Three-dimensional analyses of plastic constraint for through-thickness cracked bodies

https://doi.org/10.1016/S0013-7944(98)00102-7Get rights and content

Abstract

A three-dimensional strip yield model has been proposed to rationalize effects of out-of-plane and in-plane constraints. By use of the model, plastic constraints around a straight-through crack in finite thick plates made of strain hardening materials are analyzed. A global constraint factor α is defined to simulate the three-dimensional effects in two-dimensional analysis. Effects of thickness and stress states on the size of crack-tip plastic zone and α are studied in detail. A unique variation curve of α against normalized thickness is obtained for different combination of materials, load levels and geometry. Influences of the in-plane constraint on the α-thickness curve are analyzed as well. It is shown that the influence of T-stress can be considerable only if the plastic-zone size becomes comparable to the crack length. The difference between the present results and Newman, Bigelow and Shivakumer's three-dimensional finite element results is within 6% over a large range of thickness and stress levels. The three-dimensional shape of the plastic zone is discussed as well. Potential applications of the model are discussed and it is shown by an example that the present model can be used to explain the effects of thickness upon fatigue crack growth.

Section snippets

Greek symbols

αpglobal plastic zone based constraint factor
ΔKstress intensity factor range (MPam)
ΔKeffeffective stress intensity factor range (MPam)
ρcrack-tip plastic zone size (m)
νPoisson's ratio
νepPoisson's ratio of elastic–plastic strains
σblimit stress (MPa)
σeequivalent stress (MPa)
σijstress tensor
σysyield stress
ϵijstrain 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 KT 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 αgαg=1ATMm=1yy0)mAmwhere 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, 30σxx=KI2πr3cosθ2cos2/4+Tσyy=KI2πr3cosθ2+cos2/4σxy=KI2πrsin2sinθ2/4σzz=Tz(σxxyy), σyzzx=0So 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.

References (31)

Cited by (117)

View all citing articles on Scopus
View full text