Post on 02-Jun-2018
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Fundamentals of Materials Science and Engineering
MSE 20 (B2 and B3)
Vera Marie M. Sastine
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Why Mechanical Properties?
Need to design materials that can withstand applied load
e.g. materials used in
building bridges that can
hold up automobiles,
pedestrians
materials for and
designing MEMs
and NEMs
mater
space
explo
materials for
skyscrapers
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Stress and Strain
Stress pressure due to applied load
Tension, Compression, Shear, Torsion, and Combination
Strain response of the material tostress (i.e. physical deformation such
as elongation due to tension).
Tension
Comp
Torsion
Sh
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Common States of Stress
Simple tensionExample, for a cable
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Common States of Stress
Simple compression
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Tension and CompressionTension
Compr
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Elastic Deformation
Elastic means reversi
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Plastic Deformation
Plastic means perma
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Stress-strain Test
Initially
Elastic
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Axial Load, P
One of the important developments in
understanding mechanical properties:
The strength of a uni-axially loaded
specimen is related to the magnitude o
cross-sectional area,A
In detail
Sample calculation of surface density for Fe:
NS~ 1015atoms/cm2is true for most materials
Interplanar
Bonds (imagined
to be spring-
like)
f, UTS, Ultimate tensile strength
Pf, load at fracture
A0
, original cross-sectional area
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Sample Problem
Soln:
4
2d
A
Using for cross-sectional
area
Carbon steel has UTS=1200 MPa. Use conse
safety factor, set to 600MPa
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Hookes Law (as long as the loads were relatively small):
P, load
k, stiffness (lb/in) or N/m
, deformation
, strain
, deformation
L0, original length
E, Youngs modulus or modulus of
elasticity
Youngs Modulus
Strength the materials resistance to failure by fracture or exce
permanent deformation
Stiffness the load needed to induce a given deformation in the
ut tensio, sic vis As the Extension, so the F
To normalize the eqn, making the
stiffness purely a material property,
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A positive (tensile) strain in one direction willalso contribute a negative (compressive) strainin the other direction, just as stretching a
rubber band to make it longer in one directionmakes it thinner in the other directions
Poissons ratio (dime
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p, hydrostatic pressure needed for a unit relative decrease in volum
(-) sign indicates compressive produces a negative
The Poissons ratio is also relatedto the compressibility of the
material.
The Bulk Modulus
- K, also called the modulus of
compressibility.
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Sample Problem
Two timbers, of cross-sectional dimension bh, are
glued together using a tongue-and-groove joint as sh
the figure, and we wish to estimate the depth dof t
joint so as to make the joint approximately as strontimber itself.
If the bond fails at f, the load at failure will be ff bdP 2
Soln:
The load needed to fracture will be where f is the ultimate tensile strength of ff bhP
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Shear Stresses & Strains
yx yx
xy
yxsubscript:
stress is on theyplane in thex-direc
xysubscript:
stress is on thexplane in they-direc
xyyx For rotational equilibrium:
Shearing counterpart of Hookes Law:
G, shear modulus
For isotropic materials (properties same in all directions), there is
no Poisson-type effect to consider in shear, so that the shear strain is
not influenced by the presence of normal stresses.
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Shear Stresses & Strains
For plane stress situations (no normal or shearing stress com
the z direction), the constitutive equations are
For isotropic materials, if any two of the three properties E, known, the other is determined
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Stress Strain Curves- Importantgraphical measure of a materials
mechanical properties
Engineering Stress
Engineering Strain
Ratio of measured load over the original
specimen cross-sectional area, A0.
0A
F
E
Degree of deformation with respect to the
original length, L0.
0
0
0 L
LL
L
f
E
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Stress Strain Curves
True Stress
True Strain
Ratio of the applied load, F (or P), to the
instantaneous cross-sectional area,Ai, overwhich deformation is occurring.
i
T
A
F
Incremental increase in displacement dLdivided by the current length, L.
0
ln1
0
L
LdL
Ll
dLd
L
L
TT
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True Stress-Strain
Engg Stress-Strain
Neck forms where local x-sectional are
decreases resulting in an increase in T
On ENGG stress-strain curve, necking
decrease in stress
In engineering applications, the EnggStress-Strain Curve is More Us
critical points are emphasized!
Limitations of True Stress- Strain Curve:
when necking starts!
inaccurate at small strains
UTS
Stress-Strain Curve of Typical
Structural Steel
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Some stress-strain curves of
conventional materials