Plastic deformation in metals - WIDE University deformation in metals Motoaki MORITA School of...
Transcript of 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.
Contents1. Basic knowledge in metals2. Stress‐Strain curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary
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
Contents1. Basic knowledge in metals2. Stress‐Strain curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary
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)
Contents1. Basic knowledge in metals2. Stress‐Strain curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary
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
Contents1. Basic knowledge in metals2. Stress‐Strain curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary
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
Contents1. Basic knowledge in metals2. Stress‐Strain curve3. Microstructure4. Ideal Strength5. Slip Deformation in Metals6. Nature of Dislocation7. Prediction of Slip Deformation8. Summary
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.