ETBX Fatigue Crack Growth Module - Example 4.pdf

ETBX Fatigue Crack Growth Module - Example 4

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Fatigue Crack Growth Rate An EngineersToolbox Calculation Module

Example Problems

Example 4

A wide plate with a semi-elliptical edge crack of is subject to an oscillatory stress as shown in Figure 1.

Figure 1. Semi-elliptical crack at the edge of a plate loaded in tension

The plate is manufactured from A36 steel. The yield strength σys is 36 ksi and the fracture toughness KIC = 50 ksi-in1/2. The crack growth rate is given by the Walker

equation:

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where the material constants C, n, and m are given in terms of ksi and inches by:

Since the width b of the plate is assumed to be large compared to the crack length c, the following stress intensity factor solution is used:

where Q is a shape factor for an elliptical crack and is approximately given by:

Problem 1: For the constant amplitude load spectrum shown in Figure 2, calculate the number of cycles to failure given an initial crack length of ai = 0.10 inches. Assume the ratio of crack depth to crack length a/c = 0.50 and remains fixed during crack growth.



Figure 2. Load spectrum for Problem 1

Problem 2: Repeat Problem 1 for the load spectrum given in Figure 3.



Figure 2. Load spectrum for Problem 2

Solution

The first step in determining the number of cycles to failure is to calculate the critical crack length ac, which is given by:

The stress intensity correction factor β is a constant value due to the assumption that a/c remains constant, and due to the assumption that the plate width b is much greater than c. The β value is calculated by evaluating Q for a/c = 0.5 and substituting into the equation for KIC:

After solving for β , the ETBX Fatigue Crack Growth module can be used to calculate ac.

A picture of the module input form to calculate ac is shown in Figure 3 . Module output

is shown in Figure 4. The critical crack length for σmax = 23 ksi is calculated to be

1.758 inches.

The number of cycles to failure is calculated by choosing the Walker solution and entering ai = 0.10 inches and af = 1.758 inches. The material contants C, n, and m are based on units of ksi and inches, and thus all module inputs must be expressed in those units. The stress range ∆σ = (23 ksi - 13 ksi) = 10 ksi. The stress ratio R = (σmin /

σmax) = 13 ksi / 23 ksi = 0.565. The input form is shown in Figure 5.

Clicking the calculate button displays the solution in the output window shown in Figure 6 . The number of cycles to failure is computed to be 1,842,218 cycles.



The analysis can be easily repeated for the input spectrum given in Figure 2. The new spectrum requires that ac and R be recalculated. For σmax = 15 ksi and σmin = 5 ksi, ac

= 4.134 inches and R = 0.333. The number of cycles to failure is computed to be 2,640,201 cycles. An ETBX plot of crack growth rate da/dN versus stress intensity factor K for Problems 1 and 2 is shown in Figure 7. The crack growth plots are compared in Figure 8.



Figure 3. Module input form for calculation of critical crack length

Figure 4. Module output for critical crack length calculation



Figure 5. Module input form for cycles to failure calculation



Figure 6. Module output for cycles to failure calculation

Figure 7. Crack growth rate curves for R = 0.565 and R = 0.333



Figure 8. Comparison of crack growth plots

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ETBX Fatigue Crack Growth Module - Example 4.pdf

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