Nonlinear interface shear fracture of end notched flexure specimens

Abstract

a b s t r a c tThe nonlinear analytical solutions of an end notched flexure adhesive joint or fracture test specimen with identical or dissimilar adherends are investigated. In the current study, a cohesive zone model (with arbitrary nonlinear cohesive laws) based analytical solution is obtained for the interface shear fracture of an end notched flexure (ENF) specimen with sufficiently long bond length. It is found that the scatter and inconsistency in calculating Mode II toughness may be significantly reduced by this model. The present work indicates that the Mode II toughness G IIc under pure shear cracking condition is indeed very weakly dependent on the initial crack length. And this conclusion is well supported by the experimental results found in the literature. The parametric studies show that the interface shear strength is the most dominant parameter on the critical load. It is also interesting to note that with very short initial crack length and identical interface shear strength, higher Mode II toughness indeed cannot increase the critical load. Unlike the high insensitivity of critical load to the detailed shape of the cohesive law for Mode I peel fracture, the shape of the cohesive law becomes relatively important for the critical load of joints under pure Mode II fracture conditions, especially for joints with short initial crack length. The current study may help researchers deepen the understanding of interface shear fracture and clarify some previous concepts on this fracture mode.

A theory of one-dimensional fracture

“…Several recent research works on the topic are quoted here among many others. These are Chen et al [7], Chen [8], Zou et al [9], Wang and Qiao [10], Li et al [11], Nguyen and Levy [12], Yan and Shang [13] and Ouyang and Li [14].…”

Mode II fracture energy in the adhesive bonding of dissimilar substrates: carbon fibre composite to aluminium joints

“…This thickness value causes the product of Young's modulus and the moment of inertia to be constant in both adherents and confirms that the neutral line position is situated in the adhesive layer, as it does not coincide with the midline of the specimen. Using these specific different thicknesses for each adherent allows us to equalise their flexure stiffness, and therefore situates the neutral line in the centre of the adhesive layer Ouyang and Li [33] proposed the following equation to calculate the fracture energy from the ENF test:…”

“…In the ENF test, the calculation of the fracture energy is more sfraightforward if the neufral line position of the adhesive bond is in the cenfre of the union. To achieve this purpose, given that the Poisson's ratios for aluminium and composite have similar values (0.26 and 0.28, respectively), the following decoupling condition applies for the flexure test [33]: where hi is the thickness of the aluminium, h2 is the thickness of the composite, Ei is Young's modulus for aluminium and E2 is Young's modulus for the composite.…”

Degradación ambiental y en condiciones adversas de adhesivos estructurales : análisis y consideraciones técnicas para su aplicación industrial

“…En este tipo de ensayo, el cálculo de la energía de fractura es más sencillo si la posición neutral de la línea de unión adhesiva está en el centro de la unión. Para lograr este propósito, dado que los coeficientes de Poisson para el aluminio y el compuesto tienen valores similares (0,26 y 0,28, respectivamente), la siguiente condición de desacoplamiento se aplica para el ensayo de flexión [72]:…”

“…El uso de estos espesores específicos diferentes para cada adherente permite igualar su rigidez de flexión, y por lo tanto se sitúa la línea neutra en el centro de la capa adhesiva. Ouyang y Li [72] propusieron la siguiente ecuación para calcular la energía de fractura de la prueba ENF:…”