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

The strain energy release rate, G, and the mode-mixity phase angle, , are determined from
relative nodal pair displacements along the crack flanks obtained from the finite element analysis
by application of the CSDE method outlined in the Introduction of this thesis. h, which is the
characteristic length of the crack problem, is chosen as the face sheet thickness. The strain
energy release rate and the mode-mixity phase angle are used as the two state variables for the
extrapolation and cycle jump in the cycle jump method. These two parameters are selected since
they are the only required parameters for determination of the crack growth length.
Figures 4.5 (a) and (b) show the strain energy release rate and phase angle diagrams as a function
of the crack length obtained from the numerical simulations of the analysed debonded sandwich
beam at the maximum loading amplitude. The energy release rate increases with increasing crack
length up to 60 mm and then decreases. This can be attributed to the increasing membrane forces
as the crack length increases. Due to small membrane forces in the first cycles with increasing
crack length, the deflection at the crack tip increases, resulting in higher strain energy release
rate. However, as the crack length grows, the membrane forces increase and a larger part of the
total strain energy in the specimen goes into stretching of the debonded face sheet rather than
creating new crack surfaces, which results in a decreasing energy release rate at the crack tip.
Figure 5 (b) shows that the phase angle increases with increasing crack length, indicating that the
crack tip loading is less mode I dominated at larger crack lengths. The negative phase angle
shows the tendency of the crack to kink towards the face sheet.
(a) (b)
Figure 4.5: (a) Strain energy release rate vs. crack length (b) phase angle vs. crack length
diagrams for the debonded sandwich beam at maximum loading amplitude.
The fatigue crack growth simulation was conducted on the sandwich beam for 500 cycles. To
study the effect of the control parameter on the accuracy and speed of the simulation, simulations
with different control parameters, qy, were conducted. A reference simulation of all individual
cycles was performed to verify the accuracy of the simulations by application of the cycle jump
method. Figures 4.6 (a) and (b) show the deflection of the loading point (Y deflection) as a
function of cycles for two different control parameters, qG=q=0.05 and qG=q=0.2.
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