Mechanical Properties of Engineering Materials – Review Flashcards

These question-and-answer cards review key definitions, formulas, mechanical concepts, material behaviors and practical applications covered in the lecture on mechanical properties of engineering materials. They are designed for rapid self-testing before the exam.

What is the definition of engineering stress (σ)?

The applied force divided by the specimen’s original cross-sectional area (σ = F / A₀).

What is engineering strain (ε)?

The change in length divided by the original gauge length (ε = ΔL / L₀).

State Hooke’s Law for linear elastic behavior.

Within the elastic region, stress is proportional to strain: σ = E ε.

What property does the slope of the linear portion of a stress–strain curve represent?

Modulus of elasticity (Young’s modulus, E).

Define Poisson’s ratio (ν).

The negative ratio of lateral strain to longitudinal strain, ν = –εlat / εlong.

Typical Poisson’s ratio values for metals, ceramics and polymers are approximately?

Metals ≈ 0.33, ceramics ≈ 0.25, polymers ≈ 0.40.

What is elastic deformation?

Reversible deformation in which stress and strain are proportional and the material returns to its original dimensions when the load is removed.

What is plastic deformation?

Permanent, irreversible deformation that remains after the applied load is removed.

What does yield strength (σy) signify on a stress–strain curve?

The stress at which noticeable (usually 0.2 % offset) plastic deformation begins.

How do you locate tensile strength (TS or σUTS) on an engineering stress–strain curve?

It is the maximum stress reached before the onset of necking (for metals) or chain scission (for polymers).

Explain percent elongation (%EL).

A ductility measure defined as (Lf – L₀) / L₀ × 100 %, where Lf is the length at fracture.

Explain percent reduction of area (%RA).

Ductility measure: (A₀ – Af) / A₀ × 100 %, where Af is the minimum cross-sectional area at fracture.

Give the brief definition and SI unit of modulus of toughness.

Energy per unit volume required to fracture a material; approximated by the entire area under the stress–strain curve. Unit: J m⁻³ (or N m m⁻³).

What is true stress (σ_T)?

Instantaneous load divided by the instantaneous cross-sectional area: σT = F / Ai.

Write the expression for true strain (ε_T).

ε_T = ln (L / L₀), the natural logarithm of the instantaneous length over the original length.

For isotropic materials, give the relation among E, G and ν.

G = E / [2(1 + ν)].

For isotropic materials, give the relation between bulk modulus K and E, ν.

K = E / [3(1 – 2ν)].

What is shear stress (τ) in simple shear?

Applied shear force divided by the area over which it acts: τ = F_s / A.

Define shear modulus (G).

The ratio of shear stress to shear strain in the elastic region: τ = G γ.

Define bulk modulus (K).

The ratio of uniform hydrostatic pressure to the corresponding relative volume decrease: P = –K ΔV / V₀.

What is working stress and how is it set?

The allowable design stress: σworking = σy / N, where N is the factor of safety.

Typical engineering factors of safety (N) lie in what range?

Usually between 1.2 and 4, depending on application criticality.

Describe strain hardening (work hardening).

An increase in yield strength due to prior plastic deformation, often expressed by the true stress–strain power law σT = K εTⁿ.

What does the hardening exponent n indicate?

Material’s ability to strain-harden; ranges roughly from 0.15 for some steels to 0.5 for soft coppers.

What is elastic strain recovery during unloading?

Upon load removal, the material traces a line parallel to the initial elastic slope, recovering the elastic portion of the total strain.

Why choose a material with a high Young’s modulus for structural members?

To minimize elastic deflection under load.

State two primary ways to increase toughness in a material.

Increase both strength and ductility (i.e., raise area under the stress–strain curve).

List three basic loading modes that create normal stresses.

Simple tension, simple compression, and bi-axial tension (thin membranes).

Give two examples of shear-dominated loading.

Torsion of a shaft and simple in-plane shear of a lap joint.

How is shear strain (γ) defined geometrically?

γ = tan θ, where θ is the angular change between originally perpendicular lines.

Name a key mechanical test for brittle materials and explain why.

Compression test, because brittle materials like concrete fail unpredictably in tension but can sustain higher compressive loads.

Rank the magnitude of yield strengths at room temperature for ceramics, metals and polymers.

σy(ceramics) >> σy(metals) >> σ_y(polymers).

Why does necking act as a stress concentrator?

Because the reduced cross-section increases local stress, accelerating failure.

Define hardness in mechanical terms.

Resistance to permanent surface indentation; correlates with wear resistance and compressive strength.

Give one equation for designing a circular rod under axial load with safety factor.

d = √[ (4 F) / (π σworking) ], where σworking = σ_y / N.

Cite two applications where ceramics are preferred due to high-temperature capability.

Furnace linings and kiln refractories based on SiO₂–Al₂O₃ systems.

Why are polycrystalline diamond coatings used on dies and cutting tools?

They provide uniform hardness, high wear resistance, and resharpen by micro-fracture, extending tool life.

Explain how Ca-doped ZrO₂ functions as an oxygen sensor.

Ca creates O²⁻ vacancies that enhance ion diffusion; a voltage forms when O²⁻ ions migrate between gases of different oxygen partial pressures.

State two special properties of stainless steel.

At least 12 % Cr provides excellent corrosion resistance and good mechanical strength.

List three common applications of plain-carbon steel.

Bridges, road construction, cans and drums (food packaging).

Give two key attributes of titanium alloys.

Very high strength-to-weight ratio (TS ≈ 1400 MPa) and excellent corrosion resistance.

Name two everyday uses of aluminum based on its properties.

Electrical transmission lines and beverage cans, due to low density and good conductivity.

Why are composite materials extensively used in modern aircraft such as the Airbus A380?

To save weight, improve damage tolerance, and increase corrosion and impact resistance.

State two automotive motivations for using natural-fiber composites.

Weight reduction for fuel economy and improved recyclability from renewable resources.

Give two marine advantages of fiber-reinforced polymer composites.

Significant weight savings and excellent corrosion resistance to seawater.

Differentiate thermoplastics and thermosets regarding reheating.

Thermoplastics can be reheated and reshaped repeatedly; thermosets form permanent cross-linked structures and cannot be remelted.

What characterizes elastomers (rubbers)?

They can undergo large elastic deformations and return nearly to original shape once load is removed.

Provide four diverse engineering applications of polymers.

Fire-retardant fabrics, food packaging films, contact lenses, and gas-separation membranes.

List three typical glass applications highlighted in the lecture.

Laboratory glassware, lighting tubes, and solar power panels.

Define toughness succinctly.

Energy absorbed per unit volume up to fracture; area under the stress-strain curve.

What are stress and strain fundamentally independent of?

Specimen size; they normalize load and displacement to geometry.

How does Poisson’s ratio affect volumetric changes during loading?

If ν < 0.5, the material volume increases under tension (voids form); if ν > 0.5, volume decreases.

Explain hydrostatic compression and give one example.

Equal compressive stress in all directions, e.g., fish bodies experiencing water pressure at depth.

Why do larger elastic moduli minimize deflection?

Because for a given stress, strain equals σ/E; a larger E yields smaller strain/displacement.

What is meant by ‘true stress is higher than engineering stress after yielding’?

Because during plastic deformation the actual area decreases, so σT = F / Ai grows even if load is constant.

Why is hardness testing useful for wear applications?

Higher hardness correlates with greater resistance to surface indentation and abrasive wear, predicting longer service life.

State the basic formula for shear stress in torsion of a solid circular shaft.

τ_max = 16 M / (π d³), where M is applied torque and d the diameter.

How does factor of safety account for design uncertainties?

It purposely limits working stress below yield to accommodate material variability, unexpected loads, and analysis errors.

What is the main reason composites can be tailored for specific stiffness?

Stiffness depends on fiber type, volume fraction, and orientation, allowing designers to match mechanical requirements directionally.

Give one structural example where biaxial tension occurs.

Thin spherical pressure vessels such as beverage cans or pressurized tanks.

State the relation between true and engineering strain in uniform deformation.

εT = ln (1 + εeng).

Why is percent reduction of area a more sensitive ductility measure for metals than percent elongation?

Because it reflects local deformation at the neck, capturing ductility even when overall elongation appears small.

What role do vacancies play in ionic conductivity for Ca-doped ZrO₂ sensors?

They provide diffusion pathways for O²⁻ ions, lowering activation energy and increasing ionic mobility.

How do polycrystalline diamonds self-sharpen?

Micro-fracturing along grain boundaries exposes new sharp edges during wear.

Which modulus dominates volumetric (bulk) elastic response?

Bulk modulus (K).

If a steel rod must not yield under 220 kN with N = 5 and σ_y = 310 MPa, what diameter is required?

Approximately 67 mm, using d = √[4 F N / (π σ_y)].