Using one-dimensional wave theory, the stress and strain in the specimen can be determined from the transmitted and reflected strain pulses, respectively, as σs ¼Eb Ab As εt tð Þ ð20:1Þ es ¼ 2cb Ls ð t 0 εr tð Þdt ð20:2Þ Where σs andes are stress and strain in the specimen, εr andεt are the time resolved strain values of reflected and transmitted pulses, cb is the longitudinal bar wave speed, Eb is the Young’s modulus of the bar material, Ab is the cross-sectional area of the bar, As is the cross-sectional area of the specimen and Ls is the thickness of the specimen. 20.4 Results Three grain sizes, fine (6.1 μm dia.), medium (13.9 μm dia.) and coarse (17.4 μm dia.) were studied. The specimens displayed brittle catastrophic failure at room temperature and a graceful failure at high temperatures. Figure 20.2a shows the typical time shifted segments of the recorded pulses and Fig. 20.2b shows the corresponding force ratio variation observed for the specimens which exhibited a catastrophic brittle failure. The specimen fails at 39 μs. The occurrence of failure is marked by the peak value of the transmitted pulse, after which the magnitude of transmitted pulse drops sharply. Figure 20.2b shows that the dynamic stress equilibrium was attained at about 15 μs and was maintained up to the point of specimen failure. The pulses were analyzed only up to the point of failure (corresponding to peak transmitted) to generate the stress strain curves for the specimens showing catastrophic failure. The true compressive stress-strain curves of medium grained Ti2AlC during dynamic loading at various temperatures are represented in Fig. 20.3. A ‘⋆’ symbol is used in these plots to represent points of catastrophic failure. The dynamic experiments were conducted at an average strain rate of 500 s 1. The peak compressive stress decreases with increasing in temperature. For the experiments conducted, graceful failure was beginning to occur at 1100 C for fine grain, at 900 Cfor medium grain and at 600 C for coarse grain specimens. 0 20 40 60 80 100 -1500 -1200 -900 -600 -300 0 a Time (μs) Time (μs) Strain (με) Incident Pulse Reflected Pulse Transmitted Pulse 0 20 40 60 80 100 0 1 2 Force Ratio b Fig. 20.2 (a) Typical pulses recorded when specimen undergoes catastrophic brittle failure. (b) Corresponding force ratio variation with time during the experiment 20 Effect of Microstructure on Mechanical Response of MAX Phases 173
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