ETBX Fatigue Crack Growth Module - Example 4.pdf

ETBX Fatigue Crack Growth Module - Example 4Help Contents | Module Library 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: http://www.engrasp.com/doc/etb/mod/fm1/paris/example04.html (1 of 11)10/3/2011 4:54:32 PM 50 and remains fixed during crack growth. n.html (2 of 11)10/3/2011 4:54:32 PM .engrasp.Example 4 where the material constants C.ETBX Fatigue Crack Growth Module . calculate the number of cycles to failure given an initial crack length of ai = 0. 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 2.10 inches. http://www. Assume the ratio of crack depth to crack length a/c = 0.com/doc/etb/mod/fm1/paris/example04. 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. http://www.Example 4 Figure 2.com/doc/etb/mod/fm1/paris/example04.ETBX Fatigue Crack Growth Module .engrasp. Load spectrum for Problem 1 Problem 2: Repeat Problem 1 for the load spectrum given in Figure 3.html (3 of 11)10/3/2011 4:54:32 PM . 218 cycles.758 inches. The stress ratio R = (σmin / σmax = 23 ksi is calculated to be σmax) = 13 ksi / 23 ksi = 0. The number of cycles to failure is calculated by choosing the Walker solution and entering ai = 0.758 inches. http://www. and m are based on units of ksi and inches. and thus all module inputs must be expressed in those units.ETBX Fatigue Crack Growth Module . The input form is shown in Figure 5.engrasp. The critical crack length for 1.565.com/doc/etb/mod/fm1/paris/example04. Clicking the calculate button displays the solution in the output window shown in Figure 6 . The material contants C. the ETBX Fatigue Crack Growth module can be used to calculate ac.html (4 of 11)10/3/2011 4:54:32 PM . A picture of the module input form to calculate ac is shown in Figure 3 . which is given by: The stress intensity correction factor β is a constant value due to the assumption that a/ c remains constant.10 inches and af = 1. 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. The β value is calculated by evaluating Q for a/c = 0. n.13 ksi) = 10 ksi. The number of cycles to failure is computed to be 1. The stress range ∆σ = (23 ksi .Example 4 Figure 2.5 and substituting into the equation for KIC: After solving for β .842. Module output is shown in Figure 4. and due to the assumption that the plate width b is much greater than c. The number of cycles to failure is computed to be 2. The new spectrum requires that ac and R be recalculated.Example 4 The analysis can be easily repeated for the input spectrum given in Figure 2.333. An ETBX plot of crack growth rate da/dN versus stress intensity factor K for Problems 1 and 2 is shown in Figure 7.640. The crack growth plots are compared in Figure 8. ac = 4.html (5 of 11)10/3/2011 4:54:32 PM .201 cycles. For σmax = 15 ksi and σmin = 5 ksi.ETBX Fatigue Crack Growth Module .engrasp.134 inches and R = 0.com/doc/etb/mod/fm1/paris/example04. http://www. com/doc/etb/mod/fm1/paris/example04.Example 4 Figure 3. Module input form for calculation of critical crack length Figure 4.html (6 of 11)10/3/2011 4:54:32 PM .ETBX Fatigue Crack Growth Module .engrasp. Module output for critical crack length calculation http://www. engrasp. Module input form for cycles to failure calculation http://www.html (7 of 11)10/3/2011 4:54:32 PM .com/doc/etb/mod/fm1/paris/example04.Example 4 Figure 5.ETBX Fatigue Crack Growth Module . com/doc/etb/mod/fm1/paris/example04.engrasp.Example 4 http://www.html (8 of 11)10/3/2011 4:54:32 PM .ETBX Fatigue Crack Growth Module . Module output for cycles to failure calculation Figure 7.333 http://www.565 and R = 0. Crack growth rate curves for R = 0.engrasp.com/doc/etb/mod/fm1/paris/example04.ETBX Fatigue Crack Growth Module .html (9 of 11)10/3/2011 4:54:32 PM .Example 4 Figure 6. http://www.Example 4 Figure 8.engrasp. Inc.ETBX Fatigue Crack Growth Module . All rights reserved.html (10 of 11)10/3/2011 4:54:32 PM . Comparison of crack growth plots Help Contents | Module Library Copyright © 2001-2008 Engrasp.com/doc/etb/mod/fm1/paris/example04. Example 4 http://www.engrasp.html (11 of 11)10/3/2011 4:54:32 PM .com/doc/etb/mod/fm1/paris/example04.ETBX Fatigue Crack Growth Module .