16.Properties Related to Strength

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PROPERTIES

RELATED TO

STRENGTH


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Strength is the ability of a material to resistapplied forces without yielding or fracturing.

Strength of a material may change considerablywith respect to the way it is deformed.

Mode of stress, type of stress & rate of stress

application may affect the strength of amaterial.

Strength data are usually obtained from lab.

Tests which are performed under strictlystandardized specimens under controlledconditions. These tests also serve for obtaining- relationships.


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- curves can be grouped into three as:

Ductile Materials exhibit both elastic &

plastic behavior

Brittle Materials exhibit essentially elastic

behavior

Viscoelastic Materials exhibit large elasticdeformation


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SPECIAL FEATURES OF STRESS-STRAIN

DIAGRAMS

PLEY

F

U

A B

C

D

E


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Point A (Proportional Limit): The greatest stress(PL) that can be developed in the material

without causing a deviation from the law ofproportionality of stress to strain. In otherwords it is the stress upto which the materialresponds following Hookes Law.

Point B (Elastic Limit): Maximum stress (E) that

can be developed in a material withoutcausing permanent deformation. In otherwords it is the stress upto which thedeformations are recoverable upon unloading.


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Point C (Yield Point): The stress at which thematerial deforms appreciably without an

increase in stress. Sometimes it can berepresented by an upper and lower yieldpoints. Y,U represents the elastic strength ofthe material and

Y,L

is the stress beyondwhich the material behaves plastically.

Point D (Ultimate Strength): It is the maximumstress that can be developed in a material asdetermined from the original X-section of thespecimen.


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Point E (Fracture Strength): The stress at which thematerial breaks, fails.


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In an engineering - plot the original area(A0) & length (l0) are used when determining

stress from the load and strain fromdeformations.

In the true - plot instantaneous area &

length are used.The true values of stress & strain for

instantaneous area & length of the specimenunder tension will differ markedly, particularlyclose to the breaking point where reduction incross-section & elongation of the specimen areobserved.


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0A

PE &

0l

E

Engineering

i

TA

P &

i

Tl

True

0

ln

0

l

l

l

dl il

l

true

i

11

00

0

0000

ll

l

ll

ll

dl iil

l

l

l

eng

ii

engtrue 1ln


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DUCTILITY & BRITTLENESS

Ductility can be defined as strain at fracture.

Ductility is commonly expressed as:

a) Elongation

b) % reduction in cross-sectional area

A ductile material is the one which deformsappreciably before it breaks, whereas a brittlematerial is the one which does not.

Ductility in metals is described by:

100%

0

0

A

AAR

f

A

If %RA> 50 % Ductile metal


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TOUGHNESS & RESILIENCE

Toughness is the energy absorption capacityduring plastic deformation.

In a static strength test, the area under the- curve gives the amount of work done tofracture the specimen.

This amount is specifically called as Modulusof Toughness.

It is the amount of energy that can beabsorbed by the unit volume of materialwithout fracturing it.


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T (Joule/m3)

ufPL

u fPL

The area under the - diagram can be determinedby integration.

If the - relationship is described by a parabole.

fuT 3

2


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Resilience is the energy absorption capacityduring elastic deformation.

R

PL

PL

PLR2

1

EPL

Since

ER PL

2

2

1

If you assume PL = y

E

Ry

2

2


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YIELD STRENGTH

It is defined as the maximum stress that can

be developed without causing more than aspecified permissible strain.

It is commonly used in the design of any

structure.If a material does not have a definite yield

point to measure the allowable strains,ProofStrengthis used.

Proof strength is determined by approximatemethods such as the 0.2% OFF-SET METHOD.

At 0.2% strain, the initial tangent of the -

diagram is drawn & the intersection is located.


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T T


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DETERMINATION OF E FROM -

DIAGRAMS

For materials like concrete, cast iron & most non-ferrous metals, which do not have a linearportion in their - diagrams, E is determined by

approximate methods.1. Initial Tangent Method: Tangent is drawn to the

curve at the origin

2. Tangent Method: Tangent is drawn to the curveat a point corresponding to a given stress

3. Secant Method: A line is drawn between theorigin & a point corresponding to a given stress


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32

1


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HARDNESS

Hardness can be defined as the resistance of a

material to indentation.It is a quick & practical way of estimating the

quality of a material.

Early hardness tests were based on naturalminerals with a scale constructed solely on theability of one material to scratch another thatwas softer.

A qualitative & somewhat arbitrary hardnessindexing scheme was devised, temed as MohsScale, which ranged from 1 on the soft end for

talc to 10 for diamond.


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1. Talc

2. Gypsum

3. Calcite4. Fluorite

5. Apatite

6. Orthoclase

7. Quartz

8. Topaz

9. Corundum

10. Diamond

HARDER

An unknown material willscratch a softer one & willbe scratched by harderone.

EX:

Fingernail-(2.5)Gold, Silver-(2.5-3)

Iron-(4-5)

Glass-(6-7)

Steel-(6-7)


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The hardness of a metal is determined bypressing an indenter onto the surface of the

material and measuring the size of anindentation.

The bigger the indentation the softer is thematerial.

Common hardness test methods are: Brinell Hardness

Vickers Hardness

Rockwell Hardness


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2. Rockwell Hardness

Instead of the indentation

diameter, indentation depthis measured.

However, the surface

roughness may affect theresults.

So, an initial penetration ismeasured upto some load,

and the penetration depth ismeasured with respect tothis depth.

H = H2 H1

P1Initial

load

H1

P2Final

load

H2


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3. Vickers Hardness

Instead of a sphere aconical shaped indenter isused.

P

TopView Indentation

d2

d1

(kgf/mm2

)

2

21dd

d

Vickers Hardness =2

854.1d

P

16.Properties Related to Strength

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