Calculation of a lower bound ratchet limit part 1 – Theory, numerical implementation and verification

It is important to be able to calculate the ratchet limit of a component when performing integrity assessments of plant components. This paper details the addition of a lower bound ratchet limit calculation to the Linear Matching Method. The extension of Melan's theorem into the alternating plasticity region is explained, followed by its implementation into the Linear Matching Method calculation procedure. Finally, the convergence properties of this method are analysed by the analysis of a plate with a central hole subject to cyclic thermal and mechanical loadin

Development and implementation of the Abaqus subroutines and plug-in for routine structural integrity assessment using the linear matching method

In recent years the Linear Matching Method (LMM) has been developed as a tool for structural integrity assessments of components subjected to cyclic loading conditions. Its capabilities include, among others, calculation of the shakedown limit, ratchet limit, plastic strain range for low cycle fatigue, creep rupture time and fatigue creep interaction. The LMM is now incorporated into EDF Energy’s R5 research program for the high temperature assessment of structural components. The purpose of this paper is to describe the development of the LMM framework, its incorporation into Abaqus and current plans to take the method from being primarily research based into wider use by industry for routine structural assessments. The LMM calculations are primarily carried out using the UMAT subroutine, and the first topic discussed in this paper is the implementation of this user subroutine. This includes details of the coding scheme to allow use of multi-processors for the calculations. A brief comparison of the LMM with full cyclic FEA is also included to validate the method and to demonstrate its advantages. The second topic of this paper discusses the development of an Abaqus/CAE plug-in to aid wider adoption of the LMM as an analysis tool for industry. The structure of the plug-in is described alongside the processes used for data collection from the user and automatic configuration of the model

Linear matching method on the evaluation of cyclic behaviour with creep effect

This paper describes a new Linear Matching Method (LMM) technique for the direct evaluation of cyclic behaviour with creep effects of structures subjected to a general load condition in the steady cyclic state. The creep strain and plastic strain range for use in creep damage and fatigue assessments, respectively, are obtained. A benchmark example of a Bree cylinder subjected to cyclic thermal load and constant mechanical load is analysed to verify the applicability of the new LMM to deal with the creep fatigue damage. The cyclic responses for different loading conditions and dwell time periods within the Bree boundary are obtained. To demonstrate the efficiency and effectiveness of the method for more complex structures, a 3D holed plate subjected to cyclic thermal loads and constant axial tension is analysed. The results of both examples show that with the presence of creep the cyclic responses change significantly. The new LMM procedure provides a general purpose technique for the evaluation of cyclic behaviour, the plastic strain range and creep strain for the creep fatigue damage assessment with creep fatigue interaction

Calculation of a lower bound ratchet limit part 2 : Application to a pipe intersection and dissimilar material join

In an accompanying paper in this issue a lower bound method based on Melan's theorem was derived and implemented into the Linear Matching Method ratchet analysis procedure. This paper presents a ratchet analysis of a pipe intersection subject to cyclic thermo-mechanical loading using the proposed numerical technique. This work is intended to demonstrate the applicability of the lower bound method to a structure commonly seen in industry and also to better understand the behaviour of this component when subjected to cyclic loading. The pipe intersection considered here has multiple materials with temperature dependent properties. Verification of the results is given via full elastic-plastic analysis in Abaqus

Shakedown analysis of a composite cylinder with a cross-hole

In this study, both the lower and upper bound shakedown limits of a closed-end composite cylinder with or without a cross-hole subject to constant internal pressure and a cyclic thermal gradient are calculated by the Linear Matching Method (LMM). Convergence for upper and lower bound shakedown limits of the composite cylinders is sought and shakedown limit interaction diagrams of the numerical applications identifying the regions of reverse plasticity limit and ratchet limit are presented. The effects of temperature-dependent yield stress, material discontinuities, composite cylinder thickness and the existence of the cross-hole on the shakedown limits are discussed for different geometry parameters. Finally, a safety shakedown envelope is created by formulating the shakedown limit results of different composite materials and cylinder thickness ratios with different cross-hole sizes

Shakedown behaviour of composite cylinders with cross holes

In this study, both the lower and upper bound shakedown limits of a closed-end composite cylinder with or without a cross hole subject to constant internal pressure and a cyclic thermal gradient are calculated by the Linear Matching Method (LMM). Convergence for upper and lower bound shakedown limit of the composite cylinders is sought and shakedown limit interaction diagrams of the numerical examples identifying the regions of reverse plastic limit and ratchet limit are presented. The effects of temperature-dependent yield stress, materials discontinuities, composite cylinder thickness and the existence of cross hole on the shakedown limits are discussed for different geometry parameters. Finally, a safety shakedown envelope is created by formulating the shakedown limit results of different composite material and cylinder thickness ratios with different cross hole sizes

Ratchet limits for a crack in a welded pipe subjected to a cyclic temperature load an a constant mechanical load

This paper presents the ratchet limit analysis of a pipe with a symmetric crack in a mismatched weld by using the extended Linear Matching Method (LMM). Two loading conditions are considered: i) a cyclic temperature load and a constant internal pressure; and ii) a cyclic temperature load and a constant axial tension. Individual effects of i) the geometry of the Weld Metal (WM), ii) the size of the crack, iii) the location of the crack and iv) the yield stress of WM on the ratchet limits, maximum temperature ranges to avoid ratchetting and limit loads are investigated. Influence functions of the yield stress of WM on the maximum temperature ranges and limit loads are generated. The results confirm the applicability of the extended LMM to the cracked welded pipe

A direct method for the evaluation of lower and upper bound ratchet limits

The calculation of the ratchet limit is often vital for the assessment of the design and integrity of components which are subject to cyclic loading. This work describes the addition of a lower bound calculation to the existing Linear Matching Method upper bound ratchet analysis method. This lower bound calculation is based on Melan's theorem, and makes use of the residual and elastic stress fields calculated by the upper bound technique to calculate the lower bound ratchet limit multiplier. By doing this, the method combines the stable convergence of the upper bound method but retains the conservatism offered by the lower bound. These advantages are complemented by the ability of the Linear Matching Method to consider real 3D geometries subject to complex load histories including the effect of temperature dependent yield stress. The convergence properties of this lower bound ratchet limit are investigated through a benchmark problem of a plate with a central hole subject to cyclic thermal and mechanical loads. To demonstrate the effectiveness of the method, the ratchet limit of a thick walled pipe intersection, also subject to cyclic thermal and mechanical loads, is considered. Validation of these results is provided by full elastic-plastic FEA in Abaqus

Shakedown and limit analysis of 90° pipe bends under internal pressure, cyclic in-plane bending and cyclic thermal loading

The Linear Matching Method is used to create the shakedown limit and limit load interaction curves of 90 degree pipe bends for a range of bend factors. Two load cases are considered i) internal pressure and inplane bending (which includes opening, closing and reversed bending) and ii) internal pressure and a cyclic through wall temperature difference giving rise to thermal stresses. The effects of the ratios of bend radius to pipe mean radius (R/r) and mean radius to wall thickness (r/t) on the limit load and shakedown behaviour are presented

Mechanical study on surface treated glass fibres after thermal conditioning

The study reported the mechanical properties of glass fibres conditioned at typical temperatures for thermoplastic processing. Single fibre and bundle tensile tests were used to characterise mechanical performance on water sized (known as unsized) and -aminopropylsilane (APS) sized glass fibres thermally treated up to 400ºC, respectively. The results from both tests showed that the strength of the silane sized fibres drops significantly when the fibres are heated above 300ºC for 15 minutes. On the other hand, unsized fibres exhibited a gradual linear decrease with increasing temperatures. The failure mechanism of the fibres was discussed in this study by further analysing the results in single fibre test using Weibull cumulative function