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Machine Design Unit 1 - Lecture 1: Introduction to material behavior

Page 1 2009 Politecnico di Torino

Machine Design

Unit 1 Lecture 1Material behavior and properties

2

Material behavior and properties

Introduction to material behavior

Material behavior is the mean by which the forceand stress variables are related to the deformationand strain variables.


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Material behavior and properties


4


Tensile specimens

Basic definition of stress

Tensile test conditions

Basic definition of strainStress-strain curve and material properties

Examples of stiffness properties

Example of strength properties andmacrostructure of the fractured surface

Ultimate strain


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Tensile specimens

6

Specimen geometry (1/5)

Fillet

Head

The test specimen is composed of a sampleof the material in question and is constructedin the shape of a slender, cylindrical cross-section bar.

LG: gage length

LG


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7


According to the European standard UNI EN 10002/1

Testing temperature: 235C

Types of cross-sections:

d b b

h

h/b4 mm b>3 mm

8


LG

LO

AO

Circular cross-section specimen

LG: gage length

LO: Length between reference marks (initiallength)

AO: area of the gage cross-section (initialarea)


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Proportional specimen

, rounded to thenearest integer multiple of 5mm

Proportional specimen (2/2)

2

oA = d

4

45.65 =5.0

LG

LO

ooA65.5L =

ooGoo A5.2LLA5.1L ++


Basic definition of stress


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19

Testing machine

mobile crossbar

base

grip heads

load cell

columns

specimen

20

Specimens clamping

AA

circularspecimen

Planespecimen

Sect. A-A

wedge grip


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Test rate

The force is assumed to be applied slowly andthen maintained at a constant level. The limitsto the rate of loading are:

s

N/mm30

t

6

2

For steel

For aluminums

N/mm10

t

2

2


Basic definition of strain


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Elongation (1/2)

Strain:

Lo

L

o

o

L

LL =

Elongation: oLLL =

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Elongation (2/2)

Average stress Force

O

F

A= F

o

o

L

LL = oLLL =

Strain Elongation

Strain per cent

o

o

L

LL100%

=


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Infinitesimal element within the specimen

Along the specimen gage length the stressesand the strains are constant over anycross-section

OdF dA =

dx

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Transverse deformation (1/5)

Material undergoes both axial and transversedeformation. (Here the tensile case is shown)


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h

dx

In the linearly elastic range every infinitesimalvolume within the gage length undergoes thesame deformation


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h

b

)1(b

)1(h

)1(dx +

dx

Isotropic material


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Generally speaking

y

x

z

y1dydy +

( )x1dxdx +

( )z1zddz + zy ==


Strain-stress curve and material properties


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F- ductile material (1/4)

FyFy,low

F

Fu

local plasticdeformation

uniform plasticdeformation

Ductile material with yielding

fracture

elasticdeformation

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F- ductile material (2/4)

FY

F

elastic deformation: whenthe load is removed thematerial returns to itsoriginal state

Yield load: FY


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F- ductile material without yielding (1/2)

F

%0.2

Fu

Fp0.2 Fracture

Local plasticdeformation

Uniform plasticdeformation

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F- ductile material without yielding (2/2)

Offset yield load: Fp 0.2

%2.0 %2.0

Fu Fu

Fp 0.2 Fp 0.2

Offset strain

= 0.2%


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F- brittle material

FractureF

Fu

elastic deformation

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From F- to - (1/2)

FFu

Fy

Su

Sy

Unlike Force-strain curve F-, the stress-straincurve - does not depends on the area of thecross-section but only on the strain

SY or y= yield strengthSu or u= ultimate strength


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From F- to - (2/2)

The indicated decrease in the stress level betweenultimate stress and fracture is due to the fact that theundeformed original area is used for computing . Thestress computed using the actual area is called truestress whereas the conventional stress computedusing the original area is called engineering stress.

FFu

Fy

Sy

Su

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elasticdeformation

- curve for ductile materials 1/2

A material that behaves in ductile mannerexperiences large amount of strain before fracturing.The elastic range is much smaller then the plasticrange. A realistic plot scale is the following

F

~0,10,5% ~1025%

plastic deformation


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Linearly elastic deformation

For many commonengineering materialsthere is a portion of theforce-strain curve that islinear. The force isproportional to strain

Fp0.2

F

%2.0

KF =

Proportional limit

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Modulus of elasticity (1/2)

0.2%

Sp0.2

The constant ofproportionality is calledmodulus of elasticity orYoungs modulus

HOOKEs LAW:ut tensio sic vis

= E


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Modulus of elasticity (2/2)

Steel 2 105 0.3

Cast iron 1 105 1.8 105 0.27

Titanium 1.2 105 0.3

Aluminum 7 104 0.3

Material properties (E, ) for some selected

metallic materials

E - N/mm2

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The maximum allowable stress on steel is

about = 1000 N/mm2

The corresponding strain is

The area of the deformed section is:

Then is justifiable to define the conventionalengineering stress as:

( ) ( ) ( )

( ) ( )

2

O

O O O

A dy 1 dz 1 A 1

A 1 2 A 1 0,003 A 0,997

= =

= =

Order of magnitude for strain

0,005

E

=

=

OF/A =


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Strength of selected materialand macroscopic characteristics of failure

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Strength of selected materials

Material (minimum values)A%S

u

MPa

Sy

STEEL - Structural

(UNI EN 10025)

STEEL annealed

(UNI EN 10083)

CAST IRON

Gray

CAST IRON

Spheroidal

262222

1811119

---

1772

370500700

100200290

230320420

---

600850

10001250

400580800

1050

360430510

235275355

S 235S 275S 355

C 30C 60

41Cr436NiCrMo3

G10G20G30

Gs370-17Gs500-7Gs700-2

MPa


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Characteristics of ductile failure (1/4)

Adjacent fractured parts of a specimen, from awelded plate, placed together.

necking

welding

{

failure

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Characteristics of ductile failure (2/4 )

Plastic lips


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Ductile failure oninclined cross-section

Adjacent fractured parts of aspecimen from rolled plate placedtogether.

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Thin rolled plate, plastic flow before failure

Detail of the plastic flow



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Uniform plastic deformation

Within gage length everycross-section behaves inthe same way

Uniform plastic deformation

Elastic deformation

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Permanent deformation at Rm

Sy

m

Uniform permanentdeformation:it is a distinctivefeature of the material

but

not standardized anddifficult to measure


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Localized plastic deformation

A%: permanentstrain after fracture

u o

o

L LA% 100L

=

%

Localized plasticdeformation

A%

Sy

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Necking and proportional specimens (1/5)

Initial shape

At fracture

Lo

L

Up to = Su

Lu


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Lu

Uniform deformation dueto maximum stress Su

Strain due tonecking

aS

( ) smof a1LL ++

u o s

mo o

L L a

A% 100 100 100L L

= = +

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Depending onmaterial

Depending also on cross-section shape and size

(with shape restrictionaccording to standard)

M.J. Barba, Mem. Soc. Ing. Civils,

Pt. 1, p. 682, 1880

u o sm

o o

L L aA% 100 100 100

L L

= = +

S Oa K A=


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To compare strain measurements afterfracture of specimens with different size theyneed to be proportional; indeed, as:

S Oa K A=

s

m

o

aA% 100 100

L= +

O

m

O

AA% 100 K

L

= +

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In order A% being indicative of a materialpropriety

that is

to compare strain measurements after failure ofspecimens with different size

the specimens need to be similar; fromwhich:

O

m

O

AA% 100 K

L

= +

O OL 5,65 A =


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