Singular stresses at the tip of a sharp notch in power-law-hardening materials under antisymmetric loading

1996 ◽  
Vol 31 (6) ◽  
pp. 693-701 ◽  
Author(s):  
N. V. Kouzniak ◽  
H. P. Rossmanith ◽  
M. P. Savruk
Keyword(s):  
Power Law ◽  
Sharp Notch ◽  
Antisymmetric Loading

Stresses Due to a Sharp Notch in a Work-Hardening Elastic-Plastic Material Loaded by Longitudinal Shear

1967 ◽  
Vol 34 (2) ◽  
pp. 287-298 ◽  
Author(s):  
J. R. Rice
Keyword(s):  
Applied Stress ◽  
Power Law ◽  
Work Hardening ◽  
Plastic Material ◽  
Longitudinal Shear ◽  
Small Scale ◽  
Sharp Notch ◽  
Initial Yield Stress ◽  
Elastic Plastic ◽  
Deformation Plasticity

A work-hardening elastic-plastic stress analysis is presented for a sharp notch or, as a limiting case, a crack perturbing a remotely applied uniform stress field. Mathematical complexities are reduced through considering the kinematically simple case of antiplane longitudinal shear deformations and by employing a deformation plasticity theory rather than the more appropriate incremental theory. Consequently, a general solution is available valid for any relation between stress and strain in the work-hardening range, so long as the remotely applied stress does not exceed the initial yield stress. When a power law relates stress to a strain in the work-hardening range, the deformation theory solution is also the correct incremental solution at low applied stress levels causing yielding on a scale small compared to notch depth. For cracks, the near crack tip strain field is shown to depend on loads and geometry only through the elastic stress intensity factor when yielding is on a small scale, and the elastic-plastic boundary and lines of constant strain magnitude are circles. Extensive numerical results are tabulated for a crack, 45 deg V-notch, and 90 deg V-notch in power-law-hardening materials, and exhibited graphically for a crack.

Notch-Tip Stresses in a Creeping Solid

1984 ◽  
Vol 51 (3) ◽  
pp. 475-480 ◽  
Author(s):  
J. L. Bassani
Keyword(s):  
Strain Rate ◽  
Power Law ◽  
High Stress ◽  
Shear Loading ◽  
Antiplane Shear ◽  
Sharp Notch ◽  
Hyperbolic Sine ◽  
Notch Tip ◽  
As Stress ◽  
Sine Law

At high stress levels the creep strain rate for many materials varies as the exponential of stress while at low stresses it varies as stress to some power. An analysis is presented for a sharp notch under antiplane shear loading in a material that deforms by hyperbolic-sine-law creep, ε˙c = ε˙0[sinh(σ/σ0)]n. The asymptotic notch-tip stress intensification is weaker and the strain-rate intensification is stronger than for a power-law creeping material.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

1968 ◽  
Vol 11 (1) ◽  
pp. 169-178 ◽  
Author(s):  
Alan Gill ◽  
Charles I. Berlin
Keyword(s):  
Power Law ◽  
Response Magnitude ◽  
Single Units ◽  
Spectral Content ◽  
Hearing Sensitivity ◽  
Subjective Magnitude ◽  
Orderly Fashion ◽  
Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

How Useful is the Power Law of Practice for Recognizing Practice in Concentration Tests?

2007 ◽  
Vol 23 (3) ◽  
pp. 157-165 ◽  
Author(s):  
Carmen Hagemeister
Keyword(s):  
Logistic Regression ◽  
Reaction Time ◽  
Power Law ◽  
Error Rate ◽  
Reaction Times ◽  
Practice Effect ◽  
Practice Effects ◽  
Rate Decrease ◽  
Small Practice

Abstract. When concentration tests are completed repeatedly, reaction time and error rate decrease considerably, but the underlying ability does not improve. In order to overcome this validity problem this study aimed to test if the practice effect between tests and within tests can be useful in determining whether persons have already completed this test. The power law of practice postulates that practice effects are greater in unpracticed than in practiced persons. Two experiments were carried out in which the participants completed the same tests at the beginning and at the end of two test sessions set about 3 days apart. In both experiments, the logistic regression could indeed classify persons according to previous practice through the practice effect between the tests at the beginning and at the end of the session, and, less well but still significantly, through the practice effect within the first test of the session. Further analyses showed that the practice effects correlated more highly with the initial performance than was to be expected for mathematical reasons; typically persons with long reaction times have larger practice effects. Thus, small practice effects alone do not allow one to conclude that a person has worked on the test before.

Evidence for a solar wind origin of the power law burst lifetime distribution of the AE indices

2000 ◽  
Vol 27 (8) ◽  
pp. 1087-1090 ◽  
Author(s):  
M. P. Freeman
Keyword(s):  
Solar Wind ◽  
Power Law ◽  
Lifetime Distribution ◽  
Solar Wind Origin

Inverse Power Law Behavior in a Memory Scanning Experiment

2006 ◽  
Author(s):  
Gerardo Ramirez ◽  
Sonia Perez ◽  
John G. Holden
Keyword(s):  
Power Law ◽  
Inverse Power ◽  
Memory Scanning ◽  
Inverse Power Law

Effects of Session and Intrasession Repetition on Individual Power Law Exponents

1975 ◽  
Author(s):  
William E. Dawson ◽  
Steven P. Waterman
Keyword(s):  
Power Law
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