Publications
116 results found
Navidtehrani Y, Betegón C, Martínez-Pañeda E, 2022, A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface, Theoretical and Applied Fracture Mechanics, Vol: 121, Pages: 103555-103555, ISSN: 0167-8442
Due to its computational robustness and versatility, the phase field fracture model has become the preferred tool for predicting a wide range of cracking phenomena. However, in its conventional form, its intrinsic tension–compression symmetry in damage evolution prevents its application to the modelling of compressive failures in brittle and quasi-brittle solids, such as concrete or rock materials. In this work, we present a general methodology for decomposing the phase field fracture driving force, the strain energy density, so as to reproduce asymmetrical tension–compression fracture behaviour. The generalised approach presented is particularised to the case of linear elastic solids and the Drucker–Prager failure criterion. The ability of the presented model to capture the compressive failure of brittle materials is showcased by numerically implementing the resulting strain energy split formulation and addressing four case studies of particular interest. Firstly, insight is gained into the capabilities of the model in predicting friction and dilatancy effects under shear loading. Secondly, virtual direct shear tests are conducted to assess fracture predictions under different pressure levels. Thirdly, a concrete cylinder is subjected to uniaxial and triaxial compression to investigate the influence of confinement. Finally, the localised failure of a soil slope is predicted and the results are compared with other formulations for the strain energy decomposition proposed in the literature. The results provide a good qualitative agreement with experimental observations and demonstrate the capabilities of phase field fracture methods to predict crack nucleation and growth under multi-axial loading in materials exhibiting asymmetric tension–compression fracture behaviour.
Ai W, Wu B, Martínez-Pañeda E, 2022, A coupled phase field formulation for modelling fatigue cracking in lithium-ion battery electrode particles, Journal of Power Sources, Vol: 544, ISSN: 0378-7753
Electrode particle cracking is one of the main phenomena driving battery capacity degradation. Recent phase field fracture studies have investigated particle cracking behaviour. However, only the beginning of life has been considered and effects such as damage accumulation have been neglected. Here, a multi-physics phase field fatigue model has been developed to study crack propagation in battery electrode particles undergoing hundreds of cycles. In addition, we couple our electrochemo-mechanical formulation with X-ray CT imaging to simulate fatigue cracking of realistic particle microstructures. Using this modelling framework, non-linear crack propagation behaviour is predicted, leading to the observation of an exponential increase in cracked area with cycle number. Three stages of crack growth (slow, accelerating and unstable) are observed, with phenomena such as crack initialisation at concave regions and crack coalescence having a significant contribution to the resulting fatigue crack growth rates. The critical values of C-rate, particle size and initial crack length are determined, and found to be lower than those reported in the literature using static fracture models. Therefore, this work demonstrates the importance of considering fatigue damage in battery degradation models and provides insights on the control of fatigue crack propagation to alleviate battery capacity degradation.
Zhao Y, Wang R, Martínez-Pañeda E, 2022, A phase field electro-chemo-mechanical formulation for predicting void evolution at the Li-electrolyte interface in all-solid-state batteries, Journal of the Mechanics and Physics of Solids, Vol: 167, Pages: 1-25, ISSN: 0022-5096
We present a mechanistic theory for predicting void evolution in the Li metal electrode during the charge and discharge of all-solid-state battery cells. A phase field formulation is developed to model vacancy annihilation and nucleation, and to enable the tracking of the void-Li metal interface. This is coupled with a viscoplastic description of Li deformation, to capture creep effects, and a mass transfer formulation accounting for substitutional (bulk and surface) Li diffusion and current-driven flux. Moreover, we incorporate the interaction between the electrode and the solid electrolyte, resolving the coupled electro-chemical-mechanical problem in both domains. This enables predicting the electrolyte current distribution and thus the emergence of local current 'hot spots', which act as precursors for dendrite formation and cell death. The theoretical framework is numerically implemented, and single and multiple void case studies are carried out to predict the evolution of voids and current hot spots as a function of the applied pressure, material properties and charge (magnitude and cycle history). For both plating and stripping, insight is gained into the interplay between bulk diffusion, Li dissolution and deposition, creep, and the nucleation and annihilation of vacancies. The model is shown to capture the main experimental observations, including not only key features of electrolyte current and void morphology but also the sensitivity to the applied current, the role of pressure in increasing the electrode-electrolyte contact area, and the dominance of creep over vacancy diffusion.
Díaz A, Alegre JM, Cuesta II, et al., 2022, Notch fracture predictions using the Phase Field method for Ti-6Al-4V produced by Selective Laser Melting after different post-processing conditions, Theoretical and Applied Fracture Mechanics, Vol: 121, Pages: 1-10, ISSN: 0167-8442
Ti-6Al-4V is a titanium alloy with excellent properties for lightweight applications and its production through Additive Manufacturing processes is attractive for different industrial sectors. In this work, the influence of mechanical properties on the notch fracture resistance of Ti-6Al-4V produced by Selective Laser Melting is numerically investigated. Literature data is used to inform material behaviour. The as-built brittle behaviour is compared to the enhanced ductile response after heat treatment (HT) and hot isostatic pressing (HIP) post-processes. A Phase Field framework is adopted to capture damage nucleation and propagation from two different notch geometries and a discussion on the influence of fracture energy and the characteristic length is carried out. In addition, the influence of oxygen uptake is analysed by reproducing non-inert atmospheres during HT and HIP, showing that oxygen shifts fracture to brittle failures due to the formation of an alpha case layer, especially for the V-notch geometry. Results show that a pure elastic behaviour can be assumed for the as-built SLM condition, whereas elastic-plastic phenomena must be modelled for specimens subjected to heat treatment or hot isostatic pressing. The present brittle Phase Field framework coupled with an elastic-plastic constitutive analysis is demonstrated to be a robust prediction tool for notch fracture after different post-processing routes.
Hageman T, Martínez-Pañeda E, 2022, An electro-chemo-mechanical framework for predicting hydrogen uptake in metals due to aqueous electrolytes, Corrosion Science, Vol: 208, ISSN: 0010-938X
We present a theoretical and numerical scheme that enables quantifying hydrogen ingress in metals for arbitrary environments and defect geometries. This is achieved by explicitly resolving the electrochemical behaviour of the electrolyte, the hydrogen and corrosion reactions, the kinetics of surface adsorption, and hydrogen uptake, diffusion and trapping in mechanically-deforming solids. This new framework is used to produce maps that relate the absorbed hydrogen with the applied potential, specimen geometry and fluid velocity. We also present simplified versions of our generalised model, and benchmark predictions of these and other existing models against the generalised electro-chemo-mechanical results, establishing regimes of validity.
Islas A, Fernandez AR, Betegon C, et al., 2022, Computational assessment of biomass dust explosions in the 20L sphere, Process Safety and Environmental Protection, Vol: 165, Pages: 791-814, ISSN: 0263-8762
Determination of the explosion severity parameters of biomass is crucial for the safety management and dust explosion risk assessment of biomass-processing industries. These are commonly determined following experimental tests in the 20L sphere according to the international standards. Recently, CFD simulations have emerged as a reliable alternative to predict the explosion behavior with good accuracy and reduced labor and capital. In this work, numerical simulations of biomass dust explosions are conducted with the open-source CFD code OpenFOAM. The multi-phase (gas-solid) flow is treated in an Eulerian-Lagrangian framework, using a two-way coupling regime and considering the reactions of biomass conversion (moisture evaporation, devolatilization, and char oxidation), the combustion of volatile gases, and convective and radiative heat transfer. The model is validated with pressure-time and concentration-dependent experimental measurements of two biomass samples. Results suggest that the characteristics of the cold-flow (ı.e., turbulence levels, actual dust concentration, spatial distribution of the dust cloud, and turbophoresis effect) govern the course of the explosion process, and depend strongly on particle size, dust concentration, and ignition delay time effects. These findings may be relevant in the design of better dust explosion testing devices and to the reexamination of the guidelines for the operation of the experiment. Finally, a thorough discussion on the explosion pressures, degree of biomass conversion, flame temperature, flame propagation patterns, and the dust agglomeration effect is presented.
Valverde-González A, Martínez-Pañeda E, Quintanas-Corominas A, et al., 2022, Computational modelling of hydrogen assisted fracture in polycrystalline materials, International Journal of Hydrogen Energy, Vol: 47, Pages: 1-17, ISSN: 0360-3199
We present a combined phase field and cohesive zone formulation for hydrogen embrittlement that resolves the polycrystalline microstructure of metals. Unlike previous studies, our deformation-diffusion-fracture modelling framework accounts for hydrogen-microstructure interactions and explicitly captures the interplay between bulk (transgranular) fracture and intergranular fracture, with the latter being facilitated by hydrogen through mechanisms such as grain boundary decohesion. We demonstrate the potential of the theoretical and computational formulation presented by simulating inter- and trans-granular cracking in relevant case studies. Firstly, verification calculations are conducted to show how the framework predicts the expected qualitative trends. Secondly, the model is used to simulate recent experiments on pure Ni and a Ni–Cu superalloy that have attracted particular interest. We show that the model is able to provide a good quantitative agreement with testing data and yields a mechanistic rationale for the experimental observations.
Fernández-Sousa R, Betegón C, Martínez-Pañeda E, 2022, Cohesive zone modelling of hydrogen assisted fatigue crack growth: the role of trapping, International Journal of Fatigue, Vol: 162, ISSN: 0142-1123
We investigate the influence of microstructural traps in hydrogen-assisted fatigue crack growth. To this end, a new formulation combining multi-trap stress-assisted diffusion, mechanism-based strain gradient plasticity and a hydrogen- and fatigue-dependent cohesive zone model is presented and numerically implemented. The results show that the ratio of loading frequency to effective diffusivity governs fatigue crack growth behaviour. Increasing the density of \emph{beneficial} traps, not involved in the fracture process, results in lower fatigue crack growth rates. The combinations of loading frequency and carbide trap densities that minimise embrittlement susceptibility are identified, providing the foundation for a rational design of hydrogen-resistant alloys.
Cui C, Ma R, Martínez-Pañeda E, 2022, A generalised, multi-phase-field theory for dissolution-driven stress corrosion cracking and hydrogen embrittlement, Journal of the Mechanics and Physics of Solids, Vol: 166, Pages: 104951-104951, ISSN: 0022-5096
We present a phase field-based electro-chemo-mechanical formulation for modelling mechanics-enhanced corrosion and hydrogen-assisted cracking in elastic–plastic solids. A multi-phase-field approach is used to present, for the first time, a general framework for stress corrosion cracking, incorporating both anodic dissolution and hydrogen embrittlement mechanisms. We numerically implement our theory using the finite element method and defining as primary fields the displacement components, the phase field corrosion order parameter, the metal ion concentration, the phase field fracture order parameter and the hydrogen concentration. Representative case studies are addressed to showcase the predictive capabilities of the model in various materials and environments, attaining a promising agreement with benchmark tests and experimental observations. We show that the generalised formulation presented can capture, as a function of the environment, the interplay between anodic dissolution- and hydrogen-driven failure mechanisms; including the transition from one to the other, their synergistic action and their individual occurrence. Such a generalised framework can bring new insight into environment–material interactions and the understanding of stress corrosion cracking, as demonstrated here by providing the first simulation results for Gruhl’s seminal experiments.
Clayton T, Duddu R, Siegert M, et al., 2022, A stress-based poro-damage phase field model for hydrofracturing of creeping glaciers and ice shelves, Engineering Fracture Mechanics, Vol: 272, Pages: 1-24, ISSN: 0013-7944
There is a need for computational models capable of predicting meltwater-assisted crevasse growth in glacial ice. Mass loss from glaciers and ice sheets is the largest contributor to sea-level rise and iceberg calving due to hydrofracture is one of the most prominent yet less understood glacial mass loss processes. To overcome the limitations of empirical and analytical approaches, we here propose a new phase field-based computational framework to simulate crevasse growth in both grounded ice sheets and floating ice shelves. The model incorporates the three elements needed to mechanistically simulate hydrofracture of surface and basal crevasses: (i) a constitutive description incorporating the non-linear viscous rheology of ice, (ii) a phase field formulation capable of capturing cracking phenomena of arbitrary complexity, such as 3D crevasse interaction, and (iii) a poro-damage representation to account for the role of meltwater pressure on crevasse growth. A stress-based phase field model is adopted to reduce the length-scale sensitivity, as needed to tackle the large scales of iceberg calving, and to adequately predict crevasse growth in tensile stress regions of incompressible solids. The potential of the computational framework presented is demonstrated by addressing a number of 2D and 3D case studies, involving single and multiple crevasses, and considering both grounded and floating conditions. The model results show a good agreement with analytical approaches when particularised to the idealised scenarios where these are relevant. More importantly, we demonstrate how the model can be used to provide the first computational predictions of crevasse interactions in floating ice shelves and 3D ice sheets, shedding new light into these phenomena. Also, the creep-assisted nucleation and growth of crevasses is simulated in a realistic geometry, corresponding to the Helheim glacier. The computational framework presented opens new horizons in the modelling of iceberg
Quinteros L, García-Macías E, Martínez-Pañeda E, 2022, Micromechanics-based phase field fracture modelling of CNT composites, Composites Part B: Engineering, Vol: 236, ISSN: 0961-9526
We present a novel micromechanics-based phase field approach to model crack initiation and propagation in carbon nanotube (CNT) based composites. The constitutive mechanical and fracture properties of the nanocomposites are first estimated by a mean-field homogenisation approach. Inhomogeneous dispersion of CNTs is accounted for by means of equivalent inclusions representing agglomerated CNTs. Detailed parametric analyses are presented to assess the effect of the main micromechanical properties upon the fracture behaviour of CNT-based composites. The second step of the proposed approach incorporates the previously estimated constitutive properties into a phase field fracture model to simulate crack initiation and growth in CNT-based composites. The modelling capabilities of the framework presented is demonstrated through three paradigmatic case studies involving mode I and mixed mode fracture conditions.
Tan W, Martínez-Pañeda E, 2022, Phase field fracture predictions of microscopic bridging behaviour of composite materials, Composite Structures, Vol: 286, Pages: 1-13, ISSN: 0263-8223
We investigate the role of microstructural bridging on the fracture toughness of composite materials. To achieve this, a new computational framework is presented that integrates phase field fracture and cohesive zone models to simulate fibre breakage, matrix cracking and fibre-matrix debonding. The composite microstructure is represented by an embedded cell at the vicinity of the crack tip, whilst the rest of the sample is modelled as an anisotropic elastic solid. The model is first validated against experimental data of transverse matrix cracking from single-notched three-point bending tests. Then, the model is extended to predict the influence of grain bridging, brick-and-mortar microstructure and 3D fibre bridging on crack growth resistance. The results show that these microstructures are very efficient in enhancing the fracture toughness via fibre-matrix debonding, fibre breakage and crack deflection. In particular, the 3D fibre bridging effect can increase the energy dissipated at failure by more than three orders of magnitude, relative to that of the bulk matrix; well in excess of the predictions obtained from the rule of mixtures. These results shed light on microscopic bridging mechanisms and provide a virtual tool for developing high fracture toughness composites.
Boyce AM, Martínez-Pañeda E, Wade A, et al., 2022, Cracking predictions of lithium-ion battery electrodes by X-ray computed tomography and modelling, Journal of Power Sources, Vol: 526, Pages: 1-14, ISSN: 0378-7753
Fracture of lithium-ion battery electrodes is found to contribute to capacity fade and reduce the lifespan of a battery. Traditional fracture models for batteries are restricted to consideration of a single, idealised particle; here, advanced X-ray computed tomography (CT) imaging, an electro-chemo-mechanical model and a phase field fracture framework are combined to predict the void-driven fracture in the electrode particles of a realistic battery electrode microstructure. The electrode is shown to exhibit a highly heterogeneous electrochemical and fracture response that depends on the particle size and distance from the separator/current collector. The model enables prediction of increased cracking due to enlarged cycling voltage windows, cracking susceptibility as a function of electrode thickness, and damage sensitivity to discharge rate. This framework provides a platform that facilitates a deeper understanding of electrode fracture and enables the design of next-generation electrodes with higher capacities and improved degradation characteristics.
Simoes M, Braithwaite C, Makaya A, et al., 2022, Modelling fatigue crack growth in shape memory alloys, Fatigue and Fracture of Engineering Materials and Structures, Vol: 45, Pages: 1243-1257, ISSN: 1460-2695
We present a phase field-based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalized phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker–Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearized system is solved using a robust monolithic scheme, based on quasi-Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress-strain hysteresis, and temperature. Namely, we compute Δε − N curves, quantify Paris law parameters, and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large-scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.
Zafra A, Harris Z, Sun C, et al., 2022, Comparison of hydrogen diffusivities measured by electrochemical permeation and temperature-programmed desorption in cold-rolled pure iron, Journal of Natural Gas Science and Engineering, Vol: 98, Pages: 1-10, ISSN: 1875-5100
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{\deg}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{\deg}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.
Golahmar A, Kristensen PK, Niordson CF, et al., 2022, A phase field model for hydrogen-assisted fatigue, International Journal of Fatigue, Vol: 154, ISSN: 0142-1123
We present a new theoretical and numerical phase field-based formulation for predicting hydrogen-assisted fatigue. The coupled deformation-diffusion-damage model presented enables predicting fatigue crack nucleation and growth for arbitrary loading patterns and specimen geometries. The role of hydrogen in increasing fatigue crack growth rates and decreasing the number of cycles to failure is investigated. Our numerical experiments enable mapping the three loading frequency regimes and naturally recover Paris law behaviour for various hydrogen concentrations. In addition, Virtual S–N curves are obtained for both notched and smooth samples, exhibiting a good agreement with experiments.
Khalil Z, Elghazouli AY, Martínez-Pañeda E, 2022, A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver, Computer Methods in Applied Mechanics and Engineering, Vol: 388, Pages: 1-22, ISSN: 0045-7825
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.
Islas A, Rodríguez-Fernández A, Betegón C, et al., 2022, CFD simulations of turbulent dust dispersion in the 20 L vessel using OpenFOAM, Powder Technology, Vol: 397, Pages: 117033-117033, ISSN: 0032-5910
Dust explosions are among the most hazardous accidents affecting industrial facilities processing particulate solids. Describing the severity parameters of dust clouds is critical to the safety management and risk assessment of dust explosions. These parameters are determined experimentally in a 20 L spherical vessel, following the ASTM E1226 or UNE 14034 standards. Since their reproducibility depends on the levels of turbulence associated with the dust cloud, a computational model of the multi-phase (gas-solid) flow is used to simulate the dispersion process with the open-source CFD code OpenFOAM. The model is successfully validated against experimental measurements from the literature and numerical results of a commercial CFD code. In addition, this study considers the impact of particle size on the turbulence of the carrier phase, suggesting that particles attenuate its turbulence intensity. Moreover, the model predicts well the formation of a two-vortex flow pattern, which has a negative impact on the distribution of the particle-laden flows with dp≤ 100 μm, as most of the particles concentrate at the near-wall region. Contrarily, an improved homogeneity of dust cloud is observed for a case fed with larger particles (dp= 200 μm), as the increased inertia of these particles allows them to enter into the re-circulation regions.
Shlyannikov V, Martínez-Pañeda E, Tumanov A, et al., 2021, Mode I and Mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity, Theoretical and Applied Fracture Mechanics, Vol: 116, Pages: 1-15, ISSN: 0167-8442
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.
Shishvan SS, Assadpour-asl S, Martínez-Pañeda E, 2021, A mechanism-based gradient damage model for metallic fracture, Engineering Fracture Mechanics, Vol: 255, Pages: 1-17, ISSN: 0013-7944
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.
Isfandbod M, Martinez-Paneda E, 2021, A mechanism-based multi-trap phase field model for hydrogen assisted fracture, International Journal of Plasticity, Vol: 144, ISSN: 0749-6419
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.
Martínez-Pañeda E, 2021, Progress and opportunities in modelling environmentally assisted cracking, RILEM Technical Letters, Vol: 6, Pages: 70-77, ISSN: 2518-0231
Environmentally assisted cracking phenomena are widespread across the transport, defence, energy and construction sectors. However, predicting environmentally assisted fractures is a highly cross-disciplinary endeavour that requires resolving the multiple material-environment interactions taking place. In this manuscript, an overview is given of recent breakthroughs in the modelling of environmentally assisted cracking. The focus is on the opportunities created by two recent developments: phase field and multi-physics modelling. The possibilities enabled by the confluence of phase field methods and electro-chemo-mechanics modelling are discussed in the context of three environmental assisted cracking phenomena of particular engineering interest: hydrogen embrittlement, localised corrosion and corrosion fatigue. Mechanical processes such as deformation and fracture can be coupled with chemical phenomena like local reactions, ionic transport and hydrogen uptake and diffusion. Moreover, these can be combined with the prediction of an evolving interface, such as a growing pit or a crack, as dictated by a phase field variable that evolves based on thermodynamics and local kinetics. Suitable for both microstructural and continuum length scales, this new generation of simulation-based, multi-physics phase field models can open new modelling horizons and enable Virtual Testing in harmful environments.
Kristensen PK, Niordson CF, Martínez-Pañeda E, 2021, An assessment of phase field fracture: crack initiation and growth, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 379, Pages: 1-22, ISSN: 1364-503X
The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith's energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness-for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimisation - without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms.
Navidtehrani Y, Betegón C, Martínez-Pañeda E, 2021, A simple and robust Abaqus implementation of the phase field fracture method, Applications in Engineering Science, Vol: 6, Pages: 1-12, ISSN: 2666-4968
The phase field fracture method is attracting significant interest. Phase field approaches have enabled predicting - on arbitrary geometries and dimensions - complex fracture phenomena such as crack branching, coalescence, deflection and nucleation. In this work, we present a simple and robust implementation of the phase field fracture method in the commercial finite element package Abaqus. The implementation exploits the analogy between the phase field evolution law and the heat transfer equation, enabling the use of Abaqus’ in-built features and circumventing the need for defining user elements. The framework is general, and is shown to accommodate different solution schemes (staggered and monolithic), as well as various constitutive choices for preventing damage under compression. The robustness and applicability of the numerical framework presented is demonstrated by addressing several 2D and 3D boundary value problems of particular interest. Focus is on the solution of paradigmatic case studies that are known to be particularly demanding from a convergence perspective. The results reveal that our phase field fracture implementation can be readily combined with other advanced computational features, such as contact, and deliver robust and precise solutions. The code developed can be downloaded from www.empaneda.com/codes.
Navidtehrani Y, Betegón C, Martínez-Pañeda E, 2021, A unified Abaqus implementation of the phase field fracture method using only a user material subroutine, Materials, Vol: 14, Pages: 1-19, ISSN: 1996-1944
We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus' in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed can be downloaded from www.empaneda.com/codes.
Alegre JM, Martínez-Pañeda E, 2021, TAFMEC special issue on hydrogen embrittlement of metallic materials: Fatigue and fracture, Theoretical and Applied Fracture Mechanics, Vol: 112, Pages: 1-1, ISSN: 0167-8442
Askarinejad S, Martínez-Pañeda E, Cuesta II, et al., 2021, Mode II fracture of an MMA adhesive layer: theory versus experiment, European Journal of Mechanics A: Solids, Vol: 86, Pages: 1-9, ISSN: 0997-7538
Thick adhesive layers have potential structural application in ship construction for the joining of a composite superstructure to a steel hull. The purpose of this study is to develop a mechanics model for the adhesive fracture of such lap joints under shear loading. Modified Thick-Adherend-Shear-Test (TAST) specimens made from a MMA-based adhesive and steel adherents are designed and fabricated. Crack initiation and growth of these joints is measured and monitored by Digital Image Correlation (DIC). An attempt is made to use a cohesive zone model to predict the magnitude of shear strain across the adhesive layer both at crack initiation and at peak load, and to predict the extent of crack growth as a function of shear strain across the adhesive layer. The ability of a cohesive zone model to predict several features of specimen failure is assessed for the case of an adhesive layer of high shear ductility.
Cui C, Ma R, Martínez-Pañeda E, 2021, A phase field formulation for dissolution-driven stress corrosion cracking, Journal of the Mechanics and Physics of Solids, Vol: 147, Pages: 1-21, ISSN: 0022-5096
We present a new theoretical and numerical framework for modelling mechanically-assisted corrosion in elastic-plastic solids. Both pitting and stress corrosion cracking (SCC) can be captured, as well as the pit-to crack transition. Localised corrosion is assumed to be dissolution-driven and a formulation grounded upon the film rupture-dissolution-repassivation mechanism is presented to incorporate the influence of film passivation. The model incorporates, for the first time, the role of mechanical straining as the electrochemical driving force, accelerating corrosion kinetics. The computational complexities associated with tracking the evolving metal-electrolyte interface are resolved by making use of a phase field paradigm, enabling an accurate approximation of complex SCC morphologies. The coupled electro-chemo-mechanical formulation is numerically implemented using the finite element method and an implicit time integration scheme; displacements, phase field order parameter and concentration are the primary variables. Five case studies of particular interest are addressed to showcase the predictive capabilities of the model, revealing an excellent agreement with analytical solutions and experimental measurements. By modelling these paradigmatic 2D and 3D boundary value problems we show that our formulation can capture: (i) the transition from activation-controlled corrosion to diffusion-controlled corrosion, (ii) the sensitivity of interface kinetics to mechanical stresses and strains, (iii) the role of film passivation in reducing corrosion rates, and (iv) the dependence of the stability of the passive film to local strain rates. The influence of these factors in driving the shape change of SCC defects, including the pit-to-crack transition, is a natural outcome of the model, laying the foundations for a mechanistic assessment of engineering materials and structures.
Holte I, Srivastava A, Martínez-Pañeda E, et al., 2021, Interaction of void spacing and material size effect on inter-void flow localisation, Journal of Applied Mechanics, Vol: 88, ISSN: 0021-8936
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.
Hirshikesh, Martínez-Pañeda E, Natarajan S, 2021, Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials, Defence Technology, Vol: 17, Pages: 185-195, ISSN: 2214-9147
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement. The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency. The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations. The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle. The study is then extended to the analysis of orthotropic FGMs. It is observed that, if the gradation in fracture properties is neglected, the material gradient plays a secondary role, with the fracture behaviour being dominated bythe orthotropy of the material. However, when the toughness increases along the crack propagation path, a substantial gain in fracture resistance is observed.
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.