Mechanical Behaviour, Testing and Manufacturing Properties of Materials

CHAPTER 2 Mechanical Behavior, Testing, and Manufacturing Properties of Materials (재료의 기계적 성질)

Kalpakjian, Manufacturing Processes for Engineering Materials

© 1997 Addison Wesley

Page 2-1

Tensile-Test Specimen and Machine (b)

Figure 2.1 (a) A standard tensile-test specimen before and after pulling, showing original and final gage lengths. (b) A typical tensile-testing machine.



Page 2-2

Stress-Strain Curve Figure 2.2 A typical stressstrain curve obtained from a tension test, showing various features.



Page 2-3

Mechanical Properties of Various Materials at Room Temperature TABLE 2.1 Mechanical Properties of Various Materials at Room Temperature Metals (Wrought)

E (GPa)

Y (MPa)

UTS (MPa)

Elongation in 50 mm (%)

Aluminum and its alloys Copper and its alloys Lead and its alloys Magnesium and its alloys Molybdenum and its alloys Nickel and its alloys Steels Titanium and its alloys Tungsten and its alloys

69–79 105–150 14 41–45 330–360 180–214 190–200 80–130 350–400

35–550 76–1100 14 130–305 80–2070 105–1200 205–1725 344–1380 550–690

90–600 140–1310 20–55 240–380 90–2340 345–1450 415–1750 415–1450 620–760

45–4 65–3 50–9 21–5 40–30 60–5 65–2 25–7 0

Nonmetallic materials Ceramics 70–1000 — 140–2600 0 Diamond 820–1050 — — — Glass and porcelain 70-80 — 140 — Rubbers 0.01–0.1 — — — Thermoplastics 1.4–3.4 — 7–80 1000–5 Thermoplastics, reinforced 2–50 — 20–120 10–1 Thermosets 3.5–17 — 35–170 0 Boron fibers 380 — 3500 0 Carbon fibers 275–415 — 2000–3000 0 Glass fibers 73–85 — 3500–4600 0 Kevlar fibers 62–117 — 2800 0 Note: In the upper table the lowest values for E, Y, and UTS and the highest values for elongation are for pure metals. Multiply gigapascals (GPa) by 145,000 to obtain pounds per square in. (psi), megapascals (MPa) by 145 to obtain psi.



Page 2-4

Loading and Unloading of Tensile-Test Specimen Figure 2.3 Schematic illustration of the loading and the unloading of a tensile- test specimen. Note that, during unloading, the curve follows a path parallel to the original elastic slope.



Page 2-5

Elongation versus % Area Reduction Figure 2.4 Approximate relationship between elongation and tensile reduction of area for various groups of metals.

Area Reduction = Ao − A f × 100 Ao



Page 2-6

Construction of True Stress-True Strain Curve Figure 2.7 (a) Load-elongation curve in tension testing of a stainless steel specimen. (b) Engineering stress-engineering strain curve, drawn from the data in Fig. 2.5a. (c) True stress-true strain curve, drawn from the data in Fig. 2.5b. Note that this curve has a positive slope, indicating that the material is becoming stronger as it is strained. (d) True stress-true strain curve plotted on log-log paper and based on the corrected curve in Fig. 2.5c. The correction is due to the triaxial state of stress that exists in the necked region of a specimen.

σ = Kalpakjian, Manufacturing Processes for Engineering Materials


P l , ε = ln( ) A lo Page 2-7

Typical Values for K and n at Room Temperature TABLE 2.3 A lum inum 1100–O 2024–T4 6061–O 6061–T6 7075–O B rass 70–30, annealed 85–15, cold-rolled C obalt-base alloy, heat-treated C opper, annealed Steel Low-C annealed 4135 annealed 4135 cold-rolled 4340 annealed 304 stainless, annealed 410 stainless, annealed


K (M Pa)

n

180 690 205 410 400

0.20 0.16 0.20 0.05 0.17

900 580 2070 315

0.49 0.34 0.50 0.54

530 1015 1100 640 1275 960

0.26 0.17 0.14 0.15 0.45 0.10


Page 2-8

True Stress-True Strain Curves Figure 2.6 True stresstrue strain curves in tension at room temperature for various metals. The curves start at a finite level of stress: The elastic regions have too steep a slope to be shown in this figure, and so each curve starts at the yield stress, Y, of the material.

σ = Kε



n

Page 2-9

Temperature Effects on Stress-Strain Curves Figure 2.10 Typical effects of temperature on stress-strain curves. Note that temperature affects the modulus of elasticity, the yield stress, the ultimate tensile strength, and the toughness (area under the curve) of materials.



Page 2-10

Typical Ranges of Strain and Deformation Rate in Manufacturing Processes TABLE 2.4 Process Cold working Forging, rolling Wire and tube drawing Explosive forming Hot working and warm working Forging, rolling Extrusion Machining Sheet-metal forming Superplastic forming


True strain

Deformation rate (m/s)

0.1–0.5 0.05–0.5 0.05–0.2

0.1–100 0.1–100 10–100

0.1–0.5 2–5 1–10 0.1–0.5 0.2–3

0.1–30 0.1–1 0.1–100 0.05–2 -4 -2 10 -10


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Effect of Strain Rate on Ultimate Tensile Strength Figure 2.11 The effect of strain rate on the ultimate tensile strength for aluminum. Note that, as the temperature increases, the slopes of the curves increase; thus, strength becomes more and more sensitive to strain rate as temperature increases. Source: J. H. Hollomon.



Page 2-12

Disk and Torsion-Test Specimens Figure 2.19 Disk test on a brittle material, showing the direction of loading and the fracture path.

Figure 2.20 Typical torsion-test specimen; it is mounted between the two heads of a testing machine and twisted. Note the shear deformation of an element in the reduced section of the specimen. Kalpakjian, Manufacturing Processes for Engineering Materials


Page 2-13

Bending

Figure 2.23 Two bend-test methods for brittle materials: (a) three-point bending; (b) four-point bending. The areas on the beams represent the bendingmoment diagrams, described in texts on mechanics of solids. Note the region of constant maximum bending moment in (b); by contrast, the maximum bending moment occurs only at the center of the specimen in (a).



Page 2-14

Hardness Tests Figure 2.24 General characteristics of hardness-testing methods and formulas for calculating hardness. The quantity P is the load applied. Source: H. W. Hayden, et al., The Structure and Properties of Materials, Vol. III (John Wiley & Sons, 1965).



Page 2-15

Brinell Testing

(c)


Figure 2.27 Indentation geometry in Brinell testing; (a) annealed metal; (b) work-hardened metal; (c) deformation of mild steel under a spherical indenter. Note that the depth of the permanently deformed zone is about one order of magnitude larger than the depth of indentation. For a hardness test to be valid, this zone should be fully developed in the material. Source: M. C. Shaw and C. T. Yang.


Page 2-16

Hardness Conversion Chart


Figure 2.14 Chart for converting various hardness scales. Note the limited range of most scales. Because of the many factors involved, these conversions are approximate. © 1997 Addison Wesley

Page 2-17

S-N Curves

Figure 2.28 Typical S-N curves for two metals. Note that, unlike steel, aluminum does not have an endurance limit.



Page 2-18

Endurance Limit/Tensile Strength versus Tensile Strength Figure 2.29 Ratio of endurance limit to tensile strength for various metals, as a function of tensile strength. Because aluminum does not have an endurance limit, the correlation for aluminum are based on a specific number of cycles, as is seen in Fig. 2.15.



Page 2-19

Creep Curve Figure 2.30 Schematic illustration of a typical creep curve. The linear segment of the curve (secondary) is used in designing components for a specific creep life.



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Impact Test Specimens Figure 2.31 Impact test specimens: (a) Charpy; (b) Izod.



Page 2-21

Residual Stresses Figure 2.32 Residual stresses developed in bending a beam having a rectangular cross-section. Note that the horizontal forces and moments caused by residual stresses in the beam must be balanced internally. Because of nonuniform deformation during metalworking operations, most parts develop residual stresses.



Page 2-22

Distortion of Parts with Residual Stresses

Figure 2.33 Distortion of parts, with residual stresses, after cutting or slitting: (a) flat sheet or plate; (b) solid round rod; (c) think-walled tubing or pipe.



Page 2-23

Tri-axial stress state and Yielding Maximum-shear criterion:

τ max = k

Distortion-energy criterion:

(σ 1 − σ 2 ) + (σ 2 − σ 3 ) + (σ 3 − σ 1 ) = 2Y 2

2

2

Plane stress and plane strain:

σ z ,τ xz,τ yz =0 or ε z ,ε xz,ε yz = 0 Kalpakjian, Manufacturing Processes for Engineering Materials


Page 2-24

2

Equivalent stress and strain Equivalent stress:

1 2 2 2 1/ 2 [(σ 1 − σ 2 ) + (σ 2 − σ 3 ) + (σ 3 − σ 1 ) ] = σ 2 Equivalent strain: 1 2 2

2 2 2 [(ε 1 − ε 2 ) + (ε 2 − ε 3 ) + (ε 3 − ε 1 ) ] = ε 3 Kalpakjian, Manufacturing Processes for Engineering Materials


Page 2-25

Plastic work Specific energy ( Energy per unit volume) : ε1

ε

0

0

u = ∫ σdε = ∫ σ d ε utotal = uideal + u friction + uredundant uideal η= ≈ 30 ~ 60 % (extrusion), 75 ~ 95 % (rolling ) utotal utotal ∆T = ρc Kalpakjian, Manufacturing Processes for Engineering Materials


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Mechanical Behaviour, Testing and Manufacturing Properties of Materials

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