Chapter 6: Mechanical Properties (Part 1)

Strain

• the change in dimension of a material per unit length

• dimensionless

• m/m or cm/cm

• result of the application of stress to a material

Stress

• a force acting on an area

• normal stresses act perpendicular to the area (tensile stress → pull apart, compressive stress → squeeze inwards)

• shear stresses act parallel to the area

Elastic strain

• fully recoverable strain that develops upon applied stress, and is completely recovered when the stress is removed

• no permanent deformation

Plastic deformation/strain

when a material does not return to its original shape after stress is removed

Uniaxial Tensile Test

• Measure the resistance of a material to a slowly applied stress

• Used to determine many material properties

• typical specimen: ASTM E8 Standard

• Amount of stretching measured using a strain gauge or extensometer

Hooke’s Law Equation

σ = Eε

Strain rate

How fast you pull an object apart

Engineering stress formula

S = F/ A₀

Engineering Strain formula

e = Δl / l₀

What is the typical stress-strain in metals? What is the deformation mechanism?

<40%

Bond stretching followed by dislocation multiplication and motion

Work Hardening

dislocation multiplication

What is the typical stress-strain in ceramics? What is the deformation mechanism?

~500 MPa

much better in compression than tension

stretching of strong ionic/covalent bonds, few slip systems, no plasticity

failure after stress exceeds bond strength

What is the typical stress-strain in elastomers? What is the deformation mechanism?

• large, reversible deformation

• uncoiling and alignment of long polymer chains followed by stretching of covalent bonds

• almost no linear range

What is the typical stress-strain in thermoplastics? What is the deformation mechanism?

bond stretching, rotating, and disentangling, followed by chains siding past one another and rearranging permanently

Poisson’s Ratio Equation

v = - e_lateral / e_longitudinal

For metals, Poisson’s ratio is…

0.25 1<= v <= 0.50

Yield Strength

the point where the material transitions from elastic to plastic deformation

What is the relationship between elastic and plastic strains?

ε_tota = ε_plastic + ε_elastic

As plastic deformation begins, stress value drops from the “upper yield point” (S2). What does this mean experimentally/physically?

Certain low-carbon steels display this “yield point phenomenon.” Why do they display this phenomenon?

Luders Bands

• visible, slanted lines that appear on the surface of some mild steels and other low-carbon alloys during tensile test

• caused by dislocation motion being interfered with by interstitial atoms clustered around dislocations during slip

Is plastic deformation good or bad for load-bearing applications?

Bad, must design components so stress under operation is much less than yield strength at the temperature at which the material will be used

For shaping materials into components, you must apply stresses well above or below yield strength?

above

True or False: Young’s Modulus is dominated by atomic bonds, rather than microstructure (grain size, phases, GB)

True

Necking

one region of specimen deforms more than the rest and the cross-sectional area decreases

How does engineering stress decrease?

area is smaller at neck, so a lower force is required to continue deformation

Uniform deformation vs Non-uniform deformation

refer to graph for answer

Ultimate Tensile Strength

• strength at highest applied force or maximum stress on engineering stress-strain diagram

• deformation becomes unstable in a local area and doesn’t remain uniform

What do true stress and true strain account for?

the changing dimension of the tensile specimen during deformation

True Stress

Force acting per instantaneous cross-sectional area of specimen

σ_T = F/A

True Strain

Integrating the incremental changes in length relative to the instantaneous length

ε_T = ln(L/L₀)

Which metals do you expect to have higher melting temperatures?

metals with higher elastic modulus tend to have stronger atomic bonding, so they have higher temperatures

Modulus of resilience

elastic energy a material can absorb prior to yielding

E_r = (1/2)(yield strength)(strain at yielding)

Tensile toughness

• energy absorbed by the material prior to fracture

• area under “true” stress-strain curve

Which material has more toughness?

B

Which material has a larger E/ “stiffness”?

Steel

Ductility

ability of a material to be permanently deformed without breaking when a force is applied

%Elongation formula

%elongation = ((l_f - l₀ ) / l₀ ) * 100%

%Reduction in area formula

%RA = ((A₀ - A_f ) / A₀) * 100%

Elastic limit

• max stress a material can experience and still return to its original shape after the load is removed

• below: elastic deformation

• above: some permanent plastic deformation remains

What does yield strength correspond to?

stress at which plastic deformation starts

How can we control yield strength?

1. other dislocations (strain hardening)

2. grain size (grain strengthening)

3. point defects (solid-solution strengthening)

4. precipitations (second phases such as carbides in steel)

Why does the yield strength decrease at higher temperatures?

• decreased dislocation density

  • energy assists formation of ideal crystal structure

  • dislocations don’t interfere with each other

• increase in grain size via grain growth

  • recrystallization: new and defect-free grains grow

• strengthening due to ultra-fine particles may decrease

  • precipitates grow in size

Hardness test

measure of the resistance to penetration of the surface of a material by a hard object

qualitative measure of the properties of the material

Why can’t we establish a quantitative unit for hardness (ex. MPa)?

the stress near indenter is non-uniform

Brinell Hardness

• uses spherical indenter and measures diameter of indent

Rockwell Hardness

Brinell Hardness Number (BHN)

Why is elastic deformation also measured in a Rockwell Hardness test?

Why might a metal/alloy be more brittle for impacts?

Insufficient time for slip to occur

Impact test

• used to evaluate brittleness of a material under impact loading

• material is strained at a much higher rate than tensile test

Strain rate

how fast deformation is happening

Vickers Hardness

HV = 1.854 (P/d²)

Knoop Hardness

Tensile toughness

area under a stress-strain curve before fracture

ability of a material to absorb energy during a slow tensile test

Impact toughness

ability to absorb energy during an impact

measured using Izod and Charpy tests

Fracture toughness

ability of a material containing flaws to withstand an applied load

(flaw: pre-existing crack or void)

At low temperature, are there more or fewer thermal vibrations?

fewer

At low temperature, do dislocations have an easier or more difficult time moving?

more difficult → no assistance from the thermal vibrations

As temperature decreases, what happens to ductility and strength?

ductility decreases, strength increases

As the strain rate increases, is there more or less time for dislocations to move?

less time

If we observe a material to exhibit good ductility at room temperature, how can we know about low temperatures without repeating tensile tests?

Perform an Izod or Charpy test

Charpy test

• mgh → m = mass of pendulum

• pendulum hits behind the notch in the material

• impact energy measured by this test is the work done to fracture the specimen

• more ductile the material → more plastic deformation → higher the Charpy energy

• more brittle → less plastic deformation → less Charpy energy

The Charpy energy compared to the energy under the stress-strain curve is ___________________

usually smaller

Why should we be interested in impact and fracture toughness?

• important for load bearing structures

• need to know if material will survive the conditions that the structure will see in service

Izod test

• like a cantilever beam

Ductile to Brittle Transition Temperature (DBTT)

• transition temps are determines using Charpy and Izod tests

• ex. Titanic → snapped easily from impact of iceberg due to low temperatures

Require DBTT above or below operating temperatures?

below

True or False: FCC crystal structure typically exhibits higher absorbed energies and no transition temperature

True because dislocations can still move on many close-packed slip systems