VM143

VM143
Fracture Mechanics Stress for a Crack in a Plate

Overview

Reference:W. F. Brown, Jr., J. E. Srawley, "Plane Strain Crack Toughness Testing of High Strength Metallic Materials", ASTM STP-410, 1966.
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):
3D 20-Node Structural Solid Elements (SOLID95)
3D Structural Solid Elements (SOLID45)
2D 8-Node Structural Solid Elements (PLANE183)
3D 20-Node Structural Solid Elements (SOLID186)
3D Structural Solid Elements (SOLID185)
Input Listing:vm143.dat

Test Case

A long plate with a center crack is subjected to an end tensile stress σo as shown in the problem sketch. Determine the fracture mechanics stress intensity factor KI.

Figure 199: Finite Width Plate Problem Sketch

Finite Width Plate Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
a = 1 in
b = 5 in
h = 5 in
t = 0.25 in
σo = 0.5641895 psi

Analysis Assumptions and Modeling Notes

The problem is solved using 3D solid elements (SOLID95, SOLID45, SOLID185, and SOLID186) and using 2D plane strain elements (PLANE183). A one-quarter model is used because of symmetry. The macro FRACT is used to create the SOLID95 crack tip elements from the SOLID45 model and SOLID186 crack tip elements from the SOLID185 model using a weighted midside node position (quarter point location).

In the 3D analysis, the plane strain condition is achieved by constraining UZ degrees of freedom of all the nodes (displacements in the Z-direction). Only the back plane of nodes are shown numbered in the enlargements of the 3D model. The simpler 2D model using PLANE183 elements are created by automatic mesh generation. The KSCON command is used to create 2D crack tip elements with nodal singularity.

POST1 is used to get fracture mechanics stress intensity factor (KI) by displacement extrapolation (KCALC command), and J-Integral methods. A user file JIN1 is created in the input. It consists of path operations necessary to compute the J-Integral. In general usage, the user file would be available in the local directory rather than being created in the input.

Results Comparison

KITargetMechanical APDLRatio
Using SOLID95 and SOLID45 (3D Analysis)
By Displacement Extrapolation[1]1.02491.06201.036
By J-Integral[2]1.02491.04581.020
Using PLANE183 (2D Analysis)
By Displacement Extrapolation[1]1.02491.05871.033
By J-Integral[2]1.02491.05611.030
Using SOLID186 and SOLID185 (3D Analysis)
By Displacement Extrapolation1]1.02491.05951.034
By J-Integral2]1.02491.04931.024

  1. As parameter KI1 by KCALC command

  2. As parameter KI2