Unstrained Length Research Articles

Extensometer for semi-rigid materials

A differential capacitance extensometer is described which is capable of measuring extensions between 1 and 50% on an unstrained gauge length of one inch. With this instrument, complete tensile stress-strain curves to the point of rupture of the test piece may be obtained on semi-rigid materials.

A DISCUSSION OF THE LOAD DROP AND RELATED MATTERS ASSOCIATED WITH THE FORMATION OF A LÜDERS BAND

1. lntroduction.-In a fixed-grip experiment resulting in the occurrence of a iders band in a flat bar there is a distinct drop in the load at the instant of forma,n of the band. We have here derived a formula relating this load drop to the dth D of the Liiders band and the length L of the bar. The formula involves, in dition, the plastic contraction b introduced in our previous communication [rid Rotation in Liiders Bands (these PROCEEDINGS, 40, 565-572, 1954), on which e following discussion is largely based. Thus we have limited our attention to a use of the von Mises yield condition and have moreover taken Poisson's ratio v = 2, which is equivalent to the assumption that the material is elastically incomessible. This latter assumption is generally admissible, since the elastic displacents are small in comparison with the plastic displacements. In this connection refer also to the Remark in sec. 2 concerning the value of Poisson's ratio. References to earlier notes in these PROCEEDINGS as Notes I, II, and III will made as explained in the above-mentioned communication, which will, in turn, referred to as Note IV in the following discussion. 2. Derivation of the Formula.-Consider the bar at the yield point just before e formation of the Liiders band. The flat surface of the bar at the instant in estion is represented by the rectangle ABCD in Figure 1. Planes P1' and P2' und the elastically deformed material destined to go into the plastic or Liiders nd, which is bounded by the planes P1 and P2 indicated by the dotted lines. ngths such as 11 and D, etc., which will enter the discussion are clearly defined reference to Figure 1. Let I denote the unstrained length of the bar which has length i1' -+ 12 at the ld point. Then

The use of flat-ended projectiles for determining dynamic yield stress - II. Tests on various metallic materials

A description is given of the experimental technique devised to apply the method outlined theoretically in part I to the measurement of the dynamic compressive yield strength of various steels, duralumin, copper, lead, iron and silver. A polished piece of armour steel was employed as a target, and cylindrical specimens were fired at it at various measured velocities from Service weapons. The distance between the weapon and target was made short to ensure normal impact, and apparatus was devised for the precise measurement of striking velocity over this short range. The dynamic compressive yield strength was computed from the density of the specimen, the striking velocity, and from measurements of the dimensions of the test piece before and after test. Details are given of the accuracy of the various measurements, and of their effect on the values of yield strength. The method was found to be inaccurate at low and high velocities. For instance, with mild steel, satisfactory results were only obtainable within the range 400 to 2500 ft. /sec. The range of velocities within which satisfactory results could be obtained varied with the quality of the material tested, soft metals giving results within a much lower range than that necessary for harder materials. Because of its failure at low velocities, the method could not be employed to bridge the gap between static and dynamic tests. The rate of strain employed in the dynamic tests could not be measured, but was estimated to be of the order of 10,000 in. /in. /sec. With the materials tested little change of dynamic strength occurred within the range of striking velocities employed, probably because the rate of strain did not vary to any great extent with the striking velocity. Within the range of weapons available, that is, from a 0·303 in. rifle up to a 13 pdr. gun (calibre 3·12 in.), little change of dynamic strength occurred with alteration of the initial dimensions of the specimens, probably because the corresponding change of rate of strain was not large. In general, the dynamic compressive yield strength S was greater than the static strength Y represented by the compressive stress giving 0·2% permanent strain. For steels of various types, regardless of chemical composition and heat treatment, there was a relation between S / Y and the static strength Y , the ratio decreasing from approximately 3 when Y was 20 tons/sq. in. to 1 when Y was 120 tons/sq. in. A similar relation occurred with duralumin, S / Y varying from 2·5 at Y = 8 tons/sq. in. to 1·4 at Y = 25 tons/sq. in. Dynamic compressive yield values were obtained for soft materials such as pure lead, copper and Armco iron, which, under static conditions, gave no definite yield values. A plot of the unstrained length of the specimen X , expressed as X / L (where L = initial overall length), versus the final overall length L 1 , expressed as L 1 / L , was made for the various materials. Any specified value of X / L was associated with greater values of L 1 / L for the more ductile materials, such as copper and lead, than for the brittle materials, such as armour plate and duralumin.