Brittle-Quasibrittle Transition in Dynamic Fracture: An Energetic Signature

Dynamic fracture experiments were performed in polymethylmethacrylate over a wide range of velocities and reveal that the fracture energy exhibits an abrupt threefold increase from its value at crack initiation at a well-defined critical velocity, below the one associated with the onset of microbranching instability. This transition is associated with the appearance of conics patterns on fracture surfaces that, in many materials, are the signature of damage spreading through the nucleation and growth of microcracks. A simple model allows us to relate both the energetic and fractographic measurements. These results suggest that dynamic fracture at low velocities in amorphous materials is controlled by the brittle-quasibrittle transition studied here.

Figure 1

Measured crack velocity $v$ as a function of crack length $c$ in a typical experiment ($U_0=2.6\mathrm{J}$). The vertical lines are error bars. Top inset: Calculated quasistatic SIF $K$ as a function of $c$. Bottom inset: Schematics of the wedge-splitting test.

Figure 2

Fracture energy $\Gamma$ as a function of crack velocity $v$ for five different experiments with different stored mechanical energies $U_0$ at crack initiation: 2.0 (□), 2.6 (○), 2.9 (◊), 3.8 (+), and 4.2 J (×). The two vertical dashed lines correspond to $v_a$ and $v_b$. The two horizontal dashed lines indicate the confidence interval for the measured fracture energy $K_c^2/E$ at crack initiation. The thick gray (red) line is the curve $\Gamma (v)$ obtained by combining Eqs. (1, 2) for $v\le v_a$ and Eqs. (1, 4) for $v\ge v_a$. The correlation coefficient between this curve and the experimental points is $R=0.83$. Inset: $\Gamma$ as a function of $K_d^2/E$ (see model) for the same experiments. A crossover between two linear regimes (linear fits in black lines) occurs at $K_d^2/E=K_a^2/E\simeq 1.2\mathrm{kJ}·{\mathrm{m}}^{-2}$, $\Gamma ={\Gamma }_a\simeq 1.34\mathrm{kJ}·{\mathrm{m}}^{-2}$.

Figure 3

Microscope images ($\times 10$) taken at (a) $v=120\pm 20\mathrm{m}·{\mathrm{s}}^{-1}$, $K^2/E=1\mathrm{kJ}·{\mathrm{m}}^{-2}$, (b) $v=260\pm 30\mathrm{m}·{\mathrm{s}}^{-1}$, $K^2/E=2\mathrm{kJ}·{\mathrm{m}}^{-2}$, (c) $v=650\pm 100\mathrm{m}·{\mathrm{s}}^{-1}$, $K^2/E=7\mathrm{kJ}·{\mathrm{m}}^{-2}$. Top line: Fracture surfaces ($0.5\times 0.7{\mathrm{mm}}^2$ field of view). Bottom line: Sample sides ($0.25\times 0.7{\mathrm{mm}}^2$ field of view). Crack propagation is from left to right.

Figure 4

Surface density $\rho$ of conic marks as a function of crack velocity for all experiments shown in Fig. 2. Inset: $\rho$ as a function of $K_d^2/E$ (linear fit in black line).