Linear Matching Method Framework Research Articles

Shakedown and creep rupture analysis of printed circuit heat exchangers based on the linear matching method framework

In the field of nuclear engineering, Printed Circuit Heat Exchangers (PCHEs) have become increasingly popular and the structural integrity assessment of these key power plant components is crucial. As part of the structural integrity assessment, creep rupture analysis considers the interaction of cyclic plasticity and creep behaviour, which is vital for components subjected to cyclic thermal-mechanical loads. The Linear Matching Method (LMM) framework has included a creep rupture module based on an extended shakedown algorithm, which has been adopted by several researchers. However, the current LMM framework mainly relies on linear extrapolation and requires users to provide a large amount of data points to estimate the rupture stress. This paper introduces a Unified Creep Rupture Equation (UCRE) for characterizing the creep rupture curves of diverse steel types. The UCRE is implemented in an extended shakedown algorithm and integrated into the LMM framework. The numerical method is validated through a comparative analysis, wherein the estimated rupture curves are compared with those provided in the ECCC data sheet, as well as against alternative numerical models. Shakedown and creep rupture analyses are then performed on a PCHE core. The proposed method facilitates the parametric study of changing materials and the process of material selection. Various geometric configurations are also considered and the proposed unitary cell model is verified by comparing the results with ones from full FE models. The UCRE has been proved to be an accurate engineering tool for the prediction of rupture strengths while the LMM framework has gained improved usability and versatility for engineering applications.

Neural network-assisted probabilistic creep-fatigue assessment of hydrogenation reactor with physics-based surrogate model

In order to obtain better hydrogenation reaction efficiency, the prospective hydrogenation reactor faces harsh working conditions, including the high-stress level, high-temperature environment, long creep dwell period and degradation of material resistance, leading to significant creep-fatigue interaction at the structural critical locations. The uncertainty widely existing in such design conditions further aggravates the creep-fatigue failure risk of the hydrogenation reactor structure, and makes the damage evolution and lifetime difficult to capture and predict. According to the latest appendix A15 of the R5 Procedure, a series of probabilistic analysis practices are delivered based on Volume 2/3 regarding creep-fatigue crack initiation. In this study, the probabilistic analysis for the hydrogenation reactor is implemented by the neural network-assisted creep-fatigue surrogate model under the probabilistic Linear Matching Method Framework (pLMM), with the superior balance between the computational efficiency and prediction accuracy fully achieved. The statistical distribution of structural creep-fatigue lifetime is investigated with the physics-based modelling technology, and the reliability-centred evaluation diagram and safety factors of the hydrogenation reactor are proposed for different reliability levels, which is dedicated to facilitating the risk management of crucial components in the hydrogen industry.

Direct method-based probabilistic shakedown analysis for the structure under multiple uncertain design conditions

Maintaining shakedown during the design stage is crucial for the engineering components under cyclic loading conditions. Due to the multiplicity of uncertainty existing in the actual operating parameters, probabilistic shakedown analysis is more conducive to dealing with risk management for critical infrastructures, compared with the traditional experience-based safety factors which mainly rely on deterministic evaluations and lack statistical information for decision-making. Aimed at reasonably considering the redundancy in structural integrity assessment against cyclic load conditions, a novel direct method-based probabilistic shakedown analysis is proposed under the new probabilistic Linear Matching Method framework (pLMM). The risk of losing the shakedown state is predicted by the physics-based estimation model, where the efficient iteration is employed to derive the reliability index. In the benchmark, the probabilistic shakedown boundary is constructed, with the additional influence of the uncertain cyclic loading pattern on the reliability fully reflected. This pLMM shakedown analysis facilitates the progress from over-reliance on the conservative safety factor towards precise risk management.

Creep–Fatigue Interaction Effects on Pressure-Reducing Valve Under Cyclic Thermomechanical Loadings Using Direct Cyclic Method

Abstract Supercritical boiler system has been widely used to increase efficiency of electricity generation in power plant industries. However, the supercritical operating condition can seriously affect structural integrity of power plant components due to high temperature that causes degradation of material properties. Pressure reducing valve is an important component being employed within a main steam line of the supercritical boiler, which occasionally thermal-fatigue failure being reported. This research has investigated creep-cyclic plastic behavior of the pressure reducing valve under combined thermomechanical loading using a direct numerical method known as extended direct steady cycle analysis of the linear matching method framework (LMM eDSCA). Finite element model of the pressure-reducing valve is created based on a practical valve dimension and temperature-dependent material properties are applied for the numerical analysis. The simulation results demonstrate a critical loading component that attributes creep-fatigue failure of the valve. Parametric studies confirm the effects of magnitude of the critical loading component on creep deformation and total deformation per loading cycle. With these comprehensive numerical results, this research provides engineer with an insight into possible failure mechanisms of the pressure-reducing valve at high temperature.

Creep–Cyclic Plasticity and Damage Assessment of an SS304 Weldolet

Abstract Creep–fatigue and creep–ratcheting life assessment of an SS304 weldolet considering full creep–cyclic plasticity interaction is investigated using the extended direct steady cycle analysis within the linear matching method framework. The creep behavior is modeled using the Norton relationship, which is modified by the Arrhenius rule to account for the temperature variation within the weldolet. The introduction of a creep dwell increases the reverse plasticity resulting from the creep relaxation. This leads to both creep–fatigue and creep–ratcheting damage mechanisms at different regions within the weldment. For thermal load dominated loading combinations, creep ratcheting due to both cyclically enhanced creep and creep enhanced plasticity are observed based on the dwell period. The effect of dwell period, load and temperature on the creep–fatigue and creep–ratcheting interaction of a weldolet are presented. The simultaneous presence of various damage mechanisms at different locations within the weldment highlights the importance and requirement of the proposed creep–cyclic plasticity investigations at weld locations.

Shakedown, ratcheting and fatigue analysis of cathode coating in lithium-ion battery under steady charging-discharging process

The cyclic plasticity behaviour and failure mechanism of the cathode material in lithium-ion batteries urgently need to be understood due to the cyclic lithium-ion diffusion-induced stress during charging-discharging process. Many researches have focused on the shakedown and ratcheting responses of lithium-ion battery anode. However, the systematic investigation on the plasticity behaviour of lithium-ion battery cathode is still lacking. In this paper, the cyclic plasticity behaviour of LiNixMnyCozO2 electrode subjected to cyclic lithiation/delithiation under a constant mechanical load is investigated comprehensively. The shakedown, ratcheting and fatigue analyses of active layer are conducted using direct numerical techniques based on the Linear Matching Method framework, while coin cell electrochemical experiments are performed simultaneously to support the analysis. The effect of thickness of coating on the shakedown and ratcheting response is investigated, and the thickness is confirmed as a crucial parameter that can influence the battery performance. The strain-fatigue life curve is also obtained to effectively predict the life of active coating. Moreover, the numerical results reveal the existence of low cycle fatigue at the centre, and ratcheting mechanism on the edge of the cathode, which is consistent well with the experimental result.

A Novel Fatigue Evaluation Approach with Direct Steady Cycle Analysis (DSCA) Based on the Linear Matching Method (LMM)

The traditional Low Cycle Fatigue (LCF) evaluation method is based on elastic analysis with Neuber’s rule which is usually considered to be over conservative. However, the effective strain range at the steady cycle should be calculated by detailed cycle-by-cycle analysis for the alternative elastic-plastic method in ASME VIII-2, which is obviously time-consuming. A Direct Steady Cycle Analysis (DSCA) method within the Linear Matching Method (LMM) framework is proposed to assess the fatigue life accurately and efficiently for components with arbitrary geometries and cyclic loads. Temperature-dependent stress-strain relationships considering the strain hardening described by the Ramberg-Osgood (RO) formula are discussed and compared with those results obtained by the Elastic-Perfectly Plastic (EPP) model. Additionally, a Reversed Plasticity Domain Method (RPDM) based on the shakedown and ratchet limit analysis method and the DSCA approach within the LMM framework (LMM DSCA) is recommended to design cyclic load levels of LCF experiments with predefined fatigue life ranges.

A novel fatigue assessment approach by Direct Steady Cycle Analysis (DSCA) considering the temperature-dependent strain hardening effect

A Direct Steady Cycle Analysis (DSCA) method within the Linear Matching Method (LMM) framework is proposed to assess the fatigue life accurately and efficiently for components with arbitrary geometries and cyclic loads. Temperature-dependent stress-strain relationships considering the strain hardening described by the Ramberg-Osgood (RO) formula are discussed and compared with those results obtained by the Elastic-Perfectly Plastic (EPP) model. Additionally, a Reversed Plasticity Domain Method (RPDM) based on the shakedown and ratchet limit analysis method and the DSCA approach within the LMM framework (LMM DSCA) is recommended to design cyclic load levels of Low Cycle Fatigue (LCF) experiments with predefined fatigue life ranges. Based on the ASME code, the material properties at the mean temperature through the wall thickness are used to assess the fatigue life. However, the proposed method can estimate the fatigue life considering the temperature-dependent material properties with strain hardening effect according to the temperature distribution, which is closer to the true operating condition.

Creep-fatigue and cyclically enhanced creep mechanisms in aluminium based metal matrix composites

An aluminium (Al, 2024T3) matrix composite reinforced with continuous alumina (Al2O3) fibres is investigated under tensile off-axis constant macro stress and thermal cyclic loading. The micromechanical approach to modelling and three different fibre cross-section geometries have been employed. The effect of creep is included by considering three dwell times at the peak temperature of the thermal loading history. The presence of the hold time gives rise to different sources of failure such as cyclic enhanced creep and creep ratchetting. These failure mechanisms are carefully discussed and assessed. The linear matching method framework has been used for the direct evaluation of the crucial parameters for creep-fatigue crack initiation assessment at the steady cycle. A detailed representation of the steady-state hysteresis loops is provided by using the strain range partitioning and a method for dealing with multiaxiality is reported with regard to the algebraic sign of the Mises-Hencky equivalent stress and strain. All the results obtained have been benchmarked by fully inelastic step-by-step (SBS) analyses. The design of a long fibre metal matrix composite should consider not only the detrimental effect of their dissimilar coefficient of thermal expansion, but also the state of stress at the interface between the matrix and fibre.

Study of ratchet limit and cyclic response of welded pipe

Ratcheting and low cycle fatigue are failure mechanisms observed in components subjected to cyclic temperature and mechanical loads. Ratcheting is a global failure mechanism which leads to an incremental plastic collapse of the component whereas low cycle fatigue is a localized mechanism which leads to crack initiation. It is exacerbated by grooves, notches and changes in the geometry of the component. To estimate the remaining life of the component and predict its failure mechanism, it is important to understand how it responds to various combinations of cyclic loads. This paper includes investigation of the ratchet limit and the plastic strain range, which is associated with the low cycle fatigue, of a circumferential butt-welded pipe by using the ratchet analysis method which includes Direct Steady Cycle Analysis (DSCA) within the Linear Matching Method Framework (LMMF). The pipe is subjected to a constant internal pressure and a cyclic thermal load. The investigation is carried out by varying 1) material properties of the weld metal (WM); 2) ratio of inner radius to wall thickness; 3) weld geometry. Within the specified ranges, yield stress and the ratio of inner radius to wall thickness affect the ratchet limit curve. The cyclic thermal load plays a crucial role compared to the internal pressure in influencing the ratchet limit curve. It is observed that the pipe experiences thermal ratcheting at lower yield stress values of the WM. The results obtained are combined to create a limit load envelope, which can be used for the design of welded pipes within the specified ranges.

Recent Developments of the Linear Matching Method Framework for Structural Integrity Assessment

The linear matching method (LMM) subroutines and plug-in tools for structural integrity assessment are now in extensive use in industries for the design and routine assessment of power plant components. This paper presents a detailed review and case study of the current state-of-the art LMM direct methods applied to the structural integrity assessment. The focus is on the development and use of the linear matching method framework (LMMF) on a wide range of crucial aspects for the power industry. The LMMF is reviewed to show a wide range of capabilities of the direct methods under this framework, and the basic theory background is also presented. Different structural integrity aspects are covered including the calculation of shakedown, ratchet, and creep rupture limits. Furthermore, the crack initiation assessments of an un-cracked body by the LMM are shown for cases both with and without the presence of a creep dwell during the cyclic loading history. Finally, an overview of the in house developed LMM plug-in is given, presenting the intuitive graphical user interface (GUI) developed. The efficiency and robustness of these direct methods in calculating the aforementioned quantities are confirmed through a numerical case study, which is a semicircular notched (Bridgman notch) bar. A two-dimensional axisymmetric finite element model is adopted, and the notched bar is subjected to both cyclic and constant axial mechanical loads. For the crack initiation assessment, different cyclic loading conditions are evaluated to demonstrate the impact of the different load types on the structural response. The impact of creep dwell is also investigated to show how this parameter is capable of causing in some cases a dangerous phenomenon known as creep ratcheting. All the results in the case study demonstrate the level of simplicity of the LMMs but at the same time accuracy, efficiency, and robustness over the more complicated and inefficient incremental finite element analyses.

Advances on creep–fatigue damage assessment in notched components

AbstractIn this paper, the extended Direct Steady Cyclic Analysis method (eDSCA) within the Linear Matching Method Framework (LMMF) is combined with the Stress Modified Ductility Exhaustion method and the modified Cavity Growth Factor (CGF) for the first time. This new procedure is used to systematically investigate the effect of several load parameters including load level, load type and creep dwell duration on the creep–fatigue crack initiation process in a notched specimen. The results obtained are verified through a direct comparison with experimental results available in the literature demonstrating great accuracy in predicting the crack initiation life and the driving mechanisms. Furthermore, this extensive numerical study highlighted the possible detrimental effect of the creep–ratchetting mechanism on the crack growth process. This work has a significant impact on structural integrity assessments of complex industrial components and for the better understanding of creep–fatigue lab scale tests.

Creep rupture assessment by a robust creep data interpolation using the Linear Matching Method

The accurate assessment of creep rupture limit is an important issue for industrial components under combined action of cyclic thermal and mechanical loading. This paper proposes a new creep rupture assessment method under the Linear Matching Method framework, where the creep rupture limit is evaluated through an extended shakedown analysis using the revised yield stress, which is determined by the minimum of the yield stress of the material and the individual creep rupture stress at each integration point. Various numerical strategies have been investigated to calculate these creep rupture stresses associated with given temperatures and allowable creep rupture time. Three distinct methods: a) linear interpolation method, b) logarithm based polynomial relationship and c) the Larson–Miller parameter, are introduced to interpolate and extrapolate an accurate creep rupture stress, on the basis of discrete experimental creep rupture data. Comparisons between these methods are carried out to determine the most appropriate approach leading to the accurate solution to the creep rupture stresses for the creep rupture analysis. Two numerical examples including a classical holed plate problem and a two-pipe structure are provided to verify the applicability and efficiency of this new approach. Detailed step-by-step analyses are also performed to further confirm the accuracy of the obtained creep rupture limits, and to investigate the interaction between the different failure mechanisms. All the results demonstrate that the proposed approach is capable of providing accurate but conservative solutions.

A generalised method for ratchet analysis of structures undergoing arbitrary thermo‐mechanical load histories

SummaryA novel approach is presented based upon the Linear Matching Method framework in order to directly calculate the ratchet limit of structures subjected to arbitrary thermo‐mechanical load histories. Traditionally, ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components, respectively, in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs. The method proposed in this paper, for the first time, accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads, as opposed to an additional primary load only. The method is a strain‐based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle. The ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared with the traditional Bree solution. The method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries. Two example problems have been utilised in order to verify the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

Integrated structural analysis tool using the Linear Matching Method part 2 – Application and verification

In an accompanying paper, a new integrated structural analysis tool using the Linear Matching Method framework for the assessment of design limits in plasticity including load carrying capacity, shakedown limit, ratchet limit and steady state cyclic response of structures was developed using Abaqus CAE plug-ins with graphical user interfaces. In the present paper, a demonstration of the use of this new Linear Matching Method analysis tool is provided. A header branch pipe in a typical advanced gas-cooled reactor power plant is analysed as a worked example of the current demonstration and verification of the Linear Matching Method tool within the context of an R5 assessment. The detailed shakedown analysis, steady state cycle and ratchet analysis are carried out for the chosen header branch pipe. The comparisons of the Linear Matching Method solutions with results based on the R5 procedure and step-by-step elastic–plastic finite element analysis verify the accuracy, convenience and efficiency of this new integrated Linear Matching Method structural analysis tool.

Integrated structural analysis tool using the linear matching method part 1 – Software development

A number of direct methods based upon the Linear Matching Method (LMM) framework have been developed to address structural integrity issues for components subjected to cyclic thermal and mechanical load conditions. This paper presents a new integrated structural analysis tool using the LMM framework for the assessment of load carrying capacity, shakedown limit, ratchet limit and steady state cyclic response of structures. First, the development of the LMM for the evaluation of design limits in plasticity is introduced. Second, preliminary considerations for the development of the LMM into a tool which can be used on a regular basis by engineers are discussed. After the re-structuring of the LMM subroutines for multiple central processing unit (CPU) solution, the LMM software tool for the assessment of design limits in plasticity is implemented by developing an Abaqus CAE plug-in with graphical user interfaces. Further demonstration of this new LMM analysis tool including practical application and verification is presented in an accompanying paper.