Overview

Test Case

A rod of length and square cross-sectional area A is held at a constant stress σ_o at a temperature T_o. The rod is also subjected to a constant neutron flux Φ. The rod material has an irradiation induced creep strain rate given by the relationship dε_cr / dt = k₁σΦe - (Φt / k₂). Determine the amount of creep strain ε_cr accumulated up to 5 hours.

Figure 186: Rod Motion Problem Sketch

Material Properties	Geometric Properties	Loading
E = 300 psi k1 = 0.5 x 10-12 in4/lb neutron k2 = 1 x 1010 neutron/in2 Φ = 1 x 1010 neutron/in2-hr C1 = 0.5e-2 C2 = 1 C3 = 0 C4 = 0 C5 = 1	= 1 in A = 0.25 in2 h = 0.5 in	σo = 1 psi To = 1000°F

Analysis Assumptions and Modeling Notes

The implicit creep strain is defined using the TB,CREEP command. The constants, C1, C2, C3, C4, and C5 are derived from the generalized exponential creep equation and creep strain rate relationship.

Generalized exponential creep = ,

An integration time step of 0.1 hr is assumed over the 5 hour time range (50 substeps). POST26 is used to obtain the variation of creep strain with time. The following quantities are required for input:

Maximum fluence = 5 Φ = 5 x 1010 neutron/in2

F = σo

A = 0.25 lb

I = moment of inertia = A2/12 = 0.0052083 in4

Results Comparison