Example 2

A large center-cracked plate containing an initial crack of length 2a=10 mm is subjected to a constant amplitude cyclic tensile stress ranging from a minimum value of 100 MPa to a maximum value of 200 MPa. Assuming that the crack growth rate is governed by:

(1) Calculate the crack growth rate when the crack length 2a has the following values: 10 mm, 30 mm, and 50 mm.

(2) Assuming that the relevant fracture toughness is 60 MPa-m^1/2, estimate the number of cycles to failure.

Solution

The crack growth rate is defined by the Paris equation. The contants C and n are based on units of MPa and meters. Therefore all module inputs must be expressed in those units. The stress intensity correction factor, b, for a large center-cracked plate is 1.0. The stress range Ds = (200 MPa - 100 MPa) = 100 MPa.

(1) Calculate crack growth rate da/dN at crack length 2a = 10 mm, 30 mm, and 50 mm.

Module inputs are shown in Figure 1. Crack growth rates at 2a = 10 mm, 30 mm, and 50 mm are determined in a single calculation by defining ai = 0.005 m, af = 0.025 m, and specifying a 2-step solution. Module output is shown in Figure 2 and Figure 3 . The calculated crack growth rates are listed in Table 1 below.

Table 1. Calculated crack growth rates

2a	da/dN
10 mm
30 mm
50 mm

(2) Assuming that Kc = 60 MPa-m^1/2, estimate the number of cycles to failure.

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 4. Calculated results are shown in Figure 5. The critical crack size was determined to be 0.02864 m.

The number of cycles to failure is calculated by choosing the Paris solution and entering ai = 0.005 m and af = .02864 m, as shown in Figure 6. The module output is shown in Figure 7. The number of cycles to failure is calculated to be 704079.

Figure 1. Module input to calculate crack growth rate

Figure 2. Calculated crack growth rates

Figure 3. Calculated crack growth length

Figure 4. Module input to calculate critical crack length

Figure 5. Calculated critical crack length

Figure 6. Module input to calculate the number of cycle to failure

Figure 7. Calculated cycles to failure