The Stress Field Produced by Localized Plastic Slip at a Free Surface

1962 ◽  
Vol 29 (3) ◽  
pp. 523-532 ◽  
Author(s):  
T. H. Lin ◽  
T. K. Tung
Keyword(s):  
Free Surface ◽  
Stress Field ◽  
Closed Form ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Slip Direction ◽  
Closed Form Solutions ◽  
Plastic Slip ◽  
Stress Components ◽  
Distribution Of Stress

Uniform plastic slip is assumed to occur in a cubic region embedded at the free surface of a semi-infinite elastic solid. The slip plane and slip direction are both inclined at 45 deg to the free surface and to two opposite interior faces of the cube. The stress field produced by the slip is the same as that produced by equivalent uniform tractions acting on the faces of the cube. Closed-form solutions are obtained for all stress components by employing Papkovitch functions to calculate the effects of the equivalent surface tractions. Calculated numerical results for the distribution of stress components are shown graphically. Certain stress components are found to be discontinuous across the boundary surface of the region of plastic slip.

scholarly journals On the Finite Width Correction Factor in Composite Laminates with Elliptical Inclusion

1994 ◽  
Vol 3 (6) ◽  
pp. 096369359400300 ◽  
Author(s):  
Y. Xiong
Keyword(s):  
Closed Form ◽  
Correction Factor ◽  
Composite Laminates ◽  
Finite Width ◽  
Hard Inclusion ◽  
Closed Form Solutions ◽  
Elliptical Inclusion ◽  
Global Force ◽  
Stress Components ◽  
Force Equilibrium

A general finite width correction ( FWC) factor is derived in this letter for an anisotropic laminate with elliptical soft/hard inclusion. Using the closed-form solutions for the stress components in the laminate, the derivation of the FWC factor is based on the concept of the global force equilibrium. Some specific cases are discussed. The accuracy of the derived FWC factor is demonstrated.

Some Fundamental Thermoelastic Problems in Orthotropic Slabs

1966 ◽  
Vol 33 (1) ◽  
pp. 45-51 ◽  
Author(s):  
B. R. Baker
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Closed Form ◽  
Fourier Transforms ◽  
Broad Class ◽  
Complex Stress ◽  
Closed Form Solutions ◽  
Definite Form ◽  
Stress Components ◽  
Thermoelastic Problems

Steady-state problems of stresses in orthotropic slabs subjected to forces and temperature distribution on the faces are solved by means of Fourier transforms. The usual direct applications in the literature are shown for simple examples to lead to divergent integrals but, by introduction of generalized transforms, a very broad class of problems can be handled. As a part of these considerations, a more definite form of Saint-Venant’s principle is obtained. For a certain class of material constants, it is possible to obtain closed-form solutions for stresses when concentrated loads or temperature sources are applied to the faces of the slab. Results are presented for several examples in the form of complex stress potentials and graphs of the corresponding stress components.

XIX.—Some Triple Trigonometrical Series Equations and their Application

1971 ◽  
Vol 69 (3) ◽  
pp. 255-265 ◽  
Author(s):  
K. S. Parihar
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Trigonometric Series ◽  
Elastic Strip ◽  
Trigonometrical Series ◽  
Closed Form Solutions ◽  
Single Integral ◽  
Distribution Of Stress

SynopsisClosed form solutions of some triple equations involving trigonometric series have been obtained, in each case, by reducing them to a single integral equation. The results have been applied to determine the distribution of stress in the interior of an infinitely long elastic strip containing a pair of Griffith cracks situated on a line perpendicular to the bounding lines of the strip.

scholarly journals The distribution of stress in the neighbourhood of a crack in an elastic solid

1946 ◽  
Vol 187 (1009) ◽  
pp. 229-260 ◽  
Keyword(s):  
Tensile Stress ◽  
Elastic Body ◽  
Crack Surface ◽  
Applied Pressure ◽  
Elastic Solid ◽  
Internal Crack ◽  
Stress Components ◽  
Distribution Of Stress ◽  
Circular Cracks

The distribution of stress produced in the interior of an elastic solid by the opening of an internal crack under the action of pressure applied to its surface is considered. The analysis is given for ‘Griffith’ cracks (§2) and for circular cracks (§3), it being assumed in the latter case that the applied pressure varies over the surface of the crack. For both types of crack the case in which the pressure is constant over the entire crack surface is considered in some detail, the stress components being tabulated and the distribution of stress shown graphically. The effect of a crack (of either type) on the stress produced in an elastic body by a uniform tensile stress is considered and the conditions for rupture deduced.

scholarly journals Fracture mechanics approach to design analysis of notches, steps, and internal cut-outs in planar components

2007 ◽  
Vol 42 (6) ◽  
pp. 433-446 ◽  
Author(s):  
T. G F Gray ◽  
J Wood
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Field Intensity ◽  
Free Boundaries ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
New Information ◽  
Intensity Information ◽  
Sharp Crack ◽  
Stress Concentration Factors

A new approach to the assessment and optimization of geometric stress-concentrating features is proposed on the basis of the correspondence between sharp crack or corner stressfield intensity factors and conventional elastic stress concentration factors (SCFs) for radiused transitions. This approach complements the application of finite element analysis (FEA) and the use of standard SCF data from the literature. The method makes it possible to develop closed-form solutions for SCFs in cases where corresponding solutions for the sharp crack geometries exist. This is helpful in the context of design optimization. The analytical basis of the correspondence is shown, together with the limits on applicability where stress-free boundaries near the stress concentrating feature are present or adjacent features interact. Examples are given which compare parametric results derived from FEA with closed-form solutions based on the proposed method. New information is given on the stress state at a 90° corner or width step, where the magnitude of the stress field intensity is related to that of the corresponding crack geometry. This correspondence enables the user to extend further the application of crack-tip stress-field intensity information to square-cornered steps, external U-grooves, and internal cut-outs.

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