Title:
Discrete Equivalent Wing Crack Based Damage Model for Brittle Solids
Discrete Equivalent Wing Crack Based Damage Model for Brittle Solids
Author(s)
Jin, Wencheng
Arson, Chloé
Arson, Chloé
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Abstract
The Discrete Equivalent Wing Crack Damage (DEWCD) model formulated
in this paper couples micro-mechanics and Continuum Damage Mechanics
(CDM) principles. At the scale of the Representative Elementary Volume
(REV), damage is obtained by integrating crack densities over the unit
sphere, which represents all possible crack plane orientations. The unit sphere
is discretized into 42 integration points. The damage yield criterion is expressed
at the microscopic scale: if a crack is in tension, crack growth is
controlled by a mode I fracture mechanics criterion; if a crack is in compression,
the shear stress that applies at its faces is projected on the directions
considered in the numerical integration scheme, and cracks perpendicular to
these projected force components grow according to a mode I fracture mechanics
criterion. The projection of shear stresses into a set of tensile forces
allows predicting the occurrence of wing cracks at the tips of pre-existing
defects. We assume that all of the resulting mode I cracks do not interact,
and we adopt a dilute homogenization scheme. A hardening law is introduced to account for subcritical crack propagation, and non-associated flow rules are adopted for damage and irreversible strains induced by residual crack displacements after unloading. The DEWCD model depends on only 6
constitutive parameters which all have a sound physical meaning and can be
determined by direct measurements in the laboratory. The DEWCD model
is calibrated and validated against triaxial compression tests performed on
Bakken Shale. In order to highlight the advantages of the DEWCD model
over previous anisotropic damage models proposed for rocks, we simulated:
(a) A uniaxial tension followed by unloading and reloading in compression;
and (b) Uniaxial compression loading cycles of increasing amplitude. We
compared the results obtained with the DEWCD model with those obtained
with a micro-mechanical model and with a CDM model, both calibrated
against the same experimental dataset as the DEWCD model. The three
models predict a non linear-stress/strain relationship and damage-induced
anisotropy. The micro-mechanical model can capture unilateral effects. The
CDM model can capture the occurrence of irreversible strains. The DEWCD
model can capture both unilateral effects and irreversible strains. In addition,
the DEWCD model can predict the apparent increase of strength and
ductility in compression when the confinement increases and the increasing
hysteresis on unloading-reloading paths as damage increases. The DEWCD
model is the only of the three models tested that provides realistic values of
yield stress and strength in tension and compression. This is a significant
advancement in the theoretical modeling of brittle solids. Future work will
be devoted to the prediction of crack coalescence and to the modeling of the
material response with interacting micro-cracks.
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Date Issued
2016
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Post-print