NOTCH SENSITIVITY- SIGNIFICANCE AND FACTOR

NOTCH : SIGNIFICANCE AND EFFECT ON DESIGN

NOTCH : Defined as a purposely introduced defect (usually U-shaped or V-shaped or circular shaped) on a planar machine component.

Therefore, it causes stress concentration on its own region.

Due to this, presence of Notch plays an important role in designing components in conditions of fluctuating/ fatigue loading.

STRESS CONCENTRATION IN FATIGUE LOADING – PRACTICAL STUDY AND OBSERVATION ANALYSIS

OBSERVATION: The actual reduction in endurance limit due to stress concentration came out to be less than the values analysed by the Theoretical stress concentration factor (K_t).

Therefore, an alternate factor came in introduction to account this reduction; called Fatigue stress concentration factor (K_f).

Theoretical stress concentration factor (K_t) K_t = σ_max/σ₀ = τ_max /τ₀

Fatigue stress concentration factor (K_f)

K_f = (Endurance limit of the notch free specimen) /(Endurance limit of the notched specimen)

K_f or Fatigue stress concentration factor has a practical significance and therefore observed in all actual materials. Value of K_f depends on the grain size of the material. Fine grained materials experience greater reduction in endurance limit than Coarse grained materials due to stress concentration.

NOTCH SENSITIVITY : DEFINITION AND SIGNIFICANCE

Defined as the susceptibility of a component to succumb to the damaging effects of stress causing notches in fatigue loading conditions.

Factor governing this effect came to be known as Notch Sensitivity Factor (q).

q = (Inc. of Actual stress over Nominal stress)/(Inc. of Theoretical stress over Nominal stress)

Now,

σ₀= Nominal stress (As obtained from elementary equations)

Actual Stress = K_f σ₀

Theoretical Stress = K_t σ₀

Inc. of Actual stress over Nominal stress= K_f σ₀ – σ₀

Inc. of Theoretical stress over Nominal stress=K_t σ₀ – σ₀

Therefore,

q = (K_f σ₀ – σ₀) / (K_t σ₀ – σ₀) = σ₀ (K_f – 1) / σ₀ (K_f – 1)= (K_f – 1)/(K_t – 1)

Above equation can be modified as:

K_f = 1+ q(K_t – 1)

CONCLUSION :

1) When the material has no sensitivity to notches :

q=0 and K_f=1

2) When the material fully sensitive to notches :

q=1 and K_f= K_t

The experimental values of q for Reversed axial & bending stresses & Reversed torsional shear stresses can be taken from the design charts as per given IN DESIGN DATA BOOK MANUAL as well as DESIGN OF MACHINE ELEMENTS : V B BHANDARI book.

IN CASE OF DOUBT IN VALUES, For safe design , we should always take q=1 and K_f= K_t.