109 research outputs found
Mode I crack tip fields: strain gradient plasticity theory versus J2 flow theory
The mode I crack tip asymptotic response of a solid characterised by strain
gradient plasticity is investigated. It is found that elastic strains dominate
plastic strains near the crack tip, and thus the Cauchy stress and the strain
state are given asymptotically by the elastic K-field. This crack tip elastic
zone is embedded within an annular elasto-plastic zone. This feature is
predicted by both a crack tip asymptotic analysis and a finite element
computation. When small scale yielding applies, three distinct regimes exist:
an outer elastic K field, an intermediate elasto-plastic field, and an inner
elastic K field. The inner elastic core significantly influences the crack
opening profile. Crack tip plasticity is suppressed when the material length
scale of the gradient theory is on the order of the plastic zone size
estimation, as dictated by the remote stress intensity factor. A generalized
J-integral for strain gradient plasticity is stated and used to characterise
the asymptotic response ahead of a short crack. Finite element analysis of a
cracked three point bend specimen reveals that the crack tip elastic zone
persists in the presence of bulk plasticity and an outer J-field
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
Generalised boundary conditions for hydrogen transport at crack tips
We present a generalised framework for resolving the electrochemistry-diffusion interface and modelling hydrogen transport near a crack tip. The adsorption and absorption kinetics are captured by means of Neumann-type generalised boundary conditions. The diffusion model includes the role of trapping, with a constant or evolving trap density, and the influence of the hydrostatic stress. Both conventional plasticity and strain gradient plasticity are used to model the mechanical behaviour of the solid. Notable differences are found in the estimated crack tip hydrogen concentrations when comparing with the common procedure of prescribing a constant hydrogen concentration at the crack surfaces
Crack tip fields and fracture resistance parameters based on strain gradient plasticity
The crack tip mechanics of strain gradient plasticity solids is investigated
analytically and numerically. A first-order mechanism-based strain gradient
(MSG) plasticity theory based on Taylor's dislocation model is adopted and
implemented in the commercial finite element package ANSYS by means of a user
subroutine. Two boundary value problems are considered, a single edge tension
specimen and a biaxially loaded plate. First, crack tip fields are
characterized. Strain gradient effects associated with dislocation hardening
mechanisms elevate crack tip stresses relative to conventional plasticity. A
parametric study is conducted and differences with conventional plasticity
predictions are quantified. Moreover, the asymptotic nature of the crack tip
solution is investigated. The numerical results reveal that the singularity
order predicted by the first-order MSG theory is equal or higher to that of
linear elastic solids. Also, the crack tip field appears not to have a
separable solution. Moreover, contrarily to what has been shown in the higher
order version of MSG plasticity, the singularity order exhibits sensitivity to
the plastic material properties. Secondly, analytical and numerical approaches
are employed to formulate novel amplitude factors for strain gradient
plasticity. A generalized J-integral is derived and used to characterize a
nonlinear amplitude factor. A closed-form equation for the analytical stress
intensity factor is obtained. Amplitude factors are also derived by decomposing
the numerical solution for the crack tip stress field. Nonlinear amplitude
factor solutions are determined across a wide range of values for the material
length scale l and the strain hardening exponent N. The domains of strain
gradient relevance are identified, setting the basis for the application of
first-order MSG plasticity for fracture and damage assessment
Analysis of hydrogen permeation tests considering two different modelling approaches for grain boundary trapping in iron
The electrochemical permeation test is one of the most used methods for
characterising hydrogen diffusion in metals. The flux of hydrogen atoms
registered in the oxidation cell might be fitted to obtain apparent
diffusivities. The magnitude of this coefficient has a decisive influence on
the kinetics of fracture or fatigue phenomena assisted by hydrogen and depends
largely on hydrogen retention in microstructural traps. In order to improve the
numerical fitting of diffusion coefficients, a permeation test has been
reproduced using FEM simulations considering two approaches: a continuum 1D
model in which the trap density, binding energy and the input lattice
concentrations are critical variables and a polycrystalline model where
trapping at grain boundaries is simulated explicitly including a segregation
factor and a diffusion coefficient different from that of the interior of the
grain. Results show that the continuum model captures trapping delay, but it
should be modified to model the trapping influence on the steady state flux.
Permeation behaviour might be classified according to different regimes
depending on deviation from Fickian diffusion. Polycrystalline synthetic
permeation shows a strong influence of segregation on output flux magnitude.
This approach is able to simulate also the short-circuit diffusion phenomenon.
The comparison between different grain sizes and grain boundary thicknesses by
means of the fitted apparent diffusivity shows the relationships between the
registered flux and the characteristic parameters of traps
Cold Isostatic Pressing to Improve the Mechanical Performance of Additively Manufactured Metallic Components.
Additive manufacturing is becoming a technique with great prospects for the production of components with new designs or shapes that are difficult to obtain by conventional manufacturing methods. One of the most promising techniques for printing metallic components is binder jetting, due to its time efficiency and its ability to generate complex parts. In this process, a liquid binding agent is selectively deposited to adhere the powder particles of the printing material. Once the metallic piece is generated, it undergoes a subsequent process of curing and sintering to increase its density (hot isostatic pressing). In this work, we propose subjecting the manufactured component to an additional post-processing treatment involving the application of a high hydrostatic pressure (5000 bar) at room temperature. This post-processing technique, so-called cold isostatic pressing (CIP), is shown to increase the yield load and the maximum carrying capacity of an additively manufactured AISI 316L stainless steel. The mechanical properties, with and without CIP processing, are estimated by means of the small punch test, a suitable experimental technique to assess the mechanical response of small samples. In addition, we investigate the porosity and microstructure of the material according to the orientations of layer deposition during the manufacturing process. Our observations reveal a homogeneous distribution independent of these orientations, evidencing thus an isotropic behaviour of the material
Analysis of hydrogen diffusion in the three stage electro-permeation test
The presence of hydrogen traps within a metallic alloy influences the rate of
hydrogen diffusion. The electro-permeation (EP) test can be used to assess
this: the permeation of hydrogen through a thin metallic sheet is measured by
suitable control of hydrogen concentration on the front face and by recording
the flux of hydrogen that exits the rear face. Additional insight is achieved
by the more sophisticated three stage EP test: the concentration of free
lattice hydrogen on the front face is set to an initial level, is then dropped
to a lower intermediate value and is then restored to the initial level. The
flux of hydrogen exiting the rear face is measured in all three stages of the
test. In the present study, a transient analysis is performed of hydrogen
permeation in a three stage EP test, assuming that lattice diffusion is
accompanied by trapping and de-trapping. The sensitivity of the three stage EP
response to the depth and density of hydrogen traps is quantified. A
significant difference in permeation response can exist between the first and
third stages of the EP test when the alloy contains a high number density of
deep traps
Influence of charging conditions on simulated temperature-programmed desorption for hydrogen in metals
Failures attributed to hydrogen embrittlement are a major concern for metals
so a better understanding of damage micro-mechanisms and hydrogen diffusion
within the metal is needed. Local concentrations depend on transport phenomena
including trapping effects, which are usually characterised by a
temperature-programmed desorption method often referred to as Thermal
Desorption Analysis (TDA). When the hydrogen is released from the specimen
during the programmed heating, some desorption peaks are observed that are
commonly related to detrapping energies by means of an analytical procedure.
The limitations of this approach are revisited here and gaseous hydrogen
charging at high temperatures is simulated. This popular procedure enables
attaining high concentrations due to the higher solubility of hydrogen at high
temperatures. However, the segregation behaviour of hydrogen into traps depends
on charging time and temperature. This process and the subsequent cooling alter
hydrogen distribution are numerically modelled; it is found that TDA spectra
are strongly affected by the charging temperature and the charging time, both
for weak and strong traps. However, the influence of ageing time at room
temperature after cooling and before desorption is only appreciable for weak
traps
On the relative efficacy of electropermeation and isothermal desorption approaches for measuring hydrogen diffusivity
The relative efficacy of electrochemical permeation (EP) and isothermal
desorption spectroscopy (ITDS) methods for determining the hydrogen diffusivity
is investigated using cold-rolled pure iron. The diffusivities determined from
13 first transient and 8 second transient EP experiments, evaluated using the
conventional lag and breakthrough time methods, are compared to the results of
10 ITDS experiments. Results demonstrate that the average diffusivity is
similar between the second EP transient and ITDS, which are distinctly
increased relative to the first EP transient. However, the coefficient of
variation for the ITDS experiments is reduced by 2 and 3-fold relative to the
first and second EP transients, confirming the improved repeatability of ITDS
diffusivity measurements. The source of the increased error in EP measurements
is systematically evaluated, revealing an important influence of assumed
electrochemical boundary conditions on the analysis and interpretation of EP
experiments
Pre-notched dog bone small punch specimens for the estimation of fracture properties
In recent years, the pre-notched or pre-cracked small punch test (P-SPT) has
been successfully used to estimate the fracture properties of metallic
materials for cases in which there is not sufficient material to identify these
properties from standard tests, such as CT or SENB specimens. The P-SPT
basically consists of deforming a pre-notched miniature specimen, whose edges
are firmly gripped by a die, using a high strength punch. The novelty of this
paper lies in the estimation of fracture properties using dog-bone-shaped
specimens with different confinement levels. With these specimens, three
confinement variations have been studied. The results obtained enable the
establishment of a variation of fracture properties depending on the level of
confinement of each miniature specimen and selection of the most appropriate
confinement for this goal
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