Analysis Of Multiple Cracks Research Articles

Anti-plane analysis of multiple cracks originating from a circular hole in a magnetoelectroelastic solid

The anti-plane problem of multiple cracks originating from a circular hole in a magnetoelectroelastic solid is investigated under remotely uniform anti-plane mechanical loading and in-plane electromagnetic loadings. The boundary value problem is reduced to a Cauchy integral equation by a new mapping function and the complex variable method, which is further solved exactly. The analytic expressions of the complex potentials, the field intensity factors and the energy release rate are derived in closed-form under the assumption that the surfaces of the cracks and hole are both electrically and magnetically impermeable. The effects of crack configurations and combined loadings on the energy release rate are shown graphically. Several useful results which may have potential applications to the design and fracture analysis of magnetoelectroelastic structures are given.

Thermal shock resistance analysis methodology of ceramic coating/metal substrate systems

The paper establishes a methodology for the study of thermal shock resistance behavior of ceramic coating/metal substrate systems, based on multiple cracking analysis. The stress criterion and the toughness criterion are used to predict the failure behavior of the system. Multi-scale analysis of the thermal shock resistance of the system is made and variations of the thermal shock resistance of the system with crack density are displayed for different values of coating to substrate thickness ratio. Some critical size parameters, which control the applicability of the stress-based criterion and the fracture mechanics-based criterion for the determination of the thermal shock resistance of the coating/substrate systems, are explored.

Electro-elastostatic analysis of multiple cracks in an infinitely long piezoelectric strip: A hypersingular integral approach

The problem of an arbitrary number of arbitrarily oriented straight cracks in an infinitely long piezoelectric strip is considered here. The cracks are acted by suitably prescribed internal tractions and are assumed to be either electrically impermeable or permeable. A Green's function which satisfies the conditions on the parallel edges of the strip is derived using a Fourier transform technique and applied to formulate the electroelastic crack problem in terms of a system of hypersingular integral equations. Once the hypersingular integral equations are solved, quantities of practical interest, such as the crack tip stress and electric displacement intensity factors, can be easily computed. Some specific cases of the problem are examined.

Analysis of multiple cracks in thin coating on orthotropic substrate under mechanical and residual stresses

The analysis addresses a typical failure development pattern in thin films consisting of a system of multiple surface cracks leading to and branching along or near the interface between the film and the base material. The process is driven by thermal residual stresses and/or mechanical loading. Due to the high temperature gradients during the fabrication process, usually a net of surface cracks develops, which gives the appearance of a granular structure of the surface. A periodic array of parallel surface cracks is assumed. A “unit cell” or single cracked segment attached to the substrate is analyzed instead by assuming the channel cracks are spaced more or less uniformly and perfectly aligned in parallel in the transverse direction of the coating. The analysis is specialized to orthotropic and transversally isotropic materials. The problem is solved using FEM combined with the reciprocal theorem. Matched asymptotic procedure [Leguillon D, Sanchez-Palencia E. Computation of singular solutions in elliptic problems and elasticity. Paris: Masson; 1987; Vu-Quoc L, Tran VX. Singularity analysis and fracture energy-release rate for composites: piecewise homogenous-anisotropic materials. Comput Methods Appl Mech Engng 2006;195:5162–97] is used to derive the change of potential energy. Higher-order terms in the asymptotics are considered. The competition between penetration and debond for periodically distributed edge cracks especially near the critical value of the ratio of fracture spacing to the layer thickness is examined.

Analysis of multiple cracks in laminate composites under anti-plane static loads

This paper investigates multiple cracking of a laminate composite subjected to anti-plane loads. The laminate composite is made up of a central layer sandwiched between two layers of different properties. There is a periodic array of cracks in the central layer along the central axis of the medium. A singular integral equation is formulated in terms of the crack-face displacement. The model developed is applied to the analysis of fibre multiple cracking in fibre-matrix laminate composites. It is also applied to the analysis of matrix cracking in fibre-matrix laminate composites. Numerical results have been given for the effects of crack spacing and constituent volume fraction on the crack tip field intensity factor and stress.

Multiple Crack Analysis in Finite Plates

In this study, interactions of multiple cracks in finite rectangular plates are analyzed. A finite plate is treated as a polygon-shaped plate which can be created by contiguous crack segments embedded in an infinite plate forming an enclosed region so there are no true crack tips remaining around the plate. The problem is formulated in terms of integral equations expressed by edge dislocation distributions representing opening displacement profiles for the cracks with both normal and tangential components. To solve this boundary value problem we employ the superposition approach based on the dislocation distributions requiring the determination of crack opening displacement profiles that satisfy the traction- free condition on interior crack faces and the given boundary tractions on four exterior cracks defining the rectangular plate. Applying the method with a new point allocation scheme reducing the number of evaluation points leads to a set of linear algebraic equations in terms of unknown weighting coefficients of opening displacement profiles. These opening displacement profile components are categorized in terms of polynomial terms which are integers and wedge terms which are rational numbers approximated from irrational wedge eigenvalues to evaluate integrals in closed forms. Once the coefficients of opening displacement profile components are obtained, stress and displacement fields on the entire body, as well as stress intensity factors at the crack tips and kinks are calculated. After the accuracy of the method is shown by comparing the results for different sample problems, the strong interactions of multiple cracks in a rectangular plate under various loading conditions are demonstrated with figures and tables.

Damage Tolerance Analysis of Multiple Cracks Starting from Holes in a Plate Loaded by Bending and Tension

Damage Tolerance Analysis of Multiple Cracks Starting from Holes in a Plate Loaded by Bending and Tension

Multiple-crack analysis with the quasi-higher-order symmetric Galerkin boundary element method

This paper describes the application of the symmetric Galerkin boundary element method (SGBEM) for the analysis of a two-dimensional linear elastic crack problem. The direct SGBEM for the multiple-crack problem is derived using the Betti reciprocal theorem, resulting in a completely symmetric matrix. The auxiliary fictitious state is used to obtain the equations. This approach can deal with any number of traction-free cracks within a single domain. Two-stage interpolation method called the ‘quasi-higher-order element method’ (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher-order elements to interpolate the field variables and, for the numerical integration involved, it further uses interpolation functions to decompose the higher-order elements into lower-order elements so that the existing analytical integration can be applied. Thus, it can be embedded into the present codes with ease and also reduces the computational cost. A finite rectangular plate containing a slanting crack and a kinked crack has been analysed to check the accuracy of the proposed method. A load-carrying fillet welded joint containing several cracks is then analysed, and the stress intensity factors at the crack tips are found to be in complete agreement with the dual-boundary-element method results.

A modified Kachanov method for analysis of solids with multiple cracks

Kachanov proposed an approximate method for the analysis of multiple cracks by assuming that traction in each crack can be represented as a sum of a uniform component and a non-uniform component, and the interaction among the cracks are only due to the uniform components. These assumptions simplify considerably the mathematics and allow ‘closed-form’ solutions to be obtained for some cases. However, it is noted that the assumptions may not be valid when the cracks are very close. Therefore, an improved method of elastic solids with closely spaced multiple cracks is proposed. Unlike the Kachanov method, traction in a crack is decomposed into a linearly varying component and a non-uniform component so that the sum of the two components to be equal to the traction along the crack length. It is further assumed that the interaction effect due to the non-uniform component can be neglected, and therefore, only the effect of the linearly varying component has to be considered. The accuracy of the present method is validated by comparing the results of two and three collinear open cracks obtained by the present method with those of the exact solutions and the original Kachanov method. Applications of the approach in solving non-collinear parallel crack and friction crack problems are also presented to demonstrate the versatility and accuracy of the method.

Numerical Analysis of Multiple Cracks in Concrete Using the Discrete Approach

The discrete crack approach, which has been extensively used for analyzing single cracks, is extended for the numerical analysis of multiple cracks, based on the fictitious crack model and the crack-tip-controlled numerical algorithm. Assuming each crack as an effective crack while restraining the growth of others in turn, an explicit formulation of the mode I type crack propagation for multiple cracks is presented, and a minimum load criterion for crack extension is proposed for its numerical implementation. By eliminating invalid solutions to ensure proper crack behavior, this numerical model is capable of producing a variety of crack propagation patterns. Furthermore, a numerical technique based on the incremental stress analysis is introduced, which replaces the commonly adopted total strain approach for the discrete modeling of single cracks. The accuracy and effectiveness of this numerical method in analyzing multiple-crack problems are demonstrated through a series of parametric studies on four-point bending tests of simple plain concrete beams, as well as an experimental verification with fracture tests on real-size tunnel specimens.

Mixed Mode I, II and III analysis of multiple cracks in plane anisotropic solids by the BEM: a dislocation and point force approach

A direct boundary element method (BEM) for plane anisotropic elasticity is formulated for the generalized plane strain. It deals with the general case when the in-plane and out-of-plane deformations are coupled, including the special case when they are decoupled. The formulation is based on the distributions of point forces and dislocation dipoles following the physical interpretation of Somigliana's identity. We adopt Lekhnitskii-Eshelby-Stroh formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions systematically; the duality relations between the point force and the dislocation solutions are fully exploited. The analytical formulas for the displacement and the traction BEM are applied to the mixed mode crack analysis for multiply cracked anisotropic bodies. We extend the physical interpretation of Somigliana's identity to cracked bodies and represent the crack by the continuous distribution of dislocation dipoles. The mixed mode stress intensity factors ( K I, K II and K III) are determined accurately with the help of the conservation integrals of anisotropic elasticity.

Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method

The Laplace finite element alternating method, which combines the Laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. By the Laplace transform technique, the complicated elastodynamic fracture problem is first transformed into an equivalent static fracture problem in the Laplace transform domain and then solved by the finite element alternating method developed. To do this, an analytical solution by Tsai and Ma for an infinite plate with a semi-infinite crack subjected to exponentially distributed loadings on crack surfaces in the Laplace transform domain is adopted. Finally, the real-time response can be computed by a numerical Laplace inversion algorithm. The technique established is applicable to the calculation of dynamic stress intensity factors of a finite plate with arbitrarily distributed edge cracks or symmetrically distributed central cracks. Only a simple finite element mesh with very limited number of regular elements is necessary. Since the solutions are independent of the size of time increment taken, the dynamic stress intensity factors at any specific instant can even be computed by a single time-step instead of step-by-step computations. The interaction among the cracks and finite geometrical boundaries on the dynamic stress intensity factors is also discussed in detail. [S0021-8936(00)02103-6]

Analysis of Multiple Cracks in a Sandwiched Layer

Analysis of Multiple Cracks in a Sandwiched Layer

Frictional contact analysis of multiple cracks by incremental displacement and resultant traction boundary integral equations

Based on the merits of the dual boundary element technique, a modified dual boundary element technique is extended to deal with the frictional contact of a finite plate with arbitrarily distributed multiple cracks. Besides establishing the incremental displacement boundary integral equation on the outer boundary, the resultant traction boundary integral equation on one of the crack surfaces is also developed. Since the resultant traction instead of incremental traction on the crack surface is introduced, the computed resultant contact tractions under sliding condition satisfy the Coulomb's friction law directly. Hence, as compared with the authors' previous work, only very few computation iterations are required by this method to accurately describe the contact situations of crack surfaces. As a result, not only the linear cracks, but also other types of multiple cracks, for example, curved and kinked cracks, can be tackled. The effects of friction and interaction among cracks on the computation of stress intensity factors are also displayed.

An approximate analysis of perpendicular cracks under general in-plane loading

An approximate closed-form solution is obtained for cracks perpendicular to each other in an elastic solid under mixed-mode loading. It has been observed that torsional fatigue and the fatigue of the spline joint and shafts, often results in perpendicular cracks under general mode I and II loading. Knowledge of the variation of the stress intensity factors for this type of geometry and reduced geometry is essential for an accurate fracture mechanics analysis. To date, no analytical solution exists for this kind of geometry and loading. Kachanov's superpositioning method of analysis of multiple cracks has been extended and used to address the problem. In the application of Kachanov's method, it is necessary to calculate the average of various components of the crack tip stress fields. For the problem considered, the approximate representations for Sneddon's stress fields were developed. Using these approximate expressions it was possible to obtain the closed-form expressions for the average stresses required for use in Kachanov's method. The results indicated that at γ (radial distince to crack length) = 0.283, the proposed solution agreed with the best available numerical solution within 8% and 13% for mode I and II stress intensity factors, respectively.

A fracture mechanics analysis of multiple cracking in coatings

Recent variational mechanics analysis of composite microcracking [J. A. Nairn, J. compos. Mater. 23, 1106 (1989)] has been modified to predict the onset and propagation of multiple cracking in brittle coatings. In the modified analysis, we derived an expression for the total energy released due to the formation of a new crack across the entire cross-section of the coating. Under the assumption that the next coating crack will occur when the energy released on forming that crack reaches the critical energy release rate of the coating (the coating fracture toughness), the new analysis can be used to predict the strain required to form the first coating crack and to predict the coating crack density as a function of increasing applied strain. The predictions were compared to literature results on brittle stress analysis coatings and to experimental results on poly(methyl methacrylate) coatings applied to General Electric Lexan ® polycarbonate substrates. The agreement between theory and experiment was good.

Analysis of multiple cracks in an infinite plate under arbitrary crack surface tractions

Based on the analytical solution derived for a crack under arbitrary crack surface tractions an alternating method is presented to analyze two-dimensional mixed-mode fracture problems with multiple cracks which are arbitrarily distributed in an infinite plate. During the iterative solution process the reversed residual stresses at the location of fictitious cracks induced by other cracks are repeatedly evaluated and treated as new applied loading until the residual stresses on each crack surface are negligible. The influence of interaction effects among cracks on the determination of stresses and deformations is studied in detail. Several numerical example are solved to demonstrate the validity of the method. Good agreement between the computed stress intensity factors and referenced solutions shows the accuracy and efficiency of the this work.

Application Of A Discontinuous Strip Yield ModelTo Multiple Site Damage In Stiffened Sheets

Application Of A Discontinuous Strip Yield ModelTo Multiple Site Damage In Stiffened Sheets