Experiment 1 Failure Criteria and stress concentration.
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Transcript of Experiment 1 Failure Criteria and stress concentration.
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Experiment 1
Failure Criteria
and stress concentration
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Static failure criteria
0.05f
1. Ductile material ( )
Max. Shear theory
Distortion energy
Ductile Coulumb-Mohr
2. Brittle material ( )
Max. normal stress
Brittle Coulumb-Mohr and modification
0.05f
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Maximum shear theory
A yS Case 1
Case 2
Case 3
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Distortion energy theory
Von Mises stress
Plain stress or plain strain
In general form
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Maximum normal stress theory
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Coulumb-Mohr and modification
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S valueExternal load
For bending:
, therefore,
For torsion:
Tc= , therefore,
JFor axial load:
F= , therefore,
A
S
Mc IS
I c
JS
c
S A
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Various loadFatigue Testing
D=5mm or 10mm
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Endurance limit for cast ir
on (Sn)
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S’nSn
Sn
S’n
Correction of endurance limit
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Stress concentration and stress raisers
• Stress concentration factor
max. local stress
nominal stressfK
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Varying stress in machine element
max min
max min
2
2
a
m
S SS
S SS
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Solving problems in which the stress is a combination of alternating stress and
constant stressFor compression mean load, no effect on endurance limit
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2
Solderberg Diagram
1
Gerber line
1/ /
For shear load
1
m a
y n
m a
u n
ms as
ys ns
S KS
N S S
S KS
S N S N
S KS
N S S
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Designing for variable load and finite life
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How to raise the endurance strength
1. Autofrettage
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2. Shot peening and surface rolling
3. Heat treatment
4. Laser treatment
5. Electro polishing
6. Others
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Design Procedures
Static Load design1. Determine the external force, and configuration
of the structure.2. Determine the material of the structure.3. Find the equation(s) of the stress in the
structure.4. Determine the criteria of failure to be used.5. Find the S value of the structure.6. According to the S value find the appropriate
shape of the cross section.
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Design for the various load
1. Determine the type of the external force, and configuration of the structure.
2. Determine the material of the structure.
3. Use fully corrected endurance limit for bending, Sn.4. Apply stress concentration factors to torsion, bending and axial st
ress components.5. Multiply any alternating axial stress component by the factor .6. Enter the resultant stress in to a Mohr’s circle analysis and find th
e principle stresses.7. Find the Von mises alternating stress .
8. Find the Sa/N according the failure criteria used.
9. Compare Von mises stress with Sa/N to find the dimension of the part.
,
1
c ax
a
k
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Practices 1
1. Try to write an Excel program which can calculate the principle static stress, principle shear stress, Von Mises stress of a simply support beam of circular cross section under bending load, axial load and torsion load. (see figure in next page)
2. Use Distortion energy theory to find the dimension of the beam under the loads given in the figure in next page.
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1000
450
Fb FC
Torque
Fb=10kg
Fc=10kg
Torque=10 N-m
Material : ultimate strength = 400MPa
Yielding strength =250MPa
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Practices 2
1. Try to write an Excel program which can used the Solderburg Criteria to calculate Sa under different loading conditions and safety factor N.
2. Use Von mises stress to find the dimension of the beam under the loads given in the figure of practice 1. If all the load is varied as shown in figure (c) of following page. The surface of the beam is machined (please write a Excel program to do this).
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150a m
N
S S
S MPa