Ch06 introduction to static failure theories.pdf

MECHANICAL ENGINEERING DESIGN TUTORIAL 6, PART A: INTRODUCTION TO STATIC FAILURE THEORIES
APPROACH Theories have been developed for the static failure of metals based upon the two classes of material failure; ductile metals yield while brittle metals fracture. Thus separate failure theories exist for ductile and brittle metals: Failure Theories for Ductile Materials 1. Maximum Shear Stress (MSS) 2. Distortion Energy (DE) 3. Ductile Coulomb-Mohr (DCM) Failure Theories for Brittle Materials 1. Maximum Normal Stress (MNS) 2. Brittle Coulomb-Mohr (BCM) These theories have grown out of hypotheses and experimental data in the following manner. 1. 2. 3. 4. Experimental failure data is first collected through tensile tests. The state of stress is correlated to the experimental data using Mohr’s circle plots. A failure theory is developed from a concept of the responsible failure mechanism. A design envelope is established based upon the theoretical and empirical design equations.

In light of the extensive dependence of failure theories on experimental data, we will first review the acquisition and correlation of tensile test data to failure theory. Subsequently, the criteria and application of specific failure theories will be discussed. TENSILE TEST d0 l0 TEXT FIGURE 3-1: A typical tension-test specimen. Some of the standard dimensions used for d0 are 2.5, 6.25, and 12.5 mm and 0.505 in, but other sections and sizes are in use. Common gauge lengths l0 used are 10, 25, and 50 mm and 1 and 2 in.

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Text refers to Mechanical Engineering Design, 7th edition text by Joseph Edward Shigley, Charles R. Mischke and Richard G. Budynas; equations and examples with the prefix T refer to the present tutorial.

The tensile test is a standardized test (ASTM Standard E8 or E8m) and thus allows for the sharing of experimental data amongst researchers, typically in the form of stress-strain curves. Standard dimensions for the test-specimen are provided in Text Figure 3-1