Lecture 5 elastic region Flashcards
tensile testing is
fundamental test used to extract key properties of materials
specimens shape in tensile testing and why
dogbone shape - ends larger than middle - localize stress into the centre of the piece and not be affected by the gripping of the materiel
how is tensile testing done
two dots placed on specimen distance measured this
record the extension in the specimen gives the strain measure forced required gives stress
gauge length is the
distance between the two dots during tensile testing
loading occurs
via load cell with moving cross head - move top head up specimen clamped between two clamps
other properties measured in tensile testing
elongation after fraction - tells us about plastic deformation
gauge length at failure - another measure of ductility
engineering stress strain graph regions
elastic region - underneath straight line
uniform plastic region yielding - before UTS
nonuniform plastic region necking after UTS
elastic region
pulling bonds slightly then letting material go so it returns to its original shape
yeilding region
begin to break bonds between material such that it begins to flow - plastic deformation
necking region
localise stresses begin to occur failure
bond strength defines the
elastic region allows us to define anumber of elastic modula
what is an inset graph
due to sharp rise in stresses with little increase in strain during the elastic region on a normal stress strain graph you can not see the elastic region therefore have smaller graph showing just that region
stress
force /area
strain
change over length / length
if use original length of sample
engineering stress and strain inital length and cross sectional area
tensile stress vs compressive stress
just negative tensile materiel gets longer and thinner
compressive makes material get shorter and fatter
shear stress
applying force parallel to surface
labelled engineering stress stain curve
YMS limit of proportionality (hookes law obeyed to)
offset yield strength UTS
failure strength
How a material gets strength
all material becomes stressed and strained
eventually once you pull past UTS
local region will exhibit large amounts of strain
limit of propotionality
point beyond which hookes law is no longer obeyed - force and strain directly proportional straight line
Yield stress
stress at which yeild stress occurs hard to pinpoint typically use offset yield strength
UTS
point at which plastic deformation becomes unstable and necking begins peak value of engineering stress strain curve
fracture
point at which material breaks
YMs is
stiffness of material (not just YMs affected by shape) makes a material difficult to deform
steels typically 100Gpa
within protional region change in stress/strain can be in comprehension constant for a material
most materials follow
linear elastically hookes law region follows same line in loading and unloading
some materials follow non linear elasticity
hookes law not obeyed but loading and unloading still follow same line - use tangential moduli dont worry not on course
steeper the elastic region
greater the YMs stiffer the material diamond very stiff would be steepest 100GPa aluminium 69 GPa
Ashby diagram
takes two mechanical properties of a material and plots them against each other
Ashby diagram
takes two mechanical properties of a material and plots them against each other typically as you increase density increase YMs - elastomers vary from this density moderate but YMS low
poissons ratio
materials change cross section area with length elastic region only
normal stress is along length of material goes from lo to lo + x
cross section goes from A to smaller value lateral direction
poissons ratio equal to
- lateral strain/normal strain (negative sign to indicate it is decreasing
poissons ratio typically for metals
.33 for metals 0.25 to 0.35 for most
poissons ratio close to zero
as you pull them their cross sectional area doesnt change much
shear modulus
resistance to shear stress
shearing stress to material to produce shear strain symbol G
shear stress = G * change in length parrallel to force / length perpendicular to force
stress = modulus * strain
bulk modulus
resistance to change in volume due to hydro static loading
stress = - Bulk modulus * change in volume/original volume
bulk modulus equal to K or B
4 key elastic moduli
YMs
poissons ratio
bulk modulus
shear modulus
equations to link moduli together E G K/B v
if have two can calculate other two E = YMs G = Shear modulus K/B = bulk modulus v = possions ratio
why are all the moduli related
as all defined by bond between atoms
bond stiffness or strength
S can be realted to force that is pulling atoms apart and displacement created
Bond stiffness equation
E = S/ao
bond stiffness equation related to YMs
F = S delta(a)
Stress = force/area = force change in atomic spacing/atomic spacing ^2
strain = Change in atomic spacing/original atomic spacing
Youngs modulus = Stress/strain = Bond stiffness/original atomic spacing
E = S/ao
see power point for better explanation
YMs dependant on
atomic spacing and bond stiffness, all elastic moduli dependent on each other therefore all dependent on these can relate them all
force acting on bond stiffness could also be
temperature due to thermal expansion
youngs modulus against bond stiffness graph diagram
covalent > metallic > ionic > hydrogen > van der waals bond
covalent bond stiffness high YMs
metallic high bond stiffness
primary bonds have good bond stiffness and good mechanical properties
secondary bonds bond stiffness lower and mechanical properties not as good - may be useful
