MSE 2001 Module 1.2: Mechanical & Structural Properties

Stiffness

How much stress it takes to flex a material.

Strength

How much stress it takes to permanently deform a material.

Toughness

The energy per volume required to break a material.

Stress, σ

Applied load divided by cross-sectional area: σ = F/A.

Is stress a material property?

Yes.

Strain, ε

Fractional change in length: ε = ΔL/Li.

Is strain a material property?

Yes.

Load

Applied force; a performance parameter.

Total elongation

Absolute change in length, ΔL; a performance parameter.

What does a tensile test produce?

A stress-strain curve.

Stress-strain graph axes

Stress is on the y-axis; strain is on the x-axis.

Elastic deformation

Reversible deformation; the material returns to its original shape after unloading.

Elastic region of the stress-strain curve

The initial linear region where stress is proportional to strain.

What happens to atomic bonds during elastic deformation?

Bonds stretch like springs and return to their original configuration when unloaded.

Plastic deformation

Permanent, irreversible deformation.

Plastic region of the stress-strain curve

The nonlinear region where stress is no longer proportional to strain.

What happens microscopically during plastic deformation?

Atoms become displaced and remain displaced after unloading.

Elastic modulus, E

Material stiffness; resistance to stretching, bending, or flexing.

Where is elastic modulus on a stress-strain graph?

The slope of the linear elastic region.

Higher elastic modulus means what?

A stiffer material that resists elastic deformation more.

Lower elastic modulus means what?

A more flexible material that elastically deforms more easily.

Stress-strain relationship in the elastic region

σ = Eε.

Young's modulus, E

Elastic modulus associated with axial loading.

Shear modulus, G

Elastic modulus associated with shearing.

Bulk modulus, K

Elastic modulus associated with hydrostatic pressure.

Flexural modulus, Ef

Elastic modulus associated with bending.

Poisson's ratio

The negative ratio of transverse/lateral strain to axial/longitudinal strain during axial tensile loading.

Typical Poisson's ratio for most materials

About 0.3.

Yield stress, σy

The stress required to permanently deform the material.

Another name for yield stress

Strength.

What happens at the yield point?

The material transitions from elastic deformation to plastic deformation.

Below yield stress

Deformation is elastic and reversible.

Above yield stress

Permanent plastic deformation occurs.

Ultimate tensile strength, σUTS

Also called ultimate strength; the stress beyond which the material fails/fractures.

Where is UTS on the stress-strain curve?

At the highest stress reached on the curve.

Ductility, εf

The maximum strain or percent elongation at failure.

Another name for ductility on the stress-strain graph

Strain at break.

How can you identify a more ductile material?

It reaches a larger strain before failure.

Resilience

The amount of elastic energy per volume returned after stress is released.

Is resilience a material property?

Yes.

Where is resilience on the stress-strain curve?

The area under the linear elastic portion of the curve.

Resilience equation for linear elasticity

Ur = σy²/(2E) = σyεy/2.

Coefficient of restitution

The performance parameter corresponding to resilience.

Examples of applications requiring high resilience

Bouncing balls, shock absorbers, helmets, and protective gear.

Where is toughness on a stress-strain curve?

The area under the entire stress-strain curve up to failure.

What does toughness measure?

The energy per volume required to break a material.

Stiffness vs. strength

Stiffness is resistance to flexing; strength is resistance to permanent deformation.

Strength vs. toughness

Strength is resistance to permanent deformation; toughness is energy required to break.

Stiffness vs. toughness

Stiffness concerns flexing; toughness concerns breaking.

Airplane wing bends a lot but returns to its original shape: what is wrong?

The elastic modulus is too small; the material is not stiff enough.

Airplane wing permanently bends but does not break: what is wrong?

The yield strength is too low; the material is not strong enough.

Airplane wing breaks: what is wrong?

The toughness is too low.

Hardness

A surface property describing how difficult it is to scratch a material.

Hardness is related to what mechanical property?

Yield strength; both relate to resistance to permanent/plastic deformation.

Moh's hardness scale

A semi-quantitative scale that ranks materials by their ability to scratch one another.

How does Moh's hardness scale work?

A material can scratch another material lower on the scale but not one higher on the scale.

Vickers hardness test

A quantitative hardness test using an indenter and measuring the resulting impression.

What happens to a softer material during a Vickers test?

It is easier to indent and produces a deeper/larger indentation.

What happens to a harder material during a Vickers test?

It resists indentation more.

Hardness relationship on the Exam 1 equation sheet

Hv ≈ σy/3.

How can surface hardness be improved without changing the bulk material?

Apply a harder surface coating.

Polycarbonate lens coating example

An oxide coating can improve scratch resistance without replacing the underlying lens.

How is sound transmitted through materials?

As longitudinal strain waves, which are mechanical waves.

What material properties affect sound velocity?

Elastic modulus and density.

Sound velocity relationship

v ∝ √(E/ρ).

If elastic modulus increases, what generally happens to sound velocity?

It increases.

If density increases while E stays the same, what happens to sound velocity?

It decreases.

Acoustic impedance, Z

The acoustic resistance to sound traveling through a medium.

Acoustic impedance relationship

Z ∝ √(ρE).

What determines how much sound reflects or transmits at an interface?

The difference between the acoustic impedances of the two materials.

Large acoustic-impedance mismatch

Most of the sound is reflected.

Small acoustic-impedance mismatch

Most of the sound is transmitted.

Acoustic reflection equation

R = ((Z2 − Z1)/(Z2 + Z1))².

Acoustic transmission equation

T = 4Z1Z2/(Z2 + Z1)².

If you want maximum sound transmission, what should you choose?

Two materials with similar acoustic impedances.

If you want maximum sound reflection, what should you choose?

Two materials with very different acoustic impedances.

Why are polymers and foams useful for sound insulation?

They have much higher sound absorption than typical metals and ceramics.

Sound absorption coefficient for metals and ceramics

About 10⁻⁶ to 10⁻⁴ in the class slide.

Sound absorption coefficient for polymers and foams

About 0.01 to 0.2 in the class slide.