Unit 2 material science Flashcards
stress-strain for mild steel
relationship between stress and
strain in this initial region is proportional.
The slope of the straight line from O to A is called the modulus
of elasticity
A is proportional limit
Beginning at this point, considerable elongation of the test
specimen occurs with no noticeable increase in the tensile force (a force that tends to elongate a material)
(from B to C). This phenomenon is known as yielding
In the region from B to C , the material becomes perfectly
plastic, which means that it deforms without an increase in the
applied load.
Elongation of the test specimen in this region requires an increase
in the tensile load, and therefore the stress-strain diagram has a
positive slope from C to D.
The load eventually reaches its maximum value, (at point D) is called the ultimate stress.
Further stretching of the bar is actually accompanied by a
reduction in the load, and fracture finally occurs at a point such as
E.
what happens to the graph to a true stress stress-strain graph of mild steel
When a test specimen is stretched, lateral contraction occurs, as
previously mentioned
In the vicinity of the ultimate stress, the reduction in area of the bar
becomes clearly visible and a pronounced necking of the bar occurs.
(the graph from C starts to form a circular slope decrease)
thus fracture point is at a lower point of stress
stress-strain diagram of other materials like Al and brittle materials and solution of unclear yeild point
The presence of unclear yield point followed by large plastic
strain
these materials that behave in a ductile
manner (under certain conditions) include aluminum, copper,
aluminum alloys typically
do not have a clearly definable yield point, as shown
Brittle materials:
Materials that fail in tension at relatively low values of strain are
classified as brittle.
SOLUTION
A straight line is drawn on the stress-strain diagram parallel to the initial
linear part of the curve but offset by some standard strain,
such as 0.002
(or 0.2%).
The intersection of the offset line and the stress-strain curve
(point A in the figure) defines the yield stress.
LINEAR ELASTICITY AND HOOKE’S LAW
When a material behaves elastically and also exhibits a linear relationship between
stress and strain, it is said to be linearly elastic.
σ = Eε
σ: represents stress
ε: represents strain
E: represents Young’s modulus of elasticity
formula of change in length linear elasticity and hookes law
DEFORMATIONS OF MEMBERS UNDER AXIAL LOADING
change in length=PL/AE
Explain the behaviour of electro/magneto rheological fluids in the presence of
the external field.
In the absence of a field, the fluid can freely flow across the electrodes On the application of the field, the fluid flow across the electrodes is
impeded by the particle chains. A larger pressure gradient is required to break the
chains and btw the electrodes to maintain the relative flow of the fluid. The forming and breaking
of the chains results in a significant change in the viscosity of the fluid.
what is strain hardening CD (stress strain graphs)
the
steel begins to strain harden. During strain hardening, the material undergoes
changes in its crystalline structure, resulting in increased resistance of the material
to further deformation. Elongation of the test specimen in this region requires an
increase in the tensile load, and therefore the stress-strain diagram has a positive
slope from C to D.
what is ultimate stress
what is true stress
The load eventually reaches its maximum value, and the
corresponding stress (at point D) is called the ultimate stress.
TRUE STRESS
If the actual cross-sectional area at the narrow part of the neck is used to calculate (normally curve falls as orginal cross section is taken)
load the bar can carry does indeed diminish after the ultimate stress is reached due to the decrease in area of the bar and withstands an increase in true stress up to failure (point E’).
Series Hybrid electric Vehicle
In case of series hybrid system, the mechanical output is first converted into
electricity using a generator. The converted electricity either charges the battery or
can bypass the battery to propel the wheels via the motor and mechanical
transmission. Conceptually, it is an ICE assisted Electric Vehicle (EV).
The slope of
the straight line from O to A is called
from d to e in stress to strain why does curve decrease (necking)
modulus of elasticity.
Necking: At point
𝐷
D, the material reaches its ultimate tensile strength, which is the maximum stress it can withstand. Beyond this point, any further deformation leads to localized narrowing or “necking” in the material, which reduces the cross-sectional area at that section.
poissons ratio and formula
upper limit for poissons ratio, and possions ratio for Al, Cu, Ag, Au (ISA 1M)
When a prismatic (unifrom cross section area)bar is loaded in tension, the axial elongation is accompanied by
lateral contraction (decrease in diameter)
normal to the direction of the applied load
v=(-ε_trans)/ε_axial
The minus sign is inserted to compensate that
lateral and axial strains have opposite signs.
ε_axial = stress/E (hookes law)
The lateral strain ε’ at any point in a bar is proportional to the axial strain ε at that
same point if the material is linearly elastic
upper limit is 0.5
Al-0.33
Cu-0.34
Ag-0.37
Ag-0.42
in what way is sheer stress/strain different
and shear stress formula
moduli of elasticity in tension and shear relation
elastic constants not in slides and their relatiosn
the lengths of the sides of the element do
not change.
Instead, the shear stresses produce a change in the shape of the element
most failures are a result of shear load
the angles between the side faces change.
t avg = Fmax / A
G = E/2(1+v)
elastic constants not in slides
G shear(stress/strain)
K (Direct(stress/(volumetric strain))
2E = 3K(1-2v)
3E = 9KG/(3K +G)
shear strain definition
shear stress/strain formula
The angle γ is a measure of the distortion, or change in shape, of the
element and is called the shear strain.
SHEAR STRESS/STRAIN
For many materials, the initial part of the shear stress-strain diagram is a straight line
through the origin, just as it is in tension.
For this region, the shear stress and shear strain are proportional,
t=Gy G(sheer modulus of rigidity)
factor of safety
The ratio of the ultimate load to the allowable load is used
to define the factor of safety:
F.S = ultimate stress/allowable stress
what is power transmission
flexible drives and rigid drives
used to transmit power from one shaft to
another which rotate at the same speed or at different speeds
rigid and flexible.
there is an intermediate link such as belt, rope or chain between the driving and the driven shafts. the link is flexible
In rigid drives like gear drives, there is direct contact between the driving and the
driven shafts through the drive.
belt drives, and types of belts
flat belts
round belts
Belts are used to transmit power between two shafts by means of friction
FLAT BELTS
it has 3 elements: driving and driven pulleys and an endless belt (should be in tension to prevent slip)
FLAT BELT
rectangular cross section and the rim of the pulley is slightly crowned which helps to keep the belt running centrally on the pulley rim.
ROUND BELTS
Round belts can operate in several different
planes. They are suitable for 90 degree twist, etc
They can be stretched over the pulley and snapped into the groove
very easily, easy to replace and assemble
limited to light duties
V belts advantages and disadvantages
V – belts have trapezoidal cross – section. A groove is made on the rim of the pulley of a V to take the advantage of the wedge
action.
Positive drive as slip between belt and pulley is negligible
Higher power transmitting capacity
disadvantages:
Cannot be used for large centre distances
Costlier as compared to flat belts.
open belt drive vs crossed belt drive
An open belt drive is used when the driven pulley is desired to be
rotated in the same direction as the driving pulley.
transmitting power, one side of the belt is more tightened (‘tight side’) and the other side is ‘slack side.
crossed belt drive:
drive pulley is to be rotated in the opposite direction to
that of the driving pulley.
can transmit more power than the open belt drive as the angle of wrap is
more, but it will wear out quickly
velocity ratio of belt drives and
velocity ratio with thickness
VR=N2/N1 =d1/d2
N1=speed of driving pulley(rpm)
N2=speed of driven pulley(rpm)
d1=diameter of driving pulley
d2=diameter of driven pulley
N2/N1=d1+t/d2+t
t=thickness
velocity ratio of belt drives
with thickness of belt(t)
considered
and with slip included and defintion
N2/N1=d1/d2
N1=speed of driving pulley(rpm)
N2=speed of driven pulley(rpm)
d1=diameter of driving pulley
d2=diameter of driven pull
ey
N2/N1=d1+t/d2+t
t= thickness
When the frictional grip between the belt and the pulley becomes insufficient, some forward motion of the driving pulley without carrying the belt with it or forward motion of the belt without carrying the driven pulley with it.
N2/N1=d1+t/d2+t(1-S/100)
Let s1 = % Slip between the driving pulley and the belt, and s2 = % Slip between the belt and the
driven pulley.
s=s1+s2
flat belt formula
T1/T2 = e^μθ
Let T1 = Tension in the belt on the tight side,
T2 = Tension in the belt on the slack side, and
θ = Angle of contact in radians
μ = coefficient of friction between the belt and
the pulley
(180+2a)pi/180 rad
sina=((r1+r2)/x)
lenght of flat belt
Lc=pi(r1+r2)+2x+((r1-r2)^2)/x
v = linear velocity of the belt = (pidN)/60 in m/s
crossed belt drive formulas
Let T1 = Tension in the belt on the tight side,
T2 = Tension in the belt on the slack side, and
θ = Angle of contact in radians
μ = coefficient of friction between the belt and
the pulley
α = semi grove angle
T1/T2 = e^μθ
Degree=(180+2a)
Sina=((R1-R2)/x)
length of crossed belt drive
Lc=pi(r1+r2)+2x+((r1+r2)^2)/x
v = linear velocity of the belt = (pidN)/60 in m/s
power transmitted belts
P=(T1-T2)V
T1 = Tension in the belt on the tight side,
T2 = Tension in the belt on the slack side
v = linear velocity of the belt = (pid*N)/60 in m/s
P = Power transmitted
what are gears types
and advantages
Parallel Shafts, Spur Gears, Helical Gears,Double helical or Herringbone Gears
toothed wheels which transmit power and motion from
one shaft to another by means of successive engagement of teeth
It is a positive drive (no slip) and the velocity ratio remains constant.
can transmit very large power
centre distance between the shafts is relatively small,thus compact
can transmit motion at very low velocity, not possible with the
belt drives.
spur gears
straight teeth parallel to the axes
when two gears start rotating, contact extends across huge width, resulting in sudden application load(high impact stresses) and excess noises at high speeds
If the gears have external teeth on the outer surface of the cylinders, the shafts
rotate in the opposite direction.
In an internal spur gear, the teeth are formed on the inner surface, with a smaller gear inside, both rotate in same direction
Helical gears
the teeth are curved, each being helical in shape
both gears have have the same helix angle but in opposite direction
after starting to rotate contact occurs only at the one point of leading edge or curved teeth
the load application is gradual which results in low impact stresses and
reduction in noise
thus can be used for higher velocities and have greater load carrying capacity
disadvantage of having end thrust/axial thrust(force component on gear axis) which can cause wear
double helical structure and what is a herringbone gear ISA
equivalent to a pair of helical gears secured, one a right helix, and the other left helix
the teeth of the two rows are separated by a groove.
Axial thrust which
occurs cancels out
can be run at high speeds with less noise and
vibrations.
If the left and the right helix gears of a double helical gear meet at a
common apex and no groove in between, the gear
intersecting gears
straight bevel and spiral bevel gears
Straight Bevel
Gears
The teeth are straight, cone shaped teeth
Vary in cross section throughout their length (teeth became smaller towards the Centre)
to connect shafts at right angles which run at lower
speeds.
Spiral Bevel Gears
When the teeth of a bevel gear are inclined at an angle to the face of the
bevel
smoother in action and quieter than straight tooth due to gradual load application and low impact stresses.
tho an axial thrust is present
mitre gears ISA
and centre formula
Gears of same size and connecting two shafts at right angles to
each other
C=(d1+d2)/2=m*((T1+T2)/2)
M is modulus
skew gears
hypoid and worm
hypoid
spiral bevel gears, with the difference that hypoid gears have axes that are non-intersecting and not parallel.
worm gear
worm gears consist of a worm and a worm wheel.
worm is in the form of a threaded screw,meshes withe the the
matching wheel.
the axes of which do not intersect
and are perpendicular to each other.
characterized by high speed reduction ratio(high torque and low-speed output)
spur rack and pinton
Spur rack is a special case of a spur gear where it is made of
infinite diameter/its a straight line
spur rack and pinion combination converts rotary motion
into translator motion
gear terminologies, circular pitch
formula
pitch circles:It is the circle corresponding to the gear
Pitch cylinders – (spacing btw gears)of a pair of gears in mesh are the imaginary friction cylinders, which by pure rolling together, transmit
the same motion as the pair of gears.
Diametral Pitch – It is the number of the teeth per unit length of the
pitch circle diameter in inches.
module:ratio of the pitch diameter to the number of teeth
m=d/T
P=π*d/T
d=pitch diameter T=number of teeth
p=T/d
no SI units
circular pitch
– It is the distance measured along the circumference
of the pitch circle from a point on one tooth to the corresponding
point on the adjacent tooth.
VR formula
VR=angular velocity of follower/
Angular velocity of driven
w2/w1=N2/N1=d1/d2=T1/T2
w=2piN
P=pid1/T1=pid2/T2
Pid1N1=pid2N2
what are gear trains and Compund gear train formula
a combination of gears used to transmit motion from one shaft to another, for speed reduction etc
types of gears:simple,compund, reverted, planetary gear trains
N2/N1=T1/T2=
(W2/W1=2piN2/2piN1=N2/N1)
N2/N1N3/N2N4/N5 =
T1/T2T2/T3T3/T4*T4/T5
Speed ratio=
N1/N5=T5/T1 (intermediate gears will have no effect on velocity ratio)
simple gear train, idler ISA
a series of gears capable of receiving and transmitting motion from one gear to another
idler gears: linkage btw driven and drive gears, if idler gears are odd, driven rotates in the same direction if even they rotates opposite direction else if even they rotate in opposite direction
idler gear doesnt have any influence on the velocity ratio
compound gear train
when a series of gears are connected in such a way that 2 or more gears rotate about an axis with the same angular velocity is known as compound gear aka same size gears
reverted gears train
the axis of the first and last wheels of a compound gear coincide, it is called reverted, the firs set of gears are not connected while(gap in rod) the second set of gears are connected by a rod
planetary gear
gear train having a relative motion of axis is called planetray gear, the axis of atleast one of these gears moves relative to the frame(relative to one gear)
one gear(big gear=sun gear)
rotates,(planet gear rotates with relative motion to sun gear and it also move)
outside wheel=epicycle wheel the epicycle wheel moves on top the sun gear
used for large speed reduction possible with epicycle gears used in transmission (hybrid and series)
what is MAGNETOSTRICTIVE MATERIAL
active materials that exhibit magneto mechanical coupling.
The materials undergo a change in dimensions in response to an applied magnetic
field. The induced strain depends only on the magnitude of the applied field, and not the polarity.
EX: Terfenol – D
used in Sensors
Actuators
