A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

Abstract

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.

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

“…Direct cyclic analysis 251 was structured based on a Fourier series to calculate the structural response for any loading conditions. The Hybrid method 182,258 was implemented in the form of a lower bound ratchet analysis method by Jappy et al 182,259 They developed a strategy to evaluate ratcheting boundary through an implicit, lower bound, and multiaxial solution. 254 To assess the ratcheting steady state and its boundaries, the LMM 164,165,170,[255][256][257] was developed based on upper boundary of Koiter.…”

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

“…At present, several finite element models have been proposed to simulate the classical two-stress parameters Bree problem, such as the plane stress model [1,76], axisymmetric model [77], two-bar model and N-bar model [78,79]. An axisymmetric axial thermal gradient FE model is adopted to illustrate the nonconservatism of the two-stress parameters Bree problem and simulate the thermal membrane stress of the Type-A three-stress parameters Bree-type problem [50].…”

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

“…A recently published variation of the Hybrid method has been implemented in the form of a lower bound ratchet analysis method by Jappy et al . .…”

“…Similar to other direct ratchet analysis methods [e.g. , the existing LMM framework for ratchet analysis is restricted to providing solutions in lieu of the original premise of the classic Bree problem; whereby a constant (primary) load component is added to a predefined cyclic load history in order to ascertain the ratchet limit. The main reasoning behind doing so stems from splitting the assessment of the residual stress history into separate constant and varying residual components, respectively.…”