Use of J-integral as fracture parameter in simplified analysis of bonded joints

Abstract

The simplified analytical approaches based on beam or plates theories are commonly used to solve the stress field in bonded laminates. However, to be correctly applied, these methods require an appropriate fracture criterion. In this paper, the use of J-integral as a fracture parameter in these simplified analytical approaches is discussed. After examining its path independence, the J-integral is calculated along two particular paths showing first that this integral is equal to the product of the strain energy at the end of the joint (i.e. at the debond tip) by its thickness. This relationship reveals the partitioning of the opening mode I and the shearing mode II. Secondly, the general expression of J as a function of the loading conditions is derived. It is shown that this parameter can be related to the strain energy release rate in the cases of small scale yielding conditions and for usual fracture mechanics specimens. NomenclatureJ = Rice integral W = Strain energy density T = Tension vector s = Curvilinear abscissa u = Displacement vector U, V = x, y-components of the displacement = Stress tensor h0 = Adhesive thickness r, a~. = Shear and normal stresses in the adhesive 7, ey = Shear and normal strains in the adhesive h~ = Adherend thickness Ni, Q/ = Normal and shear forces in the adherend i Mi = Bending moment in the adherend i u~, v/ = x, y displacements of the neutral line fl~ = Bending rotation a~,, zx~. = Components of stress tensor in the adherends e, xx, 7xy = Components of strain tensor in the adherends

Comparison of solder joint fracture behavior in Arcan and DCB specimens

“…The J-integral is the predominant method to calculate the fracture energy for elastic-plastic fracture [29], and has been used extensively in the fracture analyses of layered materials (e.g. [6,8,12,[30][31][32][33]). For mixed-mode fracture of 2 mm solder joints, in particular, this method was validated in Ref.…”

An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints

“…Assuming the presence of an initial crack, judiciously localized and sized by the user, it allows for the computation of strain energy release rate or J-integral parameters at crack tip as a function of applied forces or adhesive stresses (Fraise 1993, Tong 1994, Fernlund 2007, Da Silva 2012. In the coupled stress and energy criterion approach, the crack length at initiation is not assumed but derived from the analysis (Leguillon 2002.…”

Predicting fracture of solder joints with different constraint factors

“…The J ‐integral is the major method to calculate the fracture energy for elastic‐plastic fracture, and has been used vastly in the fracture analyses of layered ductile materials (eg, Azari et al, Nourani and Spelt, Nourani and Spelt, Fernlund et al, Fraisse and Schmit, Lau, Nadimpalli and Spelt). The measured facture load was used in FEM with a nonlinear load‐geometry solution method to calculate the critical strain energy release rate at crack initiation, J ci , using an elastic‐perfectly plastic model for the solder.…”