Upon reaching the specimen the wave is partly reflected back into the input bar to form the reflected wave, and is partly transmitted to the output bar to form the transmitted wave. The strain histories εi, εr and εt, respectively corresponding with the incident wave, the reflected wave and the transmitted wave, are measured by means of strain gauges. These strain gauges are located at wellknown points on the input and the output bar, away from the specimen. The recorded signals are subsequently shifted, forward or backward, towards the interface planes with the specimen, in order to obtain forces and displacements at both ends of the specimen. The specimen dimensions given above were optimised using numerical simulations in order to have a uniaxial, homogeneous stress and deformation state in the specimen. With these assumptions the time histories of strain, strain rate and stress in the specimen can be obtained from the following expressions in Eqn. 1 [5]: t b r s 0 2 C (t) = - ( ) d L ε τ ε ∫ τ, b r s 2 C (t) = - (t) L ε ε & , b b t s (t) = A E (t) A σ ε (1) with Eb the elasticity modulus of the Hopkinson bars, As and Ab the cross section area of the specimen and of the Hopkinson bars respectively, Cb the velocity of propagation of longitudinal waves in the Hopkinson bars and Ls the specimen length. The main advantage of the Hopkinson test is that strain, strain rate and stress in the specimen are obtained without measurements on the specimen. TEMPERATURE AND STRAIN RATE SENSITIVITY RESULTS Strain rate sensitivity at room temperature As expected, the IFHSS260 shows the highest ratio between dynamic ( ε& ≈ 1000s-1) and quasi-static lower yield strength (YSdyn/YSst) close to 1.8 (Figure 2a) but also a reduction of 34% in uniform elongation (Figure 4). The micro-alloyed steel ZStE420 is characterised by a low YSdyn/YSst of 1.3 and also by a reduction of 46% in uniform elongation. The dual phase grade and the austenitic stainless steel have nearly the same ratio YSdyn/YSst close to 1.7 but do not show the same strain rate sensitivity of the yield point. Indeed, 301LN shows a continuous increase of the yield stress over the range of strain rates, while the yield strength of DP500G increases more slowly up to strain rates around 300s-1 and shows a higher strain rate sensitivity above ε& = 300s-1. This latter observation is also valid for the other ferritic steels but in a less pronounced manner. Plotting the logarithm of the yield strength versus the logarithm of strain rate has validated the strain rate dependency of strain rate sensitivity on the yield strength for IFHSS260, ZStE420 and DP500G and the almost constant strain rate sensitivity of 301LN, as illustrated in Figure 2b. 250 300 350 400 450 500 550 600 650 700 01 0.01 0.1 1 10 100 1000 10000 strain rate ε° (s-1) Lower Yield Strength (MPa) -40°C Room Temp. + 80°C 2.55 2.60 2.65 2.70 2.75 2.80 2.85 -4 -2 0 2 4 log (strain rate) log (lower yield strength) 301LN DP500 G Poly. (DP500 G) Poly. (301LN) b) ZstE420 DP500G 301LN RT IFHSS260 200 0.0 b) Figure 2: a) Influence of strain rate and temperature on the lower yield strength of the steel grades a) b) Strain rate dependency of the strain rate sensitivity on lower yield strength at room temperature
RkJQdWJsaXNoZXIy MjM0NDE=