Page 284 - Handbook of Materials Failure Analysis

280 CHAPTER 12 A nonlocal damage-mechanics-based approach

inhomogeneous nature of these joints in terms of their microstructure, mechanical,
thermal, and fracture properties. Fracture mechanics based concepts cannot be
directly used because of the problems associated with the definition of a suitable
crack-tip loading parameter such as J-integral, CTOD, etc. Again, depending upon
the location of initial crack (i.e., base, weld, buttering, different interfaces, etc.), fur-
ther crack propagation can occur in any of these materials. Moreover, for interface
cracks, there can be change in crack path from one material to the other.
The complex conditions and properties of the welded joint, as resulting from the
elaborate interaction of different microstructures with gradients in material proper-
ties, have limited the ability of currently existing methods to construct the assessment
on the basis of actual failure mechanisms of bimetallic welds. At present, the knowl-
edge of homogeneous welded joints is utilized for design, and no specific methods
exist for appraising approvable assessment of structural integrity. Simplified engi-
neering treatment models have been developed in literature [24] for resolving the
problem of dissimilar welds utilizing the concept of equivalent properties so that
the integrity assessment methods for single materials can be used for them. However,
it may be argued that the interaction between under-matched and over-matched local
microstructures is one of the key elements prohibiting the optimized estimation of
integrity of dissimilar metal welded components.
In this chapter, micromechanical models have been used for simulation of ductile
fracture initiation and propagation of cracks in the dissimilar metal welds. The appli-
cation of these damage models to predict fracture resistance behavior of dissimilar
welded joints is not systematically investigated in research literature. The approach
involves determination of micro-mechanical parameters of different material regions
of the joint, prediction of fracture resistance behavior of the joint with initial crack
located at different regions and validation by experiment.
The micro-mechanical parameters of four different materials, that is, ferrite, aus-
tenite, buttering, and weld have been determined individually by simulation of fracture
resistance behavior of SEB specimens and comparing the simulated results with those
of experiment. In order to demonstrate the effectiveness of the damage model in pre-
dicting the crack growth in the actual dissimilar metal welded specimen, simulation of
a SEB specimen with initial crack at ferrite-buttering interface has been carried out.
For simulation of ductile and cleavage fracture, different types of yield functions
and failure probability functions are used in literature [7–9,20]. A summary of dif-
ferent models which are used in the DBTT regime is provided in Table 12.1 and
effects of different parameters on fracture behavior in upper shelf and DBTT regime
are provided in Table 12.2.

2 NONLOCAL ROUSSELIER’S DAMAGE MODEL
The nonlocal formulation of Rousselier’s damage model uses nonlocal damage d
as a nodal degree of freedom in the FE mesh [17–19]. The increment of the nonlocal
˙
!
damage variable d in a material point x is mathematically defined as a weighted
_
average of the increment of the local void volume fraction f in a domain Ω, that is,