TY - JOUR

T1 - Crack propagation at the interface between viscoelastic and elastic materials

AU - Ciavarella, M.

AU - Papangelo, A.

AU - McMeeking, R.

N1 - Funding Information:
MC and AP acknowledge support from the Italian Ministry of Education, University and Research (MIUR) under the program “Departments of Excellence” ( L.232/2016 ). RM was supported by the MRSEC program of the U.S. National Science Program through Grant No. DMR-1720256 (IRG3).

PY - 2021/11/1

Y1 - 2021/11/1

N2 - Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970’s. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the “apparent” toughness in a semi-infinite crack increases between a value at very low speeds at a threshold toughness w0, to a very fast fracture value at w∞, and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli. Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum “effective” toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.

AB - Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970’s. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the “apparent” toughness in a semi-infinite crack increases between a value at very low speeds at a threshold toughness w0, to a very fast fracture value at w∞, and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli. Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum “effective” toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.

KW - Bimaterial interfaces

KW - Cohesive models

KW - Crack propagation

KW - Viscoelasticity

UR - http://www.scopus.com/inward/record.url?scp=85115985200&partnerID=8YFLogxK

U2 - 10.1016/j.engfracmech.2021.108009

DO - 10.1016/j.engfracmech.2021.108009

M3 - Article

AN - SCOPUS:85115985200

VL - 257

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

SN - 0013-7944

M1 - 108009

ER -