Creep Rate Calculator Formula
Understand the math behind the creep rate calculator. Each variable explained with a worked example.
Formulas Used
Steady-State Creep Rate
creep_rate = prefactor * pow(stress, stress_exp) * exp(-q_j / (8.314 * temp_k))Variables
| Variable | Description | Default |
|---|---|---|
stress | Applied Stress (sigma)(MPa) | 100 |
stress_exp | Stress Exponent (n) | 5 |
temp_k | Temperature(K) | 800 |
activation | Activation Energy (Q)(kJ/mol) | 250 |
prefactor | Pre-exponential Constant (A) | 10000000000 |
q_j | Derived value= activation * 1000 | calculated |
How It Works
Steady-State Creep Rate
Creep is the slow, time-dependent deformation of materials under sustained load at elevated temperatures. The secondary (steady-state) creep rate follows a power-law Arrhenius equation.
Formula
epsilon_dot = A × sigma^n × exp(-Q / (R × T))
where A is a material constant, sigma is the applied stress, n is the stress exponent (3-8 for metals), Q is the activation energy for creep, R = 8.314 J/(mol·K) is the gas constant, and T is absolute temperature.
Worked Example
A nickel alloy at 800 K under 100 MPa (A=1e10, n=5, Q=250 kJ/mol).
- 01sigma^n = 100^5 = 1 × 10^10
- 02Q/(RT) = 250000 / (8.314 × 800) = 37.57
- 03exp(-37.57) = 4.83 × 10^-17
- 04Creep rate = 1e10 × 1e10 × 4.83e-17 = 4.83 × 10^3 s^-1 ... (values depend on actual A)
Frequently Asked Questions
When does creep become significant?
Creep is generally significant at temperatures above about 40% of the melting point (in Kelvin). For steel (Tm ≈ 1800 K), creep matters above about 720 K (450°C). For aluminum (Tm ≈ 933 K), above about 370 K (100°C).
What is the stress exponent n?
The stress exponent indicates the creep mechanism. n ≈ 1 for diffusion creep (Nabarro-Herring or Coble), n ≈ 3-5 for dislocation creep, and n > 6 for power-law breakdown. Most engineering metals show n = 3-8.
How does creep lead to failure?
Creep damage accumulates through void nucleation at grain boundaries, void growth, and eventual coalescence into cracks. Tertiary creep shows accelerating strain rate before final rupture.
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