Mechanical Properties PDF

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...

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 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 - 1  Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial d F F Linear- elastic Elastic means reversible! Non-Linear- elastic d Chapter 6 - 2  Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared dplastic delastic + plastic F F Plastic means permanent! linear linear elastic elastic d dplastic Chapter 6 - 3  Engineering Stress Tensile stress, s: Shear stress, t: Ft Ft F Area, Ao Fs Area, Ao Fs Ft F Ft Ft lb f N t= s F s= = 2 or 2 Ao Ao in m original area  Stress has units: before loading N/m2 or lbf /in2 Chapter 6 - 4  Common States of Stress Simple tension: cable F F A o = cross sectional area (when unloaded) F s= s s Ao Ski lift (photo courtesy Torsion (a form of shear): drive shaft P.M. Anderson) M Fs Ao Ac Fs t = Ao M 2R Note: t = M/AcR here. Chapter 6 - 5  OTHER COMMON STRESS STATES (i) Simple compression: Ao Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) F s= Note: compressive Balanced Rock, Arches structure member National Park (photo courtesy P.M. Anderson) Ao (s < 0 here). Chapter 6 - 6 OTHER COMMON STRESS STATES (ii) Bi-axial tension: Hydrostatic compression: Pressurized tank Fish under water (photo courtesy (photo courtesy P.M. Anderson) P.M. Anderson) sq > 0 sz > 0 s h< 0 Chapter 6 - 7  Engineering Strain Tensile strain: Lateral strain: d/2 -dL e = d eL = Lo Lo wo wo dL /2 Shear strain: q x g = x/y = tan q y 90º - q Strain is always 90º dimensionless. Adapted from Fig. 6.1(a) and (c), Callister & Rethwisch 8e. Chapter 6 - 8  Stress-Strain Testing Typical tensile test Typical tensile machine specimen Adapted from extensometer specimen Fig. 6.2, Callister & Rethwisch 8e. gauge length Adapted from Fig. 6.3, Callister & Rethwisch 8e. (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 - 9  Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: s=Ee s F E e Linear- elastic F simple tension test Chapter 6 - 10  Poisson's ratio, n eL Poisson's ratio, n: eL n=- e e metals: n ~ 0.33 -n ceramics: n ~ 0.25 polymers: n ~ 0.40 Units: n > 0.50 density increases E: [GPa] or [psi] n < 0.50 density decreases n: dimensionless (voids form) Chapter 6 - 11  Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 6.7, Callister & Rethwisch 8e. Chapter 6 - 12  Other Elastic Properties t M Elastic Shear modulus, G: G simple g torsion t=Gg test M Elastic Bulk P P modulus, K: V V P P P = -K Vo Vo K pressure test: Init. vol =Vo. Special relations for isotropic materials: Vol chg. = V E E G= K= 2(1 + n) 3(1 - 2n) Chapter 6 - 13  Young’s Moduli: Comparison Graphite Metals Composites Ceramics Polymers Alloys /fibers Semicond 1200 10 00 Diamond 800 600 Si carbide 400 Tungsten Al oxide Carbon fibers only Molybdenum Si nitride E(GPa) 200 Steel, Ni Tantalum C FRE(|| fibers)* Platinum Si crystal Cu alloys Aramid fibers only 10 0 Zinc, Ti 80 Silver, Gold Glass -soda A FRE(|| fibers)* Based on data in Table B.2, Aluminum Glass fibers only 60 40 Magnesium, Tin G FRE(|| fibers)* Callister & Rethwisch 8e. Concrete Composite data based on 109 Pa 20 GFRE* CFRE * reinforced epoxy with 60 vol% of aligned G raphite G FRE( fibers)* 10 carbon (CFRE), 8 C FRE( fibers) * 6 AFRE( fibers) * aramid (AFRE), or Polyester glass (GFRE) 4 PET PS fibers. PC Epoxy only 2 PP 1 HDP E 0.8 0.6 Wood( grain) PTFE 0.4 0.2 LDPE Chapter 6 - 14  Useful Linear Elastic Relationships Simple tension: Simple torsion: d = FL o d = - n Fw o 2ML o a= L EA o EA o  r o4 G F M = moment d/2 a = angle of twist Ao Lo Lo wo 2ro dL /2 Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. Chapter 6 - 15  Plastic (Permanent) Deformation (at lower temperatures, i.e. T < Tmelt/3) Simple tension test: Elastic+Plastic engineering stress, s at larger stress Elastic initially permanent (plastic) after load is removed ep engineering strain, e plastic strain Adapted from Fig. 6.10(a), Callister & Rethwisch 8e. Chapter 6 - 16  Yield Strength, sy Stress at which noticeable plastic deformation has occurred. when ep = 0.002 tensile stress, s sy = yield strength sy Note: for 2 inch sample e = 0.002 = z/z  z = 0.004 in engineering strain, e ep = 0.002 Adapted from Fig. 6.10(a), Callister & Rethwisch 8e. Chapter 6 - 17  Yield Strength : Comparison Graphite/ Metals/ Composites/ Ceramics/ Polymers Alloys fibers Semicond 2000 Steel (4140) qt 1000 Yield strength, sy (MPa) Ti (5Al-2.5Sn) a in ceramic matrix and epoxy matrix composites, since 700 W (pure) since in tension, fracture usually occurs before yield. in tension, fracture usually occurs before yield. 600 Cu (71500) cw 500 Mo (pure) Steel (4140) a 400 Steel (1020) cd Room temperature 300 values Hard to measure , Al (6061) ag Hard to measure, 200 Steel (1020) hr ¨ Ti (pure) a Ta (pure) Cu (71500) hr Based on data in Table B.4, Callister & Rethwisch 8e. 100 a = annealed dry 70 PC hr = hot rolled 60 Nylon 6,6 ag = aged 50 Al (6061) a PET cd = cold drawn 40 PVC humid cw = cold worked PP 30 HDPE qt = quenched & tempered 20 LDPE Tin (pure) Chapter 6 - 18 10 VMSE: Virtual Tensile Testing Chapter 6 - 19  Tensile Strength, TS Maximum stress on engineering stress-strain curve. Adapted from Fig. 6.11, Callister & Rethwisch 8e. TS F = fracture or sy ultimate engineering strength stress Typical response of a metal Neck – acts as stress concentrator strain engineering strain Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. Chapter 6 - 20  Tensile Strength: Comparison Graphite/ Metals/ Composites/ Ceramics/ Polymers Alloys fibers Semicond 5000 C fibers Aramid fib 3000 E-glass fib Tensile strength, TS (MPa) 2000 Steel (4140) qt A FRE(|| fiber) 1000 W (pure) Diamond GFRE(|| fiber) Ti (5Al-2.5Sn)aa CFRE(|| fiber) Steel (4140)cw Cu (71500) Si nitride Cu (71500) hr Al oxide 300 Steel (1020) Al (6061) ag Ti (pure) a Room temperature 200 Ta (pure) values Al (6061) a 100 Si crystal wood(|| fiber) Based on data in Table B.4, Nylon 6,6 Glass-soda PC PET Callister & Rethwisch 8e. 40 PVC GFRE( fiber) a = annealed Concrete PP 30 CFRE( fiber) hr = hot rolled A FRE( fiber) H DPE ag = aged 20 Graphite LDPE cd = cold drawn cw = cold worked 10 qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy wood ( fiber) composites, with 60 vol% fibers. 1 Chapter 6 - 21  Ductility Lf - Lo Plastic tensile strain at failure: %EL = x 100 Lo smaller %EL Engineering tensile stress, s larger %EL Ao Lo Af Lf Adapted from Fig. 6.13, Callister & Rethwisch 8e. Engineering tensile strain, e Another ductility measure: Ao - Af %RA = x 100 Ao Chapter 6 - 22  Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering small toughness (ceramics) tensile large toughness (metals) stress, s Adapted from Fig. 6.13, very small toughness Callister & Rethwisch 8e. (unreinforced polymers) Engineering tensile strain, e Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Chapter 6 - 23  Resilience, Ur Ability of a material to store energy – Energy stored best in elastic region ey Ur =  sde 0 If we assume a linear stress-strain curve this simplifies to 1 Ur @ sy e y 2 Adapted from Fig. 6.15, Callister & Rethwisch 8e. Chapter 6 - 24  Elastic Strain Recovery syi D syo 2. Unload Stress 1. Load 3. Reapply load Strain Adapted from Fig. 6.17, Elastic strain Callister & Rethwisch 8e. recovery Chapter 6 - 25  Hardness Resistance to permanently indenting the surface. Large hardness means: -- resistance to plastic deformation or cracking in compression. -- better wear properties. apply known force measure size e.g., of indent after 10 mm sphere removing load Smaller indents D d mean larger hardness. most brasses easy to machine cutting nitrided plastics Al alloys steels file hard tools steels diamond increasing hardness Chapter 6 - 26  Hardness: Measurement Rockwell – No major sample damage – Each scale runs to 130 but only useful in range 20-100. – 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 - 27  Hardness: Measurement Table 6.5 Chapter 6 - 28  True Stress & Strain Note: S.A. changes when sample stretched True stress sT = F Ai sT = s1 + e  True strain eT = ln i  o  eT = ln1 + e  Adapted from Fig. 6.16, Callister & Rethwisch 8e. Chapter 6 - 29  Hardening An increase in sy due to plastic deformation. s large hardening sy 1 sy small hardening 0 e Curve fit to the stress-strain response: hardening exponent: sT = K eT  n n = 0.15 (some steels) to n = 0.5 (some coppers) “true” stress (F/A) “true” strain: ln(L/Lo) Chapter 6 - 30  Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics n  xn – Mean x= n 1 n    2 2   xi - x  – Standard Deviation s =   n -1    where n is the number of data points Chapter 6 - 31  Design or Safety Factors Design uncertainties mean we do not push the limit. Factor of safety, N Often N is sy between sw orking = 1.2 and 4 N 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. d sy sw orking = 1045 plain carbon steel: N sy = 310 MPa Lo 220,000N TS = 565 MPa 5   d /42  F = 220,000N d = 0.067 m = 6.7 cm Chapter 6 - 32  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. Chapter 6 - 33  ANNOUNCEMENTS Reading: Core Problems: Self-help Problems: Chapter 6 - 34