Title: Damage Tolerance Analysis of Critical Area on Windshield
To illustrate the process of estimating crack growth behavior,
which is necessary for setting inspection intervals.
problem focuses on a damage tolerance analysis of the windshield doubler at the
intersection of the upper windowsill and post of an airplane. The analysis goal is to estimate the crack growth
behavior of the windshield doubler. A
finite element model is developed, with extensive refinement in the window area, to
determine stresses in the part. A stress
spectrum and b-factors are used with AFGROW to
predict crack length versus flight hours.
Topics Covered: Damage
tolerance analysis, finite element analysis, crack growth analysis
Type of Structure:
Sections of Handbook: Sections
2, 5, 7, 11
Robert D. McGinty
Company Name: Mercer
Engineering Research Center
Structures Technology Group
Warner Robins, GA 31088-7810
Robert D. McGinty
This problem focuses on a
critical area of the windshield doubler at the intersection of the upper window sill and
window post #3. The doubler is shown in Figure MERC-2.1, with the expected crack path marked. It is fabricated from 0.091" thick 7075-T6
aluminum and is 1.5" wide at the crack location.
The windows are fastened to the doubler in such a way that they "float",
which means that the windows transfer only bearing loads to it. The fasteners do not exert tangential loads on
the windshield doubler.
MERC-2.1. Sketch of the Forward Fuselage
and Windshield Doubler
Finite Element Mesh
A NASTRAN finite element model (FEM) of the
forward fuselage was developed and is shown in Figure MERC-2.2. It is made up primarily of shell and beam
elements. In general, joints are modeled by
shared-nodes; fasteners are not explicitly modeled.
However, fasteners that attach the windshield doubler to airframe structure and
skin are explicitly modeled with beam elements. Rigid
elements are used occasionally, such as to simulate floating windows that transfer only
bearing loads to the windshield doubler.
Figure MERC-2.2. Structural Finite Element Model of Forward
Fuselage of the Aircraft With Mesh Refinement In Front Window Area
Loading Conditions and
Internal pressurization effects are the
dominant cause of stresses in the window area. Loads
due to maneuvers, landings, wind gusts, etc. are negligible in comparison. Internal pressurization actually refers to the
case where the cabin is maintained at sea level pressure while flying at altitudes where
atmospheric pressure is substantially less. The
pressure differential is applied to the model as an internal pressure. Note that a release valve(s) in the plane prevents
the pressure differential from exceeding 7.5 psi.
Internal pressure versus altitude. A release valve prevents the
pressure from exceeding 7.5 psi.
Mission profile data are combined with the pressurization
information in Figure MERC-2.3 to give the frequency and
amplitude of internal pressurization cycles that the plane will experience. Mission profile data consist of flight altitude
data versus time. Figure
MERC-2.4 shows a typical segment consisting of missions at several altitudes ranging
from 1,000 ft to 25,000 ft. Combining
the information in Figures MERC-2.3 and MERC-2.4 gives the internal pressurization cycles shown in Figure MERC-2.5.
Typical missions showing altitude versus time.
Time spent at each altitude is not shown.
Internal pressurization versus time for missions shown in Figure
Stresses in the forward fuselage and doubler for 1 psi
pressurization are shown in Figure MERC-2.6 below. Stresses in the doubler are assumed to scale
linearly with the imposed pressure. For
example, the stress at any point in the doubler under 7.5 psi internal pressurization will
be 7.5 times greater than its value in Figure MERC-2.6.
Maximum principal stress in forward fuselage and window doubler due to 1 si
pressurization of the fuselage. Typical crack
location is shown.
shows cycles of average tensile stress in the lower leg of the doubler. The values are the result of multiplying the
pressure cycle data in Figure MERC-2.5 by the average tensile
stress in the lower leg of the doubler predicted by the finite element analysis for 1 psi
Cycles of average tensile stress in lower leg of doubler. Stress cycles in the doubler are directly
proportional to the pressurization cycles
Crack Growth Prediction
Critical Crack Length
is defined as the time when the crack reaches a length, acrit, such that further growth would be
unstable under maximum loading conditions. This
occurs when the stress intensity factor of the crack reaches its critical value, Kc.
This value is 71 ksiÖin for
0.091" thick Al 7075-T6. The tensile
stress in the doubler at maximum loading conditions is slimit=
22.4 ksi. The critical crack length is
determined by solving
This must be solved iteratively because b is a function of crack length, a. Solving
the equation gives acrit=0.7".
Note that b-factors for this analysis were
taken from the AFGROW library.
Predicting the Crack Growth
was used to predict crack growth in the doubler due to the fuselage pressurization cycles. The crack is assumed to start as a 0.05"
radius corner crack at a fastener hole, grow to a through crack, and then grow across the
doubler until failure. Stress cycles (see Figure MERC-2.7), b-factors
from AFGROW, and material da/dN data are
combined to give the crack growth prediction in Figure MERC-2.8
below. Note that Willenborg retardation is
Predicted crack growth versus flight hours for a crack growing across the lower leg
of the doubler. Willenborg retardation is
applied to the simulation.