The elastic hysteresis of steel

Abstract

In a recent communication to the Society* one of us described a machine whereby a bar of steel 4 inches long by \ inch diameter can be submitted to direct alternating stress at the rate of 120 cycles per second or more. The machine is worked by the pull of an electromagnet excited by alternating current, the pull being magnified from 20 to 60 times by resonance between its period and that of a weight attached to one end of the piece, which behaves as a spring. The stress varies between equal limits of tension and compres sion, and may be of any desired range up to 30 tons per square inch or more. The piece is fitted with an optical extensometer by which the extreme change of length of the piece in a cycle can be observed while the machine is in action and the range of stress calculated. An independent measure of the stress can be obtained by observation with a microscope of the movement of the weight attached to the end of the piece, whose acceleration is the chief element determining the tension or compression. Full details of these measurements are given in the paper referred to, and it will suffice to state here that similar precautions to secure accuracy in the measurements of stress were taken in the course of the work to be described, and that from the agreement between the different methods it may be taken as certain that these measurements are correct to about half a ton per square inch.The present paper contains an account of experiments which we have made with the alternating stress machine with the object of measuring the energy dissipated by elastic hysteresis when steel undergoes cyclical varia tions of stress within the elastic limit. The method used is to measure the fall of temperature between the centre and ends of the test piece when it is undergoing continuous alternating stress through a constant range. The fall of temperature is proportional to the rate at which heat is being generated and conducted away, and the absolute rate of dissipation in ergs per cubic centimetre can readily be obtained by passing an electric current along the specimen when at rest, and finding the relation between the temperature and the energy dissipated by resistance.The steel used was the same material as in the previous experiments on fatigue. I t contains about 048 per cent, carbon and 0'7 manganese, and it breaks under a load of about 29 5 tons per square inch (46'5 kgrm. per * 'Boy.

Quantitative Analysis of Corneal Energy Dissipation and Corneal and Orbital Deformation in Response to an Air-Pulse in Healthy Eyes

“…The physical property describes the difference between the loading and unloading curves. 16 The behavior hails from the viscous component dissipating energy within the viscoelastic system. 25 Analysis of corneal hysteresis could reveal the viscous damping effect in the complex viscoelastic cornea.…”

“…15 By calculating the area within the loading and unloading curves of the stress-strain graph, the dissipated energy can be determined quantitatively. 16 Ishii et al 17 previously described the area within the graph produced as ''elastic hysteresis.'' They utilized a noncontact tonometer in conjunction with a high-speed camera angled at 908 to the cornea and plotted the change in corneal apex position (strain) against the amount of force applied onto the cornea by the airpulse (stress).…”

Nonlocalized Fatigue Damage of Metals and Alloys. Part 2. Interrelation between Fatigue and Inelasticity

“…Early works are known [18][19][20][21][22], where interrelation between the regularities in inelastic deformation, which is characterized by inelastic strains and inelastic strain energy, heating of specimen, damping capacity, etc., and fatigue fracture were studied, primarily, in connection with the development of methods for accelerated determination of the fatigue limit and prediction of life with the account for the influence of various factors.…”

Nonlocalized Fatigue Damage of Metals and Alloys. Part 1. Inelasticity, Investigation Methods, and Results

“…Inelastic deformation of materials leads to the occurrence of a hysteresis loop in the "stress-strain" coordinates and manifests itself in the form of such effects as heating of a specimen in the course of cyclic loading, phase shift between the stress and strain signals, horizontal displacement of the end of a cantilever specimen during its cyclic deformation (Kimball effect), damping of free vibrations, changes in the height and width of the peak on the resonance curve, etc. [68][69][70][71][72][73][74][75][76][77][78][79][80][81].…”

“…Investigation into the dissipation of energy in the material from the specimen heating was performed in [68][69][70]. This method of investigation is most efficient under high-frequency loading [70].…”