411 research outputs found
A phase field formulation for hydrogen assisted cracking
We present a phase field modeling framework for hydrogen assisted cracking.
The model builds upon a coupled mechanical and hydrogen diffusion response,
driven by chemical potential gradients, and a hydrogen-dependent fracture
energy degradation law grounded on first principles calculations. The coupled
problem is solved in an implicit time integration scheme, where displacements,
phase field order parameter and hydrogen concentration are the primary
variables. We show that phase field formulations for fracture are particularly
suitable to capture material degradation due to hydrogen. Specifically, we
model (i) unstable crack growth in the presence of hydrogen, (ii) failure
stress sensitivity to hydrogen content in notched specimens, (iii) cracking
thresholds under constant load, (iv) internal hydrogen assisted fracture in
cracked specimens, and (v) complex crack paths arising from corrosion pits.
Computations reveal a good agreement with experiments, highlighting the
predictive capabilities of the present scheme. The work could have important
implications for the prediction and prevention of catastrophic failures in
corrosive environments. The finite element code developed can be downloaded
from www.empaneda.com/code
Soft modes near the buckling transition of icosahedral shells
Icosahedral shells undergo a buckling transition as the ratio of Young's
modulus to bending stiffness increases. Strong bending stiffness favors smooth,
nearly spherical shapes, while weak bending stiffness leads to a sharply
faceted icosahedral shape. Based on the phonon spectrum of a simplified
mass-and-spring model of the shell, we interpret the transition from smooth to
faceted as a soft-mode transition. In contrast to the case of a disclinated
planar network where the transition is sharply defined, the mean curvature of
the sphere smooths the transitition. We define elastic susceptibilities as the
response to forces applied at vertices, edges and faces of an icosahedron. At
the soft-mode transition the vertex susceptibility is the largest, but as the
shell becomes more faceted the edge and face susceptibilities greatly exceed
the vertex susceptibility. Limiting behaviors of the susceptibilities are
analyzed and related to the ridge-scaling behavior of elastic sheets. Our
results apply to virus capsids, liposomes with crystalline order and other
shell-like structures with icosahedral symmetry.Comment: 28 pages, 6 figure
A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement
We present a gradient-based theoretical framework for predicting hydrogen
assisted fracture in elastic-plastic solids. The novelty of the model lies in
the combination of: (i) stress-assisted diffusion of solute species, (ii)
strain gradient plasticity, and (iii) a hydrogen-sensitive phase field fracture
formulation, inspired by first principles calculations. The theoretical model
is numerically implemented using a mixed finite element formulation and several
boundary value problems are addressed to gain physical insight and showcase
model predictions. The results reveal the critical role of plastic strain
gradients in rationalising decohesion-based arguments and capturing the
transition to brittle fracture observed in hydrogen-rich environments. Large
crack tip stresses are predicted, which in turn raise the hydrogen
concentration and reduce the fracture energy. The computation of the steady
state fracture toughness as a function of the cohesive strength shows that
cleavage fracture can be predicted in otherwise ductile metals using sensible
values for the material parameters and the hydrogen concentration. In addition,
we compute crack growth resistance curves in a wide variety of scenarios and
demonstrate that the model can appropriately capture the sensitivity to: the
plastic length scales, the fracture length scale, the loading rate and the
hydrogen concentration. Model predictions are also compared with fracture
experiments on a modern ultra-high strength steel, AerMet100. A promising
agreement is observed with experimental measurements of threshold stress
intensity factor over a wide range of applied potentials
Suppressed plastic deformation at blunt crack tips due to strain gradient effects
AbstractLarge deformation gradients occur near a crack-tip and strain gradient dependent crack-tip deformation and stress fields are expected. Nevertheless, for material length scales much smaller than the scale of the deformation gradients, a conventional elastic–plastic solution is obtained. On the other hand, for significant large material length scales, a conventional elastic solution is obtained. This transition in behaviour is investigated based on a finite strain version of the Fleck–Hutchinson strain gradient plasticity model from 2001. The predictions show that for a wide range of material parameters, the transition from the conventional elastic–plastic to the elastic solution occurs for length scales ranging from 0.001 times the size of the plastic zone to a length scale of the same order of magnitude as the plastic zone
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