On the Calculations of the Stored Energy of Cold Work

1990 ◽  
Vol 112 (4) ◽  
pp. 465-470 ◽  
Author(s):  
N. Aravas ◽  
K-S. Kim ◽  
F. A. Leckie
Keyword(s):  
Simple Technique ◽  
Mechanical Energy ◽  
Cold Work ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Displacement Curve ◽  
Stored Energy ◽  
Stress Strain Curve ◽  
Polycrystalline Metal ◽  
Simple Tension

When a metal deforms plastically, most of the mechanical energy expended in the deformation process is converted into heat and the remainder is stored in the material. A method for the calculation of the stored energy from an experimentally determined load-displacement curve of an elastic-plastic structure is presented. The method is applied to the problem of simple tension of a polycrystalline metal and a simple technique for the calculation of the stored energy from the uniaxial stress-strain curve is presented.

Determining engineering stress–strain curve directly from the load–depth curve of spherical indentation test

2010 ◽  
Vol 25 (12) ◽  
pp. 2297-2307 ◽  
Author(s):  
Baoxing Xu ◽  
Xi Chen
Keyword(s):  
Indentation Test ◽  
Strain Curve ◽  
Spherical Indentation ◽  
Displacement Curve ◽  
Large Set ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Constraint Factors ◽  
Engineering Stress ◽  
Depth Curve

The engineering stress–strain curve is one of the most convenient characterizations of the constitutive behavior of materials that can be obtained directly from uniaxial experiments. We propose that the engineering stress–strain curve may also be directly converted from the load–depth curve of a deep spherical indentation test via new phenomenological formulations of the effective indentation strain and stress. From extensive forward analyses, explicit relationships are established between the indentation constraint factors and material elastoplastic parameters, and verified numerically by a large set of engineering materials as well as experimentally by parallel laboratory tests and data available in the literature. An iterative reverse analysis procedure is proposed such that the uniaxial engineering stress–strain curve of an unknown material (assuming that its elastic modulus is obtained in advance via a separate shallow spherical indentation test or other established methods) can be deduced phenomenologically and approximately from the load–displacement curve of a deep spherical indentation test.

Evaluation of a Modified Monotonic Neuber Relation

1991 ◽  
Vol 113 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. N. Sharpe ◽  
K. C. Wang
Keyword(s):  
Plane Strain ◽  
Notch Root ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Predictive Capability ◽  
Stress Strain Curve ◽  
Interferometric Technique ◽  
Strain Stress ◽  
Concentration Factors ◽  
Elastoplastic Strains

It has been proposed in the literature that the Neuber relation be modified to read Kε/Kt×(Kσ/Kt)m=1 in order to improve its predictive capability when plane strain loading conditions exist. Kε, Kσ, and Kt are respectively the strain, stress, and elastic concentration factors. The exponent m is proposed to be 1 for plane stress and 0 for plane strain. This paper reports the results of biaxial notch root strain measurements on three sets of double-notched aluminum specimens that have different thicknesses and root radiuses. Elastoplastic strains are measured over gage lengths as short as 150 micrometers with a laser-based in-plane interferometric technique. The measured strains are used to compute Kε directly and Kσ using the uniaxial stress-strain curve. The exponent m can then be determined for each amount of constraint. The amount of constraint is defined as the negative ratio of lateral to longitudinal strain at the notch root and determined from elastic finite element analyses. As this ratio decreases for the three cases, the values of m are found to be 0.65, 0.48, and 0.36. The modified Neuber relation is an improvement, but discrepancies still exist when plastic yielding begins at the notch root.

Strain Localisation during a Tensile Test of Metallic Plates: Experimental and Numerical Results

2009 ◽  
Vol 417-418 ◽  
pp. 569-572
Author(s):  
D.A. Cendón ◽  
Jose M. Atienza ◽  
Manuel Elices Calafat
Keyword(s):  
Tensile Test ◽  
Strain Curve ◽  
Maximum Load ◽  
Surface Strain ◽  
Displacement Curve ◽  
Strain Localisation ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Fields ◽  
Developed Surface

The stress-strain curve of a material is usually obtained from the load-displacement curve measured in a tensile test, assuming no strain localisation up to maximum load. However, strain localisation and fracture phenomena are far from being completely understood. Failure and strain localisation on plane tensile specimens has been studied in this work. A deeply instrumented experimental benchmark on steel specimens has been developed. Surface strain fields have been recorded throughout the tests, using an optical extensometer. This allowed characterisation of the strain localisation and failure processes. Tests have been numerically modelled for a more detailed analysis. Preliminary results show a substantial influence of geometrical specimen defects on the strain localisation phenomena that may be critical on the stress-strain curves obtained and in the failure mechanisms.

A Critical Appraisal of Static Hardness Measurements

1981 ◽  
Vol 48 (4) ◽  
pp. 796-802 ◽  
Author(s):  
C. Rubenstein
Keyword(s):  
Critical Appraisal ◽  
Cone Angle ◽  
Large Angle ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Hardness Measurement ◽  
Stress Strain Curve ◽  
Indentation Process ◽  
Static Hardness ◽  
Subsurface Layers

A semiempirical analysis of the indentation process is made as a result of which the hardness indentation data obtained with ball, cone and square-based pyramid indenters are related to the uniaxial stress-strain curve of the indented material. It is shown that deductions from the analysis are valid only for annealed materials. The factors liable to result in erroneous hardness readings are considered and the influence of residual stresses in the surface and the subsurface layers of the material under examination are shown to explain (i) the dependence of cone and pyramid hardness on the applied load and (ii) the anomalous influence of cone angle on the measured hardness when large angle indenters are pressed into materials which have been strain-hardened prior to the hardness measurement.

Influence of Uniaxial Stress on the Stress-Strain Curve Measured by Nanoindentation

2014 ◽  
Vol 597 ◽  
pp. 17-20
Author(s):  
Ikuo Ihara ◽  
Kohei Ohtsuki ◽  
Iwao Matsuya
Keyword(s):  
Compressive Stress ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Local Area ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Compressive Stresses ◽  
Multiple Loading ◽  
Tip Radius ◽  
Uniaxial Compressive Stress

A nanoindentation technique with a spherical indenter of tip radius 10 μm is applied to the evaluation of stress-strain curve at a local area of a pure iron under the uniaxial compressive stress exerted through the iron, and the influence of the compressive stress on the estimated stress-strain curve has been examined. A continuous multiple loading method is employed to determine the stress-strain curve. In the method, a set of 21 times of loading/unloading sequences with increasing terminal load are made and load-displacement curves with the different terminal loads from 0.1 mN to 100 mN are then continuously obtained and converted to a stress-strain curve. To examine the stress dependence of the stress-strain curve, the estimation by the nanoindentetion is performed under different uniaxial compressive stresses up to 250 MPa. It has been found that the stress-strain curve determined by the nanoindentation shifts upward as the compressive stress increases and the quantity of the shift is almost equal to the uniaxial stress acting on the iron specimen. It is also noted that the yield stress (0.2 % proof stress) estimated from the stress-strain curve increases almost proportionally to the uniaxial stress and the increase ratio tends to decrease as the stress reaches around 200 MPa.

Tension-compression stress-strain curves from bending tests

1971 ◽  
Vol 6 (4) ◽  
pp. 286-292 ◽  
Author(s):  
P W J Oldroyd
Keyword(s):  
Strain Curve ◽  
Bending Moment ◽  
Uniaxial Stress ◽  
Bending Test ◽  
Compression Stress ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Bending Tests ◽  
Original Length ◽  
Annealed Copper

A formula—Nadai's bending formula—is derived which enables the tension (or compression) stress-strain curve for a material to be obtained from the curve relating bending moment to curvature for a beam of solid rectangular section. The method is extended to give a formula which covers deformations in which reversals of plastic strain occur. The results obtained from a unidirectional bending test made on annealed copper are compared with those obtained from a tensile test made on the same material and the accuracy of the stress-strain values obtained from the bending test is discussed. The results obtained from a reversed bending test are also compared with those obtained from a tension-compression test in which a specimen was first stretched and then compressed to its original length. The limitations imposed by this method of obtaining the stress-strain curve for a material are examined and the advantages its presents in the study of the behaviour of materials under uniaxial stress are outlined.

Tensile stress/strain characterization of non-linear materials

1981 ◽  
Vol 16 (2) ◽  
pp. 107-110 ◽  
Author(s):  
J Margetson
Keyword(s):  
Strain Curve ◽  
Uniaxial Stress ◽  
Aerodynamic Heating ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Characterization ◽  
Least Squares Fit ◽  
Experimental Values ◽  
Good Agreement

A uniaxial stress/strain curve is represented empirically by a modified Ramberg-Osgood equation ∊=(σ/E) + (σ/σo)m. Firstly E is extracted then σo and m are determined from two points on the experimental curve. These values are improved iteratively by a least squares fit using all the experimental points on the curve. The procedure is used to generate stress/strain relationships for a variety of materials and there is good agreement with the experimental values. The method is also applied to a simulated aerodynamic heating experiment.

Sign in / Sign up

Export Citation Format

Share Document