matl sci midterm

Stress

The pressure due to an applied load on a material

Strain

The response of a material due to stress

- Physical deformation

F, 0

Engineering Stress:

σ = ___ / A ___

Stress

σ = Engineering (Stress/Strain)

Perpendicular, Perpendicular

In the equation σ = F/A0, F is the load applied (Parallel/Perpendicular) to a specimens cross section, and A0 is the cross sectional area (Parallel/Perpendicular) to the force before its application

l, l

Engineering Strain:

ε = ∆ ___ / ___ 0

Strain

ε = Engineering (Stress/Strain)

>

For tensile strength, σ (<,>) 0

<

For compressive stress, σ (<,>) 0

Top, Bottom, Sides

Tensile stress is applied at the ________ and ____________ of a material, while shear stress is applied at opposite __________ of a material

F, S, A

Shear Stress:

𝛕 = ___ (sub) ___ / ___ 0

x, l

Shear Strain:

𝛾 = ∆ ___ / ___ 0 = tan𝜃

True

Strain is dimensionless, and can be positive or negative: True or False?

Hooke's Law

The law stating that the stress of a solid is directly proportional to the strain applied to it

- Linear

E, ε, Linear

Elastic Modulus:

σ = ___ * ___

Note: Only applies if stress and strain are __________

𝛕, 𝛾

Shear Modulus:

G = ___ / ___

Force

The derivative of the energy radius diagram gives _________

Larger, More

A steeper slope on the force radius diagram corresponds to a (Larger/Smaller) elastic modulus, which means that it can take (More/Less) stress

More, More

A deeper well in the energy radius diagram means a bond has (More/Less) energy, and a steeper slope in the force radius diagram means a bond has (More/Less) energy

Opposite

Poisson's Ratio:

v = -∑x/∑y (or any combination of dimensions)

- Transverse dimensions have the (Same/Opposite) reaction to stress as the perpendicular dimension

- Inverse contraction

Elastic Deformation

A deformation with a linear relationships between the applied force and the displacement of atoms, making it completely reversible and recoverable

- Stress and strain are proportional

Plastic Deformation

A deformation with a non-linear relationship between the applied force and displacement of atoms, causing the bonds to stretch, break, and reform which leaves planes sheared which is a permanent

- Stress and strain are not proportional

Elastic, Plastic

(Elastic/Plastic) deformation must be overcome before (Elastic/Plastic) deformation occurs

Is Not, Is

Displacement by elastic deformation (Is/Is Not) permanent, and displacement by plastic deformation (Is/Is Not) permanent

Yield Point (P)

The point in which stress and strain are no longer proportional and elastic deformation becomes plastic deformation

Yield Stress (σy)

The stress required to produce a very small, yet specified amount of plastic deformation/strain (0.002)

- Stress value of some point on plastic deformation arch

- A measure of resistance to plastic deformation

0.002, Parallel, Stress, Strain

Strain offset method:

1.) Start at __________ strain

2.) Draw a line from starting point ____________ to the linear region of the stress-strain graph

3.) Wherever this line crosses the plastic deformation arch is where the corresponding σy value is, which is the (Stress/Strain) required to do the (Stress/Strain) prior to the intercept point

Yield Point Phenomena

An abrupt transition from elastic deformation to plastic deformation

- Occurs in specific alloys such as low carbon steels

- Has 2 yield points

Lower

In materials exhibiting the Yield Point Phenomena, Lüder Bands occur in the (Lower/Higher) yield point and are locations in which dislocations start to layer

Average, Lower

In materials exhibiting the Yield Point Phenomena, yield strength is defined as the ____________ stress, at the (Lower/Higher) yield point

Ultimate Strength (UTS)

The maximum amount of stress a material can withstand

- Maximum value on stress-strain graph

Fracture Strength

The maximum amount of strain a material can withstand before failing

Necking

For metals, the UTS occurs when noticeable _____________ starts to appear, a stress concentrator

Ductility

Measure of the degree of plastic deformation a material has sustained at fracture

Ductility, l, l, l

Percent Elongation (%EL):

- A method of measuring _____________

%EL = ( ___ f - ___ 0) / ___ 0 x 100

Brittle

If %EL < 5%, the material is (Brittle/Ductile)

Ductile

If %EL > 5%, the material is (Brittle/Ductile)

Ductility, A, A, A

Reduction in Area (%RA):

- A method of measuring _____________

%RA = ( ___ f - ___ 0) / ___ 0 x 100

Elastic Strain Recovery

The amount of elastic strain a material will take before reaching its yield point

Greater

If stress is reapplied post-plastic deformation, the yield point with be (Lesser/Greater) than it was originally

- Concept can be used to strengthen materials

Plastic, F, El, Ductility

ε ___________ = ε ___ - ε ___

- A method of measuring _____________

Decrease, Increases

Yield strength, tensile strength, and modulus of elasticity (Increase/Decrease) and ductility (Increases/Decreases) as temperature Increases

Increase, Decreases

Yield strength, tensile strength, and modulus of elasticity (Increase/Decrease) and ductility (Increases/Decreases) as temperature Increases

Resilience

The ability of a material to store energy in the elastic deformation region

1/2

Modulus of Resilience:

Ur = 0∫εy σ dε

However, if we assume a linear stress-strain curve, it can be simplified to:

Ur = ___ / ___ σyεy

- The equation of a triangle with sides σy and εy and hypotenuse along the linear portion of the line

High, Low

Resilient materials have (Low/High) yield strengths and (Low/High) elastic modulus

Toughness

Energy required to break a unit volume of material

- Approximated by the area under the stress-strain curve

Linear, Linear

When calculating resilience, it can be approximated under the _____________ part of the stress-strain graph, but for calculating toughness, it cannot be approximated with just the _____________ part, and the entire area must be taken into account

Brittle Fracture

A fracture that occurs under only elastic energy

Ductile Fracture

A fracture that occurs under elastic and plastic energy

True Stress

The stress determined by the instantaneous load acting on the instantaneous cross sectional area

>

True Stress (<,>) Engineering Stress ALWAYS

Hardening

An increase in σy due to plastic deformation

Opposite, Positive, Negative

Compression and Tension have the (Same/Opposite) stress-strain graphs for small strains, With tension being both (Negative/Positive) coordinates and compression being both (Negative/Positive) coordinates

Lower, Higher

Compression and tension graphs mirror one another at (Lower/Higher) strain levels, but at (Lower/Higher) strain levels, compression has a steeper slope and isn't as flat in the plastic regime as tension

More

For the shear/torsion strength testing, the stress-strain graph is the same, except that it withstands (Less/More) elastic deformation before it has any plastic deformation

Weak

Any material with an open end will be very (Weak/Strong)

Hardness

Resistance to permanent indentation of a materials surface

More, Better

If a material has a larger hardness, it is (Less/More) resistant to cracking or deformation when under compression and has (Worse/Better) wear properties

Plastic

Hardness is proportional to tension because they both exhibit some level of resisting _____________ deformation

Temperature, Chemical

Elastic modulus is relatively unchanged without a change in ________________ or _____________ structure

Diffusion

Mass being transported by some atomic motion in a lattice

Active Diffusion

Upon applying high temperatures, the energy barriers of atomic motion can be overcome and (Passive/Active) diffusion will occur

Random

Gases and liquid have brownian/ _____________ motion

Vacancy, Interstitial

Solids may have ____________ diffusion or _______________ diffusion

Self Diffusion

In an elemental solid, atoms migrate

- The ability for atoms to move within the same type of atom

Interdiffusion

In an alloy, atoms tend to migrate from regions of high concentration to low concentration

- Atoms of one type A diffuse into another atom type B

- Occurs by either vacancy or interstitial diffusion

Vacancy Diffusion

Atoms exchange sites with vacancies, in turn leaving another vacancy in their former position which can ultimately be filled and so on

Substitutional Impurities

When a different type of atom than expected fills an atomic site in a crystal lattice

Vacancies, Activation

The rate of vacancy diffusion depends on the number of ______________ and the ______________ energy required for the exchange of location

- Need to break bonds to move

Self Diffusion, Interdiffusion

Substitution in homogeneous solutions is _______ ______________ , while substitution in heterogeneous solutions is ___________________

All

Vacancies exist at ______ temperatures

Increases, Increases

As temperature increases, the number of vacancies (Increases/Decreases) and the diffusion rate (Increases/Decreases)

Interstitial Diffusion

Smaller atoms in tetrahedral or octahedral sites can diffuse between atoms

- Jumps between interstices

Faster, More

Interstitial diffusion is (Faster/Slower) than vacancy diffusion because there are (More/Low) sites to move to

Elementary Jump

A sequential diffusion movement that makes up a greater migration distance of an atom

- Moves like Plinko

M (Mass or Moles), Area, Time

In general, J (Flux) = ___ / ( ___ * ___ )

Mol, Cm, 2, Kg, M, 2

The units for flux are ___ / ___ ^ ___ OR ___ / ___ ^ ___

Dependent, Independent

Diffusion is time (Dependent/Independent) , while flux is time (Dependent/Independent)

Independent, Concentration Gradient

Flux is time (Dependent/Independent) and is proportional to the ________________ ______________

D, C, x

Fick's First Law of Diffusion:

J = - ___ (d ___ /d ___ )

C, C, x, x, Linear

In Fick's First Law of Diffusion:

dC/dx = ( ___ 2 - ___ 1) / ( ___ 2 - ___ 1)

- Applied only if dC/dx is ___________

Diffusibility, Temperature, Lattice

In Fick's First Law of Diffusion:

D = ________________ (constant)

- Depends on mechanism of diffusion, the _______________ of the system, the type of crystal _____________ , Crystal Imperfections, and the concentration of diffusing species

Steady State Diffusion

The diffusion condition for which there is no net accumulation or depletion of diffusing species

- Flux in = Flux out

Non-Steady State Diffusion

The diffusion condition for which there is some net accumulation or depletion of diffusing species

- Flux in ≠ Flux out

Doesn't

In steady state diffusion, dC/dx (Does/Doesn't) change

Does

In non-steady state diffusion, dC/dx (Does/Doesn't) change

Down, Up

D (Diffusibility) has a negative sign if the system is moving (Up/Down) it's concentration gradient and a positive sign if the system is moving (Up/Down) it's concentration gradient

Concentration, Time, Position, Accumulation, Depletion

Fick's Second Law of Diffusion:

dC(x,t)/dt = D * d^2C(x,t)/dx^2

- Rate of change of __________________ at a specific ________ and ____________ is proportional to the curvature of the concentration profile

- Diffusion flux and concentration gradient may vary with time, resulting in a net ________________ or ________________ of the species

x, t, s, x, 2, D, t

(C( ___ , ___ ) - C0) / (C ___ - C0) = 1 - erf( z )

where z = ___ / ___ √( ___ ___ )

Break, Bonds

For an atom to jump into a vacancy site, it needs enough energy to __________ its ___________ and squeeze by its neighbors

x, 4, z, t, x, 4, z, D

In rewriting z = x / 2√Dt, we find that:

D = ___^2/ ___ ___ ^2 ___

OR

t = ___^2/ ___ ___ ^2 ___

QD, R, D

For the diffusion coefficient vs 1/T graph, the slope is - ___ / ___ and the y intercept is ln ___

Less

Diffusion in a solid will vary depending on its path:

- In general, diffusivity is greater through (More/Less) restrictive structural regions

- Bulk volume << Grain boundary << Surface species

Open, Lower, With, Smaller, Cations, Lower

Diffusion is better when:

- Crystal structure is (Open/Closed)

- (Higher/Lower) melting temperature

- Materials (With/Without) secondary bonding

- Structures with (Larger/Smaller) diffusing atoms

- (Cations/Anions)

- (Lower/Higher) density materials

=, ≠

Fick's 1st law is necessary when flux in (=/≠) flux out, while Fick's 2nd law is necessary when flux in (=/≠) flux out

Polycrystalline Structure

A crystalline structure that contains many grains of crystals

- If grains are randomly oriented, overall component properties are not directional (Isotropic)

- If grains are textured/stretched in a particular direction, the component properties are directional (Anisotropic)

Isotropic

When the grains of a polycrystalline structure are randomly oriented, the overall component properties are not directional

Anisotropic

When the grains of a polycrystalline structure are textured/stretched in a particular direction, the overall component properties are directional

Grain Boundaries

The junction in which individual crystals grew and fused to one another

- Transition from the lattice of one region to that of another