WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich1

Chair of Functional Materials

6. Mechanical Properties

Forms of Mechanical Loading

tension compression

shear torsion

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich2

Chair of Functional Materials

6. Mechanical Properties

Stress-Strain BehaviourLinearelastic Deformation

ERobert Hooke:

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich3

Chair of Functional Materials

6. Mechanical Properties

Stress-Strain BehaviourNonlinearelastic Deformation

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich4

Chair of Functional Materials

6. Mechanical Properties

Force-Separation-Curve

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich5

Chair of Functional Materials

Potentielle Energie

Anziehungskräfte

Abstoßungskräfte

Kraft

Kernabstand

Abs-k.

Anz-k.

K

K-abst.

6. Mechanical Properties

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich6

Chair of Functional Materials

6. Mechanical Properties

Influence of Temperature

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich7

Chair of Functional Materials

6. Mechanical Properties

Tensile Properties of Metals(1)

vbcV cV - Konz. gleitfähiger Versetzgb – BurgersvektorV - Abgleitgschwindigkeit

Lüders-DehnungStreck-grenzen-effekt

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich8

Chair of Functional Materials

6. Mechanical Properties

Deformation Mechanisms for MetalsBasic Concepts of Dislocations(3)

Video Versetzungsbewegung (Blasenmodell)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich9

Chair of Functional Materials

6. Mechanical Properties

Deformation Mechanisms for MetalsCharacteristics of Dislocations(1)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich10

Chair of Functional Materials

6. Mechanical Properties

Tensile Properties of Metals(3)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich11

Chair of Functional Materials

6. Mechanical Properties

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich12

Chair of Functional Materials

6. Mechanical Properties

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich13

Chair of Functional Materials

6. Mechanical Properties

Deformation Mechanisms for MetalsBasic Concepts of Dislocations(1)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich14

Chair of Functional Materials

6. Mechanical Properties

Deformation Mechanisms for MetalsBasic Concepts of Dislocations(2)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich15

Chair of Functional Materials

6. Mechanical Properties

Deformation Mechanisms for MetalsBasic Concepts of Dislocations(3)

Video Versetzungsbewegung (Blasenmodell)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich16

Chair of Functional Materials

6. Mechanical Properties

Effect of Temperature

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich17

Chair of Functional Materials

6. Mechanical Properties

Tensile Properties of Metals(2)

Zugversuch CuPK.mov

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich18

Chair of Functional Materials

6. Mechanical Properties

True Stress-Strain-Curve

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich19

Chair of Functional Materials

6. Mechanical Properties

Mechanical Behaviour of Ceramics(1)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich20

Chair of Functional Materials

6. Mechanical Properties

Mechanical Behaviour of Ceramics(2)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich21

Chair of Functional Materials

6. Mechanical Properties

Mechanical Behaviour of Polymers(1)

spröde

plastisch

hoch elastischC-CH-BrückenVan der Waals

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich22

Chair of Functional Materials

6. Mechanical Properties

Mechanical Behaviour of Polymers(2)

PolymethylmetacrylatePMMA(Plexiglas)

E-Modul sinkt mit steigender TDuktilität steigt mit steigender T

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich23

Chair of Functional Materials

6. Mechanical Properties

Tensile Properties of Metals(2)

Zugversuch CuPK.mov

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich24

Chair of Functional Materials

6. Mechanical Properties

Slip in Single CrystalsGeometrical Relationships

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich25

Chair of Functional Materials

6. Mechanical Properties

Slip in Single CrystalsGeometrical Relationships

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Chair of Functional Materials

6. Mechanical Properties

Example

Video Gleitlinienbildung

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Chair of Functional Materials

6. Mechanical Properties

Slip Systems in the fcc-Lattice

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Chair of Functional Materials

6. Mechanical Properties

Slip Systems in the bcc-Lattice(1)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich29

Chair of Functional Materials

6. Mechanical Properties

Slip Systems in the bcc-Lattice(2)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich30

Chair of Functional Materials

6. Mechanical Properties

Slip Systems in the bcc-Lattice(3)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich31

Chair of Functional Materials

6. Mechanical Properties

Slip Systems in the hcp-Lattice(3)

{1000}-[1120] →1 plane, 3 directions

{1010}-[1120] →3 planes, 1 direction

{1011}-[1120] →6 planes, 1 direction

Only few possible

slip systems!

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich32

Chair of Functional Materials6. Mechanical Properties

Slip Systems

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich33

Chair of Functional Materials

6. Mechanical Properties

Deformation twinning

Twin

Matrix

Anwendung in TWIP-Stählen=> Hohe Verformung + Festigkeit

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich34

Chair of Functional Materials

Streckgrenze [MPa]

Ver

form

bark

eit

Hochleistungswerkstoff Stahl – eine faszinierende Vielfalt

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich35

Chair of Functional Materials

6. Mechanical Properties

Slip Twinning

Atomic movement Lattice orientation Atoms move fractional atomic spacing.

Microscopic appearance

Thin lines Wide bands or broad lines

Lattice orientation

No change in lattice orientation. The steps are only visible on the surface of the crystal and can be removed by polishing. After polishing there is no evidence of slip.

Lattice orientation changes. Surface polishing will not destroy the evidence of twinning.

Deformation: Slip vs. Twinning

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich36

Chair of Functional Materials

6. Mechanical Properties

What is the maximum shear-stress ?

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Chair of Functional Materials

6. Mechanical Properties

The shear-stress-law of Schmid

kristallographische Gleitebenedefiniert AKristallographische Gleitrichtungdefiniert Fg

Schmid-Faktor

Winkel zwischen Zug- und Gleitrichtung

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich38

Chair of Functional Materials6. Mechanical Properties

2

bGR

Dislocation Sources - The Frank-Read Source

Critical radius: R=lo/2

lo: dislocation length

0l

bGo

·b

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich39

Chair of Functional Materials

6. Mechanical Properties

Plastic Deformation of Polycrystalline Materials (Cu)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich40

Chair of Functional Materials

6. Mechanical Properties

Plastic Deformation of Polycrystalline Materials

Requirement of five independent slip systems to realize any plastic deformation in polycrystals (Compatibility of deformation)

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich41

Chair of Functional Materials

6. Mechanical Properties

Plastic deformation: Single vs. polycrystal

Why such an increase of strength?

Increase due to:• Manifold of grain

orientations in polycrystals• Grain Boundaries!!!

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich42

Chair of Functional Materials

6. Mechanical Properties

Plastic deformationCharacteristics of Dislocations

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich43

Chair of Functional Materials

6. Mechanical Properties

Plastic deformation Characteristics of Dislocations

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich44

Chair of Functional Materials

Plastic Deformation of Polycrystalline Materials• Grains with the highest Schmid-factor deform first.• yield stress (= Streckgrenze) is reached when deformation of all grains occurs• any plastic deformation of polycrystalline materials needs activation of • 5 independent slip systems (Compatibility of deformation)

The role of Grain size

6. Mechanical Properties

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich45

Chair of Functional Materials

The Relation of Hall-Petch

6. Mechanical Properties

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich46

Chair of Functional Materials

Solid solution hardeningAlloying causes hardening effects due to three types of interactions between the dislocations and the alloyed atoms:

• Parelastic interaction distortion of the lattice; change in the lattice parameter a

• Dielastic interaction different shear modulus G of alloyed atoms compared to that of the matrix atoms

• chemical interaction

atomalloyedPar c

aGbF

_

2 ln

atomalloyedDiel c

GGbF

_

2 ln

20

1

6. Mechanical Properties

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich47

Chair of Functional Materials

Work Hardening

Pro

per

ty

Degree of Deformation

6. Mechanical Properties

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Chair of Functional Materials

6. Mechanical Properties

bD

ds

The Fine-Kelly-Mechanism

particle diameter surface energy

Burgers-vector

The Orowan-Mechanism

)(dfD

bGo

shear-modulus

particle distance

Volume fraction of particles

Dispersion and precipitation hardening

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich49

Chair of Functional Materials

6. Mechanical Properties

Texture hardening

Strengthening effect due to:• bad orientation between applied stress and „slip system“ • morphological texture (Hall-Petch!!)

A

B

Loading in direction A shows an enhanced yield stress

compared to direction B

WS2012/13 | BSc – Introduction in Materials Science | Prof. Dr.-Ing. Frank Mücklich50

Chair of Functional Materials

Mechanisms to enhance strength

1. Plastic deformation - at lower temperatures (no recyrstallization)

2. grain refinement – Hall Petch

3. solid solution hardening – solubility and lattice distortion

4. dispersion hardening – input of highly dispers particles

5. precipitation hardening – creation of particles (solubility)

6. texture hardening (morphology, orientation and slip systems,

6. Mechanical Properties