2 research outputs found
A multiple scales approach to crack front waves
Perturbation of a propagating crack with a straight edge is solved using the
method of matched asymptotic expansions (MAE). This provides a simplified
analysis in which the inner and outer solutions are governed by distinct
mechanics. The inner solution contains the explicit perturbation and is
governed by a quasi-static equation. The outer solution determines the
radiation of energy away from the tip, and requires solving dynamic equations
in the unperturbed configuration. The outer and inner expansions are matched
via the small parameter L/l defined by the disparate length scales: the crack
perturbation length L and the outer length scale l associated with the loading.
The method is first illustrated for a scalar crack model and then applied to
the elastodynamic mode I problem.
The dispersion relation for crack front waves is found by requiring that the
energy release rate is unaltered under perturbation. The wave speed is
calculated as a function of the nondimensional parameter kl where k is the
crack front wavenumber, and dispersive properties of the crack front wave speed
are described for the first time. The example problems considered here
demonstrate that the potential of using MAE for moving boundary value problems
with multiple scales.Comment: 25 pages, 5 figure
Effective toughness of heterogeneous brittle materials
A heterogeneous brittle material characterized by a random field of local
toughness Kc(x) can be represented by an equivalent homogeneous medium of
toughness, Keff. Homogenization refers to a process of estimating Keff from the
local field Kc(x). An approach based on a perturbative expansion of the stress
intensity factor along a rough crack front shows the occurrence of different
regimes depending on the correlation length of the local toughness field in the
direction of crack propagation. A `"weak pinning" regime takes place for long
correlation lengths, where the effective toughness is the average of the local
toughness. For shorter correlation lengths, a transition to "strong pinning"
occurs leading to a much higher effective toughness, and characterized by a
propagation regime consisting in jumps between pinning configurations