Lecture 6 plastic region Flashcards
True stress and strain
not related to initial length and area, use force/current cross sectional area, use change in length as length from current to previous
assume volume stays constant
issues with engineering stress strain
okay with small stress and strain but not very accurate after
true strain = (epsilon little t)
ln (1+engineering strain)
ln (1+ epsilon)
true stress = (sigma little t)
(1+engineering strain) engineering stress
dont use true stress strain as
it would require to measure the length and area all the time which would be difficult to do can then change to true stress and strain
true stress strain diagram
stress always rising which makes more sense
UTS is no longer easy definable on true stress strain curve
two types of strength
ultimate tensile strength max engineering stress a material can support
yielding strength elastic limit is reached onset of plastic deformation
measured in MPa steels -1000s bone cast iron 100s - aluminium 10s
why is yield strength hard to measure
should mark region where plastic region begins - bonds begin to break material begins to permanently deform
hard to pinpoint due to as plastic region get unstable region
get upper lower yield strength but dependent on method of doing test
offset yield strength or proof strength
0.002 or 2% strain follow maintain YMs then when hit stress strain curve that point is offset yield strength, sometimes unstable region is much higher therefore use larger offset (this will be defined)
yield strength different to most material properties as
not constant can alter on the material using workhardening
what is work hardending
heat to make material ductile stress beyond the yield strength below UTS becomes permanently deformed yield strength permanently increased take back to elastic region and repeat can take all the way upto the UTS
after work hardening
much larger elastic region yield strength higher but area under curve is less therefore material more brittle
how to take fit plastic part of curve up to UTS
take log curve of true stress and strain
get straight line
log of true stress = log K (intercept) + n log true strain
where n is the gradient of line constant for different materials
plastic region curve fit what happens at UTS
true strain = n (gradient of line) can use this to find UTS true stress= K*true strain ^n = Kn^n UTS stress (sigma u) = true strain / exp (n) K (MPa) is phenomenological
Definition of phenomenological
need to do experiment on material and then fit with equation - no way of telling based on materials other properties
Theoretical strength
strength a material should be at
How to calculate theoretical strength
all fracture req breaking of atomic bond
hookes law obeyed to failure therefore we go all the way up elastic region to stress which is just high enough to break material
area under stress strain curve = elastic energy per unit volume
energy (U) = 0.5 stress*strain * volume = 0.5 stress^2/ Yms
volume of material being fractured = cross sectional area * atomic distance
U/area= 0.5 stress^2 * lattice constant/ Yms
this energy per unit area at theoretical strength = energy per unit area to create new surface (2gamma)
this can be used to work the theoretical strength
theoretical strength =
2* sqroot(YM * energy to create a surface (gamma)/ lattice constant (ao)) but this is an overestimate due to force energy curve not being linear so we generally use
sqroot(YM * energy to create a surface (gamma)/ atomic distance (ao))
roughly the theoretical strength =
YMS/3
where do most materials fail in comparison the theoretical strength
most material fail before theoretical strength
due to issues with crystal structure
issues within crystal structure x4
most crystal structures are not perfect have; vacancy interstitial atom substitutional impurity atom interstitial impurity atom which lead to local weaknesses
vacancy
atom missing in crystal structure - atoms around missing bond local change in structure
local weakness
interstitial atom
atom no sitting on a real lattice site in the middle of somewhere causes bonds around it to be stretched
local weakness
substitutional impurity atom
interstitial atom
when forming materials what species of atoms that you designed to be in there but when forming impurities get in ie carbon
changes local bonding structure local weakness
also could sit in middle
