- Stress-intensity factors calculation with the interaction integral approach during solution (CINT)
- Stress-intensity factors calculation with extrapolation during postprocessing (KCALC).
- T-stress calculation using the interaction integral approach during solution (CINT).
- Material force calculation is performed during the solution (CINT).
Most fracture calculations rely on the element nodal connectivity order and must conform to the pattern
shown for each element described in the Element Reference.
11.3.1. J-Integral Calculation
The J-Integral evaluation is based on the domain integral method by Shih[ 5 ]. The domain integration
formulation applies area integration for 2-D problems and volume integration for 3-D problems. Area
and volume integrals offer much better accuracy than contour integral and surface integrals, and are
much easier to implement numerically. The method itself is also very easy to use.
The following topics concerning J-Integral calculation are available:
11.3.1.1. Understanding the Domain Integral Method
11.3.1.2. J-Integral Calculation11.3.1.1. Understanding the Domain Integral Method
For a 2-D problem, and in the absence of thermal strain, path dependent plastic strains, body forces
within the integration of area, and pressure on the crack surface, the domain integral representation
of the J-Integral is given by:
A ijj
i
i=∫∂
∂−∂
∂σ δ
11where σij is the stress tensor, uj is the displacement vector, w is the strain energy density, δij is the
Kronecker delta, xi is the coordinate axis, and q is referred to as the crack-extension vector.
The direction of q is the simple x-axis of the local coordinate system ahead of the crack tip. The q vector
is chosen as zero at nodes along the contour Γ, and is a unit vector for all nodes inside Γ except the
midside nodes, if there are any, that are directly connected to Γ. The program refers to these nodes
with a unit q vector as virtual crack-extension nodes.
The discretized form of the J-Integral is given by:
Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationNumerical Evaluation of Fracture Mechanics Parameters