1. Mechanics of Materials Lab
Lecture 11
Failure Criteria
Mechanical Behavior of Materials Sec
Jiangyu Li
University of Washington 1
Jiangyu Li, University of Washington

2. Jiangyu Li, University of Washington
Failure Mode
Ductile: yielding
Brittle: Fracture 2
Jiangyu Li, University of Washington

3. Jiangyu Li, University of Washington
Multi-axial Load
Figure: 07-01a-d
Tension or compression 3
Jiangyu Li, University of Washington

4. Maximum Normal Stress Fracture Criterion
Figure: 07-02a-b 4
Jiangyu Li, University of Washington

5. Maximum Shear Stress Yielding Criterion
Figure: 07-05 5
Jiangyu Li, University of Washington

6. Three-dimensional Stress State
Figure: 07-06a-b 6
Jiangyu Li, University of Washington

7. Octahedral Shear Stress7
Jiangyu Li, University of Washington

8. Octahedral Shear Stress Criterion
Figure: 07-08 8
Jiangyu Li, University of Washington

9. Note the difference when stress have opposite sign
Comparison
Figure: 07-11
Note the difference when stress have opposite sign 9
Jiangyu Li, University of Washington

10. 10 Jiangyu Li, University of Washington Figure: 07-12
Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,
by Norman E. Dowling. ISBN
© 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),
write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 10
Jiangyu Li, University of Washington

11. 11 Jiangyu Li, University of Washington Figure: 07-13
Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,
by Norman E. Dowling. ISBN
© 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),
write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 11
Jiangyu Li, University of Washington

12. Three-dimensional Stress State
Figure: 07-09 12
Jiangyu Li, University of Washington

13. Jiangyu Li, University of Washington
Comparison
Figure: 07-10 13
Jiangyu Li, University of Washington

14. Jiangyu Li, University of Washington
Example
For a stress state of sx=120, sy=-50, sz=200, txy=60 Mpa, and a safety factor of 2.0 again yielding, what is the minimum yield strength by (1) maximum shear stress criterion and (2) octahedral shear stress criterion 14
Jiangyu Li, University of Washington

15. Jiangyu Li, University of Washington
Load Factor Design
7. 32 A circular bar must support a axial loading of 200 kN and a torque of 1.5 kN.m. Its yield strength is 260 MPa.
What diameter is needed if load factors YP=1.6 and YT=2.5 are required. 15
Jiangyu Li, University of Washington

16. Jiangyu Li, University of Washington
Assignment
Mechanical Behavior of Materials
7.2, 7.6, 7.33 16
Jiangyu Li, University of Washington