Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

composite laminates under thermal cyclic loading using combined experimental and
computational investigations.
In all the above-mentioned studies, the simulation of fatigue crack growth was limited to only a
few cycles due to the need of a high mesh density at the crack tip and subsequently required high
computational time. This illustrates the main obstacle confronting any attempt to combine
fracture mechanics and the finite element method to simulate fatigue crack growth. To overcome
the problem of simulating many cycles different concepts of cycle jumps have been proposed by
several researchers. The cycle jump concept was first developed and applied by Billardon et al.
(1989). They called the approach the jump-in-cycle procedure. The Large Time Increments
method (LATIN) was proposed two years later by Boisse et al. (1990) and used by Cognard et al.
(1999) for thermo-mechanical problems. In the large time increments method the equations of
the initial boundary value problem are divided into two groups: (1) linear equations which are
global and (2) non-linear equations, which are local. Even though the theory of the LATIN
method is sound, after the implementation into commercial FEA software it turned out to be
computationally heavy and not so beneficial. Kiewel et al. (2000) developed a method for
extrapolation of a group of internal variables over a certain range of cycles. The extrapolation is
based on spline functions used to evaluate the state variables over jumped cycles for each
integration point in the finite element model. Fish et al. (2002) developed a new scheme for cycle
jumps where the time is decomposed into two scales: one micro-chronological (fast) and one
macro-chronological (slow). The fast micro-chronological time corresponds to the cyclic
behaviour, and the slow macro-chronological time to the global behaviour of the structure. Van
Paepegem et al. (2001) proposed a new cycle jump method based on extrapolation of the damage
parameter exploiting the explicit Euler integration formula. At each integration point of the finite
element model a local jump length is determined by imposing an input maximum jump allowed
by the user for the damage variable. The global jump length is then evaluated based on the
cumulative statistical distribution of local jumps. Cojocaru and Karlsson (2006) employed the
cycle jump method to simulate the response of thermal barrier coatings (TBC) under cyclic
thermal loading, where the structure evolves due to changing material properties during high
temperature. In this case, damage mechanics was not used. They proposed a control function that
automatically monitors the length of the cycle jump to ensure a realistic solution. Results showed
their cycle jump scheme is computationally effective and accurate.
In this chapter, the cycle jump method developed by Cojocaru and Karlsson (2006) is adopted
with some modifications to take into account the change in the geometry of the finite element
model due to the fatigue crack propagation. Two finite element routines are developed to
simulate 2D and 3D accelerated bimaterial fatigue crack growth. In the first routine the crack
only propagates at one point at the crack tip, but in the second a crack front is modelled and its
growth at different points in different directions is simulated.
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