Stress Concentration

STRESS CONCENTRATION:

The concept of stress concentration or stress increase arises from an observation that at or near the periphery of a stress raiser, the stress increases markedly with respect to the nominal or average stress in that section.

Stress concentration factor, Kt, or theoretical stress concentration factor

Stress at or near the stress raiser or max. stress in section = ──────────────────────────────── Nominal or average stress in section

Stress raiser:

1. Gear teeth 2. Lugs 3. Holes in a plate or bar 4. Shouldered or stepped shafts 5. Grooved shafts 6. Flat bar 7. Keyways and splines 8. Bolt heads 9. Screw threads

Governing factors:

Kt is a function of (a) geometry of the primary component, (b) geometry of the stress raiser, and (c) natural of the applied load (direct axial, bending, or torsion).

Methods of accessing values of Kt :

(a) The most widely used of these are design charts. e.g. "Stress Concentration Design Factors" [by PETERSON]

These charts are in the form of graphs. (p.1005)

(b) Some nomograms or nomographs available in the literature. e.g. NEUBER's nomograms.

(c) Generation of governing equations based on collection of empirical data (applying relevant curve-fitting technique).

[Note]: (1) Stress concentration can be ignored for ductile material under static loading. (2) Stress concentration has to be considered for brittle material under static loading. (3) Stress concentration has to be considered for all materials under dynamic loading. (Notch sensitivity needs to be considered too.)

Notch Sensitivity

-- Not all materials have sensitive to the presence of notch,  the value of Kt is modified to a reduced factor Kf .

σmax = Kf σo

Max. stress in notched specimen K f = Stress in notch - free specimen

Kf = fatigue stress concentration factor, ------

Notch Sensitivity, q is defined as K f - 1 q = , 0  q  1 K t - 1

Therefore, Kf = 1 + q (Kt - 1)