# Chapter 6 - ANNOUNCEMENTS -1/23 Reading: Chapter 6 Lab...

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ANNOUNCEMENTS -1/23 Lab starts on next Tuesday 1/30. Check http://web.utk.edu/%7Ekjohann1/mse201/homepage.htm TA: Mr. Sam McClure Reading: Chapter 6 Chapter 6 - 1

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Chapter 6: Mechanical Properties ISSUES TO ADDRESS. .. Stress and strain : What are they and why are they used instead of load and deformation? Elastic (reversible) behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic (irreversible) behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Toughness and ductility : What are they and how do we measure them? Chapter 6 - 2
Elastic Deformation Chapter 6 - 3 Elastic means reversible ! 1. Initial 2. Small load 3. Unload F δ bonds stretch return to initial F δ Linear elastic (metals, ceramics) Non-Linear elastic (polymers, biotissues) displacement Force or load δ F F

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Plastic Deformation (Metals) Plastic means permanent (irreversible) ! Chapter 6 - 4 F δ linear elastic Linear elastic δ plastic 1. Initial 2. Small load 3. Unload planes still sheared F δ elastic + plastic bonds stretch & planes shear δ plastic
Force and displacement are both vectors (with magnitude and direction) Force on a surface can be decomposed into: F t : normal force F s : tangential force F t F t F s F F F s Chapter 6 - 5

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Chapter 6 - 6 Engineering Stress Shear stress, τ : Area, A F s F s τ = F s A o Tensile stress, σ : original area before loading Area, A F t F t σ = F t A o 2 f 2 m N or in lb = Stress has units: N/m 2 (pascal) or lb f /in 2 F depends on the size of the sample
Common States of Stress Chapter 6 - 7 Simple tension: cable τ Note: τ = M / A c R here. A o = cross sectional area (when unloaded) F F o σ = F A o τ = F s A σ σ M M A o 2 R F s A c Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson) M = bending moment

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OTHER COMMON STRESS STATES (1) (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM σ = F A o Simple compression: Note: compressive structure member ( σ < 0 here). (photo courtesy P.M. Anderson) A o Balanced Rock, Arches National Park These are uniaxial stresses (1-D). Chapter 6 - 8
OTHER COMMON STRESS STATES (2) Bi-axial tension (2-D): Hydrostatic compression (3-D): Pressurized tank σ < 0 h (photo courtesy P.M. Anderson) Fish under water (photo courtesy P.M. Anderson) σ z > 0 σ θ > 0 Chapter 6 - 9 e.g. submarine

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Chapter 6 - 10 Tensile strain: Lateral strain: Shear strain: Strain is dimensionless. Engineering Strain θ 90º 90º - θ y x θ γ = x / y = tan ε= δ L o δ ε L = L w o Adapted from Fig. 6.1 (a) and (c), Callister 7e. δ /2 δ L /2 L o w o displacement depends on a sample’s dimension Sample volume remains constant.