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Introduction to Static Failure Theories

MECHANICAL ENGINEERING DESIGN TUTORIAL 6, PART A: INTRODUCTION TO STATIC FAILURE THEORIES | 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. Experimental failure data is first collected through tensile tests. 2. The state of stress is correlated to the experimental data using Mohr s circle plots. 3. A failure theory is developed from a concept of the responsible failure mechanism. 4. 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 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. 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 while a comparison of characteristic stress-strain .