ALJOIN Final Technical Report - Transport Research & Innovation ...

Contract N° G3RD-CT-2002-00829
Final Technical Report – draft 1
ALJOIN The numerical analyses were carried out using the both the LS-DYNA explicit code and
the FRANC2D code. Figure 16 shows the results of the analysis, in terms of distribution
of the Von Mises equivalent stress, demonstrating the crack propagation along the
centreline of the specimen. Figure 17 shows the results of the simulations done using
the FRANC2D code 1 which allows to explicitly model the crack propagation in the mesh.
As the cracks propagate, automatic remeshing algorithms delete the mesh local to the
crack tip, extend the crack, and build a new mesh around the new tip. The constant
critical crack tip opening angle (CTOA) fracture criterion was used in the simulations.
The CTOD fracture criterion assumes that the crack growth will occur when the angle
made by the upper crack surface, the crack tip, and the lower crack surface reaches a
critical value. In a two-dimensional analysis, the displacement δ, perpendicular to the
crack, at a fixed distance d behind the crack tip are monitored during the analytical
loading of the model. When the displacements are such that the critical angle CTOA
(ψC) is attained (see equation 1), the crack is advanced by releasing the crack tip nodes
until a total distance d of crack growth is achieved.
−1⎛
δ ⎞
ψ C = 2 tan ⎜ ⎟
(1)
⎝ d ⎠
Then, the applied displacements are held constant while the internal forces are returned
to equilibrium. At each load increment, the CTOA was calculated and compared to a
critical value. When the CTOA exceeded this critical value, the crack-tip node was
released and the crack advanced.
t = 0.6 s
t = 2.0 s
Figure 16 Numerical Analysis of Crack Tip Opening (CTOA) tearing tests (Von Mises
Equivalent Stress)
1 Swenson D., James M., “FRANC2D/L: A Crack Propagation Simulator for Plane Layered Structures
Version 1.4 User's Guide”, Kansas State University •Manhattan, Kansas
20