Quiz 3 Flashcards
Brittleness
Tendency to fracture when even a small load/deformation is applied. Ex: glass
Ductile
How much a material can deform without sustaining internal damage. Ex: Gummy bear or rubber
Elasticity
Ability to return to the original shape after deforming/loading the material. Ex: rubber elastic
Plasticity
Ability of a material to stay deformed after external force is removed. Ex: blacksmith, I beams
Fatigue
Weakening pf a material due to repeated loading. Ex: Barbecue propane tanks
Hardness
The ability to resist permanent change in shape due to external loads. Ex: diamonds
Resilience
The ability to absorb energy and resist impact. Ex shock absorption or blast materials
Stiffness
Ability of a metal to resist additional deformation when loading continues.
Toughness
Ability of a metal to resist fractures. Ex: superheros
ASTM
The standard to quantify parameters and enable comparison of material properties
Engineering Stress
O= F/Ao
F -force
Ao- original area of the sample cross section
Engineering Strain
E = li-lo/lo or deltal/lo
li- instantaneous length
lo - original length
Creep
Deformation at elevated temperature (over a period of time)
Shear
t = F/Ao
y = alpha + beta given alpha and beta are in radians
Torsion
If we are not deforming by parallel plates, but by twisting the material.
Poissons ratio
For elastic behaving materials the tensile force in the z direction creates z strain -> Ez. This causes a contraction in the x and y directions. If the material is isotropic the. Ex and Ey are the same:
V = -Ex/Ez = -Ey/Ez
Relationship between shear and tension in elastic behavior
E = 2G(1+V)
E- elastic modulus
G- shear modulus
V- poissons ratio
Common poisson ratio for most material
0.3
Hookes Law
During the initial stage if loading a material the stress is proportional to the strain:
o = Ee
Stress = Elastic modulus x strain
Youngs modulus
E, the slop of the initial stress strain linear relationship. As temp increases the value if E decreases! We call this, that the material became less stiff. E is a measure of stiffness of the material
Relationship can be fir torsion and shear
Torsion = G shear (t =Gy)
Stress = E shear (o= Ee)
Plastic deformation
Many materials exhibit elastic behavior up to 0.005 strain or 0.5%. Above this strain the materials crystal bonds begin to fracture -> plastic deformation. The permanent change in material is possible by the movement of dislocations.
Yielding
The transition from E -> P regimen. In many many cases we do not wish to approach this load, but is is sometimes difficult to estimate when the transition from E to P happens. We can approximate by drawing a straight line starting at 0.002 strain. This line is parallel to the initial stress strain curve. Another common value is 0.005
Ultimate Tensile Strength
As the load continues to increase past yield, the dislocations move faster and start to combine. The dislocations form voids which form micro cracks which form cracks.
Ductility
When a material fractures, it is permanently gone. We would like to have as much as possible of a warning that failure is about to happen.
%Elongation = lf-lo/lo *100
%Area reduction = Ao-Af/ Af * 100
Resilience
Amount of energy absorbed in the elastic region
U = 1/2 oy^2/E
Toughness
Amount of energy absorbed up to fracture. Area under curve.
Polymorphism
Some metals as well as nonmetals may have more than one crystal structure.
Allotropy
When polymorphism is found an elemental solids.
Ficks first law
Steady state: (when the rate of diffusion into a system is equal to the right of diffusion out of the system. No net accumulation or depletion.)
Jx= -D (dc/dx)
Jx = Flux (or flow rate) of the diffusing species in the x direction due to a concentration gradient (dc/dx)
D= diffusion coefficient, or sometimes called diffusivity.
dc/dx - the change in concentration delta C/ over the change in dimension delta x
Ficks second law
Transient non-steady state conditions.
dCx/dt = d/dx(D dCx/dx)
If we assume a semi infinite solid, with a surface concentration of the diffusing species, Cs constant then we can solve using:
(Cx-Co)/(Cs-Co) = 1-erf(x/2sqrt(Dt))
X-position of interest
t-time of interest
Co- initial bulk concentration
Cs- surface concentration
Effects of Temperature on Diffusivity
D = Do e^(-q/kT)
Do- constant
q- activation energy to start moving defects, which consequently moves atoms.
Diffusion rates from fastest to slowest
Fastest, surfaces. Examples: catalytic, converters, photographic film.
Medium, grain boundary. Examples: critical for durability of interconnections in micro electronics.
Slowest, bulk (volume). Examples: a solid piece of material.
Weight percent
The weight of a particular element relative to the total alloy weight
Atom percent
The number of moles of an element in relation to the total moles of the element in the alloy
Diffusion
Material transported by atomic motion
Inter diffusion or impurity diffusion
The process by which atoms of one metal diffuse into another
Self diffusion
Diffusion occurring in pure metals where atoms exchange positions for the same type of atom.
What conditions must be met for Adams to diffuse?
For an atom to move, two conditions must be met. One there must be an empty adjacent site, and two the atoms must have sufficient energy to break bonds with its neighboring atoms, and then caused some lattice distortion during the displacement.
Vacancy diffusion
One mechanism involves the interchanging of atoms from a normal lattice, position to an adjacent vacant, lattice site or vacancy.
Interstitial diffusion
Adams that migrate from an interest position to neighboring ones that is empty. This mechanism is for the diffusion of impurities such as hydrogen, carbon, nitrogen, and oxygen which have atoms that are small enough to fit into the interstitial positions. Host or substitutional parties rarely form interstitial and do not normally diffuse via this mechanism.
Diffusion flux
J- how fast do diffusion occurs or the right of mass transfer.
J = M/At
M- mass diffusing through
A- cross-sectional area
T- unit time
Ficks first law
J =- D dC/dx
D: diffusion coefficient
dC/dx: concentration gradient
Steady state diffusion.
The mass diffusing the species entering the plate on the high-pressure side is equal to the mass extending from the low pressure surface such that there is no net accumulation of diffusing species in the plate.
Concentration profile
When concentration see is plotted versus position or distance within the solid X, the resulting curve is termed to the concentration profile.
Concentration gradient
The slope at any given point of the concentration profile.
Driving force
What compels a reaction to occur
Are more practical diffusion, sit situation, steady state or non-steady state
Most are non-state so the diffuser flux and concentration at some particular point in solid vary with time
Fix second law
dC/dt = D (d^2C/dx^2)
Or
(Cx-Co)/(Cs-Co) = 1-erf(x/2sqrt(Dt))
What assumptions can be made about situations in which the surface concentration is held constant.
One. Before diffusion, any of the diffusing, a salute atoms in the solid are uniformly distributed with concentration Co.
Two. The value of X at the surface is zero and increases with distance into the solid.
Three. The time it taken to be zero the instant before the diffusion process begins.
T=0 C = Co at 0<=x<=infinity
Carburizing
Increasing the surface, concentration of carbon.
Factors that influence diffusion
Diffusion species, temperature
Diffusion based on temperature formula
D = Do exp(-Qd/RT)
Do- a temperature independent pre-exponential
Qd- activation energy for diffusion
R-the gas constant 8.31 J per mole Kelvin
T- temperature in Kelvin
Engineering Stres
o = F/Ao
o- stress
Engineering Strain
e = li-lo/lo = delta l/ lo
Stress strain relationship
O = Ee
o-stress
E- modulus of elasticity
e- strain
Elastic deformation
Deformation in which stress and strain are proportional.
Modulus of elasticity
E, this modulus may be thought of as stiffness or materials resistance to elastic deformation. The greater the modulus, the stiffer, the material, or the smaller, the elastic strain that results from the application of a given stress.
Sheer stress,and strain relationship
t = Gy
t- shear stress
G- shear modulus
y- strain
Poissons ratio
The ratio of lateral and axial stream
v = -ex/ez = -ey/ez
Commonly this race shows between 0.25 and 0.35
Sheer modulus related to elastic modulus related to poisons ratio
E= 2G(1+v)
Plastic deformation
Stress is no longer proportional to strain and permanent non-recoverable deformation occurs
Yielding
The stress level at which plastic deformation begins.
Proportional limit
The point of yielding may be determined as the initial departure from the line of the stress strain curve. This is sometimes called the proportional limit as indicated by point P.
Tensile strength.
The stress at the maximum on the engineering stress straight and curve. This corresponds to the maximum stress that can be sustained by a structure, intention. If the stress is applied and maintained fractures will result. All deformations to this point is uniform throughout the narrow region of the tensile specimin
Ductility
A measure of the degree of plastic deformation that has been sustained at fracture. A metal that experiences very, very little or no plastic deformation upon fracture is determined brittle. Maybe expressed by percent elongation or percent area reduction
%EL = (lf-lo/lo) 100
%RA = (Ao-Af/Ao)100
How can you qualify brittle materials reference to ductility?
Bridle materials are approximately considered to have fracture strains of less than about 5%
Resilience
The capacity of a material to absorb energy when it is deformed elastically, and then upon unloading to have this energy recovered. The associated property is the modulus of resilience Ur.
Modulus of resilience definition
Ur = integral ( o )de
Integral of stress de strain from 0 to ey
Modulus of resilience, assuming linear elasticity
Ur = 1/2 stressy strain y
Or
Ur= stressy^2/ 2E
Toughness
Toughness is a mechanical term that is used in several context for one toughness is a property that is indicative of a materials resistance to fracture when a crack is present. Toughness is also the ability of a material to absorb energy and plastically deformed before fracturing.
Stress to force relationship
Stress = Force/Area
Tre stress and strain
From the engineering stress strain diagram it may appear that less stress is required to keep deforming the material.
The issue is that the cross sectional area decreases as we do the test, so true stress is increasing. True stress = Force/ instantaneous Area
True stress
True stress = Force/ instantaneous area
True strain
True strain = ln ( li/lo)
ln - natural log
li- instantaneous length
lo- original length
True stress related to engineering stress and strain
True stress = engineering stress( 1+ engineering strain)
True strain related to engineering stress and strain
True strain = ln( 1+ engineering strain)
ln- natural log
Strain Hardening
Is related ti the slope if true stress vs true strain. The steeper the slope the more strain hardening
Strain hardening formula
True stress = k*true strain^n
k-constant
n-strain hardening exponent
Hardness
Provides a quantitative test to measure the resistance of a material to plastic deformation. These tests provide a way to measure plastic deformation without destroying the part.
Rockwell test “HR”
Consists of a machine that applies a load onto a material:
- Indenter type
-magnitude of load
-time(dwell)
The deeper the impression the softer the material.
Can a single hardness test be used on all materials?
No, scale for specific ranges of hardness is used
Brinell Test “HB”
In this test, a steel ball is pressed against a material. This impression is ~mm wide.
Tensile strength (MPa) = 3.45 * HB
Tensile strength (psi) = 500 * HB
Vickers Test “HV”
Typically done on a small scale to measure hardness of “delicate”, ie small, features. Impression is a pyramidal diamond. The bigger d1 and d2 (tip to tip measurements) the softer the material. Indent is smaller than human hair
Fatigue
Fatigue is the type of failure where the material fails below its yield strength, because of cyclical loading.
Avg Stress = (max stress+minus stress)/2
Stress range(or) = max stress - min stress.
Amplitude = stress range/ 2
Stress Ratio (R) = max stress/min stress
Is compression or tension the bigger enemy of fatigue?
Tension
Fatigue Strength
Stress after 10^7 cycles
Fatigue life
of cycles required to cause a failure for a given applied load.
Fatigue limit
The stress at or below the fatigue limit is jot significant to internally damage the material. In theory the material can serve for a long time.
What initializes fatigue
Machined surface finish
Porosity
Threads
What does the fracture surface of a material experiencing fatigue look like?
It will have riges
What does the fracture surface of a material experiencing fatigue look like?
It will have riges
