Showing papers in "Journal of The Mechanics and Physics of Solids in 1952"

Plastic instability under plane stress

Abstract: This paper examines the conditions for instability of plastic strain under plane stress for a material conforming to the Mises-Hencky yield condition and strain-hardening according to a unique relationship between root-mean-square values of shear stress (q) and incremental strain (δψ). If, under fixed loading conditions, the material undergoes a strain increment which is consistent with the applied stress system, the conditions are stable or unstable according as the increment in representative yield stress is greater or less than the increment in representative induced stress. The strain at which instability arises is found in terms of the biaxial stress ratio p2/p1 under different conditions of applied loading, and the effect is demonstrated of strain-hardening according to an empirical relation of the type q = c (a + ψ)n. The analysis is also applied to certain cases of non-uniform stress distribution. In the case of the hydrostatic bulge results are obtained showing a critical thinning ranging from 26 per cent for a non-hardening material to about 45 per cent for typical strain-hardening materials, values in general agreement with experimental data. Conditions over the punch head in the pressing of a cylindrical shell are discussed but computations are not attempted.

On discontinuous plastic states, with special reference to localized necking in thin sheets

Abstract: Permissible discontinuities of stress, velocity, and surface slope are investigated in a plastic-rigid sheet deformed in its plane. One such discontinuity of velocity is shown to be the mathematical idealization of localized necking; the necessary restrictions on the stress-state and rate of workhardening are obtained for any yield function and plastic potential. The results are illustrated by an examination of the modes of necking in notched tension strips. The constraint factors at the yield point are obtained for notches with wedge-shaped or circular roots.

The time laws of creep

Abstract: Experimental and theoretical studies of transient creep are briefly reviewed. Many creep curves begin with a rate of strain proportional to t−n where t is time and n is usually 1 (logarithmic creep), 2 3 ( Anbrade creep ) or 0 (steady state creep). Logarithmic creep can be explained by the exhaustion theory in which regions with low activation energies yield first and are then used up, leaving the less readily activated regions of higher energy to continue the process, so that the rate of creep diminishes. Experiments by Wyatt confirm a deduction of his from the exhaustion theory that a mechanical equation of state is obeyed during logarithmic creep. It is proposed that the unit process in Wyatt 's creep is the cutting of one dislocation through another ; this idea enables one to account quantitatively for the properties of the activation energy function obtained from Wyatt 's results. A brief discussion of the possibility of explaining Andrade creep by modifying the exhaustion theory is given. It appears unlikely that this problem can be solved until work hardening is introduced into the theory.

The yield phenomenon in polycrystalline mild steel

Abstract: While Cottbell 's theory of the yield point in single crystals is now widely accepted, it has to be combined with some form of grain boundary theory to explain the strength of polycrystalline iron. This paper tries to summarise and interrelate the most important macroscopic features of the yield in polycrystalline iron, and to single out the fundamental properties which must be explained. It appears that the drop in stress after the first yield is responsible for the localisation of plastic flow, and that this localisation may in turn be responsible for the macroscopic shear associated With the Luders deformation. The existence of this shear influences the pattern of the bands in the specimen and, therefore, the regularity or otherwise of the progress of the yield. It is suggested that the two essential quantities to be derived from any theory are the magnitude of the Luders strain and the sharpness of its localisation.

Calculations on the influence of friction and die geometry in sheet drawing

Abstract: Calculations of the drawing stress on the basis of the Hill - Tupper theory of sheet-drawing are reported for an extended range of angles and reductions for both smooth and rough wedge-shaped dies. The results are summarized in convenient empirical formulae. It is shown that the fractional redundant work due to inhomogeneous distortion is virtually a function only of a single geometric parameter in frictionless drawing. The redundant work does not decrease steadily as the reduction is increased, but oscillates with a decreasing amplitude.

Rheology of metals at elevated temperatures

Abstract: An account is given of the outline and progress of an examination of the general stress, time, and temperature dependence of the creep, plastic strain, and relaxation properties of several metals and metallic alloys, which, while being typical practical engineering materials, are different in their basic structures. The temperature range examined for each of these materials has been in each case chosen as the practical temperature range of use at elevated temperatures in actual engineering practice. The work involves simple tensile, torsion, and combined stress creep tests, and similar varieties of short period plastic strain tests and relaxation tests. The results, so far obtained in the work, and the inferences drawn from them, are discussed in relation to such appropriate theory as has currently been advanced, and in several cases it has been possible to suggest relations modifying or replacing those implicit in such theory.