On the shakedown analysis of welded pipes

This paper presents the shakedown analysis of welded pipes subjected to a constant internal pressure and a varying thermal load. The Linear Matching Method (LMM) is applied to investigate the upper and lower bound shakedown limits of the pipes. Individual effects of i) geometry of weld metal, ii) ratio of inner radius to wall thickness and iii) all material properties of Weld Metal (WM), Heat Affected Zone (HAZ) and Parent Material (PM) on shakedown limits are investigated. The ranges of these variables are chosen to cover the majority of common pipe configurations. Corresponding individual influence functions on the shakedown limits are generated. These are then combined to allow the creation of a safety shakedown envelope, which can be used for the design of any welded pipes within the specified ranges. The effect of temperature dependent yield stress (in PM, HAZ and WM) on these shakedown limits is also investigated

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

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

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 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

Limit, shakedown and ratchet analyses of defective pipeline under internal pressure and cyclic thermal loading

In this study, the limit load, shakedown and ratchet limit of a defective pipeline subjected to constant internal pressure and a cyclic thermal gradient are analyzed. Ratchet limit and maximum plastic strain range are solved by employing the new Linear Matching Method (LMM) for the direct evaluation of the ratchet limit. Shakedown and ratchet limit interaction diagrams of the defective pipeline identifying the regions of shakedown, reverse plasticity, ratcheting and plastic collapse mechanism are presented and parametric studies involving different types and dimensions of part-through slot in the defective pipeline are investigated. The maximum plastic strain range over the steady cycle with different cyclic loading combinations is evaluated for a low cycle fatigue assessment. The location of the initiation of a fatigue crack for the defective pipeline with different slot type is determined. The proposed linear matching method provides a general-purpose technique for the evaluation of these key design limits and the plastic strain range for the low cycle fatigue assessment. The results for the defective pipeline shown in the paper confirm the applicability of this procedure to complex 3-D structures

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