Stress-Strain at Notches by rt3463df

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									         Stress Concentrations
• Stress concentrations:
  Bolt holes, rivet holes, threads, fillets, radii,
  weld roots, pores, inclusions, surface
  scratches, etc. (Notch)
• The nominal (far field) strain may remain
  elastic in service, but the strains are often
  plastic in the notch roots.
             Stress Concentrations
• Most engineering components contain geometric
  design details that act as stress concentrations. Such
  details include fillets, rounds, bolt & rivet holes, welds,
  etc. Failure usually initiates at these locations since the
  “localized” stress is highest there.




       Stress flow lines showing the concentration of local
         stress at the tip of a groove in a tension member
     Stress Concentrations in an Airframe
                Holes
Rivets




Fillets
Stress Distribution & Stress Concentration
                                   m
                              Kt 
                                   o




           o=P/A
Stress
Distributions
Plane Stress –
Thin sections
Analytical Solutions for Kt
                    a
       Kt  1  2        ;
                    t
                             a
       if a  t , Kt  2
                             t
• Kt is the theoretical elastic stress
concentration factor (i.e.; Hooke’s law
assumed to apply - no localized yielding.)
•Both a and  are small compared to the
size of the component.
Try it!   Determine the stress concentration factors
          for the geometries shown below.



                              (i) A shallow blunt groove:
     w=100mm
                                 a = 5mm,  = 1mm

                              (ii) A deep sharp groove:
                        
                                 a = 10 mm,  = 0.1mm

                    a
  Ok…
                   a       5mm
 (i)   Kt  1  2    1 2      5.4
                          1mm
                                a  10mm
(ii)   since a   , K t  2   2        20
                                  0.1mm
In case one, the stress concentration factor is relatively
high. For most geometries encountered in practice, Kt < 3.
For case two, the groove is a crack-like defect, and needs
to be treated as a crack – Take a course in Fracture
Mechanics
    Handbook Kt for Common Geometries




Try it!               r 1.5          b 5
                              0.15;      3.33
Find Kt for r=1.5mm   h 10           r 1.5
b=5mm, and w=20mm.    Kt  2.3
               Determine the maximum local stress, , at
Try it!        the tip of a blunt notch in a flat tension bar
               made of SAE1045 steel, as shown below.
        5 kN
3                                   From previous slide
                             K t  2.3
                                      P       5000N
               5             Now,S                      167MPa
    5     10                          A (10)(3)mm      2


                            and,   K t S  2.3(167)  384MPa
                   3

          20            This is valid as long as Sy>384 MPa
                         For SAE1045 steel, Sy = 450MPa

        5 kN
Handbook Solutions for Kt
                  Peterson’s

                   Stress
                Concentration
                  Factors

               Walter D. Pilkey
               2nd ed, 1997 –
               John Wiley &
               Sons
Material Behaviour at Notch
           Root
        Localmaximum stress 
   Ks                     
           nominal stress    S
        Localmaximum strain 
   Ke                     
           nominal strain    e
    elastic behaviour :
      K t S;   K t e; K s  K e  K t
    elastic  plastic behaviour :
      K sS ;   K e e ;     and K e  K t  K s
Stress-Strain at Notches
     Solution For Notch Strain
         in Plastic regime
• Neuber’s rule:

             K t  Ks K e

• Glinka’s
                        
              (K t S)2
                          d
                2E       0
             Neuber’s Rule:

• If nominal strains remain elastic:
                K tS  E

• For REVERSED loading:
              K t S  E

								
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