Maximum Strain theory (Saint Venant) :

Maximum Strain theory (Saint Venant) failure condition:

when the maximum strain reaches the strain due to yield stress (tension) (or) Minimum strain reaches the strain due to yield stress (compression)Suman Suthari13Maximum Strain Energy theory(Haighs)Distortion Energy theory (Von mises & Hencky)11

Theory of fatigue and Design As earlier we have discussed the deigning of machine component against static loads (or) Dead load

It is difficult to design a machine component by using previous formulas when the component has discontinuity in cross section.

Dynamic loads are the loads whose magnitude and direction both can change w.r.t. time. Dynamic loadS:

Fluctuating stresses

Repeated stresses

Reversed stresses Fluctuating or Alternating Stresses :

These stresses varies in a sinusoidal manner with respect to time.

Fatigue Failure : The materials fail under fluctuating stresses at a stress magnitude which is lower than the ultimate tensile strength of the material.

Sometimes, the magnitude is even lower than the yield strength.

The phenomenon of decreased resistance of the materials to fluctuating stresses is the main characteristic of fatigue failure.

Fatigue failure are common are transmission shafts, connecting rods , gears , vehicle suspension springs and ball bearings.S.NO.Static FailureFatigue Failure1.Gradual applied loadCyclic load or Dynamic load2.Sufficient time to elongationNo noticeable elongation3.plastic flow prior to fractureBegins with crack then after failure takes place4. More lifeLess life5.Warns before failSudden 6.Design is simple as compareDesign is complex as many factors are involved The crack is more likely to occur in the regions are follows:

Regions of discontinuity , such as oil holes , key ways , screw threads etc.

34 Regions of irregularities in machining operations , such as scratches on the surfaces , stamp mark , inspection marks etc.

Internal cracks due to defects in materials like blow holes

The causes of stress concentration are as follows:

variation in properties of materials ex: internal cracks , blow hole

Load application on machine components at a point ( point load)

Ex: Meshing teeth of driving and driven gears

38 Ex: Contact between the cam and follower, Contact between rail and wheel

Contact between balls and races of ball bearings , Contact between crane hook and the chain

Abrupt changes in section

Ex: Gears, sprockets, pulleys , stepped shafts etc.

Discontinuities in the component Ex: oil holes, oil grooves, key ways , splines etc.

Machining Scratches

The chart for the stress concentration factor for a rectangular plate with hole

the stress concentration factor for a flat plate with a shoulder fillet

The stress concentration factor for a round shaft with shoulder fillet

(a) tensile force

(b) Bending Moment

(c) Torsional Moment

Theoretical stress concentration factor at the hole is

Reduction in Stress Concentration:

Additional notches and holes in tension member

Fillet radius undercutting and notch for member in bending

Drilling additional holes for shaft

Empirical relationship developed by HF Moore for the ratio c of torsional strength of a shaft having a keyway to torsional strength of a same sized shaft without key way is

Reduction of stress concentration in threaded members

Dd

Low Cycle and High Cycle Fatigue:

Low Cycle Fatigue

High Cycle FatigueStress cycles less than 1000Stress cycles more than 1000Failure of studs on truck wheel, setscrews, short lived such as missilesFailure of springs, ball bearings, gears etc.It involves plastic yielding at localized area of the componentsInvolves endurance strengthCan be ignored by taking suitable factor of safetyMust be considered and designed by using theories of fatigue failure

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