Relations between the elastic and plastic properties of pure polycrystalline metals are discussed and a systematic relation between shear modulus, Burgers vector and plastic shear strength of metals possessing the same lattice structure is proposed. In addition reasons are given for believing that in a limited temperature range malleability is related to Poisson's ratio.

XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals

Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications. Numerous investigations have been carried out, enlarging in essential points the classical concepts of cracks and methods of analysis. The qualitative features of the problems of cracks, associated with their peculiar nonlinearity as revealed in these investigations, makes the theory of cracks stand out distinctly from the whole range of problems in terms of the theory of elasticity. The chapter presents a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discusses the results obtained thereby. The object of the theory of equilibrium cracks is the study of the equilibrium of solids in the presence of cracks. However, there exists a fundamental distinction between these two problems, The form of a cavity undergoes only slight changes even under a considerable variation in the load acting on a body, while the cracks whose surface also constitutes a part of the body boundary can expand even with small increase of the load to which the body is subjected.

The mathematical theory of equilibrium cracks in brittle fracture

A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.

Mechanical properties of solid polymers

https://iopscience.iop.org/article/10.1088/0034-4885/12/1/309/pdf

Fracture and strength of solids

The resistance to tearing of a rubber vulcanizate is usually determined by loading in a specified manner a test-piece of the vulcanizate of standard shape, in which a notch has been produced, either in the molding process or by cutting the test-piece in a standard fashion. A wide variety of shapes of test-piece and notch and of methods of loading have been recommended by various authors (see, for example, Buist1).

Rupture of rubber. I. Characteristic energy for tearing

The solutions for the problem of an infinite isotropic elastic solid stressed under tension T0 and containing a single internal crack of length c on the plane z=0 are given in a form suitable for the computation of the stresses and displacements at all points. These are used to find the stress distribution on, and the displacements of, the plane situated ½a from the plane containing the crack. The normal stress σz on z=½a (as found above) is plotted as a function f(2uz) of the normal displacement uz and τrz is small compared with σz. A model is used in which the crack is considered to be bounded by the atoms centred on the planes z=±½a, these planes being the boundaries of two semi-infinite elastic solids. Equilibrium is maintained by postulating that an attractive force, f(z), acts between the atoms of these bounding planes when they are z+a apart. It is found that f(z) approximates to the law of force expected from atomic considerations, and the condition for unstable equilibrium of the crack, i.e. a value T0c of T0 such that for T0 T0c the crack spreads (c increases), is found. The surface energy is calculated from the results and the equilibrium condition is found in a form similar to that of Griffith. Agreement is found with the experimental results of Griffith. In the absence of the tension T0, the crack cannot be maintained without an inclusion to prevent closing. Possible physical models are discussed.

H A Elliott

Papers

An analysis of the conditions for rupture due to griffith cracks