CHAPTER 6 MECHANICAL PROPERTIES ISSUES TO ADDRESS Stress
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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 behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? Chapter 6 - 1
INTRODUCTION (I) • The need for – standardized language for expressing mechanical properties of materials: • STRENGTH, HARDNESS, DUCTILITY, and STIFFNESS – standardized test methods: • American Society for Testing and Materials Standards and others… Chapter 6 -
INTRODUCTION (II) The result of mechanical testing is generally a response curve or a (set of) number(s), in this case a STRESS vs. STRAIN curve Courtesy of Plastics Technology Laboratories, Inc 50 Pearl Street, Pittsfield, MA 01201 Chapter 6 -
Basic Concepts of Stress and Strain • Need to compare load on specimens of various size and shapes: – For tension and compression • Engineering Stress, σ = F / A 0 , where F is load applied perpendicular to speciment crosssection and A 0 is crosssectional area (perpendicular to the force) before application of the load. • Engineering Strain, ε = Δl / l 0 ( x 100 %), where Δl change in length, lo is the original length. – These definitions of stress and strain allow one to compare test results for specimens of different cross-sectional area A 0 and of different length l 0. Chapter 6 -
Basic Concepts of Stress and Strain • Need to compare load on specimens of various size and shapes: – For tension and compression • Engineering Stress, σ = F / A 0 , where F is load applied perpendicular to speciment crosssection and A 0 is crosssectional area (perpendicular to the force) before application of the load. • Engineering Strain, ε = Δl / l 0 ( x 100 %), where Δl change in length, lo is the original length. – For shear • Shear Stress, τ = F / A 0 , where F is load applied parallel to upper and lower specimen faces of area A 0. • Shear Strain, γ = tan θ ( x 100 %), where θ is the strain angle. These definitions of stress and strain allow one to compare test results for specimens of different crosssectional area A 0 and of different length l 0. Chapter 6 -
ENGINEERING STRESS • Tensile stress, s: • Shear stress, t: Stress has units: N/m 2 or lb/in 2 Chapter 6 - 4
ENGINEERING STRAIN • Tensile strain: Applied • Lateral strain: Resulting • Shear strain: Strain is always dimensionless. Chapter 6 - 8
COMMON STATES OF STRESS • Simple tension: cable F F A o = cross sectional Area (when unloaded) Note: σ > 0 here ! • Simple shear: drive shaft Ski lift (photo courtesy P. M. Anderson) Note: t = M/Ac. R here. Chapter 6 - 5
OTHER COMMON STRESS STATES (1) • Simple compression: Ao (photo courtesy P. M. Anderson) Balanced Rock, Arches National Park (photo courtesy P. M. Anderson) Note: compressive structure member (s < 0 here). Chapter 6 - 6
OTHER COMMON STRESS STATES (2) • Bi-axial tension: • Hydrostatic compression: (photo courtesy P. M. Anderson) Pressurized tank (photo courtesy P. M. Anderson) sh< 0 Chapter 6 - 7
OTHER COMMON STRESS STATES (3) • State of stresses in college life: σ1, classes σ2, family sh< 0 σ4, daily challenges, etc… σ3, friends, etc… Chapter 6 - 7
SIMPLE STRESS-STRAIN TESTING Typical tensile specimen Typical tensile test machine Adapted from Fig. 6. 2, Callister 6 e. gauge (portion of sample with = length reduced cross section) Adapted from Fig. 6. 3, Callister 6 e. (Fig. 6. 3 is taken from H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965. ) • Other types of tests: • compression: brittle materials (e. g. , concrete) • torsion: cylindrical tubes, shafts. • hardness: surfaces of metals, ceramics Chapter 6 - 9
Stress-Strain Testing • Typical tensile test machine extensometer • Typical tensile specimen Adapted from Fig. 6. 2, Callister 7 e. gauge length Adapted from Fig. 6. 3, Callister 7 e. (Fig. 6. 3 is taken from H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965. ) Chapter 6 -
Other Types of Application of Load Chapter 6 -
How does deformation take place in the material at an atomic scale ? • Two types of deformation : – Elastic • Reversible, no change in the shape and the size of the specimen when the load is released ! • When under load volume of the material changes ! – Plastic • Irreversible, dislocations cause slip, bonds are broken, new bonds are made. • When load is released, specimen does not return to original size and shape, but volume is preserved ! Chapter 6 -
STRESS-STRAIN CURVE Necking starts STRESS σUTS REGION I σYIELD l 0 + le REGION II HARDENING OCCURS DISLOCATION MOTION AND GENERATION ! E REGION III σFAILURE or σFRACTURE Region I : Elastic Deformation Hooke’s Law Region II: Uniform Plastic Deformation Strain is uniform across material Region III: Non-uniform Plastic Deformation is limited to “neck” region l 0 + le + lp STRAIN l 0 εYIELD εUTS Chapter 6 -
ELASTIC DEFORMATION 1. Initial 2. Small load 3. Unload Elastic means reversible! Bonds stretch and but recover when load is released. Chapter 6 - 2
LINEAR ELASTIC PROPERTIES • Modulus of Elasticity, E: (also known as Young's modulus) e • Hooke's Law (Linear): F Under Load s=Ee • Poisson's ratio, n: metals: n ~ 0. 33 ceramics: ~0. 25 polymers: ~0. 40 e. L e -n 1 e. L No load F simple tension test Units: E: [GPa] or [psi] n: dimensionless Chapter 6 - 10
NON-LINEAR ELASTIC PROPERTIES • Some materials will exhibit a non-linear elastic behavior under stress ! Examples are polymers, gray cast iron, concrete, etc… Chapter 6 -
Linear Elastic Deformation (Atomic Scale) Chapter 2: Inter-atomic Bonding ! Young’s Modulus α (d. F/dr) at ro , what else ? If we increase temperature, how will E behave ? Chapter 6 -
YOUNG’S MODULI: COMPARISON Metals Alloys Graphite Ceramics Polymers Semicond Composites /fibers E(GPa) Based on data in Table B 2, Callister 6 e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. Chapter 6 - 12
PLASTIC DEFORMATION (METALS) 1. Initial 2. Small load 3. Unload Plastic means permanent! Chapter 6 - 3
PLASTIC (PERMANENT) DEFORMATION (at lower temperatures, T < Tmelt/3) • Simple tension test: Chapter 6 - 14
YIELD STRENGTH, sy Some materials do NOT exhibit a distinct transition from elastic to plastic region under stress, so by convention a straight line is drawn parallel to the stress strain curve with 0. 2 % strain. The stress at the intersection is called the yield stress ! Chapter 6 -
HARDENING • An increase in sy due to plastic deformation. • Curve fit to the stress-strain response: Chapter 6 - 22
YIELD STRENGTH: COMPARISON Room T values Based on data in Table B 4, Callister 6 e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered Chapter 6 - 16
TENSILE STRENGTH, TS • Maximum possible engineering stress in tension. NECKING Adapted from Fig. 6. 11, Callister 6 e. FRACTURE • Metals: occurs when noticeable necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and about to break. Chapter 6 - 17
TENSILE STRENGTH: COMPARISON Room T values Based on data in Table B 4, Callister 6 e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. Chapter 6 - 18
DUCTILITY, %EL • Plastic tensile strain at failure: Adapted from Fig. 6. 13, Callister 6 e. • Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. Chapter 6 - 19
Mechanical Strength of Materials Yield Strength, Tensile Strength and Ductility can be improved by alloying, heat and mechanical treatment, but Youngs Modulus is rather insensitive to such processing ! Temperature effects : YS, TS and YM decrease with increasing temperature, but ductility increases with temperature ! Chapter 6 -
TOUGHNESS & RESILIENCE • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. RESILIENCE is energy stored in the material w/o plastic deformation ! Ur = σy 2 / 2 E TOUGHNESS is total energy stored in the material upon fracture ! Chapter 6 - 20
Resilience, Ur • Ability of a material to store energy – Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to 1 Ur @ sy e y 2 Adapted from Fig. 6. 15, Callister 7 e. Chapter 6 -
TRUE STRESS & STRAIN σT = σ (1+ ε ) εT = ln (1+ε) The material does NOT get weaker past M Chapter 6 -
HARDNESS • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. Adapted from Fig. 6. 18, Callister 6 e. (Fig. 6. 18 is adapted from G. F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957. ) Chapter 6 - 21
Hardness: Measurement • Rockwell – No major sample damage – Each scale runs to 130 but only useful in range 20100. – Minor load 10 kg – Major load 60 (A), 100 (B) & 150 (C) kg • A = diamond, B = 1/16 in. ball, C = diamond • HB = Brinell Hardness – TS (psia) = 500 x HB – TS (MPa) = 3. 45 x HB Chapter 6 -
Hardness: Measurement Table 6. 5 Chapter 6 -
HARDNESS !! 1. 2. 3. Relatively simple and cheap technique Non-destructive Related to many other mechanical properties Chapter 6 -
Variability in Material Properties • Elastic modulus is material property • Critical properties depend largely on sample flaws (defects, etc. ). Large sample to sample variability. • Statistics – Mean – Standard Deviation where n is the number of data points Chapter 6 -
Design or Safety Factors • Design uncertainties mean we do not push the limit. • Factor of safety, N Often N is between 1. 2 and 4 • Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. 5 d 1045 plain carbon steel: sy = 310 MPa TS = 565 MPa d = 0. 067 m = 6. 7 cm Lo F = 220, 000 N Chapter 6 -
Chapter 6 -
SUMMARY • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure. Note: For materials selection cases related to mechanical behavior, see slides 22 -4 to 22 -10. Chapter 6 - 24
ANNOUNCEMENTS Reading: Chapter 6 and Chapter 7 Homework : Example problems: 6. 1, 6. 2, 6. 3 Due date: 27 -04 -2011 Chapter 6 - 0
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