Mechanical Properties Flashcards
What is the definition of stress? (equation)
stress = Force / Area. Units are Pa (N/m^2)
What is the definition of strain? (equation)
strain = change in length / original length. Units are dimensionless
What is Hooke’s Law?
Stress = Young’s Modulus * strain
sigma = E epsilon
What is Poisson’s Ratio?
- lateral strain / axial strain
What is stress concentration factor?
Stresses near points of applications of concentrated loads reach values larger than average stress in the member
Stress concentration factor = maximum stress over average stress
What does viscoelastic mean?
Has both liquid and solid characteristics. Material response depends on magnitude of stress and strain rate
Difference in response when apply oscillating strain for solids, liquids, and viscoelastic materials?
Solid: in phase response, scales with applied force
Liquid: 90deg out of phase
Viscoelastic: offset of cyclic response
What is storage modulus and loss modulus? How does it relate to phase angle?
Storage modulus = “solid” part of viscoelastic material
Loss modulus = “liquid” part of viscoelastic material
Phase angle - phase shift of response, related to storage and loss modulus
What is time-temperature superposition?
higher strain rate is equivalent to low temperatures and vice versa
Explain “Entropy Elasticity”
When you have a highly entangled polymer, there is high disorder. When you stretch it, it alligns the chains. The polymer will want to return to its original entanglement to increase the entropy. The higher molecular weight you have, the higher the degree of entanglement. This corresponds to “rubbery plateau”
What are the 5 regions of temperature vs. Modulus plot for polymers? What are the different factors that impact them?
- Glassy, Hard, Brittle
- Molecular motion activated, less stiff
- Rubbery Plateau - long range elasticity, entropy driven
- Rubbery flow
- Liquid Flow
higher MW = more entanglements, delays rubbery flow (longer rubbery plateau)
cross-links makes flow less likely
more crystalline = higher Tg, glassy and brittle for longer
cross-linking prevents chain movement, and entanglements delay chain movements
What are elastomers?
High degree of cross-linking, can stretch more, increasing stiffness and Tg. Makes them less processible since they can’t melt or flow as easily. Maintained above Tg
What is a stress tensor?
sigma_i,j
i = surface normal direction
j = direction of force
[11 12 13
21 22 23
31 32 33]
11, 22, 33 are normal stresses
Others are shear stresses
12 = 21 – matrix is symmetrical
What is the stiffness and compliance matrices?
Stiffness = relates stress tensor to strain tensor
Compliance = relates strain tensor to stress tensor
Reduces values to be a 6x6 matrix, symmetry depends on crystal structure
Engineering Stress / Engineering Strain
Pressure over original area
Change in length over original area
Ultimate Tensile Strength
Maximum stress from Stress strain curve
True Stress / True strain
stress and strain calculated over actual area of sample
Yield Stress
Stress required to generate a plastic strain of 0.2%
What is critically resolved shear stress?
When the resolved shear stress is larger than the critically resolved shear stress, there will be an onset of permanent deformations
Temperature dependence of strain rate?
Plastic flow is governed by thermally activated defect motion
Higher temp = higher dislocation velocity, strain rate lower
Higher temp = lower polymer stiffness = higher chain motion
Ductility
Degree of deformation before some event (necking, failure) - strain at failure usually
Toughness
Energy required to break or fracture a specimen - integral of entire stress-strain curve
What is twinning?
A strain accomodation mechanism that doesn’t involve dislocation motion. Happens with lower stacking fault energies and more difficult cross-slips
How do dislocations govern mechanical properties?
Plastic flow is governed by dislocations. Velocity of dislocation is correlated to strength.
Hardness
Resistance to plastic deformation. Measure with Rockwell, Brinell, Knoop, Vickers
What is a burger’s vector and how do different dislocations relate to it?
burgers vector is how much a crystal will shear when a dislocation goes through. If parallel to dislocation line, it is a screw dislocation, if perpendicular, it is an edge dislocation
What kind of stresses do the area around screw and edge dislocation experience?
Screw = shear stresses only
Edge = tensile and shear stresses
Why is FCC softer than BCC despite having less slip systems?
Able to form stacking folds
What is the Ductile-to-Brittle Transition Temperature?
In BCC only, at low tempertures, very brittle but strong, at high temperatures, very ductile but weak
Due to BCC having mostly screw dislocations that are thermally activated as more energy is needed to move them
What are the 4 hardening mechanisms?
- Work Hardening
- Solid Solution
- Precipitation
- Grain Boundary
How does solid solution hardning work?
interstitial or substitutional atoms migrate to compressive / tensile regions of edge dislocations, makes them harder to move and thus plastically deform
extra stress is proportional to square root of atomic concentration
How does precipitation strengthening work?
Particles (oxides, carbides) impede dislocation motion
extra stress proportional to 1/length between particles
How does work hardening / strain hardening work?
During plastic deformation, dislocation density increases. Dislocations interact with each other and impede each other’s motion
extra stress proportional to sqrt(dislocation density)
Why do we need to anneal cold-worked metals? What are the three stages?
As we work harden, dislocations entangle, multiply, and dislocation motion becomes difficult. This makes the material become brittle, and there is a need to recover.
Recovery: dislocations of opposite signs annilate by cross-slip and climb
Recrystallization: new grains form that have low dislocation density, small, consume cold-worked grains
Grain growth: larger grains consume smaller ones, grain boundary area reduced
How does grain boundary strengthening work?
Grain boundaries are another barrier impeding dislocation motion.
extra strengthening proportional to D^-(1/2) –> D = grain size
What is martensitic strengthening?
Cool austenitic steel at high rate, creates martensite phase that is BCT and metastable.
Carbon retained in solid solution –> solid solution strengthening
Original austenite retained, lots of grain boundaries present
High dislocation density to relieve misfit stress
Carbide cementite particles present - particle strengthening
Very brittle! need to temper to relieve brittleness – heterogeneous nucleation of carbide particles by removing carbon in martensite, decompose retained austenite
What are high entropy alloys and why are they so hard?
Lots of components, brings solid solution strengthening to its maximum
What is creep?
Time dependent continued plastic deformation at constant load or stress
What are the three regions of creep? Draw curve
Draw curve! (see notes)
Stage one: strain rate high, gradually decreases
Stage two: strain rate constant, steady state creep
Stage three: strain rate high
What temperature range is creep significant?
T/Tm > 0.5 the closer the temperature is to Tm, the more creep it will experience
What are the effects of stress on creep?
Higher stress means less fracture time, higher strain rate
What are the different creep mechanisms? Why are they affected by temperature?
Dislocation movement (cross-slip, climb), diffusion, grain boundary sliding
Dislocation motion may be impeded by precipitates in the way. At higher temperature, cross-slip and dislocation climb to avoid these particles is a lot easier
Grain boundaries may elongate to accommodate the stress by diffusing atoms from the sides of the grain to the top and bottom of the grains. This is assisted at high temperatures, especially since it is vacancy mediated (need high T)
at high T, grain boundaries become weaker, so can slide against each other
Depending on temperature and stress applied, different types of mechanisms will occur
What is Griffith’s Criterion?
There is a critical crack size that is required for the crack to grow, or else nothing will happen. This depends on the elastic modulus, the surface energy of the material, and the applied stress.
Difference between ductile and brittle fracture?
Fracture is crack formation and propogation due to stress
Ductile fracture - plastic deformation with high energy absorbance before fracture, stable and preferred
Brittle fracture - no deformation, rapid crack propagation perpendicular to applied tensile stress
What are stress concentrators?
There will always be microscopic flaws, and the stress in those areas will be a lot larger due to the radius of curvature
What is Fracture Toughness Equation?
K_IC = Y /sigma_C sqrt(\pi a)
Y = dimensionless, relates to specimen, crack sizes, geometries
\sigma_C = critical stress for crack propagation
a = size of crack
K_IC related to resistance to brittle fracture when crack is present [MPa sqrt(m)]
We want a higher K value
What variables impact fracture toughness?`
lower fracture toughness from lower temperature, higher strain rate, more solid solution hardening, increased grain size
How do we test for fracture toughness?
Impact testing - use low temp, high strain rate, (charpy test)
Testing for lower level of KIC so matl works better at higher T
What is Fatigue?
Dynamic and fluctuating stresses - failure possible at lower loads than at static
Brittle-like in nature even in ductile, very little plastic deformation associated with failure
Why do BCC and FCC fatigue S-N curves look different?
Has to do with the number of available slip systems for plastic deformation
How does fatigue failure work? How can we improve fatigue resistance?
Comes from crack initiation, propagation, and failure - mostly from surface defects. We can make this better by designing the shape of the metal better, getting rid of surface markings, case hardening (diffuse carbon to outer layer), shot peening (plastically deform outer layer) to improve fatigue behavior
What is the Hall-Petch Equation?
Strengthening related to grain size - larger number of grains means more dislocations pule up at boundaries, dislocations multiply
sigma_y = sigma_0 + K d^(-1/2)
