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 (6-10%) 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 problem below comes from the PECivilClick FE Mechanical question bank 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)
The ratio of lateral strain to longitudinal strain in a material under uniaxial stress is called:
A) Shear modulus
B) Poisson's ratio
C) Modulus of elasticity
D) Bulk modulus
Answer: B) Poisson's ratio
Poisson's ratio \((\nu)\) is defined as:
\(\nu = -\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}\)
\(\boxed{\text{Poisson's ratio}}\)
For most metals, \(\nu\) ranges from 0.25 to 0.35:
- Steel: \(\nu \approx 0.30\)
- Aluminum: \(\nu \approx 0.33\)
- Rubber: \(\nu \approx 0.50\) (incompressible)
The negative sign indicates lateral strain is opposite to longitudinal strain.
Problem 2 — A. Properties (e.g., chemical, electrical, mechanical, physical, thermal)
The relationship G = E/[2(1+ν)] relates which properties?
A) Yield strength, tensile strength, and hardness
B) Bulk modulus, shear modulus, and strain
C) Thermal expansion, conductivity, and diffusivity
D) Shear modulus, elastic modulus, and Poisson's ratio
Answer: D) Shear modulus, elastic modulus, and Poisson's ratio
This is a fundamental relationship for isotropic elastic materials:
\(G = \frac{E}{2(1 + \nu)}\)
where:
- \(G\) = shear modulus (modulus of rigidity)
- \(E\) = elastic modulus (Young's modulus)
- \(\nu\) = Poisson's ratio
For steel (\(E = 200\) GPa, \(\nu = 0.30\)):
\(G = \frac{200}{2(1.30)} = 77\) GPa
\(\boxed{\text{Shear modulus, elastic modulus, and Poisson's ratio}}\)
Problem 3 — A. Properties (e.g., chemical, electrical, mechanical, physical, thermal)
A steel bar (α = 12 \(\times\) 10\(^{-6}\)/°C) is 500 mm long at 20°C. What is its length at 120°C?
A) 500.06 mm
B) 501.2 mm
C) 506 mm
D) 500.6 mm
Answer: D) 500.6 mm
Thermal expansion formula:
\(\Delta L = \alpha L_0 \Delta T\)
\(\Delta L = 12 \times 10^{-6} \times 500 \times (120 - 20)\)
\(\Delta L = 12 \times 10^{-6} \times 500 \times 100 = 0.6\) mm
Final length:
\(L = L_0 + \Delta L = 500 + 0.6\)
\(\boxed{L = 500.6 \text{ mm}}\)
Problem 4 — A. Properties (e.g., chemical, electrical, mechanical, physical, thermal)
Electrical resistivity of a material is defined as:
A) ρ = A/RL
B) ρ = RA/L
C) ρ = R/A
D) ρ = L/RA
Answer: B) ρ = RA/L
Electrical resistivity:
\(\boxed{\rho = \frac{RA}{L}}\)
where:
- \(\rho\) = resistivity (Ω·m)
- \(R\) = resistance (Ω)
- \(A\) = cross-sectional area (m\(^{2}\))
- \(L\) = length (m)
Conductivity \(= 1/\rho\) (reciprocal of resistivity)
Typical values at 20°C:
- Copper: \(1.68 \times 10^{-8}\) Ω·m
- Aluminum: \(2.65 \times 10^{-8}\) Ω·m
Problem 5 — A. Properties (e.g., chemical, electrical, mechanical, physical, thermal)
Which property measures a material's ability to conduct heat?
A) Heat capacity
B) Thermal conductivity
C) Thermal diffusivity
D) Specific heat
Answer: B) Thermal conductivity
Thermal conductivity \((k)\) measures the rate of heat transfer through a material:
\(q = -k\frac{dT}{dx}\) (Fourier's law)
\(\boxed{\text{Thermal conductivity}}\)
Units: W/(m·K) or BTU/(hr·ft·°F)
Typical values:
- Copper: 401 W/(m·K)
- Aluminum: 237 W/(m·K)
- Steel: 50 W/(m·K)
Thermal diffusivity \(= \frac{k}{\rho c}\)
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, about 6-10 percent. 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
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.