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MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Instructor : Professor Soon Hyung Hong
Rm. 2405
Dept. of Materials Science & Engineering
KAIST
Tel. 042-869-3327, Fax. 042-869-3310
E-mail : [email protected]
Class Time： Monday
13:00 - 14:30
Wednesday 13:00 - 14:30
Evaluation : Midterm Exam. 50%
Final Exam.
50%
Text Books :
1. T.H. Courtney, Mechanical Behavior of Materials, McGraw-Hill,
2nd. Ed., 2000
2. G.E. Dieter, Mechanical Metallurgy, 3rd Ed., McGraw- Hill, 1988
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
References :
1. D. Hull and D. J. Bacon, Introduction to Dislocations, 4th Ed. Pergamon
Press, 2001
2. N.E. Dowling, Mechanical Behavior of Materials, Prentice-Hall, Inc., 1993
3. Hael Mughrabi Ed., Plastic Deformation and Fracture of Materials, Materials
Science and Technology, Vol. 6, VCH, 1993
4. R.W. Cahn and P. Haasen, Physical Metallurgy, Part Ⅱ, 3rd Ed. NorthHolland Physics Publishing, 1983
5. R.W. Hertzburg, Deformation and Fracture Mechanics of Engineering
Materials, 2nd Ed., John Wiley & Sons, 1983
6. Iain Le May, Principles of Mechanical Metallurgy, Elsevier Science
Publishing Co., Inc., 1981
7. J. Bressers, Creep and Fatigue in High Temperature Alloys, Applied
Science Publ. England, 1981
8. R.M. Caddell, Deformation and Fracture of Solids, Prentice-Hill Book
Co., 1980
9. R.W. Davidge, Mechanical Behavior of Ceramcis, Cambridge University
Press, 1979
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
10. Fatigue and Microstructure, ASM Materials Science Seminar, 1979
11. H. Mughrabi, Mechanisms of Metal Fatigue in Strength of Metals and
Alloys, Ed. P. Haasen, V. Gerold and G. Kostorz, Pergamon, 1615-1638,
1979
12. D.R. Axelard, Micromechanics of Solids, Elsevier Scientific Publishing Co.,
1978
13. W. Johnson and P.B. Mellor, Engineering Plasticity, Van Nostrand
Reinhold Co., London, 1975
14. J.B. Conway , R.H. Stentz and J.T. Berling, Fatigue, Tensile and Relaxation
Behavior of Stainless Steel, U.S.A.E.C., 1975
15. C.R. Wylie, Advanced Engineering Mathematics, McGraw-Hill Book Co.,
New York, 1975
16. A.C. Ugural and S.K. Fenster, Advanced Strength and Applied Elasticity,
American Elsevier, 1975
17. C.R. Barrett, W.D. Nix and A.S. Tetelman, The Principles of Engineering
Materials, Prentice-Hall, 1973
18. Progress in Flaw Growth & Fracture Toughness Testing, STP 536 ASTM,
1972
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
19. W.A. Backofen, Deformation Porcessing, Addison Wesley, 1972
20. G. Sines, Elasticity and Strength, Allyn and Bacon, Inc., Boston, 1969
21. J.J. Gilman, Micromechanics of Flow in Solids, McGraw-Hill, 1969
22. R.W.K. Honeycombe, The Plastic Deformation of Solids,
Arnold Press, 1968
23. W.J. McGregor Tegart, Elements of Mechanical Metallurgy,
MacMillan, 1966
24. N.H. Polakowski and E.J. Ripling, Strength and Structure of
Engineering Materials, Prentice-Hall Inc., 1966
25. F.A. McClintock and A.S. Argon, Mechanical Behavior of Materials,
Addison Wesley, 1966
26. A.S. Tetelman and A.J. McEvily, Fracture of Structural Materials,
John Wiley & Sons, Inc., New York, 1966
27. F.Garofalo, Fundamentals of Creep and Creep-Rupture in Metals,
McMillan Co, 1965
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
28. H.W. Hayden, W.G. Moffatt and J. Wulff, The Structure and Properties of
Materials, Volume Ⅲ. Mechanical Behavior, John Wiley and Sons, Inc.,
New York, 1960
29. A.H. Cottrell, Mechanical Properties of Matter, John Wiley, 1964
30. J. Weertmen and J. R. Weertmen, Elementary Dislocation Theory
MacMillan,1964
31. A.J. Kennedy, Processes of Creep and Fatigue in Metals, John Wiley &
Sons, Inc., 1963
32. D. McLean, Mechanical Properties of Metals, John Wiley & Sons, 1962
33. W.D. Kingary, Introduction to Ceramics, John Wiley and Sons, Inc., New
York, 1960
34. J.F. Nye, Physical Properties of Crystals, Oxford University Press, Oxford,
1957
35. A.H. Cottrell, Dislocations and Plastic Flow in Crystals, Oxford, 1953
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Contents of Lecture
Week
1
2
3
4
5
6
7
8
9
10
11
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13
14
15
16
Contents
Overview of Mechanical Behavior of Materials
Elastic Deformation of Materials
Elastic Deformation of Materials
Elementary Dislocation Theory
Plastic Deformation of Materials
Strengthening Mechanisms of Materials
Strengthening Mechanisms of Materials
Midterm Examination
Mechanical Behavior of Composite Materials
High Temperature Deformation of Materials
High Temperature Deformation of Materials
Fracture Behavior of Materials
Fracture Mechanics and Toughening Mechanism
Fracture Mechanics and Toughening Mechanism
Fatigue Behavior of Materials
Final Examination
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Chap. 1 Overview of Mechanical Behavior of Materials
1-1. Introduction
Mechanical Behavior - The responds of a solid to externally applied or
internally generated force.
Mechanical
behavior
- Deformation
- Fracture
Microstructure
- Microscopic level
- Macroscopic level
Basic assumption to analyse the mechanical behavior is that the materials
are continuous, homogeneous and isotropic.
• Continuous - do not contain voids or empty spaces.
• Homogeneous - have identical properties at all points.
• Isotropic - properties do not vary with direction or orientation.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Real Materials
• Defects (point, line, planar, volume defects)
→ macroscopically continuous
• Several phases (ferrite, pearlite, precipitate)
→ statistically homogeneous
• Grains with different orientations
→statistically isotropic
Materials in Special Cases
• Anisotropic Materials
- Single Crystals
- Fiber Reinforced Composites
- Textured Materials
• Discontinuous Materials - Composite Materials
- Porous Materials
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
1-2. Concept of Stress & Strain
External Force → (External) Stress → Strain
External Force
1) Surface Force : Pressure
(= traction)
2) Body Force : Gravitational force, magnetic force,
force due to thermal stress ……
Stress : The distribution of forces acting in a material.
Force per unit area.
units : Pa or MPa
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
If uniform distribution,
Tensile Stress
 =
P
0
A
Compressive Stress
 =
P
0
A
Shear Stress
Dept. of Materials Science and Engineering
 =
P
A
MS 514 Mechanical Behavior of Solids
If non-uniform distribution - general case
Stress at point 0 on plane mm
 = lim
A  0
ΔP
ΔA
ΔA : area surrounding the point 0
P : force acting on A
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Normal Stress and Shear Stress
Normal Stress : stress component normal to the plane
P
 =
cos 
A
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Shear Stress : stress component parallel to the plane
 =
P
sin 
A
shear stress in x-direction
P
sin  sin 
A
P
 =
sin  cos 
A
 =
shear stress in y-direction
True Stress and Engineering Stress
Deformation - causes a change of cross-sectional area .
True Stress : load divided by instantaneous cross-sectional area.
 =
P
A
scientific purpose
A : instantaneous cross-sectional area
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Engineering Stress : load divided by initial cross-sectional area
S=
P
A0
engineering purpose
A0 : initial cross-sectional area
Relation between True Stress and Engineering Stress
σ=
A
P
P
=
 0
A A0
A
A0
L + ΔL
L
=
= 0
=1+e
A
L0
L0
 σ=
P
(1 + e) = S(1 + e)
A0
Dept. of Materials Science and Engineering
( e : engineering strain)
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Strain : The ratio of the change in length to the original length (dimensionless). or
The change in length per unit length.
If uniform distribution
Tensile Deformation
Tensile Strain

ΔL
L0
L
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Engineering Strain : The change in length per initial unit length.
ΔL L - L0
e=
=
L0
L0
engineering purpose
True strain : The change in length per instantaneous unit length.
L
ε=
dL
L
=
ln
L L
L0
0
Shear Deformation
γ=
scientific purpose
Shear Strain
a
= tan θ  θ
h
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Relation between True Strain and Engineering Strain
ΔL L - L0
L
e=
=
=
-1
L0
L0
L0
L
L0 + ΔL
=
=1+e
L0
L0
L
ε = ln
= ln(1 + e)
L0
If non-uniform distribution
x
x
increases by the amount of
Tensile Strain at a point
ε = lim (
Δx 0
Δu
du
)=
Δx
dx
Dept. of Materials Science and Engineering
u
u ,
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Shear Strain at a point
τ
ΔU
y
τ
γ = lim (
y0
Δu
du
)=
Δy
dy
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
1-3. Elastic Deformation
External force on solids → Change in shape & microstructure
"Deformation"
1) Elastic Deformation :
When the load is released, the solid return to original dimension.
Deformation which is time-independent or time-dependent and recoverable.
2) Plastic Deformation :
When the load is released, the solid does not return to original dimension.
Deformation which is time-independent or time-dependent and permanent.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Hooke's Law - Elastic Deformation
The extension of a solid is linearly related to the force( F ) &
initial length( L0 ), and is inversely related to the cross-sectional area( A ).
Tensile Deformation
δL
F

L0
A
δL 
F L0
A
ε  σ
 = E 
σ
: tensile stress

: tensile strain
E
: elastic modulus or Young's modulus
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Shear Deformation
δL
F

L
A
  G 
τ
: shear stress

: shear strain
G : shear modulus
Figure 1.2
Dept. of Materials Science and Engineering
  
MS 514 Mechanical Behavior of Solids
Linear Elasticity and Nonlinear Elasticity
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Linear Elasticity :
The strain is a single-valued function of the stress.
The loading and unloading segments of the σ-ε curve are coincident.
Non-linear Elasticity
1) Viscoelasticity : Nonlinear time-dependent elasticity
The σ-ε relationship depends on the sense of loading. Also, the level of
stress is dependent on the strain rate.
Modulus = f(strain rate)
2) Rubber Elasticity : Nonlinear time-independent elasticity
The extensive elastic strain up to the order of a thousand percent over a
limited temperature range in elastomers.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
1-4. Plastic Deformation
1. Stress-Strain Curve of Ductile Materials - Tension Test
1) Proportional Limit A' : The stress at which the stress-strain curve
deviate from linearity.
Slope = Elastic Modulus
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
2) Elastic Limit A : The greatest stress that the material can withstand
without experimenting a permanent strain when
the load is removed.
3) Yield Strength B : The stress which produce a small amount of permanent
deformation, generally equal to a strain of 0.002.
4) Ultimate Tensile Strength : The max. load divided by the original area of
the specimen.
 UTS 
PMAX
A0
5) Fracture Stress : The load at fracture divided by the final cross-sectional
area.
F 
PF
AF
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
6) Ductility : Reduction of Area ( RA )
RA =
A0  A F
 100
A0
7) Toughness : The measure of the work per unit volume required to cause
fracture.
Toughness =

lf
l0
P dl
=
Al

f
0
 d
→Area under the true stress-strain curve.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Stress-Strain Curve of Brittle Materials
Completely brittle materials
→ ex. most ceramics (Fig 1-4 a)
Brittle materials with slight ductility
→ ex. cast iron, intermetallic compound (Fig 1-4 b)
Brittleness : not an absolute property!
ex. W : brittle at R.T., ductile at high temp.
TiAl : brittle at R.T., ductile at high temp.
Metals : brittle in tension, ductile under
hydrostatic compression
∴Brittleness = f (temp., stress state, strain rate, microstructure,
atmosphere)
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Necking Criteria
The force reaches a maximum at the start of necking.
F= A
dF = 0 =  dA + A d
d
dA
dl
= 
=
= d

A
l
σ=
dσ
dε
Formulation of True Stress-True Strain Behavior
Holomon's equation
σ = K  εn
n : strain hardening coefficient (0.02-0.5)
A constant indicating the strain hardening behavior of material.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
K : strength coefficient
True stress at a true strain of unity.
For the definition of
n=
d(log σ) d(ln σ) ε dσ
=
=
d(log ε)
d(ln ε) σ dε
when necking occurs :
σ=
dσ
dε
K  ε n = K  n ε n-1
since
 = u
(max. uniform strain)
up to the strain just before necking
 εu = n
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Yield Point Phenomena
- Plastic flow commenses at a stress equal to upper yield point and
then continues at a lower yield point.
- Plastic deformation is heterogeneously distributed along the gage
length during the initial stage of plastic deformation( Lüder's strain).
- Y.P. phenomena are observed in steels, polymers and ceramics.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Strain Rate Sensitivity
Flow Stress = f (strain rate)
  K'  m
m : strain rate sensitivity ( 0-1 )
A measure of the strain rate hardening behavior.
m = 0, not strain rate sensitive
m = 1, stress increases linearly with strain rate.
→ viscous solids
K' : A constant signifies a flow stress at a true strain rate of unity.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Dept. of Materials Science and Engineering
Prof. S.H. Hong, KAIST
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
1-5. Fracture
Fracture process is accompanied by a crack nucleation and crack
propagation.
1. Tensile Fracture : Ductile Fracture or Brittle Fracture
Ductile Fracture :
- Ductile fracture is characterized by a finite % R.A. and formation of
a neck prior to fracture.
- The heterogeneous plastic deformation at internal boundaries
(e.g. grain boundaries or interface boundaries between precipitates
or inclusions and the matrix ) nucleates cracks or voids and then
to promote their subsequent growth.
- In a tensile test, this produces an internally penny-shaped crack,
with final tensile separation happening by shearing of the "tube"
surrounding the crack. → "Cup and Cone" fracture
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
Brittle Fracture :
- Brittle fracture is characterized by zero or limited (few %) R.A. and no
necking prior to fracture.
- Pre-existing surface or internal cracks serve as the crack nuclei.
- Stress is concentrated at the tip of such flaws and when the resulting
stress magnification attains a critical value, crack propagation results.
- In some "less-brittle" solids, microscopic plastic deformation proceeds
crack nucleation, and may also accompany crack propagation.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
2. Creep Fracture
- Void nucleation takes place at region of microscopic heterogeneous
deformation. The nucleated voids grow by the creep deformation.
- Creep fracture takes place when the void volume fraction attains some
critical value or when the intervoid spacing becomes small enough that
voids link up by permanent deformation rather than by continuing to
grow individually.
Dept. of Materials Science and Engineering
MS 514 Mechanical Behavior of Solids
Prof. S.H. Hong, KAIST
3. Fatigue Fracture
- Plastic deformation takes place in a microscopic scale, rather than
macroscopic scale, during fatigue.
- Local stress concentration at microstructural inhomogeneities promote
the nucleation of cracks.
- The crack continues to grow slowly in a direction normal to the stress
axis and the crack growth rate is dependent on the fatigue conditions.
After a crack has grown to some critical length, it advances rapidly and
fatigue fracture ensues.
Dept. of Materials Science and Engineering