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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