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

An accelerated simulation of fatigue crack growth (the cycle jump method) developed in the
previous chapter is performed on the STT specimens. The energy release rate and mode-mixity
phase angle are chosen as state variables in the cycle jump method. Figures 5.30 (a) and (b) show
the strain energy release rate and phase angle diagrams as a function of crack length obtained
from the finite element analysis of the STT specimens at maximum fatigue load in each cycle.
G (J/m 2 )
450
350
250
150
STT H100
STT H45
-20
50
20 40 60 80 100 120
Crack length (mm)
-25
(a)
(b)
Figure 5.30: Energy release rate and phase angle as a function of crack length for the STT
specimens.
The energy release rate increases with increasing crack length up to 60 mm and then decreases
due to the increasing membrane forces as the crack propagates. In smaller crack lengths with
increasing crack length, because of small membrane forces, the deformations at the crack tip
increase, which leads to higher energy release rate. However, as the crack propagates, resulting
in at increasing membrane forces, a larger part of the strain energy is used to stretch the
debonded face sheet rather than create new crack surfaces, decreasing energy release rate at the
crack tip. Figure 5.30 (b) shows that the mode-mixity phase angle magnitude increases with
increasing crack length, which indicates the existence of higher mode II loading at the crack tip
at larger crack lengths. The negative phase angle illustrates the tendency of the crack to kink
towards the face sheet. The fatigue crack propagation simulation was conducted on the STT
specimens for 100000 cycles. In order to study the effect of the control parameters on the
accuracy and speed of the simulation, simulations with different control parameters, qy, were
carried out. Figures 5.31 (a) and (b) show the crack length as a function of cycles for four
different control parameters qG=q=0.05, 0.1, 1.5 and 0.2. A significant dependency on the
control parameters is seen in the simulations of the H45 specimens. Large deviations are
observed between the simulations using 0.15 and 0.25 as control parameters. However, the
simulation results converge at smaller control parameters. During the initial cycles the
simulations using qG=q=0.15 and 0.25 control parameters show small differences but as an
unstable crack growth zone is approached the deviations increase. This takes place due to the
111
Phase angle ()
Crack length (mm)
20 40 60 80 100 120
-5
-10
-15
STT H100
STT H45