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PE Mechanical

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7.1 Ferrous/Non-Ferrous Metals, Polymers, Ceramics & Composites

Key Takeaways

  • Engineering stress and strain use initial dimensions ($\sigma = P/A_0$, $\epsilon = \Delta L / L_0$), whereas true stress and true strain account for instantaneous dimensions ($\sigma_T = \sigma(1+\epsilon)$, $\epsilon_T = \ln(1+\epsilon)$) up to the onset of necking.
  • The elastic behavior of isotropic materials is governed by Hooke's Law and the fundamental elastic relationship: $E = 2G(1 + \nu) = 3K(1 - 2\nu)$, where $E$ is Young's modulus, $G$ is shear modulus, $K$ is bulk modulus, and $\nu$ is Poisson's ratio.
  • Modulus of resilience ($u_r \approx S_y^2 / (2E)$) quantifies elastic strain energy absorption per unit volume, while modulus of toughness ($u_t$) represents total energy absorption capacity up to fracture (area under the complete stress-strain curve).
  • Plain carbon steel tensile strength correlates to Brinell hardness ($S_{ut} \approx 500 \times HB \text{ [psi]}$); austenitic stainless steels (304/316, FCC) are non-magnetic and non-hardenable by heat treatment, while martensitic grades (410/440C, BCT) are quench-hardenable.
  • Continuous fiber-reinforced composites obey the Rule of Mixtures: longitudinal modulus is Voigt upper-bound ($E_{c,l} = V_f E_f + V_m E_m$), while transverse modulus is Reuss lower-bound ($E_{c,t} = \frac{E_f E_m}{V_m E_f + V_f E_m}$).
Last updated: August 2026

Ferrous/Non-Ferrous Metals, Polymers, Ceramics & Composites

Material selection and mechanical property characterization form the cornerstone of mechanical component design, structural integrity analysis, and failure prevention. On the NCEES PE Mechanical exam, materials questions assess your ability to interpret stress-strain curves, compute elastic and plastic deformation parameters, convert between hardness scales and tensile strength, evaluate anisotropic composite behavior, and select optimal alloys, polymers, or ceramics for severe thermal, chemical, and mechanical environments.

1. Broad Classification of Engineering Materials

Engineering materials are broadly categorized into five primary families based on atomic bonding, crystal structure, and macroscopic physical behavior:

+---------------------------------------------------------------------------------------------------------+
|                                 CLASSIFICATION OF ENGINEERING MATERIALS                                  |
|                                                                                                         |
|   1. FERROUS METALS        Plain carbon steels (1018, 1045), alloy steels (4140, 4340), stainless       |
|                            steels (304, 316, 410), tool steels, cast irons (gray, ductile, white).       |
|   2. NON-FERROUS METALS    Aluminum alloys (6061, 7075), copper alloys (brass, bronze), titanium         |
|                            (Ti-6Al-4V), nickel-based superalloys (Inconel 625, 718), magnesium.          |
|   3. POLYMERS              Thermoplastics (PE, PP, PVC, PTFE, Nylon) vs. Thermosets (epoxy, phenolic,    |
|                            polyester); elastomers (nitrile, neoprene, silicone, EPDM, polyurethane).    |
|   4. CERAMICS & GLASSES    Alumina (Al2O3), silicon carbide (SiC), silicon nitride (Si3N4), zirconia;    |
|                            extreme hardness, high melting point, brittle in tension, high compression.  |
|   5. COMPOSITES            Fiber-reinforced polymers (CFRP, GFRP), metal-matrix (MMC), ceramic-matrix    |
|                            (CMC); anisotropic properties, high specific strength and specific stiffness.|
+---------------------------------------------------------------------------------------------------------+

2. Uniaxial Tensile Testing & The Engineering Stress-Strain Curve

The standard ASTM E8 uniaxial tensile test subjects a standardized dog-bone specimen of original gauge length $L_0$ and original cross-sectional area $A_0$ to quasi-static axial tension until fracture.

+---------------------------------------------------------------------------------------------------------+
|                                  ENGINEERING STRESS-STRAIN CURVE (DUCTILE STEEL)                        |
|                                                                                                         |
|   Stress (sigma)                                                                                        |
|        ^                                                                                                |
|        |                                          Ultimate Tensile Strength (S_ut)                      |
|        |                                                    * * *                                       |
|        |                                              * *           *                                   |
|        |                     Yield Strength (S_y) *                   *                                 |
|        |                             *                                  *  Fracture Point (sigma_f)     |
|        |                           *                                      X                             |
|        |                         *                                                                      |
|        |      Proportional      *                                                                       |
|        |      Limit (sigma_pl) *                                                                        |
|        |                      * |                                                                       |
|        |                     *  |                                                                       |
|        |                    *   |                                                                       |
|        |                   *    |                                                                       |
|        |                  *     |                                                                       |
|        +-----------------+------+-----------------------------------------------> Strain (epsilon)      |
|        0               0.002   epsilon_y                                        epsilon_fracture        |
|                        (0.2% offset)                                                                    |
|        |<-- ELASTIC -->|<------------------------ PLASTIC DEFORMATION ------------------------>|        |
+---------------------------------------------------------------------------------------------------------+

Definitions of Key Stress-Strain Parameters

ParameterMathematical DefinitionPhysical Description & Significance
Engineering Stress ($\sigma$)$\sigma = \frac{P}{A_0}$Axial load $P$ divided by original undeformed cross-sectional area $A_0$.
Engineering Strain ($\epsilon$)$\epsilon = \frac{\Delta L}{L_0} = \frac{L - L_0}{L_0}$Elongation $\Delta L$ divided by original gauge length $L_0$. Unitless (or $\text{in/in}$, $\text{mm/mm}$).
Proportional Limit ($\sigma_{pl}$)$\sigma = E \cdot \epsilon$Highest stress at which stress is strictly proportional to strain.
Elastic Limit$\sigma \le \sigma_{el}$Greatest stress a material can sustain without permanent plastic deformation upon unloading.
0.2% Offset Yield Strength ($S_y$)Offset line $\sigma = E(\epsilon - 0.002)$Standard engineering yield strength determined by drawing a line parallel to the elastic slope starting at $\epsilon = 0.002$ ($0.2%$ strain).
Ultimate Tensile Strength ($S_{ut}$)$S_{ut} = \frac{P_{\max}}{A_0}$Maximum engineering stress sustained on the curve; marks the onset of macroscopic localized necking.
Fracture Strength ($\sigma_f$)$\sigma_f = \frac{P_{\text{fracture}}}{A_0}$Engineering stress at final rupture (lower than $S_{ut}$ due to necking area reduction).
Modulus of Elasticity ($E$)$E = \frac{\Delta \sigma}{\Delta \epsilon} = \frac{\sigma}{\epsilon}$Slope of the linear elastic region (Young's Modulus). Carbon steel: $E \approx 29 \times 10^6 \text{ psi} \approx 200 \text{ GPa}$; Aluminum: $E \approx 10 \times 10^6 \text{ psi} \approx 69 \text{ GPa}$.
Shear Modulus ($G$)$G = \frac{\tau}{\gamma}$Ratio of shear stress to shear strain in elastic shear/torsion. Steel: $G \approx 11.5 \times 10^6 \text{ psi} \approx 79 \text{ GPa}$.
Poisson's Ratio ($\nu$)$\nu = -\frac{\epsilon_{\text{lateral}}}{\epsilon_{\text{axial}}}$Ratio of lateral contracting strain to longitudinal tensile strain. Structural metals: $\nu \approx 0.28 - 0.33$. Rubber: $\nu \approx 0.50$.

Isotropic Elastic Constants Interrelation

For homogeneous, isotropic, linearly elastic materials, only two independent elastic constants exist. Young's modulus, shear modulus, bulk modulus ($K$), and Poisson's ratio are related by:

E=2G(1+ν)E = 2G(1 + \nu)

E=3K(1−2ν)E = 3K(1 - 2\nu)

G=E2(1+ν)=3K(1−2ν)2(1+ν)G = \frac{E}{2(1 + \nu)} = \frac{3K(1 - 2\nu)}{2(1 + \nu)}

K=E3(1−2ν)K = \frac{E}{3(1 - 2\nu)}

3. Resilience, Toughness & Ductility Measures

+---------------------------------------------------------------------------------------------------------+
|                                 RESILIENCE VS. TOUGHNESS COMPARISON                                     |
|                                                                                                         |
|   MODULUS OF RESILIENCE (u_r)                           MODULUS OF TOUGHNESS (u_t)                      |
|   - Elastic strain energy absorbed per unit volume      - Total strain energy absorbed per unit volume  |
|   - Area under ELASTIC portion only                     - Area under ENTIRE curve up to fracture        |
|   - Formula: u_r = (S_y)^2 / (2E)                       - Approximated: u_t ~ ((S_y + S_ut)/2) * eps_f  |
|   - Crucial for springs, shock absorbers, flexures      - Crucial for crashworthiness, armor, impact    |
+---------------------------------------------------------------------------------------------------------+

Ductility Indicators

Ductility represents the degree of permanent plastic deformation a material undergoes prior to fracture:

Percent Elongation (%EL)=Lf−L0L0×100%\text{Percent Elongation (\%EL)} = \frac{L_f - L_0}{L_0} \times 100\%

Percent Reduction in Area (%RA)=A0−AfA0×100%\text{Percent Reduction in Area (\%RA)} = \frac{A_0 - A_f}{A_0} \times 100\%

  • Ductile Materials: $%EL \ge 5%$ (typically $15-35%$ for structural low-carbon steel, aluminum, brass). Exhibit pronounced necking, cup-and-cone shear fractures ($45^\circ$ shear lip).
  • Brittle Materials: $%EL < 5%$ (e.g., gray cast iron, high-carbon tool steels, ceramics). Exhibit minimal plastic deformation and flat, cleavage fracture surfaces perpendicular to the maximum tensile stress axis.

4. True Stress, True Strain & Hollomon's Flow Law

Because engineering stress ($σ = P/A_0$) and engineering strain ($ε = \Delta L/L_0$) use fixed initial dimensions, they fail to capture the true physical state of the material during large plastic deformations. True stress ($\sigma_T$) and true strain ($\epsilon_T$) account for instantaneous cross-sectional area ($A_i$) and instantaneous length ($L_i$).

+---------------------------------------------------------------------------------------------------------+
|                                  ENGINEERING VS. TRUE STRESS-STRAIN CURVES                              |
|                                                                                                         |
|   Stress                                                                                                |
|     ^                                                            True Stress-Strain Curve               |
|     |                                                        /-- (sigma_T = K * eps_T^n)                |
|     |                                                  /-----                                           |
|     |                                      * * * * * - - - - - - - (Necking onset at eps_T = n)         |
|     |                                * *           *                                                    |
|     |                          * *                   *   Engineering Curve                              |
|     |                     * *                          *                                                |
|     |                   *                                *                                              |
|     |                 *                                    X Final Fracture                             |
|     |               *                                                                                   |
|     +-------------+-----------------------------------------------------> Strain                        |
+---------------------------------------------------------------------------------------------------------+

Conversion Formulas (Valid up to the onset of necking, assuming constant volume $A_0 L_0 = A_i L_i$):

σT=PAi=PA0(A0Ai)=σ(1+ϵ)\sigma_T = \frac{P}{A_i} = \frac{P}{A_0} \left(\frac{A_0}{A_i}\right) = \sigma (1 + \epsilon)

ϵT=∫L0LdLL=ln⁡(LL0)=ln⁡(1+ϵ)\epsilon_T = \int_{L_0}^{L} \frac{dL}{L} = \ln\left(\frac{L}{L_0}\right) = \ln(1 + \epsilon)

Hollomon's Power Law for Plastic Flow / Strain Hardening

In the uniform plastic deformation regime (between yield and necking), true stress and true strain obey the empirical constitutive relationship:

σT=KϵTn\sigma_T = K \epsilon_T^n

Where:

  • $K = \text{strength coefficient (true stress at } \epsilon_T = 1.0\text{)}$
  • $n = \text{strain hardening exponent (work hardening exponent, typically } 0.10 \le n \le 0.50\text{)}$

[!IMPORTANT] Considère's Criterion: At the onset of necking (maximum load in the tensile test, $dP = 0$), the strain hardening exponent is mathematically equal to the true strain at necking: $n = \epsilon_{T,\text{necking}}$. Materials with higher $n$ values (e.g., austenitic stainless steel, $n \approx 0.40-0.50$) resist necking and exhibit superior stretch-formability in deep drawing.

5. Hardness Testing Methods & Tensile Strength Correlations

Hardness measures a material's resistance to localized surface plastic indentation or abrasion.

+---------------------------------------------------------------------------------------------------------+
|                                     HARDNESS TESTING COMPARISON TABLE                                   |
|                                                                                                         |
|   TEST METHOD     INDENTER                     LOAD / PRELOAD          READOUT SCALE                    |
|   ------------    -------------------------    --------------------    ------------------------------   |
|   Brinell (HB)    10 mm hardened steel/WC ball 3000 kgf (500 kg soft)  HB = 2P / [pi*D*(D - sqrt(D^2-d^2))]|
|   Rockwell B(HRB) 1/16-inch steel ball         100 kgf (10 kgf minor)  Dial / Digital gauge depth (0-100)|
|   Rockwell C(HRC) 120-degree diamond Brale     150 kgf (10 kgf minor)  Dial / Digital gauge depth (0-100)|
|   Vickers (HV)    136-degree diamond pyramid   1 to 120 kgf            HV = 1.854 * P / d_avg^2         |
|   Knoop (HK)      Elongated diamond pyramid    Micro-loads (<1 kgf)    HK = 14.229 * P / L^2 (thin films)|
|   Shore Durometer Pointed indentor pin         Spring-loaded indent    Shore A (soft rubber), D (plastics|
+---------------------------------------------------------------------------------------------------------+

Steel Tensile Strength vs. Brinell Hardness Correlation

For plain carbon and low-alloy steels in the range of $100 \le HB \le 500$, the ultimate tensile strength correlates linearly with the Brinell Hardness number:

Sut≈500×HB[psi]S_{ut} \approx 500 \times HB \quad [\text{psi}]

Sut≈0.50×HB[kpsi]S_{ut} \approx 0.50 \times HB \quad [\text{kpsi}]

Sut≈3.45×HB[MPa]S_{ut} \approx 3.45 \times HB \quad [\text{MPa}]

6. Ferrous & Non-Ferrous Alloys Metallurgy

+---------------------------------------------------------------------------------------------------------+
|                                        FERROUS ALLOYS TAXONOMY                                          |
|                                                                                                         |
|   +---------------------------------------+---------------------------------------+                     |
|   | PLAIN CARBON & ALLOY STEELS           | CAST IRONS (>2.14% Carbon)            |                     |
|   | - Low Carbon (<0.25% C): 1018, A36    | - Gray Iron: Flake graphite, damping  |                     |
|   | - Medium Carbon (0.25-0.60% C): 1045  | - Ductile Iron: Spherical nodules     |                     |
|   | - High Carbon (>0.60% C): 1095, tool  | - White Iron: Cementite, wear resist  |                     |
|   | - Alloy Steels: 4140 (Cr-Mo), 4340    | - Malleable Iron: Irregular clumps    |                     |
|   +---------------------------------------+---------------------------------------+                     |
|   | STAINLESS STEELS (>10.5% Chromium)                                            |                     |
|   | - Austenitic (304, 316): FCC, non-magnetic, corrosion resistant, non-hardenable by heat treatment   |
|   | - Ferritic (430): BCC, magnetic, moderate corrosion resistance, non-hardenable by heat treatment     |
|   | - Martensitic (410, 440C): BCT, magnetic, hardenable by quench & temper, high strength/hardness     |
|   | - Precipitation-Hardening (17-4 PH): High strength via Cu/Nb precipitates, good corrosion resistance|
|   +-------------------------------------------------------------------------------+---------------------+|
+---------------------------------------------------------------------------------------------------------+

Cast Iron Types & Properties

  • Gray Cast Iron: Flake graphite in a ferrite/pearlite matrix. Outstanding vibrational damping capacity, excellent machinability, high thermal conductivity, and high compressive strength ($S_c \approx 3-4 \times S_t$). Brittle in tension due to stress concentrations at sharp flake tips. Used in engine blocks and machine tool beds.
  • Ductile (Nodular) Iron: Spheroidal graphite nodules produced by adding small amounts of magnesium or cerium before pouring. High tensile strength, ductility ($10-18% EL$), and impact toughness. Used in automotive crankshafts and pressure pipe.
  • White Cast Iron: Massive cementite ($Fe_3C$) with virtually no free graphite due to rapid cooling. Extremely hard ($>450$ HB), wear resistant, but brittle and unmachinable. Used in slurry pump liners and grinding balls.
  • Malleable Cast Iron: Formed by prolonged annealing of white iron at $950^\circ\text{C}$, decomposing cementite into irregular temper carbon clumps. Moderate ductility and toughness. Used in pipe fittings and brackets.

Non-Ferrous Alloys Overview

  • Aluminum Alloys: Low density ($\rho \approx 0.098 \text{ lbm/in}^3 \approx 2.7 \text{ g/cm}^3$), high thermal/electrical conductivity, protective native oxide film ($Al_2O_3$).
    • Wrought Series: 1xxx (Pure Al, $>99.0%$), 2xxx (Al-Cu, 2024, aerospace, high strength), 3xxx (Al-Mn, 3003, beverage cans), 5xxx (Al-Mg, 5052, marine), 6xxx (Al-Mg-Si, 6061, architectural/structural extrusions), 7xxx (Al-Zn-Mg-Cu, 7075, ultra-high strength).
    • Tempers: -O (Annealed), -H (Strain hardened), -T6 (Solution heat treated and artificially aged for peak precipitation hardening).
  • Copper Alloys: High electrical/thermal conductivity, excellent corrosion resistance.
    • Brass: Copper-Zinc alloy (e.g., Cartridge brass 70Cu-30Zn), ductile and easily formed.
    • Bronze: Copper-Tin alloy (often with Al, Si, or P additions), high strength and wear resistance.
  • Titanium Alloys (Ti-6Al-4V): Outstanding strength-to-weight ratio, exceptional corrosion resistance up to $450^\circ\text{C}$, biocompatible. $\alpha+\beta$ dual-phase structure.
  • Nickel Superalloys (Inconel 625, 718): Maintain high tensile strength, creep resistance, and oxidation resistance at extreme temperatures ($>700^\circ\text{C}$ / $1300^\circ\text{F}$). Used in gas turbine blades and rocket nozzles.

7. Polymers, Ceramics & Fiber Composites

Polymers: Thermoplastics vs. Thermosets

  • Thermoplastics: Linear and branched molecular chains linked by weak secondary (van der Waals) bonds. Soften and melt reversibly upon heating; recyclable.
    • Examples: Polyethylene (PE), Polypropylene (PP), Polyvinyl Chloride (PVC), Polytetrafluoroethylene (PTFE / Teflon), Polyamide (Nylon).
    • Glass Transition Temperature ($T_g$): Below $T_g$, polymer is rigid and glassy; above $T_g$, amorphous regions become rubbery and flexible.
  • Thermosets: Heavily cross-linked, three-dimensional covalent networks. Do not melt upon heating; decompose/char at high temperatures. Permanent shape once cured.
    • Examples: Epoxy, Phenolic (Bakelite), Polyester, Polyurethane.

Engineering Ceramics & Glasses

  • Covalent and ionic atomic bonds yield extreme hardness, high melting points ($>2000^\circ\text{C}$), high compressive strength, and chemical inertness, but low fracture toughness ($K_{Ic} \approx 2-5 \text{ MPa}\sqrt{\text{m}}$) and high susceptibility to tensile stress concentrations.
  • Common Technical Ceramics: Alumina ($Al_2O_3$), Silicon Carbide ($SiC$), Silicon Nitride ($Si_3N_4$), Zirconia ($ZrO_2$, transformation toughened).

Fiber-Reinforced Polymer (FRP) Composites

Composites combine high-strength stiff reinforcement fibers (carbon, glass, aramid/Kevlar) embedded within a ductile matrix (epoxy, vinyl ester, polyester).

+---------------------------------------------------------------------------------------------------------+
|                                 RULE OF MIXTURES (CONTINUOUS FIBERS)                                    |
|                                                                                                         |
|   1. LONGITUDINAL LOADING (Iso-strain condition: eps_c = eps_f = eps_m):                                |
|      E_{c,l} = V_f E_f + V_m E_m = V_f E_f + (1 - V_f) E_m          (Voigt Upper Bound)                 |
|                                                                                                         |
|   2. TRANSVERSE LOADING (Iso-stress condition: sigma_c = sigma_f = sigma_m):                            |
|      \frac{1}{E_{c,t}} = \frac{V_f}{E_f} + \frac{V_m}{E_m} \implies E_{c,t} = \frac{E_f E_m}{V_m E_f + V_f E_m}  (Reuss Lower Bound)  |
+---------------------------------------------------------------------------------------------------------+

Where $V_f$ and $V_m = (1 - V_f)$ are the volume fractions of fiber and matrix, respectively.

8. Step-by-Step Worked Problem: Tensile Test & Hardness Analysis

Problem Statement

A standard cylindrical steel tensile specimen with initial diameter $d_0 = 0.505 \text{ in}$ ($A_0 = 0.200 \text{ in}^2$) and gauge length $L_0 = 2.000 \text{ in}$ is loaded in tension. The following test data are recorded:

  • 0.2% offset yield load: $P_y = 13,000 \text{ lbf}$
  • Maximum sustained tensile load: $P_{\max} = 21,000 \text{ lbf}$
  • Specimen gauge length at maximum load: $L_i = 2.360 \text{ in}$
  • Modulus of Elasticity: $E = 30 \times 10^6 \text{ psi}$
  • Measured Brinell hardness of the stock alloy: $HB = 210$

Calculate:

  1. The 0.2% offset yield strength ($S_y$) and the Modulus of Resilience ($u_r$).
  2. The Ultimate Tensile Strength ($S_{ut}$) and the True Stress ($\sigma_T$) at maximum load.
  3. The estimated $S_{ut}$ based on the empirical Brinell hardness correlation and compare it with the measured value.
+---------------------------------------------------------------------------------------------------------+
|                                     STEP-BY-STEP SOLUTION PROCEDURE                                     |
|                                                                                                         |
|   STEP 1: Calculate Yield Strength & Modulus of Resilience                                              |
|           S_y = P_y / A_0 = 13,000 lbf / 0.200 in^2 = 65,000 psi (65.0 ksi)                             |
|           u_r = (S_y)^2 / (2 * E) = (65,000 psi)^2 / (2 * 30 * 10^6 psi)                                |
|           u_r = 4,225,000,000 / 60,000,000 = 70.42 in-lbf/in^3 (psi)                                    |
|                                                                                                         |
|   STEP 2: Calculate Ultimate Tensile Strength & True Stress at Maximum Load                             |
|           S_ut = P_max / A_0 = 21,000 lbf / 0.200 in^2 = 105,000 psi (105.0 ksi)                        |
|           Engineering strain at P_max: eps = (2.360 - 2.000) / 2.000 = 0.360 / 2.000 = 0.180 in/in      |
|           True stress (via conversion formula up to necking):                                           |
|           sigma_T = S_ut * (1 + eps) = 105,000 psi * (1 + 0.180) = 105,000 * 1.180 = 123,900 psi (123.9 ksi)|
|                                                                                                         |
|   STEP 3: Hardness Correlation for Tensile Strength                                                     |
|           S_{ut,est} = 500 * HB = 500 * 210 = 105,000 psi (105.0 ksi)                                   |
|           Comparison: The empirical hardness estimate matches the tensile test result exactly (105.0 ksi)!|
+---------------------------------------------------------------------------------------------------------+

9. Common Exam Traps & PE Pro-Tips

  • Trap 1 — True Stress vs. Engineering Stress after Necking: The relationship $\sigma_T = \sigma(1+\epsilon)$ is valid only up to the onset of necking ($S_{ut}$). Beyond necking, deformation is non-uniform, and true stress must be computed directly from the instantaneous neck cross-section: $\sigma_T = P / A_{\text{neck}}$.
  • Trap 2 — Confusing Resilience and Toughness: Modulus of resilience ($u_r$) integrates elastic strain energy up to yield ($S_y^2 / 2E$). Modulus of toughness ($u_t$) integrates the entire area under the curve up to fracture. High strength does not guarantee high toughness if the material lacks ductility.
  • Trap 3 — Misidentifying Stainless Steel Heat Treatability: Austenitic stainless steels (304, 316) cannot be hardened by quenching and tempering because they remain FCC at room temperature without phase transformation. Only cold working (strain hardening) increases their strength. Martensitic stainless steels (410, 440C) are fully hardenable by quench and temper.
Test Your Knowledge

A structural steel component has a measured Young's modulus E = 200 GPa and a shear modulus G = 78 GPa. Assuming homogeneous isotropic elastic behavior, what is the Poisson's ratio of this steel?

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B
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D
Test Your Knowledge

Which of the following stainless steel grades is non-magnetic in the annealed condition and CANNOT be hardened by conventional quenching and tempering heat treatments?

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B
C
D
Test Your Knowledge

A mechanical engineer needs to design a high-energy absorption surge spring. Two candidate alloy steels exhibit identical elastic moduli (E = 30 Mpsi), but Alloy A has a yield strength of 75 ksi while Alloy B has a yield strength of 150 ksi. What is the ratio of the modulus of resilience of Alloy B to Alloy A (u_r,B / u_r,A)?

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B
C
D
Test Your Knowledge

A continuous unidirectional carbon-fiber epoxy composite has a fiber volume fraction V_f = 0.60. The carbon fibers have an elastic modulus E_f = 230 GPa, and the epoxy matrix has an elastic modulus E_m = 3.5 GPa. Using the Rule of Mixtures (Voigt upper bound), what is the longitudinal elastic modulus of the composite?

A
B
C
D
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7.2 Iron-Carbon Equilibrium Phase Diagram & Heat Treatment Processes

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