VM193

VM193
Evaluation of Stress Intensity Factor for an Inclined Crack Using XFEM Method

Overview

Reference:	Liu, X.Y., Ziao, Q.Z., and Karihaloo, B.L., "XFEM for direct evaluation of mixed-mode SIFs in homogenous and bi-materials", International Journal for Numerical Methods in Engineering, vol. 59, pp. 1103-1118, 2004
Analysis Type(s):	Static Analysis (ANTYPE = 0)
Element Type(s):	2D 4-Node Structural Solid (PLANE182)
Input Listing:	vm193.dat VM193 requires a supplemental .cdb input file which is too long to include full input listings. This file must be downloaded and placed in your working directory for the test case to run properly. Additionally, the geometry and mesh should be regenerated. Download link: MAPDL Test Case Files for 2024 R2 : vm193a.cdb : vm193b.cdb : vm193c.cdb : vm193d.cdb

Test Case

A 2D plate with length L is subjected to uniform tension loading. An inclined crack of length 2a is modeled with 4 different angles, , , , and . The singularity-based XFEM method is used to account for crack tip singularity effects. Stress intensity factors for each case are computed using CINT,TYPE,SIFS.

Figure 296: Problem Sketch for 2D Inclined Crack

Material Properties

Geometric Properties

E = 100 Pa

= 0.3

L = 10 m

Crack length, 2a = 1 m

= 1 Pa

Analysis Assumptions and Modeling Notes

The problem is solved using 2D PLANE182 elements with plane stress element behavior. The plate is constrained along the X, Y direction at location X = -5 meters and Y = 0 meters, and along the Y direction at location X = 5 meters and Y = 0 meters. The 2 crack tip node components (CRKTIPELEM1 and CRKTIPELEM2) and the number of paths surrounding this crack tip are defined using the CINT command. Mode 1 (K1) and Mode 2 (K2) stress intensity factors obtained from contours 2, 3, 4, 5, and 6 are then averaged and compared against the reference solution.

Figure 297: Finite Element Model of 2D Inclined Crack

Results Comparison

Angle	Value	Tip Node Component	Target	Mechanical APDL	Ratio
0°	K1	CRKTIPELEM1	1.253	1.269	1.013
	K1	CRKTIPELEM2	1.253	1.269	1.013
	K2	CRKTIPELEM1	0.000	0.000	1.000
	K2	CRKTIPELEM2	0.000	0.000	1.000

Angle	Value	Tip Node Component	Target	Mechanical APDL	Ratio
30°	K1	CRKTIPELEM1	0.940	0.951	1.012
	K1	CRKTIPELEM2	0.940	0.951	1.012
	K2	CRKTIPELEM1	0.543	0.556	1.025
	K2	CRKTIPELEM2	0.543	0.556	1.025

Angle	Value	Tip Node Component	Target	Mechanical APDL	Ratio
45°	K1	CRKTIPELEM1	0.627	0.634	1.011
	K1	CRKTIPELEM2	0.627	0.634	1.011
	K2	CRKTIPELEM1	0.627	0.642	1.024
	K2	CRKTIPELEM2	0.627	0.642	1.024

Angle	Value	Tip Node Component	Target	Mechanical APDL	Ratio
60°	K1	CRKTIPELEM1	0.313	0.316	1.011
	K1	CRKTIPELEM2	0.313	0.316	1.011
	K2	CRKTIPELEM1	0.543	0.556	1.023
	K2	CRKTIPELEM2	0.543	0.556	1.023