Quantification Of Three-Dimensional Elastic-Plastic Crack-Tip Stress Fields
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Date
2018-06-01
Authors
Yusoff, Norwahida
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Conventional structural integrity assessments are formulated based on plane
strain fracture toughness to provide a conservative estimate of failure. However, such
approach often leads to unnecessary repair and shutdown of structures. This
conservatism has been minimized by the two-parameter fracture mechanics 𝐽 − 𝑇/𝑄.
However, the 𝐽 − 𝑇/𝑄 approach is incapable of quantifying three-dimensional cracktip constraint loss that leads to the emergence of new three-dimensional techniques in fracture mechanics. Amongst the quantification approaches that have been recently proposed, the 𝐽 − ∆𝜎 approach holds the key requirements of the 𝐽 − 𝑇/𝑄 theory, and
has been shown to be able to quantify the in-plane and out-of-plane constraint losses
in high and low constraint geometries through the use of parameter 𝐽/𝑧𝜎. Although
the 𝐽 − ∆𝜎 approach has established an important feature of the three-dimensional
crack-tip fields, the application of 𝐽/𝑧𝜎 to other fracture conditions is still lacking.
Therefore, this research is motivated to further assess the nature of crack-tip constraint
loss in complex fracture problems such as blunted crack-tips, corner fields and
description of complete stress fields around three-dimensional crack-tip.
The elastic perfectly-plastic three-dimensional crack-tip fields in contained
yielding and full plasticity conditions have been respectively examined through the
means of boundary layer formulations (BLF), and a full-field analysis of compact
tension (CT) specimens, with reference to limiting two-dimensional solutions to allow
the pattern of constraint loss to be recognized. The results show that the out-of-plane
constraint in BLF and CT models is lost from a plane strain condition at the midplane
to a plane stress field near the free-surface. The parameter 𝐽/𝑧𝜎 has been shown to be
able to unify the out-of-plane constraint loss in CT specimens into a single curve
regardless of load and specimen thickness. The nature of constraint loss in term of
𝐽/𝑧𝜎 has been observed to be dependent on the angle around the crack-tip. Based on
the complete definition of 𝐽/𝑧𝜎, analytical solutions for three-dimensional crack-tip
stress fields have been developed, which appear to be in good agreement with the
numerically-predicted crack-tip fields. The elastic-plastic corner fields have been
characterized numerically and experimentally, wherein both solutions are shown to be
relatively comparable. Therefore, it can be concluded that the 𝐽 − ∆𝜎 approach is an appropriate
approach as it is capable of quantifying the effect of in-plane and out-of-plane
constraints, and providing a complete description of three-dimensional crack-tip fields.
As the 𝐽 − ∆𝜎 approach adopts the key requirements of the 𝐽 − 𝑇/𝑄 theory while
taking account both in-plane and out-of-plane constraint effects, it addresses the
limitation of the two-parameter approach, and thus further reduces the conservatism
aspect of the plane strain framework, and can be usefully integrated into the existing
structural integrity assessment codes such as the R6, the British Standard BS 7910, the
American Petroleum Institute Fitness-for-Service API 579 and the Structural Integrity
Assessment Procedure for European Industry (SINTAP).