On the effects of a crack propagating toward the interface of a bimaterial system

This paper deals with the influence of matrix cracks on the failure mode of bimaterial systems and composite materials. In order to investigate such an influence, the stress field near a crack embedded into the more yielding material and propagating perpendicularly to the interface, has been analyzed by using systematic numerical simulations. Such analysis has shown that the crack propagation give rises to transversal stresses that can damage the reinforcing materials when this has low modulus, as glass fibers, or low transversal strength, such as carbon fibers. Moreover, the longitudinal stress concentration can damage the reinforcing material only if this has high stiffness, as in the case of aramid and carbon fibers.Also, the numerical results have permitted to implement simple formulas that allows the user an accurate evaluation of the SIF as well as to predict possible debonding or fiber splitting phenomena. Finally, the SIFs evaluated numerically have been corroborated by experimental tests carried out by using an efficient procedure based on RGB digital photoelasticity.     

Critical study of existing solutions for a penny-shaped interface crack, comparing with a new boundary element solution allowing for frictionless contact

A numerical study of the fundamental problem of a pressurized penny-shaped crack at the interface of two dissimilar half spaces is carried out allowing for the possibility of frictionless contact between crack faces. A new, highly accurate axi-symmetric formulation of the boundary element method (BEM) for the solution of elastic contact problems is employed. The correctness and accuracy of available predictions of different kinds for several key characteristics of the solution of this problem are checked. First, comparison of the BEM results for the near-tip contact length shows a very good agreement with some existing predictions. Second, the global solution obtained by BEM is compared with existing asymptotic solutions, obtained with both the open and the frictionless contact models. BEM results show that at the closest neighborhood to the crack tip the global solution of the problem is governed by the first term of the asymptotic solution of the frictionless contact model (up to a distance of the order of a fraction of the near-tip contact length). After a small transition region, in an adjacent surrounding zone whose extent is almost independent of the near-tip contact length, the global solution of the problem is governed by the first term of the asymptotic solution of the open model. As a result of the comparison presented, the regions in which the classical fracture parameters, stress intensity factor (SIF) and energy release rate, can be accurately obtained from the global numerical solution of a crack of this kind have been determined. Third, BEM results and previous estimations show certain discrepancies with a recently published closed form solution of the near-tip contact length and the mode II SIF of the frictionless contact model. A new closed form expression of this mode II SIF, derived from the asymptotic solution of the open model, is proposed in this paper.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Transient thermoelectroelastic response of a functionally graded piezoelectric strip with a penny-shaped crack

Transient response of a penny-shaped crack in a plate of a functionally graded piezoelectric material (FGPM) is studied under thermal shock loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are completely insulated. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations which are solved numerically. The intensity factors vs. time for various crack size, crack position and material nonhomogeneity are obtained.     

Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor

In this paper we investigate the stress intensity factors (SIFs) of multiple penny-shaped cracks in an elastic solid cylinder under mode I (axial tension) loading. The cracks are located symmetrically and in parallel to one another in the isotropic cylinder. The fractal-like finite element method (FFEM) is employed to study the interaction of multiple cracks and to demonstrate the efficiency of the FFEM for multiple crack problems. The results show that the SIF values of the inner cracks, which are denoted as crack number 1,2,3,…,(n+1)/2 of a stack of n parallel cracks, are lower than the SIF values of a single crack by between 16% and 48%. Also, the outermost crack, that is the crack closest to the boundaries of a multiple cracked body, has the highest SIF values and is, therefore, likely to fail first.     

A penny-shaped crack in a functionally graded piezoelectric strip under thermal loading

The mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip with a penny-shaped crack is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. The thermal and electromechanical problems are reduced to singular integral equations and solved numerically. The stress and electric displacement intensity factors are presented for different crack size, crack position and material nonhomogeneity.     

Fracture of a finite piezoelectric layer with a penny-shaped crack

This paper studies a penny-shaped crack in a finite thickness piezoelectric material layer. The piezoelectric medium is subjected to a thermal flux on its top and bottom surfaces. Both thermally insulated crack and heated crack are considered. Numerical solution for the finite layer thickness is obtained through the solution of a pair of dual integral equations. The result reduces to the closed form solution when the thickness of the piezoelectric layer becomes infinite. Exact expressions for the stress and electric displacement at the crack border are given as a function of the stress intensity factor, which is determined by the applied thermal flux. This paper is useful for the reliability design of piezoelectric materials in thermal environments.     

Fracture analysis of a magnetoelectroelastic solid with a penny-shaped crack by considering the effects of the opening crack interior

A magnetoelectroelastic analysis for a penny-shaped crack embedded in an infinite piezoelectromagnetic material is made. Taking into account the fact that electric and magnetic fields can permeate through the opening crack, the electric and magnetic boundary conditions at the crack surfaces are assumed to be semi-permeable, or depend nonlinearly on the crack opening displacement. For the case of a circular crack normal to the poling direction, the associated mixed boundary value problem is reduced to solving dual integral equations by applying the Hankel transform technique. An entire magnetoelectroelastic field is obtained in simple and explicit form. Numerical results for a cracked BaTiO₃-CoFe₂O₄ material reveal the dependence of the electric displacement and magnetic induction at the crack surfaces with applied mechanical loading. The influences of applied electric and magnetic loadings on normalized fracture parameters are illustrated graphically for a vacuum circular crack. The impermeable and permeable cracks can be treated as two limiting cases of the present.     

Finite element study of a penny-shaped crack along the interface in a bi-material cylinder

A contemporary approach to the analysis of interface cracks in bi-material cylinders using finite elements is presented. From results obtained with a commercial finite element code using regular and singular isoparametric elements, three fracture mechanics techniques are considered to study the interface crack problem and are presented in a fundamental manner. These are the stress intensity factor evaluation by the crack opening displacement method, the strain energy release rate evaluation using the modified crack closure integral method, and the J-integral evaluation using the virtual crack extension technique. Only the finite element results in the vicinity of the crack are then needed. The accuracy of the proposed approach is assessed by solving standard test problems with known solutions. In particular, the mode I problem of a penny-shaped crack in a homogeneous isotropic cylinder under remote tension loading is used as a standard test case. Finally, the mixed-mode (I and II) problem of a penny-shaped crack along the interface in a bi-material cylinder under three loading conditions is studied in detail. Numerical results are presented to quantify the combined effects of geometry and material discontinuities on the strain energy release rate.     

Improved quarter-point crack tip element

We present a modification to the quarter-point crack tip element and employ this element in two-dimensional boundary integral fracture analysis. The standard singular element is adjusted so that the near-tip crack opening displacement satisfies a known constraint: the coefficient of the term which is linear in the distance to the tip must vanish. Stress intensity factors calculated with the displacement correlation technique are shown to be highly accurate, and significantly more accurate than with the standard element. The improvements are especially dramatic for mixed-mode problems involving curved and interacting cracks.     

Fracture mechanics in fatigue calculations as the assistance in structural design. Case study

A case study originated from a request to perform fatigue calculations on a partial penetration weld in a steel casting on a new heavy lift ship. The ship has a special lifting system for lifting and transporting topsides of offshore oil/gas platforms. There are many sizes of offshore platforms so the lift system is designed to move along the vessel on rails, which are part of the main deck of the ship hull. The loads passing into the rails during lift operations are large, and massive steel castings of complex shapes are used to distribute these loads into the hull. The castings are very thick so it is difficult to achieve full penetration welds, and therefore the initial design proposed partial penetration welds. In order to decide if the partial penetration welds were adequate, a fatigue assessment was carried out using a fracture mechanics approach based on BS7910. Different possibilities of the bevelling of castings edges in preparation for welding were considered in the stress analysis and in the crack growth estimations. In the areas of the ship hull which experienced high dynamic stress ranges none of the different possibilities showed acceptable fatigue life, and would demand re-design. The stress intensity factors obtained through the extensive finite element analysis were compared with the analytical solutions available in literature. Both results showed good correspondence.     

Antiplane crack analysis of a functionally graded material by a BIEM

Elastostatic analysis of an antiplane crack in a functionally graded material (FGM) is performed by using a hypersingular boundary integral equation method (BIEM). An exponential law is applied to describe the spatial variation of the shear modulus of the FGM. A Galerkin method is applied for the numerical solution of the hypersingular traction BIE. Both unidirectional and bidirectional material gradations are investigated. Stress intensity factors for an infinite and linear elastic FGM containing a finite crack subjected to an antiplane crack-face loading are presented and discussed. The influences of the material gradients and the crack orientation on the stress intensity factors are analyzed.     

Fracture analysis of a piezoelectric layer with a penny-shaped and energetically consistent crack

The problem of an eccentric penny-shaped crack embedded in a piezoelectric layer is addressed by using the energetically consistent boundary conditions. The Hankel transform technique is applied to solve the boundary-value problem. Then two coupling Fredholm integral equations are derived and solved by using the composite Simpson’s rule. The intensity factors of stress, electric displacement, crack opening displacement and electric potential together with the energy release rate are further given. The effects of the thickness of a piezoelectric layer and the discharge field inside the penny-shaped crack on the fracture parameters of concern are discussed through numerical computations. The observations reveal that an increase of the discharge field decreases the stress intensity factor and the energy release rate. An eccentric penny-shaped crack is easier to propagate than a mid-plane one in a piezoelectric layer, and the geometry of the crack along with the layer thickness have significant influences on the electrostatic traction acting on the crack faces. The solutions for a penny-shaped dielectric crack in an infinite or a semi-infinite piezoelectric material can be obtained easily.     

Complex variable method of computing Jk for bi-material interface cracks

A method using functions of a complex variable is developed for evaluation of J₁ and a modified J₂ integrals for bi-material interface cracks. This method, used in conjunction with the finite element method, would be useful in the prediction of stress intensity factors for cracks lying between the interface of two dissimilar materials. Since the direct evaluation of J₂ poses difficulties in modeling the singular behavior in the near vicinity around the crack tip for bi-material crack problems, it is modified by evaluating it around a contour path of small radius from the crack tip within the singularity dominated zone. It is shown that the stress intensity factors for a bi-material interface crack can be accurately evaluated using these j_k integrals.     

Finite element analysis of bi-material interface notch crack behaviour

The finite element method is extended to the analysis of the behaviour of an interface crack in bi-material specimen with a central hole. First, only the notch effect is considered, the field of stress and variation of the stress concentration factor as a function of the Young’s modulus ratio are determined. Secondly, the notch interface crack behaviour is investigated, the variations of the stress intensity factor versus the Young’s modulus ratio and crack length are shown as well as the distribution of stresses in the plate and along the interface.     

Optimal and noise-robust extraction of Fracture Mechanics parameters from kinematic measurements

The paper is devoted to an optimal (i.e. noise-robust) determination of stress intensity factors and crack tip locations based on a displacement field measured over an arbitrarily shaped domain. As the minimization of the noise sensitivity is included within the proposed extraction technique, this is especially dedicated to corrupted displacement fields, e.g. as measured by an optical technique. The main idea is to construct for mode I and II fields an extracting function so that its L₂ scalar product with the actual displacement field yields the sought parameter. The extracting function is also constrained to be orthogonal to a set of admissible elastic fields. Two applications are considered to illustrate the technique. The first example deals with a fatigue crack in steel for which small scale yielding occurs. A second example with a low signal/noise ratio illustrates the capability of the approach to analyze a crack in silicon carbide with sub-pixel openings.     

Influence of bimaterial interface on kinking behaviour of a crack growth emanating from notch

The mechanism of crack deviation by an interface modifies considerably the behaviour of bimaterials fracture. Their fracture resistance is highly affected by the difference of the elastic properties of the bonded materials. In this work, the finite element method is applied to analyze the behaviour of a crack emanating from semicircular notch root growing in interface ceramic/metal composites and perpendicularly to this interface. The obtained results showed that the crack grew to interface from harder material, its energy decreased at the approach of the interface, in this case was retarded; an inverse phenomenon occurs if the crack is propagated towards a lower strength material and its energy increases, it has tendency to accelerate. The effects of geometry on the crack deflection near the interface are also discussed.     

Applications of conservation integral to indentation with a rigid punch

When a substrate of the brittle material is indented by a relatively rigid, square-ended punch, a singular stress field and K-dominant region will arise at the near-surface adjacent to the punch corners. The singularity of this stress field is identical with the mode I crack. The stress intensity factor in this case represents the intensification of the stress fields induced by indentation. In present article, a new method to determine the stress intensity factors of the indentation problems is developed based on the conservation law. The physical meanings of the proposed method and some numerical analysis have been investigated.     

Stress field near interface edge of elastic-creep bi-material

Stress fields on elastic-creep bi-material interfaces with different geometry of the interface edge are analyzed by finite element method. The results reveal that the stress highly concentrates near the interface edge at the loading instant and it gradually decreases as the creep-dominated zone expands from the small-scale creep to the large-scale creep. The stress singularity due to creep which resembles the HRR stress singularity appears near the interface edge in all cases. The stress intensity near the interface edge time-dependently decreases and becomes constant when the transition reaches the steady state. The magnitude is scarcely influenced by the edge shape of elastic material, though it depends on the edge shape of creep material. The stress intensity during the transition can be approximately predicted by the J-integral at the loading instant.