Aldino Piva

Crack propagation in an orthotropic medium

Abstract In this paper, the partial differential equations related to elastodynamic plane problems in an orthotropic medium are reduced by means of composite transformations to a first order elliptic system of the Cauchy-Riemann type. This result justifies the representation of stress and displacement fields in terms of holomorphic functions defined into appropriate complex domains. The above formulation has been used to solve the boundary value problem concerned with the steady state propagation of a finite straight crack in an orthotropic medium. Some asymptotic results are also represented and briefly discussed.

Biaxial load effects on a crack between dissimilar media

Abstract An analysis of the in-plane biaxial loading of two dissimilar materials with a crack along their common interface is considered. The elastic solution is obtained by the application of the complex variable technique coupled with the principle of superposition. The stress and displacement fields near the tip of the crack are described and the influence of the load parallel to the crack direction is shown. Then a failure criterion is formulated to discuss the debonding along the interface or the brittle fracture of the elastic system. In particular the effect of the non-singular terms on the critical applied tensile stress and on the deviation of the interfacial crack into one of the adjacent media is analyzed.

Crack propagation in an orthotropic medium under general loading

Abstract The elastodynamic response of a finite crack steadily propagating in an orthotropic medium, acted upon at infinity by uniform biaxial and shear loads, is studied. In particular, the effects of varying crack velocity as well as the ratio of shear load to tensile load are described. The action of material orthotropy on various quantities describing the crack propagation characteristics is pointed out.

Fracture behaviour by two cracks around an elliptic rigid inclusion

Abstract An analysis is presented for the in-plane biaxial loading of an elastic system consisting of a partially bonded rigid elliptic inclusion embedded in an infinite matrix where the bond imperfections are two symmetric cracks. The boundary value problem is formulated through the complex variable technique in the case of linearly elastic matrix under general biaxial loading at infinity. The elastic solution is obtained for a simplified model by assuming incompressibility and plane strain conditions for the matrix. In particular, stress and displacement fields are represented and discussed. Moreover, a stress criterion, which permits to take into account, either the crack extension at the interface or its deviation into the matrix, is considered to study the fracture response of the elastic system.

An alternative complex variable formulation for an inclined crack in an orthotropic medium

Abstract Of concern in this paper is the study of the elastostatic fracture response of an orthotropic plate with an inclined crack and subjected at infinity to a biaxial uniform load. To this end an unconventional approach to the derivation of the complex variable expressions of the elastic fields is proposed. The above formulation has been used to solve the boundary value problem as superposition of Mode-I and Mode-II crack problems and it is shown that the near tip asymptotic expressions of stress and displacement fields are affected by non-singular terms originated by load biaxiality. The maximum tensile stress criterion is applied in order to investigate the effects of non-singular terms on the angle of crack extension.

On the inclined crack problem in an orthotropic medium under biaxial loading

Abstract The problem of an inclined crack in an orthotropic medium under biaxial loading is analyzed. A suitable coordinate transformation is introduced and two decoupled systems of the Cauchy–Riemann type are obtained in terms of complex potentials. The crack problem is solved by using the method of analytic continuation and closed form expressions of the near tip stress and displacement fields are derived. The influence of load biaxiality on the stress intensity factors, as well as on the local stress components is studied and graphically represented. Moreover, the action of material orthotropy on various quantities describing the crack characteristic is pointed out.

Plane strain interfacial fracture analysis of a bimaterial incompressible body

Abstract In a previous paper an analysis of the biaxial loading of two dissimilar media with a crack along the common interface was studied. Here, a further discussion of the above problem is reported assuming plane strain conditions, incompressible media and biaxial and shear loading at infinity. A global fracture criterion also taking account of the applied shear stress is considered to discuss the brittle fracture response of the elastic system. Particular attention is paid to analysing the influence of the load parallel to the crack direction and that of the shear stress on the critical applied tensile stress, as well as on the branching angles. Some results illustrating the criterion formulated are represented graphically.

Crack paths in sheets of brittle material

Abstract In this paper a new method based on the maximum tensile stress criterion is proposed in order to predict the crack paths in sheets of brittle materials under biaxial loading. The proposed approach allows to obtain the crack trajectory avoiding integral representations and is more simple and direct that the perturbation techniques introduced in [34–37]. Moreover, the above method takes into account of some experimental features concerning the asymptotic behaviour of crack paths. In view of applications to slightly curved cracks, the knowledge of the stress intensity factors K I and II is needed and in this aim the perturbation method of [37] is used for a slightly curved elliptical arc crack.

Parameter estimation from measured displacements of crack edges in an isotropic material

Abstract In recent years, inverse problems have been extensively treated in several branches of science. The approach is to determine the optimal estimates of the model parameters by minimizing a selected measure-of-fit between the responses of the system and the model. Relatively few contributions have been made in solid mechanics to estimate the elastic parameters from some sort of measured data. Within the framework of Fracture Mechanics, much work has been carried out to identify both the location and magnitude of cracks from experimentally measured responses. Less work, however, has been done to identify the parameters of elastic bodies from crack information. The purpose of the present paper is to identify the elastic parameters of an isotropic material, as well as the crack width and magnitude of the load applied at infinity causing Mode I displacement, from measured displacements of crack edges. This paper consists of two parts. In the first part, the expressions for the three mode displacements of crack edges in a linear elastic, homogeneous and isotropic material are derived through the complex variable approach. In the second part, a statistical identification method, based on Taylor expansion of experimental data in the neighbourhood of initial parameters, is used. The experimental data are Mode I and III displacements, measured in the middle of the crack width. A number of experimental data equal to or less than the number of identified parameters is used. It is also shown that unsatisfactory results are obtained using a least-squares method. The convergence of the identified parameters for various numbers and types of experimental data is illustrated.

Biaxial Load Effect on Crack Initiation for Orthotropic Materials

This paper is concerned with the study of the elastostatic fracture response of an orthotropic plate with an inclined crack and subjected at infinity to a biaxial uniform load. To this end an unconventional approach to the derivation of the complex variable expressions of the elastic fields is proposed. The above formulation has been used to solve the boundary value problem as superposition of Mode-I and Mode-II crack problems and it is shown that the near tip asymptotic expressions of stress and displacement fields are affected by non-singular terms originated by load biaxiality. The maximum circumferential tensile stress criterion is applied in order to investigate the effects of non-singular terms on the angle of crack extension.