34 results found
Díaz A, Cuesta II, Martinez-Paneda E, et al., Analysis of hydrogen permeation tests considering two different modelling approaches for grain boundary trapping in iron, International Journal of Fracture, ISSN: 0376-9429
The electrochemical permeation test is one of the most used methods forcharacterising hydrogen diffusion in metals. The flux of hydrogen atomsregistered in the oxidation cell might be fitted to obtain apparentdiffusivities. The magnitude of this coefficient has a decisive influence onthe kinetics of fracture or fatigue phenomena assisted by hydrogen and dependslargely on hydrogen retention in microstructural traps. In order to improve thenumerical fitting of diffusion coefficients, a permeation test has beenreproduced using FEM simulations considering two approaches: a continuum 1Dmodel in which the trap density, binding energy and the input latticeconcentrations are critical variables and a polycrystalline model wheretrapping at grain boundaries is simulated explicitly including a segregationfactor and a diffusion coefficient different from that of the interior of thegrain. Results show that the continuum model captures trapping delay, but itshould be modified to model the trapping influence on the steady state flux.Permeation behaviour might be classified according to different regimesdepending on deviation from Fickian diffusion. Polycrystalline syntheticpermeation 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 bymeans of the fitted apparent diffusivity shows the relationships between theregistered flux and the characteristic parameters of traps.
Cuesta II, Martinez-Paneda E, Díaz A, et al., 2019, The essential work of fracture parameters for 3D printed polymer sheets, Materials and Design, Vol: 181, ISSN: 0264-1275
Additive manufacturing is becoming increasingly popular in academia and industry. Accordingly, there has been a growing interest in characterizing 3D printed samples to determine their structural integrity behaviour. We employ the Essential Work of Fracture (EWF) to investigate the mechanical response of polymer sheets obtained through additive manufacturing. Our goal is twofold; first, we aim at gaining insight into the role of fibre reinforcement on the fracture resistance of additively manufactured polymer sheets. Deeply double-edge notched tensile (DDEN-T) tests are conducted on four different polymers: Onyx, a crystalline, nylon-reinforced polymer, and three standard polymers used in additive manufacturing – PLA, PP and ABS. Results show that fibre-reinforcement translates into a notable increase in fracture resistance, with the fracture energy of Onyx being an order of magnitude higher than that reported for non-reinforced polymers. On the other hand, we propose the use of a miniature test specimen, the deeply double-edge notched small punch specimens (DDEN-SP), to characterize the mechanical response using a limited amount of material. The results obtained exhibit good alignment with the DDEN-T data, suggesting the suitability of the DDEN-SP test for measuring fracture properties of additively manufactured polymers in a cost-effective manner.
Martinez-Paneda E, Harris ZD, Fuentes-Alonso S, et al., On the suitability of slow strain rate tensile testing for assessing hydrogen embrittlement susceptibility, Corrosion Science, ISSN: 0010-938X
The onset of sub-critical crack growth during slow strain rate tensile testing(SSRT) is assessed through a combined experimental and modeling approach.A systematic comparison of the extent of intergranular fracture and expectedhydrogen ingress suggests that hydrogen diffusion alone is insufficient to ex-plain the intergranular fracture depths observed after SSRT experiments ina Ni-Cu superalloy. Simulations of these experiments using a new phase fieldformulation indicate that crack initiation occurs as low as 40% of the timeto failure. The implications of such sub-critical crack growth on the validityand interpretation of SSRT metrics are then explored.
Martinez-Paneda E, Cuesta II, Fleck NA, 2019, Mode II fracture of an elastic-plastic sandwich layer, Journal of Applied Mechanics 87(3): 031001, Vol: 87, ISSN: 0021-8936
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.
Martinez-Paneda E, Fuentes-Alonso S, Betegon C, 2019, Gradient-enhanced statistical analysis of cleavage fracture, European Journal of Mechanics A: Solids, Vol: 77, ISSN: 0997-7538
We present a probabilistic framework for brittle fracture that builds upon Weibull statistics and strain gradient plasticity. The constitutive response is given by the mechanism-based strain gradient plasticity theory, aiming to accurately characterize crack tip stresses by accounting for the role of plastic strain gradients in elevating local strengthening ahead of cracks. It is shown that gradients of plastic strain elevate the Weibull stress and the probability of failure for a given choice of the threshold stress and the Weibull parameters. The statistical framework presented is used to estimate failure probabilities across temperatures in ferritic steels. The framework has the capability to estimate the three statistical parameters present in the Weibull-type model without any prior assumptions. The calibration against experimental data shows important differences in the values obtained for strain gradient plasticity and conventional J2 plasticity. Moreover, local probability maps show that potential damage initiation sites are much closer to the crack tip in the case of gradient-enhanced plasticity. Finally, the fracture response across the ductile-to-brittle regime is investigated by computing the cleavage resistance curves with increasing temperature. Gradient plasticity predictions appear to show a better agreement with the experiments.
Ivan Cuesta I, Martinez-Paneda E, Diaz A, et al., 2019, Cold isostatic pressing to improve the mechanical performance of additively manufactured metallic components, Materials, Vol: 12, ISSN: 1996-1944
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.
Hirshikesh, Natarajan S, Annabattula RK, et al., 2019, Phase field modelling of crack propagation in functionally graded materials, Composites Part B: Engineering, Vol: 169, Pages: 239-248, ISSN: 0961-9526
We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case studies are addressed to demonstrate the potential of the proposed modelling framework. Specifically, we (i) gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations, (ii) accurately reproduce the crack trajectories observed in graded photodegradable copolymers and glass-filled epoxy FGMs, (iii) benchmark our predictions with results from alternative numerical methodologies, and (iv) model complex crack paths and failure in three dimensional functionally graded solids. The suitability of phase field fracture methods in capturing the crack deflections intrinsic to crack tip mode-mixity due to material gradients is demonstrated. Material gradient profiles that prevent unstable fracture and enhance crack growth resistance are identified: this provides the foundation for the design of fracture resistant FGMs. The finite element code developed can be downloaded from www.empaneda.com/codes.
Martinez-Paneda E, Deshpande VS, Niordson CF, et al., 2019, The role of plastic strain gradients in the crack growth resistance of metals, Journal of the Mechanics and Physics of Solids, Vol: 126, Pages: 136-150, ISSN: 0022-5096
Crack advance from short or long pre-cracks is predicted by the progressive failure of a cohesive zone in a strain gradient, elasto-plastic solid. The presence of strain gradients leads to the existence of an elastic zone at the tip of a stationary crack, for both the long crack and the short crack cases. This is in sharp contrast with previous asymptotic analyses of gradient solids, where elastic strains were neglected. The presence of an elastic singularity at the crack tip generates stresses which are sufficiently high to activate quasi-cleavage. For the long crack case, crack growth resistance curves are predicted for a wide range of ratios of cohesive zone strength to yield strength. Remarkably, this feature of an elastic singularity is preserved for short cracks, leading to a severe reduction in tensile ductility. In qualitative terms, these predictions resemble those of discrete dislocation calculations, including the concept of a dislocation-free zone at the crack tip.
Martinez-Paneda E, Fleck NA, 2019, Mode I crack tip fields: Strain gradient plasticity theory versus J2 flow theory, European Journal of Mechanics A: Solids, Vol: 75, Pages: 381-388, ISSN: 0997-7538
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.
Juul KJ, Martinez-Paneda E, Nielsen KL, et al., 2019, Steady-state fracture toughness of elastic-plastic solids: Isotropic versus kinematic hardening, Engineering Fracture Mechanics, Vol: 207, Pages: 254-268, ISSN: 0013-7944
The fracture toughness for a mode I/II crack propagating in a ductile material has been subject to numerous investigations. However, the influence of the material hardening law has received very limited attention, with isotropic hardening being the default choice if cyclic loads are absent. The present work extends the existing studies of monotonic mode I/II steady-state crack propagation with the goal to compare the predictions from an isotropic hardening model with that of a kinematic hardening model. The work is conducted through a purpose-built steady-state framework that directly delivers the steady-state solution. In order to provide a fracture criterion, a cohesive zone model is adopted and embedded at the crack tip in the steady-state framework, while a control algorithm for the far-field, that significantly reduces the number of equilibrium iterations is employed to couple the far-field loading to the correct crack tip opening. Results show that the steady-state fracture toughness (shielding ratio) obtained for a kinematic hardening material is larger than for the corresponding isotropic hardening case. The difference between the isotropic and kinematic model is tied to the non-proportional loading conditions and reverse plasticity. This also explains the vanishing difference in the shielding ratio when considering mode II crack propagation as the non-proportional loading is less pronounced and the reverse plasticity is absent.
Cuesta II, Willig A, Diaz A, et al., 2019, Pre-notched dog bone small punch specimens for the estimation of fracture properties, Engineering Failure Analysis, Vol: 96, Pages: 236-240, ISSN: 1350-6307
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.
Martinez-Paneda E, 2019, On the finite element implementation of functionally graded materials, Materials, Vol: 12, ISSN: 1996-1944
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the element level by means of the two most commonly used schemes: (i) nodal based gradation, often via an auxiliary (non-physical) temperature-dependence, and (ii) Gauss integration point based gradation. These formulations are extensively compared by solving a number of paradigmatic boundary value problems for which analytical solutions can be obtained. The nature of the notable differences revealed by the results is investigated in detail. We provide a user subroutine for the finite element package ABAQUS to overcome the limitations of the most popular approach for implementing FGMs in commercial software. The use of reliable, element-based formulations to define the material property variation could be key in fracture assessment of FGMs and other non-homogeneous materials.
Martinez-Paneda E, Golahmar A, Niordson CF, 2018, A phase field formulation for hydrogen assisted cracking, Computer Methods in Applied Mechanics and Engineering, Vol: 342, Pages: 742-761, ISSN: 0045-7825
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/codes.
Mathew T, Natarajan S, Martinez-Paneda E, 2018, Size effects in elastic-plastic functionally graded materials, Composite Structures, Vol: 204, Pages: 43-51, ISSN: 0263-8223
We develop a strain gradient plasticity formulation for composite materials with spatially varying volume fractions to characterize size effects in functionally graded materials (FGMs). The model is grounded on the mechanism-based strain gradient plasticity theory and effective properties are determined by means of a linear homogenization scheme. Several paradigmatic boundary value problems are numerically investigated to gain insight into the strengthening effects associated with plastic strain gradients and geometrically necessary dislocations (GNDs). The analysis of bending in micro-size functionally graded foils shows a notably stiffer response with diminishing thickness. Micro-hardness measurements from indentation reveal a significant increase with decreasing indenter size. And large dislocation densities in the vicinity of a crack substantially elevate stresses in cracked FGM components. We comprehensively assess the influence of the length scale parameter and material gradation profile to accurately characterize the micro-scale response and identify regimes of GNDs relevance in FGMs.
Martinez-Paneda E, Fleck NA, 2018, Crack growth resistance in metallic alloys: the role of isotropic versus kinematic hardening, Journal of Applied Mechanics-Transactions of the ASME, Vol: 85, ISSN: 0021-8936
The sensitivity of crack growth resistance to the choice of isotropic or kinematic hardening is investigated. Monotonic mode I crack advance under small scale yielding conditions is modeled via a cohesive zone formulation endowed with a traction–separation law. R-curves are computed for materials that exhibit linear or power law hardening. Kinematic hardening leads to an enhanced crack growth resistance relative to isotropic hardening. Moreover, kinematic hardening requires greater crack extension to achieve the steady-state. These differences are traced to the nonproportional loading of material elements near the crack tip as the crack advances. The sensitivity of the R-curve to the cohesive zone properties and to the level of material strain hardening is explored for both isotropic and kinematic hardening.
Martínez Pañeda E, 2018, Strain gradient plasticity-based modeling of damage and fracture, Publisher: Springer International Publishing, ISBN: 9783319633831
Martinez-Paneda E, del Busto S, Betegon C, 2017, Non-local plasticity effects on notch fracture mechanics, Theoretical and Applied Fracture Mechanics, Vol: 92, Pages: 276-287, ISSN: 0167-8442
We investigate the influence of gradient-enhanced dislocation hardening on the mechanics of notch-induced failure. The role of geometrically necessary dislocations (GNDs) in enhancing cracking is assessed by means of a mechanism-based strain gradient plasticity theory. Both stationary and propagating cracks from notch-like defects are investigated through the finite element method. A cohesive zone formulation incorporating monotonic and cyclic damage contributions is employed to address both loading conditions. Computations are performed for a very wide range of length scale parameters and numerous geometries are addressed, covering the main types of notches. Results reveal a strong influence of the plastic strain gradients in all the scenarios considered. Transitional combinations of notch angle, radius and length scale parameter are identified that establish the regimes of GNDs-relevance, laying the foundations for the rational application of gradient plasticity models in damage assessment of notched components.
del Busto S, Betegon C, Martinez-Paneda E, 2017, A cohesive zone framework for environmentally assisted fatigue, Engineering Fracture Mechanics, Vol: 185, Pages: 210-226, ISSN: 0013-7944
We present a compelling finite element framework to model hydrogen assisted fatigue by means of a hydrogen- and cycle-dependent cohesive zone formulation. The model builds upon: (i) appropriate environmental boundary conditions, (ii) a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, (iii) a mechanical behavior characterized by finite deformation J2 plasticity, (iv) a phenomenological trapping model, (v) an irreversible cohesive zone formulation for fatigue, grounded on continuum damage mechanics, and (vi) a traction-separation law dependent on hydrogen coverage calculated from first principles. The computations show that the present scheme appropriately captures the main experimental trends; namely, the sensitivity of fatigue crack growth rates to the loading frequency and the environment. The role of yield strength, work hardening, and constraint conditions in enhancing crack growth rates as a function of the frequency is thoroughly investigated. The results reveal the need to incorporate additional sources of stress elevation, such as gradient-enhanced dislocation hardening, to attain a quantitative agreement with the experiments.
Martinez-Paneda E, Natarajan S, Bordas S, 2017, Gradient plasticity crack tip characterization by means of the extended finite element method, Computational Mechanics, Vol: 59, Pages: 831-842, ISSN: 0178-7675
Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from www.empaneda.com/codes.
Papazafeiropoulos G, Muniz-Calvente M, Martinez-Paneda E, 2017, Abaqus2Matlab: a suitable tool for finite element post-processing, Advances in Engineering Software, Vol: 105, Pages: 9-16, ISSN: 0965-9978
A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from the image processing and the integrated graph-plotting features of Matlab but also opens up new opportunities in results post-processing, statistical analysis and mathematical optimization, among many other possibilities. The software architecture and usage are appropriately described and two problems of particular engineering significance are addressed to demonstrate its capabilities. Firstly, the software is employed to assess cleavage fracture through a novel 3-parameter Weibull probabilistic framework. Then, its potential to create and train neural networks is used to identify damage parameters through a hybrid experimental–numerical scheme, and model crack propagation in structural materials by means of a cohesive zone approach. The source code, detailed documentation and a large number of tutorials can be freely downloaded from www.abaqus2matlab.com.
Martinez-Paneda E, Papazafeiropoulos G, Muniz-Calvente M, 2017, ABAQUS2MATLAB: A NOVEL TOOL FOR FINITE ELEMENT POST-PROCESSING, 7th International Conference on Mechanics and Materials in Design (M2D), Publisher: INEGI-FEUP, Pages: 185-186
Fuentes-Alonso S, Martinez-Paneda E, 2017, CRACK TIP MECHANICS IN DISTORTION GRADIENT PLASTICITY, 7th International Conference on Mechanics and Materials in Design (M2D), Publisher: INEGI-FEUP, Pages: 509-510
Martínez-Pañeda E, Niordson CF, Deshpande VS, et al., 2017, Gradient effects on crack tip mechanics, Pages: 757-758
© 2017 ICF 2017 - 14th International Conference on Fracture. All rights reserved. In this work a general framework for damage and fracture assessment accounting for the role of geometrically necessary dislocations (GNDs) is provided. Crack tip fields are characterized, within both infinitesimal and finite deformation theories, by means of different strain gradient plasticity (SGP) formulations and their finite element implementation. Moreover, the impact of SGP theories on fracture and damage problems is further assessed by modeling crack growth initiation and subsequent resistance. Results show a strong influence of GNDs, revealing the need to incorporate its influence in continuum models in order to adequately characterize behavior at the small scales involved in crack tip deformation.
Martínez-Pañeda E, Del Busto S, Betegón C, 2017, A mechanistic framework for hydrogen embrittlement, Pages: 816-817
© 2017 Chinese Society of Theoretical and Applied Mechanics. All Rights Reserved. A new mechanism-based approach for hydrogen assisted cracking is proposed. The modeling framework incorporates: (i) the role of statistically stored and geometrically necessary dislocations on crack tip stresses and hydrogen diffusion, (ii) a novel dislocation-based approach to deal with the reversibly trapped hydrogen concentration and (iii) a cohesive zone formulation to account for hydrogen-lowering of the fracture resistance. Finite element computations are conducted, with a control algorithm being employed to ensure convergence in crack propagation studies. Results reveal a very good agreement with the experiments and the important implications of the results in the understanding of hydrogen embrittlement mechanisms are thoroughly discussed.
Ductile damage modeling within the Small Punch Test (SPT) is extensively investigated. The capabilities of the SPT to reliably estimate fracture and damage properties are thoroughly discussed and emphasis is placed on the use of notched specimens. First, different notch profiles are analyzed and constraint conditions quantified. The role of the notch shape is comprehensively examined from both triaxiality and notch fabrication perspectives. Afterwards, a methodology is presented to extract the micromechanical-based ductile damage parameters from the load-displacement curve of notched SPT samples. Furthermore, Gurson-Tvergaard-Needleman model predictions from a top-down approach are employed to gain insight into the mechanisms governing crack initiation and subsequent propagation in small punch experiments. An accurate assessment of micromechanical toughness parameters from the SPT is of tremendous relevance when little material is available.
Martinez-Paneda E, Niordson CF, Bardella L, 2016, A finite element framework for distortion gradient plasticity with applications to bending of thin foils, International Journal of Solids and Structures, Vol: 96, Pages: 288-299, ISSN: 0020-7683
A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the constitutive inclusion of the plastic spin, as proposed by Gurtin (2004) through the prescription of a free energy dependent on Nye’s dislocation density tensor. The proposed numerical scheme is developed by following and extending the mathematical principles established by Fleck and Willis (2009). The modeling of thin metallic foils under bending reveals a significant influence of the plastic shear strain and spin due to a mechanism associated with the higher-order boundary conditions allowing dislocations to exit the body. This mechanism leads to an unexpected mechanical response in terms of bending moment versus curvature, dependent on the foil length, if either viscoplasticity or isotropic hardening are included in the model. In order to study the effect of dissipative higher-order stresses, the mechanical response under non-proportional loading is also investigated.
Martinez-Paneda E, Niordson CF, Gangloff RP, 2016, Strain gradient plasticity-based modeling of hydrogen environment assisted cracking, Acta Materialia, Vol: 117, Pages: 321-332, ISSN: 1359-6454
Finite element analysis of stress about a blunt crack tip, emphasizing finite strain and phenomenological and mechanism-based strain gradient plasticity (SGP) formulations, is integrated with electrochemical assessment of occluded-crack tip hydrogen (H) solubility and two H-decohesion models to predict hydrogen environment assisted crack growth properties. SGP elevates crack tip geometrically necessary dislocation density and flow stress, with enhancement declining with increasing alloy strength. Elevated hydrostatic stress promotes high-trapped H concentration for crack tip damage; it is imperative to account for SGP in H cracking models. Predictions of the threshold stress intensity factor and H-diffusion limited Stage II crack growth rate agree with experimental data for a high strength austenitic Ni-Cu superalloy (Monel®K-500) and two modern ultra-high strength martensitic steels (AerMet™100 and Ferrium™M54) stressed in 0.6 M NaCl solution over a range of applied potential. For Monel®K-500, KTH is accurately predicted versus cathodic potential using either classical or gradient-modified formulations; however, Stage II growth rate is best predicted by a SGP description of crack tip stress that justifies a critical distance of 1 μm. For steel, threshold and growth rate are best predicted using high-hydrostatic stress that exceeds 6 to 8 times alloy yield strength and extends 1 μm ahead of the crack tip. This stress is nearly achieved with a three-length phenomenological SGP formulation, but additional stress enhancement is needed, perhaps due to tip geometry or slip-microstructure.
Martinez-Paneda E, del Busto S, Niordson CF, et al., 2016, Strain gradient plasticity modeling of hydrogen diffusion to the crack tip, International Journal of Hydrogen Energy, Vol: 41, Pages: 10265-10274, ISSN: 0360-3199
In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental measurements of crack tip deformation and high levels of lattice hydrogen concentration are predicted within microns to the crack tip. The important implications of the results in the understanding of hydrogen embrittlement mechanisms are thoroughly discussed.
Martinez-Paneda E, Niordson CF, 2016, On fracture in finite strain gradient plasticity, International Journal of Plasticity, Vol: 80, Pages: 154-167, ISSN: 0749-6419
In this work a general framework for damage and fracture assessment including the effect of strain gradients is provided. Both mechanism-based and phenomenological strain gradient plasticity (SGP) theories are implemented numerically using finite deformation theory and crack tip fields are investigated. Differences and similarities between the two approaches within continuum SGP modeling are highlighted and discussed. Local strain hardening promoted by geometrically necessary dislocations (GNDs) in the vicinity of the crack leads to much higher stresses, relative to classical plasticity predictions. These differences increase significantly when large strains are taken into account, as a consequence of the contribution of strain gradients to the work hardening of the material. The magnitude of stress elevation at the crack tip and the distance ahead of the crack where GNDs significantly alter the stress distributions are quantified. The SGP dominated zone extends over meaningful physical lengths that could embrace the critical distance of several damage mechanisms, being particularly relevant for hydrogen assisted cracking models. A major role of a certain length parameter is observed in the multiple parameter version of the phenomenological SGP theory. Since this also dominates the mechanics of indentation testing, results suggest that length parameters characteristic of mode I fracture should be inferred from nanoindentation.
Martinez-Paneda E, Garcia TE, Rodriguez C, 2016, Fracture toughness characterization through notched small punch test specimens, Materials Science and Engineering A: Structural Materials: Properties, Microstructure and Processing, Vol: 657, Pages: 422-430, ISSN: 0921-5093
In this work a novel methodology for fracture toughness characterization by means of the small punch test (SPT) is presented. Notched specimens are employed and fracture resistance is assessed through a critical value of the notch mouth displacement . Finite element simulations and interrupted experiments are used to track the evolution of as a function of the punch displacement. The onset of crack propagation is identified by means of a ductile damage model and the outcome is compared to the crack tip opening displacement estimated from conventional tests at crack initiation. The proposed numerical–experimental scheme is examined with two different grades of CrMoV steel and the differences in material toughness captured. Limitations and uncertainties arising from the different damage phenomena observed in the lowest toughness material examined are thoroughly discussed.
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