Shock Waves Produced by Small Stress Increments in Annealed Aluminum

1966 ◽  
Vol 33 (4) ◽  
pp. 907-916 ◽  
Author(s):  
M. J. Kenig ◽  
O. W. Dillon
Keyword(s):  
Experimental Data ◽  
Wave Theory ◽  
Stress Strain ◽  
Wave Speeds ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Wide Range ◽  
Case Type ◽  
Shock Wave Theory ◽  
New Phenomena

Experimental data on the propagation of shear waves in annealed aluminum subjected to biaxial prestresses in the plastic range are presented. In addition, experimental evidence of the catastrophic straining at one “point” in a specimen while other “points” are not affected is given for annealed aluminum. Such evidence is not consistent with the material possessing a smooth stress-strain relation, but is compatible with the stair-case type of response. A shock wave theory which is a generalization of our previous work to the case of a biaxial prestress is also described. This theory is applied to the experimentally determined staircase stress-strain relation for aluminum. The same stress-strain relation is used for a wide range of strain rates and predicts a variety of wave speeds which are shown to be consistent with the experimental data. It is found that the biaxial prestress does not lead to any new phenomena but does modify some specific values. Some illustrative boundary-value problems are also discussed.

A Three-Stage Explicit Stress-Strain Relations for Stainless Steel Alloys Applicable in Tension and Compression at Elevated Temperatures

2012 ◽  
Vol 730-732 ◽  
pp. 691-696
Author(s):  
Abdella Kenzu
Keyword(s):  
Stainless Steel ◽  
Elevated Temperatures ◽  
Full Range ◽  
Elastic Behaviour ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Wide Range ◽  
Tension And Compression ◽  
Linear Elastic Behaviour

Presented in this paper is an explicit full-range stress-strain relation for stainlesssteel alloys applicable at normal and elevated temperatures. The relation utilizes an approxima-tion of the closed form inversion of a highly accurate three-stage stress-strain relation recentlyobtained from the Ramberg-Osgood equation. The three stage inversion is formulated using anappropriate rational function assumption to approximate the fractional deviation of the actualstress-strain relation from an idealized linear elastic behaviour. The temperature dependenceon the stress-strain relation is then introduced by modifying the basic mechanical propertiesof stainless steel to account for the temperature e ects. The proposed approximate inversionis applicable over the full-range of the stress well beyond the elastic region up to the ultimatestress. Moreover, the inversion can be applied to both tensile and compressive stresses. Theproposed approximate inversion is tested over a wide range of material parameters as well as awide range of temperatures. It is shown that the new expression results in stress-strain curveswhich are both qualitatively and quantitatively in excellent agreement with experimental re-sults and the fully iterated numerical solution of the full-range stress-strain relation for normalas well as elevated temperatures

Stress-Strain Relation in Rubber Blocks under Compression. I

1959 ◽  
Vol 32 (2) ◽  
pp. 409-419
Author(s):  
Géza Schay ◽  
Péter Ször
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Cross Section ◽  
Experimental Error ◽  
Stress Strain ◽  
General Applicability ◽  
Empirical Constant ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Good Agreement

Abstract For the stress-strain relation of differently shaped rubber blocks submitted to compression, an equation of general applicability is deduced, starting from the idea that compression work must be done also against the tension arising through the increase of the free surface. In this equation the stress is not a function of the compression ratio only, but of the ratio of the fixed to the free surface as well. Besides the shear modulus of the block's substance, this equation involves a single empirical constant which changes only slightly with the shape of the block's cross section. The validity of the equation obtained was tested by measurements performed by the authors on cylinders as well as by data on quadratic prisms published in previous literature. The calculated values are in good agreement with the experimental data within the limits of experimental error.

scholarly journals Novel Ring Compression Test Method to Determine the Stress-strain Relations and Mechanical Preperties of Metallic Materials

2021 ◽  
Author(s):  
Guang-Zhao Han ◽  
lixun Cai ◽  
Chen Bao ◽  
Bo Liang ◽  
Yang Lv ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Test Method ◽  
Metallic Materials ◽  
Compression Tests ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Ring Compression ◽  
Wide Range

Abstract Although there are methods for testing the stress–strain relation and strength, which are the most fundamental and important properties of metallic materials, their application to small size specimens is limited. In this study, a new dimensionless elastoplastic load–displacement (EPLD-Ring) model for compressed metal rings with isotropy and constitutive power law is proposed to describe the relation between the geometric dimensions, Hollomon law parameters, load, and displacement based on energy density equivalence. Furthermore, a novel test method for the rings is developed to obtain the elastic modulus, stress–strain relation, yield strength, and tensile strength. The universality and accuracy of the model are verified within a wide range of imaginary materials via finite element analysis (FEA), and the results show that the stress–strain relations obtained with the model are more consistent with those inputted in the FEA software. Additionally, for seven metallic materials, a series of ring compression tests with various dimensions were performed. It was found that the stress–strain relations and mechanical properties predicted by the model are in agreement with the normal tensile test results. It is believed that the new method is reliable and effective for testing the mechanical properties of small size materials and tube components.

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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