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.
