Complex Thermomechanical Loading Research Articles

A data-driven underground gas storage production system string failure prediction model for time-varying reliability analysis

In underground gas storage (UGS) systems, the production tubing string system undergoes complex thermo-mechanical loading conditions, leading to fatigue damage accumulation and potential failure risks. To accurately assess the fatigue reliability and mitigate risks, it is crucial to develop a data-driven physics-informed uncertainty modeling approach that captures the coupled thermo-mechanical effects and accounts for various uncertainties. This study proposes a data-driven physics-informed modeling method based on thermo-mechanical coupling for fatigue reliability assessment and risk mitigation in critical UGS systems. A quantitative analysis method is introduced, which relies on small-scale multi-stage loading experiments and combines the stochastic degradation process with time-series reliability theory. To analyze the fatigue life of joints under complex loading conditions, a modified S-N curve model is developed. This model takes into account the influences of the dimension coefficient, stress concentration factors, surface finish coefficients, and thermal load. It considers the uncertainties associated with different temperature loads and surface finish on fatigue life. By integrating physics-informed modeling, uncertainty quantification, and fatigue damage accumulation analysis, this approach provides a comprehensive framework for fatigue reliability assessment and risk mitigation in critical UGS systems. It enables informed decision-making for safe and reliable operations, as well as optimized maintenance strategies, ultimately enhancing the overall system performance and mitigating potential failures.

Investigating the controls of ice-wedge initiation and growth using XFEM

Ice-wedges are periglacial landforms that develop as a result of thermal contraction-cracking in continuous permafrost regions, which appear as polygonal networks on the ground surface. Given their complex thermo-mechanical loading history, very few related numerical models have so far been developed. In this study, 2-D eXtended finite element simulations are employed to represent the formation process of ice-wedges and to investigate the effect of select environmental controls on crack initiation and growth. Seventeen combinations of soil type and temperature–time series are used in four case studies addressing model testing, the permafrost stress regime, the freezing volumetric expansion of porewater, and a new remeshing process introduced to simulate ice-wedge growth over multiple years. The model testing shows good agreement with field observations from the Arctic and demonstrates the ability of the modelling procedure to reproduce the salient features of thermal contraction-cracking. The permafrost stress regime is found to be strongly affected by soil type and climate, with coarse-grained soils and cold climates leading to higher tensile stresses than fine-grained soils and warm climates. Higher tensile stress are also predicted for saturated soils due to the freezing volumetric expansion of porewater.

A multiscale finite element modeling for predicting the surface integrity induced by thermo-mechanical loads during high-speed milling of Ti-6Al-4V

High-speed milling (HSM) of Ti-6Al-4V is subjected to complex thermo-mechanical loads, leading to alteration in metallurgical conditions within the cutting deformation zones, adversely impacting the mechanical performances of manufactured products. Hence, inclusive insight into microstructural alterations within the Adiabatic Shear Band (ASB) and the milled surface becomes essential for better service performance. This study first developed a Finite Element (FE) milling model to simulate the machining process of Ti-6Al-4V. The proposed FE model is validated through experimental results regarding cutting forces (CFs), cutting temperature (CT), and chip geometry, where the absolute relative error between simulations and experiments was less than 15 %. Secondly, Zenner-Holloman (Z-H) and Hall-Petch (H-P) equations were incorporated into a user-defined subroutine to simulate dynamic recrystallization (DRX) for grain size and microhardness prediction. Simulation results revealed that the grains became finer in the ASB than on the milled surface. In particular, when the cutting speed and feed rate were increased to 350 m/min and 0.30 mm/tooth, the grain size in the ASB decreased from 14 to 0.68 and 0.44 µm, while in the topmost milled surface, it reduced to 7.06 and 6.75 µm, respectively. Conversely, microhardness exhibited an inverse correlation with grain size and increased with cutting speed and feed rate. Furthermore, the impact of increased plastic strain and temperature on the grains during chip segmentation was also examined. Finally, the proposed FE model validity was established by comparing simulated results with experimental data using advanced characterization techniques. This research significantly contributes to a comprehensive understanding of microstructural evolution and its implications for the mechanical performance of machined titanium components.

An analysis method to assess in-Calandria corium retention time in PHWRs

In Pressurized Heavy Water Reactors (PHWRs), during a postulated severe accident involving the core collapse, the core internals would fall onto the Calandria bottom and form a debris bed. Under such conditions, the core debris bed would be contained by the Calandria, which also facilitates its cooling by the Calandria vault water. In absence of any accident management action, the Calandria temperatures would rise, causing loss of material strength that may also threaten the structural integrity of Calandria. The gross structural failure of Calandria would limit its ability to further retain the core debris and would jeopardize the in-vessel accident management strategies. The knowledge of structural degradation of Calandria with time till its ultimate failure is important for formulating and assessing the severe accident management guidelines. Assessment of Calandria failure under accident conditions involves several important aspects such as complex thermo-mechanical loadings, temperature dependent elastic-plastic and creep modeling, flexibility of different parts and boundary constraints etc. In view of this, a systematic analysis method based on the sequentially coupled thermo- mechanical analysis has been devised and used for the structural assessment of Calandria. The failure assessment has been carried out as per the specified failure criteria for prominent failure modes including large unbounded deformations and plastic instability, large inelastic strains/ ductility exhaustion and creep-stress rupture. The paper covers various considerations taken into account during the analyses along with few case studies on Indian PHWRs.

A probabilistic-phase field model for the fracture of brittle materials

We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abe et al 2003 J. Am. Ceram. Soc. 86 1019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Three-dimensional microstructure reconstruction for two-phase materials from three orthogonal surface maps

Introduction: A full three-dimensional (3D) microstructure characterization that captures the essential features of a given material is oftentimes desirable for determining critical mechanisms of deformation and failure and for conducting computational modeling to predict the material’s behavior under complex thermo-mechanical loading conditions. However, acquiring 3D microstructure representations is costly and time-consuming, whereas 2D surface maps taken from orthogonal perspectives can be readily produced by standard microscopic procedures. We present a robust and comprehensive approach for such 3D microstructure reconstructions based on three electron backscatter diffraction (EBSD) maps from orthogonal surfaces of two-phase materials.Methods: It is demonstrated that processing surface maps by spatial correlation functions combined with principal component analysis (PCA) results in a small set of unique descriptors that serve as a representative fingerprint of the 2D maps. In this way, the differences between surface maps of the real microstructure and virtual surface maps of a reconstructed 3D microstructure can be quantified and iteratively minimized by optimizing the 3D reconstruction.Results: To demonstrate the applicability of the method, the microstructure of a metastable austenitic steel in the two-phase region, where austenite and deformation-induced martensite coexist at room temperature, was characterized and reconstructed. After convergence, the synthetic 3D microstructure accurately describes the experimental system in terms of physical parameters such as volume fractions and phase shapes.Discussion: The resulting 3D microstructures represent the real microstructure in terms of their characteristic features such that multiple realizations of statistically equivalent microstructures can be generated easily. Thus, the presented approach ensures that the 3D reconstructed sample and the associated 2D surface maps are statistically equivalent.

Thermally-activated hardening recovery in viscoplastic materials with kinematic hardening at high temperatures

In this work, a new constitutive model is proposed to describe the thermally-activated hardening recovery mechanism in metallic materials. This model takes up the concept of hardening recovery variable, which is extended to the case of kinematic hardening within a thermo-viscoplastic formulation including high temperature dependencies for both elastic and viscoplastic properties. The model is identified for AISI 316L austenitic stainless steel using experimental data from uni-axial tests conducted over a wide range of temperature (from room temperature to 1273 K) and at two different strain rates (2.5×10−4 and 2.5×10−3 s−1). Validation is further achieved with rather good agreements by comparing the simulated responses with additional experimental data where the material is subjected to complex thermomechanical loading paths while other examples are presented to provide a better insight of the model and to illustrate its predictive capabilities.

Application of the finite element moment scheme to the investigation of thin elastic shells of inhomogeneous structure

The work is devoted to the problem of developing a universal method for studying the deformation, buckling, postbuckling behavior and vibrations of thin and medium-thickness shells of complex shape and structure under the action of mechanical and thermal loads. A wide class of shells is considered: of constant and smooth-variable thickness, with ribs and cover plates, channels and cavities, holes, sharp bends of the mid-surface, and with a multilayer structure of the material. The method is based on the positions of the 3D geometrically nonlinear theory of thermoelasticity without the use of simplifying hypotheses of the theory of shells. The development of the computational model is based on the use of a universal isoparametric spatial finite element with multilinear shape functions, which is the same for all sections of the shell with stepwise variable thickness. The governing equations are constructed in accordance with the requirements of the finite element moment scheme. The mid-surface of the shell’s casing is taken as a single reference surface. All matrices of governing equations for a universal spatial multilayer finite element are obtained in explicit form by analytical integration. This speeds up the execution of calculations in the algorithmic implementation of the method. Such an approach, based on a unified methodology, makes it possible to study the behavior of multilayer shells with different geometric features in terms of thickness under complex thermo-mechanical loading.

Full-field analysis of damage under complex thermomechanical loading

This study combines infrared thermography, digital image correlation and machine learning to measure respectively temperature, strain and damage fields at high temperature. This is applied to thermomechanical fatigue (TMF) testing in presence of severe gradient for typical out-of-phase loading condition. This type of loading is challenging when dealing with thin sheets due to buckling risk induced by high temperature compression. For a Co-based superalloy (Haynes 188), this study demonstrates full-field identification/validation of both behaviour and damage models. Thermal gradient model is the key point in this analysis. With the coupling of TMF measurements by machine learning and DIC, local fatigue micro-crack growth rate and localisation are assessed through jump in displacement. TMF finite element analysis, of loading and damage, validates the whole model framework.

Using machine learning to predict lifetime under isothermal low-cycle fatigue and thermo-mechanical fatigue loading

In this article, machine learning is used to predict lifetime under isothermal low-cycle fatigue and thermo-mechanical fatigue loading, both of which represent the most complex loadings that couple creep, fatigue and oxidation damage. A uniaxial fatigue and fatigue–creep dataset, which was obtained for temperatures of between 300°C and 600°C for a low-alloy martensitic steel, is utilized in this study. Two different machine learning based approaches to lifetime prediction are demonstrated. The first approach is based only on a shallow neural network, whereas the second approach is proposed as a combination of a sequence learning based model – either long short-term memory network or gated recurrent unit – with the shallow neural network. A good correlation between the experiment and the prediction suggests that lifetime under complex thermo-mechanical loading can be reasonably predicted via the proposed machine learning based damage models.

A temperature dependent constitutive model for functional fatigue in shape memory alloys

Functional fatigue is a vital aspect when considering the design of components made with shape memory alloys, since it can affect their short- and long-term behavior. With this in mind, a constitutive model considering the functional fatigue in shape memory alloys is developed. The functional fatigue is based on the residual strain, residual stress, residual martensite and a defect volume fraction, which are assumed to all evolve in a similar manner. The evolution is prescribed based on a saturation differential equation which is exponentially dependent on temperature. The residual martensite and defect volume fraction are defined to influence the development of hardening through a hardening energy term and the reduction in dissipation with an appropriate limit function. The model is validated by simulating several experiments of cyclic isothermal and isobaric tests. A fit and prediction is also offered for a set of complex thermomechanical loading paths. The results demonstrate the strong applicability of the model to capture the degradation of the transformation response associated with cyclic loads, even when different temperatures and loads are applied. Moreover, the results point out areas of improvement, such as the use of a logarithmic evolution for the saturation of the internal variables.

Development of a constitutive model considering functional fatigue and pre-stretch in shape memory alloy wires

Shape memory alloy (SMA) wires integrate functionality into composites and encourage the design and creation of adaptable smart structures. Upon the application of cyclic loading, however, the functional properties of SMA wires can decrease significantly resulting in functional fatigue. To simulate this cyclic behavior, an SMA material model with logarithmically evolving and temperature dependent functional fatigue is developed. Pre-stretch is also considered to simulate structures with embedded pre-stretched SMA wires. The material model is fit to a set of tests (constant strain, isobaric, isothermal tension, isothermal cyclic tension) performed on SMA wires. The fit demonstrates an excellent agreement with the experimental results with minor discrepancies. The simulations show the capabilities of the model to evolve the residual strains, residual stresses, hysteresis and hardening in the presence of cyclic loading. Additionally, the isobaric actuation behavior and the reorientation response of the model are validated using experiments from the literature. The fitted and validated model is then used to simulate the response of a rubber specimen with two embedded SMA wires subjected to cyclic thermal loading. The simulated rubber specimen illustrates the loss of functionality after the applied cyclic loading and highlights the importance of not exceeding design temperature loads. Furthermore, the complex thermomechanical loading in the SMA wires displays the importance of including temperature or stress dependence for defining functional fatigue.

Performance of Cast Iron under Thermal Loading: Effect of Graphite Morphology

Cast iron is an important engineering material, used extensively in industrial applications. Despite being often exposed to complex thermomechanical loading, its performance under such conditions is not fully identified because of its complex microstructure. In this work, a response of cast iron to pure thermal loading is studied employing a micromechanical approach. Specifically, 2D representative volume elements (RVEs) are generated employing material characterisation data and analysed using a finite-element approach. These RVEs comprise a ferritic matrix enveloping a single graphite particle, represented as an ellipse. The developed numerical strategy allows a parametric analysis of the effects of graphite morphology and boundary conditions applied. In addition, a model with a graphite particle modelled as a void is investigated to study the accuracy of the obtained results for the thermal load. The obtained results are expected to be useful in the future design of this engineering alloy.

Dynamic Response of Three-Layered Annular Plates in Time-Dependent Temperature Field

The paper presents a solution to the dynamic response of three-layered, annular plates that are thermo-mechanically loaded. Time-dependent forces are considered to act on the facings of the plate. The thermal loading is defined by a flat, axisymmetric temperature field whose profile is expressed by the stationary or increase in time temperature differences between the plate edges. The cases of the plates loaded only thermally or mechanically have been examined. The problem has been solved analytically and numerically using the approximation methods: orthogonalization and finite difference. The selected reactions of an exemplar plate have been compared with the results obtained for the plate analyzed by the finite element method (FEM). The critical temperature differences and critical loads and corresponding dynamic buckling modes have been analyzed in detail. The numerous results presented for the dynamic responses have an important and practical meaning in the design process of plate structures subjected to complex thermo-mechanical loads.

Buckling and vibrations of the shell with the hole under the action of thermomechanical loads

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and vibrations of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, under complex thermomechanical loading. The technique is based on the geometrically nonlinear equations of three-dimensional thermoelasticity, the finite element formulation of the problem in increments, and the use of the moment finite-element scheme. A thin shell is considered by this method as a three-dimensional body. We approximate a shell by one spatial universal finite element (FE) throughout the thickness. The universal FE is based on an isoparametric spatial FE with polylinear shape functions for coordinates and displacements. The universal element has additional variable parameters introduced to expand its capabilities. The method of modal analysis of the shell is based on an approach that at each current stage of thermomechanical loading takes into account the stresses accumulated at the previous stages. The developed algorithm allows one to study geometric nonlinear deformation and buckling of elastic shells of an inhomogeneous structure with a thin and medium thickness, as well as to study small vibrations of the shells relative to the reference deformed state caused by static loading, taking into account large displacements and a prestressed state. An analysis of the stability and vibration of the spherical panel with the hole is carried out. The effect on the frequencies and mode shapes of the shell of the sequential action of thermal and mechanical loads is investigated.

Registration and processing of experimental data in research of martensitic transformations in TiNi alloys by acoustic emission method

The characteristics of the software and hardware system for recording acoustic emission in a wide frequency range are given. This system is used in studies of structural and phase transformations of metals and alloys under complex thermo-mechanical loading. The software and hardware system is the author’s development of the team and provides an affordable solution for recording and processing data in real time, which is a determining factor in the choice of technology for the study of structural-phase transformations of metals and alloys by method of acoustic emission. The requirements for acoustic emission technique differ slightly from the approaches common in the field of non-destructive testing. The hardware complex consists of a standard ADC with a sampling rate of at least 10 MHz, which provides spectrum registration in the range up to 1 MHz. The cascade of amplifiers are provides requirements for study by method of acoustic emission. The set includes a low-noise heater, an Arduino-based recording unit for related experimental parameters (temperature, mechanical stress, strain), and a personal computer. The software part of the system is a light scientific open source shell for conducting a physical experiment - the “dotScope”, developed by the author’s team. The program includes an extensible plugins system for working with various ADCs, plugins for real-time data processing, and plugins for post-processing.

Postbuckling Behavior of Carbon-Nanotube-Reinforced Composite Toroidal Shell Segments Subjected to Thermomechanical Loadings

Motivated by evident absence of studies on doubly curved closed nanocomposite shells under complex thermomechanical loading conditions, this paper presents an analytical investigation on the buckling and postbuckling behavior of the carbon-nanotube-reinforced composite toroidal shell segment surrounded by an elastic foundation, exposed to preexisting thermal loadings and subjected to axial compression, external pressure, and combined mechanical loads. Carbon nanotubes are reinforced into the matrix phase through uniform or functionally graded distributions. The material properties of the constituents are assumed to be temperature dependent, and the effective properties of the nanocomposite are estimated by an extended rule of mixture. Two temperature conditions and various situations of mechanical loads are considered. Basic equations are established within the framework of the classical shell theory taking into account the geometrical nonlinearity and surrounding medium-shell interaction. Multiterm solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and the Galerkin method is applied to obtain nonlinear load-deflection relations from which buckling loads and postbuckling paths are determined. Numerical examples are carried out, interesting discussions are given, and beneficial and deteriorative effects of various factors are analyzed.

Thermomechanical fatigue in 9-12Cr steels: Life prediction models and the effect of tensile dwell periods

This paper is concerned with the assessment of life prediction models for thermomechanical fatigue (TMF), with specific application to P91 steel. A program of TMF tests, including dwell periods, are performed to determine the role of thermomechanical loading on fatigue life. As expected, fatigue life under conventional TMF testing (no dwells) is governed by maximum applied stress and inelastic strain-range. However, with the introduction of dwell periods, at maximum tensile stress during TMF loading, in-phase loading becomes the life-limiting case. This is attributed here to increased microstructural degradation and oxidation, associated with the dwell at peak temperature. Analysis of commonly used TMF life prediction models shows that the effect of dwell periods currently cannot be predicted for in-phase loading. Thus, it is concluded that physically-motivated approaches are required to successfully predict fatigue life under more complex (service) thermomechanical loading histories.

Thermo-mechanical fatigue evaluation of a thermal barrier coating bond-coatless system

Thermal barrier coating systems are often subjected to complex thermo-mechanical loading involving a combination of mechanical stresses under complex thermal gradients, in addition to the contribution of oxidation to the damage processes. Recently, a thermal-barrier coating bond-coatless system has been developed using prior-surface treatments. Atmospheric plasma spray (APS) Yttria-Stabilized-Zirconia (YSZ) is deposited on the AM1 nickel-based single crystalline superalloy substrate. The substrate has been either grit-blasted or laser textured before thermal spraying. The durability of these systems are investigated performing out-of-phase load controlled thermo-mechanical fatigue (TMF) tests in the 500–1100 °C and 120–700 MPa temperature and stress ranges. The contribution of a prior thermal over-aging of 200 h at 1100 °C has also been investigated. The damage mechanisms during out-of-phase TMF of the different TBC bond-coat-less systems have been studied and compared to the ones obtained during isothermal creep at 1100 °C/120 MPa. It is shown that a prior thermal over-aging favors cycling ratcheting during TMF cycling due to the degradation of the substrate microstructure. In addition, the coating damage mechanisms are observed to depend on the prior-surface treatment and thermal over-aging. Cracks perpendicular to the interface in the top coat have been observed whatever the specimens and microstructural state. Top coats are debonded for grit-blasted substrates while crack bifurcation above key holes is observed for laser textured substrates, leading to a better top coat TMF durability.

Predicting microstructure evolution for friction stir extrusion using a cellular automaton method

Friction stir extrusion (FSE) offers a solid-phase synthesis method consolidating discrete metal chips or powders into bulk material form. In this study, an FSE machine tool with a central hole is driven at high rotational speed into the metal chips contained in a chamber, mechanically stirs and consolidates the work material. The softened consolidated material is extruded through the center hole of the tool, during which material microstructure undergoes significant transformation due to the intensive thermomechanical loadings. Discontinuous dynamic recrystallization is found to have played as the primary mechanism for microstructure evolution of pure magnesium chips during the FSE process. The complex thermomechanical loading during the process drives the microstructure evolution. A three-dimensional finite element process model is developed using commercial software DEFORM 11.0 to predict the thermal field, mechanical deformation and material flow during the FSE process. Using the simulated thermomechanical loadings as input, a cellular automaton model is developed to simulate the dynamic evolution of the material grain microstructure. The predicted grain size is in good agreement with the experimentally measured grain size. This numerical study provides a powerful analysis tool to simulate the microstructure transformation for friction stir-based processes.