March/April 2003 EXPERIMENTAL TECHNIQUES 35 N TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TECHNIQUES by Hasan Sofuoglu A NEW TECHNIQUE USED IN OBTAINING TRUE STRESS- TRUE STRAIN CURVES FOR CONSTANT STRAIN-RATES True Strain, True Stress, , [MPa] 0 0.04 0.08 0.12 0.16 0.2 0.24 0 0.2 0.4 0.6 0.8 LEGEND v=5.1 mm/min. v=12.7 mm/min. ε σ Fig. 1: True stress-true strain diagram of white plasticine T he flow stress, , is a function of strain, strain-rate, and temperature, i.e.,  = f (ε, T ). Although met- ˙ ε, als can be considered as strain-rate insensitive in cold forming processes they are strain-rate sensi- tive in hot forming processes. The sensitivity of metal to strain-rate can be shown by using (-ε) curves obtained for the constant strain-rates. Thus, tests for characterizing high temperature flow behavior of metals must be conducted in such a way that the strain-rate is maintained constant throughout the test. This is usually done by using computer controlled, i.e., expensive test equipment. In general, when strain-rate increases, the flow stress of metal usually in- creases. When the proposed technique is used, there will be no need to use expensive test equipment to obtain (-ε) curves for constant strain-rates. BASIC THEORETICAL BACKGROUND: From a compression test, the true strain can be written as H ε = ln (1) H 0 where H 0 is the original and H is the final height of the specimen. Denoting the instantaneous deformation velocity by V = dH / dt, the strain-rate is given by dε d H dH ˙ ε = = ln = . (2)   dt dt H Hdt 0 Substituting for V into Eq. 2 yields V ˙ ε = , (3) H but from Eq. 1, H = H exp(ε) (4) 0 Then, substituting Eq. 4 into Eq. 3 gives V ˙ ε = . (5) H exp(ε) 0 Eq. 5 indicates that the strain-rate, during constant defor- mation speeds of the compression test, changes throughout the experiment. In order to achieve constant strain-rate, the speed of the crosshead (deformation speed) must change ex- ponentially. This can be achieved by employing an open-loop controlled system where the speed of the crosshead of the machine is continuously adjusted. So far, researchers have used this method when they have an open-loop controlled machine which is computer controlled, and hence, it becomes very expensive. When an open-loop controlled machine is not available an alternative technique is needed to obtain constant strain- Associate Professor, Sofuoglu is in the Department of Mechanical Engineering,Kar- adeniz Technical University,Trabzon, Turkey. rate data from a constant speed-testing machine. In this study, a new technique is developed to collect (, ε) data and to plot the (, ε) curves for constant strain-rate by using a displacement controlled screw-driven compression testing machine in which the crosshead moves with a predetermined constant velocity. The strain-rate can then be calculated us- ing these compression test data in association with Eq. 5. The new technique requires performing more compression experiments at different deformation speeds. EXPERIMENTAL PROCEDURE In this study, all of the experiments are conducted by util- izing non-metallic modeling materials, namely, plasticine. Using plasticine as a modeling medium is the most conven- ient technique to simulate the plastic deformation of metals as observed in forging, 1 rolling, 2 and extrusion processes. 3 Different colors of plasticine are usually referred to as dif- ferent types of materials. 4 In this study, two types of plas- ticine, black and white, are used. In order to obtain true stress-true strain curves, (-ε), for different strain-rates, , simple compression tests were con- ˙ ε ducted at V = 2.54 mm / min. (0.1 ipm) and V = 5.1 mm/ min. (0.2 ipm) for black plasticine and at V = 5.1 mm / min. (0.2 ipm) and V = 12.7 mm / min. (0.5 ipm) for white plas- ticine. Then, (-ε) curves for two deformation speeds were