Elastic-plastic analysis of growing cracks

Journal Article · Tue Jan 01 04:00:00 EST 1980 · Am. Soc. Test. Mater., Spec. Tech. Publ.; (United States)

DOI:https://doi.org/10.1520/STP36972S· OSTI ID:5848075

Rice, J R; Drugan, W J; Sham, T L

The elastic-plastic stress and deformation fields at the tip of a crack which grow in an ideally plastic solid under plane strain, small-scale yielding conditions is discussed. Asymptotic analysis suggests a crack-tip stress state similar to that of the classical Prandtl field, but containing elastic unloading between the centered fan region and the trailing constant stress plastic region. The near tip expression for the rate of opening displacement delta at distance r from the growing tip is found to have the same form suggested by Rice and Sorensen, delta = ..cap alpha..J/sigma/sub 0/ + ..beta..(sigma/sub 0//E)a ln (R/r), but now the presence of the elastic wedge causes ..beta.. to have the revised value of 5.08 (for Poisson ratio ..nu.. = 0.3). Here, a = crack length, sigma/sub 0/ = yield strength, E = elastic modulus, and J denotes the far-field value (1 - ..nu../sup 2/) K/sup 2//E for the small scale yielding conditions considered. The parameters ..cap alpha.. and R cannot be determined from the asymptotic analysis, but ..cap alpha.. is approximately the same for stationary and growing cracks, and R scales approximately with the size of the plastic zone, being about 15 to 30% larger. For large scale yielding, a similar form applies with possible variations in ..cap alpha.. and ..beta.., at least in cases which maintain triaxial constraint at the crack tip, but in the fully yielded case R is expected to be proportional to the dimension of the uncracked ligament. The model crack growth criterion of Rice and Sorensen, requiring a critical delta at some fixed r from the tip, is reexamined. Results suggest that the J versus ..delta..a relation describing growth will be dependent on the extent of yielding, although it is suggested that this dependency might be small for highly ductile materials, provided that a similar triaxial constraint is maintained in all cases.

• Research Organization: Brown Univ., Providence, RI
• DOE Contract Number: AC02-80ER10556
• OSTI ID: 5848075
• Report Number(s): ASTM-STP-700
• Journal Information: Am. Soc. Test. Mater., Spec. Tech. Publ.; (United States), Journal Name: Am. Soc. Test. Mater., Spec. Tech. Publ.; (United States); ISSN ASTTA
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360103* -- Metals & Alloys-- Mechanical Properties
CRACK PROPAGATION
ELASTICITY
EQUATIONS
FINITE ELEMENT METHOD
FRACTURE MECHANICS
MECHANICAL PROPERTIES
MECHANICS
NUMERICAL SOLUTION
OPENINGS
PLASTICITY
SOLIDS
STRESSES
TENSILE PROPERTIES