TEST 3 Flashcards
What is normal Stress and its formula
F/A
Force per unit area where force is perpendicular to the cross section of the item
What is shear stress and its formula
F/A
Force per unit area where force is parallel to the cross section
What are the types of normal stress
Tensile and Compression
What is engineering strain
delta (L)/L
What is poisson’s ratio
coaxial strain/ perpendicular strain
v= -ℨx/ℨz = -ℨy/ℨz
Poisson’s ratio for metals
~.33
Poisson’s ratio for ceramics
~.25
Poisson’s ratio for polymers
~.40
What is Young’s Modulus E
sigma= Eℨ
What is shear modulus? G
tau= Gy
What is ultimate tensile stress
The maximum stress in a stress vs strain graph
What is the difference between elastic and plastic deformation
Plastic deformation can not be reversed
What separates elastic and plastic deformation
yield stress
How to calculate Young’s modulus E from stress vs strain graph
Slope in linear elastic regime
How to calculate resilience from stress vs strain graph
area under elastic area
How to calculate yield stress
.2% offset of elastic region
What is tensile stress
maximum stress
What is max strain
strain right before failure
what is toughness
area underneath the s-s curve
area reduction formula
delta area/ initial area
Formula for true stress
sigmaT= sigma(1+ strain)
True strain
strain (t)= ln(1+ strain)
Is dislocation easier in metals or ceramics/glass
Metals
What will an s-s curve look like for brittle materials
curve is mostly linear before failure
What will an s-s curve look like for elastomers
Elastomers will have much greater max strain
Why do some materials deform plastically?
Materials deform plastically because the internal energy is lower than elastic deformation
Dislocation with burgers vector in close packed plane will give what kind of surface and what sized vector
smooth surface
small burgers vector
Dislocation motion occurs along __ and in ____
Close packed planes, close packed directions
WHERE THE ATOMS TOUCH EACH OTHER
Slip plane, direction, system number for FCC
Plane (111)
Direction <1(-1)0>
4*3=12
Slip plane, direction, system number for BCC
{110}
<-111>
6*2=12
What is the slip system
Slip plane+ slip direction
What is the schmid factor
cos θ cos λ
θ: angle to slip plane normal from axis
λ: angle to slip direction from axis
Formula for resolved shear stress
σR= σcosθcosλ
σR= σ*schmid factor
How would you find θ and λ given the vector directions of Slip plane normal, slip direction, and force
Dot product the two vectors to find the angle
What is resolved shear stress
tau=σ*schmid factor
When will slip occur
When criticial resolved shear stress is reached
σ*schmid factor >_ tau criticial
Compare toughness before fracture for brittle and ductile materials
Ductile materials exhibit large toughness before fracture
Brittle materials exhibit low toughness before fracture
Compare fracture profiles of
soft metals
ductile typical metals
brittle materials
soft metals will have a small large change in area with the cross section being basically 0
typical ductile materials will have a some change in area of cross section
brittle materials will have ~0 change in area of cross section
What are the 5 stages of ductile fracture
- Necking
- Cavity Formation
- Cavity Coalescence
- Crack propagation
- Fracture
What is a transgranular fracture
When fracture occurs within grain of crystal; along crystal planes
What is intergranular fracture
when fracture occurs on grain boundaryu
Formula for max stress
σm= 2σ* sqrt(a/pt)
σm: max stress
σ: applied stress
a: half length of crack
pt: radius of curvature of crack
What is K= Yσ sqrt( pi * a)
K is stress intensity factor
σ:
Y: geometry factor ; ~1
σ: normal stress external
What is K(IC) = sqrt( 2 * E* y)
Fracture Toughness for brittle materials
E: Young’s modulus
y: specific surface energy
What is failure criterion
K >_ K(IC)
What can the griffith criterion predict
expected fracture stress
What formula is this: σc= sqrt[(2Ey/(pi*a)]
Griffith criterion formula
Why are ceramics stronger in compression
Ceramics are so weak in tension because tensile fractures are a result of fracture propagation and fractures result from defects. there are a lot of defects in ceramics
What will increase with cold work?
dislocation density
What does this formula mean
%CW= [(Ao-Ad)/Ao]*100
%CW and how it realtes to % change in cross sectional area
What are four ways to strengthen metal
Grain size
solid solution
cold work
precipatates
How does change in grain size affect strength
Grain boundaries resist dislocation motion
What formula is this and what trend does it tell us
σy= σ1 + ky /sqrt(d)
where
σy: yield stress
d: average grain diameter
σ1: CONSTANT
ky: constant
grain size decreases –> yield stress increases
What are the two types of solid solution strengthening?
Interstitial impurity
substitutional impurtiy
How does solid solution strengthening work?
Creates stress field that restricts dislocation movement
What trend is seen in increasing percentage of impurity?
strength increases
ductility decreases
How does cold work affect dislocations
After cold work, rolling affects grain orientation and shape
Dislocations become more entangled with one another -> dislocation movement becomes more difficult
How does precipitation strengthening work
A precipitate of an impurity forms on metal which restricts movement of dislocations
What is aging
Holding a rapidly quenched solid solution at a given temperature for some time
What are the three stages of heating after cold work
recovery
recrystallization
grain growth
What does recovery do to a metal
allows metals to decrease their internal energy by rearranging or decreasing dislocations
What equation is this:
d^n - do^n =Kt
do: initial grain diameter
n,K: constants
t: time
d: new grain diameter
Basic trend for metals and impurities
ANYTHING added to a metal that restricts motion of dislocations will increase yield stress and decrease ductility
Two major glass strengthening methods?
Tempering: Rapid cooling from softening temps.
Ion exchange: smaller alkali ions are replaced by larger ions, restricting motion of dislocations
What does a phase diagram show
shows all equilibrium states under a range of given conditions
What are metastable structures
A system that may not be at equilibrium but the rate of approach to equilibrium is so slow that the system can exist for a finite or indefinite time.
What equation is F=C +2-P
Gibbs Phase Rule
P: Number of phases
C: Number of components at point
F: # of variables that can be changed independently without changing the number of phases present
What is solubility limit
maximum concentration of solute thatmay dissolve in solvent as solid solution
What is a binary isomorphous system
two components are totally soluble in one another at all proportions
How to determine phase composition from a T vs composition graph?
draw a horizontal line and the corresponding values give the concentration of each phase
What is homogenous nucleation
nuclei form in the bulk of the liquid metal
what is heterogenous nucleation
impurity of daughter phase already exists so easier to form; does not require supercooling or undercooling
