1. Ken Youssefi Mechanical & Aerospace Engr., SJSU Discontinuity in Cross Section Stepped shafts Discontinuity

2. Ken Youssefi Mechanical & Aerospace Engr., SJSU Water filter fatigue failure Discontinuity in Cross Section Bracket with screw holes High stress

3. Ken Youssefi Mechanical & Aerospace Engr., SJSU Discontinuity in Cross Section Infrared analysis reveals the points of greatest stress on a Renault part’s surface caused by weld points and helps estimate fatigue limits for those critical areas (bottom).

4. Ken Youssefi Mechanical & Aerospace Engr., SJSU Discontinuity in Cross Section Bolt failure at the junction of the thread and solid section. Location of higher stresses. Discontinuity

5. Ken Youssefi Mechanical & Aerospace Engr., SJSU Concept of Stress Concentration Theoretical stress concentration factor, K t Maximum stress at the discontinuity Nominal stress, max stress with no discontinuity K t is used for normal stresses and K ts for shear stresses.

6. Ken Youssefi Mechanical & Aerospace Engr., SJSU 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. Elliptical hole 2b2b 2a2a For a circular hole K t = 3 The equation can be applied to a longitudinal crack where b << a

7. Ken Youssefi Mechanical & Aerospace Engr., SJSU 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.

8. Ken Youssefi Mechanical & Aerospace Engr., SJSU Photoelasticity Apparatus

9. Stress Distribution using Photoelasticity Method Ken Youssefi Mechanical & Aerospace Engr., SJSU

10. Ken Youssefi Mechanical & Aerospace Engr., SJSU 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 gauges for precise measurement of the stress. The method is sensitive to temperature and humidity.

11. Ken Youssefi Mechanical & Aerospace Engr., SJSU

12. Ken Youssefi Mechanical & Aerospace Engr., SJSU 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. R = ρL / A Resistivity Wire length Cross section Resistance

13. Ken Youssefi Mechanical & Aerospace Engr., SJSU Wheatstone Bridge Circuit Schematic 3-Element strain gauge Rosettes 0°/45°/90°

14. Ken Youssefi Mechanical & Aerospace Engr., SJSU

15. Strain gauges are placed a t the location of maximum stress Ken Youssefi Mechanical & Aerospace Engr., SJSU

16. Ken Youssefi Mechanical & Aerospace Engr., SJSU 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.

17. Ken Youssefi Mechanical & Aerospace Engr., SJSU Stress Concentration Factor Round shafts in axial Tension

18. Ken Youssefi Mechanical & Aerospace Engr., SJSU Stress Concentration Factor Round section with a fillet Bending Torsion

19. Ken Youssefi Mechanical & Aerospace Engr., SJSU Stress Concentration Factor Flat plate in Tension with a hole Flat plate in Bending with a hole