A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
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Materials & Material Properties
Ch. 4 - Material Properties, Airframe Stress Analysis and Sizing (Niu)
& Ch. 4 - Materials, Airframe Structural Design (Niu)
The materials bible: Military Handbook - Metallic Materials and
Elements for Aerospace Vehicle Structures, MIL-HDBK-5G, 1999
(new editions are issued every couple of years - always use the
latest).
Primary Materials Selection Critera
 Static strength efficiency
 Fatigue strength
 Fracture toughness and crack growth rate
 Corrosion and embrittlement properties
 Compatibility with other materials
 Environmental suitability
 Availability and cost
 Fabrication characteristics
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
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Despite all the materials and alloys available, aluminum alloys
continue to find prominence in most aircraft.
For pressurized fuselage cabins and lower wing skins -- two areas
prone to fatigue through the long-continued application and
relaxation of tension stresses -- the standard material is an
aluminum alloy 2024-T3
For upper wing skins that have to withstand mainly compression
stresses as the wing flexes upward during flight, 7075-T6 is most
often used. 7075-T6 is also used extensively for military fighter
aircraft structures, which generally have stiffer wings and -- except
for the cockpit area -- an unpressurized fuselage. 7075-T6 is
almost twice as "strong" as 2024-T3, and therefore the weight can
be reduced correspondingly in suitable application.
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Aluminum Alloy Groups
 Group 1000
 Group 2000
 Group 3000
 Group 4000
 Group 5000
 Group 6000
 Group 7000
contains 99% elemental aluminum
Copper as the major alloying element
Manganese as the major alloying element
Silicon as the major alloying element
Magnesium as the major alloying element
Magnesium and Silicon as the major alloying
elements
Zinc as the major alloying element
Basic Tempers used for aluminum alloys
 O Annealed
 F As fabricated
 H Strain hardened
 T Heat treated (all aluminum alloys used in primary aircraft
applications are the heat treated tempers)
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A typical heat treat designation for an extrusion is shown below:
7050-T6511
T6 - type of heat treatment (6=solution heat treated and
artificially aged)
5 - means materials has been stress relieved
1 - material was stretched to accomplish stress relief
(2 if compressive methods are used)
1 - indicated minor straightening was used to meet straightness
and flatness tolerances (0 if straightening is not allowed)
See MIL-HDBK-5 for complete description of symbols used.
Group 2000 - Primarily used in tension applications where fatigue
and damage tolerant design is critical, e.g., lower
wing surfaces, pressurized fuselage skin, etc.
Group 7000 - Primarily used in compression applications where
fatigue and damage tolerant design is not critical,
e.g., upper wing surfaces, wing ribs, floor beams,
etc.
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Stress-Strain Curves
Uniaxial tensile and compression tests are generally performed to
obtain the following basic mechanical properties:
E
Ec

Fty
Ftu
Fcy
Fcu
 u (or eu )
Young's modulus in tension
Young's modulus in compression
Poisson's ratio
yield stress in tension (defined by .2% offset)
ultimate stress in tension
yield stress in compression (defined by .2% offset)
ultimate stress in compression
strain when ultimate stresses is reached
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A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Ftu
Fty
Fpl
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Some Symbols, Abbreviations, etc. used in MIL-HDBK-5
E
Ec
Es
Et
e
ee
ep
F
Fty
Ftu
G
Modulus of elasticity in tension
Modulus of elasticity in compression
Secant modulus of elasticity
Tangent modulus of elastcity
Elongation in percent, unit deformation or strain
Elastic strain
Plastic strain
stress
Design tensile yield stress at which permanent strain is .002
Design tensile ultimate stress
Modulus of rigidity, shear modulus
t
c
u
y
subscript meaning tension property
subscript meaning compression property
ultimate property
yield property
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
A
B
S
L
LT
ST
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A basis for mechanical property values - at least 99% of the
population values will fall with a 95% confidence level
B basis for mechanical property values - at least 90% of the
population values will fall with a 95% confidence level
S basis for mechanical property values - minimum
guaranteed value and its statistical assurance level is
unknown
Longitudinal, or parallel to direction metal was worked
(grain direction) - greatest strength direction
Long Transverse, or perpendicular to grain direction (in the
long transverse direction) - second greatest strength
direction
Short Transverse, or perpendicular to grain direction (in the
short transverse direction) - weakest strength direction
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
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A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Fracture Toughness and Crack Growth Rate
 The toughness of a material may be defined as the ability of a
component with a crack or defect to sustain a load without
catastrophic failure.
 Material toughness is also known as the quality of a material to
resist failure in the presence of a fatigue crack.
 Fracture toughness and fatigue resistance must be considered
when designing tension components in an airframe.
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A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Consider a flat plate (thin or thick) with a
crack in it as shown (length 2a) and
subjected to a tensile stress. At the crack
tip, a stress concentration will occur. The
stress concentration can be characterized
by a stress intensity factor K  f ( , a) .
Through theoretical and experimental
work, one finds that K    a c . The
"constant" c depends on crack geometry
and location (centered crack, edge crack,
etc.); however, c  1.

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
Note that the units of K are ksi in (or equivalent).
Perform tests (theoretical and experimental) by applying tensile
stress until the crack grows in length. We find that this critical
stress intensity factor KC (when crack growth begins) varies with
plate thickness and with the material tested as shown below.
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Note that for "thin" plates, the stress state is plane stress and for
"thick" plates, the stress state is plane strain. We note that K
becomes constant at the extremes of plate thickness, and we call
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A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
these the critical stress intensity factor K IC for plane stress and
plane strain. Note that in this case, K IC is larger for 2024-T3 then
it is for 7075-T6 (for both thin and thick plates). The subscript I
denotes a mode I failure (pulling the crack apart).
What does all this mean from a design standpoint? Consider the
relation again:
KC    a
Material
Selection
Design
Stress
Allowable flaw size or
NDT flaw detection size
We see that a larger value of KC means that
 for a given crack length (a), a larger stress ( ) can be applied
before failure by fracture; or,
 for a given design stress ( ), the material can have longer
cracks before failure by fracture.
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A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
Thus,
 K IC represents the maximum stress intensity factor that would
cause failure.
 K IC also represents the fracture toughness of the material
(material's resistance to fracture).
 K IC is a material property.
There are three modes of failure that we can consider:
I - tensile mode
II - shear mode
III - tearing or
transverse shear
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Knowing K IC for a material and its design stress
( ys , yield stress in tension), we can "calculate" the
critical crack length aC at which the crack will grow.
Alternately, if we know the crack length, we can
determine the maximum stress that can be applied.
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
The data above can be plotted as below (Fracture stress as a
percent of Ftu vs. critical crack length.
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Note that as the crack length becomes small, the material has a
fracture strength that is almost 100% of its ultimate strength. As
the crack length increases, the fracture strength decreases.
We note again, that for a given critical crack length, a material like
2024-T3 has a greater fracture strength then does 7075-T6. Hence,
the reason that for pressurized fuselage cabins and lower wing
skins -- two areas prone to fatigue through the long-continued
application and relaxation of tension stresses -- 2024-T3 would be
preferred over 7075-T6.
Rule of thumb: As the yield stress  y increases, KC decreases.
Thus a very high strength material will generally have poor
fracture toughness properties. A low strength material (which
generally has a high ductility) will have better fracture toughness
properties.
Remember: Rules of Thumb can kill people. Know your stuff …
A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu)
It should be noted that the value of K IC will depended on the
direction in which the crack is oriented within a plate of
dimensions L, T and S.
In the figure to the right, the first
letter represents the opening
direction of the crack and the
second letter represents the
orientation of the crack length.
Thus TL means a crack will open
in the T direction and that the
crack length is oriented in the L
direction.
The table below gives values of
K IC for crack with various
orientations in the plate for
various materials.
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Consider a plate with a fastener hole subjected to cyclic tensile
load (cracks develop as shown). We can develop date that shows
how crack length will increase vs. number of cycles:
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What does this cyclic load data tell you?
 For a given number of cycles (for example, 12 x103 ), a crack
will grow longer in 7075-T6 then in 2024-T3.
 For any material, if sufficient load cycles are applied, the crack
will grow in length until it reaches the critical length aC , at
which point failure is eminent.
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Other factors to be considered in material selection:
 Corrosion and embrittlement properties
 Compatibility with other materials
 Environmental suitability
 Availability and cost
 Fabrication characteristics
We don't have time to consider these. Corrosion prevention and
control is an important issue. Control measures include paint
films, metal clading, and cadmium and chromium plating on steel
alloys.
Composite Materials - we will look at these later.
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Use the web resources! For example, from the AERO 405 link,
http://aero.stanford.edu/aa241/structures/structuraldesign.html, you
find the following:
Materials
Choice of materials emphasizes not only strength/weight ratio but
also:
Fracture toughness
Crack propagation rate
Notch sensitivity
Stress corrosion resistance
Exfoliation corrosion resistance
Acoustic fatigue testing is important in affected portions of
structure.
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Doublers are used to reduce stress concentrations around splices,
cut-outs, doors, windows, access panels, etc., and to serve as tearstoppers at frames and longerons.
Generally DC-10 uses 2024-T3 aluminum for tension structure
such as lower wing skins, pressure critical fuselage skins and
minimum gage applications. This material has excellent fatigue
strength, fracture toughness and notch sensitivity. 7075-T6
aluminum has the highest strength with acceptable toughness. It is
used for strength critical structures such as fuselage floor beams,
stabilizers and spar caps in control surfaces. It is also used for
upper wingskins.
For those parts in which residual stresses could possibly be
present, 7075-T73 material is used. 7075-T73 material has superior
stress corrosion resistance and exfoliation corrosion resistance, and
good fracture toughness. Typical applications are fittings that can
have detrimental preloads induced during assembly or that are
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subjected to sustained operational loads. Thick-section forgings are
7075-T73, due to the possible residual stresses induced during heat
treatment. The integral ends of 7075-T6 stringers and spar caps are
overaged to T73 locally. This unique use of the T73 temper
virtually eliminates possibility of stress corrosion cracking in
critical joint areas.
Miscellaneous Numbers
Although the yield stress of 7075 or 2024 Aluminum is higher, a
typical value for design stress at limit load is 54,000 psi. The
density of Aluminum is .101 lb / in^3
Minimum usable material thickness is about 0.06 inches for high
speed transport wings. This is set by lightning strike requirements.
(Minimum skin gauge on other portions of the aircraft, such as the
fuselage, is about 0.05 inches to permit countersinking for flush
rivets.
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On the Cessna Citation, a small high speed airplane, 0.04 inches is
the minimum gauge on the inner portion of the wing, but 0.05
inches is preferred. Ribs may be as thin as 0.025 inches. Spar webs
are about 0.06 inches at the tip.
For low speed aircraft where flush rivets are not a requirement and
loads are low, minimum skin gauge is as low as 0.016 inches
where little handling is likely, such as on outer wings and tail
cones. Around fuel tanks (inboard wings) 0.03 inches is minimum.
On light aircraft, the spar or spars carry almost all of the bending
and shear loads. Wing skins are generally stiffened. Skins
contribute to compression load only near the spars (which serve as
stiffeners in a limited area). Lower skins do contribute to tension
capability but the main function of the skin in these cases is to
carry torsion loads and define the section shape.
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In transport wings, skin thicknesses usually are large enough, when
designed for bending, to handle torsion loads.
Fuel density is 6.7 lb/gallon.