ch07 - 2/11/2011 Chapter 7: Mechanical Properties Elastic...

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2/11/2011 1 Chapter 7 - 1 ISSUES TO ADDRESS. .. Stress and strain : What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic 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 7: Mechanical Properties Chapter 7 - 2 Elastic means reversible ! Elastic Deformation 2. Small load F d bonds stretch 1. Initial 3. Unload return to initial F d Linear- elastic Non-Linear- elastic Chapter 7 - 3 Plastic means permanent ! Plastic Deformation (Metals) F d linear elastic linear elastic d plastic 1. Initial 2. Small load 3. Unload planes still sheared F d elastic + plastic bonds stretch & planes shear d plastic Chapter 7 - 4 Stress has units: N/m 2 or lb f /in 2 Engineering Stress Shear stress, t : Area, A o F t F t F s F F F s t = F s A o Tensile stress, s : original area before loading s = F t A o 2 f 2 m N or in lb = Area, A o F t F t Chapter 7 - 5 Simple tension: cable Note: t = M / Ac R here. Common States of Stress o s = F A o t = F s A s s M M A o 2 R F s A c Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson) A o = cross sectional area (when unloaded) F F Chapter 7 - 6 (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o s = F A Simple compression: Note: compressive structure member ( s < 0 here). (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (i) A o Balanced Rock, Arches National Park
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2/11/2011 2 Chapter 7 - 7 Bi-axial tension: Hydrostatic compression: Pressurized tank s < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (ii) Fish under water s z > 0 s q > 0 Chapter 7 - 8 Tensile strain: Lateral strain: Strain is always dimensionless. Engineering Strain Shear strain: q 90º 90º - q y x q g = x / y = tan e = d L o Adapted from Fig. 7.1 (a) and (c), Cal ister & Rethwisch 3e. d /2 L o w o - d e L = L w o d L /2 Chapter 7 - 9 Stress-Strain Testing • Typical tensile test machine Adapted from Fig. 7.3, Cal ister & Rethwisch 3e. (Fig. 7.3 is taken from H.W. Hayden, W.G. Mof at , and J. Wulf , The Structure and Properties of Materials , Vol. I I, Mechanical Behavior , p. 2, John Wiley and Sons, New York, 1965.) specimen extensometer • Typical tensile specimen Adapted from Fig. 7.2, Cal ister & Rethwisch 3e. gauge length Chapter 7 - 10 Linear Elastic Properties Modulus of Elasticity, E : (also known as Young's modulus) Hooke's Law : s = E e s Linear- elastic E e F F simple tension test Chapter 7 - 11 Poisson's ratio, n Poisson's ratio, n : Units: E : [GPa] or [psi] n : dimensionless n > 0.50 density increases n < 0.50 density decreases (voids form) e L e - n e n = - L e metals : n ~ 0.33 ceramics : n ~ 0.25 polymers : n ~ 0.40 Chapter 7 - 12 Mechanical Properties • Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 7.7, Cal ister & Rethwisch 3e.
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2/11/2011 3 Chapter 7 - 13 • Elastic Shear modulus, G : t G g t = G g Other Elastic Properties simple
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This note was uploaded on 02/18/2012 for the course BME 340 taught by Professor Dr.garybledsoe during the Spring '12 term at MO St. Louis.

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ch07 - 2/11/2011 Chapter 7: Mechanical Properties Elastic...

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