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

S23(
t3
)
t y,
jump q yt
cyc
(4.5)
S ( t ) S ( t )
23
3
12
2
Since the cycle jump is determined for a set of state variables, the allowed jump t jump is chosen
as the minimum of the computed allowed jump times for each variable:
jump
t t
t t
/
cyc min y,
jump cyc
(4.6)
To extrapolate the state variables after each jump the Heun integrator is used :
S23( t3
) S jump ( t t
jump t jump
1
y
2
( t3
t
jump ) y(
t3
)
3 )
(4.7)
By substituting Equation (4.4) into Equation (4.7):
y(
t
2
jump
3 t
jump ) y(
t3
) S23(
t3
) t
jump S23( t3
) S12(
t2
)
(4.8)
2tcyc
The above extrapolation scheme is most suitable for structures with slowly evolving properties,
in a quasi-linear manner. In case of more non-linear behaviour, higher order integrators could be
implemented. However, the extrapolation scheme is able to capture highly non-linear behaviour
by conducting shorter or no jumps. This, of course, does not save so much computational time,
but ensures at least an acceptable solution.
After having introduced the controlled cycle jump procedure, it is now of interest to investigate
the extrapolation accuracy and the computational efficiency of the cycle jump method
implemented in a finite element fatigue crack growth routine. Two different finite element
routines incorporating the cycle jump method have been developed in this chapter. The first
routine is based on a 2D finite element model suitable for 2D and axisymmetric fatigue crack
growth, and the second is based on a 3D finite element model which can be used in any 3D
fatigue crack growth simulation.
4.3 Face/Core Fatigue Crack Growth in Sandwich Beams
The cycle jump method described before will now be implemented in a FE-based numerical
routine for investigating fatigue crack propagation in the face/core interface of a sandwich beam.
Interface fatigue crack growth in a sandwich beam consisting of 2.8 mm thick plain-woven Eglass/epoxy
face sheets over a 50 mm thick Divinycell H130 PVC foam core is simulated by a
commercial finite element code, ANSYS version 11. Face sheet and core material properties are
67
( t
)