Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

A 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 to 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.

/pdf/a-generalised-method-for-ratchet-analysis-of-structures-48a56s9ebg.pdf

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

Ensuring sufficient safety against ratcheting is a fundamental requirement in pressure vessel design. However, determining the ratchet boundary using a full elastic plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new lower bound ratchet analysis approach, similar to the previously proposed Hybrid method but based on fully implicit elastic-plastic solution strategies. The method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one Finite Element model suitable for solving the cyclic stresses (Stage 1) and performing the augmented limit analysis to determine the ratchet boundary (Stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method evaluates a consistent lower bound estimate of the ratchet boundary, which has not previously been clearly demonstrated for other lower bound approaches. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and current upper bound methods.

/pdf/a-fully-implicit-lower-bound-multi-axial-solution-strategy-3v4avzmzsn.pdf

A fully implicit, lower bound, multi-axial solution strategy for direct ratchet boundary evaluation: implementation and comparison

Shakedown analysis and assessment method of four-stress parameters Bree-type problems

An advanced lower and upper bound shakedown analysis method to enhance the R5 high temperature assessment procedure

Ensuring sufficient safety against ratchet is a fundamental requirement in pressure vessel design. Determining the ratchet boundary can prove difficult and computationally expensive when using a full elastic-plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit Finite Element methods, similar to conventional elastic-plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic-plastic solution. The second stage calculates the constant loads which can be added to the steady cycle whilst ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength is updated throughout the analysis, thus satisfying Melan’s Lower bound ratchet theorem. This is achieved utilizing the same elastic plastic model as the first stage, and a modified radial return method. The proposed methods are shown to provide better agreement with upper bound ratchet methods than other lower bound ratchet methods, however limitations in these are identified and discussed.

/pdf/a-fully-implicit-lower-bound-multi-axial-solution-strategy-3fomxnamvn.pdf

A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

A new direct method for calculation of lower bound shakedown limits based on Melan’s theorem and a novel, non-smooth multi-surface plasticity model is proposed and implemented in a Finite Element environment. The load history is defined by a finite number of extreme points defining the load-envelope of a periodic load set. The shakedown problem is stated as a plasticity problem in terms of a finite number of independent yield conditions, solved for a residual stress field that satisfies a piecewise, non-smooth yield surface defined by the intersection of multiple yield surfaces. The implemented Finite Element procedure is applied to two shakedown problems and the results compared with lower and upper bound elastic shakedown solutions given by the Linear Matching Method, LMM. The example analyses show that the proposed Elastic-Shakedown Multi Surface Plasticity (EMSP) method defines robust lower bound shakedown limits between the LMM lower and upper bound limits, close to the LMM upper bound.

A Multi-Surface Plasticity Method for Lower Bound Shakedown Load


 Unless detailed inelastic analysis is utilised, high temperature codes base creep relaxation during a dwell period within a cycle on the start-of-dwell equivalent stress. The relaxation of the equivalent stress is then taken to be governed by a uniaxial creep law for the material being considered. Elastic follow-up is also included in such calculations. With this approach, only equivalent values of stress and creep strain rate are obtained and the stress multiaxiality is therefore assumed to remain at its initial value as the stress relaxes. Codes suggest that the stress drop is limited to a small fraction (typically 20%) of the initial equivalent stress to ensure that this assumption does not lead to significant inaccuracy. This paper reports creep relaxation results for a cruciform plate subjected to displacement-controlled biaxial loading. The initial biaxial loading ratio, the geometry of the cruciform plate and the value of the power in a power-law creep model are varied and these lead to variations in the elastic follow-up describing the creep relaxation. The biaxial stress ratio is generally found to change as relaxation occurs and a multiaxial ductility approach is used to evaluate the associated effect on creep damage accumulation. This is compared with the creep damage estimated by assuming relaxation is simply controlled by the equivalent stress with no change in multiaxial stress state during relaxation. For biaxial plane stress with one principal stress initially being negative, it is found that significant equivalent stress drops (up to about 40% of the initial value) can be allowed without the simplified equivalent stress approach becoming inaccurate. More care is required for positive stress biaxiality and the influence of multiaxial stress changes is found to depend on the initial stress biaxiality and the degree of elastic follow-up. The results will be used to propose improved guidance for simplified inelastic calculations.

The Influence of Multiaxial Stress Relaxation on Component Creep Damage Accumulation

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Papers

A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

A fully implicit, lower bound, multi-axial solution strategy for direct ratchet boundary evaluation: implementation and comparison

A Multi-Surface Plasticity Method for Lower Bound Shakedown Load

The Influence of Multiaxial Stress Relaxation on Component Creep Damage Accumulation