VM293

VM293
Evaluation of Stress Intensity Factor KI Using the Unstructured Mesh Method (UMM)

Overview

Reference:Rice, J.R., Mathematical Analysis in the Mechanics of Fracture, Chapter 3, pg. 222, 1968
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):3D 4-Node Tetrahedral Structural Solid with Nodal Pressures (SOLID285)
Input Listing:vm293.dat

VM293 includes 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

vm293.cdb

Test Case

A rectangular block with an embedded penny-shaped crack is subjected to a tensile stress, P, as shown in the problem sketch. Symmetry boundary conditions are considered in this analysis. The stress intensity factor KI is determined using the CINT command.

Figure 511: Problem Sketch

Problem Sketch

Material Properties Geometric PropertiesLoading
E = 200,000 MPa
μ = 0.3
H = 200 mm
L = 40 mm
W = 40 mm
a = 5 mm
Uniform tension (applied to top and bottom surfaces), P = 100 MPa

Analysis Assumptions and Modeling Notes

The problem is sovled using 3D 4-node tetrahedral structural elements (SOLID285). Because of symmetry conditions implied in the problem, on 1/8 of the model is analyzed. The block is subjected to a tensile stress and the stress intensity factor KI is computed at the crack tip nodes. The crack front and the path surrounding the crack front are defined using the CINT command. The computed stress intensity factor is then compared against the reference solution.

Results Comparison

Crack Tip NodeTargetMechanical APDLRatio
236252.30252.361.000
242252.30247.220.980
243252.30247.850.982
244252.30249.750.990
245252.30254.791.010
246252.30252.711.002
247252.30250.440.993
248252.30252.451.001
249252.30253.461.005
250252.30251.810.998
251252.30249.720.990
252252.30250.740.994
253252.30252.721.002
254252.30253.361.004
255252.30253.261.004
256252.30250.970.995
257252.30248.050.983

Figure 512: Variation of KI of the Crack Tip Nodes with Angles

Variation of KI of the Crack Tip Nodes with Angles