Sizing Procedures - Aerospace Engineering Courses …aeweb.tamu.edu/haisler/aero405/Lecture_Notes/A03... · Web viewCh. 4 - Material Properties, Airframe Stress Analysis and Sizing

A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu) 1

Materials & Material PropertiesCh. 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


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.


Aluminum Alloy Groups

Group 1000 contains 99% elemental aluminum Group 2000 Copper as the major alloying element Group 3000 Manganese as the major alloying element Group 4000 Silicon as the major alloying element Group 5000 Magnesium as the major alloying element Group 6000 Magnesium and Silicon as the major alloying

elements Group 7000 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)


A typical heat treat designation for an extrusion is shown below:

7050-T6511T6 - type of heat treatment (6=solution heat treated and

artificially aged)5 - means materials has been stress relieved1 - 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.


Stress-Strain Curves

Uniaxial tensile and compression tests are generally performed to obtain the following basic mechanical properties:

Young's modulus in tensionYoung's modulus in compressionPoisson's ratioyield stress in tension (defined by .2% offset)ultimate stress in tensionyield stress in compression (defined by .2% offset)ultimate stress in compression

(or ) strain when ultimate stresses is reached


tuF

tyF

plF


Some Symbols, Abbreviations, etc. used in MIL-HDBK-5

Modulus of elasticity in tensionModulus of elasticity in compressionSecant modulus of elasticityTangent modulus of elastcityElongation in percent, unit deformation or strainElastic strainPlastic strain

F stressDesign tensile yield stress at which permanent strain is .002Design tensile ultimate stress

G Modulus of rigidity, shear modulus

t subscript meaning tension propertyc subscript meaning compression propertyu ultimate propertyy yield property


A A basis for mechanical property values - at least 99% of thepopulation values will fall with a 95% confidence level

B B basis for mechanical property values - at least 90% of thepopulation values will fall with a 95% confidence level

S S basis for mechanical property values - minimum guaranteed value and its statistical assurance level is unknown

L Longitudinal, or parallel to direction metal was worked (grain direction) - greatest strength direction

LT Long Transverse, or perpendicular to grain direction (in thelong transverse direction) - second greatest strength direction

ST Short Transverse, or perpendicular to grain direction (in theshort transverse direction) - weakest strength direction







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.


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 . Through theoretical and experimental work, one finds that . The "constant" c depends on crack geometry and location (centered crack, edge crack, etc.); however, .

Note that the units of K are (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 (when crack growth begins) varies with plate thickness and with the material tested as shown below.


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


these the critical stress intensity factor for plane stress and plane strain. Note that in this case, 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:

We see that a larger value of 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.Thus,

Material Selection

Design Stress

Allowable flaw size or NDT flaw detection size


represents the maximum stress intensity factor that would cause failure.

also represents the fracture toughness of the material (material's resistance to fracture).

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

A03 - Ch. 4, Material Properties, Airframe Stress Analysis and Sizing (Niu) 19Knowing for a material and its design stress (

, yield stress in tension), we can "calculate" the critical crack length at which the crack will grow.

Alternately, if we know the crack length, we can determine the maximum stress that can be applied.


The data above can be plotted as below (Fracture stress as a percent of vs. critical crack length.


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 increases, 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 …


It should be noted that the value of 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 for crack with various

orientations in the plate for various materials.



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:


What does this cyclic load data tell you? For a given number of cycles (for example, ), 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 , at which point failure is eminent.


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.


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 toughnessCrack propagation rateNotch sensitivityStress corrosion resistanceExfoliation corrosion resistance

Acoustic fatigue testing is important in affected portions of structure.

http://aero.stanford.edu/aa241/structures/structuraldesign.html


Doublers are used to reduce stress concentrations around splices, cut-outs, doors, windows, access panels, etc., and to serve as tear-stoppers 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


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.


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.


In transport wings, skin thicknesses usually are large enough, when designed for bending, to handle torsion loads.

Fuel density is 6.7 lb/gallon.

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Sizing Procedures - Aerospace Engineering Courses …aeweb.tamu.edu/haisler/aero405/Lecture_Notes/A03... · Web viewCh. 4 - Material Properties, Airframe Stress Analysis and Sizing