TY - JOUR

T1 - Void formation and roughening in slow fracture

AU - Afek, Itai

AU - Bouchbinder, Eran

AU - Katzav, Eytan

AU - Mathiesen, Joachim

AU - Procaccia, Itamar

PY - 2005/1/1

Y1 - 2005/1/1

N2 - Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Postmortem analysis of the resulting fracture surfaces of ductile and brittle materials on the Îm-mm and the nm scales, respectively, reveals self-affine cracks with anomalous scaling exponent ζâ‰0.8 in 3 dimensions and ζ≠0.65 in 2 dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2 dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.

AB - Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Postmortem analysis of the resulting fracture surfaces of ductile and brittle materials on the Îm-mm and the nm scales, respectively, reveals self-affine cracks with anomalous scaling exponent ζâ‰0.8 in 3 dimensions and ζ≠0.65 in 2 dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2 dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.

UR - http://www.scopus.com/inward/record.url?scp=27944476472&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.066127

DO - 10.1103/PhysRevE.71.066127

M3 - Journal article

AN - SCOPUS:27944476472

VL - 71

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 066127

ER -