arXiv subjects

E. Martínez-Pañeda

Publications and source records attributed to E. Martínez-Pañeda.

89 records · Page 5Linked to original sources

arXiv2021

Comparison of hydrogen diffusivities measured by electrochemical permeation and temperature-programmed desorption in cold-rolled pure iron

The diffusivity of hydrogen in cold-rolled pure iron is investigated using permeation and desorption methods. Electrochemical charging, electro-permeation and thermal desorption spectroscopy (TDS) experiments are conducted. Firstly, the relation between the charging current and the hydrogen concentration is established. Secondly, permeation experiments are conducted at 22, 40 and 67°C to quantify the diffusivity dependence on temperature. Finally, the diffusivity is estimated by using two types of desorption experiments and Fick's law: (i) a `rest time' method, by which we measure the hydrogen content of samples held at room temperature for different times, and (ii) isothermal desorption experiments at temperatures ranging from 22 to 80°C, fitting the resulting desorption rate versus time curves. Good agreement is obtained between the isothermal desorption and permeation approaches, with observed differences discussed and rationalised. Moreover, measured diffusivity values for cold-rolled pure iron are also found to be comparable to those reported in the literature. This work demonstrates that isothermal desorption experiments are a convenient approach to determine hydrogen diffusivity over a wide range of temperatures, as facilitated by new TDS systems with fast heating rates.

cond-mat.mtrl-sci↗

arXiv2021

A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver

We present a generalised phase field-based formulation for predicting fatigue crack growth in metals. The theoretical framework aims at covering a wide range of material behaviour. Different fatigue degradation functions are considered and their influence is benchmarked against experiments. The phase field constitutive theory accommodates the so-called AT1, AT2 and phase field-cohesive zone (PF-CZM) models. In regards to material deformation, both non-linear kinematic and isotropic hardening are considered, as well as the combination of the two. Moreover, a monolithic solution scheme based on quasi-Newton algorithms is presented and shown to significantly outperform staggered approaches. The potential of the computational framework is demonstrated by investigating several 2D and 3D boundary value problems of particular interest. Constitutive and numerical choices are compared and insight is gained into their differences and similarities. The framework enables predicting fatigue crack growth in arbitrary geometries and for materials exhibiting complex (cyclic) deformation and damage responses. The finite element code developed is made freely available at www.empaneda.com/codes.

cs.CE↗

arXiv2021

Mode I and Mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity

In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress-strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor's dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIF) are evaluated as a function of the intrinsic material length, characterising the scale at which gradient effects become significant. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress-strain state are determined. In pure mode I, the geometrically necessary dislocation (GND) density is located symmetrically with respect to the blunted crack tip. On the contrary, under pure mode II, the GND density becomes concentrated in the blunted and sharp parts of the crack tip. In this case, fracture initiation is shown to be likely to occur near the blunted region of the crack tip, where both the stress triaxiality and the GND density are at their maximum. The relation between the equilibrium state of dislocation densities and the intrinsic material length as well as the plastic SIF as a function of the work hardening exponent is discussed.

physics.app-ph↗

arXiv2021

A mechanism-based gradient damage model for metallic fracture

A new gradient-based formulation for predicting fracture in elastic-plastic solids is presented. Damage is captured by means of a phase field model that considers both the elastic and plastic works as driving forces for fracture. Material deformation is characterised by a mechanism-based strain gradient constitutive model. This non-local plastic-damage formulation is numerically implemented and used to simulate fracture in several paradigmatic boundary value problems. The case studies aim at shedding light into the role of the plastic and fracture length scales. It is found that the role of plastic strain gradients is two-fold. When dealing with sharp defects like cracks, plastic strain gradients elevate local stresses and facilitate fracture. However, in the presence of non-sharp defects failure is driven by the localisation of plastic flow, which is delayed due to the additional work hardening introduced by plastic strain gradients.

cs.CE↗

arXiv2021

A mechanism-based multi-trap phase field model for hydrogen assisted fracture

We present a new mechanistic, phase field-based formulation for predicting hydrogen embrittlement. The multi-physics model developed incorporates, for the first time, a Taylor-based dislocation model to resolve the mechanics of crack tip deformation. This enables capturing the role of dislocation hardening mechanisms in elevating the tensile stress, hydrogen concentration and dislocation trap density within tens of microns ahead of the crack tip. The constitutive strain gradient plasticity model employed is coupled to a phase field formulation, to simulate the fracture process, and to a multi-trap hydrogen transport model. The analysis of stationary and propagating cracks reveals that the modelling framework presented is capable of adequately capturing the sensitivity to the hydrogen concentration, the loading rate, the material strength and the plastic length scale. In addition, model predictions are compared to experimental data of notch tensile strength versus hydrogen content on a high-strength steel; a very good agreement is attained. We define and implement both atomistic-based and phenomenological hydrogen degradation laws and discuss similarities, differences and implications for the development of parameter-free hydrogen embrittlement models.

cond-mat.mtrl-sci↗

arXiv2020

Applications of phase field fracture in modelling hydrogen assisted failures

The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of phase field-based multi-physics models in transforming the engineering assessment and design of structural components in hydrogen-containing environments. First, we present a theoretical and numerical framework coupling deformation, diffusion and fracture, which accounts for inertia effects.Several constitutive choices are considered for the crack density function, including choices with and without an elastic phase in the damage response. The material toughness is defined as a function of the hydrogen content using an atomistically-informed hydrogen degradation law. The model is numerically implemented in 2D and 3D using the finite element method. The resulting computational framework is used to address a number of case studies of particular engineering interest. These are intended to showcase the model capabilities in: (i) capturing complex fracture phenomena, such as dynamic crack branching or void-crack interactions, (ii) simulating standardised tests for critical components, such as bolts, and (iii) enabling simulation-based paradigms such as Virtual Testing or Digital Twins by coupling model predictions with inspection data of large-scale engineering components. The evolution of defects under in-service conditions can be predicted, up to the ultimate failure. By reproducing the precise geometry of the defects, as opposed to re-characterising them as sharp cracks, phase field modelling enables more realistic and effective structural integrity assessments.

physics.app-ph↗

arXiv2020

Interaction of void spacing and material size effect on inter-void flow localisation

The ductile fracture process in porous metals due to growth and coalescence of micron scale voids is not only affected by the imposed stress state but also by the distribution of the voids and the material size effect. The objective of this work is to understand the interaction of the inter-void spacing (or ligaments) and the resultant gradient induced material size effect on void coalescence for a range of imposed stress states. To this end, three dimensional finite element calculations of unit cell models with a discrete void embedded in a strain gradient enhanced material matrix are performed. The calculations are carried out for a range of initial inter-void ligament sizes and imposed stress states characterised by fixed values of the stress triaxiality and the Lode parameter. Our results show that in the absence of strain gradient effects on the material response, decreasing the inter-void ligament size results in an increase in the propensity for void coalescence. However, in a strain gradient enhanced material matrix, the strain gradients harden the material in the inter-void ligament and decrease the effect of inter-void ligament size on the propensity for void coalescence.

physics.app-ph↗

arXiv2020

Simulation of hydrogen permeation through pure iron for trapping and surface phenomena characterisation

There is a need for numerical models capable of predicting local accumulation of hydrogen near stress concentrators and crack tips to prevent and mitigate hydrogen assisted fracture in steels. The experimental characterisation of trapping parameters in metals, which is required for an accurate simulation of hydrogen transport, is usually performed through the electropermeation test. In order to study grain size influence and grain boundary trapping during permeation, two modelling approaches are explored; a 1D Finite Element model including trap density and binding energy as input parameters and a polycrystalline model based on the assignment of a lower diffusivity and solubility to the grain boundaries. Samples of pure iron after two different heat treatments - 950C for 40 minutes and 1100C for 5 minutes - are tested applying three consecutive rising permeation steps and three decaying steps. Experimental results show that the finer grain microstructure promotes a diffusion delay due to grain boundary trapping. The usual methodology for the determination of trap densities and binding energies is revisited in which the limiting diluted and saturated cases are considered. To this purpose, apparent diffusivities are fitted including also the influence of boundary conditions and comparing results provided by the constant concentration with the constant flux assumption. Grain boundaries are characterised for pure iron with a binding energy between 37.8 and 39.9 kJ/mol and a low trap density but it is numerically demonstrated that saturated or diluted assumptions are not always verified, and a univocal determination of trapping parameters requires a broader range of charging conditions for permeation. The relationship between surface parameters, i.e. charging current, recombination current and surface concentrations, is also studied.

physics.app-ph↗

arXiv2020

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.

physics.app-ph↗

arXiv2020

Fracture in distortion gradient plasticity

In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye's tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic stress singularity. This finding is verified by detailed finite element analyses using a new numerical framework, which builds upon a viscoplastic constitutive law that enables capturing both rate-dependent and rate-independent behaviour in a computationally efficient manner. Numerical analysis is used to gain further insight into the stress elevation predicted by distortion gradient plasticity, relative to conventional J2 plasticity, and the influence of the plastic spin under both mode I and mixed-mode fracture conditions. It is found that Nye's tensor contributions have a weaker effect in elevating the stresses in the plastic region, while predicting the same asymptotic behaviour as constitutive choices based on the plastic strain gradient tensor. A minor sensitivity to X, the parameter governing the dissipation due to the plastic spin, is observed. Finally, distortion gradient plasticity and suitable higher order boundary conditions are used to appropriately model the phenomenon of brittle failure along elastic-plastic material interfaces. We reproduce paradigmatic experiments on niobium-sapphire interfaces and show that the combination of strain gradient hardening and dislocation blockage leads to interface crack tip stresses that are larger than the theoretical lattice strength, rationalising cleavage in the presence of plasticity at bi-material interfaces.

cond-mat.mtrl-sci↗

arXiv2020

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.

physics.chem-ph↗

arXiv2020

Creep Behaviour and Tensile Response of Adhesively Bonded Polyethylene Joints: Single-Lap and Double-Strap

The static and time-dependent behaviours of adhesively bonded polyethylene Double-Strap (DS) joints were investigated to assess the viability of this joint configuration relative to the Single-Lap (SL) joints. Both experiments and finite element simulations are conducted. First, we individually characterise the tensile and creep behaviour of the adhesive and adherent materials; an epoxy-based adhesive and polyethylene, respectively. This information is used to develop suitable constitutive models that are then implemented in the commercial finite element package ABAQUS by means of user material subroutines, UMATs. The numerical models are used to design the creep tests on the adhesive joints. Afterwards, an extensive experimental campaign is conducted where we characterise the static and creep behaviour of two joint configurations, SL and DS joints, and three selected values of the overlap length. In regard to the static case, results reveal an increase in the failure load with increasing overlap length, of up to 10% for an overlap length of 39 mm. Also, slightly better performance is observed for the SL joint configuration. For the creep experiments, we show that the DS adhesive joint configuration leads to much shorter elongations, relative to the SL joints. These differences diminish with increasing overlap length but remain substantial in all cases. In both joint configurations, the elongation increases with decreasing overlap length. For instance, increasing the overlap length to 39 mm led to a 50% and a 30% reduction in elongation for SL and DS joints, respectively. Moreover, the numerical predictions show a good agreement with the experiments. The stress redistribution is investigated and it is found that the shear stress is highly sensitive to the testing time, with differences being more noticeable for the DS joint system.

physics.app-ph↗

arXiv2020

Numerical study of interface cracking in composite structures using a novel geometrically nonlinear Linear Elastic Brittle Interface Model: mixed-mode fracture conditions and application to structured interfaces

Interface cracking is one of the most prominent failure modes in fibre reinforced polymer (FRP) composites. Recent trends in high-tech applications of FRP composites exploit the limits of the load bearing capacity, generally encompassing the development of notable nonlinear effects from geometrical and material signatures. In this investigation, we present a comprehensive assessment of the new Linear Elastic Brittle Interface Model (LEBIM) in geometrically nonlinear applications undergoing mixed-mode fracture conditions. This interface model for triggering fracture events is formulated through the advocation of continuum-like assumptions (for initial non-zero interface thickness) and allows the incorporation of the potential role of the in-plane deformation effects. The performance of the present interface model is demonstrated through the simulation of specimens with mixed-mode delamination, with special attention for its application in samples equipped with structured interfaces. Current predictions exhibit an excellent agreement with respect to experimental data, validating the proposed methodology.

cond-mat.mtrl-sci↗

arXiv2019

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.

cond-mat.mtrl-sci↗

arXiv2019

Mode II fracture of an elastic-plastic sandwich layer

The shear strength of a pre-cracked sandwich layer is predicted, assuming that the layer is linear elastic or elastic-plastic, with yielding characterized by either J2 plasticity theory or by a strip-yield model. The substrates are elastic and of dissimilar modulus to that of the layer. Two geometries are analysed: (i) a semi-infinite crack in a sandwich layer, subjected to a remote mode II K-field and (ii) a centre-cracked sandwich plate of finite width under remote shear stress. For the semi-infinite crack, the near tip stress field is determined as a function of elastic mismatch, and crack tip plasticity is either prevented (the elastic case) or is duly accounted for (the elastic-plastic case). Analytical and numerical solutions are then obtained for the centre-cracked sandwich plate of finite width. First, a mode II K-calibration is obtained for a finite crack in the elastic sandwich layer. Second, the analysis is extended to account for crack tip plasticity via a mode II strip-yield model of finite strength and of finite toughness. The analytical predictions are verified by finite element simulations and a failure map is constructed in terms of specimen geometry and crack length.

cond-mat.mtrl-sci↗

arXiv2018

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.

cond-mat.mtrl-sci↗

arXiv2017

Modeling damage and fracture within strain-gradient plasticity

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large deformations generally occur in the vicinity of a crack, the numerical framework of the chosen SGP theory is developed for allowing large strains and rotations. The material model is implemented in a commercial finite element (FE) code by a user subroutine, and crack-tip fields are evaluated thoroughly for both infinitesimal and finite deformation theories by a boundary-layer formulation. An extensive parametric study is conducted and differences in the stress distributions ahead of the crack tip, as compared with conventional plasticity, are quantified. As a consequence of the strain-gradient contribution to the work hardening of the material, FE results show a significant increase in the magnitude and the extent of the differences between the stress fields of SGP and conventional plasticity theories when finite strains are considered. Since the distance from the crack tip at which the strain gradient significantly alters the stress field could be one order of magnitude higher when large strains are considered, results reveal that the plastic size effect could have important implications in the modelization of several damage mechanisms where its influence has not yet been considered in the literature.

cond-mat.mtrl-sci↗