Materials Selection and Mechanical Properties Exercises

These exercises practise materials selection as an engineering decision, not a property-table lookup. They cover specific stiffness, allowable stress, elastic constants, ductility, hardness screening, anisotropy, thermal stress, fatigue relevance, corrosion allowance, inspection evidence, and lifecycle trade-offs.

The goal is to decide whether a material, product form, surface condition, manufacturing route, and inspection plan can support the actual load, environment, service life, and failure consequence.

Assume simplified screening models unless an exercise states otherwise. Real materials selection should also check product form, processing route, heat treatment, surface condition, temperature, environment, statistical scatter, joining, inspection access, repair, supply chain, cost, and validation evidence.

How to Use These Exercises

For each material-selection calculation, define:

1. the functional requirement being protected;
2. the load case, environment, and service life;
3. the product form, process route, and surface condition;
4. the property evidence and its limitations;
5. the inspection or validation action needed before release.

The common mistake is comparing material names instead of material-process systems. The useful decision is not “steel versus aluminium” in the abstract. It is a specific grade, product form, heat treatment, surface condition, manufacturing route, and inspection plan.

Use the exercises as selection gates: reject an attractive property when its evidence is not representative, change allowable stress when the failure mode changes, select orientation-specific data, require additional inspection, update corrosion or fatigue assumptions, or block a substitution until the material-process-surface system is revalidated.

Exercise 1: Specific Stiffness Comparison

A lightweight bracket is stiffness-limited. Compare specific stiffness:

for two candidates:

Material	Elastic modulus	Density
Aluminium alloy	70 GPa	2700 kg/m3
Magnesium alloy	45 GPa	1800 kg/m3

Solution

Aluminium alloy:

Magnesium alloy:

Engineering Comment

The two materials have similar specific stiffness in this simplified screen. The decision should therefore move to corrosion, flammability constraints, casting or forming route, joining, surface protection, fatigue, cost, inspection, and supply risk.

Specific stiffness is useful for mass-sensitive screening, but it does not select the material by itself.

Exercise 2: Allowable Stress with Safety Factor

A component material has yield strength:

The design uses a static safety factor:

Calculate allowable stress:

Solution

Allowable stress:

Engineering Comment

The allowable stress is 150 MPa for this static yield screen. This does not cover fatigue, fracture, corrosion, wear, creep, buckling, weld quality, heat-affected zones, or manufacturing defects.

A useful allowable stress must be tied to a failure mode and evidence basis.

Exercise 3: Shear Modulus from Young’s Modulus and Poisson’s Ratio

An isotropic material has:

and:

Estimate shear modulus:

Solution

Shear modulus:

Engineering Comment

The estimated shear modulus is 80.8 GPa. This relation assumes isotropic linear elastic behavior. It should not be applied blindly to composites, strongly textured products, wood, additively manufactured parts, or layered materials.

When directionality matters, test orientation and load direction must match the component.

Exercise 4: Ductility from Tensile Test Elongation

A tensile specimen has initial gauge length:

After fracture, the final gauge length is:

Calculate percent elongation:

Solution

Percent elongation:

Engineering Comment

The specimen shows 22 percent elongation. That suggests useful ductility in the tested condition, but ductility can change with product form, orientation, strain rate, temperature, heat treatment, welds, aging, and environment.

Ductility is valuable because it helps redistribute stress and gives warning before fracture, but it is not a substitute for toughness or fatigue evidence.

Exercise 5: Hardness Screening After Heat Treatment

A heat-treated batch has target hardness range:

Five measurements are:

Specimen	HRC
1	43.1
2	44.0
3	46.8
4	42.7
5	43.6

Does the batch pass the hardness screen?

Solution

The allowable upper limit is:

Specimen 3 is:

Therefore the batch does not pass the screen.

Engineering Comment

One out-of-range value is enough to trigger review. High hardness can indicate over-hardening, reduced ductility, increased cracking sensitivity, or incorrect heat-treatment response.

The engineering action should not be only retesting. It should check heat-treatment records, furnace uniformity, quench conditions, material lot, part geometry, and whether the measured location is representative.

Exercise 6: Directional Strength in an Anisotropic Product

A rolled plate has tensile strength:

Direction	Tensile strength
Longitudinal	520 MPa
Transverse	410 MPa

A bracket is loaded mainly transverse to the rolling direction. The applied design stress is:

Calculate safety factor using the correct transverse strength and compare it with the incorrect longitudinal assumption.

Solution

Correct transverse safety factor:

Incorrect longitudinal safety factor:

Engineering Comment

Using the longitudinal value would overstate the safety factor from 1.78 to 2.26. That is a serious selection error when directionality controls failure.

Material evidence should state product orientation, rolling direction, build direction, grain flow, or layup direction whenever anisotropy matters.

Exercise 7: Thermal Stress from Constrained Expansion

A bar is fully constrained and heated by:

The material has:

and thermal expansion coefficient:

Estimate thermal stress:

Solution

Thermal stress:

Engineering Comment

The constrained thermal stress is about 72.5 MPa. Thermal stress can dominate when dissimilar materials are joined, coatings are applied, parts are welded, electronics are potted, or structures cycle between operating and ambient temperature.

Material selection should include thermal expansion compatibility, not only room-temperature strength.

Exercise 8: Fatigue Relevance from Stress Range

A shaft material has static yield strength:

The shaft sees cyclic stress between:

and:

Calculate stress amplitude and mean stress.

Solution

Stress amplitude:

Mean stress:

Engineering Comment

The maximum stress is below yield, but the component still needs fatigue review because cyclic stress amplitude is 110 MPa. Static yield strength does not prove fatigue life.

The selection should check surface finish, stress concentrations, residual stress, corrosion, heat treatment, and expected cycles.

Exercise 9: Corrosion Allowance

A steel component is expected to corrode at:

The service interval is:

The design includes corrosion allowance:

Estimate metal loss and remaining allowance.

Solution

Metal loss:

Remaining allowance:

Engineering Comment

The corrosion allowance has only 0.28 mm remaining after the expected interval. That may be acceptable or weak depending on uncertainty, localized corrosion, coating damage, inspection interval, fluid chemistry, and consequence of loss of wall thickness.

Corrosion selection should include protection system, inspection plan, environment monitoring, and replacement criteria.

Exercise 10: Inspection Method Coverage

A production release plan has 80 fatigue-critical parts. The selected non-destructive testing method is qualified to detect flaws larger than:

The fracture assessment assumes no flaw larger than:

Is the inspection method adequate for the assumption?

Solution

The inspection method detects flaws larger than 0.8 mm, but the analysis assumes flaws are no larger than 0.5 mm:

Therefore the inspection method is not adequate for the flaw-size assumption.

Engineering Comment

This is a common evidence gap. The analysis assumes a smaller maximum flaw than the inspection process can reliably detect. The team must improve inspection sensitivity, revise the fracture assessment, change the process route, reduce stress, or add proof testing.

Inspection evidence must match the defect size that controls failure.

Exercise 11: Lifecycle Cost Trade-Off

Two material-process options satisfy nominal strength:

Cost element	Option A	Option B
Raw material and fabrication	18,000 USD	28,000 USD
Coating or protection	7,000 USD	2,000 USD
Expected maintenance over life	19,000 USD	8,000 USD
Expected downtime cost	24,000 USD	10,000 USD

Calculate total lifecycle screen cost for each option.

Solution

Option A:

Option B:

Difference:

Engineering Comment

Option B costs more initially but has the lower lifecycle screen by 20,000 USD. The decision should still test uncertainty in maintenance, downtime, corrosion performance, inspection, repair, supplier risk, and field accessibility.

The cheapest raw material is not necessarily the cheapest engineering material system.

Review Checklist

When reviewing a materials selection decision, ask:

• Are requirements stated before material names?
• Is the comparison based on material-process-surface systems, not generic material labels?
• Do stiffness, strength, toughness, fatigue, wear, corrosion, temperature, and inspection match the failure mode?
• Are product form, orientation, heat treatment, welding, additive build direction, or coating state controlled?
• Does property evidence match the component’s environment, temperature, strain rate, and service life?
• Can the inspection method detect the defects assumed in the analysis?
• Are substitution rules and production-release criteria explicit?
• Are uncertainty, property scatter, supplier variability, and test orientation reflected in the margin rather than hidden behind nominal values?
• Does lifecycle cost include manufacturing yield, protection, maintenance, downtime, repair, and replacement?
• Is the final choice traceable from requirement to property evidence, processing route, inspection method, and residual risk?

Good materials selection makes the hidden assumptions visible before they become cracks, corrosion, distortion, scrap, downtime, or unsafe service.