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Unformatted text preview: Draft Lecture Notes in: FRACTURE MECHANICS Victor E. Saouma Dept. of Civil Environmental and Architectural Engineering University of Colorado, Boulder, CO 80309-0428 Draft Contents 1 INTRODUCTION 1 1.1 Modes of Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Examples of Structural Failures Caused by Fracture . . . . . . . . . . . . . . . . 2 1.3 Fracture Mechanics vs Strength of Materials . . . . . . . . . . . . . . . . . . . . . 3 1.4 Major Historical Developments in Fracture Mechanics . . . . . . . . . . . . . . . 6 1.5 Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 PRELIMINARY CONSIDERATIONS 1 2.1 Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.1.1 Indicial Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.2 Tensor Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.3 Rotation of Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.4 Trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.5 Inverse Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.6 Principal Values and Directions of Symmetric Second Order Tensors . . . 6 2.2 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Force, Traction and Stress Vectors . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Traction on an Arbitrary Plane; Cauchy’s Stress Tensor . . . . . . . . . . 8 E 2-1 Stress Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.4 Spherical and Deviatoric Stress Tensors . . . . . . . . . . . . . . . . . . . 10 2.2.5 Stress Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.6 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Kinematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Strain Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Compatibility Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Fundamental Laws of Continuum Mechanics . . . . . . . . . . . . . . . . . . . . . 14 2.4.1 Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.2 Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.3 Conservation of Mass; Continuity Equation . . . . . . . . . . . . . . . . . 16 2.4.4 Linear Momentum Principle; Equation of Motion . . . . . . . . . . . . . . 16 2.4.5 Moment of Momentum Principle . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.6 Conservation of Energy; First Principle of Thermodynamics . . . . . . . . 18 2.5 Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....
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This note was uploaded on 11/10/2010 for the course AEROSPACE AE 1202 taught by Professor Dr.adib during the Spring '10 term at Sharif University of Technology.

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lecfrac - Draft Lecture Notes in: FRACTURE MECHANICS Victor...

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