Chapter 3: Materials · Ahmet Çelik

Source note: Source is Juvinall and Marshek, Fundamentals of Machine Component Design, 5th ed., Chapter 3 (pp. 89 to 130). The project copy of the book is a plain-text extraction, so figures are not available and several equation layouts are scrambled. Eqs. (3.1) to (3.7) are rebuilt from the extracted symbols and checked against the book’s own numbers. Eq. (3.15) is the least certain reconstruction. Worked examples: Sample Problems 3.1, 3.2, and 3.3 are included in short form. End-of-chapter problems are skipped. Appendix C property tables, Appendix F (MIL-HDBK-5J), and Appendixes C-19 to C-24 are referenced but not reproduced. The book gives the Ashby chart indices without derivation. The long list of common plastics (pp. 109 to 111) is condensed into a table. Added background is in blockquotes marked as such.

0. Overview

Chapter 3 summarizes the material knowledge a component designer uses daily: reading the tensile test in engineering and true terms, what cold work does to strength and ductility, energy-absorbing capacity, estimating strength from hardness, the pitfalls of handbook data, machinability, the main material families (cast iron, steel, nonferrous alloys, plastics, composites), Ashby selection charts, and a rational material selection procedure.

Core definitions and vocabulary

Best material: the one with the best value, the ratio of overall performance to total cost. Total cost is the fabricated part, including labor and overhead (§3.1).
Engineering stress and strain: $\sigma = P/A_0$ , $\epsilon = \Delta L/L_0$ , based on original area and length (§3.2).
Notation: $\sigma$ = normal stress from loads (tension, compression, bending). $\tau$ = shear stress (torsion, transverse shear). $S$ with subscripts = strength, a material property, used for all strengths including shear (§3.2).
Elastic limit $S_e$ : highest stress after which the material returns exactly to its original length (point A, Fig. 3.1) (§3.2).
Proportional limit: stress where the curve first deviates from a straight line. Point A approximates it for most engineering materials. Hooke’s law holds below it (§3.2).
Modulus of elasticity (Young’s modulus) $E$ : slope of the curve from the origin to the proportional limit (§3.2).
Yield strength $S_y$ : stress at which significant plastic yielding first occurs. Found by the 0.2 percent offset method when yielding is gradual (point B) (§3.2).
Ultimate strength $S_u$ : engineering stress at the greatest load the specimen withstands (§3.2).
Area ratio $R$ : $A_0/A_f$ . Reduction in area $A_r$ : $\Delta A/A_0$ (§3.3).
Ductility: usually measured as percent elongation and percent reduction in area in tension. 5 percent elongation at failure marks the brittle-to-ductile transition (SP 3.1 comments).
True stress $\sigma_T$ : load divided by the area existing while the load acts, $P/A_f$ (§3.4).
True strain $\epsilon_T$ : sum of length increments each divided by the current length, $\ln(L_f/L_0)$ (§3.4).
Strain-strengthening exponent $m$ and coefficient $\sigma_0$ : constants of $\sigma_T = \sigma_0 \epsilon_T^m$ . $\sigma_0$ is the true stress at a true strain of unity (§3.4).
Resilience: capacity to absorb energy in the elastic range. Modulus of resilience $R_m$ : energy per unit volume to the elastic limit (§3.5).
Toughness: total capacity to absorb energy without fracture. Modulus of toughness $T_m$ : energy per unit volume to fracture (§3.5).
Machinability: relative cutting speed for a fixed tool life under standard cutting conditions (§3.8).
Hardenability: ease with which steel can be hardened. Measured by the Jominy end-quench test (§3.10).
Case hardening: hardening only the surface layer (the case) (§3.10).
Composite: two or more dissimilar constituents that stay distinct and separate on a macroscopic level (§3.12.2).
Selection index SI: (availability)(performance)/(total cost) (§3.14.4).

Key relations (all in book)

Constant-volume relations for necking: (3.1) to (3.3) (§3.3).
True stress and strain: (3.4), (3.5) (§3.4).
Elastic and plastic lines: (3.6), (3.7) (§3.4).
Energy capacity: (3.8) to (3.10) (§3.5).
Hardness to strength: (3.11) to (3.13) (§3.6).
Shear modulus: (3.14) (§3.7). Machinability: (3.15) (§3.8).

1. Introduction (§3.1)

Physical picture: material and process selection are part of designing any component, not an afterthought (§3.1).

Factor	Book’s point
Strength and rigidity	Traditional key factors
Reliability and durability	Equally important as strength
Extreme operating temperatures	Must be considered carefully
Recyclability, energy, pollution	Increasing influence on choices
Cost and availability	Vital. Both vary with time, so alternatives must be re-evaluated as markets change

The useful life of most components ends with fatigue failure or surface deterioration (Ch. 8 and Ch. 9) (§3.1).
Data sources named: Appendix C (C-1 physical constants, later tables for mechanical properties), Appendix F (MIL-HDBK-5J, over 1700 pages of aircraft metal data), matweb.com (search by material or by required properties), machinedesign.com. Consult metallurgists and materials specialists when needed (§3.1).

2. The Static Tensile Test: “Engineering” Stress-Strain Relationships (§3.2)

Physical picture: the standard tensile test is the basic test of strength and rigidity. It gives the engineering stress-strain curve (Fig. 3.1, one line: hot-rolled 1020 steel on a nonlinear strain scale with points A, B, C, F and $S_e = 36$ , $S_y = 39$ , $S_u = 66$ ksi) (§3.2).

Governing equations

\sigma = \frac{P}{A_0}, \qquad \epsilon = \frac{\Delta L}{L_0}

$P$ load, $A_0$ original unloaded area, $\Delta L$ change in length under load, $L_0$ original unloaded length.

Points on the curve (Fig. 3.1, hot-rolled 1020 steel)

Point	Property	Value	Notes
A	Elastic limit $S_e$	36 ksi	Approximates the proportional limit. Not a standard lab determination
B	Yield strength $S_y$ (0.2% offset)	39 ksi	Standard lab determination. Unloading from B leaves 0.2 percent permanent elongation
C	Ultimate strength $S_u$	66 ksi	Greatest load the specimen withstands
F	Fracture		End of the curve

Assumptions and validity range

Soft steel yields suddenly at a clearly defined stress. Other materials yield gradually, so the offset method is used: a line parallel to the elastic portion, offset 0.2 percent strain (§3.2).
Some materials deviate slightly from linearity from the origin. They have no true proportional limit and no definite $E$ . The computed $E$ depends on which part of the curve is used (§3.2).
Yield strength at a specified small offset is a standard laboratory determination. Elastic limit and proportional limit are not (§3.2).

3. Implications of the “Engineering” Stress-Strain Curve (§3.3)

Physical picture: Fig. 3.2 replots Fig. 3.1 on a linear strain scale, with two extra abscissa scales: area ratio $R$ and area reduction $A_r$ . On this scale the elastic portion lies almost on the vertical axis (§3.3).

Four implications (§3.3)

Elastic strains are tiny. At the 36-ksi elastic limit, $\epsilon = \sigma/E = 0.0012$ . Strain at ultimate and at fracture is about 250 and 1350 times this.
Calculated elastic stresses at a notch can be fictitious. If a notch makes the surface strain 3 times the nominal $P/AE$ , a nominal stress of 30 ksi (strain 0.001) gives 0.003 at the notch. The computed elastic notch stress is 90 ksi, above $S_u$ , yet the member is not altered in any normally detectable way.
Strain after necking is hard to measure. Local elongation in the neck is far larger than elsewhere, so elongation depends on gage length. Better: measure the fracture area and assume constant volume.
Unloading and reloading. Unloading follows a line of slope $E$ , and reloading returns to the same curve. A specimen unloaded and retested is effectively a new, cold-worked specimen.

Governing equations (constant volume)

A_0 L_0 = A_f(L_0 + \Delta L) = A_f L_0 (1 + \epsilon)

A_f = \frac{A_0}{1 + \epsilon} \tag{3.1}

R = \frac{A_0}{A_f} = 1 + \epsilon \tag{3.2a}

\Delta A = A_0 - A_f = A_0\left(1 - \frac{1}{1 + \epsilon}\right) \tag{3.2b}

A_r = \frac{\Delta A}{A_0} = 1 - \frac{1}{1 + \epsilon} = 1 - \frac{1}{R} \tag{3.3}

Subscripts 0 and f: initial and final values.

Book numbers for point 3: unit original area and very short unit gage length, fracture area 0.4. Then $R = 1/0.4 = 2.5$ , $A_r = 0.6$ (60 percent), gage length grows to 2.5, $\epsilon = 1.5$ .

Book numbers for point 4 (Fig. 3.2):

Load to D (62 ksi) and unload along DG with slope $E = 30 \times 10^6$ psi. At G the specimen is permanently stretched to 11/10 of its length, so its area is 10/11 of the original.
New yield strength: $62/(10/11) = 68$ ksi.
New ultimate strength: $66/(10/11) = 73$ ksi.
New reduction in area: from 10/11 (at G) to 10/25 (at F), 56 percent, compared with 60 percent on the original area.

Sample Problem 3.1, Strength and Ductility after Cold Work (pp. 93 to 94)

Given: critical location of a hot-rolled AISI 1020 part cold-worked during fabrication to point C of Fig. 3.2. Find $S_u$ , $S_y$ , and ductility ( $\epsilon$ , $R$ , $A_r$ at fracture).

Assumption: after cold work, the stress-strain curve of the location starts at point H.

At H the material is permanently stretched to 1.3 times its length, so its area is $A_0/1.3$ .
On the new area: $S_y = S_u = 66(1.3) = 85.8$ ksi.
Area at F is $A_0/2.5$ , so $R = A_H/A_F = 2.5/1.3 = 1.92$ .
Eq. (3.3): $A_r = 1 - 1/1.92 = 0.480$ , or 48 percent.
Eq. (3.2a): $\epsilon = R - 1 = 0.92$ , or 92 percent.

Comments: severe cold work (to point C or beyond) exhausts the ductility, so $S_y = S_u$ . Strength and ductility of metals change substantially during cold-working fabrication processes.

Solution workflow, properties after cold work

Locate the prestrain point on Fig. 3.2 and its permanent stretch ratio (for example 11/10 at G, 1.3 at H).
New area = original area / stretch ratio.
New strength = engineering stress at the prestrain point (or $S_u$ if beyond it) divided by the area fraction.
New $R$ = (stretch ratio at fracture) / (stretch ratio at prestrain). Then $A_r = 1 - 1/R$ and $\epsilon = R - 1$ .

4. The Static Tensile Test: “True” Stress-Strain Relationships (§3.4)

Physical picture: once a material is stretched to many times its maximum elastic strain (perhaps 20 or 30 times), engineering stress becomes fictitious because the real area is much smaller. True stress and true strain use current dimensions (§3.4).

Governing equations

True stress, using Eq. (3.1) for $A_f$ :

\sigma_T = \frac{P}{A_f} = \frac{P}{A_0}(1 + \epsilon) = \sigma(1 + \epsilon) = \sigma R \tag{3.4}

True strain:

\epsilon_T = \sum \frac{\Delta L}{L} = \int_{L_0}^{L_f} \frac{dL}{L} = \ln\frac{L_f}{L_0} = \ln R = \ln(1 + \epsilon) \tag{3.5}

Elastic region:

\sigma_T = E\epsilon_T \tag{3.6}

Plastic strain-strengthening region:

\sigma_T = \sigma_0 \epsilon_T^{\,m} \tag{3.7}

$\sigma_0$ strain-strengthening coefficient (true stress at $\epsilon_T = 1$ ), $m$ strain-hardening exponent (slope on log-log axes). The book writes $\sigma_0$ rather than $S_0$ although it is a material property, following common usage (footnote 2).

Book numbers (hot-rolled 1020, Figs. 3.2 and 3.3)

True stress at B, C, F: $39(1) = 39$ , $66(1.3) = 86$ , $45(2.5) = 113$ ksi. True stress rises continuously to fracture.
Fig. 3.3 constants: $E = 30 \times 10^3$ ksi, $S_y = 39$ ksi, $\sigma_0 = 115$ ksi, $m = 0.22$ , $\epsilon_{Tf} = 0.92$ .
Strain increment example: a unit-length bar stretched to 5, then to 5.1. Engineering strain added: $0.1/1 = 0.1$ . True strain added: $0.1/5 = 0.02$ .

Three regions on log-log axes (Fig. 3.3, Fig. 3.4)

Region	Equation	Log-log appearance	Meaning of the constant
Elastic	$\sigma_T = E\epsilon_T$ (3.6)	Straight line of unit slope through $(\epsilon_T = 1, \sigma_T = E)$	$E$ = stress for an elastic strain of unity
Plastic strain-strengthening	$\sigma_T = \sigma_0\epsilon_T^m$ (3.7)	Straight line of slope $m$	$\sigma_0$ = true stress at true strain of unity
Transition	Empirical curve (I or II in Fig. 3.4)	Between the two lines	”Ideal” material: elastic limit at the intersection of the two lines. Real $S_e$ may be higher or lower

Assumptions and validity range

$E$ is strictly the ratio of engineering stress and strain, but with negligible error also of true stress and strain (§3.4).
For metals, engineering and true strain are essentially equal below several times the maximum elastic strain (§3.4).
Strain-hardening data (Datsko [2], Appendix C-2) are typical values. They vary with small differences in composition and processing, especially true strain at fracture $\epsilon_{Tf}$ (§3.4).

Sanity check: $\epsilon_{Tf} = \ln R_f = \ln 2.5 = 0.92$ , matching Fig. 3.3.

5. Energy-Absorbing Capacity (§3.5)

Physical picture: some parts are designed to absorb energy rather than to carry load. Energy involves loads and deflections, so it is an area under the stress-strain curve (Fig. 3.5, one line: curve with the elastic triangle up to $S_e$ and the total area to fracture strain $\epsilon_f$ shaded) (§3.5).

Governing equations

Modulus of resilience (elastic triangle):

R_m = \frac{1}{2}(S_e)\left(\frac{S_e}{E}\right) = \frac{S_e^2}{2E} \tag{3.8}

Modulus of toughness (total area to fracture):

T_m = \int_0^{\epsilon_f} \sigma\, d\epsilon \tag{3.9}

Rough approximation:

T_m \approx \frac{S_y + S_u}{2}\,\epsilon_f \tag{3.10}

Units: energy per unit volume (for example in·lb/in³, which reduces to psi).

Assumptions and validity range

In practice $S_y$ replaces $S_e$ in Eq. (3.8), because $S_y$ is easier to estimate and very close to $S_e$ (footnote 3).
Eq. (3.9) is often integrated graphically. Eq. (3.10) is only a rough approximation (§3.5).
Energy-absorbing members usually see impact. Charpy and Izod tests estimate impact energy capacity at various temperatures more accurately [5] (§3.5).

6. Estimating Strength Properties from Penetration Hardness Tests (§3.6)

Physical picture: Brinell and Rockwell testers measure resistance to permanent deformation under a particular mix of triaxial compression and steep stress gradient. They are convenient and nondestructive (§3.6).

Governing equations

S_u = K_B H_B \tag{3.11}

$H_B$ Brinell hardness number, $K_B$ proportionality constant, $S_u$ in psi. $K_B \approx 500$ for most steels.

S_y = 1.05\,S_u - 30{,}000 \text{ psi} \tag{3.12}

With $K_B = 500$ :

S_y = 525\,H_B - 30{,}000 \text{ psi} \tag{3.13}

Assumptions and validity range

$K_B$ is a function of the strain-hardening exponent $m$ (Datsko [1, 2]). Fig. 3.6 (one line: $K_B$ from about 300 to 1000 vs. $m$ from 0 to 0.7, curves for indentation-to-ball diameter ratios $d/D$ of 0.2 to 0.6) gives the empirical relation.
Eqs. (3.12) and (3.13) apply to stress-relieved, not cold-worked, steels (§3.6).
Fig. 3.7 (one line: approximate conversions between Brinell, Rockwell B and C, Vickers, Shore, and $S_u$ of steel).

Sample Problem 3.2, Steel Strength from Hardness (pp. 98 to 100)

Given: AISI 4340 heat-treated to 300 Bhn. Find $S_u$ and $S_y$ .

Assumptions: the hardness-strength and yield-ultimate correlations are accurate enough.

Eq. (3.11): $S_u = 500(300) = 150{,}000$ psi.
Eq. (3.12): $S_y = 1.05(150{,}000) - 30{,}000 = 127{,}500$ psi.

Comments: Eq. (3.12) is a good estimate for stress-relieved (not cold-worked) steels. Test data would refine the estimate.

7. Use of “Handbook” Data for Material Strength Properties (§3.7)

Physical picture: ideally, strength data come from specimens matching the part in composition and in all mechanical and thermal history. Such data are rarely available, so handbook data (Appendix C) are used, and different references often contradict each other (§3.7).

Questions to ask of handbook data (§3.7)

Is the value a single test, or an average, median, typical, or minimum of several? Scatter depends on how well composition, thermal history, and mechanical history are controlled. Mean and standard deviation are often the right description (§6.14).
Do composition, size, heat treatment, and mechanical working of the test specimens match the actual part in its final as-fabricated condition?
Are the data consistent within themselves and with accepted results for similar materials? Are they reasonable?

Governing equation (from elastic theory)

G = \frac{E}{2(1 + \nu)} \tag{3.14}

$G$ shear (torsional) modulus, $E$ tensile elastic modulus, $\nu$ Poisson’s ratio.

8. Machinability (§3.8)

Physical picture: machining cost depends on material cost and on ease of machining. Published empirical machinability ratings are useful but sometimes unreliable or contradictory. Datsko showed machinability is a secondary property set by three primary properties (§3.8).

Governing equation

V_{60} = \frac{1150\,k}{H_B}\,(1 - A_r)^{1/2} \tag{3.15}

$V_{60}$ cutting speed (ft/min) for 60-min tool life under standard cutting conditions, $k$ thermal conductivity (Btu/(h·ft·°F)), $H_B$ Brinell hardness number, $A_r$ area reduction at fracture.

Decision rule: $k$ is about the same for all metals, so machinability of a metal depends essentially on hardness and ductility (§3.8).

9. Cast Iron (§3.9)

Physical picture: cast iron is a four-element alloy of iron, carbon (2 to 4 percent), silicon, and manganese, sometimes with added alloying elements. Properties depend strongly on the cooling rate during solidification, which depends on casting size, shape, and foundry practice. So, unlike other engineering materials, cast iron is usually specified by mechanical properties rather than chemical analysis (§3.9).

What the high carbon content does (§3.9)

Molten iron is very fluid, so it pours into intricate shapes.
Carbon precipitating during solidification offsets normal shrinkage, giving sound sections.
Graphite gives excellent machinability (even at wear-resisting hardness), damps vibration, and aids boundary lubrication.
“Chilled” surfaces (heat removed fast during solidification) keep carbon combined as iron carbides: an extremely hard, wear-resistant surface.

Per-type lookup (properties in Appendix C-3)

Type	Structure	Key properties	Typical applications
Gray iron	Graphite flakes	Good wear resistance even in soft grades. Flakes weaken it in tension, so compressive strength is 3 to 5 times tensile	Engine blocks, machine bases and frames, gears, flywheels, brake disks and drums
Ductile (nodular) iron	Mg causes carbon to form small spheres (nodules)	Substantial ductility, better tensile strength, stiffness, and impact resistance than gray iron. Spec “60-40-18” = $S_u$ 60 ksi, $S_y$ 40 ksi, 18% elongation	Crankshafts, heavy-duty gears, door hinges
White iron	Chilled mold surfaces deny time for carbon precipitation	Extremely hard, wear-resistant, brittle. White fracture surface	Ball mills, extrusion dies, cement mixer liners, railroad brake shoes, rolling mill rolls, crushers, pulverizers
Malleable iron	Not in the book	Not in the book	Heavy-duty parts with bearing surfaces: trucks, railroad, construction, farm equipment

Design rule: exploit the gray iron strength differential, for example ribs on the compression side of a member in bending (§3.9).

10. Steel (§3.10)

Physical picture: steel is the most widely used material for machine components. Composition, thermal treatment, and mechanical treatment give a huge property range (§3.10).

Three basic relationships (§3.10)

#	Relationship	Design consequence
1	All steels have essentially the same modulus of elasticity	If rigidity governs, all steels perform equally. Choose the least costly, including fabrication
2	Carbon content, almost alone, sets the maximum hardness. Maximum potential hardness rises with carbon up to about 0.7 percent	Small, regularly shaped parts reach the same hardness and strength in plain carbon steel as in costlier alloy steel
3	Alloying elements (Mn, Mo, Cr, Ni, others) make steel easier to harden	Potential hardness is reached with less drastic heat treatment: (a) large sections harden deeper into the core, (b) irregular parts prone to quench warpage harden with milder treatment

Plain carbon steel classes (§3.10)

Class	Carbon content
Low-carbon	Less than 0.3%
Medium-carbon	0.3 to 0.5%
High-carbon	Above 0.5%

Typical uses by carbon level: Appendix C-4b. Properties: Appendixes C-4 to C-8.

Jominy end-quench test (ASTM A-255, SAE J406b) (§3.10, Fig. 3.8)

Heat a 1-in. diameter, 4-in. long bar above its critical temperature.
Suspend it, water-quench the bottom end, let the top end air-cool.
Grind and measure Rockwell C hardness at 1/16-in. steps from the quenched end.
The distance the hardening reaches measures the hardenability given by the alloying elements.

Table 3.1, relative hardenability factor $f$ (Datsko [2]), in order of decreasing effectiveness

Element	Valid concentration (%)	Factor
Boron	B < 0.002	$f_B = 17.23\,B^{0.0268}$
Manganese	Mn < 1.2	$f_{Mn} = 3.46\,Mn + 1$
Manganese	1.2 < Mn < 2.0	$f_{Mn} = 5.125\,Mn - 1$
Molybdenum	Mo < 1.0	$f_{Mo} = 3.0\,Mo + 1$
Chromium	Cr < 2.0	$f_{Cr} = 2.18\,Cr + 1$
Silicon	Si < 2.0	$f_{Si} = 0.7\,Si + 1$
Nickel	Ni < 2.0	$f_{Ni} = 0.4\,Ni + 1$

Book examples: 1 percent Mn gives $f = 4.46$ . 2 percent Cr gives only a little more, 5.36. The table is incomplete (vanadium is a notable omission), and elements have secondary effects, but it guides the cheapest route to a required hardenability (§3.10).

Other steel classes (§3.10)

Class	Definition or purpose	Notes
Through-hardening alloy steel	Hardened through the section	One of the two main alloy steel classes
Carburizing alloy steel	Tough core with a relatively shallow, hard surface layer	Nitriding and other surface processes also used
HSLA (high-strength low-alloy)	Low-cost steels with much of the benefit of regular alloy steels, first developed around 1940	Higher strength than plain carbon steel allows weight reduction at little or no added part cost. Substantial automotive use
Stainless	Minimum 10.5 percent chromium, by definition	Wrought: austenitic, ferritic, martensitic, precipitation hardening (Appendix C-8). Cast: heat-resistant or corrosion-resistant
Iron-based superalloys	Elevated temperature service, as in turbines	Austenitic types used above 1000°F (538°C), martensitic types below. High-temperature strength and resistance to creep, oxidation, corrosion, wear. Gas turbines, jet engines, heat exchangers, furnaces (Appendix C-9)

Case-hardening processes (§3.10)

Process	What it does	Steels	Key note
Carburizing	Adds carbon to the surface of low-carbon steel, then heat-treats	Low-carbon	High surface hardness (Appendix C-7)
Cyaniding	Adds nitrogen and carbon to the surface	Low- and medium-carbon	Similar to carburizing
Nitriding	Adds nitrogen to an already machined and heat-treated part	”Nitralloy” (contains Al) for maximum case hardness, also medium-carbon alloy steels such as 4340	1000°F (538°C) or less, no quench, so no distortion
Induction and flame hardening	Heat only the surface, then quench and temper	Medium-carbon and alloy	Surface-only heating

11. Nonferrous Alloys (§3.11)

Alloy family	Designation	Strengths	Limits and notes	Data
Aluminum	4 digits wrought, 3 digits cast, then a temper designation	Hundreds of wrought and cast alloys	Casting shrinkage 3.5 to 8.5 percent by volume with no shrinkage-offsetting mechanism like carbon in cast iron. Hot shortness and gas absorption need controlled foundry practice	C-10, C-11, tempers C-12
Copper	Brasses (mainly Cu and Zn), bronzes (mainly Cu and Sn)	Good electrical and thermal conductivity, corrosion resistance	Low strength-to-weight. Strain-hardens when worked. Annealing, welding, or brazing heat restores ductility. Small additions improve strength, heat-softening resistance, machinability	C-13
Magnesium	ASTM system (decoded below)	Lightest engineering metals	Tempers same as aluminum	C-14
Nickel (incl. superalloys)	Nickel, Duranickel (over 94% Ni), Monel (Ni-Cu), Hastelloy (Ni-Mo, Ni-Mo-Cr), Inconel, Incoloy, Rene, Udimet (Ni-Cr, Ni-Cr-Fe)	Corrosion resistance, strength and toughness from 2000°F (1093°C) down to -400°F (-240°C). Monel strong and tough below zero, resists stress corrosion cracking. Several Hastelloys resist oxidation with useful strength and creep properties near 2000°F		C-15
Titanium		Nonmagnetic, extremely corrosion-resistant, low thermal conductivity, outstanding strength-to-weight	Very expensive, difficult to machine	C-16
Zinc	Die-cast alloys, plus ZA-12 castable by various methods	Inexpensive, moderate strength, low melting point, so cheap die casting	Limited use in other forms. Automotive parts, building hardware, office machine parts, toys	C-17

Aluminum heat treatment (differs from steel) (§3.11)

Solution treat: hold at elevated temperature until the hardening constituents (Cu, Mg, Mn, Si, Ni) dissolve.
Quench.
Age-harden: some hardening elements precipitate throughout the structure. Some alloys age at room temperature, others need elevated temperature (artificial aging).

Magnesium designation (ASTM) (§3.11)

Two letters: alloying elements of greatest and second greatest concentration.
Two digits: their percentages, rounded to whole numbers.
Serial letter: variation in composition, minor constituents, or impurities.
Temper designation, as for aluminum.

Letter	Element	Letter	Element	Letter	Element
A	Aluminum	K	Zirconium	Q	Silver
E	Rare earths	L	Lithium	S	Silicon
H	Thorium	M	Manganese	Z	Zinc

Book example: AZ31B-H24 = 3 percent aluminum, 1 percent zinc, strain-hardened.

12. Plastics and Composites (§3.12)

12.1 Plastics (§3.12.1)

Physical picture: plastics are synthetic organic materials. Monomers combine into polymers by polymerization, usually with heat, pressure, or both (Fig. 3.9, one line: monomers and repeating units for polyethylene, polypropylene, PVC, polystyrene, PTFE, polymethyl acrylate). Longer chains raise molecular weight and change properties drastically (§3.12.1).

Chain length vs. state (Fig. 3.10)

Molecule	State
CH₄ (methane)	Gas
C₂H₆ (ethane)	Heavier gas
C₅H₁₂ (pentane)	Liquid
C₁₈H₃₈ (paraffin)	Wax
About C₁₀₀H₂₀₂	Tough enough to be useful: low-molecular-weight polyethylene
Nearly half a million CH₂ units per chain	Toughest grade: high-molecular-weight polyethylene

Structure tradeoffs

Choice	Result	Why
Minimal side branching	Higher density, rigid crystalline structure, more mold shrinkage	Chains pack tightly, giving strong intermolecular attraction
Extensive side branching	More flexible amorphous material, less mold shrinkage and distortion	Branches keep chains from fitting closely
Cross-linked	Better resistance to heat, chemical attack, and creep (dimensional stability)	Chains join irreversibly into a network during molding
Linear	Less brittle (more impact-resistant), easier processing, better for complex shapes	Chains stay linear and separate after molding

Copolymerization: chains built from two monomers. Alloying: strictly mechanical mixing, no chemical bonds (§3.12.1).
Naming: traditional “thermoplastic” (softens with heat) and “thermosetting” (does not). Preferred: “linear” and “cross-linked”. Cross-linking starts by heat, chemical agents, irradiation, or a combination (§3.12.1).
Rule of thumb: thermoplastics are generally impact resistant, thermosets generally heat resistant (§3.12.1).

Reinforcement (§3.12.1)

Reinforcement	Effect	Cost
Glass fiber	Strength up by a factor of two or more	Base
Carbon fiber (10 to 40 percent carbon)	Tensile strength up to 40 ksi. Versus glass: less mold shrinkage, lower expansion, better creep, wear resistance, toughness	Substantially higher

Commercially most important glass-reinforced thermosets: polyester and epoxy (§3.12.1).

Handbook data warning for plastics (§3.12.1)

The §3.7 pitfalls apply even more to plastics.
Published values come from standardized, simple, reproducible molding conditions. Real molding conditions can give significantly different strengths.
Temperature and loading rate affect plastics much more than metals.
Data: Appendix C-18a (common plastics), C-18b (thermoplastics with and without glass), C-18c (typical applications).

Common plastics, condensed from the book’s list [4]

Plastic	Type	Strong points	Limits
ABS	Thermoplastic	Very tough yet hard and rigid, little water absorption (dimensional stability), high abrasion resistance, easily electroplated	Fair chemical resistance
Acetal	Thermoplastic	Very strong and stiff, exceptional dimensional stability, creep and vibration-fatigue resistance, low friction, abrasion and chemical resistance, keeps properties in hot water, little tendency to stress-crack	None listed
Acrylic	Thermoplastic	High optical clarity, outdoor weathering, hard glossy surface, electrical properties, transparent colors	Fair chemical resistance
Cellulosics	Thermoplastic	Tough and hard, broad property range by compounding, brilliant colors	Fair to poor dimensional stability
Fluoroplastics (PTFE, FEP, PFA, CTFE, ECTFE, ETFE, PVDF)	Thermoplastic	Excellent electrical and chemical resistance, low friction, high-temperature stability	Low to moderate strength, high cost
Nylon (polyamide)	Thermoplastic	Outstanding toughness and wear resistance, low friction, electrical and chemical resistance	Hygroscopic, poorer dimensional stability than most engineering plastics
Phenylene oxide	Thermoplastic	Excellent dimensional stability, good mechanical and electrical properties over a wide temperature range	Attacked by some hydrocarbons
Polycarbonate	Thermoplastic	Highest impact resistance of any rigid transparent plastic, outdoor stability, creep resistance	Fair chemical resistance, some aromatic solvents cause stress cracking
Polyester	Thermoplastic (also thermoset)	Dimensional stability, electrical properties, toughness, chemical resistance	Not strong acids or bases, notch-sensitive, not for outdoor or hot-water service
Polyethylene (LD, MD, HD, UHMW)	Thermoplastic	Light, easy to process, low cost, excellent chemical and electrical properties. LD flexible and tough, MD and HD stronger and more rigid	Poor dimensional stability and heat resistance
Polyimide	Thermoplastic	Heat resistance 500°F continuous, 900°F intermittent, high impact and wear resistance, low expansion	Hard to process conventionally, high cost
Polyphenylene sulfide	Thermoplastic	Chemical and heat resistance (450°F continuous), low-temperature strength, flame-retardant	High processing temperature
Polypropylene	Thermoplastic	Flex and stress-crack resistance, chemical and electrical properties, good impact strength above 15°F, light, low cost	Impact strength stated only above 15°F
Polystyrene	Thermoplastic	Low cost, easy to process, rigid, crystal clear, little moisture absorption	Brittle, low heat resistance, poor outdoor stability
Polysulfone	Thermoplastic	Highest heat deflection temperature of melt-processible thermoplastics, tough, strong, stiff, stable at high temperature	Notch-sensitive, high processing temperature, high cost
Polyurethane	Thermoplastic (also thermoset)	Tough, extremely abrasion- and impact-resistant, films, moldings, flexible foams	UV exposure causes brittleness, lower properties, yellowing
PVC	Thermoplastic	Rigid grades: hard, tough, electrical properties, outdoor stability, moisture and chemical resistance. Low cost	Flexible grades have lower properties, heat resistance low to moderate
Alkyd	Thermoset	Electrical properties, heat resistance, faster molding than most thermosets, no volatile by-products
Allyl (diallyl phthalate)	Thermoset	Outstanding dimensional stability and electrical properties, easy to mold, moisture and chemical resistance at high temperature
Amino (urea, melamine)	Thermoset	Abrasion and chip resistance, solvent resistance. Urea molds faster and costs less. Melamine has a harder surface and more heat and chemical resistance
Epoxy	Thermoset	Exceptional mechanical strength, electrical properties, adhesion to most materials, little mold shrinkage, some cure without heat or pressure
Phenolic	Thermoset	Low cost, good balance of mechanical, electrical, thermal properties	Black and brown only
Polyester	Thermoset (also thermoplastic)	Balanced properties, unlimited colors, no volatiles in curing, low-cost molds, used with glass as “fiber-glass”	Considerable mold shrinkage
Polyurethane	Thermoset (also thermoplastic)	Flexible or rigid, outstanding toughness, abrasion and impact resistance, large foamed parts
Silicone	Thermoset	Heat resistance -100 to +500°F, electrical properties, body tissue compatibility, many forms	High cost

12.2 Composites (§3.12.2)

Physical picture: a composite combines dissimilar constituents that stay distinct on a macroscopic level. It is not macroscopically homogeneous and not isotropic, so properties depend on direction. Combinations can be designed for better thermal and mechanical properties (§3.12.2).

Strength-to-weight: some composites reach four times that of high-strength metals. Stiffness-to-weight: up to seven times (§3.12.2).
Common example: strong fibers (glass, carbon, boron) bonded in nylon, epoxy, or polyester (§3.12.2).

Constituent	Materials	Role
Matrix	Plastic resins, sometimes metals	Supports, surrounds, and positions the reinforcement, and transfers load to it
Reinforcement	Glass, carbon, SiC, Kevlar (aramid)	Gives strength and stiffness
Reinforcement forms	Short, long, continuous, randomly oriented, woven (cloth), particulates (fillers)	Form and orientation set properties
Fillers	Glass beads in a thermoplastic (lower cost), mica in a phenolic (electrical properties, processing)	Usually cost reduction or specific properties

Size effect: small-diameter fibers have higher tensile strength than the parent material. Glass fiber is much stronger than sheet glass (§3.12.2).
Orientation: parallel, woven, random, wound, angled. Plies with strong directionality are stacked into laminates for better strength and stiffness (§3.12.2).
Stiffness analysis needs at least: two Young’s moduli, a shear modulus, and a Poisson’s ratio (§3.12.2).
Types on the charts: CFRP (carbon-fiber-reinforced polymer), GFRP (glass), KFRP (Kevlar), Al-SiC (SiC-reinforced aluminum). Polymer, metal, and ceramic matrix composites (PMC, MMC, CMC) in refs. [17] to [19] (§3.12.2).
Data: Appendix C-18 (glass-filled epoxy and polyester, wood-flour-filled phenolic), C-18b (glass-reinforced thermoplastics, typically 30 percent glass).

13. Materials Selection Charts (§3.13)

Physical picture: Ashby’s charts plot material classes against two properties so that candidate classes stand out. They are for rough calculations only. Final design uses the actual properties of the chosen material, followed by experimental verification and testing. Classes and abbreviations: Appendix C-19 (§3.13).

What “strength” means on the charts (Figs. 3.11 to 3.13)

Material class	Strength plotted
Metals and polymers	Yield strength
Ceramics and glasses	Compressive strength
Elastomers	Tear strength
Composites	Tensile strength

Strength-stiffness chart (§3.13.1, Fig. 3.11: S in MPa vs. E in GPa, log-log, with guide lines)

Index (maximize)	Design situation
$S^2/E = C$	Energy storage per unit volume, as in springs
$S/E = C$	Radius of bending, as in elastic hinges
$S^{3/2}/E = C$	Deflection under load, as in diaphragms

Ranking for maximum $S^2/E$ with no other limits: engineering ceramics, then elastomers, engineering alloys (steels), engineering composites, engineering polymers, woods, polymer foams (§3.13.1).

Link to §3.5 (algebra on Eq. 3.8): $S^2/E$ is twice the modulus of resilience of Eq. (3.8) with $S$ in place of $S_e$ , so it ranks elastic energy storage per unit volume.

General background (not in the book): for an elastic hinge of thickness $t$ bent to radius $\rho$ , surface strain is $t/2\rho$ . Keeping stress at or below $S$ gives $\rho \ge tE/2S$ , so a high $S/E$ allows a tight bend without yielding.

Strength-density chart (§3.13.2, Fig. 3.12: S in MPa vs. density in Mg/m³)

Ranges: strength 0.1 to 10,000 MPa, density 0.1 to 20 Mg/m³.
Guide lines for minimum-weight design:

Index (maximize)	Component
$S/\rho = C$	Rotating disks
$S^{2/3}/\rho = C$	Beams (shafts)
$S^{1/2}/\rho = C$	Plates

The constant grows as a guide line moves up and to the left. The best strength-to-weight materials sit in the upper left corner.

Strength-temperature chart (§3.13.3, Fig. 3.13: strength at temperature vs. temperature, lozenges per class)

Class	Limit
Ceramics	Only class with strength above 1000°C
Metals	Become soft at 800°C
Polymers	Little strength above 200°C

For engineering alloys the plotted “strength” is a short-term (one-hour) yield strength. Long loading (for example 10,000 h) gives lower strength and calls for creep and creep-rupture design (§3.13.3).

14. Engineering Material Selection Process (§3.14)

14.1 Introduction (§3.14.1)

Physical picture: material selection rests on experience, but a rational method helps. Performance specifications for the machine lead to component specifications, and material is usually specified when detailed component drawings are made (§3.14.1).

Table 3.2, general characteristics of the application: capacity (power, load, thermal), motion (kinematics, vibration, dynamics, controllability), interfaces (appearance, space limits, load types, environmental compatibility), cost (initial, operating), life, reliability, safety and health, noise, producibility, maintainability, geometry (size, shape), rigidity, elastic stability (buckling), weight, uncertainties (load, environment, cost).

Selection is based on (§3.14.1):

Availability of the material in the form and shape needed.
Total cost, initial and future.
Material properties as they relate to service performance.
Processing into a finished part.

Other factors (§3.14.1): limits of material properties, pressure to reduce cost, energy efficiency through weight reduction, material shortages, ease of recovery and recycling, disposal, legal and health issues.

Figure 3.14 flow (one line): identify application characteristics, then component specifications, then required material properties, then candidate materials considering cost and availability, then specify the best material, followed by fabrication and verification testing, evaluation, and failure analysis of the component.

Several performance requirements are weighed against the controlling properties. Candidates narrow to one or a few for testing in detail design. Testing may cover material integrity and variability, process effects, mating parts, or the whole machine in simulated or real service. Parts in service may be monitored, and failures lead to material or design corrections (§3.14.1).
Selection, like design, is iterative and needs experience, training, know-how, and art. Experience with a small repertoire of materials reduces reliance on materials engineers (§3.14.1).

14.2 Sources of Information on Material Properties (§3.14.2)

Sources: technical articles, company reports, trade literature, handbooks, internet documents, compendiums at large companies and agencies such as NASA. Appendix C, typical uses in C-3a to C-3c, C-4b, C-8, C-10, C-11, C-18c, C-23. Small design subset: C-20 (§3.14.2).
Property data are statistical (mean and standard deviation). A single handbook value is a typical value. Variation shows as ranges or scatter bands. Critical applications may need the frequency distributions of the property and of the service parameter (§3.14.2).
Computerized selection systems (for example grantadesign.com) offer material comparison, specifications, selection systems, examples, process information, and updated costs (§3.14.2).

14.3 Material Selection Factors (§3.14.3)

Four principal factors: (1) availability, (2) cost, (3) material properties: mechanical, physical, chemical, dimensional, (4) manufacturing processes: machining, formability, joinability, finishing and coatings. A wrong choice compromises function, service life, and cost (§3.14.3).

Table 3.3, characteristics of the material (condensed)

Category	Examples of subfactors
Mechanical properties	Strength, elasticity, hardness, Poisson’s ratio, damping, impact, toughness, fatigue, creep, wear, stiffness, shear
Physical properties	Density, electrical, magnetic, optical, conduction, expansion, flammability, melting point, specific heat, emissivity, absorptivity
Chemical properties	Corrosion resistance, degradation, composition, bonding, structure, oxidation, stability, embrittlement, environmental factors
Dimensional properties	Size, shape, flatness, profile, surface finish, stability, tolerances
Manufacturing processes	Castability, coatability, heat treatability, hardenability, formability, machinability, joinability, weldability
Availability	In stock, order elsewhere, order requirements, suppliers, special processing
Cost	Raw material, quantity, predicted service life, added fabrication
Legal	Code compliance, environmental, health, recyclability, disposability, product liability

Translating service performance into properties (§3.14.3)

Service requirement	Related property
Wear	Hardness
Stiffness	Modulus of elasticity
Weight	Density

Availability questions (§3.14.3)

Total time to obtain the material?
More than one supplier?
Available in the required geometry?
Limit on the amount available?
Probability of future availability?
Special processing required?
Will special processing limit availability?

The designer sets the procurement timeline to match the schedule (§3.14.3).

Economics (§3.14.3)

Use cost as an initial screening factor, but true prices come only from vendor quotes, since pricing structures are complex. Fig. 3.15 (one line: bulk cost in $/lbm vs.$ /in.³ for metals, polymers, elastomers, precious metals).
Use total life-cycle cost: (1) initial material, (2) processing and manufacturing, (3) installation, (4) operation and maintenance. Also anticipated service life, shipping and handling, recyclability, disposal.

Manufacturing links (§3.14.3)

Material and process constrain each other: the material dictates feasible forming, joining, and fastening methods, and a chosen process limits the material (Appendix C-21).
Formability and joinability: shearing, blanking, piercing, bending, spinning, drawing, peening, welding, brazing, soldering, threading, riveting, stapling, adhesive bonding (Appendix C-22).
Finishing and coatings: book example, low-carbon steel trencher teeth hard-faced by welding give a wear-resistant, lower-cost part.

Table 3.4, treatments and coatings [10]

Heat treatments	Surface treatments	Coatings
Age hardening, annealing, flame hardening, induction hardening, normalizing, quench hardening, solution treating, stress relieving, tempering	Anodizing, boronize, carbonitride, carburize, chromating, cyanide, nitride, oxides, phosphating	Hard surfacing, metallize, organosols, paints, plasma, plastisols, plating

14.4 Selection Procedure (§3.14.4)

Physical picture: selection usually means deciding with insufficient or inaccurate data, multiple and sometimes competing constraints, and no clear-cut objective. The method links functional requirements to material requirements to cut the candidate list (§3.14.4).

Basis: (1) engineering performance for the application, (2) relative importance of required properties, (3) availability and final cost of the component (§3.14.4).

Solution workflow (book steps a to d)

(a) Determine the purpose. Set service performance requirements (book example: a heavy-load, high-speed gear at elevated temperature needs a different material than a low-speed, low-torque gear at room temperature). Translate operating conditions and environment into critical material properties (Table 3.3).
(b) Select a suitable material. Screen and rank candidates with the selection charts (§3.13) and Appendix C-23 (candidate materials for common components). Use experience and typical uses, and do not reinvent the wheel (book example: Appendix C-10 suggests 6063-T6 aluminum for lightweight fuel tanks). Use failure analysis of similar failed parts (Appendix C-24 links properties to failure modes). Keep in mind that most lives end in fatigue or surface deterioration (pitting, spalling, wear). Pick a few candidates, reconsider fabrication, joining, availability, and cost. Ask: “Should this material be evaluated further?”
(c) Final evaluation and recommendation. Include manufacturing and finishing. Rank by the selection index. Expect a compromise, since the best engineering and best economic solutions usually differ.
(d) Test, test, test. Test the candidate under simulated operating conditions, possibly test the product itself. Extent of testing depends on total cost, service conditions, and experience. Weigh uncertainty and risk: consequences of failure must enter the selection.

Selection index

SI = \text{Selection Index} = \frac{(\text{availability})(\text{performance})}{(\text{total cost})}

The higher the SI, the better the choice. SI can rank candidates (§3.14.4).

14.5 Summary (§3.14.5)

Steps, iterative: (1) analysis of requirements, (2) identification of materials, (3) selection and evaluation of candidates, (4) testing and verification. Final choice is a compromise of availability, properties, processes, and economics, using experience, know-how, the selection index, and knowledge of failure modes (§3.14.5).

Sample Problem 3.3, Selecting a Bolt Material (p. 124)

Given: bolt machined from wrought stainless steel, yield strength at least 88 ksi to avoid plastic deformation (Fig. 3.16).

Assumptions: Appendix C-8 data accurate. Selection on machinability and properties. Cost and availability relatively unimportant.

Appendix C-8 “typical uses” lists classes 303, 414, 410, 431 for bolts.
Eliminate 303 and 410: yield strength below 88 ksi, so the bolt would yield.
414 and 431 have yield strengths above 88 ksi.
Eliminate 431: poor machinability.
Select class 414: fair machinability and yield strength above 88 ksi.

Comments: the choice must meet the property requirements. Cost and availability normally also enter the selection.

15. Common Exam Traps

“σ and S mean the same thing.” False. σ is stress caused by loads, S is a strength property of the material. Shear stress is τ, while S covers all strengths including shear (§3.2).
“Elastic limit and proportional limit are standard test values.” False. Only yield strength at a specified offset (0.2 percent) is a standard laboratory determination (§3.2).
“Every material has a well-defined E.” Some materials have no true proportional limit, and their E depends on the part of the curve used (§3.2).
“A calculated elastic notch stress above $S_u$ means the part is visibly damaged.” False. The 90-ksi notch stress in the book is fictitious. The real strain, 0.003, is barely perceptible (§3.3, point 2).
“Elongation at fracture from a gage length is exact.” It depends on gage length because of necking. Use fracture area and constant volume instead (§3.3, point 3).
” $A_r = 1 - R$ .” False. $A_r = 1 - 1/R$ (Eq. 3.3), and $R = 1 + \epsilon$ (Eq. 3.2a).
“Cold work leaves strength and ductility unchanged.” False. Prestrain to D raises $S_y$ to 68 ksi and $S_u$ to 73 ksi and lowers $A_r$ . Prestrain to C makes $S_y = S_u$ = 85.8 ksi (§3.3 point 4, SP 3.1).
“Engineering stress falls after ultimate, so the material weakens.” True stress rises continuously to fracture. Engineering stress uses the original area (§3.4).
“True strain equals engineering strain.” Only below several times the maximum elastic strain. In general $\epsilon_T = \ln(1 + \epsilon)$ (Eq. 3.5).
“Resilience and toughness are the same.” Resilience is elastic energy to $S_e$ , $S_e^2/2E$ . Toughness is total energy to fracture (Eqs. 3.8, 3.9).
” $T_m = \epsilon_f(S_y + S_u)/2$ is exact.” It is a rough approximation. Impact capacity needs Charpy or Izod tests (§3.5).
” $S_u = 500 H_B$ and $S_y = 1.05 S_u - 30$ ksi work for any metal in any condition.” $K_B \approx 500$ holds for most steels and depends on m. Eq. (3.12) is for stress-relieved, not cold-worked, steels. $S_u$ comes out in psi (§3.6).
“A handbook value is a guaranteed minimum.” It may be one test, an average, median, typical, or minimum value. A single handbook value should be read as typical (§3.7, §3.14.2).
“Alloy steel is stiffer than carbon steel.” False. All steels have essentially the same E (§3.10).
“Alloying raises the maximum attainable hardness.” False. Carbon sets maximum hardness (up to about 0.7 percent C). Alloying raises hardenability, so less drastic quenches and deeper hardening reach it (§3.10).
“Gray iron is equally strong in tension and compression.” False. Compressive strength is 3 to 5 times tensile, so ribs go on the compression side (§3.9).
“Cast iron is specified by chemical composition.” Usually by mechanical properties, because cooling rate dominates (§3.9).
“Nitriding needs a quench.” False. It runs at 1000°F or less with no quench, so no distortion, on already machined and heat-treated parts (§3.10).
“Aluminum is hardened like steel.” False. Solution treat, quench, then age-harden by precipitation (§3.11).
“Thermoplastics are the heat-resistant group.” Reverse. Thermoplastics are generally impact resistant, thermosets generally heat resistant (§3.12.1).
“Plastic data sheets match my molded part.” Published values come from standardized molding. Temperature and loading rate matter more than for metals (§3.12.1).
“Composites can be analyzed with one E and one ν.” False. They are not isotropic. At least two Young’s moduli, a shear modulus, and a Poisson’s ratio are needed (§3.12.2).
“Ashby chart values are design values.” False. Rough calculations only. Final design uses actual properties and testing (§3.13).
“Chart strength at temperature holds for long-term loads.” For alloys it is a one-hour yield strength. Long loading needs creep design (§3.13.3).
“Material cost is the price per pound.” Use total life-cycle cost: material, processing, installation, operation, maintenance. True prices need vendor quotes (§3.14.3).
“The best engineering material is also the cheapest solution.” Usually not. The final material is a compromise (§3.14.4).

16. Quick-Reference Summary

Use engineering stress and strain for elastic design and for reading handbook strengths. Switch to true stress and strain when strains are many times the elastic strain, such as when predicting cold-work effects. Get cold-worked properties from the area reduction at the prestrain point. Estimate strength from Brinell hardness for steels with $K_B \approx 500$ , and use the $S_y$ correlation only for stress-relieved steel. Treat every handbook number as typical and question its source. For steel: rigidity alone never justifies an alloy steel, carbon sets maximum hardness, alloying buys hardenability. Use Ashby charts to choose a material class, then actual data and tests for the final choice. Rank candidates with SI = (availability)(performance)/(total cost).

Workflow A, cold-worked properties (§3.3, SP 3.1)

Read the prestrain point and its permanent stretch ratio $L/L_0$ .
Area fraction = $L_0/L$ .
New $S_y$ = stress at prestrain point / area fraction. New $S_u$ = original $S_u$ / area fraction (equal to $S_y$ if prestrained to ultimate or beyond).
New $R = R_{fracture}/R_{prestrain}$ , $A_r = 1 - 1/R$ , $\epsilon = R - 1$ .

Workflow B, strength from hardness (§3.6, SP 3.2)

$S_u = K_B H_B$ (psi), $K_B \approx 500$ for most steels.
If stress-relieved (not cold-worked): $S_y = 1.05 S_u - 30{,}000$ psi, or $525 H_B - 30{,}000$ psi.
Convert other hardness scales with Fig. 3.7.

Workflow C, true values from test data (§3.4)

$\epsilon = \Delta L/L_0$ or, from areas, $R = A_0/A_f$ and $\epsilon = R - 1$ .
$\sigma_T = \sigma R$ .
$\epsilon_T = \ln R$ .
In the plastic region fit $\sigma_T = \sigma_0 \epsilon_T^m$ .

Workflow D, hardenability comparison (§3.10)

Pick elements and concentrations within the Table 3.1 limits.
Compute each factor $f$ .
Compare factors per percent added (and cost) to find the cheapest route.

Workflow E, material selection (§3.14.4, SP 3.3)

Define service requirements and translate them into properties.
Screen classes with Ashby charts, candidates with Appendix C typical uses.
Eliminate candidates failing a hard limit (for example $S_y$ below requirement).
Eliminate on processing (for example poor machinability).
Rank survivors by SI, check availability and life-cycle cost.
Test under simulated service.

Key Takeaways

Best material = best value: overall performance / total cost (§3.1).
$S_y$ by 0.2 percent offset is the standard yield value (§3.2).
Cold work raises strength and uses up ductility, computed via constant volume (§3.3, SP 3.1).
True stress $\sigma_T = \sigma R$ and true strain $\epsilon_T = \ln R$ describe large strains (§3.4).
Resilience $S_e^2/2E$ is elastic energy, toughness is total energy to fracture (§3.5).
For steels $S_u \approx 500 H_B$ psi, $S_y \approx 1.05 S_u - 30$ ksi if stress-relieved (§3.6).
All steels share one E, carbon sets maximum hardness, alloying sets hardenability (§3.10).
Selection: requirements, candidates, evaluation by SI, then testing (§3.14).

Quick-Reference Table

Quantity	Formula	Units	When to use
Engineering stress	$\sigma = P/A_0$	psi, ksi, MPa	Elastic design, handbook data
Engineering strain	$\epsilon = \Delta L/L_0$	dimensionless	Tensile test
Area after stretch	$A_f = A_0/(1 + \epsilon)$ (3.1)	in², mm²	Constant volume
Area ratio	$R = A_0/A_f = 1 + \epsilon$ (3.2a)	dimensionless	Elongation from fracture area
Area change	$\Delta A = A_0[1 - 1/(1 + \epsilon)]$ (3.2b)	in², mm²	Constant volume
Reduction in area	$A_r = 1 - 1/R$ (3.3)	dimensionless or %	Ductility measure
True stress	$\sigma_T = \sigma(1 + \epsilon) = \sigma R$ (3.4)	psi, ksi, MPa	Large strains
True strain	$\epsilon_T = \ln(L_f/L_0) = \ln R = \ln(1 + \epsilon)$ (3.5)	dimensionless	Large strains
Elastic line	$\sigma_T = E\epsilon_T$ (3.6)	psi, ksi	Elastic region
Strain-strengthening	$\sigma_T = \sigma_0\epsilon_T^m$ (3.7)	psi, ksi	Plastic region, cold-work prediction
Modulus of resilience	$R_m = S_e^2/2E$ (3.8)	in·lb/in³, J/m³	Elastic energy capacity ( $S_y$ for $S_e$ in practice)
Modulus of toughness	$T_m = \int_0^{\epsilon_f}\sigma\,d\epsilon$ (3.9)	in·lb/in³, J/m³	Energy to fracture
Toughness estimate	$T_m \approx \epsilon_f(S_y + S_u)/2$ (3.10)	in·lb/in³, J/m³	Rough estimate
Ultimate from hardness	$S_u = K_B H_B$ , $K_B \approx 500$ (3.11)	psi	Steels
Yield from ultimate	$S_y = 1.05 S_u - 30{,}000$ (3.12)	psi	Stress-relieved steels
Yield from hardness	$S_y = 525 H_B - 30{,}000$ (3.13)	psi	Stress-relieved steels
Shear modulus	$G = E/2(1 + \nu)$ (3.14)	psi, GPa	Isotropic material with E and ν known
Machinability	$V_{60} = (1150k/H_B)(1 - A_r)^{1/2}$ (3.15)	ft/min	Relative machining speed, 60-min tool life
Hardenability factors	Table 3.1 (for example $f_{Mn} = 3.46Mn + 1$ )	dimensionless	Comparing alloying routes
Ashby energy storage	maximize $S^2/E$	MPa²/GPa	Springs
Ashby elastic hinge	maximize $S/E$	dimensionless	Elastic hinges
Ashby diaphragm	maximize $S^{3/2}/E$	MPa $^{3/2}$ /GPa	Diaphragms
Ashby min weight	maximize $S/\rho$ , $S^{2/3}/\rho$ , $S^{1/2}/\rho$	MPa $^n$ /(Mg/m³)	Rotating disks, beams (shafts), plates
Selection index	$SI = (\text{availability})(\text{performance})/(\text{total cost})$	relative	Ranking candidate materials