Lecture 15 Fatigue of Engineering

Materials

Jayant Jain Assistant Professor,

Department of Applied Mechanics, IIT Delhi, Hauz Khas, 110016

Vibration and Resonance

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

Loading and unloading a part is never completely reversible energy is always lost this fact is

pronounced when loading is in vibration

Damping coefficient Measures the degree to which

a material dissipates vibrational energy

Loss coefficient Fraction of the stored energy not returned on

unloading

Applications in which resonance or fast elastic response is required (bells, high-speed relays and springs) require materials with low . Applications in which it is desirable to damp vibration (sound isolation of buildings, suppression of vibration in machine tools) use material with high .

Fatigue is failure that occurs in structures that undergo repeated cyclic stress, for example bridges and connecting rods

Fatigue

Bridge Connecting rod

Types of Cyclic Loading

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

(a) Low amplitude acoustic vibration (b) High-cycle fatigue: cycling below the yield strength (c) Low-cycle fatigue: cycling above the yield strength but below the the tensile strength

High-cycle fatigue loading is most significant in engineering terms

Fatigue

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

Depends on the amplitude of the stress and the number of cycles Loading cycles can be in the millions for an aircraft; fatigue testing must employ millions of fatigue cycles to provide meaningful design data

Fatigue failures occur due to cyclic loading at stresses below a materials yield strength

Fatigue test

A common method of testing fatigue resistance is the Wohler rotating rod test. One end of the specimen is mounted in a rotating chuck and a load suspended from the other end. The specimen experiences cyclic forces, from tension to compression in a sinusoidal cycle, as it rotates.

S-N Curves

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

Fatigue characteristics are measured and plotted on S-N curve

Endurance limit e: stress amplitude below which fracture does not occur at all or only after a very large number of cycles (>107)

R value of -1 indicates the mean stress is zero

Fatigue of cracked components

Large structures-particularly welded structures such as bridges, ships, oil rigs and nuclear pressure vessels always contain cracks All we have to make sure that the size of these cracks is less than the critical crack size to avoid any catastrophic failure We need to determine the safe life of the structure i.e. how many number of cycles structure can last prior to failure

Fatigue of cracked components

Cyclic stress intensity factor

Its value increases with time because

crack grows in tension

Because cracks don't

propagate in compression

Fatigue crack-growth rates for

precracked material

Fatigue of cracked components

Crack growth rate is give by;

a0 and af is the initial and final

crack length. At af crack becomes

unstable

We now have an expression for the fatigue life of a component

Catastrophic failure

occurs when Kmax = Kc

Threshold value: below which

crack does not grow

Typical

values of

m = 2.5-6

Paris

region

Fatigue mechanism: LCF

Uncracked component

General plasticity roughens the

surface and a crack forms there

propagating along a slip path and

then by the mechanism normal

to the tensile axis

Intrusions and protrusions: Crack

nucleating sites

LCF: Plastic strains > elastic strains

app

> Y

How cracks form in high-cycle fatigue

When the stress is below the general yield Any notch, scratch or change of section stress concentrates there A crack initiates in the zone of stress concentration Sudden changes of section or scratches are very dangerous in HCF

Fatigue mechanism: HCF

Uncracked component HCF: Elastic strains > Plastic strains

app <

Y

Question

A high strength steel plate is subjected to fatigue with a maximum tensile stress of 120 MPa and a minimum compressive stress of 40 MPa. If the edge crack length is 5 mm and fracture toughness of steel plate is 70 MPam1/2, estimate the fatigue life. The Value of constant C can be taken as 1.5x10-9 and m = 3.