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This project is an experimental study on plastic deformation in ductile materials such as aluminum and steel. The objective is to stimulate interest in engineering undergraduate students the importance of plasticity in structural design and metal forming. It is proposed as a supplemental lab activity for the junior level Mechanics of Materials course. Torsion tests were performed on circular cylindrical bars to obtain torque-twist curves (the torsional shear stress vs torsional shear strain plots). The 0.2% offset yield shear strength, k, were estimated from these curves. The bars were twisted well into their plastic regions, and as the elastic/plastic torsion continued, the torques seemed to approach their limiting values. Experimental estimates for the limiting torques were in reasonable agreement with the values predicted by the so-called sand heap analogy. This states that the stress surface for a fully plastic cross-section is obtained by piling dry sand on a horizontal base whose shape is identical to the cross-section of the bar. For a circular cross-section, the sand heap is a cone, and the limiting torque is equal to (k a /G) times the volume of the cone, where a is the radius. The specimens were twisted to a predetermined maximum value. The directions of twist were subsequently reversed. After unloading and reloading from the initial loading phase, the materials seemed to yield in the reverse direction with lesser yield strength values. This shows that the torsional plastic deformation for metallic materials is one direction affects plastic deformation in the reversed direction and demonstrates the Bauschinger Effect in torsion. INTRODUCTION In this work, prismatic bars of circular cross sections have been loaded in torsion to study their responses in elastic and elastic-plastic domains. The purpose was to experimentally demonstrate the plastic deformation that takes place when the torque exceeds the amount that causes the bar to yield. This is an extension of the torsion test where the torques are such that yielding does not take place, and the torque twist characteristic is linear. When a bar is twisted beyond the elastic range (yielding), there is a non-linear torque-twist behavior. Simple analytical solutions for the deformation and stresses in a bar subject to axial torsion exist only for circular cross-sections. One of the simplest ways to study elastic as well as elastic-plastic behavior analytically is to assume an elastic-perfectly plastic representation of the stress-strain curve. For the case of torsion, this would be the shear stress vs. shear strain curve as shown in Figure 1. The shear stress varies linearly with shear strain in the elastic region, and reaches a constant value and stays constant in the plastic region. Sometimes this representation is termed as one of “zero hardening.” However, most ductile materials exhibit strain hardening where in the plastic region, the shear stress monotonically increases with shear strain.

Torsion Tests to Study Plastic Deformation in Ductile Materials