Page 282 - Handbook of Materials Failure Analysis

278 CHAPTER 12 A nonlocal damage-mechanics-based approach

6.9 Effect of Specimen Size on Probability of Cleavage Fracture
in the DBTT Regime .........................................................................304
6.10 Analysis of SEB Specimen with Crack at the Ferrite-Buttering
Interface .......................................................................................304
7 Conclusion ....................................................................................................... 306
References ............................................................................................................ 307

1 INTRODUCTION
For safety-critical plant components made of ductile materials, finite-element (FE)
approaches which use material damage constitutive models are able to predict the
failure behavior and the corresponding process with high accuracy [1–3]. For struc-
tural integrity assessment under various postulated and design loading conditions,
the fracture resistance data of the base metal, weld metal as well as dissimilar welded
joints, in terms of J-R curves are required not only in the upper-shelf, but also in the
ductile-to-brittle transition (DBT) temperature regime [4–6]. Due to the accrual of
irradiation damage in the nuclear reactor environment, the ductile materials may
exhibit DBT behavior even at room temperature. It is well established that the frac-
ture resistance behavior depends not only on the specimen geometry, but also upon
the specimen size, crack-depth, loading and boundary conditions in the upper-shelf
as well as in the DBT temperature regime [2,3].
Experiments may only be conducted on standard fracture mechanics specimens in
the laboratory to determine the J-R curves as it will not only be expensive and time-
consuming, but also be impossible in several situations to conduct fracture tests on
actual reactor components with small-size surface cracks under actual loading condi-
tions. Damage mechanics approaches [7,8] offer an impressive alternative to predict
the J-R curves of the components with various postulated cracks and loading condi-
tions. In the last three decades, damage-mechanics-based models like Rousselier’s
[7], Gurson’s model (and its modified versions) [8,9] have become powerful tools
in the safety analysis of nuclear reactor components, for example, pressure vessels,
shell-nozzle junctions, pipings, headers, elbows, etc. These damage models predict
the material behavior on the basis of the micromechanical processes (i.e., void nucle-
ation, growth, and coalescence) leading to ductile fracture.
The conventional local damage-mechanics approaches suffer from the problem of
mesh-dependency of the results [10–16] and it does not allow the use of small-size ele-
ments near the crack-tip (for a converged solution) to simulate large stress gradients in
the DBTT regime. Nonlocal regularization of the material state variables can alleviate
this problem and this has been investigated by various researchers over the years [15–
19]. Recently, the authors have developed a nonlocal version of the Rousselier’s damage
model and showed that the results of this model are mesh-independent [17–19].
The ability of the nonlocal damage models to predict the effect of specimen
size, geometry, crack-depth, loading and boundary conditions, etc., on the load-
displacement and fracture resistance behavior has not been studied so much in detail
in the research literature. In this chapter, we use the nonlocal Rousselier’s model to