A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode I and mode II fracture energies

Abstract

The present paper deals with the derivation of an interface model characterized by macroscopic fracture energies which are different in modes I and II, the macroscopic fracture energy being the total energy dissipated per unit of fracture area.It is first shown that thermo-dynamical consistency for a model governed by a single damage variable, combined with the choice of employing an equivalent relative displacement and of a linear softening in the stress-relative displacement law, leads to the coincidence of fracture energies in modes I and II. To retrieve the experimental evidence of a greater fracture energy in mode II, a micro-structured geometry is considered at the typical point of the interface where a Representative Interface Element (RIE) characterized by a periodic arrangement of distinct inclined planes is introduced. The interaction within each of these surfaces is governed by a coupled damage-friction law.A sensitivity analysis of the correlation between micromechanical parameters and the numerically computed single-point microstructural response in mode II is reported. An assessment of the capability of the model in predicting different mixed mode fracture energies is carried out both at the single microstructural interface point level and with a structural example. For the latter a double cantilever beam with uneven bending moments has been analyzed and numerical results are compared with experimental data reported in the literature for 1 different values of mode mixity.

A mixed-mode cohesive-zone model accounting for finite dilation and asperity degradation

“…Accordingly, on C the displacement field is allowed to be discontinuous. Following Serpieri and Alfano (2011) and Serpieri et al (2015), the main features of the present formulation are:…”

“…The progressive degradation of the interlocking effect, due to the rupture of the asperities and associated flattening of the fracture surface is captured by a progressive reduction of the inclination angles of the microplanes in the RIA. In the following subsection the essential features of the model proposed by Serpieri and Alfano (2011) and Serpieri et al (2015) are recalled. Subsequently, in Sections 2.2 and 2.3 the two above mentioned enhancements of the model are described in more detail.…”

“…In order to use, on each microplane, an associated-type damage evolution law with the use of a single damage variable in a neater and thermodynamically consistent way, the same fracture energy in modes I and II are employed (Serpieri et al, 2015). At the macro-scale, the increase in fracture energy which is typically measured for increasing mode-II/mode-I ratio is retrieved thanks to the interaction between interlocking and friction captured by the multi-scale model.…”

“…Unlike the models in Serpieri and Alfano (2011) and Serpieri et al (2015), here the finite depth of the asperities is accounted for in the formulation by enforcing equilibrium of the interfacing parts of the RIA in the deformed configuration, so that the progressive reduction of the contact area for an increasing opening displacement is considered.…”

“…The micro-model is characterized by defining a representative interface area (RIA) with sawtooth asperities according to the scheme proposed by Serpieri and Alfano (2011) and, more recently, discussed by Serpieri et al (2015).…”