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

2. Chapter 7 - 2 Elastic means reversible! Elastic Deformation 2. Small load F  bonds stretch 1. Initial3. Unload return to initial F  Linear- elastic Non-Linear- elastic

3. Chapter 7 - 3 Plastic means permanent! Plastic Deformation (Metals) F  linear elastic linear elastic  plastic 1. Initial2. Small load3. Unload planes still sheared F  elastic + plastic bonds stretch & planes shear  plastic

4. Chapter 7 - 4  Stress has units: N/m 2 or lb f /in 2 Engineering Stress Shear stress,  : Area, A o F t F t F s F F F s  = F s A o Tensile stress,  : original cross-sectional area before loading  = F t A o 2 f 2 m N or in lb = Area, A o F t F t

5. Chapter 7 - 5 Simple tension: cable Note:  = M/A c R here. Common States of Stress o   F A o   F s A  M M A o 2R2R 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) FF

6. Chapter 7 - 6 (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o   F A Simple compression: Note: compressive structure member (  < 0 here). (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (i) A o Balanced Rock, Arches National Park

7. Chapter 7 - 7 Bi-axial tension: Hydrostatic compression: Pressurized tank   < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (ii) Fish under water  z > 0  

8. Chapter 7 - 8 Tensile strain: Lateral strain: Strain is always dimensionless. Engineering Strain Shear strain:  90º 90º -  y xx   =  x/y = tan   L o Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 4e.  /2 L o w o   L  L w o  L

9. Chapter 7 - 9 Stress-Strain Testing Typical tensile test machine Adapted from Fig. 7.3, Callister & Rethwisch 4e. (Fig. 7.3 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.) specimen extensometer Typical tensile specimen Adapted from Fig. 7.2, Callister & Rethwisch 4e. gauge length

10. Chapter 7 - 10 Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law:  = E   Linear- elastic E  F F simple tension test

11. Chapter 7 - 11 Poisson's ratio, Poisson's ratio, : Units: E: [GPa] or [psi] : dimensionless > 0.50 density increases < 0.50 density decreases (voids form) LL  -   L  metals: ~ 0.33 ceramics: ~ 0.25 polymers: ~ 0.40

12. 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, Callister & Rethwisch 4e.

13. Chapter 7 - 13 Elastic Shear modulus, G:  G   = G  Other Elastic Properties simple torsion test M M Special relations for isotropic materials: 2(1  ) E G  3(1  2 ) E K  Elastic Bulk modulus, K: pressure test: Init. vol =V o. Vol chg. =  V P PP P = -K  V V o P  V K V o

14. Chapter 7 - 14 Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers E(GPa) Based on data in Table B.2, Callister & Rethwisch 4e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. Young’s Moduli: Comparison 10 9 Pa

15. Chapter 7 - 15 Simple tension:  FLFL o EA o  L  Fw o EA o Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. Useful Linear Elastic Relationships F A o  /2  L LoLo w o Simple torsion:  2ML o  r o 4 G M = moment  = angle of twist 2ro2ro LoLo

16. Chapter 7 - 16 (at lower temperatures, i.e. T < T melt /3) Plastic (Permanent) Deformation Simple tension test: engineering stress,  engineering strain,  Elastic+Plastic at larger stress pp plastic strain Elastic initially Adapted from Fig. 7.10 (a), Callister & Rethwisch 4e. permanent (plastic) after load is removed

17. Chapter 7 - 17 Stress at which noticeable plastic deformation has occurred. when  p = 0.002 Yield Strength,  y  y = yield strength Note: for 2 inch sample  = 0.002 =  z/z   z = 0.004 in Adapted from Fig. 7.10 (a), Callister & Rethwisch 4e. tensile stress,  engineering strain,  yy  p = 0.002

18. Chapter 7 - 18 Room temperature values Based on data in Table B.4, Callister & Rethwisch 4e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered Yield Strength : Comparison

19. Chapter 7 - VMSE: Virtual Tensile Testing 19

20. Chapter 7 - 20 Tensile Strength, TS Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. Adapted from Fig. 7.11, Callister & Rethwisch 4e. yy strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering TS stress engineering strain Maximum stress on engineering stress-strain curve.

21. Chapter 7 - 21 Tensile Strength: Comparison Based on data in Table B4, Callister & Rethwisch 4e. 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. Room temperature values

22. Chapter 7 - 22 Plastic tensile strain at failure: Ductility Another ductility measure: 100x A AA RA% o fo - = x 100 L LL EL% o of   LfLf AoAo AfAf LoLo Adapted from Fig. 7.13, Callister & Rethwisch 4e. Engineering tensile strain,  Engineering tensile stress,  smaller %EL larger %EL

23. Chapter 7 - 23 Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Toughness Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Adapted from Fig. 7.13, Callister & Rethwisch 4e. very small toughness (unreinforced polymers) Engineering tensile strain,  Engineering tensile stress,  small toughness (ceramics) large toughness (metals)

24. Chapter 7 - 24 Resilience, U r Ability of a material to store energy –Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to Adapted from Fig. 7.15, Callister & Rethwisch 4e. yyr 2 1 U 

25. Chapter 7 - 25 Elastic Strain Recovery Adapted from Fig. 7.17, Callister & Rethwisch 4e. Stress Strain 3. Reapply load 2. Unload D Elastic strain recovery 1. Load yoyo yiyi

26. Chapter 7 - 26 Mechanical Properties Ceramic materials are more brittle than metals. Why is this so? Consider mechanism of deformation –In crystalline, by dislocation motion –In highly ionic solids, dislocation motion is difficult few slip systems resistance to motion of ions of like charge (e.g., anions) past one another

27. Chapter 7 - 27 Room T behavior is usually elastic, with brittle failure. 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials. Adapted from Fig. 7.18, Callister & Rethwisch 4e. Flexural Tests – Measurement of Elastic Modulus F L/2  = midpoint deflection cross section R b d rect.circ. Determine elastic modulus according to: F x linear-elastic behavior  F  slope = (rect. cross section) (circ. cross section)

28. Chapter 7 - 28 3-point bend test to measure room-T flexural strength. Adapted from Fig. 7.18, Callister & Rethwisch 4e. Flexural Tests – Measurement of Flexural Strength F L/2  = midpoint deflection cross section R b d rect.circ. location of max tension Flexural strength: Typical values: Data from Table 7.2, Callister & Rethwisch 4e. Si nitride Si carbide Al oxide glass (soda-lime) 250-1000 100-820 275-700 69 304 345 393 69 Material  fs (MPa) E(GPa) (rect. cross section) (circ. cross section)

29. Chapter 7 - 29 Mechanical Properties of Polymers – Stress-Strain Behavior Fracture strengths of polymers ~ 10% of those for metals Deformation strains for polymers > 1000% – for most metals, deformation strains < 10% brittle polymer plastic elastomer elastic moduli – less than for metals Adapted from Fig. 7.22, Callister & Rethwisch 4e.

30. Chapter 7 - 30 Decreasing T... -- increases E -- increases TS -- decreases %EL Increasing strain rate... -- same effects as decreasing T. Influence of T and Strain Rate on Thermoplastics 20 40 60 80 0 00.10.20.3 4°C 20°C 40°C 60°C to 1.3  (MPa)  Plots for semicrystalline PMMA (Plexiglas) Adapted from Fig. 7.24, Callister & Rethwisch 4e. (Fig. 7.24 is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.)

31. Chapter 7 - Representative T g values (  C): PE (low density) PE (high density) PVC PS PC - 110 - 90 + 87 +100 +150 Selected values from Table 11.3, Callister & Rethwisch 4e. 31 Stress relaxation test: -- strain in tension to   and hold. -- observe decrease in stress with time. Relaxation modulus: Time-Dependent Deformation time strain tensile test oo (t)(t) There is a l arge decrease in E r for T > T g. (amorphous polystyrene) Adapted from Fig. 7.28, Callister & Rethwisch 4e. (Fig. 7.28 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) 10 3 1 10 -3 10 5 60100140180 rigid solid (small relax) transition region T(°C) TgTg E r (10 s) in MPa viscous liquid (large relax)

32. Chapter 7 - 32 Hardness Resistance to permanently indenting the surface. Large hardness means: -- resistance to plastic deformation or cracking in compression. -- better wear properties. e.g., 10 mm sphere apply known force measure size of indent after removing load d D Smaller indents mean larger hardness. increasing hardness most plastics brasses Al alloys easy to machine steelsfile hard cutting tools nitrided steelsdiamond

33. Chapter 7 - 33 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

34. Chapter 7 - 34 Hardness: Measurement Table 7.5

35. Chapter 7 - 35 True Stress & Strain Note: S.A. changes when sample stretched True stress True strain Adapted from Fig. 7.16, Callister & Rethwisch 4e.

36. Chapter 7 - 36 Hardening Curve fit to the stress-strain response:  T  K  T  n “true” stress (F/A) “true” strain: ln(L/L o ) hardening exponent: n =0.15 (some steels) to n =0.5 (some coppers) An increase in  y due to plastic deformation.   large hardening small hardening  y 0  y 1

37. Chapter 7 - 37 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

38. Chapter 7 - 38 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. Design or Safety Factors 5 1045 plain carbon steel:  y = 310 MPa TS = 565 MPa F = 220,000N d L o d = 0.067 m = 6.7 cm

39. Chapter 7 - 39 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). Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Summary Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches  y.

40. Chapter 7 - 40 Core Problems: Self-help Problems: ANNOUNCEMENTS Reading: