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.

Measurement of Monotonic Biaxial Elastoplastic Stresses at Notch Roots

1991 ◽  
Vol 58 (4) ◽  
pp. 916-922 ◽  
Author(s):  
W. N. Sharpe
Keyword(s):  
Effective Stress ◽  
Notch Root ◽  
Sheet Material ◽  
Thin Sheet ◽  
Strain Curve ◽  
Local Stress ◽  
Uniaxial Stress ◽  
Maximum Deviation ◽  
Principal Stresses ◽  
Interferometric Technique

Biaxial principal strains were measured at the roots of notches in aluminum specimens with a laser-based interferometric technique. Interference patterns from three tiny indentations spaced 150 or 200 micrometers apart in an orthogonal pattern were monitored with a microcomputer-controlled system. Elastoplastic strains up to one percent were measured in real time with a resolution of 25 microstrain. Procedures were developed for computing the two principal stresses from the incremental strain data using J2-flow theory. The validity of the computations was checked by computing the stresses in smooth tensile specimens. Anisotropy in the thin sheet material leads to errors in the computed lateral stresses (which should be zero), but the maximum deviation of the computed effective stress from the uniaxial stress is only five percent. Three kinds of double-notched specimens were prepared to vary the amount of constraint at the notch root. These were tested under monotonic tensile loading and the biaxial notch-root strains recorded. There is considerable variation among the strains once the elastic limit is passed. This is due primarily to the local inhomogeneity of plastic strain, since the gage length of the measurement is only a few times larger than the grain size of the material. Local biaxial stresses were computed from the measured strains for the three cases. The nature of the material’s stress-strain curve tends to smooth out the variations among tests, particularly when the effective stress is computed. It is discovered that the local stress predicted by the Neuber relation agrees very closely with the measured local effective stress.

Joint Inclination Effect on Strength, Stress-Strain Curve and Strain Localization of Rock in Plane Strain Compression

2005 ◽  
Vol 495-497 ◽  
pp. 69-76 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Plane Strain ◽  
Strain Softening ◽  
Strain Curve ◽  
Plane Strain Compression ◽  
Peak Strength ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Softening Behavior ◽  
Ideal Plastic ◽  
Joint Inclination

Peak strength, mechanical behavior, and shear band (SB) of anisotropic jointed rock (JR) were modeled by Fast Lagrangian Analysis of Continua (FLAC). The failure criterion of rock was a composite Mohr-Coulomb criterion with tension cut-off and the post-peak constitutive relation was linear strain-softening. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. A FISH function was written to find automatically elements in the joint. For the lower or higher joint inclination (JI), the higher peak strength and more apparent strain-softening behavior are observed; the failure of JR is due to the slip along the joint and the new generated SBs initiated at joint’s two ends. For the lower JI, the slope of softening branch of stress-strain curve is not concerned with JI since the new and longer SBs’s inclination is not dependent on JI, as can be qualitatively explained by previous analytical solution of post-peak slope of stress-strain curve for rock specimen subjected to shear failure in uniaxial compression based on gradient-dependent plasticity. For the higher JI, the post-peak stress-strain curve becomes steeper as JI increases since the contribution of the new SBs undergoing strain-softening behavior to axial strain of JR increases with JI. For the moderate JI, the lower strength and ideal plastic behavior beyond the elastic stage are found, reflecting that the inclined joint governs the deformation of JR. The present numerical prediction on anisotropic peak strength in plane strain compression qualitatively agrees with triaxial experimental tests of many kinds of rocks. Comparison of the present numerical prediction on JI corresponding to the minimum peak strength of JR and the oversimplified theoretical result by Jaeger shows that Jaeger’s formula has overestimated the value of JI.

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.

Elastoplastic strain concentration factors in finite thickness plates

2003 ◽  
Vol 38 (1) ◽  
pp. 31-36 ◽  
Author(s):  
P Livieri ◽  
G Nicoletto
Keyword(s):  
Finite Element Modelling ◽  
Notch Root ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Elastoplastic Material ◽  
Elastoplastic Strain ◽  
Material Behaviour ◽  
Factor Ratio ◽  
Concentration Factors ◽  
Elastoplastic Strains

The paper presents a comparison of a detailed finite element modelling of elastoplastic strains at a notch root with experimental Moire interferometric data. The three-dimensional nature of the local constraint at a notch root for elastic or elastoplastic material behaviour is confirmed. The elastoplastic analysis shows that the stress concentration factor ratio from the mid-plane and the surface is practically insensitive to the actual σ—ε. relationship when the nominal stress achieves the yield stress.

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.

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