Page 370 - Biaxial Multiaxial Fatigue and Fracture
P. 370
354 c. CAL~ R. CITARELLA AND M. PERRELLA
Fatigue Growth Calculation. During fatigue crack growth, the relation between the incremental
size and the number of load cycles may be represented by a number of crack growth laws, such
as PARIS, FORMAN, RHODES or NASGRO. Alternatively, a tabulated form can be used to
supply-
During the fatigue analysis, there are options on the method of computing the dN values:
1. the SIF’s are constant over the step;
2. the SIF’s at the previous step and the current step are used to compute the dN value over the
last crack growth step. This requires two analysis to be performed before the first dN value
is computed (backward correction)
3. the previous two results are used to predict a guess for the dN over the next step. This may
be inaccurate as the SIF’s may change significantly over the step cforwardprediction).
Crack modelling. In this section, the modelling and discretization strategy of implementation of
the DBEM for three dimensional crack problems is presented. Because of the continuity
requirements of the displacements and tractions for the existence of traction boundary integral
equations and co-planar characteristic of crack surfaces, special consideration has to be taken
for modelling discretization. In order to maintain efficiency and simplicity of the boundary
elements, the present formulation uses discontinuous quadratic element for the crack modelling.
The general modelling strategy can be summarised as follows:
Crack surfaces are modelled with discontinuous quadratic quadrilateral elements;
Surfaces intersecting a crack surface are modelled with edge-discontinuous quadrilateral or
triangular elements;
The displacement integral equation is applied for collocation on one of the crack surfaces (say
the upper surface G+);
The traction integral equation is applied for collocation on the opposite crack surface (say the
upper surface GJ;
The displacement integral equation is applied for collocation on all other surfaces.
The requirement of the continuity on udx) and t,(x) for the existences of the displacement and
traction boundary integral equations is satisfied by the fact that discontinuous elements are used
on crack surfaces. The above strategy is robust as it maintains the consistency with the theory
and, at the same time, allows effective modelling of general edge or embedded crack problems.
Edge crack is defined here when the crack front intersects the boundary surface, while in the
embedded crack the crack front is positioned in the interior of the problem domain. Note that
the increment of an edge crack requires remesh of the boundary surfaces intersecting the crack
surface.
Results related to three-dimensional crack propagation
This time the complex specimen undergoes a fatigue load with P,,=27.7 KN and R=O.1 and
the frequency adopted on the fatigue machine is 10 Hz.
The analysis has been divided in two part:
1. the propagation of the elliptical part through crack up to a condition that immediately
precede the through crack appearance; for such analysis the part-through fracture toughness
was assumed K1~=1320 MPa.mm”* (from NASGRO database and correspondingly to A1
22 19-T87)
2. the initial part of the through crack propagation, when the phenomena is still three-
dimensional because of the differences between the two crack front sizes.