Page 274 - Mechanical Behavior of Materials

7

Yielding and Fracture under

Combined Stresses

7.1 INTRODUCTION
7.2 GENERAL FORM OF FAILURE CRITERIA
7.3 MAXIMUM NORMAL STRESS FRACTURE CRITERION
7.4 MAXIMUM SHEAR STRESS YIELD CRITERION
7.5 OCTAHEDRAL SHEAR STRESS YIELD CRITERION
7.6 DISCUSSION OF THE BASIC FAILURE CRITERIA
7.7 COULOMB–MOHR FRACTURE CRITERION
7.8 MODIFIED MOHR FRACTURE CRITERION
7.9 ADDITIONAL COMMENTS ON FAILURE CRITERIA
7.10 SUMMARY

OBJECTIVES

• Develop and employ three basic criteria for predicting failure under multiaxial stresses:
maximum normal stress fracture criterion, maximum shear stress yield criterion, and
octahedral shear stress yield criterion.
• Compare and discuss these basic criteria as to applicability and extensions.
• Explore fracture of brittle materials under multiaxial stresses in tension or compression,
where either of two modes of fracture may occur, tension or shear, with the degree of
compression affecting the shear mode.

7.1 INTRODUCTION

Engineering components may be subjected to complex loadings in tension, compression, bending,
torsion, pressure, or combinations of these, so that at a given point in the material, stresses often
occur in more than one direction. If sufficiently severe, such combined stresses can act together to
cause the material to yield or fracture. Predicting the safe limits for use of a material under combined
stresses requires the application of a failure criterion.
A number of different failure criteria are available, some of which predict failure by yielding,
others failure by fracture. The former are specifically called yield criteria, the latter fracture criteria.

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