Accurate modelling of plastic and creep deformation, along with the associated damage mechanisms in 316H stainless steel under high-temperature and complex loading conditions, is essential for ensuring the long-term structural integrity of power plant components. Robust physics-based models contribute to more accurate life assessment procedures, thereby improving safety and extending component service life under creep conditions. However, current approaches often lack accurate microstructure-sensitive models that can correlate experimentally observed local creep damage with key microstructural features such as grain orientation and morphology in creep damage prediction. To address this knowledge gap, a combined modelling and experimental approach is employed to investigate creep damage initiation in 316H stainless steel at 550 degrees C. A crystal plasticity finite element (CPFE) model is developed to simulate the primary and secondary stages of creep deformation. To accurately predict local deformation under realistic boundary conditions, a new modelling strategy is introduced, embedding crystal plasticity domains within larger-scale geometries. Furthermore, a novel methodology is introduced to define damage initiation criterion by employing a classification algorithm to correlate experimentally observed creep damage with internal variables from the CPFE model. This data-driven approach enables the development of a predictive equation for identifying damaged grain boundaries. This equation represents a significant advancement over phenomenological approaches, such as the stress-modified ductility exhaustion (SMDE) model. The proposed model predicts approximately 67% of observed creep cavities at grain boundaries in the analysed regions, demonstrating the strong potential of a data-driven modelling framework for microstructure-sensitive damage prediction.

Reliability analysis of complex engineering structures faces significant computational challenges, particularly when estimating small failure probabilities that are critical for aerospace safety requirements. The high computational cost of evaluating limit state functions through numerical methods such as finite element or boundary element analysis often makes direct Monte Carlo simulation prohibitive. This study employs the Global-Error Active Learning Function (GEALF) method, which strategically selects training points to maintain accuracy while substantially reducing computational demands. The approach is further enhanced through multi-fidelity modelling, using low-fidelity models for global exploration and reserving computational expensive high fidelity evaluations for critical regions near the limit state. The methodology is demonstrated through two examples. First, a two-dimensional analytical multimodal function validates the approach against Monte Carlo simulation, achieving errors below 1.32% with only 36 high-fidelity and 75 low-fidelity evaluations compared to the benchmark 108 Monte Carlo samples. Second, a shallow shell structure under cabin pressure is analysed and the stress intensity factor was evaluated using the Dual Boundary Element method. The multi-fidelity approach requires approximately 35 high-fidelity and 80 low-fidelity evaluations, compared to the 267 training points needed for traditional Kriging-based Monte Carlo simulation. This shows a computational cost reduction of around 60% in terms of numbers of high-fidelity calls. While relative errors increase for very small failure probabilities (reaching 5.43% at ~ 10-6), the accuracy remains within acceptable level.

Conveyance tube manufacturing is an energy-intensive process which promotes rapid surface oxidation of curved surfaces. Previous works used computational, experimental, and theoretical techniques to assess oxidation of curved surfaces. Fast, flexible computational predictions of oxide thickness can provide the continuous data necessary to generate a spatiotemporal stress profile for application to the high-level Advanced Oxide Scale Failure Diagram (AOSFD) developed in this work. To demonstrate the application of the AOSFD to conveyance tube normalisation, the oxide states after induction vs. gas-barrel heating were compared. Induction heating technology is an example of a current technological development in high-temperature steel processing which offers improved operational control and suitability for decarbonised steel processing. Current frequency control during induction heating decreases the resultant strain magnitude in the oxide thereby eliminating the compressive failure modes observed during gas-barrel heating. Higher-than-typical temperatures result in an increased tensile strain component, increasing interfacial failure probability during induction heating. However, the advantages of induction heating technology, in terms of oxide failure management, can only be achieved with sufficient electromagnetic design controls. This conclusion agrees with purely temperature-based studies of oxide failure, but the AOSFD approach accommodates the mechanical and kinetic phenomena of the oxide by combining diffusion and fracture mechanics analyses into a single diagram which is quick and simple to apply to industrial contexts which demand oxidation control on curved surfaces.

Mechanical behaviour of engineering alloys is dependent upon their microstructure which can be affected by processing and heat-treatment. In traditional mechanics the microstructural dependence is simplified by introducing laws that govern the behaviour of continuum solids and adjust their parameters according to the average properties of the material. This approach has served industrial applications well in most cases, however in high value and safety sensitive components, seemingly negligible changes to the microstructure can significantly alter the outcome of a safety assessment analysis making the current average continuum laws over-simplified, overly conservative, and potentially costly. For example, small changes in the welding parameters used in manufacturing a steam generator can affect the texture of the weld, thus influencing its hardening behaviour and residual stress profile which can in turn decide its estimated safe life [1]. For this reason, detailed experimental characterisation techniques combined with microstructural simulations have been developed in the recent decades which can underpin and predict the behaviour of materials at small length scales with precision [2]. The downfall, however, has been the transition of these computationally expensive models along with limited number of detailed characterisation to statistically representative robust models that can predict the behaviour of an industrial scale component. SINDRI is a project which aims to tackle this issue. It employs the recent advances in high-throughput characterisation technique such as high angular resolution electron back-scatter diffraction with state-of-the-art modelling. The high-fidelity characterisation data informs computationally expensive microstructural simulation techniques (e.g. crystal plasticity finite element), whose uncertainty is quantified using machine learning algorithms (e.g. Gaussian Process). The resulting approach is a route to build probabilistic models that can capture the variation in the mechanical behaviour of service components informed by the statistical distribution of key features within its microstructure. This paper provides a case study of this approach focusing on residual stress of a weldment. The variability of the weld residual stress as response to changes in its microstructural texture is quantified. The texture variation within a weldment has been extracted. Crystal plasticity analysis is used to connect the variation in texture to changes in the yield stress, simplified through Gaussian Process to avoid performing hundreds of crystal plasticity simulations. The variation in the yield stress is used to estimate the variability in the weld residual stress. It is argued that such changes in the residual stress as function of microstructure can be used within a probabilistic framework to assess the integrity of safety sensitive components.

This study introduces a Bayesian-informed framework for fatigue life prediction in shallow shell structures. The methodology focuses on inferring the Equivalent Initial Flaw Size Distribution (EIFSD), a critical parameter for structural durability. Bayesian inference, combined with a Co-Kriging surrogate model, enables statistically robust predictions while accounting for uncertainties in material properties, geometry, and loading. The Dual Boundary Element Method (DBEM) is employed for crack propagation due to its efficiency and re-meshing-free modelling. To improve inference efficiency, an iterative parameter space narrowing strategy is proposed. Instead of exhaustively sampling the entire space, the method begins with coarse discretisation to locate high-probability EIFSD regions, then refines them adaptively. A numerical example involving a fuselage window under cabin pressure demonstrates the method. Surrogate models trained on DBEM-generated data significantly reduce computational cost. The proposed strategy achieves high-precision inference, with only 0.059% error in the inferred mean and 5.2% in standard deviation, while reducing CPU time by 52% compared to dense sampling.

Steel components in advanced gas-cooled reactors (AGRs) are subject to multiaxial deformation at high temperatures. Neutron diffraction has been used to study the {111}, {200}, {220} and {311} grain family, also known as lattice plane, response during in-situ loading and relaxation of notched bars of 316H stainless steel at 550 degrees C. These experimental conditions have been modelled using a multiscale approach that employs finite element models at the continuum, component, scale as boundary conditions for a crystal plasticity finite element model. For the bar with the highest triaxiality factor at the diffracting region, the CPFE model was in good agreement with the experiment results. The most notable difference was the reduced accumulation of intergranular strain in the {200} grain family and significant stiffness difference in the {220} grain family in the transverse direction. For the bar with the lowest triaxiality factor at the diffraction region, the agreement between the CPFE model and experiment was acceptable but poorer than the bar with the higher triaxiality factor. This is due to the CPFE sensitivity to the macroscopic boundary conditions applied. Reasonable agreement was achieved for the relaxation dwells. The modelling has shown that multiaxial conditions, enforced by the multiscale approach, cause an increase in stiffness in the CPFE response, resulting in the reduction in the intergranular strain accumulated.

Components in civil nuclear power plants are subject to high temperatures and pressures. Current methods to perform structural integrity assessments on said components are often overly conservative and cannot predict complex loading conditions. This is partially due to these approaches accounting for only macroscopic material behaviour and ignoring behaviour at a granular level. This has led to increased popularity in crystal plasticity finite element (CPFE) modelling due to its ability to simulate macroscopic and mesoscopic behaviour from a mechanistic perspective. A key factor in the accuracy of CPFE modelling is the boundary conditions applied. Periodic conditions allow the simulation of uniaxial stress states however, exploring more complex loading conditions is challenging. This paper presents a multiscale methodology to apply complex loading conditions to a CPFE model. The material used in this study is Type 316H stainless steel. A macroscopic finite element model is produced of the desired component. At the region of interest, the resulting displacements generated are interpolated and applied to the surfaces of a CPFE model. To partially validate this approach, uniaxial and biaxial simulations have been performed. The uniaxial simulations demonstrate that this approach captures uniaxial behaviour accurately at the macro- and meso-scale, as evidenced by comparisons with lattice plane deformation measured by diffraction techniques. The biaxial simulations match qualitatively well with experimental findings, but more quantitative comparisons must be drawn to exhibit the predictive capabilities.

A coupled crystal plasticity phase field damage framework has been developed and applied to modelling damage initiation. A novel implementation of a grain misorientation angle dependent critical energy release rate has been used to determine a reduction in the local critical energy release rate resulting from the effects of intergranular carbide precipitates and grain boundary misorientation. When applied to a notched high temperature 316H austenitic stainless steel specimen, a good correlation between experimental results and void nucleation statistics for a misorientation dependent critical energy release rate was obtained. This has been evaluated through comparison with correlative electron microscopy experimental results, showing the potential of phase field models in the area of early damage formation. Additions to include plastic strain and creep deformation effects were made, and comparisons were drawn with experimental data to investigate the contributions of microstructural geometry properties such as the difference in and average values of Schmid factors across grain boundaries, as well as the loading direction stress and dislocation densities. The limitations to this approach and opportunities for further work in this area are discussed, with specific interest in the need for additional literature data characterising grain boundary carbide precipitation and cavity nucleation analysis.

Residual stresses are a crucial factor in assessing the integrity of welded joints. These stresses are known to influence the joint's strength under additional loading, with the altered grain structure at and near the joint a complicating factor. Consequently, a mesoscale model is essential to understand the accumulation of damage in components subjected to external loading, as well as the impact of prior loads on failure. This study addresses the interplay between loading direction and grain morphology, explicitly investigating damage accumulation. The mesoscale model includes a coupled crystal plasticity and a phase field fracture model to estimate the deformation induced during a laser beam weld of 316H stainless steel. The displacement boundary condition was derived from a mechanical model of the weld, with the application of a Chaboche model. The temperature field required for the grain growth and mechanical models were obtained through a thermal fluid dynamics framework. Investigation of crack initiation and propagation was carried using a phase-field fracture model, which allowed the consideration of prior loading. This study indicated that the direction of loading plays an important role in damage susceptibility. The modified grain structure based on the welding simulation showed a different strain at failure compared to the 316H stainless steel parent material. The achieved strain at failure was found to be lower in normal loading compared to the transverse direction. Presently, the crystal plasticity model fails to estimate the macroscopic residual stresses, illustrated by damage propagation resulting in earlier than expected ductile failure upon reloading. The potential causes are addressed and discussed in detail.

Electron beam welding is an advanced joining technique which induces narrow weld region with minimal heat affected zone and weld-induced distortion. This reduces residual stresses in the joints which can be detrimental to structural performance of components in safety critical industries. Being an autogenous process, electron- beam welding generates a highly textured, columnar microstructure in the weld zone which have distinct properties when compared to the parent material region. Determining mechanical properties of the weld material assists in accurate assessment of the joint. However, extracting weld material specimens to determine plastic properties becomes increasingly cumbersome in thinner weld joints. An alternate approach has been demonstrated in this work wherein mechanical properties were derived using the weld microstructure in a crystal plasticity finite element (CPFE) framework. The initial calibration of the CPFE parameters was done using experimental data from thick weldment. These calibrated values were used to obtain the elastic and elastic-plastic properties of thinner weld materials by deforming corresponding synthetic microstructures whose attributes were determined by Electron Backscatter Diffraction analysis. The resultant properties were incorporated in a finite element (FE) based weld simulation to determine the residual strain. These results were compared with the residual strain data obtained using X-ray diffraction and good agreement was observed.

Fatigue crack growth in thick-section metals is typically controlled by an internal plane strain region where strong triaxial constraint of the crack tip occurs. However, the crack tip stress state in this region is challenging to measure. We have used neutron diffraction to study the plane strain section of fatigue crack tips in situ. A stroboscopic form of neutron diffraction using a moving frame-of-reference was developed to measure crack tip strains as a function of phase in the fatigue loading cycle without interrupting the cyclic load. Using point measurements of near-tip strain in 7475-T7351 aluminium alloy in conjunction with finite element analysis, we can estimate the extent of the crack tip plastic zone, verifying that it is small for this material and set of loading conditions.

Within the NeT project [1], Task Group 8 examines a steel plate (French grade 18MND5 close to ASTM A508 Gr.3) containing a five pass “slot” weld made with Ni base alloy (Alloy 52) consumables. NeT TG8 has been organized to address welding repair issues. The TG8 round robin specimen is closely based upon the TG4 design [2], except for the plate thickness that is increased up to 30 mm for more thermal inertia, self-clamping conditions and to reduce distortions that may affect the accurate definition of residual measurement position. It thus presents all the advantages and challenges of the TG4 specimens, namely, the generation of a complex 3D residual stress distribution in a compact, portable specimen that is amenable to rapid measurement of residual stresses by diverse techniques, with a significant volume of weld metal that undergoes multiple high temperature thermo-mechanical load cycles. The use of a nickel-based alloy as filler metal adds considerable residual stress measurement challenges, while this configuration undergoes a complex mismatch behaviour with the base metal where phase transformations and tempering effects occur in the Heat Affected Zone (HAZ). The residual stress measurement and simulation round robins for TG8 are ongoing. What is presented here is therefore the first phase results of the behaviour of the TG8 specimens. Finite element simulation results are compared with residual stresses determined experimentally thanks to different techniques. The agreement between stresses measured by the Contour Method and by neutron diffraction is generally very good, simulation exhibits complex behaviour that help to interpreted some of the measurements and the lessons learned will allow to conduct a second phase benchmark with possible improvement in residual stresses assessments and in-depth analyses for a better understanding of such a dissimilar weldment.

A tool to implement a length scale dependency to classical crystal plasticity simulations is presented. Classical crystal plasticity models do not include a size effect; therefore, the size of the grain does not influence the simulated deformation. Classical crystal plasticity advancements have been through the inclusion of stress or strain gradient based constitutive models to improve the simulation of length scale dependent deformation. However, this tool presents an alternative to implementing a length scale, where the influence of slip pile-up in the form of dislocations at grain boundaries as a potential to explaining the Hall-Petch effect in materials. This is achieved by calculating the slip distance in adjacent grains for each slip system, by assuming the total slip length spans the grain in the slip direction. These calculations can occur in two ways. The first is the analysis occurs at the start of the simulation, therefore, only occurs once. If this approach is used, the computational cost of this tool is minute. However, if the simulations consider large deformations, during which it is expected that the grains are going to undergo large rotations, then it would be advantageous to the have the tool recalculate the information during the analysis. Consequently, the computational cost would depend on the resolution of the modelled geometry, the number of grains, and the number of slip systems. The tool also provides a capability to develop constitutive models based on complex grain boundary features which can be implemented in classical crystal plasticity models and gradient based crystal plasticity models. The described calculation process is implemented through a Fortran subroutine, which has been designed to be easily used in crystal plasticity simulations. The presented tool also includes Python code designed to link with microstructures built using DREAM.3D to extract the required input data to the Fortran subroutine. The proposed tool is not limited to classical crystal plasticity formulations, instead the data extracted and outputted from the Fortran subroutine can be used to serve alternative purposes in both stress and strain gradient crystal plasticity models. The proposed tool can be modified to extract additional data to that presented. The slip distance in the adjacent grain, the distance from the grain boundary of the current calculation point, and the interaction between slip systems between grains can be used in any crystal plasticity constitutive models.

Generic hollow pump bodies made from aluminium alloy 2014A forgings have been solution heat treated and quenched into either cold water or polyalkylene glycol (PAG) solutions. An industry standard PAG type synthetic quenchant was evaluated, and the influence of two concentrations of the PAG solution on residual stress in the pump bodies was characterised, using neutron and X-ray diffraction. These residual stresses were then compared to those resulting after a pump in the as quenched condition was subject to a widely known but controversial commercial vibratory stress relieving procedure. The use of neutron diffraction allowed the through thickness residual stresses to be evaluated in the pumps. Results demonstrate that PAG quenching is highly effective at significantly reducing residual stress when compared to cold water quenching, but the impact is non uniform and cannot be simply quantified. In this investigation, we prove the effect of vibratory stress relief is negligible, and much less than that achieved by PAG quenching.

To ensure a more representative simulation of meso‑scale and macro-scale deformation, it is important the underlying constitutive relations are advanced to more effectively incorporate the micro-mechanisms such as those operative near the grain boundaries. Critical features necessary for accurate predictions include the influence of grain size, morphology, and misorientation on the local deformation. In this study, a length scale dependence is incorporated into classical crystal plasticity simulations. The implementation is based on the influence of dislocation slip pile-up at grain boundaries based on the Hall-Petch theory in materials. This was achieved by applying a purpose-built algorithm to extract the slip distance in adjacent grains along each slip direction. This extracted data was used to adjust the critical resolved shear stress within the grain. The adjusted slip law was then implemented in constitutive models to predict the yield stress and hardening evolution of material for different grain sizes. The interaction of the slip systems between grains was also considered, which resulted in the adjustment in the extent of slip transfer permitted between grains based on misorientation. The proposed approach can be applied in both finite element and spectral methods for solving the continuum differential equations. The accuracy of the proposed model was investigated by considering the meso‑scale predictions using two-dimensional simulations, in addition to macro-scale predictions using three-dimensional models. Furthermore, the validity of the method was experimentally supported by tracking the development of intragranular residual elastic stresses, measured via high-resolution electron backscatter diffraction. The discussed results highlight a new potential of enhancing the way in which complex grain boundary interactions contribute to local deformation in crystal plasticity simulations.

Steel components in the boilers of nuclear reactors are subject to high temperatures and varying loading conditions. This can introduce time-dependent and time-independent plasticity, which can interact with one another. Specimens of 316H austenitic stainless steel were heated to 550 °C and tensile pre-strained to 8%, 11% and 14% followed by 200 h, 280 MPa creep tests. These tests showed an increase in creep resistance with increasing tensile pre-strain. Macroscale simulations using RCC-MR deformation laws proved ineffective at predicting this interaction. Microscale crystal plasticity simulations proved effective at predicting the trends observed experimentally, hence demonstrating the potential of crystal plasticity as a predictive tool for structural integrity analysis.

Weld residual stress and fracture behavior of 316L electron beam weldments, which are of particular interest in power generation industry, were investigated in this work. Two butt-weld joints were manufactured in stainless steel 316L plates of 6 mm and 25.4 mm thicknesses. Three complementary methods were used to measure the three orthogonal components of the residual stress in the weld coupons, and fracture tests were conducted on single edge notched bending specimens extracted from different regions of the welds and parent metals. The residual stress measurements showed a maximum value of 450 MPa in longitudinal direction, while it was less than 150 MPa in the other two orthogonal directions, revealing that in our material, and with the chosen weld parameters, the residual stresses were biaxial. The fracture resistance of the weldment and parent material was similar, with material microstructure differences being more significant than the measured residual stresses. The study suggests that 316L electron beam weldments are not susceptible to fracture failure due to their high ductility and ability to relieve residual stresses through gross plasticity. Electron beam welding may therefore be suggested as a reliable manufacturing technology for safety critical 316L components.

This paper presents results from a numerical and experimental investigation motivated by the need to explore the effectiveness of residual stress relief techniques in aluminium alloy engineering components of complex geometry. Quenching is part of the heat treatment to establish mechanical properties. It can create high levels of residual stress in an engineering component. Finite element analysis (FEA) was used to predict the residual stresses generated by quenching and the location of peak residual stresses corresponding to probable in service failure sites. The residual strains and stresses were characterised using neutron diffraction techniques in components with high and low quench stresses to validate a FEA study, and also to appraise the evolution of a commercial stress relief method. An excellent correlation existed between the simulations and measurements.

Small punch test offers unique capabilities in extracting material properties from a very small volume of material. This is an attractive prospect for measuring the properties of hazardous materials such as those in the nuclear industry. Although standards are being developed for formalising small punch test, the uncertainty associated with its results due to issues with misalignment, sample geometry deviation, friction coefficients and damage evolution have not been fully understood. In this article, the effects of mechanical properties, damage parameters, friction coefficients, pre-tightening condition and geometry uncertainty on the small punch test response of ductile materials are evaluated by finite element analyses. A comprehensive sensitivity study has been carried out on the variation of the reaction force induced by above factors and their influences have been quantified and ranked at various stages of small punch testing. It was observed that the material mechanical properties and geometrical dimension deviations have significant effects on all stages of small punch test. However, damage parameters and friction coefficients mainly play roles at the maximum load point. The uncertainty in values measured for yield stress and ultimate tensile strength from small punch test of a sample with ±5% deviation in thickness from standard value was calculated to be of the same order of magnitude of the respective material properties. A nominalization method for considering the specimen thickness deviation is provided which can help to eliminate the effect of specimen thickness deviation in the measurements carried out by small punch test.

In this study we investigated the evolution of meso-scale internal stresses and those effects on local deformation behaviour during incremental plastic and creep deformation in type 316H stainless steel at 550 degrees C, using in-situ X-ray synchrotron diffraction and crystal plasticity modelling. Owing to the fast data accusation rate of synchrotron diffraction technique, for the first time, the transient behaviour of different grain families was captured during initial fast stress relaxation period of the displacement controlled creep dwells. Significantly it is found that the evolution of internal stresses during time independent plastic deformation is distinct from that during time dependent creep deformation. During plastic deformation, lattice strains in the {311) grain family exhibit linear behaviour whereas during creep deformation it exhibits non-linear behaviour, instead the {1 11) grain family exhibit linear behaviour. A novel unified constitutive law was devised within crystal plasticity framework based on the theoretical physics; the model successfully predicts the macroscopic deformation behaviour as well as the distinction between the evolution of meso-scale internal stresses during plastic and creep deformation, therefore, correctly accounting for the effect of internal stresses generated during plastic deformation on the subsequent creep deformation. The validated model has elucidated the grain-neighbouring effects on individual grain deformations. (c) 2021 Elsevier Ltd. All rights reserved.