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[CO,CE]MF1-1 [RO]gray Metal Forming [RO]gray Computation of Principal

Stresses and Direction in 3D

Abstract

This short note, is intended to accompany the textbook, and fillsome of the gaps in the it. One of those gaps is the most efficientway to compute the principal stresses (strains) and Directions givena stress (strain) tensor characterizing the stress state at a point.

Contents

1 Principal Stresses in Three Dimensions 2

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1 Principal Stresses in Three Dimensions

1.   Assuming that you are given a state of stress in the three dimensionalspace, whether it comes from previous calculations or experimental measure-ments, we need to reduce those 6 components given as:

σ =   σxτ xyτ xzτ yxσyτ yzτ zxτ zyσz   (1)

to the three principal components,   σ1   > σ2   > σ3, which are acting solely(alone) on the principal planes.

2.   Here is how we should proceed.

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