Abnormal response of ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$ to high strain-rate loading

Herein, we report on the response of the MAX phase, ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$, to shock wave compression at strain rates above ${10}^4{\mathrm{s}}^{-1}$. The shock response was determined by measuring the rear, free surface, and velocity of samples—subjected to impact by high-velocity projectiles launched by a gas-gun—using interferometry. The effects of temperature and sample thickness on the dynamic yield and dynamic tensile (spall) strengths were studied. The most important result of this work is the unique dual nature, at high strain rates, of the response of ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$, in that it is reminiscent of both metals and ceramics. For low-energy impacts, the elastic response is reminiscent of ductile metals. However, for high-energy impacts, it performed like a hard ceramic with quite high work hardening rates. In other words, ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$ behaves like nothing before it and thus must reflect its nanolayered structure. This work not only provides results on the dynamic mechanical properties of ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$, but is a critical first step toward understanding the response of ripplocations in layered solids to high strain rates.

Figure 1

(a) Comparison between edge dislocations and ripplocations in a generic lattice. Both deformation micromechanisms allow the relative movement of one plane of atoms over another. However, in the case of dislocation, there is only in-plane strain, and climb is required to deform out of plane. Additionally, two dislocations of the same sign repel, but two ripplocations of the same sign attract [15]. (b) For ripplocations, $c$-axis strain is embedded, and can be observed in MD simulations of graphite. (c) Snapshots of ripplocation boundaries formed when a cylindrical indenter is loaded edge-on into, from left to right, plastic cards, thin steel sheets, and graphite (MD simulation). Images adapted with permission from Refs. [14, 15, 17].

Figure 2

(a) Typical SEM microstructure of a polished and etched ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$ sample studied herein. (b) XRD pattern of the ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$ sample.

Figure 3

(a) Velocity histories of ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$/PMMA interfaces recorded after impacts of different strengths. Sample and impactor thicknesses and impactor velocities are listed next to the waveforms. The inset shows a determination of $u_{\mathrm{HEL}}$ used for estimating ${\sigma }_{\mathrm{HEL}}$. (b) Shock velocities $U_s$ (open squares, right-hand $y$ axis) and stress ${\sigma }_H$ (open circles, left-hand $y$ axis) at Hugoniot determined from the velocity histories shown in (a) as a function of particle velocity $u_p$. Filled squares correspond to the ultrasonic speed of sound in ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$. The dashed line is a linear approximation. The dotted line is the Hugoniot hydrostat $p_H={\rho }_0{U}_s{u}_p$. Inset shows a departure of ${\sigma }_H$ values from the hydrostat. Error bars correspond to the uncertainty in determinations of $U_s$ and $u_p$.

Figure 4

(a) Free sample surface velocity histories of 3-mm-thick ${\mathrm{Ti}}_3\mathrm{Si}{\mathrm{C}}_2$ samples, preheated to different temperatures, $T_0$ (labeled by the waveforms in inset). Inset zooms on short times. Arrows and dotted lines show the waveforms’ parameters used for determining the yield and spall strengths. (b) Stress at ${\sigma }_{\mathrm{HEL}}$(open circles), yield $Y$ (filled circles), offset yield $Y_{0.1}$ (filled squares), and spall strength ${\sigma }_{\mathrm{sp}}$ (filled red triangles) as a function of $T_0$. Dashed and dotted lines are the linear fits of $Y, Y_{0.1}$, and ${\sigma }_{\mathrm{HEL}}$, respectively. Solid line reproduces results of Ref. [53] obtained under compression using a strain rate of $\approx {10}^{-4}{\mathrm{s}}^{-1}$. Error bars correspond to the typical uncertainty of the property measured.

Figure 5

Normalized strain hardening moduli θ determined based on $Y_{0.1}-Y$ (filled circles) and $Y_{0.2}-Y_{0.1}$ (open circles) increments as a function of $T_0$. Error bars correspond to the relatively high, ≈10%, uncertainty in the determination of $\theta$.

Figure 6

Free surface velocity histories for samples of different thicknesses (indicated to the right of waveforms) shock loaded at $T_0$ of (a) 300 K and (b) 900 K.

Figure 7

Log-log plot of ${\sigma }_{\mathrm{HEL}}$(filled symbols) and ${\sigma }_{\mathrm{HEL}0.1}$(open symbols) as a function of propagation distance at 300 and 900 K. Solid and dashed lines are the power fits $\sigma \left(h\right)={\sigma }_0{\left(h/\phantom{h{h}_0}{h}_0\right)}^{-\alpha }$. Error bars correspond to typical uncertainties in stress measurements for the 0.5- and 3-mm-thick samples.

Figure 8

Normalized strain hardening moduli as a function of HEL for various materials [56, 57, 58, 59, 60, 61, 62].