Yield Point Behavior Research Articles

Plastic shallow shells under combined loads

Details of an experimental program, concerned with shallow spherical shells under combined lateral and inplane pressure loading, are described. The available theoretical analyses are reviewed and their predictions are compared to the experimentally obtained results. Yield point and post-yield behavior of the shells is discussed and some recommendations regarding the analysis and design of these shells are made.

Simplified Plastic Analysis of Edge-Restrained Shallow Shells

Abstract This paper gives a brief review of recent theoretical and experimental work on compressed and edge-restrained shallow shells. Yield point and post-yield point behavior of these shells is discussed and the available theoretical results are viewed in light of some experimental evidence. It is shown that the solutions for edge-restrained shallow shells are contained in the solutions for the compressed shallow shells.

Cyclic yield behavior of polycrystalline niobium

Previous investigations have shown the room temperature upper and lower yield point stress of b.c.c. iron and molybdenum can be completely removed by initially “elastic” cyclic stressing above the fatigue limit. The work described in this paper shows that the upper and lower yield point stresses in niobium can also be removed under these same conditions. The cyclic stress-strain curve of niobium was found cyclically to strain soften at small strain amplitudes and cyclically to strain harden at larger strains. Under constant cyclic strain amplitudes in the inelastic region, niobium cyclically strain hardens and quickly reaches a stable hysteresis loop. The cyclic yield point behavior described is explained in terms of localized cumulative multiplication of mobile dislocations.

The influence of specimen size, polycrystal grain size, and yield point behaviour on the fatigue strength of low-carbon steel

I t is shown, by comparison of fatigue and yield strength results previously reported for several materials, that a rational explanation can be given of the seemingly complicated manner in which the fatigue properties of annealed low-carbon steel depend on the number of grains in a specimen cross-section, the polycrystal grain size and the yield point behaviour. This dependence varies according to whether the fatigue stress is greater than, equal to, or less than the yield stress of the same material.

Grain-size dependence of discontinuous yielding in strain-aged steels

Recent studies of discontinuous yielding in polycrystalline metals support interpretations of the Hall-Petch relationship which relate k y to the local stress required to spread yielding across grain-boundaries at a yield front. Changes in yield-point behaviour due to strain-ageing can be rationalised on the assumption that the growth of k y provides a measure of the increase in the average value of this local stress. In low-carbon steels, the first phase of ordinary strain-ageing is concerned with Cottrell-atmosphere formation. In test-pieces aged within this first stage, mobile dislocations are almost certainly released by unpinning, but after later stages of ageing the magnitude of the discontinuous yield becomes insensitive to continued solute segregation to dislocations: yield-nucleation by unpinning is then unlikely. After the first stage of ageing it is probable that mobile dislocations are nucleated from grain-boundaries. Thus a reduction in solute segregation at boundaries, by quenching from ~700°C before prestraining, is accompanied by a decrease in the second-stage (“plateau”) values of Luders strain and k y . It is suggested that prestraining causes a reduction in the stress required to generate dislocations from boundaries and that the final slow increase in k y is due to a transfer of interstitial solute from grain interiors to unsaturated grain-boundaries.

Strain rate sensitivity and yield point behavior in mild steel

An empirical description of the rate sensitive behavior of mild steel based on a logarithmic dependence of flow stress on strain rate is examined in detail. It is shown that the law provides a good representation of the material response for strains up to about 5.0 percent. The delayed yield phenomenon, which is a striking characteristic of mild steel behavior is included and a mechanism previously found to be accurate in representing the delay time under constant stress is used to determine the delay time under complex stress histories. The relaxation from the upper yield point resulting from the delay time in a constant strain rate situation is prescribed by the rate sensitive behavior of the material.It is shown that the response of the material is a functional of the stress history and has a fading memory in strain as well as time. The characteristic memory strain is found to be small so that for large strains the influence of the history is small and an equation-of-state representation is appropriate. For small strains and strain histories of rapidly changing type the integral representation must be used.The theory is applied to the prediction of the response of a beam subject to constant rate of curvature and the predicted response compared with published experimental data. In addition, the transverse impact of a mass on a beam is investigated and the theory is used to predict the onset of yielding in the beam. This problem is of importance in the design of highway guard-rails.

The effects of dislocation locking and strain ageing on the fatigue limit of low-carbon steel

The fatigue behaviour of a low-carbon steel has been investigated with the object of clarifying the roles of initial dislocation locking and of strain ageing in the development of the fatigue limit. Comparisons of performances of two conditions of grain size (90 and 2500 grains/mm 2) were made in push-pull at 200 c/s. S-N curves were determined at room temperature in annealed, prestrained, quenched and quenchaged conditions; and at − 60°C in annealed and prestrained conditions. Observations were made of changes in damping, metallographic features and in tensile yield point behaviour during fatigue. In annealed, fine grained specimens the spread of plasticity appeared to be an important factor limiting the spread of fatigue damage. Striations were developed in a small proportion (<4 per cent) of surface grains by cyclic stresses just below the fatigue limit but, in general, they did not spread beyond grain boundaries and prologned cycling did not eliminate the sharp yield point. Stresses slightly above the limit were just sufficient to cause these plastic nuclei to grow. In contrast, with coarse grained specimens, stresses close to the limit caused rather widespread plastic deformation and eliminated the sharp yield point in the early stages of the test. The fatigue limit/U.T.S. ratio of annealed, fine grained specimens was superior to that of coarse grained specimens but prestraining removed this difference. In tests at − 60°C annealed, fine grained specimens appeared to retain a fatigue limit but none was observed with coarse grained specimens. It is concluded that initial dislocation locking makes an important contribution to the high fatigue limit of fine grained steels, but that it is unlikely to be important in a coarse grained steel of low yield strength/U.T.S. ratio. However, coarse grained and prestrained specimens did show a fatigue limit at room temperature. The relocking of dislocations by strain ageing may be important in these cases.

Yield Points and Delay Times in Single Crystals

Stress-strain curves and transient creep curves for single crystals are obtained from calculations based on the observed behavior of dislocations in LiF, and the strain rate equation, ε̇=bnv. The pronounced yield drops and apparent ``delay times'' predicted by the calculations are observed experimentally. This agreement between calculation and experiment implies that further consideration of the calculations may give some insight into the yield point and transient creep behavior of single crystals. Several parameters are varied in the calculation in order to determine the effect of such things as testing machine speed, machine hardness, rate of dislocation multiplication, work-hardening rate, number of mobile dislocations initially present, and the dependence of dislocation velocity on stress. The parameter that most strongly influences the yield points and transient creep behavior of a given material is n0, the number of mobile dislocations initially present. The wide range of observed yield point and transient creep behavior of various materials can be rationalized in terms of how dislocation velocity varies with stress; the less sensitive is the velocity to the applied stress, the more pronounced will be the yield drop or delay time. The calculation is applicable only when n0≠0; and the yield points and yield drops develop continuously and relatively gradually as dislocation motion and multiplication begin before the upper yield point is reached. The upper yield stress is not closely related to the stress required to unpin dislocations. It is necessary to distinguish between this type of yield point, which is commonly observed, and the Cottrell type of yield point in which dislocation motion begins at the upper yield stress, and in which the upper yield stress is related to the unpinning stress.

The effect of oxygen on the mechanical properties of zone-refined niobium

The yield point behaviour of niobium containing varying quantities of oxygen has been investigated. Oxygen raises the yield stress at 293°K and 77°K. Twinning is observed in zone-melted niobium at 77° K but this is inhibited by oxygen additions.