dynamic loading

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Faculty of Aerospace Engineering

AE1202 Structures and MaterialsAE1202 Structures and MaterialsAE1202 Structures and MaterialsAE1202 Structures and Materials

03 Dynamic loadsIr. Vincent Brugemann

ALOHA AIRLINES, BOEING 737-200,

NEAR MAUI, HAWAII APRIL 1988 8000 meter

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Dynamic loads

• Two important types of dynamic loads:

• Fatigue

• Impact

• Related subjects that will be discussed:

• Stress variations

• Barely Visible Impact Damage

• Damage tolerance

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Cyclic bending loads

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• Cracks started at inner side of rim

• Promoted by wear

1998: InterCityExpressMunich to Hamburg

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Fatigue

• Dimensioning factor: number of cycles until failure

• Happens below yield stress

• Depends on:

• Type of fatigue load

• Constant

• Variable

• Stress level

• Frequency

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Fatigue loadVariable amplitude

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Fatigue loading Variable amplitude

•‘Flight cycle’ loading:

020406080

100120140160180200

0 5 10 15 20 25 30 35 40time [s]

stre

ss [M

Pa]

-40

-30

-20

-10

0

10

20

30

T [°

C]

stress [MPa] t [°C]

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Fatigue load Constant amplitude

• Parameters:

• Waveform (block, sine)

• Frequency

• Stresses (2 required)

• Maximum

• Minimum

• Amplitude

• Mean

• Stress ratio:

max

min

σσ=R

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average stresssigmam

Fatigue load Constant amplitude

• Wöhler curve (S-N curve)

Fatigue limit: the maximal stress level without any fatigue during the service life

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Three stages of fatigue

• Initiation of cracks

• We assume that there are no cracks present if we can not detect

them

• Crack growth

• Material property

• Failure (Residual fracture)

• Fracture toughness KIc

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Crack initiation metal

• Surface roughness and irregularities give a peak stress at the

surface that lead to microplastic deformations at the surface

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Crack initiation metal

• Micro-plasticity causes larger surface disturbances

• Increase of stress peaks, initiation of microcracks

first cycle second cycle

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Fatigue

• Electron micrograph of

• fatigue fracture surface

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Fatigue

~2mm

Cracks grow perpendicular to the loading direction

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Dynamic loads


• Fatigue

• Impact





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Impact

• The deformation process during the collision of two or more

objects

• Typical impacts causing damage to aircraft structures:

• Birds

• Missiles / Other airplanes

• Runway debris

• Hail stones

• Parts of aircraft

• Tools

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Impact: hailstrike (2003)

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Impact: Birdstrike and (Un)contained engine failure

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Birdstrike with leading edge of wing

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Blade off experiment

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Accident in 2000 with the ConcordeMost probable cause: impact of metal object in the fuel tank

Runway debris

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Impact process

• Impact speed: Speed of projectile at the point of impact

• Impact energy: Kinetic energy at the point of impact

• Strain rate: dε/dt caused by the impact in the material

impact velocity[m/s]

strain rate[s-1]

Physical material behavior

<50 <10 Mostly elastic, local plasticity50-500 10-103 Plastic

500-1000 103-104 Viscous material strength important1000-3000 105-106 Liquid behavior3000-12000 106-107 Hydro dynamic material behavior,

compressibility>12000 >107 Explosive impact, materials

transform to the gas phase

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Impact: energy transfer

• Kinetic energy of projectile transferred in:

• Kinetic energy of the structure

• Acoustic vibrations (noise)

• Deformation energy of the clamping of the structure

• Internal elastic and plastic energy

• Fracture energy

• Damping & Friction (transfer to heat)

• The amount of energy that a material will dissipate until fracture

is of importance

Sadegh

Highlight

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Energy dissipation of materials

material σultimate

MPaE-modulus

MPaεultimate

%Ufracture

10-3 J/mm

Aramid/epoxy 1400 62500 2.3 16.1E-glass/epoxy 1700 36500 4.6 39.1Carbon/epoxy 1500 150000 1.0 7.5Al 2024-T3 450 72000 12 56Glare 2 1230 65600 5.1 37.8

Ufracture: surface under stress-strain curve of a material

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Impact failure modes

delaminations

fracture by bending deformation

plugging

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Impact testing

• Impact test methods; high strain rate testing

• Materials:

• Charpy test

• Izod test

• Drop tower (~10 m/s)

• Air gun (~100 m/s or higher)

• Structures:

• Drop tower or air gun

• Determination of BVID

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Impact testing• Charpy and Izod test methods

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Drop tower (Vmax=10m/s)

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Air Gun

• Maximum speed about 100m/s

• Air guns can reach higher speeds (up to hypervelocity)

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Dynamic loads


• Fatigue

• Impact





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Stress concentrations

• Local disturbance, change in stiffness

• e.g. Holes, cut-outs, thickness changes, cracks

• Disturbance of stress flow

• Two types:

• Due to a geometrical notch

• Governed by Kt

• Stress concentrations

• Due to a crack

• Governed by K

• Stress intensity

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Stress concentrations

•Looking at any cross section of the sheet: • normal stresses are constant

• no stress concentrations

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Stress concentration factor Kt

Kt =σpeak

σnom

σnom =W

W-d S

σ

y

w

P

σpeakσnom

S

d

P

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Stress concentration

• Elliptical hole: • At point A: Kt = 1 +2a/b

• At point B: Kt = -1

W

For a round hole: Kt=3

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Question

• Calculate the stress concentration for these 3 cases:

Round hole

Kt=3 Kt=1+2d/3d=5/3

Ad

d

B d

3d

C

d

d/3

Oval holeh=3w

Oval hole3h=w

Kt=1+2*3d/d=7

K t = 1 +2a/b

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Question

• What if the height of the hole decreases to 0?

• In other words: when we get a crack in stead of a hole?

K t = 1 +2a/b

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Stress intensity

• Describing stresses around a crack tip in linear elastic materials

• Stress intensity (K) depends on:

• Crack geometry (Y)

• crack length (a)

• nominal stress (σ)

aYK ⋅= πσ

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Stress intensity factor

• Theory is only valid:

• For materials that are linear elastic until fracture

• When crack growth is perpendicular to the loading

• Crack growth rate at a certain K-value depends on material

aYK ⋅= πσ

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When will failure occur?

• When K reaches the critical value

• Fracture toughness (KIc) is a material property

• Specimen will fail when either:

• Critical crack length (acr) is reached for given stress

• Critical stress (σcr) is reached for given crack length

2

Icr

cr

I

σY

K

π

1aor

aπY

Kσ

cc

⋅=

⋅=

aπY

Kσ

cIcr ⋅

=

aYK ⋅= πσ

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Dynamic loads


• Fatigue

• Impact





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Impact damage Metals

• At low impact energy: dent

• At high impact energy: dent in combination with cracks (when

stress > σultimate on side opposite impact-side)

• With thick plate: plugging

• Damage can be detected easily

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Impact damage Composites

• Composites are sensitive for impact damage because of:

• relatively low interlaminar strength

• relatively brittle matrix and fibers

• Impact damage

• Low energy, Delaminations most on the side opposite the impact-side

• Higher energy, Delaminations, and fiber fracture due to the high

bending stresses

• Effect of impact damage:

• Reduction of compressive strength

• Poor detectability of low energy impact damage

• Design for damage tolerance

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Compression after impact

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Composites: BVID


• Impact energy below BVID level creates damage which is difficult to

detect => dangerous situation

• In case of damage below BVID, compressive stresses could lead to

unexpected failure of structure

• Design for compressive stress level at BVID

• Damage can be visibly detected and repaired

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Question

• Give examples of impacts on aircraft structures, two at low speed

and two at high speed

• Why is the speed range of an impact important?

Answers:1) Low speed: tool drop, airport collisions

High speed: bird impact, ballistic, engine explosion

2) The speed range governs the type of deformation Low speed: Elastic deformation dominatesHigh speed: Energy dissipation by plastic deformation and fracture

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Regulations

• Development of concepts

Safe Life

Damage Tolerance

Fail safe

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Damage Tolerance: The ability of the structure to sustain anticipated loads in the presence of fatigue, corrosion or accidental damage until such damage is detected through inspections or malfunctions and is repaired.

Fail-safe is the attribute of the structure that permits it to retain required residual strength for a period of un-repaired use after failure or partial failure of a principal structural element.

Safe life of a structure is that number of events such asflights, landings, or flight hours, during which there is a low probability that the strength will degrade below its design ultimate value due to fatigue cracking.

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Where to fit the B787 and the A350?

Safe Life

Fail safe

Damage Tolerance

No growth concepts…?

?

?

?

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Damage tolerance

• Damage resistance:

• Ability to withstand the formation of damage

• Damage tolerance:

• Effect of damage on the function of the structure

• Depends on properties of the structure & of the materials

• Residual strength:

• Strength of damaged structure

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Summary

• Fatigue

• Three stages: Initiation, crack growth, failure

• Occurs below the yield limit due to micro plasticity

• Impact

• Deformation process during collision

• Effect on structure is dependant on kinetic energy of bodies

• Alterations to the homogeneous stress state

• Concentration due to geometrical notches

• Intensity due to cracks

• Barely visible impact damage (BVID)

• Especially important for composite materials

• Design with the strength at BVID (when the damage becomes visible)

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dynamic loading

Documents

materialsae1202 structures

stress ratio

stress variations

peak stress

maximal stress level

type of fatigue

constant amplitude parameters

materials cracks