1. **Problem Statement:** Given the flow law for creep strain rate $$\dot{\varepsilon} = A \sigma_d^n \exp\left(-\frac{Q}{RT}\right)$$ and the frictional strength law $$\tau = c + \mu \sigma_n,$$ we want to understand how to calculate the strain rate $$\dot{\varepsilon}$$ for a given material under stress conditions, using the parameters $A$, $n$, and $Q$ from the provided table. 2. **Formula Explanation:** - $$\dot{\varepsilon}$$ is the strain rate (s$^{-1}$). - $A$ is a material constant with units GPa$^{-n}$ s$^{-1}$. - $\sigma_d$ is the differential stress (GPa). - $n$ is the stress exponent (dimensionless). - $Q$ is the activation energy (kJ mol$^{-1}$). - $R$ is the gas constant, approximately 8.314 J mol$^{-1}$ K$^{-1}$. - $T$ is the absolute temperature in Kelvin. 3. **Important Notes:** - Activation energy $Q$ must be converted to J mol$^{-1}$ by multiplying by 1000. - Temperature $T$ must be in Kelvin. - Stress $\sigma_d$ must be in GPa to match units of $A$. 4. **Step-by-step Calculation Example:** Suppose we want to calculate $$\dot{\varepsilon}$$ for dry granite at $\sigma_d = 0.1$ GPa and $T = 600$ K. - From the table for granite: $$A = 5.0 \times 10^{-3}$$ GPa$^{-n}$ s$^{-1}$, $$n = 3.2,$$ $$Q = 123$$ kJ mol$^{-1}$. - Convert $Q$ to J mol$^{-1}$: $$Q = 123 \times 1000 = 123000 \text{ J mol}^{-1}$$ - Calculate the exponential term: $$\exp\left(-\frac{Q}{RT}\right) = \exp\left(-\frac{123000}{8.314 \times 600}\right) = \exp(-24.65) \approx 1.95 \times 10^{-11}$$ - Calculate $$\sigma_d^n$$: $$0.1^{3.2} = 10^{-3.2} = 6.31 \times 10^{-4}$$ - Calculate $$\dot{\varepsilon}$$: $$\dot{\varepsilon} = 5.0 \times 10^{-3} \times 6.31 \times 10^{-4} \times 1.95 \times 10^{-11} = 6.16 \times 10^{-17} \text{ s}^{-1}$$ 5. **Interpretation:** This very low strain rate indicates that at 600 K and 0.1 GPa differential stress, dry granite deforms extremely slowly by creep. 6. **Summary:** To find strain rate for any material: - Use the given $A$, $n$, and $Q$. - Convert $Q$ to J mol$^{-1}$. - Calculate the exponential term with temperature $T$ in Kelvin. - Raise differential stress $\sigma_d$ to power $n$. - Multiply all terms to get $$\dot{\varepsilon}$$. This method applies to all materials in the table.