Experiment 1

Failure Criteria

and stress concentration

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

Maximum shear theory

A yS Case 1

Case 2

Case 3

Distortion energy theory

Von Mises stress

Plain stress or plain strain

In general form

Maximum normal stress theory

Coulumb-Mohr and modification

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

Various loadFatigue Testing

D=5mm or 10mm

Endurance limit for cast ir

on (Sn)

S’nSn

Sn

S’n

Correction of endurance limit

Stress concentration and stress raisers

• Stress concentration factor

max. local stress

nominal stressfK

Varying stress in machine element

max min

max min

2

2

a

m

S SS

S SS

Solving problems in which the stress is a combination of alternating stress and

constant stressFor compression mean load, no effect on endurance limit

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

Designing for variable load and finite life

How to raise the endurance strength

1. Autofrettage

2. Shot peening and surface rolling

3. Heat treatment

4. Laser treatment

5. Electro polishing

6. Others

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.

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

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.

1000

450

Fb FC

Torque

Fb=10kg

Fc=10kg

Torque=10 N-m

Material : ultimate strength = 400MPa

Yielding strength =250MPa

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).

150a m

N

S S

S MPa