mse 3143 ceramic materials - manisa celal bayar...

Assoc.Prof. Dr. Emre YALAMAÇRes.Asst. B.Şölen AKDEMİR

MSE 3143Ceramic Materials

Mechanical Properties of Ceramics

12017-2018 Fall

OUTLINE Elasticity & Strength

Stress & Strain Behaviour Of Materials

Young’s Modulus

Poisson’s Ratio

Strength

Strength Measurements

Fracture Toughness

Hardness and Indentation Test

Estimation of Compressive Strength

Indentation Fracture Toughness

Nanoindentation Method2

ELASTICITY & STRENGTH

3

• Load Defined as Stress (s)

• Unit of Stress is psi(pound per sqaure inch) or MPa

• Deformation Strain = Strain rate (e)

• Strain unit is deformation cm/cm

• Strain type depends on bond energy, stress and temperature.

• Elastic Deformation: Once the forces are no longer applied, the object returns

to its original shape.

E= Young’s modulus (=Elastic Modulus)

G = Shear Modulus t = G g

• Volumetric Modulus of Elasticity

s = E e

4

a) Brittle Fracture diagram typically

observed in ceramics

b) Ductile Fracture diagram observed in

materials that can deform plastically

(with no distinct yield point)

c) Ductile Fracture diagram with a yield point

observed in low carbon steels.

d) Stress & Strain diagram of Elastomers.

STRESS & STRAIN BEHAVIOUR OF MATERIALS

Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Usein Design, 3rd edition, Taylor&Francis, 2006

5

E= YOUNG’S MODULUS / ELASTIC MODULUS

• The magnitude of the elastic modulus is determined by the

strength of the atomic bonds in the material.

e

sECalculation from the plot of stress&strain diagram

Atomic bond EBonding Type E (GPa)

Organic Materials 10

Weak Ionic Bond (NaCl) 44.2

Aluminium 69

Iron – Nickel alloys 200

Strong Covalent Bond(Diamond) 1035

6

• In single crystalline materials, Young’s Modulus’ value depends on

crystallographic orientation.

• Anisotropy

• In single Iron crystalline:


Crystallographicdirections

E (GPa)

[111] direction 283

[100] direction 124

• Many materials encountered by an engineer are made up of more than one

composition or phase and have elastic modulus intermediate between the moduli

of the two constituent phases.

bbaaVEVEE

• Porosity is also a factor affecting the elasticity.

)9.09.11( 2

0 PPEE


Ea, Eb : elastic moduli of the constituents

Va, Vb : volume fractions

E : estimated elastic modulus of the mixture

E0 : elastic modulus of nonporous material

P : volume fraction of pores

E= YOUNG’S MODULUS(ELASTIC MODULUS)

Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006

E= YOUNG’S MODULUS(ELASTIC MODULUS)

Effect of temperature on the elastic modulus


• When a tensile load is applied on the material, the length of the sample increases slightly and

the thickness decreases slightly. The ratio of the thickness changes to the length changes is

referred to as Poisson’s ratio, ν.

ll

dd

/

)1(2 GE

POISSON’S RATIO


• For isotropic and polycrystalline ceramics, Poisson’s ratio,

Young’s Modulus, and the shear modulus are related by

• Poisson’s ratio typically varies from 0.1 to 0.5.

• Values for various materials at room temperature are listed in table

POISSON’S RATIO


Young’s Modulus for Some Ceramics

G

STRENGTH

Strength

TheoreticalStrength

CompressiveStrength

Tensile Strength

YieldStrength

FlexuralStrength

Fracture(Breaking) Strength

Ultimate Strength

• Theoretical strength can be defined as the tensile stress required to break atomic bonds and

pull a structure apart.

• The theoretical strength for ceramic materials typically ranges from 1/10 or 1/5 times of the

elastic modulus.

• However, the theoretical strength is not available during material production or due to

structural defects.

2/1

0

a

Eth

gs

sth: theoretical strength

E : elastic modulus

a0 : interatomic spacing

g : fracture surface energy

STRENGTH

• The presence of a defects such as a crack, pore or inclusion in a ceramic material results in

stress concentration.

Elliptic crack model

STRENGTHEffect of Defects on Strength

2/1

2

s

s c

a

mInglis

2/1

c

EA

f

gsGriffith

2/1

2

c

E

Y

Zf

gs

EvansandTappin

STRENGTH MEASUREMENT


A

Pts

Ceramic materials are not generally characterized by tensile testing because of the high cost of

test specimen fabrication and the requirement for extremely good allignment of the load train

during testing.

STRENGTH MEASUREMENTTensile Testing

Tensile Strength of

Ceramics at Room

Temperature

In ceramic materials (e.g. refractory bricks and building bricks), the compression strength

is usually measured.

Because the compression strength of a ceramic material is usually much higher than the

tensile strength.

It is often beneficial to design a ceramic component so that it supports heavy loads in

compression rather than tension.

Residual compressive stresses are created in the material to increase the tensile strength.

Example: Concrete prestressed with steel bars and safety glasses

In general, compressive strength increases with decreasing grain size.

STRENGTH MEASUREMENTCompressive Strength

Why the compressive strength of ceramic materials is

higher than their tensile strength?


Ceramic Material

Metallic Material

Ceramic Material

Ceramic materials exhibit low tensile strength due to structural defects such as surface

cracks, void-porosity, impurities and grain growth during production.

Because pores, impurities and surface cracks are centers of stress intensity.

The crack appears easily from these spots under the applied load and progress rapidly in

fragile materials like ceramics.

As a result, fracture occurs at low stress (load) values.

However, under compressive strength, it is important to break atomic bonds instead of

structural defects in ceramic materials.


The bend strength is defined as the maximum tensile stress at failure and is often referred to

as the modulus of rupture (MOR).

I

McS

M : moment

I : the moment of inertia

c : distance from the neutral axis to

the tensile surface

STRENGTH MEASUREMENTBend Strength (Flexure test)

Richerson, D.W.; Modern CeramicEngineering: Properties, Processing and Usein Design, 3rd edition, Taylor&Francis, 2006

The strength characterization data for ceramics are reported in terms of MOR or bend strength.

Specimens are relatively inexpensive and testing is straightforward and quick.

However, there is a severe limitation on the usability of MOR data for ceramics; the measured

strength will vary significantly depending on the size of the specimen tested and whether it is

loaded in three-point or four-point.

To understand this magnitude and reason for this variation, data generated fot hot-pressed

Si3N4 during the late 1970s is used.

STRENGTH MEASUREMENT

Testing Type MOR (MPa)

3-point bend testing 930

4-point bend testing 724

Uniaxial tensile testing 552

Which of these strengths

should an engineer use?

Why are they different??

Silicon Nitride (Si3N4) samples produced by hot isostatic pressing.

3-Point Bending: The peak stress occurs only along a single line on the

surface of the test bar opposite to the point of loading. The stress

decreases linearly along the length of the bar and into the thickness of

the bar, reaching zero at the bottom supports and at the neutral axis,

respectively. The probability of the largest flaw in the specimen being

at the surface along the line of peak stress is very low.

The 4-point bending test result is lower than the 3-point bending result.

4-Point Bending: The peak stress is present over the area of the tensile

face between the load points. The area and volume under peak tensile

stress or near peak tensile stress is much greater for four-point bending

than for three-point bending, and thus the probability of a larger flaw

being exposed to high stress is increased.

BENDING STRENGTH

Calculating Bending Strength

Example4-point bending is applied to a 5x5x120 mm SiC bar. The inner (inner span) spacing

of the touch points is 40 mm and the outer (outer span) spacing is 80 mm.

a) If the measured load at failure is 200 N, what is the bending strength of this

specimen?

b) Is it possible to say that the calculated bending strength is the bending

strength of SiC? Why?

In many applications, materials are subjected to multiaxial stress fields. Very few data are

available for the response of ceramics to multiaxial stress fields.

The illustrated sample test provides a biasing datum that has been

subjected to a biaxial stress stance. The defect in the material is

subjected to simultaneous tensile and shear stresses.

Biaxial loading frequently occurs at the contact zone between two ceramic parts or between a

ceramic and a metal part, especially during relative motion due to mechanical sliding or

thermal cycling. Under certain conditions, very localized surface tension stresses are much

higher than the applied load.

Many engineers are not aware of this mechanism of tensile stress generation, yet it is a

common cause of chipping, spalling, cracking, and fracture of ceramic components.

BIAXIAL STRENGTH

STRENGTH DATA


continues

STRENGTH DATA

Examples of strength vs.

temperature for typical

polycrystalline oxide ceramics.


STRENGTH DATA

Strength versus temperature for

carbide and nitride ceramics and

superalloy metals.


Until now, discussions have considered strength and

fracture in terms of critical flaw size. An alternative

approach considers fracture in terms of crack surface

displacement and the stresses at the tip of the cracks.

This is the fracture mechanics approach.

The stress concentration at a crack tip is denoted by the

stress intensity factors KI, KII and KIII. The subscripts refer to

the direction of the load application according to the crack

position.

If the load is perpendicular to the crack, as is typically the

case in a tensile or bend test as indicated by KI. Mode I is

most frequently encountered for ceramic materials..

The critical stress intensity factor (KIC) is

the stress intensity factor at which the

crack will propagate and lead to fracture.

This is also called fracture toughness.

FRACTURE TOUGHNESS

The parameters associated with Mode I stress intensity factor are:

For plane strain:

2/1

21

2

gEK

I 2/12 gEK

I

2/1YcKaI

s

For plane stress:

For the applied stress sa and crack length 2c:

FRACTURE TOUGHNESS

Fracture toughness can be found by many methods.

Two common methods are bending and indentation.

In the bend test, a notch is introduced, usually using

a diamond-tipped copper cutting Wheel, into the

tensile side of the specimen.

The notch is flat but it can also be in chevron-shaped.

FRACTURE TOUGHNESS

Carter, C.B.; Norton, M.G.; ’’Ceramic Materials: Science and Engineering’’, Springer, 2007

a = c

Y = x

P = Fmax

L = (S1-S2)

b = B

3-Point = 4-Point notations

FRACTURE TOUGHNESSKıc From Bending Strength Test

A Si3N4 specimen with 10 mm width, 16 mm thickness and 200 mm length shall be

measured for toughness with split bar test. The width of split is 100 mm and the

depth is 8 mm. The internal and external discharge ranges are 60 and 120 mm

respectively. If the maximum load value of the test apparatus measured during

printing is 400 N, what is the toughness of the sample?

FRACTURE TOUGHNESSCalculation of Fracture Toughness

Example

Hardness of a ceramic material is measured by an indentation test. The hardness is generally

determined by dividing the applied load by the projected area.

HARDNESS and INDENTATION TEST

FIGURE 16.15 Plasticity under the indenter (the shaded

area) causes the deviation from Hertzian behavior.


FIGURE 16.14 Indentation stress versus indentation strain.

Deviation from what is called ‘’Hertzian’’ behavior.

Mohs Hardness Values


ESTIMATION OF Compressive STRENGTH


a = 2 for a Vickers indenter

INDENTATION FRACTURE TOUGHNESSKıc from indentation test

is dimensionless constant, which for ceramicshas an average value of 0.016±0.004


NANOINDENTATION METHOD• Thin films and surfaces

• The low loads used mean that the extent of cracking is much smaller than in conventional

indentation methods.

• Two parameters are often of most interest in nanoindentation testing:

• Elastic modulus

• Hardness

• Nanoindentation is a powerful technique because the

shape of the load-displacement curve can be used to

identify effects such as phase transformations, cracking,

and film delamination during indentation. It is also

important in studying the mechanical properties of

nanomaterials, such as carbon nanotubes.Carter, C.B.; Norton, M.G.; ’’Ceramic Materials: Science and Engineering’’, Springer, 2007

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ANY QUESTIONS?

mse 3143 ceramic materials - manisa celal bayar...

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