The Mechanics of Ozone Cracking

1962 ◽  
Vol 35 (1) ◽  
pp. 200-209 ◽  
Author(s):  
M. Braden ◽  
A. N. Gent

Abstract Experimental measurements are described of the growth of a cut in a stretched rubber sheet under the action of an atmosphere containing ozone. A well-defined rate of crack growth is obtained, substantially independent of the applied tensile stress when this exceeds a critical value necessary for growth to occur at all. The rate of growth is found to be similar for a number of polymers and principally determined by the ozone concentration when the mobility of the polymer molecules is sufficiently high. When the molecular mobility is inadequate, crack growth is retarded. The critical condition is found to be similar for all the polymers examined, and largely independent of the conditions of exposure; it appears to reflect an energy requirement for growth of about 40 ergs/cm2 of newly-formed surface. The effect of the degree of vulcanization and the presence of additives, including antiozonants, on these two factors has also been examined. The dialkyl-p-phenylene diamines are found to confer protection by raising the critical energy required for growth to occur, in contrast to other protective agents which affect only the rate of crack propagation.

1960 ◽  
Vol 33 (4) ◽  
pp. 1156-1165
Author(s):  
M. Braden ◽  
A. N. Gent

Abstract In Part I an experimental study was reported of the factors determining the rate of propagation of a cut through a stretched rubber sheet under the action of an atmosphere containing ozone. It was remarked that no growth took place from a small razor cut made in one edge of the test pieces unless a critical value of the applied tensile stress was exceeded. The value was quite small, of the order of 100 g/cm2 for a soft natural rubber vulcanizate. In the present part an examination is reported of the conditions necessary for a crack to form or, being present, to grow.


1991 ◽  
Vol 77 (6) ◽  
pp. 816-823
Author(s):  
Yutaka KANETSUKI ◽  
Osamu KAIDA ◽  
Masato KAISO ◽  
Masaaki KATSUMATA

1974 ◽  
Vol 47 (1) ◽  
pp. 202-212 ◽  
Author(s):  
A. N. Gent

Abstract A survey is given of the mechanics of rupture of a simple adhesive joint, comprising two relatively rigid adhering members joined by a layer of a deformable adhesive. Several different modes of failure are treated in terms of a critical energy requirement for growth by unit area of a pre-existing interfacial flaw or debond. They are: (i) Tensile rupture of joints with thick or thin adhesive layers, (ii) Shear rupture, (iii) Separation by stripping apart stiff or flexible adherends, i.e. cleavage. In addition, the stresses set up in joints by shrinkage of the adhesive, for example due to differential thermal contraction, are evaluated. Attention is drawn to probable sites and conditions for failure.


2017 ◽  
Vol 09 (04) ◽  
pp. 571-630 ◽  
Author(s):  
Junyoung Lee

In this paper, we prove the fiberwise convexity of the regularized Hill’s lunar problem below the critical energy level. This allows us to see Hill’s lunar problem of any energy level below the critical value as the Legendre transformation of a geodesic problem on [Formula: see text] with a family of Finsler metrics. Therefore the compactified energy hypersurfaces below the critical energy level have the unique tight contact structure on [Formula: see text]. Also one can apply the systolic inequality of Finsler geometry to the regularized Hill’s lunar problem.


Author(s):  
RICARDO SIMÃO ◽  
FRANCISCO ROSENDO ◽  
LUCAS WARDIL

The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.


Author(s):  
Lallit Anand ◽  
Sanjay Govindjee

This chapter presents conditions for determining the limits of elastic behaviour for isotropic materials. The stress invariants of equivalent pressure, equivalent shear stress, and equivalent tensile stress are defined. These are then used to define common yield conditions, viz. the pressure-independent Mises and Tresca yield conditions, as well as the pressure-dependent Coulomb-Mohr and the Drucker-Prager yield conditions. Rankine’s failure criterion for brittle materials in tension, that is failure in a brittle material will initiate when the maximum principal stress at a point in the body reaches a critical value, is also discussed.


1984 ◽  
Vol 4 (2) ◽  
pp. 219-228 ◽  
Author(s):  
L. Lanotte ◽  
C. Luponio ◽  
F. Porreca

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