failure theories

Topics: Elasticity, Fatigue, Materials science Pages: 39 (2806 words) Published: October 9, 2013
Design of Machine Elements, July - Nov 2013

Design of Machine Elements, July - Nov
2013
ME3350
Narasimhan Swaminathan: n.swaminathan@iitm.ac.in
Indian Institute of Technology Madras - Chennai 600 036

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Design of Machine Elements, July - Nov 2013

Outline

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Design of Machine Elements, July - Nov 2013
Failure of materials

Outline I
1

2

Failure of materials
Classification
Failure of Materials
Ductile materials
Von-mises criterion
Factor of safety in Von-mises criterion

3
4

Mohr and Mohr-Coulomb theory for Ductile materials
How to decide if material is ductile or brittle?
Brittle materials
Dowling factors to predict failure in brittle materials

5

6
7

Stress concentrations
Stress concentrations
Problem
solution
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Design of Machine Elements, July - Nov 2013
Failure of materials

Outline II
8

Fatigue

9

Life

10

Stress-Life approach (High fatigue limits)
Corrections to fatigue strengths
Stress concentration in fatigue and notch sensitivity
Applying Stress concentration in Fatigue

11

Effects of mean stresses

12

Designing for high cycle fatigue with mean stress

13

Finding factor of safety with Good man diagrams
Multiaxial fatigue

14

Fracture mechanics

15

References
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Design of Machine Elements, July - Nov 2013
Failure of materials
Classification

Classification Recap
Loads
1
2

Static loads
Dynamic loads - Fatigue

Geometry
1

Flawed materials - Static loads and Dynamic loads

Materials
1
2

Ductile
Brittle

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Design of Machine Elements, July - Nov 2013
Failure of Materials

Outline I
1

2

Failure of materials
Classification
Failure of Materials
Ductile materials
Von-mises criterion
Factor of safety in Von-mises criterion

3
4

Mohr and Mohr-Coulomb theory for Ductile materials
How to decide if material is ductile or brittle?
Brittle materials
Dowling factors to predict failure in brittle materials

5

6
7

Stress concentrations
Stress concentrations
Problem
solution
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Design of Machine Elements, July - Nov 2013
Failure of Materials

Outline II
8

Fatigue

9

Life

10

Stress-Life approach (High fatigue limits)
Corrections to fatigue strengths
Stress concentration in fatigue and notch sensitivity
Applying Stress concentration in Fatigue

11

Effects of mean stresses

12

Designing for high cycle fatigue with mean stress

13

Finding factor of safety with Good man diagrams
Multiaxial fatigue

14

Fracture mechanics

15

References
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Design of Machine Elements, July - Nov 2013
Failure of Materials
Ductile materials

Von-mises criterion
Von-mises yield criterion
When the distortion strain energy density becomes equal to a critical value the material yields or and we consider it to be a failure unless mentioned otherwise. If σ0 is the uniaxial yield strength of the material and σ1 , σ2 and σ3 are the principal stress, then material fails when

1
fvm = √
2

(σ1 − σ2 )2 + (σ1 − σ3 )2 + (σ2 − σ3 )2 = σ0

(1)

If we knew the stress tensor σij , we can use
fvm =

3J2 = σ0
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Design of Machine Elements, July - Nov 2013
Failure of Materials
Ductile materials

Von-mises criterion
Von-mises yield criterion
When the distortion strain energy density becomes equal to a critical value the material yields or and we consider it to be a failure unless mentioned otherwise. If σ0 is the uniaxial yield strength of the material and σ1 , σ2 and σ3 are the principal stress, then material fails when

1
fvm = √
2

(σ1 − σ2 )2 + (σ1 − σ3 )2 + (σ2 − σ3 )2 = σ0

(1)

If we knew the stress tensor σij , we can use
fvm =

3J2 = σ0

(2)

[ J2 is the second invariant of the deviatoric component of σij ]

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Design of Machine Elements, July - Nov 2013
Failure of Materials
Ductile materials

Factor of safety
N=

Sy
fvm

(3)

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