Material Properties and Processing is 7-11 questions on the FE Mechanical exam. It is more conceptual than the mechanics areas and rewards reading rather than problem-grinding, which makes it easy to postpone and easy to underprepare.
Seven to eleven questions is more than Heat Transfer is worth. Treat it as a real block, not as the area you review on the train.
Exam weight: NCEES lists Material Properties and Processing at 7-11 questions of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Material Properties and Processing
The specification covers mechanical and thermal properties, material selection, corrosion, thermal treatment, phase diagrams and phase transformations, testing, and manufacturing processes. Expect to read a stress-strain curve for yield strength, modulus and toughness, to read a binary phase diagram with the lever rule, and to identify the effect of a heat treatment on hardness or ductility.
Failure mechanisms sit here as well as in design: fatigue and the endurance limit, creep at elevated temperature, and the ductile-to-brittle transition. Manufacturing items ask which process suits a geometry or a production volume rather than requiring a process calculation.
5 Free Material Properties and Processing Practice Problems
Each materials problem below comes from the FEExamClick FE Mechanical question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — A. Properties (e.g., chemical, electrical, mechanical, physical, thermal)
A copper rod has a thermal conductivity of 385 W/(m-K) and a cross-sectional area of 1.2 x 10^-4 m^2. If the temperature gradient along the rod is 200 K/m, the steady-state heat transfer rate (W) through the rod is most nearly:
Answer: D) 9.2
Refer to the Fourier's Law of Conduction section (p. 209) in the Heat Transfer chapter of the FE Reference Handbook.
Fourier's law of heat conduction:
$$q = k \times A \times (dT/dx)$$
$$q = 385 W/(m-K) \times 1.2 x 10^{-4} m^2 \times 200 K/m$$
$$\boxed{q = 385 \times 1.2 x 10^{-4} \times 200 = 9.24 W}$$
Problem 2 — B. Stress-strain diagrams
A steel specimen with a 0.505-in. diameter and a 2.000-in. gauge length is subjected to a tensile test. The load at the 0.2% offset yield point is 9,800 lbf. The yield strength (ksi) is most nearly:
Answer: B) 49
Refer to the Mechanical section (p. 122) in the Materials Science/Structure of Matter chapter of the FE Reference Handbook.
The 0.2% offset yield strength is the engineering stress at the 0.2% offset:
$$A_0 = \dfrac{\pi}{4}d^{2} = \dfrac{\pi}{4}(0.505)^{2} = 0.2003\ \text{in}^{2}$$
$$\boxed{\sigma_y = \dfrac{P}{A_0} = \dfrac{9{,}800\ \text{lbf}}{0.2003\ \text{in}^{2}} = 48{,}927\ \text{psi} = 48.9\ \text{ksi}}$$
The yield strength is most nearly 49 ksi.
Problem 3 — E. Engineered materials (e.g., composites, polymers)
A unidirectional carbon fiber/epoxy composite has a fiber volume fraction of 0.60. The modulus of the carbon fiber is 230 GPa and the modulus of the epoxy matrix is 3.5 GPa. Using the rule of mixtures, the longitudinal modulus (GPa) of the composite is most nearly:
Answer: A) 139
Refer to the Composite Materials section (p. 124) in the Materials Science/Structure of Matter chapter of the FE Reference Handbook.
The rule of mixtures for the longitudinal (fiber direction) modulus:
$$E_L = E_f \times V_f + E_m \times V_m$$
where:
\(V_f = 0.60 (fiber volume fraction)\)
\(V_m = 1 - V_f = 0.40 (matrix volume fraction)\)
$$E_L = 230(0.60) + 3.5(0.40)$$
$$\boxed{E_L = 138 + 1.4 = 139.4 GPa}$$
The longitudinal modulus is most nearly 139 GPa.
Note: The transverse modulus is much lower and calculated using the inverse rule of mixtures.
Problem 4 — G. Phase diagrams, phase transformation, and heat treating
Using the lever rule, if an alloy at 40% B is in a two-phase region between α (20% B) and β (70% B), what is the weight percent of α phase?
Answer: A) 60%
Using the lever rule:
$$wt\% \alpha = \frac{x_\beta - x}{x_\beta - x_\alpha} \times 100$$
Given:
- \(x = 40\%\) (overall composition)
- \(x_\alpha = 20\%\) (α phase composition)
- \(x_\beta = 70\%\) (β phase composition)
$$wt\% \alpha = \frac{70 - 40}{70 - 20} \times 100 = \frac{30}{50} \times 100$$
$$\boxed{wt\% \alpha = 60\%}$$
$$wt\% \beta = 100 - 60 = 40\%$$
Problem 5 — I. Corrosion mechanisms and control
A uniform corrosion rate of 0.5 mm/year is measured for a steel tank wall that is currently 12 mm thick. The minimum allowable wall thickness is 6 mm. The estimated remaining service life (years) of the tank is most nearly:
Answer: C) 12
Refer to the Corrosion section (p. 117) in the Materials Science/Structure of Matter chapter of the FE Reference Handbook.
For uniform corrosion, the remaining service life is:
$$t_{life} = (current thickness - minimum thickness) / corrosion rate$$
$$t_{life} = (12 mm - 6 mm) / 0.5 mm/year$$
$$t_{life} = 6 / 0.5 = 12 years$$
Note: This assumes constant corrosion rate and single-sided attack. In practice:
- Corrosion rate may increase with time (as protective scale breaks down)
- Both inner and outer surfaces may corrode
- Localized corrosion (pitting) could cause penetration sooner
- A safety factor is typically applied
Using the FE Reference Handbook for Material Properties and Processing
The Materials Science chapter carries the property tables, the iron-carbon diagram and the lever rule. Property tables are the ones to find fast, because a question giving you a material name and asking for a modulus or a coefficient of thermal expansion is a pure lookup. Search for thermal expansion and for modulus of elasticity during practice so you know which table each lives in.
Four Mistakes That Cost Points
- Confusing strength with stiffness. Modulus of elasticity governs deflection; yield strength governs permanent deformation. Heat treating a steel changes strength substantially and modulus almost not at all, and questions are built directly on that distinction.
- Applying the lever rule to the wrong side. The fraction of a phase is proportional to the length of the opposite tie-line segment. Taking the adjacent segment inverts the answer, and the inverted value is always an option.
- Assuming every material has an endurance limit. Steels show a fatigue limit; aluminium alloys generally do not, so they fail eventually under cyclic loading regardless of stress level. Questions probe exactly this difference.
- Reading ultimate strength as the failure point. On an engineering stress-strain curve the ultimate strength is the peak, but fracture occurs later at a lower engineering stress after necking. Questions about where fracture occurs exploit the gap.
Frequently Asked Questions
How many materials questions are on the FE Mechanical exam?
NCEES specifies 7-11 questions from Material Properties and Processing out of 110. That is the same weight as Heat Transfer and more than Electricity and Magnetism.
Do I need to memorise phase diagrams?
No. The iron-carbon diagram is in the handbook, and any other diagram will be supplied with the question. What you need is the ability to read one: identify phases in a region, find a composition at temperature, and apply the lever rule in the right direction.
How much manufacturing process detail is tested?
Enough to match a process to a requirement. You should recognise casting, forming, machining, welding and additive processes and know their typical tolerances, volumes and geometries. Process parameter calculations are rare.
Is corrosion actually on the exam?
It appears as a concept: galvanic pairing, the role of a more anodic material, and common protection methods such as coatings and cathodic protection. Expect recognition questions rather than electrochemical calculations.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Mechanics of Materials practice problems — 9-14 questions on the exam
- FE Mechanical Mechanical Design and Analysis practice problems — 10-15 questions on the exam
- FE Mechanical Heat Transfer practice problems — 7-11 questions on the exam
Done with materials? Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline. Or test yourself against the clock with the free FE Mechanical practice exam: 20 timed questions in the CBT format.