Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems

1976 ◽  
Vol 98 (4) ◽  
pp. 289-295 ◽  
Author(s):  
C. F. Shih ◽  
J. W. Hutchinson
Keyword(s):  
Plane Stress ◽  
Large Scale ◽  
Crack Opening ◽  
Opening Displacement ◽  
Stress Strain ◽  
Linear Elastic ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Crack Problems ◽  
Scale Yielding

Fully plastic plane stress solutions are given for a center-cracked strip in tension and an edge-cracked strip in pure bending. In the fully plastic formulation the material is characterized by a pure power hardening stress-strain relation which reduces at one limit to linear elasticity and at the other to rigid/perfect plasticity. Simple formulas are given for estimating the J-integral, the load-point displacement and the crack opening displacement in terms of the applied load for strain hardening materials characterized by the Ramberg-Osgood stress-strain relation in tension. The formulas make use of the linear elastic solution and the fully plastic solution to interpolate over the entire range of small and large scale yielding. The accuracy of the formulas is assessed using finite element calculations for some specific configurations.

Mechanical Characteristics of Bamboo

2012 ◽  
Vol 525-526 ◽  
pp. 609-612 ◽  
Author(s):  
Tadashi Shioya ◽  
Toshikatsu Asahina
Keyword(s):  
Fracture Toughness ◽  
Crack Opening ◽  
Water Concentration ◽  
Longitudinal Direction ◽  
Fiber Density ◽  
Opening Displacement ◽  
Stress Strain ◽  
Damping Characteristics ◽  
Strain Relation ◽  
Stress Strain Relation

Fracture toughness, stress-strain relation and the damping characteristics of bamboo are investigated. The fracture toughness of bamboo in tearing along the longitudinal direction is measured by the use of newly devised apparatus in which the crack opening displacement is controlled in a constant velocity and a quasi-steady extension of the crack is maintained. The stress-strain relation of bamboo is examined in a reversible elastic range using a conventional tensile test in the longitudinal direction. Repeated tensile loading tests show that the stress-strain relation has a strong non-linear hysteresis and that it converses to a steady loop. The damping of bamboo is measured by the use of inverted torsion pendulum apparatus. The specimen is taken so that damping of twisting longitudinal bar is measured. The damping coefficient of bamboo is much larger than that of metals. The mechanical properties of bamboo are examined in terms of water concentration and fiber density in the bamboo.

scholarly journals REFINED STUDY OF STRESS-STRAIN STATE NEAR THE CRACK TIP UNDER CYCLIC LOADING IN A DAMAGED MEDIUM

2017 ◽  
Vol 17 (2) ◽  
pp. 105-115
Author(s):  
L.V. Stepanova
Keyword(s):  
Plane Stress ◽  
Strain State ◽  
Crack Tip ◽  
Stress Conditions ◽  
Original Formulation ◽  
Stress Strain ◽  
Linear Elastic ◽  
Crack Problems ◽  
Growing Crack ◽  
The Continuum

The article is devoted to the fatigue growing crack problems in damagedmedia and mutual effects of damage on the evolution of the stress-strain statenear the crack tip and vice versa. The new asymptotic study of fatigue crackgrowth in an isotropic linear elastic material based on the continuum damagemechanics in the coupled (elasticity damage) formulation under plane strainand plane stress conditions is proposed. 1) The new numerical solution of thetwo-point boundary value problem for non-linear ordinary differential equationsto which the fatigue crack growing problem reduces is obtained; 2) The newanalytical presentation of stress, strain and continuity fields both for plane strainand plane stress conditions is given. The results obtained differ from Zhao andZhang’s solution where the original formulation of the problem for plane stressconditions has been proposed.

scholarly journals Limit analysis of narrow support elements in W7-X considering the serration effect of the stress–strain relation at 4K

2011 ◽  
Vol 86 (6-8) ◽  
pp. 1462-1465 ◽  
Author(s):  
E. Briani ◽  
C. Gianini ◽  
F. Lucca ◽  
A. Marin ◽  
J. Fellinger ◽  
...  
Keyword(s):  
Limit Analysis ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation

Analytical stress-strain relation for soils

2021 ◽  
Author(s):  
Kristian Krabbenhoft ◽  
J. Wang
Keyword(s):  
Test Data ◽  
Narrow Range ◽  
Strain Range ◽  
Data Sets ◽  
Soil Tests ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Typical Test ◽  
Typical Soil

A new stress-strain relation capable of reproducing the entire stress-strain range of typical soil tests is presented. The new relation involves a total of five parameters, four of which can be inferred directly from typical test data. The fifth parameter is a fitting parameter with a relatively narrow range. The capabilities of the new relation is demonstrated by the application to various clay and sand data sets.

Stress-Strain Relations and Vibrations of a Granular Medium

1957 ◽  
Vol 24 (4) ◽  
pp. 585-593
Author(s):  
J. Duffy ◽  
R. D. Mindlin
Keyword(s):  
Energy Dissipation ◽  
Contact Forces ◽  
Face Centered Cubic ◽  
Stress Strain ◽  
Differential Stress ◽  
Elastic Bodies ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Face Centered ◽  
Experimental Values

Abstract A differential stress-strain relation is derived for a medium composed of a face-centered cubic array of elastic spheres in contact. The stress-strain relation is based on the theory of elastic bodies in contact, and includes the effects of both normal and tangential components of contact forces. A description is given of an experiment performed as a test of the contact theories and the differential stress-strain relation derived from them. The experiment consists of a determination of wave velocities and the accompanying rates of energy dissipation in granular bars composed of face-centered cubic arrays of spheres. Experimental results indicate a close agreement between the theoretical and experimental values of wave velocity. However, as in previous experiments with single contacts, the rate of energy dissipation is found to be proportional to the square of the maximum tangential contact force rather than to the cube, as predicted by the theory for small amplitudes.

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