The Propagation of a Crack by a Rigid Wedge in an Infinite Power Law Viscoelastic Body.

1978 ◽  
Author(s):  
J. R. Walton ◽  
A. Nachman
Keyword(s):  
Power Law ◽  
Viscoelastic Body ◽  
Infinite Power

The Propagation of a Crack by a Rigid Wedge in an Infinite Power Law Viscoelastic Body

1979 ◽  
Vol 46 (3) ◽  
pp. 605-610 ◽  
Author(s):  
J. R. Walton ◽  
A. Nachman
Keyword(s):  
Stress Intensity Factor ◽  
Power Law ◽  
Simple Formula ◽  
Crack Surface ◽  
Finite Thickness ◽  
Viscoelastic Body ◽  
Crack Tip ◽  
Closed Form Solutions ◽  
Closing Crack ◽  
Infinite Power

Closed-form solutions are obtained for the problem of a crack propagated by a 2-dimensional rigid wedge of finite thickness in an infinite power law viscoelastic body. The distance from the crack tip to the point of contact with the wedge is determined from the assumption that in the vicinity of the crack tip, forces of cohesion act to produce a smoothly closing crack with continuous stresses. Finally, a simple formula expressing the stress-intensity factor as a function of the speed of penetration and the length of the free crack surface is exhibited.

A Comparison of the Dynamic Transient Anti-Plane Shear Crack Energy Release Rate for Standard Linear Solid and Power-Law-Type Viscoelastic Materials

1991 ◽  
Vol 113 (4) ◽  
pp. 222-229 ◽  
Author(s):  
J. M. Herrmann ◽  
J. R. Walton
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Power Law ◽  
Release Rate ◽  
Shear Crack ◽  
Viscoelastic Body ◽  
Laplace Transforms ◽  
Failure Zone ◽  
Standard Linear Solid ◽  
Standard Linear

The problem of a semi-infinite mode III crack that suddenly begins to propagate at a constant speed is considered for a general linear viscoelastic body. It is shown that the results of an earlier paper for the Laplace transforms of the stress and displacement with the Laplace transform variable s being real and positive are valid, with minor modification, for complex values of s such that Re(s)>0. Therefore, these Laplace transforms can be inverted by means of a Bromwich path integral. Under the assumption that a Barenblatt-type failure zone exists at the crack tip, the energy release rate (ERR) and the work done in the failure zone (WFZ) are calculated through numerical inversion of Laplace transforms. The ERR and WFZ for the standard linear solid and power law material models are contrasted and also compared with the elastic and quasi-static results. The graphs and table illustrate considerable differences in the ERR and WFZ for these different models. These differences may be important to predictions of stable versus unstable crack speeds based upon a critical ERR fracture criterion.

A Self-Consistent Analysis of the Stiffening Effect of Rigid Inclusions on a Power-Law Material

1984 ◽  
Vol 106 (4) ◽  
pp. 317-321 ◽  
Author(s):  
J. M. Duva
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Constitutive Relation ◽  
Power Law ◽  
Nonlinear Boundary ◽  
Viscous Material ◽  
Spherical Inclusions ◽  
Self Consistent ◽  
Infinite Power ◽  
Stiffening Effect

An approximate constitutive relation is derived for a power-law viscous material stiffened by rigid spherical inclusions using a differential self-consistent analysis. This approach consists of two parts: the formulation of a self-consistent differential equation, and the solution of an associated kernel problem, a nonlinear boundary value problem for an isolated inclusion in an infinite power-law viscous matrix.

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.

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