Mixed mode cohesive law

Abstract

A traction-separation relation to model the fracture process is presented. The cohesive law captures the linear elastic and softening behaviour prior to fracture. It also allows for different fracture parameters, such as fracture energy, strength and critical separation in different mode mixities. Thus, the fracture process in mode I (peel), in mode II (shear) or in mixed mode (a combination of peel and shear) can be modelled without the limitation of a common fracture energy in peel and shear. Examples are given in form of FEimplementations of the normalised cohesive law, namely for the Unsymmetrical Double Cantilever Beam (UDCB) specimen and the Mixed-mode double Cantilever Beam (MCB) specimen. Both specimens are adhesively bonded and loaded in mixed-mode.

Influence of adhesive thickness on local interface fracture and overall strength of metallic adhesive bonding structures

“…It is used to describe the ratio between the cohesive stress and separation displacement before the adhesive damage occurs, which is similar to the stiffness coefficient of a spring. Obviously, the initial stiffness is dominated by the elastic properties together with the adhesive thickness t. In the present investigation, following the way in the previous researches [27,28], initial stiffness could be expressed as…”

Thickness-dependent fracture characteristics of ceramic coatings bonded on the alloy substrates

“…Note that the bilinear CZM constitutive equation used here (Eq. (7)) is not directly coupled, not like the quadratic function and the coupled separation laws [29,30]. Considering that the predictions based on the CZM appear to be insensitive to the details of the traction-separation law generally, being dependent on two characteristic parameters, i.e., the strength and the toughness [31], the simple bilinear separation laws were used here, the tension and shear directions were coupled through the mixed-mode failure criterion Eq.…”

Interfacial stress analysis and prediction of debonding for a thin plate bonded to a curved substrate

“…With this approach, the fracture energy is the same in all mode mixities. This is often regarded as a drawback, as the experimental evidence indicates the fracture energy to be often significantly larger in mode II than in mode I (Högberg 2006). b2.…”

“…The cohesive laws are not derived from a potential. Laws of this type have been proposed by Xu and Needleman (1993), and Högberg (2006), among others. These laws allow for different fracture energies in different mode mixities.…”