Three-dimensional analyses of plastic constraint for through-thickness cracked bodies
Section snippets
Greek symbols
αp global plastic zone based constraint factor ΔK stress intensity factor range ΔKeff effective stress intensity factor range ρ crack-tip plastic zone size (m) ν Poisson's ratio νep Poisson's ratio of elastic–plastic strains σb limit stress (MPa) σe equivalent stress (MPa) σij stress tensor σys yield stress ϵij strain tensor
Three-dimensional strip yield modeling
As a complement to LEFM, strip yield models are mainly developed under small- scale yielding (SSY) conditions, so the analysis of this paper mainly focuses on SSY conditions in which the crack-tip plastic zone is fully enclosed by a K or K–T dominated elastic field.
In the coordinate, as shown in Fig. 1, the 3D constraints for any sheet element along the normal plane of the crack front line, or plane with z=constant, consist of in-plane and out-of-plane constraints. The in-plane constraint is
Results and analyses
In all the following analyses, f(Th, k) and Th are taken from , . Except for special explanation, k1=k1(n) and k2=1 are assumed.
Comparison with 3D finite element analyses[9]
To reveal the 3D constraint effects of through-thickness cracks, Newman and his coworkers have conducted detailed FE analysis[9]. A global constraint factor αg similar to the present α was defined by them to simulate 3D effects in 2D crack analyses. Instead of plastic zone size rp, an average of the normal stresses acting over the yielded material on the uncracked ligament was used to calculate the constraint factor αgwhere Am is the projected area on the uncracked
3D shape of plastic zone in finite thick plates
A first approximation of the 3D shape of plastic zone can be made by applying the yield criterion directly to elastic solutions. When the first two terms of the asymptotic solutions are taken into account, stresses near the tip of a mode I elastic crack, except the corner points where the crack front line is intersected with free surfaces of the body, can be expressed as29, 30So the von Mises'
Conclusions
A three-dimensional strip yield model has been developed for straight-through cracks in finite thick plates of strain hardening materials. This model incorporates a nonuniform singular plastic zone cohesive stress that is a function of three-dimensional stress constraints in the plastic zone and the strain hardening exponent n of the material. A global plastic constraint factor α is defined to simulate three-dimensional effects in two-dimensional crack analyses. Various factors that influence
Acknowledgements
The work was supported by the Chinese National Distinguished Young Scientist Foundation, Chinese National Natural Science Foundation, and Australian DSTO Center-of-Expertise program. I am grateful to Dr Francis Rose for his helpful discussions.
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