The following URL shows the power relation between stress and strain for a brittle material.
http://www.grimer2.freeserve.co.uk/pge17.htm Because the stress-strain curve of a brittle material is virtually a straight line it is important to stress (no pun intended <g>) that this stress-strain curve is plotted conventionally with the anthropomorphic pressure datum at P = 0.0, E = 0.0 and the point of failure at P = 1.0, E = 1.0. P and E are thus anthropomorphic measures of stress and strain which view the material as initially under no stress and no strain. In contrast, the domometric measures of stress and strain in the power relation "strain = stress^1.01" originate at x = 1.0, y = 1.0. At this point the brittle specimen has failed. In other words, there is no brittle specimen - only debris. And debris is not a specimen. The specimen is the interaction between the debris. Put in terms of Multifactor Analysis of Variance, the debris is A plus B. The specimen is the interaction term AB. As in Russell's "Barber Paradox" we have to distinguish between the Barber qua barber and the man Figaro. In other words, we have to distinguish between the individual and his office. Unfortunately, in the service of efficiency, language is necessarily ambiguous and relies upon the context and common sense of the hearer to convey meaning. It also relies upon hearers of goodwill, qui habet aures audiendi audiat. Words can always be construed perversely by someone of ill will. Anthropomorphically, P = 0.0, E = 0.0, is viewed as the point where no stress is applied to the specimen. The specimen, on the other hand, sees it as the point where the all round Beta-atmosphere pressure is holding the specimen together - or if one prefers to express the same idea in more traditional terms, the point where the tension in the quasi-fluid phase is balanced by the compression in the quasi solid phase to give us a prestressed material. One interesting aspect of the ->1 power laws which govern self similar brittle materials is that it is possible to calculate the maximum stress (strength) and maximum strain from a knowledge of only three points close to the anthropomorphic stress-strain origin. This seems so anti-intuitive (though obviously mathematically logical) that I had to actually work through an example myself to remove the emotional block. Theoretically such a procedure would be an ideal non-destructive means of assessing the strength of a brittle material, a procedure far superior to such empirical alternatives as measurement of the dynamic modulus of elasticity for example. It is clear that one could never hope to discover that the relations between stress and strain for brittle materials are ->1 power curves without coming to that discovery from the wider context of higher order power curves such as those for gravel, slag and Leca concretes. http://www.grimer2.freeserve.co.uk/pge14.htm If proof is required the reader only has to go to the International Critical Tables and re-plot the data on the PV relations for gases to see that the fact they are also ->1 power laws has been missed completely. Even the power laws for water and water vapour have been missed and they are far more obvious. In fact the power laws for all self similar materials (the majority) have been missed, or dismissed as "coincidence" or "empirical". If the Nobel prizewinnner, P.W.Bridgman can have overlooked, not only the power laws for water, but also all the power laws for the all the organic fluids he investigated, see example at: http://www.grimer2.freeserve.co.uk/pge16.htm then anyone without some theoretical basis for a search such as Beta-atmosphere pressure would have also missed them. Nowhere is the failure to embed results in a wider context more flagrently demonstrated than in the purblind invention of the quantum by a coterie that flatly refused to acknowledge the existence of a substantial aether, a cabal of materialist reductionists who naively imagined that they could forever enthrone Quetzalcoatl at the heart of science. Cheers Grimer =============================================== Fairy tales don't tell us that dragons exist. We already know that. Fairy tales tell us that dragons can be killed. G. K. Chesterton ===============================================
