Inclusion and Misfit Effects in Hydrostatic Tension

1988 ◽  
Vol 55 (2) ◽  
pp. 355-360 ◽  
Author(s):  
Benjamin Wilner
Keyword(s):  
Numerical Solution ◽  
Spherical Particle ◽  
Elastic Constants ◽  
Normal Stresses ◽  
Governing Equations ◽  
Hydrostatic Tension ◽  
Elastic Plastic ◽  
Plastic Matrix ◽  
Matrix Subject

A study of the effect of an elastic spherical particle embedded in an infinite elastic-plastic matrix subject to hydrostatic tension is presented. Two types of particles will be considered: (1) a perfectly fitting inclusion, (2) a misfitting one. A numerical solution is developed to solve the governing equations. Various combinations of elastic constants and power hardening coefficients are studied for different load levels. The analysis is concentrated on the interfacial normal stresses and its dependence on the different parameters.

Experimental Determination of the Two-Dimensional State of Stress and the Orthotropic Elasticity Coefficients for Coatings

1990 ◽  
Vol 203 ◽  
Author(s):  
Richard J. Farris ◽  
M. A. Maden ◽  
K. Tong
Keyword(s):  
Elastic Constants ◽  
Physical Property ◽  
The State ◽  
Normal Stresses ◽  
Free Standing ◽  
Vibrationally Excited ◽  
Plane Shear ◽  
Plane Normal ◽  
State Of Stress ◽  
The One

ABSTRACTThe state of stress for a uniform coating away from the edges reduces to that of plane stress, two in-plane normal stresses, and an in-plane shear stress. For this state, the interface between the coating and the substrate is totally stress free. Since the substrate and the coating are not interacting mechanically, an internal section of the substrate can be removed creating a tensioned drum-like membrane without altering the stress state. Holographic interferometry of vibrationally excited membranes is used to evaluate the stress. Using this technique, up to thirty vibrational modes can be obtained. This high degree of redundancy enables one to determine the one shear and two normal stresses that act in the plane of the coating. The only physical property requires is the coating density. The density is obtained from commonly reported literature values. Simple variations on the membrane vibration scheme, e.g., cutting the membrane to create a uniaxially tensioned ribbon, enables one to determine the in-plane Poisson's ratio and shearmodulus.In separate but related experiments on commercially made free-standing films with residual orientation, the above techniques, combined with special free and axially constrainedcompressibility experiments should enable all of the Poisson's ratios and elasticmoduli for an orthotropic material (nine elastic constants) to be determined. Methods for measuring the state of stress and the elastic constants are required to predict the state of stress in complex coating geometries.

scholarly journals Plastic deformations in the ring spherical shells

2018 ◽  
Vol 251 ◽  
pp. 04060
Author(s):  
Avgustina Astakhova
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Thin Shells ◽  
Stress Dependence ◽  
Strain Intensity ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Development Area

In the present work the results of the study of plastic deformations distribution in the thickness in ring spherical shells are presented. Resolving differential equations system is based on the Hirchhoff-Lave hypothesis, linear thin shells theory and small elastic-plastic deformations theory. The studying of the development area of plastic deformations in shells thickness are performed with using the results of the elastic solutions method. The basic relations of elastic solutions method that allow to determine the distribution areas of plastic deformations in shells thickness and along the generatrix are presented. The diagram of intense stress dependence from the strain intensity with linear hardening is received. The numerical solution is performed by orthogonal run method. Long and short spherical shells under the operation of three evenly distributed ring loads are observed. The shells have a tough jamming along the contour at the bottom and at the top. Dependency between tension intensity and deformations intensity is accepted for the case of a material linear hardening. Area of plastic deformations in shells thickness for three kinds of ring spherical shells are shown. The results for the loads differed by the value in twice are presented.

The interaction of a fibre tangle with an airflow

1967 ◽  
Vol 27 (3) ◽  
pp. 561-580 ◽  
Author(s):  
Paul A. Taub
Keyword(s):  
Unsteady Flow ◽  
Numerical Solution ◽  
Analytical Model ◽  
Method Of Characteristics ◽  
Solution Procedure ◽  
Governing Equations ◽  
Stress Strain ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Flow Configurations

An analytical model of the interaction of a fibre tangle with an airflow is proposed. This model replaces the discrete fibres by a continuum medium with a non-linear stress-strain law. The governing equations have been examined for one-dimensional unsteady flow configurations and have been found to possess five characteristic directions.A numerical-solution procedure, based upon the method of characteristics, has been outlined and applied to the flow within a dilation chamber. A fibre sample is located at the centre of the chamber, which is alternately pressurized and depressurized.

A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks

1968 ◽  
Vol 35 (2) ◽  
pp. 379-386 ◽  
Author(s):  
J. R. Rice
Keyword(s):  
Plastic Material ◽  
Crack Tip ◽  
Plastic Zone Size ◽  
Crack Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Direct Evaluation ◽  
Strain Concentration ◽  
Hydrostatic Tension ◽  
Elastic Plastic

A line integral is exhibited which has the same value for all paths surrounding the tip of a notch in the two-dimensional strain field of an elastic or deformation-type elastic-plastic material. Appropriate integration path choices serve both to relate the integral to the near tip deformations and, in many cases, to permit its direct evaluation. This averaged measure of the near tip field leads to approximate solutions for several strain-concentration problems. Contained perfectly plastic deformation near a crack tip is analyzed for the plane-strain case with the aid of the slip-line theory. Near tip stresses are shown to be significantly elevated by hydrostatic tension, and a strain singularity results varying inversely with distance from the tip in centered fan regions above and below the tip. Approximate estimates are given for the strain intensity, plastic zone size, and crack tip opening displacement, and the important role of large geometry changes in crack blunting is noted. Another application leads to a general solution for crack tip separations in the Barenblatt-Dugdale crack model. A proof follows on the equivalence of the Griffith energy balance and cohesive force theories of elastic brittle fracture, and hardening behavior is included in a model for plane-stress yielding. A final application leads to approximate estimates of strain concentrations at smooth-ended notch tips in elastic and elastic-plastic materials.

An Elastic-Plastic Stress Analysis of the Specimen Used in the Torsional Kolsky Bar

1980 ◽  
Vol 47 (2) ◽  
pp. 278-282 ◽  
Author(s):  
Eric K. C. Leung
Keyword(s):  
Numerical Solutions ◽  
Elastic Stress ◽  
Dynamic Testing ◽  
Kolsky Bar ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Elastic Plastic ◽  
Applied Torque ◽  
Torsional Kolsky Bar ◽  
Tubular Specimens

This paper examines the stress concentration, the yielding process, and the growth of the elastic-plastic boundary as a function of applied torque in tubular specimens with a short thin-walled section. Although the analysis is entirely quasi-static, it can, under the proper circumstances, be applied to the deformation of short specimens as generally used for dynamic testing in the torsional Kolsky bar. In the analysis, the governing equations for both elastic and elastic-plastic analyses are presented, the latter taking into account work hardening. Numerical solutions of these equations employ the finite-element method. The elastic stress distribution in the specimen and the elastic-plastic enclaves are presented for various loading stages.

Deforming of Elastic-Plastic Medium with Self-Similar Restriction

2016 ◽  
Vol 685 ◽  
pp. 305-309 ◽  
Author(s):  
Alexandr A. Mantsybora ◽  
Maxim M. Rusanov
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Large Deformation ◽  
Half Space ◽  
Elastic Waves ◽  
Plastic Medium ◽  
Elastic Plastic ◽  
Deformation State ◽  
Similar Restriction ◽  
Self Similar

The problem of shock deforming of elastic-plastic half-space with large deformation was examined. We have obtained that the deformation state can be changed in two types of simple plastic waves and two types of shock elastic waves in the case of self-similar medium motion. The speeds and characteristics of plastic waves were examined. The numerical solution of boundary value problem was found.

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