PLANE STRAIN DEFORMATION NEAR A CRACK TIP IN A POWER LAW HARDENING MATERIAL

1967 ◽  
Author(s):  
J. R. Rice ◽  
G. F. Rosengren
Keyword(s):  
Plane Strain ◽  
Power Law ◽  
Crack Tip ◽  
Hardening Material ◽  
Plane Strain Deformation

The Stress Field Due to a Line Load Acting on a Half Space of a Power-Law Hardening Material (A Comparison Between Plane Strain and Plane Stress)

1973 ◽  
Vol 40 (1) ◽  
pp. 288-290 ◽  
Author(s):  
C. Atkinson
Keyword(s):  
Exact Solution ◽  
Stress Field ◽  
Plane Strain ◽  
Half Space ◽  
Power Law ◽  
Elastic Material ◽  
Plane Stress ◽  
Strain Fields ◽  
Line Load ◽  
Hardening Material

The exact solution is given for a line load acting on a half space of a power-law elastic material under conditions of plane stress. This solution is compared with the corresponding solution under plane-strain conditions; see Aruliunian [1]. A marked difference is found between the plane-stress and plane-strain fields for different values of the hardening exponent.

The Stiffening Effect of Rigid Elliptical Inclusions on a Power-Law Material

1989 ◽  
Vol 111 (4) ◽  
pp. 368-371 ◽  
Author(s):  
J. M. Duva ◽  
Dirck Storm
Keyword(s):  
Plane Strain ◽  
Constitutive Relation ◽  
Power Law ◽  
Cross Sections ◽  
Particle Shape ◽  
Elliptical Cross ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
Single Inclusion ◽  
Stiffening Effect

An approximate constitutive relation is derived for plane strain deformation in a power-law viscous matrix reinforced with long rigid inclusions with elliptical cross sections. The analysis is based on the differential self-consistent scheme and numerical calculations estimating the influence of a single inclusion on the material surrounding it. In particular, the effects of particle shape and material nonlinearity are reported.

Transverse Stress for the Elastic-Plastic Plane Strain Problems

2011 ◽  
Vol 121-126 ◽  
pp. 550-553
Author(s):  
Chang Lu Tian ◽  
Shu Li Wang
Keyword(s):  
Plane Strain ◽  
Power Law ◽  
Transverse Stress ◽  
Hardening Material ◽  
Elastic Plastic

A relation to determine the transverse stress in terms of in-plane stresses for elastic-plastic plane strain problems in a power-law hardening material is presented. The results might prove useful in the elastic-plastic analyses of plane strain problems

Blunting of a Plane Strain Crack Tip Into a Shape With Vertices

1977 ◽  
Vol 99 (4) ◽  
pp. 290-297 ◽  
Author(s):  
Robert M. McMeeking
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Crack Tip ◽  
The Body ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Crack Tips ◽  
Stress And Deformation ◽  
Material Points ◽  
Growth Of Voids

When monotonically increasing tensile opening loads are applied to a cracked, plane strain, elastic-plastic body, the crack tip will blunt until fracture occurs. At least within the rigid-plastic model for nonhardening material, the shape of the blunted tip is not unique. The blunted tip shape may have two or more sharp corners, or be smoothly curved. When the shape involves corners, the opening is predominantly accommodated by shearing of the material at the corners. This shearing transports material from the interior of the body onto the crack surface. In contrast, the smoothly blunted crack tip involves no such transfer of material points from the interior. However, the smoothly blunted crack, which was originally sharp, involves infinite strains on the crack tip surface. The crack with corners on the tip has large but finite strains on the crack tip surface. The stress and deformation field in front of a crack with two corners and with three corners on the tip, as calculated using the slip line method, is presented for the nonhardening, fully plastic, deeply cracked, double edge-notched thick panel. As in the case of the smoothly blunted crack tip, the elevated stress between the crack tips cannot be maintained very close to the crack tip, due to a lack of constraint. The stress distribution in the case of the crack tip with vertices on it differs from that of the smoothly blunted crack tip case. In particular, immediately in front of the crack tip with three corners, the stress is higher than that immediately in front of the smoothly blunted crack tip. An approximation for a power law hardening material indicates that the maximum stresses near the blunted crack tip is much the same for a crack with vertices on the tip as for a smoothly blunted crack tip. The details of the stress distribution, though, will depend on the mechanism by which the crack blunts. These results for stress and strain and some calculations of the growth of voids near the crack tips indicate the same fracture process could lead to different fracture toughnesses, depending on the type of mechanism by which the crack blunts.

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