Impact of Residual Stress and Elastic Follow-Up on Fracture

Abstract

The presence of tensile residual stress in cracked structures combined with external loading leads to circumstances where a structure may fail at a lower applied load than when residual stresses are not present. This is taken into consideration in the fracture assessment codes which are usually invoked to determine whether a cracked structure is fit-for-purpose. These codes typically attempt to decompose the stresses present in the structure under consideration into either “secondary” or “primary” components, in order to simplify the assessment and avoid the need for detailed numerical modeling. It is acknowledged that whether a given residual stress field should be classified as “secondary” or as “primary” is dependent on the level of associated elastic follow-up (EFU). However, although there is a significant body of work related to the influence of EFU on the high temperature creep behavior of uncracked structures, the EFU concept has not yet been rigorously applied to the fracture assessment of cracked structures. This paper represents a first step towards a more rigorous application of the EFU concept to the fracture assessment of cracked structures containing residual stresses. Insight is provided into the influence of residual stress and EFU on fracture by considering the behavior of a simple three-bar assembly. Having introduced the concept, a three-bar type test rig capable of generating fit-up residual stresses with varying levels of EFU in a compact-tension fracture-specimen is presented. Results, produced using this test rig, from two cases with identical levels of initial residual stress but different levels of associated EFU are considered. It is concluded that EFU is important in determining how the residual force in the specimen changes (and therefore how the component of crack driving force associated with the residual force changes) as damage accumulates in the specimen subsequent to fracture initiation.

The effects of long-range residual stress, elastic follow-up and applied load on creep crack incubation and material toughness

“…This reduction in stiffness is a result of non-linear deformation such as plasticity, creep and the initiation and growth of cracks. 5–7 Importantly, the elastic follow-up results in additional strain accumulation than would be expected from pure stress relaxation as illustrated in Figure 1 but less than for primary stress alone. A definition of elastic follow-up is provided later.…”

“…Two new test rigs were constructed each based on a classical three-bar system 6,7 illustrated in Figure 2. The rigs were developed to introduce long-range residual stresses into a laboratory specimen through strain incompatibility in the system.…”

“…The contribution of a residual stress to the primary stress at the stress concentration depends not only on the accommodation of the original misfit through permanent deformation but also it is governed by the elastic follow-up caused by the changes in relative stiffness in the structure. The effects of elastic follow-up and relaxation of residual stresses, as a result of localised plastic deformation and fracture, were explored in detail through a series of experiments by Smith and colleagues 6,7 using a multiple bar system.…”

Creep deformation and stress relaxation of a martensitic P92 steel at 650 °C

“…To estimate the elastic follow-up in a structure, there are various models designed so then that complex structures can be described by a set of series and parallel springs. Several benchmark models, discussed in earlier studies [7,10,[43][44][45][46][47][48], adopt series, parallel, and combination systems. In the present work, a combination of bars was employed experimentally (see Section 2.3), while, for simplicity, the simulation was subjected to a series bar model.…”

Elastic follow-up and relaxation of residual stresses

“…By substituting equations (27), (29), and (30) into equation (21), the elastic follow-up factor in bar 1 is…”