Chapter IV Learning from Failure

Introduction “ The concept of failure is central to the design process, and it is by

thinking in terms of obviating failure that successful designs are achieved.

It has long been practically a truism among practicing engineers and

designers that we learn much more from failures than from success.

Indeed, the history of engineering is full of examples of dramatic failures

that were once considered as confident extrapolations of successful

designs; it was the failures that ultimately revealed the latent flaws in

design logic that were initially masked by large factors of safety and a

design conservatism that relaxed with time.”

Timoshenko History of Strength of Materials, 1953, New York, McGraw Hill.

Design Against Failure

Schematic of the design process for a generic engineering component.

The failure focus identifies the type (or mode) of failure the designer will focus on or specifically design against, given the material characteristic and the operating conditions of the component.

Engineering

Component

Failure Focus

GTE: Design Issues

Anatomy

Aerodynamics

Propulsion

Materials

Structural Integrity

Design Cycle

The Final Product

Crash of United DC-10

Modes of Failure

Ductile Failure

Brittle Failure

Fatigue Failure

Vibration and Resonance

Corrosion Failure

Creep Damage

Plastic Instability

Buckling

Transition Temperature

Failure Types

(a) Brittle fracture (b) Ductile fracture (c) Completely ductile fracture

Failure Types

Fracture :

The component breaks. This type of failure is generally signified by some active part of our component breaking under load.

Yielding :

The component sustains plastic, non-recoverable, deformation. This type of failure is most commonly localized and often leads to eventual rupture of the component.

Failure Types

Ductile Brittle

Ductile Failure Necking Void Nucleation Void Coalescence

Crack Propagation

Fracture

Ductile Failure

Brittle Fracture

Rapid Fractures (speed of sound)

Stresses Below Yield

Little or no Plasticity

Triggered from an Initiation site

Low Temperatures

High Strain Rate

Steels: B.C.C. VS F.C.C.

Phase Transformation (HAZ)

Brittle Fracture

• Flow chart of static failure analysis

Fatigue :

The component experiences a time dependent failure mechanism known as fatigue. This type of mechanism is still the subject of intense research, since it is not yet fully understood. Many engineering components are exposed to time dependent, dynamic, loading. Under these conditions the material of construction becomes tired and will fail at a significantly lower stress intensity than it could sustain in a static manner.

Buckling :

The component experiences a form of elastic instability with large lateral deflections under compressive loading. This type of failure is mostly experienced by slender columns under axial loads, and thin walled pressure vessels subject to external pressure (e.g. vacuum vessels). A component will buckle under a load significantly lower than the yield compressive load for the same component. Once buckled, the component can no longer sustain any significant load.

Fatigue Failure

Fatigue of Metals

Crack initiation and propagation. Cyclic or random loading. Thermo-mechanical loading. Fretting fatigue. Corrosion fatigue.

DeHavilland Comet Crash

First production commercial jet airliner.

Influenced modern aircraft

design by two failures. Within two years of service two

planes fell apart during ascent. After 60 design modification it

again resumes flight. Once again plane crashes after 30

minutes of flight. Airlines grounded, certificate of

airworthiness revoked and production line suspended.

Comet Crash-I

Comet Crash-I

Comet Crash-I

Fuselage was tested in pressurized water tanks. Evidence of fatigue cracking was found that originated from the aft lower corner

of the forward escape hatch and also from the right-hand aft corner of the windows.

These locations feature sharp right hand corners which cause local areas of high

stress-concentration.

Creep :

At elevated temperatures there is long-term, relatively slow, plastic deformation of the component under steady load. The effect is attributed to the fact that key material properties such as yield strength and ultimate tensile strength are generally obtained from tests of the material at ambient temperatures. Loaded components exposed to higher temperatures, such as gas turbine blades, or heat exchanger piping, suffer this type of slow deformation.

Excessive deflection :

The component experiences elastic or plastic deformation beyond some permitted bound. The technical term for this type of failure is excessive-deflection.

Wear is the progressive damage, involving material loss, which occurs on the surface of a component as result of its motion relative to the adjacent working parts. John Williams

Wear

Wear Depends

Geometry of the surface

Applied load

The rolling and sliding velocities

Environmental conditions

Mechanical, Thermal, Chemical and Metallurgical properties

Physical, Thermal and Chemical properties of the lubricant

Type of Wear

Abrasion Wear

Abrasive wear occurs when a harder material is rubbing against a softer material

Ref.: www.substech.com

Two Body Wear

Three Body Wear

Abrasion Wear Gouging abrasion Large particles High compression loads High stress or grinding abrasion Smaller particles High compression load Low stress or scratching abrasion No compression load Scratching abrasion while material is sliding Polishing abrasion

Ref.: www. mesto.com

The impingement of solid particles, or small drops of liquid or gas on the solid

surface cause wear what is known as erosion of materials and components.

Advantages Cutting, drilling and polishing of brittle material

Ref.: dcu.ie/~stokesjt/Thermal Spraying/Book/Chapter1

Erosion Wear

Solid Particle Erosion Surface wear by impingement of solid particles carried by a gas or fluid. e.g. Wear of helicopter blade leading edges in dusty environments. Liquid Drop Erosion Surface wear by impingement of liquid drops. e.g. Wear of centrifugal gas compressor blades by condensate droplets. Cavitation Erosion Surface wear in a flowing liquid by the generation and implosive collapse of gas bubbles. e.g. Fluid-handling machines as marine propellers, dam slipways, gates, and all other hydraulic turbines.

Type of Erosion Wear

Two bodies sliding over or pressed into each other which promote the material transfer from one to another.

𝑉

𝐿= 𝐾

𝑃

3σ𝑦

Where V = wear volume L = sliding velocity P = applied load σy = yield stress of softer material K = wear coefficient

Ref.: www.substech.com

Friction/Adhesive Wear

Galling wear : Severe adhesion actually leads to material flow up from the surface.

Galling Wear

Fretting wear of splined shaft– small oscillatory motion abrades surface – looks like rust – surface looks pitted.

Fretting Wear

Surface fatigue: Two surfaces contacting to each other under pure rolling, or rolling with a small amount of sliding in contact. Contact fatigue: As one element rolls many times over the other element Maximum shear stress is higher than fatigue limit

Ref.:W.A. Glaeser and S.J. Shaffer, Battelle Laboratories

Pitting surface fatigue : large roller thrust bearing race, compressive stress developed between roller bearing and race pitting. Material actually fatigued and removed from surface!!

Pitting Wear

Brinelling : brinelling of

bearing race due to static

overload. Note brinelling more

of a static failure (indentation)

versus fatigue or wear failure.

Brinelling Wear

A wear process where a material loss from the surface by forces of another surface acting on it in a sliding motion in the form of thin sheets.

Mechanisms of delamination wear Plastic deformation of the surface. Cracks are nucleated below the surface. Crack propagation from these nucleated cracks and joining with neighbouring one After separation from the surface, laminates form wear debris

Ref.: K Kato, M Bai, N Umehara, Y Miyake

Delamination Wear

Material Selection

Durability :

Matching of dominant or primary criteria such as strength, hardness, elastic behavior, toughness, magnetic, electric & thermal properties.

Longevity:

Depends on corrosion & heat resistance as well as resistance to wear, dynamic loading, shock, creep and stress corrosion.

Manufacturability:

Refers to castability, machinability and surface finish requirements.

Stress

Principal Stresses

For any state of stress, we can find a set of planes on which only normal stresses act and the shearing stresses are zero.

Called Principal Planes and the normal stresses acting on these planes are Principal Stresses denoted as σ1, σ2 and σ3.

Convention, σ1> σ2 > σ3.

The principal directions are orthogonal to each other.

Ductile vs. Brittle Material

Ductile material : Well defined yield point– Failure on yielding.

Brittle material : No yield point & sudden failure – Failure on failure load.

Theories of Failure

Max. principal stress theory – Rankine Max. principal strain theory – St. Venants Max. strain energy – Beltrami Distortional energy – von Mises Max. shear stress theory – Tresca Octahedral shear stress theory

Important Parameters

Maximum Principal Stress

Maximum Shear Stress

Maximum Principal Strain

Maximum Principal Stress Theory

Maximum principal stress reaches tensile yield stress (Y).

Estimate principal stresses σ1, σ2 & σ3.

Apply yield criteria:

Maximum Principal Strain Theory Failure occurs when maximum value of applied strain exceeds

the strain value corresponding to yield point of the material.

If ‘Y’ is the yield stress then under uni-axial loading yield strain is defined as

εy = Y/E

Maximum strain developed in the design component should be less than εy.

Principal stresses σ1, σ2 & σ3 corresponds to principal strains ε1, ε2 & ε3 .

Strain Energy Theory

Failure at any point in a body is defined when the energy density in the body at the applied load equals the energy density corresponds to the elastic limit of the material.

Uni-axial loading :

i. σ = Eε ( Hooke’s Law)

ii. Strain energy density :

Body subjected to principal stresses :

For the onset of yielding :

Yield function

U=1/2E [σ12 + σ2

2 + σ32 - 2 ν (σ1σ2 + σ2σ3 + σ1σ3)]

Y2/2E=1/2E [σ12 + σ2

2 + σ32 - 2 ν (σ1σ2 + σ2σ3 + σ1σ3)]

von Mises Criteria (Distortion Energy Criteria)

Failure occurs when equivalent stress (von Mises stress) reaches the yield stress of the material.

von –Mises yield criteria also suggests a failure or yielding when the elastic energy of distortion reaches a critical value. von Mises criteria is also known as maximum distortion energy criteria.

Tresca Theory (Maximum Shear Stress Theory)

Failure/yielding occurs when the maximum shear stress at a point equals the maximum shear stress at yield.

Maximum shear stress less than 0.5 Y (No failure).

Shear stress yield = 0.5 (Tensile stress yield)

Tresca Theory (Cont…)

In terms of principal stresses σ1, σ2 & σ3 .

Maximum shear stresses.

Yield function :

The Design Problem

(a) Use any necessary assumptions to estimate the maximum

bending moment experienced by the arm when the table is

subjected to your chosen value of the design force, W.

Aeroplane service table (schematic, not to scale), dimensions in mm

(b) Is a failure predictor (theory of failure) required in order to

predict the failure of these arms by yielding? Why or why not?

(c) List the possible modes of failure for the major elements of the service

table.

(d) On the basis of reasoned argument, decide upon a suitable factor of

safety to be used in the design of the arm to resist yielding in bending.

Tabulate your calculation. Does the resulting factor of safety seem

reasonable?

(e) Design the arm to resist yielding. Ignore details of the end

connections.

(f) To ensure the suitability of the table for certain uses (e.g. meals

and writing), it is desirable not only that the table and its

support arms avoid any gross structural damage, but also that

the vertical displacement of the table's near edge under the

design loads be kept to within, say, 10 mm. Indicate the method

by which you would incorporate this second mode of failure

into your design process. There is no need to perform the

calculations for this part of the design.

(g) Suggest reasons why designers might take more care with such

devices than with (say) the design of seats in railway carriages

or street-cars (trams) for structural integrity.

Project Title" AIRLINE SERVICE TRAY” (a) Estimation of design force W & maximum bending moment

Wide range of service loads involving a fair amount of educated guesswork. Begin by tabulating some likely forces to get a feel of magnitude of W

Source of load Range Force

Meal tray < 5kg 50 N

books < 1kg 10 N

Writing activity 20 N

Elbow (proportion of torso weight) ~ 100 N

Briefcase/travel bag ~20 kg ~200N

Sitting ~100 kg ~1000 N (excessive)

On the basis of the above list choose W=200/2=100 N (note: Since we are designing one of the table arms, so the design force W needs to be force on one arm, hence the division by 2.)

Force estimation

Moment Estimation

Arbitrarily/conservatively

choose the line of action of

vertical force W to be 50

mm from the outer tip of

the unfolded table (i.e. 600

mm from the lower hinge)

MP = 100 N x 300mm = 30x10 3Nmm MQ = 100N x 600mm = 60x10 3Nmm

(Note: moment varies along arm PQ and is maximum at Q)

(b) Comments on need for a theory of failure

No, a theory of failure(i.e. a means for combining the various stresses in a multi axial

stress situation into a single quantity to be used for predicting failure) is not necessary

here.

This is because the table arms are subjected only to BENDING stresses, which are

uniaxial.

Laboratory tests (to determine Sy) can be applied directly.

The component will begin to yield when the bending stress equals the yield stress Sy.

Note: The above statement assumes that shear stresses are negligible compared to

bending stresses. An experienced designer will usually make this assumption for long

beams like the table arms. Its validity can be checked latter.

If shear stresses are not ignored, then the stress situation is multi axial, and theory of

failure would be needed to predict the onset of yielding.

Theories of failure such as maximum shear stress (Tresca) and maximum shear strain

energy (Von Mises) can be used.

(c) Possible modes of failure for service table

Yielding of table top in bending

Fracture of table top in bending

Yielding of supported arm in bending

Fracture of supported arm in bending

Shearing failure of hinge pin at Q.

Shearing failure of hinge pin at P.

Tearing (shear failure) of slot at “P”

Compression failure of reaction point at “Q”

Excessive deflection of table (vertical).

Excessive deflection of table (lateral sway)

Buckling of lower (compressive) flange of arm.

Excessive friction in hinges.

Factors of Safety

Design factor of safety (Fd) is used for handling systematically the many and varied uncertainties associated with specific design situation.

Commonly Fd is applied to design in two ways:

i. Reduce the known strength (Sy/Fd)

ii. Increase the predicted load (Fd x W)

The choice of a proper Fd is entirely the result of good engineering judgment.

A General Rule(Fd) Stationary structures and components (e.g. pressure vessels

and their supporting structures) Fd 2 to 4.

Components where mass and inertia are criteria of operational performance (I.C. Engines), the constitutive models of structural performance are generally more precisely determined. Moreover, substantial care is taken to select and test material properties. (Fd 1.5 to 2)

Steel ropes made up of many strands of high tensile steel wire are used in cranes or in structural support applications, where failure could be life threatening. (Fd 12)

These thumb rules are the result of considerable experience in the design of engineering structures and components.

Estimation of Safety Factor

In the following determination of Fd, the main issue is that

the size of the sub factors l1,l2,l3,s1,s2,s3…s5 depends in each

case upon the level of uncertainty concerning the relevant

quantity, not upon the magnitude of the quantity itself.

Values given on next slide are subjective estimates, lying

within ranges commonly used.

Factor Relevance to design Range of values

Value

Fo Seriousness of failure 1.0-1.4 1.0

Uncertainties associated with load estimates l1 Magnitude of load 1.0-1.6 1.5

l2 Rate of loading 1.2-3.0 1.3

l3 Load sharing 1.0-1.6 1.5

Material and modeling related uncertainties s1 Variation in material properties 1.0-1.6 1.1

s2 Manufacturing uncertainties 1.0-1.6 1.1

s3 Environmental, Operational 1.0-1.6 1.1

s4 Effects of stress concentration Can be high 1.5

s5 Reliability of mathematical model 1.0-1.6 1.5

Fd=F0 x l1 x l2 x l3 x s1 x s2 x s3 x s4 x s5 = 6.42 =6.0

Estimation of Fd

Bending of Beam

Pure bending results in circular arc deflection.

R is radius of arc.

ϴ is the arc in radians.

c is the distance from n.a. to extreme fiber.

fmax is maximum normal stress in extreme fiber.

M is the bending moment.

I is moment of inertia.

𝑓𝑚𝑎𝑥 = 𝑀𝑐

𝐼

𝑀

𝐼=

𝑓

𝑐=

𝐸

𝑅

Design Arm Against Yielding

𝐷𝑒𝑠𝑖𝑔𝑛 𝑖𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦: 𝜎𝐵,𝑀𝑎𝑥 ≤ 𝑆𝑦

𝐹𝑑

𝜎𝐵,𝑀𝑎𝑥 = maximum bending stress in the arm.

Max. bending stress occur at the outer fibers of arm.

𝐼𝑛 𝑔𝑒𝑛𝑒𝑟𝑎𝑙, 𝜎𝐵 = 𝑀𝑦

𝐼𝑥𝑥

Bending stress will vary along the length of arm, due to variation in M,y and Ixx.

𝑀 = 60 × 103N.mm

Design of the arm is to calculate ‘t’.

Express Ixx in terms of ‘t’.

y=15mm

d=30mm

b=20mm

x x

t

𝐼𝑥𝑥 = 𝑏𝑑3

12−

𝑏𝑜𝑑3

12=

𝑏𝑑3

12−

𝑏−𝑑 𝑑−2𝑡 3

12

𝑀𝑦𝑚𝑎𝑥

𝐼𝑥𝑥 ≤

𝑆𝑦

𝐹𝑑

𝐼𝑥𝑥 ≥ 𝐹𝑑𝑀𝑦𝑚𝑎𝑥

𝑆𝑦

𝐼𝑥𝑥 = 6×6×103×15

145= 37242𝑚𝑚4

t = 6mm

Bicycle Crank Spider Arm

Cup and Cone Dimples Dull Surface Inclusion at the bottom of the dimple

Ductile

Shiny Grain Boundary cracking

Brittle Intergranular

Shiny Cleavage fractures Flat

Brittle Transgranular

Beachmarks Striations (SEM) Initiation sites Propagation zone Final fracture zone

Fatigue

Mode of fracture Typical surface characteristics

S-N Curve

Some materials, such as steel, show an endurance limit stress below which the fatigue life is essentially infinite. Other materials may not show such behavior but an effective endurance limit may be specified at some large number of cycles.

Haigh Diagram

Fatigue test using a non-zero mean stress are often presented in a Haigh diagram.

Design Against Fatigue

Modern bicycle wheels are complex structures of a hub, a light rim and spokes (36).

Each of these spokes are pretension by means of a small threaded nut, so that net compression of any spoke is avoided.

Design spokes against fatigue failure

Load Distribution in Spokes

Load P is acting between hub & ground.

Spokes directly above hub experience

an increase in tensile force, ΔT = λ1P.

Spokes below experience decrease of

tensile force, ΔT = λ2P.

Horizontal position ΔT = 0.

λ = f (#, geometry, pattern dim spokes).

λ1 = + 0.04 & λ2 = -0.08

The Design Problem

a. Determine the values of initial (pretension) force To, which could be

needed to ensure that the tension T in the spokes is always greater

than 0.3To.

Solution:

Design for worst case:

Weight of the rider =95 kg.

Center of mass nearest to the rear wheel (x=0.40L)

𝑆𝑈 = 880 𝑀𝑃𝑎 𝑆𝑌 = 880 𝑀𝑃𝑎 E = 880 𝑀𝑃𝑎

Taking moments about the front axle:

𝑃 = 𝑊𝐿−𝑥

𝐿

𝑃 = 95 × 9.81𝐿 − 0.4𝐿

𝐿

P = 559 N

λ1 = +0.04 (Upper spokes)

λ2 = -0.08 (Lower spokes)

∆𝑇𝑢𝑝𝑝𝑒𝑟 = 𝜆1𝑃

∆𝑇𝑢𝑝𝑝𝑒𝑟 = 0.04 × 559 = 𝟐𝟐. 𝟒𝑵

∆𝑇𝑙𝑜𝑤𝑒𝑟 = 𝜆2𝑃

∆𝑇𝑙𝑜𝑤𝑒𝑟 = −0.08 × 559 = −𝟒𝟒. 𝟕𝑵

𝑇𝑚𝑎𝑥 = 𝑇𝑜 + ∆𝑇𝑢𝑝𝑝𝑒𝑟

𝑇𝑚𝑎𝑥 = (𝑇𝑜+22.4)𝑁

𝑇𝑚𝑖𝑛 = 𝑇𝑜 + ∆𝑇𝑙𝑜𝑤𝑒𝑟

𝑇𝑚𝑖𝑛 = (𝑇𝑜−44.7)𝑁

𝑇𝑎𝑚𝑝 = 𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛

2= 33.5 𝑁

Tamp is the load amplitude on the spokes.

Require 𝑇 ≥ 0.3𝑇𝑜 in order to provide some safety against compression &buckling .

0.3 To = Tmin

To = 63.9 N

RMS Titanic

The Royal Mailing Steamer Titanic was a British passenger ship, which sank on April 15 1912 in North Atlantic ocean.

Titanic Statistics

883 ft long, 93 ft beam wide.

61 ft from waterline to boat deck.

One of the fastest ships.

Built by Harland & Wolff in Belfast.

She was the Largest ship in the world.

Licensed to carry 2603 passengers.

Crew of 944 (3547 in all).

Titanic Unsinkable She was made of medium carbon steel.

She was fitted with 16 transverse separate water-tight compartments (bulk-heads).

Each compartment can be rendered water-tight quickly by closing of water tight doors.

Contain and isolate incoming water in case of puncture (Olympic and Britannic).

Titanic Stuck in Iceberg

Titanic Sinks

Titanic Struck an iceberg on April 14,1912.

153 km south of NF.

The unsinkable sank early next morning.

Over 1500 died.

Reasons of Collapse

How Titanic Collapse

Why Failed ?

Use of medium carbon steel with low transition temperature.

Brittle Fracture.

Square Hatches.

Welded Vs. Riveted.

Design of Ship (Sagging Vs. Hogging).

Equilibrium.

Sagging

Hogging

Why Failed ?

Inadequate lifeboats.

Self-confidence and arrogance off British Ship Building Engineers was a major contributing factor to the sinking of the Titanic.

Lessons Learned

Improved Designs: CAD/CAM

Advances in Materials

Radar can give ships a visual picture of location relative to other ships.

Better weather forecasting

Better navigation systems

Iceberg patrols to warn ships

Advanced satellite communications

Liberty Ships

History of Liberty Ships

Allies Were Losing a Large Number of Transport Ships due to Aerial Assaults, Mine Fields and U-Boat Attacks

Lend-Lease Act: President Roosevelt Announced a $350 million Emergency Shipbuilding Program.

Between 1941-1945, 2751 were built. Cost $127k each.

Liberty Ships

1. Riveted vs. welded structure. 2. environmental consideration.

Lessons Learned

Improved Design.

Improved Material Properties.

Improved Fabrication Techniques.

Quality Assurance.

Skilled Labor

Failure of Tacoma Bridge

Tacoma Narrows Bridge Suspension bridge : cables anchored to earth in their ends and

supported by towers. TNB linked Tacoma and Gig harbor. Width 39ft, unsupported span 2800ft was necessary due to poor

bottom conditions and swift currents in Narrows. The stiffness girders were unusually narrow; 8ft in comparison

with their length. Depth to span ratio of 1/350 over twice that of Golden Gate

bridge. Width to span ratio 1/72, Golden Gate is 1/57.

On November 7, 1940 four months after opening violent oscillation led to the collapse.

Collapse of TNB

1. Collapse of TNB due to wind blowing

Lack of Bending & Torsional Rigidity

What Went Wrong ?

Resonance due to Turbulent Wind Blowing Over Bridge Deck (42 MPH).

Aerodynamic Instability (Negative Damping) Producing Self-Induced Vibrations.

Now, Wind Tunnel Testing is Compulsory.

The Challenger Disaster

The Challenger Disaster

What Went Wrong ?

Explosion caused failure of rocket booster due to failure of an O-ring as a result of cold temp.

Pressurized Joint Deflection

What Went Wrong ?

Engineers at Morton-Thiokol knew of potential failure of O-ring and notified VP Engineering months prior to launch and again on night before lift off, recommending no launch !!!

The Challenger Disaster: Reason

Managers consulted with NASA executives and voted to proceed responding to business and political pressures.

Engineer responsible for identifying concerns blew whistle in public

investigation; had career ruined and sued for damages.

Lessons Learned

The engineer has obligations.

Avoid conflict of interest.

Do not yield to management pressure.

Think! Think! Think of Consequences!

Effect of extreme temp on performance.

Document events/actions/decisions and meetings for future reference.