# Stress-Strain at Notches by rt3463df

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```									         Stress Concentrations
• Stress concentrations:
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

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

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