Concept of Stress Concentration

1
Concept of Stress Concentration
Kt is used for normal stresses and Kts for shear
stresses.
2
Concept of Stress Concentration
Consider an elliptical hole in an infinitely
large plate loaded in uniform tension. Using the
theory of elasticity the theoretical stress
concentration factor is given by the equation
below.
2b
2a
Elliptical hole

• For a circular hole Kt 3

• The equation can be applied to a longitudinal
  crack where b ltlt a

3
Stress Concentration Factor
Stress concentration factor is found using
experimental methods.

• Photoelasticity a plane polarized light is
  passed thru a photelastic material (all
  transparent plastics) resulting in a colorful
  fringe pattern indicating the intensity of the
  stress.

4
Stress Concentration Factor

• Brittle Coating a specially prepared lacquers
  are usually applied by spraying on the actual
  part. After air drying, the part is subjected to
  stress. A pattern of small cracks appear on the
  surface. Data could be used to locate strain
  gages for precise measurement of the stress. The
  method is sensitive to temperature and humidity.

5
Stress Concentration Factor

• Electrical strain gauges

The method is the most popular and widely
accepted for strain measurements and stress
analysis. The strain gauge consists of a grid of
strain-sensitive metal foil bonded to a plastic
backing material. When the gauge is subjected to
a mechanical deformation, its electrical
resistance changes proportionally. The change in
voltage is converted to strain and the stress is
calculated from the strain.
6
Stress Concentration Factor

• Finite Element method

• The CAD model is subdivided into many small
  pieces of simple shapes called elements.

• FEA program writes the equations governing the
  behavior of each element taking into
  consideration its connectivity to other elements.

• These equations relate the unknowns, for example
  displacements in stress analysis, to known
  material properties, restraints and loads.

• The program assembles the equations into a large
  set of simultaneous algebraic equations
  (thousands or even millions).

• These equations are then solved by the program to
  obtain the stress distribution for the entire
  model.

7
Stress Concentration Factor
8
Stress Concentration Factor
Round section with a fillet
9
Stress Concentration Factor
Flat plate with a hole