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Manufacturing Processes for Engineering Materials, 4th ed.Kalpakjian • SchmidPrentice Hall, 2003

Chapter 2Fundamentals of the

Mechanical Behavior of Materials


Types of Strain

FIGURE 2.1 Types of strain. (a) Tensile, (b) compressive, and (c) shear. All deformation processes in manufacturing involve strains of these types. Tensile strains are involved in stretching sheet metal to make car bodies, compressive strains in forging metals to make turbine disks, and shear strains in making holes by punching.


Tension Test

Figure 2.2 (a) Original and final shape of a standard tensile-test specimen. (b) Outline of a tensile-test sequence showing stages in the elongation of the specimen.


Mechanical Properties of MaterialsMETALS (WROUGHT) E (GPa) Y (MPa) UTS (MPa) ELONGATION

(%) in 50 mmPOISSONÕSRATIO (ν)

Aluminum and its alloysCopper and its alloysLead and its alloysMagnesium and its alloysMolybdenum and its alloysNickel and its alloysSteelsStainless steelsTitanium and its alloysTungsten and its alloys

69-79105-150

1441-45

330-360180-214190-200190-20080-130

350-400

35-55076-1100

14130-30580-2070105-1200205-1725240-480344-1380550-690

90-600140-1310

20-55240-38090-2340345-1450415-1750480-760415-1450620-760

45-565-350-921-540-3060-565-260-2025-7

0

0.31-0.340.33-0.35

0.430.29-0.35

0.320.31

0.28-0.330.28-0.300.31-0.34

0.27NONMETALLIC MATERIALSCeramicsDiamondGlass and porcelainRubbersThermoplasticsThermoplastics, reinforcedThermosetsBoron fiberCarbon fibersGlass fibers (S, E)Kevlar fibers (29, 49, 129)Spectra fibers (900, 1000)

70-1000820-1050

70-800.01-0.11.4-3.42-50

3.5-17380

275-41573-8570-11373-100

------------

140-2600-

140-

7-8020-12035-1703500

2000-53003500-46003000-34002400-2800

0-0-

1000-510-1

00

1-25

3-43

0.2-

0.240.5

0.32-0.40-

0.34-----

Note: In the upper table the lowest values for E, Y, and UTS and the highest values for elongation are for thepure metals. Multiply GPa by 145,000 to obtain psi, and MPa by 145 to obtain psi. For example, 100 GPa =14,500 ksi, and 100 MPa = 14,500 psi.

Table 2.1 Typical mechanical properties of various materials at room temperature.


Loading and Unloading

FIGURE 2.3 Schematic illustration of loading and unloading of a tensile-test specimen. Note that during unloading, the curve follows a path parallel to the original elastic slope.


True Stress-True-Strain Curves in Tension

FIGURE 2.5 (a) True stress-true-strain curve in tension. Note that, unlike in an engineering stress-strain curve, the slope is always positive, and the slope decreases with increasing strain. Although stress and strain are proportional in the elastic range, the total curve can be approximated by the power expression shown. On this curve, Y is the yield stress and Yf is the flow stress. (b) True-stress true-strain curve plotted on a log-log scale. (c) True stress-true-strain curve in tension for 1100-O aluminum plotted on a log-log scale. Note the large difference in the slopes in the elastic and plastic ranges. Source: After R. M. Caddell and R. Sowerby.


Power Law Material Behavior

MATERIAL K (MPa) nAluminum, 1100-O

2024-T45052-O6061-O6061-T67075-O

Brass, 70-30, annealed85-15, cold-rolled

Bronze (phosphor), annealedCobalt-base alloy, heat treatedCopper, annealedMolybdenum, annealedSteel, low-carbon, annealed

1045 hot-rolled1112 annealed1112 cold-rolled4135 annealed4135 cold-rolled4340 annealed17-4 P-H annealed52100 annealed304 stainless, annealed410 stainless, annealed

180690210205410400895580720207031572553096576076010151100640120014501275960

0.200.160.130.200.050.170.490.340.460.500.540.130.260.140.190.080.170.140.150.050.070.450.10

Note: 100 MPa = 14,500 psi.

σ = Kεn

Table 2.3 Typical values of K and n in Eq. (2.11) at room temperature.


True Stress -True Strain Curves for

Various Metals

FIGURE 2.6 True-stress-true-strain curves in tension at room temperature for various metals. The point of intersection of each curve at the ordinate is the yield stress Y; thus, the elastic portions of the curves are not indicated. When the K and n values are determined from these curves, they may not agree with those given in Table 2.3, because of the different sources from which they were collected. Source: S. Kalpakjian.


Strain Rate Effects

Table 2.5 Approximate range of values for C and m in Eq. (2.16) for various annealed materials at true strains ranging from 0.2 to 1.0.

CMATERIAL TEMPERATURE, C psi x 103 MPa mAluminumAluminum alloysCopperCopper alloys (brasses)LeadMagnesiumSteel Low-carbon Medium-carbon StainlessTitaniumTitanium alloysTi-6Al-4V*

Zirconium

200-500200-500300-900200-800100-300200-400

900-1200900-1200600-1200200-1000200-1000815-930200-1000

12-245-535-360-2

1.6-0.320-2

24-723-760-5

135-2130-59.5-1.6120-4

82-14310-35240-20415-1411-2

140-14

165-48160-48415-35930-14900-3565-11830-27

0.07-0.230-0.20

0.06-0.170.02-0.30.1-0.2

0.07-0.43

0.08-0.220.07-0.240.02-0.40.04-0.30.02-0.30.50-0.800.04-0.4

* At a strain rate of 2 x 10-4 s-1.Note: As temperature increases, C decreases and m increases. As strain increases, C increases and m mayincrease or decrease, or it may become negative within certain ranges of temperature and strain.Source: After T. Altan and F.W. Boulger.

σ = C Ý ε m


Barreling In Compression

FIGURE 2.15 Barreling in compression of a round solid cylindrical specimen (7075-O aluminum) between flat dies. Barreling is caused by interfaces, which retards the free flow of the material. See also Figs. 6.1 and 6.2. Source: K. M. Kulkarni and S. Kalpakjian.

FIGURE 2.16 Schematic illustration of the plane-strain compression test. The dimensional relationships shown should by satisfied for this test to be useful and reproducible. This test give the yield stress of the material in plane strain, Y’. Source: After A. Nadai and H. Ford.

Plane Strain Compression


Disk Test

FIGURE 2.19 Disk test on a brittle material, showing the direction of loading and the fracture path. This test is useful for brittle materials, such as ceramics, carbides, and round specimens from grinding wheels.

Torsion-Test

FIGURE 2.20 A typical torsion-test specimen. It is mounted between the two heads of a machine and is twisted. Note the shear deformation of an element in the reduced section of the tubular specimen.


Bending Tests

FIGURE 2.23 Two bend test methods for brittle materials. (a) three-point bending; (b) four-point bending. The lower sketches represent the bending moment diagrams. Note the region of constant maximum bending moment in diagram (b), whereas the maximum bending moment occurs only at the center of the specimen in diagram (a).


Hardness Tests

FIGURE 2.24 General characteristics of hardness testing methods. The Knoop tst is known as a microhardness test because of the light load and small impressions. Source: After H. W. Hayden, W. G. Moffatt, and V. Wulff.


Brinell Hardness Test

FIGURE 2.25 Indentation geometry for Brinell hardness testing: (a) annealed metal; (b) work-hardened metal. Note the difference in metal flow at the periphery of the impressions.

Hardness vs. Yield Stress

FIGURE 2.26 Relation between Brinell hardness and yield stress for aluminum and steels. For comparison, the Brinell hardness (which is always measured in kg/mm2) is converted to psi units in the scale on the left.


Indentation Depth

FIGURE 2.27 Bulk deformation in mild steel under a spherical indenter. Note that the depth of the deformed zone is about one order of magnitude larger than the depth of indentation. For a hardness test to be valid, the material should be allowed to fully develop this zone. This difference in depth is why thinner specimens require smaller indentations. Source: Courtesy of M. C. Shaw and C. T. Yang.

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