Implementation of Ductile Damage Models to Determine Constraint Parameters for Ductile Materials: Phase 1 — Generic Constraint Conditions

Abstract It has been observed that steels which are operating in the ductile regime demonstrate greater resistance to tearing under conditions of reduced crack-tip constraint. Constraint is influenced by both geometry and load conditions. For example, fracture toughness specimens with shorter cracks relative to wall thickness, or those subjected to tension as opposed to bending, will demonstrate reduced constraint. Constraint may be quantified by an elastic T-Stress or the elastic-plastic Q parameter. R6, a set of structural integrity guidelines widely used in the nuclear industry, suggests that the effective fracture toughness of a material at reduced constraint may be calculated using a material-specific toughness locus. To define this locus, it is usually necessary to perform laboratory tests on the material at various levels of constraint, which are both expensive and time consuming. For cleavage (low-temperature) fracture, it is also possible to consult look-up tables, which require the calculation of the Weibull stress parameter. This paper details findings from an investigation into a method to determine the parameters defining failure loci for steels. The work involves the use of finite element analysis and two damage models which consider void growth in ductile materials. The first model is the Rice and Tracey model, which determines void growth based on stress triaxiality and plastic strain, and the second is the GTN local approach, which considers void initiation, growth and coalescence to define a yield surface for the material. The yield surface is governed by numerous parameters which enable the definition of the void volume fraction of the material at the various stages preceding fracture. Previous work has demonstrated independence of the parameters used to define the toughness loci to the critical void size when defined using the Rice and Tracey approach. The work presented in this paper demonstrates similar behaviour using the GTN model, with independence of the constraint benefit to the governing parameters. The toughness determined using the GTN approach is calculated from J-R type curves obtained by simulating crack growth in idealised constraint scenarios: specifically applying a T-Stress to boundary layer models, where a boundary layer model is an idealised high constraint scenario. It is shown in this paper that, whilst independence is demonstrated to the GTN parameters, there are discrepancies between the toughness loci derived using the GTN model and those using the Rice and Tracey approach. The reasons for this are discussed and are predicted to be due to load order effects, in that constraint reduces through loading, which may not be captured accurately using the boundary layer model. An introduction to the next phase of work, which does accurately include these effects, is also provided.