A micromechanical model of a hard interface with micro-cracking damage

Abstract

Bonding techniques are increasingly used in many industrial fields. Modelling the under-load damaging behavior of hard structural adhesives is still an open challenge. This work proposes a new hard interface analytical model with evolutive micro-cracking damage. The model is obtained within a rigorous theoretical framework combining asymptotic theory and micromechanical homogenization. Main new features are: (i) the adoption of two dual homogenization approaches; (ii) the formulation of a thermodynamically-based damage evolution law for hard interfaces. The interface model is able to describe both ductile and brittle damage behavior of hard structural adhesives. Provided examples on the structural behavior, under several loads, suggest the suitability of the proposed interface model as a modelling strategy for hard structural adhesives with micro-cracking damage.

Numerical Assessment of Damage Parameters for a Hard Interface Model

“…In this section, a brief overview of the imperfect interface model is proposed. For an extensive description of the formulation, one refers to [ 16 ]. The model consists of a law of hard imperfect contact coupled with a damage evolution law.…”

“…Note that by including Equations ( 5 ), ( 7 ) or ( 8 ) in the expression of the interface stiffness tensor (Equation ( 4 )), a different dependency of the imperfect interface law on the crack density , is obtained. Particularly, it has been previously established by authors that the KS scheme allows us to describe imperfect interfaces with ductile damaging behaviour, while the WG scheme is suitable to describe interfaces with brittle damaging behavior [ 16 ].…”

“…In this section, a possible description of the evolving behaviour of the cracks density is given by drawing on further works by authors [ 11 , 16 ]. Damage in the adhesive joint is assumed to be caused by a microcracks accumulation and damage parameter is assumed to strictly increase in time.…”

“…The hard imperfect interface model with damage formulated by authors in [ 16 ] has been chosen to apply an estimation procedure of damage parameters. In particular, this interface model is suitable to describe structural adhesives as stiff as substrates [ 17 ].…”

“…These parameters represent respectively a damage viscosity ( ) and a damage energy threshold ( ) and they are related to the damage evolution law, as detailed in what follows. Note that the model sensitivity on these parameters has been already investigated by authors in [ 16 ], thus it is not the subject of this work.…”