Permeable cracks between two dissimilar piezoelectric materials

An interfacial crack with electrically permeable surfaces between two dissimilar piezoelectric ceramics under electromechanical loading is investigated. An exact expression for singular stress and electric fields near the tip of a permeable crack between two dissimilar anisotropic piezoelectric media are obtained. The interfacial crack-tip fields are shown to consist of both an inverse square root singularity and a pair of oscillatory singularities. It is found that the singular fields near the permeable interfacial crack tip are uniquely characterized by the real valued stress intensity factors proposed in this paper. The energy release rate is obtained in terms of the stress intensity factors. The exact solution of stress and electric fields for a finite interfacial crack problem is also derived.     

Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.     

Strip-electromechanical model solution for piezoelectric plate cut along two semi-permeable collinear cracks

A strip electric saturation and mechanical yielding model solution is proposed for a piezoelectric plate cut along two equal collinear semi-permeable mode-I cracks with electrical polarization reaching a saturation limit and normal stress reaching a yield stress along a line segment in front of the cracks. By using Stroh formalism and complex variable technique, we derived the analytical solution for the field quantities. Three different situations are investigated when developed electrical saturation zone is bigger/smaller or equal to the developed mechanical yield zone. Numerical results show that the effect of different electric boundary conditions on the crack opening displacement and crack opening potential drop is significant and should not be ignored. The influence of electric load displacement on the energy release rate is also investigated for PZT-4, PZT-5H and BaTiO₃ ceramics, and it may assists for the correct choosing of ceramic for specific job.     

A thermodynamics-based cohesive model for interface debonding and friction

A constitutive model for interface debonding is proposed which is able to account for mixed-mode coupled debonding and plasticity, as well as further coupling between debonding and friction including post-delamination friction. The work is an extension of a previous model which focuses on the coupling between mixed-mode delamination and plasticity. By distinguishing the interface into two parts, a cracked one where friction can occur and an integral one where further damage takes place, the coupling between frictional dissipation and energy loss through damage is seamlessly achieved. A simple framework for coupled dissipative processes is utilised to derive a single yield function which accurately captures the evolution of interface strength with increasing damage, for both tensile and compressive regimes. The new material model is implemented as a user-defined interface element in the commercial package ABAQUS and is used to predict delamination under compressive loads in several test cases.     

A continuum model for fiber reinforced materials with debonding

A continuum theory for a fiber-reinforced material with debonding between the constituents is presented. The debonding phenomenon is simulated by imposing the continuity of the normal displacements at the fiber-matrix interfaces while allowing free tangential slip there. The derived theory is of the lowest order and is obtained by using a first order expansion in the displacements in the fiber and matrix phases. The theory is applied to investigate the effect of debonding on the propagation of waves in a boron/epoxy fiber reinforced material. It is shown that an additional mode of propagation is obtained as compared with the usual case of perfect bonding     

A novel time dependent cohesive zone model for the debonding interface between solid propellant and insulation

A novel time dependent cohesive zone model (CZM) is proposed in this paper based on two main assumptions. Firstly, ultimate cohesive parameters are inherent and fixed for a given non-aging bond interface. The apparent cohesive parameters are time related variables. Secondly, relaxation response of the interface is the main reason for the time dependent traction. Numerical simulation shows that the traction, critical displacement as well as damage initiation displacement will increase with imposed loading rate and parameter λ for single Maxwell box based model. N single Maxwell box connected in parallel construct the N Maxwell box based model, and each Maxwell box bears 1/N traction of the interface. Double cantilever beam (DCB) is utilized to investigate the structure response with the single Maxwell box based model including constant stretch and relaxation test. Quite good agreement between the numerical and experimental reaction force–displacement curves is obtained from stretch test of Double cantilever sandwich beam (DCSB) specimen with four different N Maxwell box based model, especially when the number of the Maxwell box is 7. It is a fact that the model will be more adaptive with more Maxwell box connected in parallel which can be revealed by the verification test.     

On the interaction between two inclined cracks under biaxial load

Summary An analysis of the in-plane biaxial loading of an infinite homogeneous and isotropic elastic plate with two inclined collinear cracks of equal length is performed. The boundary value problem is solved by using the complex potentials method. The influence of the lateral load on the local stress distributions as well as on the crack tips behaviour is analyzed and the features of the interaction are described.

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Sommario Viene studiato il problema piano di due fessure inclinate ed allineate, di uguale lunghezza, in una lastra piana infinita di materiale elastico omogeneo ed isotropo, in regime di carico biassiale. Il problema dei valori al contorno viene risolto mediante la tecnica di potenziali complessi. Vengono analizzati gli effetti del carico laterale sia sui campi locali degli sforzi che sul comportamento delle estremitá delle fessure e descritte le modalità di interazione.

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Financial support of the National Research Council (C.N.R.) through research contribution N. 80.02203.07.     

An investigation on two cracks perpen-dicular to the interfaces in a piezolectric layer bonded to two half spaces by the schmidt method

The behavior of two collinear anti-plane shear cracks in'a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks. Project supported by the Post Doctoral Science Foundation of Heilongijang Province, the Natural Science Foundation of Heilongjing Province and the Science Research Foundation of Harbin Institute of Technology(HIT. 2000. 30).     

Investigation of the stability of a composite in compression along two parallel structural cracks at the layer interfaces

The scientific results of this paper were obtained by means of a program written with the support of the Alexander von Humboldt Foundation (Bonn-Bad Godesberg, Germany).     

A planar problem of failure of structural materials in compression along two parallel cracks

Institute of Mechanics of the Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 4, pp. 29–38, April, 1991.     

Theoretical model for elliptical tube laterally impacted by two parallel rigid plates

An analytical model is developed to study the crushing behavior and energy absorption capability of a single elliptical tube impacted by two parallel rigid plates, with and without consideration of the strain hardening effect. The four-hinge collapse mechanism is used, and the governing equation is derived from Lagrange equations of the second kind. The numerical simulation of the dynamic response of the elliptical tube under impact using the finite element explicit code LS-DYNA is performed. The reaction force-displacement curve and displacement-time curve of the plate obtained from the two methods are in good agreement.     

A capillary force model for interactions between two spheres

Based on the method of energy principle, an analytical approach for computing the capillary force for sphere/sphere geometry is presented in this paper. In modeling the capillary force, we consider spheres with both equal and non-equal radii, for both symmetric and asymmetric configurations at liquid/solid interfaces. We use numerical analysis to investigate the validity and efficiency of the derived model. The effect of various parameters including humidity, distance between two spheres, radii of spheres and contact angles on the meniscus force are investigated. Finally the results obtained from the model are compared with experimental measurements, and the accuracy and precision of the presented approach is verified.     

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

The generalized Dugdale crack model is used to formulate two-parameter failure criteria for the cases of quasibrittle state and developed plastic zones at a mode I crack tip. The failure criteria relate the fracture strength characteristics and the stress mode at the crack tip through the plastic constraint factor. The critical state of bodies with cracks under uni-and biaxial loading is analyzed in the cases of plane stress and plane strain using the Tresca and von Mises yield criteria. A small-scale yield criterion, which is an analytic relation between the critical stress intensity factor and T-stresses, is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 47–57, July 2007.     

An interaction integral method for 3D curved cracks in nonhomogeneous materials with complex interfaces

This work derives an interaction integral for the computation of mixed-mode stress intensity factors (SIFs) in three-dimensional (3D) nonhomogeneous materials with continuous or discontinuous properties. The present method is based on a two-state integral by the superposition of actual and auxiliary fields. In 3D domain formulation of the interaction integral derived here, the integrand does not involve any derivatives of material properties. Furthermore, the formulation can be proved to be still valid even when the integral domain contains material interfaces. Therefore, it is not necessary to limit the material properties to be continuous for the present formulation. On account of these advantages, the application range of the interaction integral can be greatly enlarged. This method in conjunction with the finite element method (FEM) is employed to solve several representative fracture problems. According to the comparison between the results and those from the published lectures, good agreement demonstrates the validation of the interaction integral. The results show that the present interaction integral is domain-independent for nonhomogeneous materials with interfaces.     

Relations between a micro-mechanical model and a damage model for ductile failure in shear

Gurson type constitutive models that account for void growth to coalescence are not able to describe ductile fracture in simple shear, where there is no hydrostatic tension in the material. But recent micro-mechanical studies have shown that in shear the voids are flattened out to micro-cracks, which rotate and elongate until interaction with neighbouring micro-cracks gives coalescence. Thus, the failure mechanism is very different from that under tensile loading. Also, the Gurson model has recently been extended to describe failure in shear, by adding a damage term to the expression for the growth of the void volume fraction, and it has been shown that this extended model can represent experimental observations. Here, numerical studies are carried out to compare predictions of the shear-extended Gurson model with the shear failures predicted by the micro-mechanical cell model. Both models show a strong dependence on the level of hydrostatic tension. Even though the reason for this pressure dependence is different in the two models, as the shear-extended Gurson model does not describe voids flattening out and the associated failure mechanism by micro-cracks interacting with neighbouring micro-cracks, it is shown that the trends of the predictions are in good agreement.     

Dynamic behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips

The dynamic interaction of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips subjected to the anti-plane shear harmonic stress waves was investigated. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is jump of displacement across the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter, the circular frequency of the incident waves and the thickness of the strip upon stress, electric displacement and magnetic flux intensity factors of cracks.     

Viscoplastic approach for rate-dependent failure analysis of concrete joints and interfaces

In this work, a new rate-dependent interface model for computational analysis of quasi-brittle materials like concrete is presented. The model is formulated on the basis of the inviscid elastoplastic model by [Carol, I., Prat, P.C., López, C.M., 1997. “A normal/shear cracking model. Interface implementation for discrete analysis”. Journal of Engineering Mechanics, ASCE, 123 (8), pp. 765–773.]. The rate-dependent extension follows the continuous form of the classical viscoplastic theory by [Perzyna, P., 1966. “Fundamental problems in viscoplasticity”. Advances in Applied Mechanics, 9, pp. 244–368.]. According to [Ponthot, J.P., 1995. “Radial return extensions for viscoplasticity and lubricated friction”. In: Proceedings of International Conference on Structural Mechanics and Reactor Technology SMIRT-13, Porto Alegre, Brazil, (2), pp. 711–722.] and [Etse, G., Carosio, A., 2002. “Diffuse and localized failure predictions of Perzyna viscoplastic models for cohesive-frictional materials”. Latin American Applied Research (32), pp. 21–31.] it includes a consistency parameter and a generalized yield condition for the viscoplastic range that allows an straightforward extension of the full backward Euler method for viscoplastic materials. This approach improves the accuracy and stability of the numerical solution. The model predictions are tested against experimental results on mortar and concrete specimens that cover different stress paths at different strain rates. The results in this work demonstrate, on one hand, the capabilities of the proposed elasto–viscoplastic interface constitutive formulation to predict the rate-dependency of mortar and concrete failure behavior, and, on the other hand, the efficiency of the numerical algorithms developed for the computational implementation of the model that include the consistent tangent operator to improve the convergence rate at the finite element level.     

Finite-part integral and boundary element method for interaction between two parallel planar cracks in three-dimensional finite bodies

By using the Somigliana representation and the concepts of finite-part integrals, a set of hypersingular integral equations of the interaction between two parallel planar cracks in a three-dimensional finite body subjected to arbitrary loads is derived, and then its numerical method is proposed by the finite-part integral method combined with the boundary element method. According to the analytic theory of hypersingular integral equations, the square root models of displacement discontinuities in the elements near the crack front are applied, and thus the computational precision is raised. Based on this, the stress intensity factors can be directly calculated. Finally, the stress intensity factors of several typical interaction problems are calculated.     

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

The current work models a weak(soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micr...