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DESIGN is the ultimate function of engineer-ing in the development of products and pro-cesses, and an integral aspect of design is the use of mechanical properties derived from me-chanical testing. The basic objective of product design is to specify the materials and geometric details of a part, component, and assembly so that a system meets its performance require-ments. For example, minimum performance of a mechanical system involves transmission of the required loads without failure for the pre-scribed product lifetime under anticipated envi-ronmental (thermal, chemical, electromagnetic, radiation, etc.) conditions. Optimum perfor-mance requirements may also include additional criteria such as minimum weight, minimum life cycle cost, environmental responsibility, human factors, and product safety and reliability.

This chapter introduces the basic concepts of mechanical design and its general relation with the properties derived from tensile testing. Prod-uct design and the selection of materials are key applications of mechanical property data derived from testing. Although existing and feasible product shapes are of infinite variety and these shapes may be subjected to an endless array of complex load configurations, a few basic stress conditions describe the essential mechanical be-havior features of each segment or component of the product. These stress conditions include the following:

● Axial tension or compression

● Bending, shear, and torsion

● Internal or external pressure

● Stress concentrations and localized contact loads

Mechanical testing under these basic stress con-ditions using the expected product load/time profile (static, impact, cyclic) and within the ex-pected product environment (thermal, chemical,

electromagnetic, radiation, etc.) provides the de-sign data required for most applications.

In conducting mechanical tests, it is also very important to recognize that the material may contain flaws and that its microstructure (and properties) may be directional (as in composites) and heterogeneous or dependent on location (as in carburized steel). To provide accurate mate-rial characteristics for design, one must take care to ensure that the geometric relationships be-tween the microstructure and the stresses in the test specimens are the same as those in the prod-uct to be designed.

It is also important to consider the complexity of materials selection for a combination of prop-erties such as strength, toughness, weight, cost, and so on. This chapter briefly describes design criteria for some basic property combinations such as strength, weight, and costs. More de-tailed information on various performance in-dices in design, based on the methodology of Ashby, can be found in the article “Material Property Charts” in Materials Selection and De-sign, Volume 20 of ASM Handbook. The mate-rials selection method developed by Ashby is also available as an interactive electronic prod-uct (Ref 1).

Product Design

Design involves the application of physical principles and experience-based knowledge to develop a predictive model of the product. The model may be a prototype, a simplified mathe-matical model, or a complex finite element model. Regardless of the level of sophistication of the model, reaching the product design ob-jectives of material and geometry specifications for successful product performance requires ac-curate material parameters (Ref 2).

Fig. 1 Bar under axial tension

Modern design methods help manage the complex interactions between product geometry, material microstructure, loading, and environ-ment. In particular, engineering mechanics (from simple equilibrium equations to complex finite element methods) extrapolates the results of basic mechanical testing of simple shapes un-der representative environments to predict the behavior of actual product geometries under real service environments.

In the following sections, a simple tie bar is used to illustrate the application of mechanical property data to material selection and design and to highlight the general implications for me-chanical testing. Material subjected to the basic stress conditions is considered in order to estab-lish design approaches and mechanical test methods, first in static loading and then in dy-namic loading and aggressive environments.

More detailed reference books on mechanical design and engineering methods are also listed in the “Selected References” at the end of this chapter.

Design for Strength in Tension

Figure 1 shows an axial tensile load applied to a tie bar representing, for example, a boom crane support, cable, or bolt. For this elementary case, the stress in the bar is uniformly distributed over the cross section of the tie bar and is given by:

r ⳱ F/A (Eq 1)

where F is the applied force and A is the cross-sectional area of the bar. To avoid failure of the bar, this stress must be less than the failure stress, or strength, of the material:

r ⳱ F/A ⬍ r_f (Eq 2)

where rf is the stress at failure. The failure stress,rf, can be the yield strength, ro, if per-manent deformation is the criterion for failure, or the ultimate tensile strength,ru, if fracture is the criterion for failure. In a ductile metal or polymer, the ultimate tensile strength is defined as the stress at which necking begins, leading to fracture. In a brittle material, the ultimate strength is simply the stress at fracture. Typical values of yield and ultimate tensile strength for various materials are summarized in Tables 1, 2, and 3. These typical values are intended only for

general comparisons; design values should be based on statistically based minimum values or on minimum values published in the purchase specifications of materials (such as ASTM stan-dards).

Equation 2 combines the performance of the part (load F) with the part geometry (cross-sec-tional area A) and the material characteristics (strengthrf). The equation can be used several ways for design and material selection. If the material and its strength are specified, then, for a given load, the minimum cross-sectional area can be calculated; or, for a given cross-sectional area, the maximum load can be calculated. Con-versely, if the force and area are specified, then materials with strengths satisfying Eq 2 can be selected.

Factor of Safety. Normally, designs involve the use of some type of a factor of safety. This factor, which is always greater than unity, is used in the design of components to ensure that the component can satisfactorily perform its in-tended purpose. The factor of safety is used to account for the uncertainties that exist in the real-world use of any component. Two main classifications of factors affect the factor of safety in a design, and they are these:

● Uncertainties associated with the material properties of the component itself, including the expected properties of the materials used to fabricate the component, as well as any uncertainties introduced by manufacturing and fabrication processing

● Uncertainties associated with the level and type of loading the component will see, as well as the actual service conditions and any environmental condition the component may experience

The factor of safety is used to establish a target stress level for the design. This is sometimes re-ferred to as the allowable stress, the maximum allowable stress, or simply, the design stress. In order to determine this allowable stress condi-tion, the failure stress is simply divided by the safety factor. Safety factors ranging from 1.5 to 10 are typical. The lower the uncertainty is, the lower the safety factor.

Design for Strength, Weight, and Cost If minimum weight or minimum cost criteria must also be satisfied, Eq 2 can be modified by introducing other material parameters. To illus-trate, the area A in Eq 2 is related to density and mass by A⳱ M/qL, where M is the mass of the bar, L is the length of the bar, andq is the

ma-terial density. Solving Eq 2 for F and substitut-ing for A:

F ⬍ r A ⳱ (r /q)(M/L)_{f f} (Eq 3) From Eq 3 it is clear that, to transmit a given load, F, the material mass will be minimized if the property ratio (rf/q) is maximized. The strength-to-weight ratio of a material is an im-portant design and performance index; Fig. 2 is a plot developed by Ashby for comparison of materials by this design criterion. Similarly, ma-terial selection for minimum mama-terial cost can be obtained by maximizing the parameter (rf/ qc), or strength-to-cost ratio, where c represents the material cost per unit weight. These types of performance indexes for design and the use of materials property charts like Fig. 2 are de-scribed in more detail in Ref 7 and in the articles

“Material Property Charts” and “Performance

Table 1 Typical room-temperature tensile properties of ferrous alloys and superalloys

Strength in tension, MPa (ksi) Modulus of elasticity, GPa (10⁶psi) Material

0.2% offset

yield strength Ultimate Tension Shear

Elongation in 50 mm (2 in.), % Cast irons

Gray cast iron . . . 140 (20) 105 (15) 40 (6) 1

White cast iron . . . 415 (60) 140 (20) 55 (8) . . .

Nickel cast iron, 1.5% nickel . . . 310 (45) 140 (20) 55 (8) 1

Malleable iron 230 (33) 345 (50) 170 (25) 70 (10) 14

Ingot iron, annealed 0.02% carbon 165 (24) 290 (42) 205 (30) 85 (12) 45

Steels

Wrought iron, 0.10% carbon 205 (30) 345 (50) 185 (27) 70 (10) 30

Steel, 0.20% carbon

Hot-rolled 275 (40) 415 (60) 200 (29) 85 (12) 35

Cold-rolled 415 (60) 550 (80) 200 (29) 85 (12) 15

Annealed castings 240 (35) 415 (60) 200 (29) 85 (12) 25

Steel, 0.40% carbon

Hot-rolled 290 (42) 485 (70) 200 (29) 85 (12) 25

Heat-treated for fine grain 415 (60) 620 (90) 200 (29) 85 (12) 25

Annealed castings 240 (35) 450 (65) 200 (29) 85 (12) 15

Steel, 0.60% carbon

Hot-rolled 435 (63) 690 (100) 200 (29) 85 (12) 15

Heat-treated for fine grain 540 (78) 825 (120) 200 (29) 85 (12) 15

Steel, 0.80% carbon

Hot-rolled 505 (73) 825 (120) 200 (29) 85 (12) 10

Oil-quenched, not drawn 860 (125) 1240 (180) 200 (29) 85 (12) 2

Steel, 1.00% carbon

Hot-rolled 570 (83) 930 (135) 200 (29) 85 (12) 10

Oil-quenched, not drawn 965 (140) 1515 (220) 200 (29) 85 (12) 1

Nickel steel, 3.5% nickel, 0.40% carbon, max.

hardness for machinability

1035 (150) 1170 (170) 200 (29) 85 (12) 12

Silicomanganese steel, 1.95% Si, 0.70% Mn, spring tempered

895 (130) 1200 (174) 200 (29) 85 (12) 1

Superalloys (wrought)

A286 (bar) 760 (110) 1080 (157) 180 (26) . . . 28

Inconel 600 (bar) 250 (36) 620 (90) . . . . . . 47

IN-100 (60 Ni-10Cr-15Co, 3Mo, 5.5Al, 4.7Ti) 850 (123) 1010 (147) 215 (31) . . . 9

IN-738 915 (133) 1100 (159) 200 (29) . . . 5

Source: Ref 3–5

Table 2 Typical room-temperature tensile properties of nonferrous alloys Heavy nonferrous alloys (⬃8–9 g/cm³)

Copper Cu Annealed 33 (4.8) 209 (30) 125 (18) 60

Cold drawn 333 (48) 344 (50) 112 (16) 14

Free-cutting brass 61.5 Cu, 35.5 Zn, 3 Annealed 125 (18) 340 (49) 85 (12) 53

Pb Quarter hard, 15%

reduction

85 Cu, 15 Zn Annealed, 0.070 mm grain

70 (10) 270 (39) 85 (12) 48

Extra hard 420 (61) 540 (78) 105 (15) 4

Aluminum bronze 89 Cu, 8 Al, 3 Fe Sand cast 195 (28) 515 (75) . . . 40

Extruded 260 (38) 565 (82) 125 (18) 25

Beryllium copper 97.9 Cu, 1.9 Be, 0.2 Ni

A (solution annealed)

. . . 500 (73) 125 (18) 35

HT (hardened) 1035 (150) 1380 (200) 125 (18) 2

Manganese bronze 58.5 Cu, 39 Zn, 1.4 Soft annealed 205 (30) 450 (65) 90 (13) 35

(A) Fe, 1 Sn, 0.1 Mn Hard, 15% reduction 415 (60) 565 (82) 105 (15) 25

Phosphor bronze, 5% (A)

95 Cu, 5 Sn Annealed, 0.035 mm grain

150 (22) 340 (49) 90 (13) 57

Extra hard, 0.015 mm grain

635 (92) 650 (94) 115 (17) 5

Cupronickel, 30% 70 Cu, 30 Ni Annealed at 760⬚C 140 (20) 380 (55) 150 (22) 45

Cold drawn, 50%

reduction

540 (78) 585 (85) 150 (22) 15

Light nonferrous alloys (⬃2.7 g/cm³for Al alloys;⬃1.8 g/cm³for Mg alloys)

Aluminum Al Sand cast, 1100-F 40 (5.8 or 6) 75 (11) 60 (9) 22

Extruded 69–105 (10–15) 195 (28) 40 (6) 5–8

Rolled 115–140 (17–20) 200 (29) 40 (6) 2–10

Magnesium alloy 90 Mg, 10 Al, 0.1 Cast, condition F 85 (12) 150 (22) 45 (7) 2

AM100A Mn Cast, condition T61 150 (22) 275 (40) 45 (7) 1

Magnesium alloy 91 Mg, 6 Al, 3 Zn, Cast, condition F 95 (14) 200 (29) 45 (7) 6

AZ63A 0.2 Mn Cast, condition T6 130 (19) 275 (40) 45 (7) 5

(continued)

Indices” in Materials Selection and Design, Vol-ume 20 of ASM Handbook.

Design for Stiffness in Tension

In addition to designing for strength, another important design criterion is often the stiffness or rigidity of a material. The elastic deflection of a component under load is governed by the stiffness of the material. For example, if a bridge or building is designed to avoid failure, it may still undergo motion under applied loads if it is not sufficiently rigid. As another example, if the tie bar in Fig. 1 were a bolt clamping a cap to a pressure vessel, excessive elastic change in length of the bolt under load might allow leak-age through a gasket between the cap and vessel.

Elastic change in length occurs when an axial load is applied to the bar and is given by:

DL ⳱ eL (Eq 4)

whereDL is the change in length and e is the strain in the bar. In the elastic range of defor-mation, axial stress is proportional to the strain:

r ⳱ Ee (Eq 5)

where the proportionality factor is E, the elastic modulus of the bar material.

The elastic modulus can be considered a physical property, because it is fundamentally related to the bond strength between the atoms or molecules in the material; that is, the stronger the bond, the higher the elastic modulus. Thus,

Table 3 Typical room-temperature tensile properties of plastics

Material Tensile strength, MPa (ksi) Elongation, % Modulus of elasticity, GPa (10⁶psi)

Thermosets

EP, reinforced with glass cloth 350 (51) . . . 175 (25)

MF, alpha-cellulose filler 50–90 (7–13) 0.6–0.9 9 (1)

PF, no filler 50–55 (7–9) 1.0–1.5 5–7 (0.7–1)

PF, wood flour filler 45–60 (7–9) 0.4–0.8 6–8 (0.87–1.16)

PF, macerated fabric filler 25–65 (4–9) 0.4–0.6 6–9 (0.87–1)

PF, cast, no filler 40–65 (6–9) 1.5–2.0 3 (0.43)

Polyester, glass-fiber filler 35–65 (5–9) . . . 11–14 (1.6–2.0)

UF, alpha-cellulose filler 55–90 (8–13) 0.5–1.0 10 (1.5)

Thermoplastics

ABS 35–45 (5–7) 15–60 1.7–2.2 (0.25–0.32)

CA 15–60 (2–9) 6–50 0.6–3.0 (0.1–0.4)

CN 50–55 (7–9) 40–45 1.3–15.0 (0.18–2)

PA 80 (12) 90 3.0 (0.43)

PMMA 50–70 (7–10) 2–10 . . .

PS 35–60 (5–9) 1–4 3.0–4.0 (0.4–0.6)

PVC, rigid 40–60 (6–9) 5 2.4–2.7 (0.3–0.4)

PVCAc, rigid 50–60 (7–9) . . . 2.0–3.0 (0.3–0.4)

ABS, acrylonitrile-butadiene-styrene; CA, cellulose acetate; CN, cellulose nitrate; EP, epoxy; MF, melamine formaldehyde; PA, polyamide (nylon); PF, phenol for-maldehyde; PMMA, polymethyl methacrylate; PS, polystyrene; PVC, polyvinyl chloride; PVCAc, polyvinyl chloride acetate; UF, urea formaldehyde. Source: Ref 6

Table 2 (continued)

Metal or alloy

Approximate composition,

% Condition

0.2% offset tensile yield strength,

MPa (ksi)

Tensile strength, MPa (ksi)

Tensile modulus of elasticity, GPa (10⁶psi)

Elongation in 50 mm (2 in.),

%

Titanium alloys (⬃4.5 g/cm³) Commercial ASTM

grade 2 Ti

98 Ti . . . 275 (40) 345 (50) 103 (15) 20

Ti-5Al-2.5Sn 92 Ti, 5 Al, 2.5 Sn . . . 825 (120) 860 (125) 110 (16) 8–10

Ti-3Al-2.5V 94 Ti, 3 Al, 2.5 V Annealed 560 (81) 655 (95) 103 (15) 29

Cold worked and stress relieved

760 (110) 895 (130) 103 (15) 19

Ti-6A1-4V 90 Ti, 6 Al, 4 V Solution treated and aged bar (1–2 in.)

965 (140) 1035 (150) 110 (16) 8

Annealed bar 825 (120) 895 (130) 110 (16) 10

Mill annealed . . . 925 (134) . . . . . .

the elastic modulus does not vary much in ma-terial with a given type of crystal structure or microstructure. For example, the elastic modu-lus of most steels is typically about 200 GPa (29

⳯ 10⁶psi) for steels of various composition and strength levels (Fig. 3). However, the modulus can vary with direction if the material has an anisotropic structure. For example, Fig. 4 is a plot of the tensile and compressive modulus for type 301 austenitic stainless steel. Transverse and longitudinal values vary, as do values for tensile and compressive loads. At low stresses, the tension and compressive moduli are, by the-ory and experiment, identical. At higher stresses, however, differences in the compressive and

ten-sile moduli can be observed due to the effects of deformation (e.g., elongation in tension). Typi-cal values of elastic moduli are given in Table 4 for various alloys and metals.

Equations 1 and 5 can be combined with Eq 4 to give the design equation:

DL ⳱ FL/AE ⬍ d (Eq 6)

whered is the design limit on change in length of the bar. Just as the strength, or load-carrying capacity, of the tie bar is related to geometry and material strength (Eq 2), the stiffness of the bar is related to geometry and the elastic modulus of the material. Again, part performance (force,

Fig. 2 Strength, rf, plotted against density, q, for various engineered materials. Strength is yield strength for metals and polymers, compressive strength for ceramics, tear strength for elastomers, and tensile strength for composites. Superimposing a line of constant rf/q enables identification of the optimum class of materials for strength at minimum weight.

F, and deflection,d) is combined with part ge-ometry (length, L, and cross-sectional area, A) and material characteristics (elastic modulus, E) in this design equation. To assure that the change in length is less than the allowable limit for a given force and material, the geometry param-eters L and A can be calculated; or, for given dimensions, the maximum load can be calcu-lated. Alternatively, for a given force and geo-metric parameters, materials can be selected whose elastic modulus, E, meets the design cri-terion given in Eq 6.

Similar to design for strength, additional cri-teria involving minimum weight or cost can be incorporated into design for stiffness. These cri-teria lead to the macri-terial selection parameters weight ratio (E/q) and modulus-to-cost ratio (E/qc), values that can be found in Ref 7 and ASM Handbook, Volume 20.

Mechanical Testing for

Stress at Failure and Elastic Modulus In Eq 2 and 6, the material propertiesrfand E play critical roles in design of the tie bar.

These properties are determined from a simple tensile test described in detail in Chapter 3,

“Uniaxial Tensile Testing.” The elastic modulus E is determined from the slope of the elastic part of the tensile stress strain curve, and the failure stress, rf, is determined from the tensile yield strength,ro, or the ultimate tensile strength,ru. Tensile-test specimens are cut from represen-tative samples, as described in more detail in Chapter 3. In the example of the tie bar, test pieces would be cut from bar stock that has been processed similarly to the tie bar to be used in the product. In addition, the test piece should be

Fig. 3 Stress-strain diagram for various steels. Source: Ref 8

machined such that its gage length is parallel to the axis of the bar. This ensures that any aniso-tropy of the microstructural features will affect performance of the tie bar in the same way that they influence the measurements in the tensile test. For example, test pieces cut longitudinally and transverse to the rolling direction of hot rolled steel plates will exhibit the same elastic modulus and yield strength, but the tensile strength and ductility will be lower in the trans-verse direction because the stresses will be

per-pendicular to the alignment of inclusions caused by hot rolling (Ref 10).

During tension testing of a material to mea-sure E andrf, in addition to the change in length due to the applied axial tensile loads, the mate-rial will undergo a decrease in diameter. This reflects another elastic property of materials, the Poisson ratio, given by:

m ⳱ ⳮe /e_{t l} (Eq 7)

where et is the transverse strain and el is the longitudinal strain measured during the elastic part of the tension test. Typical values of␯ range from 0.25 to 0.40 for most structural materials, but␯ approaches zero for structural foams and approaches 0.5 for materials undergoing plastic deformation. While the Poisson effect is of no consequence in the overall behavior of the tie bar (since the decrease in diameter has a negli-gible effect on the stress in the bar), the Poisson ratio is a very important material parameter in parts subjected to multiple stresses. The stress in one direction affects the stress in another di-rection via␯. Therefore, accurate measurements of the Poisson ratio are essential for reliable de-sign analyses of the complex stresses in actual part geometries, as described later. Typical val-ues of Poisson’s ratio are given in Table 4.

Table 4 Elastic constants for polycrystalline metals at 20⬚C (68 ⬚F)

Elastic modulus (E) Bulk modulus (K) Shear modulus (G)

Metal GPa 10⁶psi GPa 10⁶psi GPa 10⁶psi Poisson’s ratio,m

Aluminum 70 10.2 75 10.9 26 3.80 0.345

Brass, 30 Zn 101 14.6 112 16.2 37 5.41 0.350

Chromium 279 40.5 160 23.2 115 16.7 0.210

Copper 130 18.8 138 20.0 48 7.01 0.343

Iron, soft 211 30.7 170 24.6 81 11.8 0.293

Iron, cast 152 22.1 110 15.9 60 8.7 0.27

Lead 16 2.34 46 6.64 6 0.811 0.44

Magnesium 45 6.48 36 5.16 17 2.51 0.291

Molybdenum 324 47.1 261 37.9 125 18.2 0.293

Nickel, soft 199 28.9 177 25.7 76 11.0 0.312

Nickel, hard 219 31.8 188 27.2 84 12.2 0.306

Nickel-silver, 55Cu-18Ni-27Zn 132 19.2 132 19.1 34 4.97 0.333

Niobium 104 15.2 170 24.7 38 5.44 0.397

Silver 83 12.0 103 15.0 30 4.39 0.367

Steel, mild 211 30.7 169 24.5 82 11.9 0.291

Steel, 0.75 C 210 30.5 169 24.5 81 11.8 0.293

Steel, 0.75 C, hardened 201 29.2 165 23.9 78 11.3 0.296

Steel, tool steel 211 30.7 165 24.0 82 11.9 0.287

Steel, tool steel, hardened 203 29.5 165 24.0 79 11.4 0.295

Steel, stainless, 2Ni-18Cr 215 31.2 166 24.1 84 12.2 0.283

Tantalum 185 26.9 197 28.5 69 10.0 0.342

Tin 50 7.24 58 8.44 18 2.67 0.357

Titanium 120 17.4 108 15.7 46 6.61 0.361

Tungsten 411 59.6 311 45.1 161 23.3 0.280

Vanadium 128 18.5 158 22.9 46.7 6.77 0.365

Zinc 105 15.2 70 10.1 42 6.08 0.249

Source: Ref 9

Fig. 4 Tensile and compressive modulus at half-hard and full-hard type 301 stainless steel in the transverse and lon-gitudinal directions. Source: Ref 5

Sonic methods also offer an alternative and more accurate measurement of elastic proper-ties, because the velocity of an extensional sound wave (i.e., longitudinal wave speed, VL) is directly related to the square root of the ratio of elastic modulus and density as follows:

V_L⳱ (E/q)1/2 (Eq 8)

By striking a sample of material on one end and measuring the time for the pulse to travel to the other end, the velocity can be calculated.

Combining this with independent measurement of the density, Eq 8 can be used to calculate the elastic modulus (Ref 8).

Hardness-Strength Correlation

Correlation of hardness and strength has been examined for several materials as summarized in Ref 11. In hardness testing, a simple flat, spherical, or diamond-shaped indenter is forced under load into the surface of the material to be tested, causing plastic flow of material beneath the indenter as illustrated in Fig. 5. It would be

expected, then, that the resistance to indentation or hardness is proportional to the yield strength of the material. Plasticity analysis (Ref 12) and empirical evidence (summarized in Ref 11) show that the pressure on the indenter is ap-proximately three times the tensile yield strength of the material. However, correlation of hard-ness and yield strength is only straightforward when the strain-hardening coefficient varies di-rectly with hardness. For carbon steels, the fol-lowing relation has been developed to relate

expected, then, that the resistance to indentation or hardness is proportional to the yield strength of the material. Plasticity analysis (Ref 12) and empirical evidence (summarized in Ref 11) show that the pressure on the indenter is ap-proximately three times the tensile yield strength of the material. However, correlation of hard-ness and yield strength is only straightforward when the strain-hardening coefficient varies di-rectly with hardness. For carbon steels, the fol-lowing relation has been developed to relate

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