Extension of the Simple Plastic Theory to Take Account of the Strain-hardening Range

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Abstract
In the simple plastic theory commonly used for mild steel it is assumed that after yielding has occurred in either tension or compression, straining can continue indefinitely at constant stress. Such an assumption has been found satisfactory for low carbon steels having a plastic range corresponding to eight to ten times the strain at yield, but for steels of greater strength this range is often considerably shorter, and it becomes necessary to take into account the strain-hardening range beyond. To obtain experimental data, four steels were selected, varying in carbon content from 0·28 to 0·89 per cent, and having widely different stress-strain relations. For each steel a number of simply supported beams of square section were subjected to a symmetrical two-point loading; tension specimens were prepared from the unyielded ends of these beams and tested in a spring-loaded autographic testing machine to determine upper and lower yield stresses. In addition, two tension specimens from each steel were tested in a lever type of machine, and the stress-strain relations through the plastic range and the initial stages of the strain-hardening range were obtained with the aid of a “Gerard” extensometer***. This information gave good support to the theoretical work, whereby the behaviour of these steels in flexure can be correlated with the tensile properties.

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