Abstract

In order to obtain Mode II fracture toughness of unidirectional fiber composite materials, the End-Loaded Split (ELS) has enjoyed great success because of its higher stability. As a result, crack growth initiation and propagation values are obtained, the latter being especially used in interlaminar progressive damage models. The propagation values must be obtained when the Failure Process Zone (FPZ) has completely developed. In delamination tests of unidirectional composites, such as those contemplated in ISO 15114, the dimension of the FPZ can be neglected against the rest of the dimensions of the specimen, whereby the self-similar crack growth is reached just after the initiation of the crack propagation. However, in adhesive joints, the dimension of the FPZ increases significantly due to the plasticity of the adhesives. And even it can be larger than the entire length reserved for crack propagation. When this occurs, only initiation values are obtained, always inferior to the values of propagation, being these values too conservative to reproduce the behaviour of the joint. In this paper we present a methodology to define the configuration of the ELS test and the specimen dimensions required to obtain propagation results in adhesive joints. The methodology defined is based on two criteria that take into account the length of the FPZ and the stability of the test. As a result, a domain of validity of the test is obtained, which, for a certain type of adhesive and specimen configuration, it indicated is there will be propagation or not.

Abstract

En este trabajo se presenta y valida numéricamente un novedoso procedimiento de extrapolación para predecir las leyes cohesivas de uniones adhesivas en modo I y II.

En primer lugar, partiendo de los métodos de reducción de datos basados en la variación de la flexibilidad recientemente propuestos para extraer las leyes cohesivas, se definen nuevas expresiones factorizadas con respecto a la carga aplicada y a los espesores de adhesivo y adherente de la flexibilidad (C0i), la Integral–J (J0i) y el desplazamiento de la punta de la grieta (Δ0i) para cada modo de fractura.

Suponiendo que todos los efectos asociados al daño se incluyen en la longitud de grieta equivalente, y de acuerdo con las expresiones polinómicas de J0i, C0i y Δ0i con respecto a la misma, se obtienen relaciones invariantes entre J0i-C0i y Δ0i-C0i para cualquier relación de espesores adhesivo-adherente de un sistema material y configuración de ensayo determinados, tanto en modo I como en modo II.

Por último, se presenta un procedimiento de extrapolación basado en las curvas calibradas J0i-C0i y Δ0i-C0i, que permite estimar las leyes cohesivas para un amplio rango de relación de espesores adhesivo-adherente de un sistema material dado procesando únicamente la curva carga-desplazamiento del ensayo.

Abstract

The fundamentals of new analytical models based on energy and coenergy of deformation are explained to analytically address asymmetric interlaminar fracture tests. After reviewing some concepts of laminated beam theory, the energy release rate as a function of coenergy is determined from a global point of view, including in an unprecedented way the contribution of hygrothermal stresses. On the other hand, after the determination of the J integral in the cohesive zone, the conditions required for the asymmetric fracture tests to occur in pure mode in linear elastic fracture are explained, based on the forces and displacements of the crack tip. Furthermore, knowing these forces and displacements, it is possible to determine the energy release rate that corresponds to each fracture mode.

Abstract

A novel method is presented for the determination of mode II cohesive law for the characterization of delamination in thin adhesive joints The proposed method is based on the three point end notched flexure test. The data reduction method used is the Beam Theory including Bending Rotation effects method (BTBR), which includes the effect of local deformations, shear and bending rotations. By this method, the initial crack length, the apparent crack length during the crack advance, and the mode II resistance curve are determined. The relative shear displacement at the crack tip is determined as a function of the apparent crack advance that occurs when the generation of the fracture zone progresses. In order to determine the shear displacement an analytical analytical model based on the classical theory of beams is used. Finally, the fracture toughness versus the shear relative displacement is represented and the cohesive law is determined by numerical derivation.