Example 1

A thick-walled cyclinder has an outer diameter of 1.5 m and a wall thickness of 100 mm. The working internal pressure of the cylinder is 15 MPa and K_IC for the material is 38 Mpa-m^1/2. Non-destructive testing reveals that no flaw above 10 mm exists in the cylinder. Estimate the number of pressurization cycles that the cylinder can safely withstand using the Paris Equation with material constants C = 3 x 10^-12 (for K in Mpa-m^1/2) and n = 3.8.

Solution

Assume that the flaw is sharp, of length 2a, and perpendicular to the hoop stress. From the ETBX Pressure Vessels module, the maximum hoop stress is calculated from the equation:

For this physical configuration, assume that the crack is small in comparison to the cylinder. The stress intensity correction factor, b, for a large center-cracked plate is 1.0. The material contants C and n are based on units of MPa and meters, and thus all module inputs must be expressed in those units.

The Fatigue Crack Growth module provides a solution to calculate the critical crack size a_c at which fast fracture occurs. The module input form is shown in Figure 1 . Calculated results are shown in Figure 2 . The critical crack size is 0.0413 meters, or 41.3 mm.

Non-destructive testing has shown that no flaw greater than 2a = 10 mm in size exists in the cylinder. Therefore ai = 5 mm, or 0.005 meters. The number of cycles to failure is calculated by choosing the Paris solution and entering ai = 0.005 inches and af = 0.0413 meters. The stress range for a pressurization cycle is Ds = (s_max - s_min) = (105.5 MPa - 0 MPa) = 105.5 MPa. The input form is shown in Figure 3 .

Clicking the calculate button displays the solution in the output window shown in Figure 4 . The number of cycles to failure is 86,353 cycles.

Figure 1. Module input to calculate critical crack length

Figure 2. Calculated critical crack length

Figure 3. Module input to calculate cycles to failure

Figure 4. Calculated cycles to failure