tensile properties and rheology Flashcards
eq for stress using force
σ = force/A_0
where A_0 = cross-sectional area from sample
units for stress?
N/m^2 or Pa or GPa
conversion for Mpa
10^6 Pa
conversion for GPa
10^9 Pa
eq for strain
ε = ΔL / L_0
where ΔL = change in length of sample
L_0 = initial length
what are engineering stress and strain?
uses the fixed undeformed cross-sectional area A_0 in calculations
units for strain
NO units or sometimes a %
eq for stress and strain combined
σ = Eε
where σ = stress
ε = strain
E = elastic modulus
eq for E
E = σ/ε
units for E
N/m^2 or Pa or GPa
what does a higher gradient of the stress-strain curve mean?
stiffer material
what does a higher value for E mean in the stress-strain curve?
steeper gradient = stiffer material
how does plastic flow/mobility affect material properties?
lack of plastic flow/mobility = undergoes elastic deformation and breaks (brittle material)
what is ductility?
the amount of plastic strain a material can withstand
what is plastic flow/mobility also known as?
yielding behaviour
what is plastic flow/mobility?
a material undergoing a rearrangement of its internal molecular or microscopic structure
what is plasticity?
ability for the polymer chains to move over each other
how is plastic deformation observed on a stress-strain curve?
the line is no longer linear but a curve - the strain is causing a deviation from the linear proportionality of stress to strain
is plastic deformation reversible or irreversible?
irreversible
what is necking?
after yielding, when the cross-sectional area decreases, all subsequent deformation takes place in the neck, the neck becomes smaller and stress increases until the specimen fails
what is the natural draw ratio?
the ratio at which the neck reaches a certain diameter and doesn’t continue shrinking until failure
what is drawing?
new material after the neck shoulders necks down which continues until this new neck is the whole gage length of the specimen
there is more strain but the stress remains effectively the same
what is strain hardening?
the stress needed to increase the strain beyond the proportional limit in a ductile material
the material requires an ever-increasing stress to continue straining
occurs once the whole sample is necked, molecules are aligned parallel to the stretching direction
what are the axes for a stress-strain curve?
strain on x, stress on y
what is the elastic region?
where stress is proportional to strain and the deformation is completely reversible
the gradient of the straight-line at the start of the curve gives the elastic modulus
how is the yield value found from a stress-strain curve?
from the top of the first peak
what is cold drawing?
when the neck extends, the polymer chains unravel and align themselves parallel to the direction of the applied stress
what is ultimate tensile strength?
the maximum stress sustained during the test and can equate to the strength at which the material breaks
what are the units for ultimate tensile strength?
Pa or MPa or GPa
what is toughness?
the ability of the material to deform plastically and to adsorb energy in the process before fracture
what can increase toughness?
a good combination of strength and ductility
what are the units for toughness?
energy per volume
what is stiffness?
Young’s modulus, a measure of the force required to deform the material
units for stiffness?
Pa or MPa or GPa
what factors affect the tensile properties of polymers?
1) crosslinking density
2) intermolecular forces
3) Tg
4) crystallinity
5) MW
how does increasing crosslinker density affect mechanical properties?
increases modulus and strength (higher strength = steeper curve)
reduces ductility (%strain values - the ability of chains to move past each other without breaking)
how does increasing intermolecular forces affect mechanical properties?
increases modulus and strength
reduces ductility (H-bonds act as physical crosslinks)
how does changing temperature affect mechanical properties?
above the Tg the polymer is hugely more ductile (longer curves) have no plastic deformation
lower strength
increased toughness
what is rubber elasticity?
the behaviour of polymeric solids made up of flexible chains joined in a 3D network
high elasticity means it can be reversibly deformed to several times its original length
stretching the network reduces the conformation freedom and the entropy of the system
relaxation gives recovery, if chemical crosslinks are broken it is irreversible
how does MW affect tensile properties?
higher MW = higher tensile strength until a maximum
lower Mw = loose bonding by vdw and high mobility so low strength
higher Mw = large chain entanglement so high strength
how does increasing crystallinity affect mechanical properties?
increased modulus and strength, increasing yield stress
increased crystallinity = increased intermolecular bonds which act as physical crosslinks, so similar to increasing crosslinking
decreased toughness
what is the elongation at yield?
the strain at which the yield has occurred
what is the elongation at break?
the point at which the material breaks at the end of the curve
how do you distinguish brittle plastics from tough and hard plastics on stress-strain curves?
brittle has much steeper curve, tougher has shallower curve, harder has a longer line going into higher strains (the full necking, drawing, then strain hardening)
what are elastomers?
above the Tg, entirely flexible, no plastic deformation, high ductility
what is the spectrum from viscous to elastic materials?
viscous, viscoelastic liquids, viscoelastic solids, elastic
what material types does rheology describe?
viscous and viscoelastic
viscosity vs modulus?
viscosity is the proportionality constant between applied force and resulting speed for viscous materials
modulus is the proportionality constant between applied force (mass) and resulting deformation for elastic (solid) materials
how does the force applied affect viscous materials?
more force applied = liquid moves faster, less force applied = liquid moves slower
the same force applied to both a thin and thick liquid, the thick liquid moves slower
how does the force applied affect elastic materials?
more force applied = more deformation
more force (mass) applied to a soft spring gives more deformation than to a stiff spring
how is viscosity measured?
1) finger test - tacky, prone to stinginess of sudden brittle fracture
2) flow cups - the duration for a given volume to flow through the orifice at the bottom of the cup
3) rotational tests - rheometer and viscometer = sample put inbetween two plates and the top plate rotated to apply shear
4) extensional tests
eq for shear stress
τ = F/A
where A is the area of the top plate
eq for shear rate
Ẏ = v/h = dv/dh
where v = velocity of the top plate in ms^-2
h = height in m
eq for strain in terms of h
dx/h
where dx is the deformation in the x direction
h = height of the sample
eq for viscocity
μ = τ/Ẏ
= shear stress/shear rate so the gradient of the graph
what factors affect viscosity?
temp
shear rate - rate the force is being applied at (movement of the top plate)
what is ideally viscous flow?
the viscosity is independent of shear stress
what are flow curves?
shear rate on x axis, shear stress on y axis
what is shear thinning?
viscosity decreases as shear rate increases
compare flow curves for ideal viscosity, shear thinning, and shear thickening
ideal viscous = diagonal linear lines
shear thinning = curve initially going vertically up at the start of x then plateau
shear thickening = curve plateau along the start of the x axis before going up
why does shear thinning occur and how?
due to changes in molecular orientations and/or alignment in the direction of flow
with applied shear:
- entanglements at rest unfold and align
- suspension agglomerates at rest break up
- emulsion droplets which are spherical elongate
- dispersions have particles align
overall disorder at rest (high viscosity) becomes ordered (low viscosity) with applied shear and causes shear thinning
what is shear thickening?
viscosity increases with increasing shear rate (cornstarch liquid more viscous with force)
why does shear thickening occur?
when there is a high conc of solids which can’t readily flow past each other and so increase viscosity
what is the phase angle?
the difference (lag) between the stimulus and response measurements in oscillation measurements
can’t exceed 90deg otherwise the plates would be pushed apart
how is the phase angle different for ideally viscous compared to ideally elastic materials?
ideally viscous = 90deg bc energy is lost as the material moves (viscous) which gives a delayed response
ideally elastic = 0deg bc no delay between stimulus and response
what is G*
the complex shear modulus, defines the overall stiffness of the sample
eq for G*
T_A / Y_A
where T_A = shear stress
Y_A = shear strain
what is G’
along the x axis = the storage modulus = elastic modulus if the phase angle = 0 then G’=G*
what is G”
along the y axis = the loss modulus = viscous modulus if the phase angle = 90 then G” = G*
what does G’ relate to?
the amount of energy stored and recovered with each cycle
what does G” relate to?
the amount of energy lost and not recovered with each cycle
how do G” and G’ change between viscous and elastic materials?
viscous G”» G’
Gel point G” = G’
elastic G’»G”
for the flow of a viscous liquid e.g. shower gel what are G” and G’
for a viscoelastic solid G’ > G” = gel-like structure
what is amplitude sweep?
the amplitude is ramped while frequency and temp are held constant
what is thixotropy?
frequency held constant while amplitude (shear) is stepped from low to high to low to monitor structure before, during, and after destructive shear, shows the recovery of structure following shear
what is the time test?
amplitude, frequency and temp are held constant and properties monitored over time (changes in structure over time)
what is amplitude sweep used for?
to understand the inner structure (soft, stiff, LVR)
to monitor deformation
describe amplitude sweep graph
low strain on x axis = plateau = gel-like G’>G”
temp below gel point = curve going down = liquid G”>G’
x = strain then two graphs with G” and G’ separately on y
what is the LVR?
the linear viscoelastic region which is the range in which the test can be carried out without destroying the structure of the sample
what does the time sweep tell us?
if a sample is unstable (drying or degrading)
to study the structure build (gelation or cure) or recovery (after loading or pre-shear)
what is thixotropy important for?
coating quality, levelling, self-healing behaviour
what will be observed in thixotropy for self-healing properties?
1) at low shear = at rest = solid G’>G”
2) high shear = structural decomposition= liquid = G”>G’ = shear thinning
3) low shear = structural regeneration = solid = G’>G”
