STRESS CONCENTRATION

FACTORS CLASS NOTES FOR

MECHANICAL ENGINEERING

It is increase in stress due to a

discontinuity in a body under loading.

Discontinuities are quite common.

Stress increase depends on the type

and extent of a discontinuity.

  Stress increases due to the following discontinuities. 

(i)                 Key seat in a shaft

(ii)               Threads on a bolt

(iii)             Oil holes in a machine part

(iv)              Notch in a machine part

(v)                Groove in a machine part

(vi)              Tool mark(s)

(vii)            Scratches

(viii)          Fillets

(ix)              Splined shaft

(x)                Flaws or inclusions

(xi)              Abrupt change of cross section

(xii)            Dent(s)

Stress Concentration Factor, k

k=Stress at a discontinuity/stress based on net cross section at the discontinuity

k is always greater than 1

Stress concentration factor depends on the following criterions.

(i)                 Geometry of the discontinuity—It is called Form stress concentration factor

(ii)               Location of the discontinuity in the part

(iii)             Overall dimensions of the part

(iv)               Material(ductile or brittle)

(v)                Type of loading—It is called Load concentration factor

(vi)              Method of manufacture

The value of ‘k’ is different under different types of loading for the same continuity. The value of ‘k’ is also different for the same type of load when applied gradually/suddenly/impact load.

Firstly k_t is the stress concentration factor in tension

Secondly k_c is the stress concentration factor in compression

Thirdly k_b is the stress concentration factor in bending

Fourthly k_tor is the stress concentration factor in torsion

Fifthly  k_buck is the stress concentration factor in buckling

Sixthly k_fatigue is the stress concentration factor in fatigue (reversal loading)

k_complex is the stress concentration factor in complex loading (more than one type of load acting simultaneously)

DETERMINATION OF ‘k’

(i)                 For simple discontinuity—Empirical equations are available.

(ii)               For a complex discontinuity—It is found by photo-elasticity

(iii)             Standard graphs are available for few cases—refer Design of Machine Elements by Spott.

Empirical relation for an elliptical hole k = (1+2a/b) σ

Where ‘a’ is semi major axis of the ellipse

‘b’ is the semi- minor axis of the ellipse

If a/b is large, crack will develop

When a/b is small, k_t will be relatively small.

Further when  a/b = 1 it becomes a circle. The value of k becomes =3 i.e. stress concentration for a hole is 3 times the normal stress.

σ_{stress concentration} = 3 σ_{normal stress}

HOW TO ACCOUNT FOR STRESS COCEMNTRATION IN DESIGN

Design stress = σ_design= k σ_nominal

This design stress < a_llowable

σ_allow = (σ_yp/FOS)             for ductile materials

σ_allow = (σ_ult/FOS)             for brittle materials

Stress concentration is highly dangerous in case of brittle materials because of no stress redistribution. Stress concentration in brittle material causes a physical fracture.