Crack onset and growth at the fibre–matrix interface under a remote biaxial transverse load. Application of a coupled stress and energy criterion

A theoretical model for prediction of the critical load generating a crack onset at the fibrematrix interface under a remote biaxial transverse load is presented. In particular, this work is focused on the tension dominated failure. After an abrupt onset the crack grows unstably up to achieving an arrest length. A simple plane strain model of a single circular inclusion surrounded by an unbounded matrix allows to obtain conclusions approximately valid for a dilute fibre packing. Linear isotropic elastic behaviour is assumed for both inclusion and matrix. Two classical elastic solutions for both perfectly bonded and partially debonded circular inclusions are used together with a coupled stress and energy criterion, proposed recently in the framework of Finite Fracture Mechanics, and a phenomenological law for fracture toughness of interface cracks growing in fracture mixed mode. The obtained analytical and semi-analytical expressions make easy to study the influence of all the dimensionless parameters governing the fibrematrix system behaviour: Dundurs elastic bimaterial constants $\alpha$ and $\beta$, the interface brittleness number $\gamma$, the load biaxiality parameter $\eta$, and the fracture mode-sensitivity parameter $\lambda$. A size effect of the inclusion radius on the critical load is predicted, smaller inclusions being stronger and less dependent on the secondary load. Finally, an experimental procedure for measurement of the fibre-matrix interface fracture and strength properties is proposed.Ministerio de Ciencia e InnovaciónJunta de AndalucíaMinisterio de Educació

Formulación simétrica de las ecuaciones integrales de contorno para materiales elásticos anisótropos en 2D

II CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Madrid, 25 al 28 de noviembre, 1997El estudio presente forma la base teórica de la implementación de un código del Método de los Elementos de Contorno (MEC) Simétrico para el análisis tensional de materiales anisótropos homogéneos en estados de defomación plana generalizada o tensión plana. Se discuten algunas ventajas que tiene el MEC Simétrico frente al enfoque convencional. Se desarrolla un planteamiento débil y simétrico de las Ecuaciones Integrales de Contorno (EIC) para un problema elástico mixto. Se introducen expresiones explícitas para los núcleos integrales que aparecen en estas EIC. Se desarrolla un procedimiento simple para la regularización de la integral hipersingular que se precisa para un cálculo eficaz de la forma cuadrática. correspondiente.The present study providcs the theorclical basis for an implementation of a Symmetrical Boundary Element Method (SBEM) code for stress analysis of anisotropic ho· mogeneous materials subjected to a generalised plane deformation or plane stre~s state. Sorne advantages of SBEM over the conventional approach are discussed. A weak symmetrical formula.tion of Boundary Integral Equations for a mixed clastic problem is given. Explicit expressions of the integral kcrnels are introduced. A simple procedure of regularization of the hypersingular integral, required for an efficient evaluation of the corresponding quadratic form, is develope

Formulación de la identidad de Somigliana de tensiones en la elasticidad anisótropa bidimensional

CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Málaga en 1999El desarrollo de las aplicaciones de los materiales compuestos requiere cada vez más aplicaciones de los métodos numéricos, y en particular del Método de los Elementos de Contorno (MEC), al análisis tensional de los materiales anisótropos elásticos, para modelar desde un punto de vista macroscópico los materiales compuestos. El MEC se aplica a la resolución numérica de la Ecuaciones Integrales de Contorno (EIC) correspondientes a un problema elástico. El presente trabajo desarrolla una formulación general de una de estas EIC, llamada Identidad de Somigliana de Tensiones, considerándola no sólo en los puntos de contorno suaves sino también en las esquinas. Resultado de un análisis asintótico es la formulación de esta EIC en forma de suma de términos libres y una integral en el sentido de Parte Finita de Hadamard. Las fórmulas analíticas que se presentan de los tensores coeficientes de los términos libres pueden implementarse con facilidad en códigos basados en el MEC

Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion

The plane strain problem of a single circular cylindrical inclusion embedded in an unbounded matrix subjected to a remote uniform uniaxial transverse tension is studied. A theoretical model for the simultaneous prediction of \emph{the initial size of a crack originated at the inclusion/matrix interface} (or equivalently the initial polar angle of this crack) and of \emph{the critical remote tension required to originate this crack} is developed. Isotropic and linear elastic behaviour of both materials, with the inclusion being stiffer than the matrix, is assumed. The interface is considered to be strong (providing continuity of displacements and tractions across the interface surface) and brittle. The model developed is based on the classical analytic solutions for the above-mentioned inclusion problem without and with a crack situated at the inclusion/matrix interface and a recently introduced coupled stress and energy criterion of failure by Leguillon (\emph{Eur. J. Mech. A/Solids, 21, pp. 61--72, 2002}). A new dimensionless structural parameter $\gamma$, depending on bimaterial and interface properties together with the inclusion radius $a$, which plays a key role in characterizing the interface crack onset, is introduced. Asymptotic behaviour of the predicted critical remote tension and the interface crack length/polar angle at the onset are characterized for small and large values of $\gamma$ and $a$. A size effect inherent to this problem is predicted and analysed. The following asymptotic characteristics of this size effect are noteworthy: \emph{i)} for small inclusion radii $a$, the polar angle of the crack at onset is constant (independent of $a$), whereas the critical remote tension increases with decreasing $a$, being inversely proportional to the square root of $a$; \emph{ii)} for large inclusion radii $a$, the length of the crack at onset and the critical remote tension are approximately constant.Ministerio de Educación, Cultura y DeporteJunta de Andalucí

Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates

The authors are indebted to Professors Federico París and Antonio Blázquez (University of Seville) for inspiring discussions. The authors wish to thank the Royal Society (UK) International Exchanges Scheme (award # IE141234), the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (Projects MAT2012-37387 and MAT2015-71036-P) for supporting this research.Peer reviewedPostprin

Workshop 2 Expanding Horizons: New strategies for multifield fracture problems across scales in heterogeneous systems for energy, health and transport

NewFrac Workshop-2 is especially focused on Phase Field and Finite Fracture Mechanics. It is open to senior researchers and PhD students in fracture mechanics.Horizonte 2020 (Unión Europea) 86106