Plastic deformation in metals - WIDE University deformation in metals Motoaki MORITA School of...

Plastic deformation in metals

Motoaki MORITA

School of Internet (SOI)Advanced Topics for Marine Technology and Logistics 2012, Date: 26th Jan 2013

Assistant professor, ph.D.

1

Contents1. Basic knowledge in metals2. Stress‐Strain curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary

reference：http://www.gotemba3776.jp/197_singizyutu.htm

Definition of Metalmetallic luster (shiny)

accessory

ductility and malleability

electric (heat) conductiongold, platinum

copper

wire rod and foil etc.

Iron, Aluminum

Electrical cable

Metallic bonds

＋＋＋＋

＋＋＋＋

＋＋＋＋

＋＋＋＋

negative electron ＋ positive ion

Negative (Free) electrons work like adhesive agent

Ionic bonds

Ductility and Malleability of Metal

＋ー＋ー

ー＋ー＋

＋ー＋ー

ー＋ー＋

negative ion ＋ー

Why does metal have ductility and malleability?…. Because it is characteristic of the bonds.

positive ion

Ductility and Malleability of Metal

＋＋＋＋

＋＋＋＋

＋＋＋＋

＋＋＋＋

stable arrangement of atoms after the plastic deformation

＋ー＋ー

ー＋ー＋

＋ー＋ー

ー＋ー＋

＋＋＋＋

＋＋＋＋

＋＋＋＋

＋＋＋＋

＋ー＋ー

ー＋ー＋

＋ー＋ー

ー＋ー＋

unstable arrangement of ions by rebound

Metallic bonds Ionic bonds

free electron ＋ metal ion negative ion(anion)

＋ー positive ion(cation)

Why does metal have ductility and malleability?…. Because it is characteristic of the bonds.

Engineer Stress and Engineer Strain

Stress is defined as the load per unit area of a material.

stress = load / cross sectional area

FA0

Strain is defined as extension per unit length.

strain = extension / original length

0

0

Stress

Strain

A0

F

0

before after

specimen

jig

jig

Tensile Test Machine

information available from tensile test・load・elongation Reference:

http://www.rutlandplastics.co.uk/materials_datasheets_tensile.shtml

reference：http://www.iguma.com/tech/shibori1.htm

Small load

elastic deformation

plastic deformation

Plastic Deformation

Stress‐Strain Curve of Metals

A: yieldB: necking C: fracture y A

BC

UTS

stress/strain;Elastic modulus

yield : plastic deformation occurs

strain, ε

stress, σ

/MPa

O

necking (local deformation)

fracture

Change of Shape on Deformation Process

uniform deformation

y A

BC

A: yieldB: necking C: fracture

O strain, ε

stress, σ

/MPa

Contents1. Basic Knowledge in Metals2. Stress‐Strain Curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary

Face Centered Cubic Body Centered Cubic Hexagonal Close Packed

AluminumCupper

Austenitic stainless steel

Iron（R.T.）Low Carbon Steel

TitaniumMagnesium

Influence of crystal structure on the property

Crystal Lattice

−273℃1536℃(melting point) 1392℃911℃780℃

temperature

crystal structure

magnetism

ferromagnetismparamagnetism

none

paramagnetism

b.c.c. f.c.c. b.c.c.

none

transformation: change of crystal structure or microstructure transformation temperature: the temperature to transform

Dependence of Property on Temperature

perfect crystal ・・・ no defect

Structure

Defects in metal

Reference: M. Kato: “nyumon‐teniron”, syukabo, (2007), 2. (in Japanese)

interstitial atom substitutional atom

grainboundary

vacancy

dislocation

Point defect

Plane defect line defect

0.1mm

grain boundary

grain

Grain boundary

Single crystal: one grainPolycrystal: many grains

Crystal Orientation

crystal orientation→ array direc on from a viewpoint

specimen

(a)

(b)

0.1mm

crystal orientation in a grain→ same

crystal orientations among grains・・・difference

Anisotropy of grains

formation of steps

Surface Observation after Deformation

A polished specimen like mirrorBefore deformation

After deformation

deformationdeformation

Deformation in metals

Before deformation

After deformationmechanism?

Mechanism of deformation

Ideal strength‐Deformation in a Perfect Crystal‐

force to deform a perfect crystal

max m sin 2 xb

b

a

τ: critical resolved shear stress (CRSS)(necessary shear stress to start deformation)a: lattice spacing (slip plane spacing)b: interatomic distance

When x<<b, Hooke's law is satisfied

G G

x / a m sin 2 x

b

2mxb

max Gb2a

G2

Ideal strength

x

Small shear strain and stress

G

Fe and Steel

Al and its alloys

Copper and Its alloys

concrete（compression strength）

Engineering Plastic

Fiber Reinforced Plastics (FRP)

0 1,000 2,000 3,000 4,000 5,000 6,000 10,000

(3,500MPa)

(6,400MPa)

(10,400MPa)

Ideal tensile strength

To calculate ideal of tensile strength, using 1/7.5×G (G: shear modulus)

MPa

Range of strength in various materials

Actual strength is much lower than ideal strength

Line defect（dislocation ）

欠陥の存在により小さいエネルギーで原子の並びをずらすことが可能

Slip deformation(a) (b)

(c)(d)

difficult to move flat carpet

making a hole ( hole = defect = dislocation)

easy to move the hole

The force to move the hole is smaller than one to move the carpet

Carpet Model of Dislocation

Various deformations mechanism

1.Slip deformation (almost materials)

1.Twin deformation (Mg, Ti)2.Grain boundary slide(High temperature and/or other factor(s))

3.Creep deformation (high temperature)

PierlsPo

tential

Force to Move DislocationPeierls Potential: dislocation needs to beyond the potential

Pierels Stress: stress to move the dislocation in the potential= Yield Stress

b½ b

Slip Plane and Slip Direction

→ Specific crystal plane (slip plane) and crystal direction (slip direction)

Path of dislocation

PierlsPo

tential

PierlsPo

tentialdislocation dislocation

Slip plane: close‐packed planeSlip direction: the direction of the nearest atom

Slip direction

Slip plane

（1）（2）

Which Crystal Plane is Main Slip Plane??

equilateral triangle circle

S2

S1

0.780.854

0.78 / 0.85 91[%]

S1 1.4 1.22 2 0.854

S2 2 0.39 0.78

1.4

1.2hight：

Area: 0.39 per a circle

1

11

Area of (1)

1

squareS1 111

circleS2 2 0.39

0.78

S2

S1

0.78

1 0.78 78[%]

1

11

area: 0.39 per a circle

1

Area of (2)

Slip direction

Slip plane

Slip plane is (1)

（1）（2）

92.9[%]78[%]

Slip Plane in fcc

Equivalent Slip Plane in fcc

Crystal lattice of Mg

・Number of main slip plane: 1・Slip direction of each slip plane: 2

Poor workability

Workability of hcp metal

Slip Deformation in Metals

Slip direction

Slip PlaneDislocation

When the stress is applied to the material,dislocation moves

In the case of edge dislocation

stress

stress

stress

stress

Process of slip deformation

b

b: interatomic distance

Many dislocations must operate

Large Deformation

deformation

dislocationSlip plane Slip plane

Frank‐Read Source

Increase‐Mechanism of Dislocations

TS

[%]

[Pa]

× fracture

y

work hardening

Work Hardening

Frank‐Read Source

grain boundary

interaction

direction direction

Dislocation pile‐upsnτ

1, 2, 3 …………………………… n

τn = nτ

large influence of interaction small influence of interaction

Strengthened Metals by Grain Size

Hall‐Petch relationship

y 0 Kd1/2

σy: yield stressσ0: material constantK: Hall‐Petch coefficientd: grain size

small grain size→small space

large grain size→large space

dislocation

One kind of strength mechanism in metal

Crystal lattice of Mg

・Number of main slip plane: 2・Slip direction: 1

Poor workability

Workability of hcp metal

Plastic deformation in magnesium alloys at low temperature

Slip direction

The main deformation mechanism(at room temperature)

Slip plane

→ Basal slip system

plas c workability → poor

texture control → distribute prefer slip plane for a work

Magnesium alloys

Basal slip system→ no deforma on along c‐axis

To improve the plastic workability...

Efficient use of texture for plastic workability improvement

perpendicular to the work directionBasal plane tilting to the work direction

plastic workability difficult easy

Texture control : the prefer orientation plane is installed for easy slip.

Deformation texture at high temperaturephenomena at high temperatureslip deformationtwinrecrystallizationgrain boundary migration.... etc..

Expression of crystal orientation

Inverse pole figure→ The description method of the relationship between crystal orientation and compressional axis.

The angular factors →α and β

strain ratestrain ratestrain

temperaturedeformation

mode

texture

51

Inverse pole figure (about α angle)

a1a2

a3

c

a1a2

a3

c

Compression axis

c‐axisα

compressional axis

52

Inverse pole figure (about β angle)

a1a2

a3

c

a1a2

a3

c

ββ

β

The texture under uniaxial compression at high temperature in magnesium alloys

initial texture

Mg‐6%Al‐1%Zn = 1.0, = 1.0x10‐4, T = 723K,

Peak of texture→ (α, β) = (0, 30)

L. Helis et al.; Thesis of doctor (2006)→ Stable orienta on of slip deforma on

Peak of texture→ α = 90

Slip deformation??

.

random texture 1.0

Objective

The simulation of crystal rotation by Taylor theory isadopted to understand the formation textureaccompanied by slip deformation in the magnesiumalloys.

Description of deformation by one slip system

Slip deformation

ui

x j

dij ij

n

b

The normal to slip plane Slip direction

n n1 i n2 j n3 kb b1 i b2 j b3 k

dij(k ) :

ij(k ) :

12

(mij m ji)

12

(mij m ji)mij

(k ) b1n1 b1n2 b1n3

b2n1 b2n2 b2n3

b3n1 b3n2 b3n3

strain velocity tensor

rigid body rotation

Taylor’s full constraints modelThe strain (rate) compatibility among the grains assembled in a polycrystals is necessarily if all crystals undergo the same shape change as the entire sample.

Dij 0.5 0 0

0 0.5 00 0 1

Dij dij dij(k )

k

D: strain rate of sampled: strain rate of a graind(k): strain rate accompanied by slip system k

uniaxial compression

Condition equation

many combinations of slip systems

Taylor theory

During deformation...Operating slip systems → The most convenient for deformation

Based on the principal of minimum work

i

iiW : critical resolved shear stress ：shear strain rateW : internal plastic work rate

.

Slip system

Type 1 1 1 1 Type 2 (300 K) 1 40 80

Crystal rotation by slip deformation

slip plane

plastic deformation by slip. lattice spin (Ω).lattice axis matched tensile axis according to the restraint condition.

restraints condition for uniaxial tensile stress : lattice axis direction = tensile axis direction

a lattice lattice axis tensile axis

slip direction

Ω

(a) (b) (c)

Ω

A D

CB

A D

CB

A

D

C

B

Results (Type 1 and Type 2)

(a) (b)

(c)

preferred orientations by slip deformation→ (α, β) = (30, 30), (90, 30)

Type 1= Type 2

Experimental result vs Simulation result

Preferred orientation in experiment → (α, β) = (30, 0)

Preferred orientation in experiment → (α, β) = (30, 30), (90, 30)

Not fit → the formation mechanism is not slip deformation

Mg‐6%Al‐1%Zn = 1.0, = 1.0x10‐4, T = 723KMg‐6%Al‐1%Zn = 1.0, = 1.0x10‐4, T = 573K..

Tradition band of crystal rotationIn the case of bcc metals

I.L. Dillamore et al., texture (1974)

recrystallization→ on the tradi on band of crystal rota onlattice curvature formed by orientation splitting

In the case of magnesium alloys

Combination of slip deformation and recrystallization???

Potential nuclei of recrystallization ?

Conclusion・The path of crystal rotation due to slip deformation was predicted by Taylor theory and gave an advantage on understanding of deformation texture.

・In the case of magnesium alloys in compressional test at high temperature, the texture formation mechanism may be the combination with slip deformation and recrystallization.

Summary・Main deformation in metal is slip deformation

・The mechanism of slip deformation occurs by the movement of dislocations

・On the limited crystal plane and to crystal direction, slip deformation occurs.

Plastic deformation in metals - WIDE University deformation in metals Motoaki MORITA School of...

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