A specimen has an initial diameter of 200mm and a length of 700mm. At a stress of 40MPa and a temperature of 538oC the steady state strain rate is about 2×10−4% per hour. Find the primary creep elongation and the steady state creep elongation after 5000 hours given that the creep deformation at that time is 7.2mm.
To calculate the primary creep elongation and steady state creep elongation, we need to use the Norton-Bailey equation for creep deformation:
ε = A * σ^n * t^m * exp(-Q/RT)
Where:
ε = Creep elongation
A = Material constant
σ = Applied stress
n = Stress exponent
t = Time
m = Time exponent
Q = Activation energy
R = Universal gas constant
T = Temperature in Kelvin
Given:
Initial diameter (D) = 200mm
Length (L) = 700mm
Stress (σ) = 40MPa
Temperature (T) = 538oC = 811K
Steady-state strain rate = 2×10−4% per hour = 2×10^-6 per hour
Creep deformation at 5000 hours = 7.2mm
Let's proceed step by step:
Step 1: Calculate the initial cross-sectional area (A_i) of the specimen using the formula:
A_i = π * (D/2)^2
Step 2: Calculate the final cross-sectional area (A_f) of the specimen after creep deformation occurs. As the length remains constant, the diameter increases due to elongation.
A_f = A_i + ε * L
Step 3: Calculate the primary creep elongation (ε_primary) using the Norton-Bailey equation. For primary creep, the strain rate is relatively high at the beginning and decreases over time.
ε_primary = A * σ^n * t^m * exp(-Q/RT)
Since the value for ε_primary is not given, we need to rearrange the equation to solve for ε_primary:
ε_primary = ε * t / (A * σ^n * exp(-Q/RT))
Step 4: Calculate the steady-state creep elongation (ε_steady) using the Norton-Bailey equation. For steady-state creep, the strain rate is constant over time.
ε_steady = ε * t / (A * σ^n * exp(-Q/RT))
Step 5: Calculate the time exponent (m) using the formula:
m = log10(ε_steady / ε_primary) / log10(t_steady / t_primary)
Step 6: Calculate the material constant (A) using the formula:
A = ε_primary * t_primary / (σ_primary^n * exp(-Q/RT_primary))
Step 7: Calculate the strain rate at the specified time using the formula:
strain_rate = A * σ^n * t^m * exp(-Q/RT)
Step 8: Calculate the primary creep elongation (ε_primary) for the given time (5000 hours) using the strain rate equation:
ε_primary = strain_rate * t_primary / 100
Step 9: Calculate the steady-state creep elongation (ε_steady) at the given time (5000 hours) using the specified creep deformation value:
ε_steady = creep_deformation - ε_primary
By following these steps, you can calculate the primary creep elongation and the steady-state creep elongation after 5000 hours for the given parameters.