VM-WB-MECH-093

VM-WB-MECH-093
C*-Integral Calculation for a Single-Edge Cracked Plate Using Pre-Meshed Crack

Overview

Reference:

Kanninen, M. F., & Popelar, C. H. (1985). Advanced fracture mechanics (p. 550). Oxford University Press.

Solver(s):

Ansys Mechanical

Analysis Type(s):

Static Analysis

Element Type(s):

2-D Structural Solid Element

Test Case

A rectangular plate with an edge crack is subjected to a tensile load . The load is applied instantly and held for 1000 hours. The C* integral is then determined using Pre-Meshed Crack and compared against the reference solution.

Figure 125: Two-Dimensional Fraction Problem Sketch

Material Properties

Geometric Properties

E=200000 MPa

= 0.3

Parameters for strain hardening creep

C1 = 5 x 10^-12

C2 = 3

C3 = 0

C4 = 0

L = 100 mm

a = 2.5 mm

b = 20 mm

c = 17.5 mm

= 150 MPa

Analysis Assumptions and Modeling Notes

The problem is solved using 2-D structural solid element with plane strain element behavior. One half of the plate is modeled and symmetric boundary conditions are considered. The crack tip nodes and the number of paths surrounding the crack tip nodes are defined using Pre-Meshed Crack. The computation is completed in two steps. In the first step, the instal loading is applied on the top edge. In the second tep, the load is held for 1000 hours. The C* integral is computed for the crack tip nodes by averaging the C* integral values from contour 2 to contour 9.

The reference value for the C* integral is determined using the following equation:

where

A = 5 x 10^-12

a = 2.5

c = 17.5

C₁ = 17.5

h₁ = 8.57 (according to the reference material)

P = 3000

Results Comparison

Result	Target	Mechanical	Error (%)
C*-Integral	0.032	0.03312687	3.5215