Mechanics of Materials Lab Lecture 11 Failure Criteria Mechanical Behavior of Materials Sec. 7.1-7.6 Jiangyu Li University of Washington 1 Jiangyu Li, University of Washington

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

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

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

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

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

Octahedral Shear Stress 7 Jiangyu Li, University of Washington

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

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 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 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. 10 Jiangyu Li, University of Washington

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 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. 11 Jiangyu Li, University of Washington

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

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

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

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

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