1. 1 Jiangyu Li, University of Washington Lecture 23 Plasticity Mechanical Behavior of Materials Sec. 12.1-12.5 Jiangyu Li University of Washington Mechanics of Materials Lab

2. 2 Jiangyu Li, University of Washington Secant Modulus

3. 3 Jiangyu Li, University of Washington Stress-Strain Curve

4. 4 Jiangyu Li, University of Washington Deformation Plasticity Theory Axial and torsion

5. 5 Jiangyu Li, University of Washington Example Consider a material with a uniaixal stress-strain curve of the Ramberg-Osgood form, and the case of axissymmetric loading:  2=  3=  –Derive  1 as a function of  and material constants

6. 6 Jiangyu Li, University of Washington Rheological Modeling of Nonlinear Hardening

7. 7 Jiangyu Li, University of Washington Loading-Unloading

8. 8 Jiangyu Li, University of Washington Loading-Unloading

9. 9 Jiangyu Li, University of Washington Comparison

10. 10 Jiangyu Li, University of Washington Cyclic Loading

11. 11 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

12. 12 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

13. 13 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

14. 14 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

15. 15 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

16. 16 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

17. 17 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

18. 18 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

19. 19 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

20. 20 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

21. 21 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

22. 22 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

23. 23 Jiangyu Li, University of Washington Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition, by Norman E. Dowling. ISBN 0-13-186312-6. © 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 07458.

24. 24 Jiangyu Li, University of Washington

25. 25 Jiangyu Li, University of Washington Assignment Mechanical Behavior of Materials 12.12, 12.19