A coupled hydrogen (H) diffusion and higher-order strain gradient plasticity model is used to predict H localization in the ferrite (α) and austenite (γ) phases of super duplex steel under plane stress conditions. The geometry and finite element (FE) mesh are derived from optical micrograph images of the phase morphology, ensuring a realistic representation of the alloy’s microstructure. The model highlights the role of individual phases in coupled diffusion–mechanics interactions and demonstrates that the phase morphology significantly impacts the localization of H in the material. The results indicate that plastic strains in the ferrite phase exert a much greater influence on the spatial distribution of H than in the austenite phase. Finally, results of the model compare well with in situ X-ray diffraction (XRD) measurements of the temporal evolution of the strain induced by H charging. These findings provide valuable insight for future alloy design strategies aimed at mitigating H localization and preventing embrittlement.

Experiments involving abrupt non-collinear changes in the direction of loading in the plastic range have been performed on micron-scale, single crystal Cu cantilever beams to provide the first data of its kind on non-proportional loading. The data is used to assess whether existing strain gradient plasticity (SGP) theories are capable of reproducing complex deformation histories representative of micron-scale metal forming processes, for which non-proportional loading is common. The data is also used to explore an issue that has arisen in efforts to develop SGP that is sufficiently accurate for engineering applications and yet not overly complex. Specifically, using a combination of experimentation and computation, the paper examines the differences in predictions made by two classes of theories presently in the mainstream, termed “incremental” and “non-incremental”, when non-proportional plastic loading occurs at the micron scale. Orthogonal bend experiments are performed on Cu single crystal cantilever beams with square cross-sections that are symmetrically oriented with respect to the vertical and horizonal bending axes. In Stage 1, the force applied to the end of the cantilever is vertical, producing bending in the vertical plane. Abruptly, in Stage 2, a horizontal force is applied with either the vertical force held constant (force control) or the vertical end-displacement of the beam held constant (displacement control). Three cantilever sizes, with widths of the square cross-section of 2, 5 and 20 microns, have been tested. The strength elevation for cantilever widths decreasing from 20 to 2 microns is about a factor of three as compared to what would be expected based on conventional plasticity theory. The incremental and non-incremental SGP theories both capture the full non-proportional loading history, including the size effect. However, they differ in their predictions of behavior in the early portion of Stage 2, due to the abrupt change in the loading path. This difference will be assessed with the aid of experimental test data.

This paper presents a finite element implementation of strain gradient plasticity (SGP) and coupled hydrogen diffusion. The model encompasses stress-assisted diffusion, solute swelling, and multiple trap sites. The primary achievement of this paper is that a new transport term, that is driven by plastic strain gradients, has been developed and implemented with the finite element method (FEM). The model is applied to the problem of biaxial loading of a solid, under plane strain conditions, featuring a circular hole to investigate the extended transport equation. The results show that the hydrogen concentration increases significantly compared to conventional stress-assisted diffusion. In addition, the localization of hydrogen occurs in regions where there is a restriction on the plastic strain state, such as is often the case around microstructural sites. Together with other mechanisms at play during hydrogen embrittlement this preferential segregation could be used to explain the intergranular fracture mode often observed in experiments.

This paper presents an elastoplastic framework for mechanical-electrochemical damage in metals for simulating corrosion fatigue. The proposed numerical approach combines classical rate-independent isotropic von Mises elastoplasticity with an electrochemical kinetics model to simulate anodic dissolution-driven corrosion. The model's capabilities are demonstrated through benchmark tests and experiments. A hollow specimen was tested in a water environment, incorporating a membrane electrode for corrosion potential measurement and potential drop for crack initiation detection. The formulation accurately reproduces key features of corrosion fatigue, including diverse pit morphologies, time-dependent corrosion kinetics and the formation of multiple crack initiation sites, consistent with experiments.

This paper presents an in-situ observation, using neutron imaging, of delayed crack propagation in a high-strength martensitic steel specimen. Delayed cracking is believed to be caused by hydrogen embrittlement occurring due to the slow diffusion and accumulation of hydrogen ahead of a crack front, causing decreased ductility and eventual cracking under constant load. The experiment involved mechanical loading of a single-edge-notch bend specimen while submerged in an electrolyte solution (H<inf>2</inf>O + 3.5% NaCl) under cathodic polarization to facilitate hydrogen ingress. Intermittent crack propagation was observed for 12 h after the environment had been removed. The stress state at each crack configuration was extracted from a three-dimensional elastic–plastic finite element simulation, which was tailored to match the quantitative information acquired from the neutron radiographs of the fracture process. To gain insight into the evolution of hydrogen concentration with crack propagation, a modeling scheme for stress-assisted hydrogen diffusion was also employed.

To enhance the fundamental understanding for micromechanical lath martensite deformation, the microstructure as well as macro- and microscopic tensile properties of as -quenched 15-5 PH stainless steel are systematically analysed depending on the austenitisation temperature. Based on electron backscatter diffraction (EBSD) and backscattered electron (BSE) analysis, it is noted that the martensite morphology alters from a less defined to a more clearly defined parallel arrangement of the block and lath structure with increasing temperature. For an indepth quantification of the hierarchical boundary strengthening contributions in relation to local stress/strain heterogeneity, separate high-fidelity virtual microstructures are realised for the different scales (prior austenite grains, packets and blocks). This is consistent with the materials transformation process. The virtual microstructures are simulated employing the crystal plasticity finite element method (CPFEM) adapted for handling high dislocation density and encompassing all relevant strengthening mechanisms by boundaries, dislocations and solute atoms. While accurately capturing the measured size -dependent stress-strain behaviour, the simulations reveal in line with the experiments (Hall-Petch) that blocks are the most effective dislocation motion barrier, causing increased strain hardening and stress/strain heterogeneity. Furthermore, since strain localisation is predicted strongest in the distinct block structure, the experimentally observed early plastic material yielding is thought to be favoured here.

Background: The mechanical characterization of the cyclic elastoplastic response of structural materials at elevated temperatures is crucial for understanding and predicting the fatigue life of components in nuclear reactors. Objective: In this study, a comprehensive mechanical characterization of 304L stainless steel has been performed including metallography, tensile tests, fatigue tests, fatigue crack growth tests and cyclic stress-strain tests. Methods: Isothermal tests were conducted at both room temperature and 300 °C for both the rolling direction and the transverse direction of the hot rolled steel. Mechanical properties were extracted from the uniaxial experiments by fitting relevant material models to the data. The cyclic plasticity behavior has been modelled with a radial return-mapping algorithm that utilizes the Voce nonlinear isotropic hardening model in combination with the Armstrong-Frederick nonlinear kinematic hardening model. The plasticity models are available in commercial FE software and accurately capture the stabilized hysteresis loops, including a substantial Bauschinger effect. Results: The material exhibits near isotropic properties, but its mechanical performance is generally reduced at high temperatures. Specifically, in the rolling direction, the Young’s modulus is reduced by 16 % at 300 °C, the yield strength at 0.2 % plastic strain is lower by 23 %, and the ultimate tensile strength is lower by 30 % compared to room temperature. Fatigue life is also decreased, leading to an accelerated fatigue crack growth rate compared to room temperature. A von Mises radial return mapping algorithm proves to be effective in accurately modelling the cyclic plasticity of the material. The algorithm has also been used to establish a clear correlation between energy dissipation per cycle and cycles to failure, leading to the proposal of an energy-based fatigue life prediction model. Conclusions: The material exhibits reduced mechanical performance at elevated temperatures, with decreased monotonic strength, compared to room temperature. Fatigue life is also compromised, resulting in accelerated fatigue crack growth. The material’s hardening behavior differs at room temperature and elevated temperature, with lower peak stress values observed at higher temperatures. The radial return mapping algorithm can be used to determine the dissipated energy per cycle which together with fatigue testing has been used to propose a low cycle fatigue life prediction model at both temperatures.

The prediction of the cyclic deformation behaviour in lath martensite-based high-strength steels requires constitutive models that reflect the local stress and strain fields as accurately as possible. At the same time, the constitutive models should act as efficiently as possible in order to achieve the required high number of cycles in a finite time. Only few research works have studied the sensitivity of the local cyclic deformation in lath martensite to the power law-based flow rule (Hutchinson or Chaboche-Cailletaud) and the active body-centred cubic (bcc) slip systems ({110}(111) and {112}(111)) in the crystal plasticity finite element method (CPFEM). This paper, therefore, aims to provide some guidance in the selection of suitable flow rule and slip systems. Based on full-field micromechanical modelling of a medium-carbon steel under symmetric strain-controlled cyclic loading, it can be shown that the two most commonly used flow rules according to Hutchinson and Chaboche-Cailletaud are equally capable of predicting the local stress and strain distributions within the hierarchical martensitic microstructure. However, using the Hutchinson flow rule increases the computational performance for the quasi-rate-independent problem considered here. The local distributions found differ strongly from those in the parent austenitic microstructure. If plastic deformation is assumed not only on the slip systems {110}(111), as often done, but also on the {112}(111) type, a redistribution of the bimodal distributed local stresses occurs at a significantly lower stress level. The unimodal distributed local strains are less affected by this. In addition, it is found that slightly different critical resolved shear stress (CRSS) values for both slip system types influence the local stress and strain distributions less severely than the additional plastic slip activation in the material.

To predict and better understand the creep-fatigue behaviour of austenitic cast iron D5S under tension and compression dwell at 800 degrees C, a physics-based crystal plasticity model that describes the complex rate-and temperature-dependent deformation of the material as a function of the dislocation density is implemented. In addition to the tension and compression dwell direction, the effect of three different dwell times (30, 180 and 600 s) on the creep-fatigue properties is investigated. The dislocation density-based crystal plasticity simulations are compared to experimental tests from a prior work. While relaxation tests and low-cycle fatigue (LCF) tests without dwell assist in systematically identifying the material parameters, creep-fatigue (CF) data is used to validate the predictions. The virtual testing is performed on a large-scale representation of the actual test specimen with a polycrystalline structure. To analyse the fatigue damage mechanism, small-scale predictions are also conducted using a micromechanical unit cell approach. Here, a single graphite nodule frequently found in the material is embedded into the austenitic matrix. In the present work, a close agreement is achieved between the predicted CF behaviour and the experimental results. Consistent with the experimental findings, the simulation results show that the addition of compression dwell leads to an uplift of the overall tensile stress level, which significantly reduces the fatigue life of the material. The unit cell studies demonstrate that during this uplift, a strong localisation of stresses and strains arises at the graphite/matrix interface, triggering the nucleation and growth of cavities and/or debonding.

Metastable austenitic stainless steel (304L) samples with a rectangular cross-section were plastically deformed in torsion during which they experienced multiaxial stresses that led to a complex martensitic phase distribution owing to the transformation induced plasticity effect. A three-dimensional character-ization of the phase distributions in these cm-sized samples was carried out by wavelength-selective neutron tomography. It was found that quantitatively correct results are obtained as long as the samples do not exhibit any considerable preferential grain orientation. Optical microscopy, electron backscatter diffraction, and finite element modeling were used to verify and explain the results obtained by neutron tomography. Altogether, neutron tomography was shown to extend the range of microstructure charac-terization methods towards the meso-and macroscale.