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We investigate the influence of microstructural traps on hydrogen diffusion and embrittlement in the presence of cyclic loads. A mechanistic, multi-trap model for hydrogen transport is developed, implemented into a finite element framework, and used to capture the variation of crack tip lattice and trapped hydrogen concentrations as a function of the loading frequency, the trap binding energies and the trap densities. We show that the maximum value attained by the lattice hydrogen concentration during the cyclic analysis exhibits a notable sensitivity to the ratio between the loading frequency and the effective diffusion coefficient. This is observed for both hydrogen pre-charged samples (closed-systems) and samples exposed to a permanent source of hydrogen (open-systems). Experiments are used to determine the critical concentration for embrittlement, by mapping the range of frequencies where the output is the same as testing in inert environments. We then quantitatively investigate and discuss the implications of developing materials with higher trap densities in mitigating embrittlement in the presence of cyclic loads. It is shown that, unlike the static case, increasing the density of “beneficial traps” is a viable strategy in designing alloys resistant to hydrogen assisted fatigue for both closed- and open-systems.

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.

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.

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.

Aluminium based nanostructured materials with additions of 0.5, 1 and 1.5 wt.% of zirconium have been produced and sintered using the spark plasma sintering technique in order to promote the nucleation of ZrAl3 platelets. The mechanical behaviour of all these nanocomposites was determined by means of the Small Punch Test. Zirconium additions significantly decrease the mechanical properties of these products when sintering time at the sintering temperature (625 °C) is short (3 min). Nevertheless, when the sintering time increases to 1 h (intermetallic crystallization), the zirconium additions show the expected effect: the stiffness and the yield strength increase while ductility and toughness decrease. The maximum load increases until a 0.5 wt.% Zr is attained and suddenly drops when the Zr content surpasses 1 wt.%. © 2012 Elsevier B.V. All rights reserved., The authors want to acknowledge the financial support of the Ministerio de Educación y Ciencia (Plan Nacional I+D+i), through the project numbers MEC-04-MAT2004-06992-C02-01 and MAT2008-06879-C03-00.

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.

A hot rolled API X-70 steel plate and its heat-affected zone (the region with the maximum hardness and lowest toughness of the welded joint made using this steel) were employed to obtain the material’s room temperature elasto-plastic fracture toughness, JIc, by means of small punch tests (SPTs) using both conventional un-notched samples and longitudinally-notched SPT specimens. In the latter case, the notches were manufactured by micromachining different notch depth-to-thickness ratios (a/t = 0.3 and 0.4). The representative toughness parameter used with the conventional SPT tests was the maximum strain measured directly in the failed region, while in the case of the notched samples, the consumed energy until the initiation of a crack from the tip of the notch was considered the most useful parameter of choice. The onset of crack initiation was determined directly from the load-displacement plot of each test with the aid of scanning electron microscope observations performed on different samples over which interrupted tests had been conducted. These tests were interrupted at different percentages of the maximum registered load. A simple correlation between the energy consumed until the initiation of crack growth in the notched SPT sample and the critical J value obtained using standard tests (J-R curves) was determined, defining an easy and promising way to derive fracture toughness from miniature SPT tests.

A new methodology to determine the elasto-plastic fracture toughness, JIc, by means of notched small punch tests (SPT) samples is reported. Standard SPT samples were used after being longitudinally notched machined from the centre of one side of the sample to the centre of the opposite side, producing a notch depth-to-thickness ratio a/t= 0.4. The onset of crack initiation was experimentally determined directly from the experimental load-displacement plot of the test and also with the aid of scanning electron microscope observations performed on different samples, with tests being interrupted at different percentages of the maximum registered load. The test was also modelled using finite element analysis and the J-integral was evaluated as a contour integral in ABAQUS. The obtained results were compared with the critical J values of the steel determined using standard tests (J–R curves) and the differences found were duly justified.

The typical heat-affected zone developed in an X-70 steel, usually used in pipeline manufacture, has been simulated via thermal treatment. A non-equilibrium microstructure consisting of bainite, with ferrite and some martensite, has been produced and mechanically characterised, resulting in much greater hardness and strength and a lower ductility and toughness than the corresponding base metal. This also has a lower ductility. Different single-edge notched bending specimens with different crack lengths (a/W between 0.1 and 0.5) were experimentally tested to assess the fracture behaviour of this product under different degrees of constraint. The J–a resistance curves at room temperature were determined, and the obtained results were explained by the effect of constraint on ductile crack growth.

In this paper finite element simulations of mismatched welded joints at different temperatures have been performed in order to analyse the influence of temperature on their fracture behaviour and to obtain their transition curves. Cleavage is described by means of the Beremin micromechanical model. The ductile failure model is based on the so-called complete Gurson model. Both fracture mechanisms have been implemented in FORTRAN and introduced in ABAQUS by two user subroutines. The weld configuration significantly affects the stress and strain fields and different transition curves are obtained for the different configurations. The highest transition curve is obtained for the narrowest overmatched weld, being its transition temperature the lowest.

In this work, an analysis and numerical study have been carried out in order to determine the best candidate brick from the thermal point of view by the finite element method. With respect to the ecological design and the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviours, which fulfils all thermal requirements of the new CTE Spanish rule for further energy savings. The conduction, convection and radiation phenomena are taking into account in this study for four different types of bricks varying the material conductivity obtained from the experimental tests. Based on the previous thermal analysis, the best candidate was chosen and then a full 1.05 × 0.35 × 1.0 m. wall made of these bricks was simulated for fifteen different compositions and temperature distribution is also provided for some typical configurations. The major variables influencing the thermal conductivity of these walls are illustrated in this work for different concrete and mortar properties. The finite element method (FEM) is used for finding accurate solutions of the heat transfer equation for light concrete hollow brick walls. Mathematically, the nonlinearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of four hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. In order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given. Finally, conclusions of this work are exposed.

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. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

A ductile-failure model for analysing the fracture behaviour of welded joints has been implemented. Finite element analyses of mismatched welded joints have been performed using the computational cell methodology applied to SE(B) specimens. Different crack lengths, material mismatching, and widths of weld metal have been considered. Ductile parameters have been experimentally and numerically obtained. The influence of geometry and material mismatching on the fracture behaviour of cracked welded joints has been validated by means of a testing program. In addition, the experimental results have been explained through the crack tip constraint, which has been numerically determined.

By means of finite element analyses of plane strain crack tip stress fields from homogeneous and heterogeneous modified boundary layer formulations, as well as homogeneous and mismatched full field solutions, a new constraint parameter β m has been established for overmatched welded joints, allowing the material mismatching effect on the crack tip stress fields to be quantified. In the case of complete specimens, both geometry and material mismatching affect the crack tip stress fields, and a total constraint parameter β T can be defined. This approach allows to quantify the stress fields directly from the values of the remote applied load.

— A ductile medium strength steel has been modelled by means of the Gurson model, and been used to investigate the effect of crack tip constraint in several fracture mechanics specimens. Both numerical and experimental results have been obtained, in the course of the crack extension process, for single edge notch bending specimens with different crack length-to-width ratios. The geometries with the shorter cracks always exhibited higher J values at initiation and steeper J crack growth resistance curves, and these results have been explained in terms of the stress and strain fields and damage development in the region ahead of the crack tip.

The characterization of the mechanical behaviour of structural materials, with the exception of material hardness, is a destructive procedure which requires direct extraction of test specimens from the component to analyse. Because this component needs to be operative, these specimens have to be as small as possible, in order not to affect the behaviour of the component and in order to allow easy reparation of the ‘damaged’ component. However, tests with miniaturized specimens are not defined in standards. Thus, the results obtained with these tests have to be interpreted in order to obtain the actual properties of the components from which the specimens have been extracted (Lucas et al., 2002). The small punch test (SPT) is very useful in all applications that require the characterization of the mechanical behaviour of structural materials or operational components without compromising their service (Lucon, 2001), as in the case of nuclear or thermal plants. Another application is the study of small testing zones. Thus, this test has been recently applied to the mechanical characterization of metallic coatings (Penuelas et al, 2009) or the heat affected zone of welds (Rodriguez et al, 2009), which are practically impossible to characterize by means of the conventional mechanical tests. Advance constitutive models frequently include parameters that have to be identified through numerical simulation of tests and mathematical optimization of variables, because they cannot often be directly measured in laboratory. In this paper, an inverse methodology for the identification of the mechanical and damage properties of structural steels has been developed. Thus, from the load-displacement curves obtained during the non-standard SPT, the mechanical and damage properties will be obtained. Moreover, this methodology also allows simulating the SP test with numerical methods. Structural steels may exhibit creep behaviour and behave according to the Hollomon’s law (σ = K·epn). Besides, ductile fracture of metallic materials involves micro-void nucleation and growth, and final coalescence of neighbouring voids to create new surfaces of a macro-crack. The ductile failure process for porous materials is often modelled by means of the Gurson model (Gurson, 1977), which is one of the most widely known micro-mechanical models for ductile fracture, and describes the progressive degradation of material stress capacity. In this model, which is a modification of the von Mises one, an elastic–plastic matrix material is considered and a new internal variable, the void volume fraction, f, is introduced. Although the original Gurson model was later modified by many authors, particularly by Tvergaard and Needleman (Tvergaard, 1981; Tvergaard, 1982; Tvergaard & Needleman, 1984), the resultant model is not intrinsically able to predict coalescence, and is only capable of

Plane-strain elastic-plastic crack-tip fields have been modeled with modified boundary layer formulations based on the first two terms K and T, of the elastic field. These formulations match the appropriate full field solutions. Compressive T stresses reduce the stresses by an amount which is independent of radial distance, corresponding to the introduction of a second term in addition to the dominant plastic singularity. Geometries which maintain J-dominance are characterized by zero or positive T stresses, while geometries with negative T stresses can be described by a two-parameter characterization using J and T into full plasticity.

The critical J integral and crack tip opening displacement, CTOD, at cleavage instability of a low carbon high strength steel were obtained from three point bending specimens with different crack to width ratios (0.04 < a/W < 0.48). The geometry dependence of the elastoplastic toughness parameters has been correlated with the T stress. The obtained results have been explained by means of a local cleavage fracture criterion applied to the brittle to ductile transition behaviour of the steel., Support for this work was provided by CICYT (Spain), Project Reference Number PB92-1084-C02.