PROPERTIES PROPERTIES RELATED TO RELATED TO STRENGTHSTRENGTH

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

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

Mode of stress, type of stress & rate of Mode of stress, type of stress & rate of stress application may affect the strength of stress application may affect the strength of a material.a material.

Strength data are usually obtained from lab. Strength data are usually obtained from lab. Tests which are performed under strictly Tests which are performed under strictly standardized specimens under controlled standardized specimens under controlled conditions. These tests also serve for conditions. These tests also serve for obtaining obtaining σσ--εε relationships. relationships.

σσ--εε curves can be grouped into three as: curves can be grouped into three as:

• Ductile MaterialsDuctile Materials → → exhibit both elastic & exhibit both elastic & plastic behaviorplastic behavior

• Brittle MaterialsBrittle Materials → → exhibit essentially exhibit essentially elastic behaviorelastic behavior

• Viscoelastic MaterialsViscoelastic Materials → → exhibit large exhibit large elastic deformationelastic deformation

SPECIAL FEATURES OF STRESS-SPECIAL FEATURES OF STRESS-STRAIN DIAGRAMSSTRAIN DIAGRAMS

σPL

σE

σY

σF

σU

A B

C

D

E

Point A (Proportional Limit):Point A (Proportional Limit): The greatest The greatest stress (stress (σσPLPL) that can be developed in the ) that can be developed in the material without causing a deviation from material without causing a deviation from the law of proportionality of stress to strain. the law of proportionality of stress to strain. In other words it is the stress upto which the In other words it is the stress upto which the material responds following Hooke’s Law.material responds following Hooke’s Law.

Point B (Elastic Limit):Point B (Elastic Limit): Maximum stress ( Maximum stress (σσEE) ) that can be developed in a material without that can be developed in a material without causing permanent deformation. In other causing permanent deformation. In other words it is the stress upto which the words it is the stress upto which the deformations are recoverable upon deformations are recoverable upon unloading.unloading.

Point C (Yield Point):Point C (Yield Point): The stress at which The stress at which the material deforms appreciably without the material deforms appreciably without an increase in stress. Sometimes it can an increase in stress. Sometimes it can be represented by an upper and lower be represented by an upper and lower yield points. yield points. σσY,U Y,U represents the elastic represents the elastic strength of the material and strength of the material and σσY,L Y,L is the is the stress beyond which the material stress beyond which the material behaves plastically.behaves plastically.

Point D (Ultimate Strength):Point D (Ultimate Strength): It is the It is the maximum stress that can be developed maximum stress that can be developed in a material as determined from the in a material as determined from the original X-section of the specimen.original X-section of the specimen.

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

In an engineering In an engineering σσ--εε plot the original plot the original area (Aarea (A00) & length (l) & length (l00) are used when ) are used when determining stress from the load and determining stress from the load and strain from deformations.strain from deformations.

In the true In the true σσ--εε plot instantaneous area & plot instantaneous area & length are used.length are used.

The true values of stress & strain for The true values of stress & strain for instantaneous area & length of the instantaneous area & length of the specimen under tension will differ specimen under tension will differ markedly, particularly close to the markedly, particularly close to the breaking point where reduction in cross-breaking point where reduction in cross-section & elongation of the specimen are section & elongation of the specimen are observed.observed.

0A

PE &

0lE

Engineeri

ng

iT A

P &

iT l

Tru

e

0

ln0

l

l

l

dl il

l

true

i

11

00

0

0000

l

l

l

ll

ll

dl ii

l

l

l

l

eng

ii

engtrue 1ln

For For εεengeng ≤≤ 0.1 0.1 →→ ln(1+0.1) ln(1+0.1) ≈≈ 0.1 0.1

For small strains For small strains εεtruetrue ≈≈ εεengeng

itrue A

P &

0A

Peng

If you assume no volume change:

ii lAlAV 00i

i l

lAA 0

0

engengi

eng

i

true l

l

l

lA

P 100

0

engengtrue 1

DUCTILITY & DUCTILITY & BRITTLENESSBRITTLENESS

Ductility can be defined as strain at fracture.Ductility can be defined as strain at fracture. Ductility is commonly expressed as:Ductility is commonly expressed as:

a)a) ElongationElongation

b)b) % reduction in cross-sectional area% reduction in cross-sectional area A ductile material is the one which deforms A ductile material is the one which deforms

appreciably before it breaks, whereas a appreciably before it breaks, whereas a brittle material is the one which does not.brittle material is the one which does not.

Ductility in metals is described by:Ductility in metals is described by:

100%0

0

A

AAR fA

If %RIf %RAA >> 50 50 %% → →

Ductile metalDuctile metal

TOUGHNESS & TOUGHNESS & RESILIENCERESILIENCE

ToughnessToughness is the energy absorption is the energy absorption capacity during plastic deformation.capacity during plastic deformation.

In a static strength test, the area under In a static strength test, the area under the the σσ--εε curve gives the amount of work curve gives the amount of work done to fracture the specimen.done to fracture the specimen.

This amount is specifically called as This amount is specifically called as Modulus of Toughness.Modulus of Toughness.

It is the amount of energy that can be It is the amount of energy that can be absorbed by the unit volume of material absorbed by the unit volume of material without fracturing it.without fracturing it.

σ

ε

T (Joule/m3)σuσfσPL

εuεfεPL

The area under the σ-ε diagram can be determined by integration.

If the σ-ε relationship is described by a parabole.

fuT 3

2

ResilienceResilience is the energy absorption is the energy absorption capacity during elastic deformationcapacity during elastic deformation..

R

εPL ε

σPL

σ PLR2

1

EPL

Since

E

R PL2

2

1

If you assume σPL = σy E

R y

2

2

YIELD STRENGTHYIELD STRENGTH It is defined as the maximum stress that can It is defined as the maximum stress that can

be developed without causing more than a be developed without causing more than a specified permissible strain.specified permissible strain.

It is commonly used in the design of any It is commonly used in the design of any structure.structure.

If a material does not have a definite yield If a material does not have a definite yield point to measure the allowable strains, point to measure the allowable strains, “Proof Strength”“Proof Strength” is used. is used.

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

At 0.2% strain, the initial tangent of the At 0.2% strain, the initial tangent of the σσ--εε diagram is drawn & the intersection is diagram is drawn & the intersection is located.located.

DETERMINATION OF E FROM DETERMINATION OF E FROM σσ--εε DIAGRAMS DIAGRAMS

For materials like concrete, cast iron & most For materials like concrete, cast iron & most non-ferrous metals, which do not have a linear non-ferrous metals, which do not have a linear portion in their portion in their σσ--εε diagrams, E is determined diagrams, E is determined by approximate methods.by approximate methods.

1.1. Initial Tangent Method:Initial Tangent Method: Tangent is drawn to Tangent is drawn to the curve at the originthe curve at the origin

2.2. Tangent Method:Tangent Method: Tangent is drawn to the Tangent is drawn to the curve at a point corresponding to a given curve at a point corresponding to a given stressstress

3.3. Secant Method:Secant Method: A line is drawn between the A line is drawn between the origin & a point corresponding to a given origin & a point corresponding to a given stressstress

32

1

ε

σ

HARDNESSHARDNESS Hardness can be defined as the Hardness can be defined as the

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

the quality of a material.the quality of a material. Early hardness tests were based on Early hardness tests were based on

natural minerals with a scale constructed natural minerals with a scale constructed solely on the ability of one material to solely on the ability of one material to scratch another that was softer.scratch another that was softer.

A qualitative & somewhat arbitrary A qualitative & somewhat arbitrary hardness indexing scheme was devised, hardness indexing scheme was devised, temed as Mohs Scale, which ranged from temed as Mohs Scale, which ranged from 1 on the soft end for talc to 10 for 1 on the soft end for talc to 10 for diamond.diamond.

1.1. TalcTalc

2.2. GypsumGypsum

3.3. CalciteCalcite

4.4. Fluorite Fluorite

5.5. ApatiteApatite

6.6. OrthoclasOrthoclasee

7.7. QuartzQuartz

8.8. TopazTopaz

9.9. CorundumCorundum

10.10. DiamondDiamond

HARDER

An unknown material will scratch a softer one & will be scratched by harder one.

EX:

•Fingernail-(2.5)

•Gold, Silver-(2.5-3)

•Iron-(4-5)

•Glass-(6-7)

•Steel-(6-7)

The hardness of a metal is determined The hardness of a metal is determined by pressing an indenter onto the surface by pressing an indenter onto the surface of the material and measuring the size of of the material and measuring the size of an indentation.an indentation.

The bigger the indentation the softer is The bigger the indentation the softer is the material.the material.

Common hardness test methods are:Common hardness test methods are: Brinell HardnessBrinell Hardness Vicker’s HardnessVicker’s Hardness Rockwell HardnessRockwell Hardness

1. Brinell Hardness1. Brinell Hardness

• Load P is pressed for Load P is pressed for 30 sec. and the 30 sec. and the indentation diameter indentation diameter is measured as d.is measured as d.

P

D

d 22

2

dDDD

P

Brinell Hardness =

(kgf/mm2)

2. Rockwell Hardness2. Rockwell Hardness• Instead of the indentation Instead of the indentation

diameter, indentation diameter, indentation depth is measured.depth is measured.

• However, the surface However, the surface roughness may affect the roughness may affect the results.results.

• So, an initial penetration So, an initial penetration is measured upto some is measured upto some load, and the penetration load, and the penetration depth is measured with depth is measured with respect to this depth.respect to this depth.

ΔΔH = HH = H22 – H – H11

P1Initia

l load

H1

P2Final load

H2

3. Vickers Hardness3. Vickers Hardness

• Instead of a sphere a Instead of a sphere a conical shaped indenter conical shaped indenter is used.is used.

P

Top View

Indentation

d2

d1

(kgf/mm2)

221 dd

d

Vicker’s Hardness =

2854.1

d

P