mechanical behaviour, testing and manufacturing properties of materials

1Kalpakjian, Manufacturing Processes for Engineering Materials © 1997 Addison Wesley

CHAPTER 2

Mechanical Behavior, Testing, and Manufacturing Properties of Materials

(재료의기계적성질)

-2Kalpakjian, Manufacturing Processes for Engineering Materials © 1997 Addison Wesley

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.


Stress-Strain CurveFigure 2.2 A typical stress-strain curve obtained from a tension test, showing various features.


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 Diamond Glass and porcelain Rubbers Thermoplastics Thermoplastics, reinforced Thermosets Boron fibers Carbon fibers Glass fibers Kevlar fibers

70–1000 820–1050

70-80 0.01–0.1 1.4–3.4

2–50 3.5–17

380 275–415 73–85

62–117

— — — — — — — — — — —

140–2600 —

140 —

7–80 20–120 35–170 3500

2000–3000 3500–4600

2800

0 — — —

1000–5 10–1

0 0 0 0 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.


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.


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

100×−

=

o

fo

AAA

ductionArea Re


Construction of True Stress-True Strain CurveFigure 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 triaxialstate of stress that exists in the necked region of a specimen.

)ln(,oll

AP

= = εσ


Typical Values for K and n at Room Temperature

TABLE 2.3K (M Pa) n

Aluminum1100–O2024–T46061–O6061–T67075–O

Brass70–30, annealed85–15, cold-rolled

Cobalt-base alloy, heat-treatedCopper, annealedSteel

Low-C annealed4135 annealed4135 cold-rolled4340 annealed304 stainless, annealed410 stainless, annealed

180690205410400

900580

2070315

53010151100640

1275960

0.200.160.200.050.17

0.490.340.500.54

0.260.170.140.150.450.10


True Stress-True Strain CurvesFigure 2.6 True stress-true 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.

nKεσ =


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.


Typical Ranges of Strain and Deformation Rate in Manufacturing Processes

TABLE 2.4

Process True strainDeformation rate

(m/s)Cold working

Forging, rollingWire and tube drawing

Explosive formingHot working and warm working

Forging, rollingExtrusion

MachiningSheet-metal formingSuperplastic forming

0.1–0.50.05–0.50.05–0.2

0.1–0.52–51–10

0.1–0.50.2–3

0.1–1000.1–10010–100

0.1–300.1–1

0.1–1000.05–2

10-4

-10-2


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.


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.


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 bending-moment 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).


Hardness TestsFigure 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).


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.


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.


S-N Curves

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


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.


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.


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


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.


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.


Tri-axial stress state and Yielding

Maximum-shear criterion:

Distortion-energy criterion:

Plane stress and plane strain:

k= maxτ

2213

232

221 2)()()( Y=−+−+− σσσσσσ

0,,0,, == yzxzzyzxzz or εεεττσ


Equivalent stress and strain

Equivalent stress:

Equivalent strain:

σσσσσσσ =− +− +− 2/1213

232

221 ])()()[(

21

εεεεεεε =−+−+− 21

213

232

221 ])()()[(

32


Plastic work

cuT

rollingextrusionuu

uuuu

ddu

volumeunitperEnergyenergySpecific

total

total

ideal

redundantfrictionidealtotal

ρ

η

εσεσε ε

=∆

≈=

++=

== ∫ ∫

)(%95~75),(%60~30

:)(1

0 0

mechanical behaviour, testing and manufacturing properties of materials

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