Linear matching method for design limits in plasticity

In this paper a state-of-the-art numerical method is discussed for the evaluation of the shakedown and ratchet limits for an elastic-perfectly plastic body subjected to cyclic thermal and mechanical load history. The limit load or collapse load, i.e. the load carrying capacity, is also determined as a special case of shakedown analysis. These design limits in plasticity have been solved by characterizing the steady cyclic state using a general cyclic minimum theorem. For a prescribed class of kinematically admissible inelastic strain rate histories, the minimum of the functional for these design limits are found by a programming method, the Linear Matching Method (LMM), which converges to the least upper bound. By ensuring that both equilibrium and compatibility are satisfied at each stage, a direct algorithm has also been derived to determine the lower bound of shakedown and ratchet limit using the best residual stress calculated during the LMM procedure. Three practical examples of the LMM are provided to confirm the efficiency and effectiveness of the method: the behaviour of a complex 3D tubeplate in a typical AGR superheater header, the behaviour of a fiber reinforced metal matrix composite under loading and thermal cycling conditions, and effects of drilling holes on the ratchet limit and crack tip plastic strain range fora centre cracked plate subjected to constant tensile loading and cyclic bending moment

Cyclic J integral using linear matching method

The extended version of the latest Linear Matching Method (LMM) has the capability to evaluate the stable cyclic response, which produces cyclic stresses, residual stresses and plastic strain ranges for the low cycle fatigue assessment with cyclic load history. The objective of this study is to calculate ΔJ through the LMM and suggest future development directions. The derivation of the ΔJ based on the potential energy expression for a single edge cracked plate subjected to cyclic uniaxial loading condition using LMM is presented. To extend the analysis so that it can be incorporated to other plasticity models, material Ramberg-Osgood hardening constants are also adopted. The results of the proposed model have been compared to the ones obtained from Reference Stress Method (RSM) for a single edge cracked plate and they indicate that the estimates provide a relatively easy method for estimating ΔJ for describing the crack growth rate behaviour by considering the complete accumulated cycle effects

Cyclic J-integral using the linear matching method

The extended version of the latest Linear Matching Method (LMM) has the capability to evaluate the stable cyclic response, which produces cyclic stresses, residual stresses and plastic strain ranges for the low cycle fatigue assessment with cyclic load history. The objective of this study is to calculate ΔJ through the LMM and suggest future development directions. The derivation of the ΔJ based on the potential energy expression for a single edge cracked plate subjected to cyclic uniaxial loading condition using LMM is presented. To extend the analysis so that it can be incorporated to other plasticity models, material Ramberg-Osgood hardening constants are also adopted. The results of the proposed model have been compared to the ones obtained from Reference Stress Method (RSM) for a single edge cracked plate and they indicate that the estimates provide a relatively easy method for estimating ΔJ for describing the crack growth rate behaviour by considering the complete accumulated cycle effects

A parametric study on creep-fatigue strength of welded joints using the linear matching method

This paper presents a parametric study on creep-fatigue strength of the steel AISI type 316N(L) weldments of types 1 and 2 according to R5 Vol. 2/3 Procedure classification at 550◦C. The study is implemented using the Linear Matching Method (LMM) and is based upon a latest developed creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Parametric models of geometry and FE-meshes for both types of weldments are developed in this way, which allows variation of parameters governing shape of the weld profile and loading conditions. Five configurations, characterised by individual sets of parameters, and presenting different fabrication cases, are proposed. For each configuration, the total number of cycles to failure N⋆ in creep-fatigue conditions is assessed numerically for different loading cases including normalised bending moment M and dwell period t. The obtained set of N⋆ is extrapolated by the analytic function, which is dependent on M, t and geometrical parameters (α and β). Proposed function for N⋆ shows good agreement with numerical results obtained by the LMM. Thus, it is used for the identification of Fatigue Strength Reduction Factors (FSRFs) intended for design purposes and dependent on t, α, β

Creep-fatigue life assessment of high-temperature weldments using the linear matching method

This poster discusses Creep-fatigue life assessment of high-temperature weldments using the linear matching method

Novel direct method on the life prediction of component under high temperature-creep fatigue conditions

This paper presents a novel direct method, within the Linear Matching Method (LMM) framework, for the direct evaluation of steady state cyclic behaviour of structures subjected to high temperature – creep fatigue conditions. The LMM was originally developed for the evaluation of shakedown and ratchet limits. The latest extension of the LMM makes it capable of predicting the steady state stress strain solutions of component subjected to cyclic thermal and mechanical loads with creep effects. The proposed iterative method directly calculates the creep stress and cyclically enhanced creep strain during the dwell period for the assessment of the creep damage, and also creep enhanced total strain range for the assessment of fatigue damage of each load cycle. To demonstrate the efficiency and applicability of the method to assess the creep fatigue damage, two types of weldments subjected to reverse bending moment at elevated temperature of 550C are simulated by the proposed method considering a Ramberg-Osgood model for plastic strains under saturated cyclic conditions and a power-law model in “time hardening” form for creep strains during the dwell period. Further experimental validation shows that the proposed direct method provides a general purpose technique for the creep fatigue damage assessment with creep fatigue interaction

Creep-fatigue life assessment of cruciform weldments using the linear matching method

This paper presents a creep-fatigue life assessment of a cruciform weldment made of the steel AISI type 316N(L) and subjected to reversed bending and cyclic dwells at 550C using the Linear Matching Method (LMM) and considering different weld zones. The design limits are estimated by the shakedown analysis using the LMM and elastic-perfectly-plastic material model. The creep fatigue analysis is implemented using the following material models: 1) Ramberg-Osgood model for plastic strains under saturated cyclic conditions; 2) power-law model in “time hardening” form for creep strains during primary creep stage. The number of cycles to failure N? under creep-fatigue interaction is defined by: a) relation for cycles to fatigue failure N dependent on numerical total strain range "tot for the fatigue damage !f ; b) long-term strength relation for the time to creep rupture t dependent on numerical average stress ¯ during dwell t for the creep damage !cr; c) non-linear creep-fatigue interaction diagram for the total damage. Numerically estimated N? for different t and "tot shows good quantitative agreement with experiments. A parametric study of different dwell times t is used to formulate the functions for N? and residual life L? dependent on t and normalised bending moment ˜M , and the corresponding contour plot intended for design applications is created

Modelling of the behaviour of a welded joint subjected to reverse bending moment at high temperature

The paper is concerned with the modeling of the behaviour of welds when subjected to severe thermal and mechanical loads where the maximum temperature during dwell periods lies in the creep range. The methodology of the life assessment method R5 is applied where the detailed calculations are carried out using the linear matching method (LMM), with the objective of generating an analytic model. The linear matching method has been developed to allow accurate predictions using the methodology of R5, the UK life assessment method. The method is here applied to a set of weld endurance tests, where reverse bending is interrupted by creep dwell periods. The weld and parent material are both Type 316L(N) material, and data were available for fatigue tests and tests with 1 and 5 h dwell periods to failure. The elastic, plastic, and creep behavior of the weld geometry is predicted with the LMM using the best available understanding of the properties of the weld and parent material. The numerical results are translated into a semi-analytic model. Using the R5 standard creep/fatigue model, the predicted life of the experimental welds specimens are compared with experimental data. The analysis shows that the most severe conditions occur at the weld/parent material interface, with fatigue damage concentrated predominantly in the parent material, whereas the creep damage occurs predominantly in the weld material. Hence, creep and fatigue damage proceed relatively independently. The predictions of the model are good, except that the reduction in fatigue life due to the presence of the weld is underestimated. This is attributed to the lack of separate fatigue date for the weld and parent material and the lack of information concerning the heat affected zone. With an adjustment of a single factor in the model, the predictions are very good. The analysis in this paper demonstrates that the primary properties of weld structures may be understood through a number of structural parameters, defined by cyclic analysis using the linear matching method and through the choice of appropriate material data. The physical assumptions adopted conform to those of the R5 life assessment procedure. The resulting semi-analytic model provides a more secure method for extrapolation of experimental data than previously available

Structural integrity assessment of superheater outlet penetration tubeplate

In recent years, the Linear Matching Method (LMM) has been well developed for the integrity assessment of the component subjected to cyclic thermal and mechanical loads. In this paper, the fatigue damage of a superheater outlet penetration tubeplate is assessed in detail using the LMM with an ABAQUS 3D finite element model. The significant thermal transients of the component are due to the out of phase steam temperature oscillations. The primary loading on the component is from pressure (steam and gas) and system moment on the penetration and tail pipes. A transient thermal analysis is performed in the first step to determine the component temperature history during the cycle. Then these temperature solutions are used as an input to the structural analysis to obtain the elastic stress history caused by these temperature loads. A shakedown analysis is thereafter carried out and the evaluation of the steady cyclic behaviour of tubeplate during the steady state cycle is then achieved using the LMM. The elastic, plastic and total strain ranges over the steady state cycle are evaluated for the fatigue damage assessment. Both the constant and changing residual stress solutions associated with the steady state cycle are obtained. The comparisons of stress and strain range calculations for out of phase temperature oscillations by the LMM and other methodologies are given in the paper. Finally, a LMM ratchet limit analysis is carried out to assess the capacity of the component subjected to the existing thermal transients to withstand an additional primary loads including both pressure and moment. The temperature dependent elastic-plastic properties are adopted throughout the LMM assessment

A simplified creep-reverse plasticity solution method for bodies subjected to cyclic loading

An extension of the upper bound shakedown theorem to load histories in excess of shakedown has been applied recently to the evaluation of a ratchet limit and the varying plastic strain magnitudes associated with a varying residual stress field. Solutions were obtained by the Linear Matching Method. In the present paper, this technique is extended to the evaluation of creep-reverse plasticity mechanism for bodies subjected to thermal cyclic loading including creep effects. The accumulated creep strain, the varying flow stress and the corresponding varying residual stress field during a creep dwell time are evaluated as well as the elastic follow-up factor. Three alternative computational strategies are discussed with differing but related assumptions. The problem of a plate with a central circular hole is discussed, subjected to cyclic thermal load. All three methods provide similar values for the elastic follow-up factor, indicating that the result is insensitive to the range of assumptions made. The simplest method, Method 1, is suggested as the basis of a general purpose method for use in life assessment