Dual-parameter elastic-plastic fracture criterion of metals and alloys in the plane strain case

1987 ◽  
Vol 3 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Zhuang Tao
Keyword(s):  
Plane Strain ◽  
Fracture Criterion ◽  
Metals And Alloys ◽  
Elastic Plastic ◽  
Plane Strain Case

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Design of stationary plane strain drawing based on the ideal flow theory and a fracture criterion

2007 ◽  
Vol 196 (3-4) ◽  
pp. 127-137 ◽  
Author(s):  
K.-H. Chung ◽  
K. Chung ◽  
Sergei Alexandrov
Keyword(s):  
Plane Strain ◽  
Fracture Criterion ◽  
Flow Theory ◽  
Ideal Flow ◽  
The Ideal

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

scholarly journals Plane-Strain Compressive Strength of Columnar-Grained and Granular-Snow Ice

1977 ◽  
Vol 18 (80) ◽  
pp. 505-516 ◽  
Author(s):  
R. Frederking
Keyword(s):  
Compressive Strength ◽  
Strain Rate ◽  
Failure Mechanism ◽  
Plane Strain ◽  
Uniaxial Compressive Strength ◽  
Ice Cover ◽  
Anisotropic Structure ◽  
Compression Tests ◽  
Isotropic Structure ◽  
Plane Strain Case

Abstract An ice cover impinging on a long straight structure is assumed to be under a condition of plane strain. A technique is described for performing plane-strain compression tests, and results are presented for the strain-rate dependence of strength. The plane-strain compressive strength of ice having anisotropic structure (columnar-grained ice) is at least two and a half times the uniaxial compressive strength, whereas the plane-strain compressive strength of ice having an isotropic structure (granular-snow ice) is at most 25% greater than the uniaxial case. The greater plane-strain compressive strength of columnar grained ice when the loading and confining directions are in the plane of the ice cover, can be attributed to its anisotropic structure, which leads to a different failure mechanism for the plane-strain case.

Forced Flexural Vibrations of Sandwich Plates in Plane Strain

1960 ◽  
Vol 27 (3) ◽  
pp. 535-540 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Plane Strain ◽  
Sandwich Plate ◽  
Classical Method ◽  
Separation Of Variables ◽  
Flexural Vibration ◽  
Time Dependent ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Transverse Deflection ◽  
Plane Strain Case

On the basis of the new flexural theory of elastic sandwich plates recently developed [1–3], the problem of general forced flexural vibration of sandwich plates in the plane-strain case is solved. The classical method of separation of variables combined with the Mindlin-Goodman procedure [4] for treating time-dependent boundary conditions is used. As an example, the results are made use of in solving the problem of a simply supported sandwich plate in plane strain with one of the two end sections prescribed a transverse deflection varying with time.

Virtual Methods in Creep Crack Growth Predictions in 316H Stainless Steels

2007 ◽  
Author(s):  
Masataka Yatomi ◽  
Kamran M. Nikbin
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Stainless Steels ◽  
Creep Crack Growth ◽  
Crack Propagation Rate ◽  
Creep Model ◽  
Elastic Plastic ◽  
Creep Crack ◽  
Plastic Creep ◽  
Plane Strain Crack

The paper discusses numerically based virtual techniques of creep crack growth predictions in a fracture mechanics component. The material properties used are for 316H stainless steels and the constitutive behaviour of the steel is described by a power law creep model. A damage-based approach is used to predict the crack propagation rate in compact tension (C(T)) specimens and the data are correlated against an independently determined C* parameter. Elastic-plastic-creep analyses are performed using two different crack growth criteria to predict crack extension under plane stress and plane strain conditions. The NSW and NSW-MOD strain exhaustion models are applied to compare to the experimental data and FE predictions. The plane strain crack growth rate predicted from the numerical analysis is found to be less conservative than the plane strain NSW model but more conservative than plane strain NSW-MOD model, for values of C* within the limits of the present creep crack growth testing standards. At higher loads and C* values, the plane strain crack growth rates, predicted using an elastic-plastic-creep material response, approach is considered and compared to the plane strain NSW-MOD model.

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