laminates under transverse loading, using the finite element method. First, we conducted drop-weight impact tests on CFRP cross-ply laminates. A ply crack was generated at the center of the lowermost ply, and then a butterfly-shaped interlaminar delamination was propagated at the 90/0 ply interface. Based on these experimental observations, we present a numerical simulation of interlaminar damage propagation, using a cohesive zone model to address the energy-based criterion for damage propagation. This simulation can address the interlaminar delamination with high accuracy by locating a fine mesh near the damage process zone, while maintaining computational efficiency with the use of automatic mesh generation. The simulated results of interlaminar delamination agreed well with the experiment results. Moreover, we demonstrated that the proposed method reduces the computational cost of the simulation.     

Experimental analysis for singularities in crack normal to bimaterial interface

Three kinds of the model of crack normal to the bimaterial interface are studied by an experimental method. The highly sensitive moire interferometry technique is employed to obtain the displacement fields near the crack tip. The singularities of the three kinds of model are determined and analyzed by the experimental method and compared and discussed.     

Kinking of a crack under dynamic loading conditions

Summary A method is presented to analyze elastodynamic stress intensity factors at the tip of a branch which emanates at velocity v and under an angle from the tip of a semi-infinite crack, when the faces of the semi-infinite crack are subjected to impulsive normal pressures. By taking advantage of self-similarity, the system of governing equations is reduced to a set of two Laplace's equations in half-plane regions. The solutions to these equations, which are coupled along the real axes of the half-planes, are obtained by using complex function theory together with summations over Chebychev polynomials. For small values of the Mode I and Mode II stress intensity factors and the corresponding flux of energy into the crack tip have been computed.     

Stability of a viscoelastic plate under dynamic loading

Tashkent Polytechnic Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 78–87, September, 1991.     

Numerical analysis of large elastic-plastic deformation of beams due to dynamic loading

Numerical calculations were performed for two examples of the response of elastic-plastic beams subjected to dynamic loads. These were a simply supported, axially restrained beam under suddenly applied uniform pressure, and an axially restrained, clamped beam with a central mass that is impacted by a projectile. Large elastic-plastic deflections were considered, and the method of finite differences was used. Two different constitutive equations were assumed: the elástic-perfectly plastic relation, and a special elastic-viscoplastic, strain hardening model. Analysis of the results included examining the interaction between the bending moment and the axial force, the variation of the axial force, bending moment and deflection with time, and the propagation velocities of the various phenomena during motion. Experiments were carried out in which a rifle projectile hit a central mass which had been fastened to a clamped beam. Comparison between the theoretical and experimental dynamic deflections shows good agreement for relatively short response times.