N
-JR
Figure 4-2: (a) 20 node isoparametric element in natural coordinate system and (b)
Quarter point singular element with the ( = -1 face collapsed in local Cartesian
coordinate system. [31]
been found that rectangular quadratic isoparametric elements (and brick elements)
have singular stiffness (singular total strain energy) at the crack tip [30]. For
the three-dimensional case, 20-node isoparametric elements were used. 20-node
brick elements collapse and form wedge shaped elements at the crack tip. One
of the element faces collapses at the crack tip to form the wedge shape as shown
in the Fig. 4-2. Fig. 4-2(a) shows a 20 node isoparametric element in universal
coordinate system, and Fig. 4-2(b) depicts its quarter point singular version with
the = -1 face collapsed in local Cartesian coordinate system.
This element is the best crack tip element for FEA solution of mixed mode
SIF analysis of orthotropic materials [24] [42]. Around the crack tip the size of the
elements should be very small to reduce the error in calculating SIFs. A typical
example of crack tip element length (Li) is 0.002in. The enlarged figure of the
meshing around the crack tip can be seen in Fig. 4-4 on page 34. All the nodes
had to be aligned along the material coordinate system to get the desired result.
Two different orientations (101) and (121) (on {111} plane) were used to
analyze the effect on SIF. The crack lies on the {111} plane (Fig. 3-1 on page 24),
and the crack direction was aligned along family of either (101) or (121) directions.