Introduction to Physical Metallurgy and Engineering Materials

Introduction to Physical Metallurgy and Engineering Materials
MODULE‐I (16 Lectures) Classification of Engineering Materials, Engineering properties of materials. Characteristic property of metals, bonding in solids, primary bonds like ionic, covalent and metallic bond, crystal systems, common crystal structure of metals, representations of planes and directions in crystals, atomic packing in crystals, calculation of packing density, voids in common crystal structures and imperfections crystals. Chapter-1
Introduction to Engineering Materials
Materials play an important role for our existence, for our day to day needs ,and even for our
survival. In the stone age the naturally accessible materials were stone, wood, bone, fur etc
Gold was the 1st metal used by the mankind followed by copper. In the bronze age Copper
and its alloy like bronze was used and in the iron age they discovered Iron (sponge iron &
later pig iron).
Engineering Materials
Choice of Material
New Materials
New Products
Number of Materials
40 – 80,000!
General Definition of Material
According to Webster’s dictionary, materials are defined as ‘substances of which something is composed or made’ Engineering Material: Part of inanimate matter, which is useful to engineer in the practice of
his profession (used to produce products according to the needs and demand of society)
Material Science: Primarily concerned with the search for basic knowledge about internal
structure, properties and processing of materials and their complex interactions/relationships
Material Engineering: Mainly concerned with the use of fundamental and applied knowledge
of materials, so that they may be converted into products, as needed or desired by the society
(bridges materials knowledge from basic sciences to engineering disciplines)
Note: Material science is the basic knowledge end of materials knowledge spectrum, where as, material engineering is applied knowledge end and there is no demarcation line between the two subjects of interest Evolution of Engineering Materials
Why Material Science & Engineering is important to technologists? Examples:
Mechanical engineers search for high temp material so that gas turbines, jet engines
etc can operate more efficiently and wear resistance materials to manufacture bearing
Electrical engineers search for materials by which electrical devices or machines can
be operated at a faster rate with minimum power losses
Aerospace & automobile engineers search for materials having high strength-toweight ratio
Electronic engineers search for material that are useful in the fabrication &
miniaturization of electronic devices
Chemical engineers search for highly corrosion-resistant materials
Note: All these demands may be fulfilled when the internal structure and engineering
properties are known to an engineer or technologist
Classification It is the systematic arrangement or division of materials into groups on the basis of some
common characteristic
1. According to General Properties
2. According to Nature of Materials
3. According to Applications 1. According to General Properties
(a). Metals (e.g. iron, aluminium, copper, zinc, lead, etc)
Iron as the base metal, and range from plain carbon (> 98 % Fe) to (i). Ferrous: high alloy
steel (< 50 % alloying elements), e.g. cast iron, wrought iron, steel, alloys like high-speed
steel, spring steel, etc
(ii). Non-Ferrous: Rest of the all other metals and their alloys, e.g. copper, aluminium, zinc
lead, alloys like brass, bronze, duralumin, etc
(b). Non-Metals (e.g. leather, rubber, asbestos, plastics, etc)
2. According to Nature of Materials
(a). Metals: e.g. Iron & Steel, Alloys &Superalloys, Intermetallic Compounds, etc
(b). Ceramics: e.g. Structural Ceramics (high-temperature load bearing), Refractories
(corrosion-resistant, insulating), Whitewares (porcelains), Glass, Electrical Ceramics
(capacitors, insulators, transducers), Chemically Bonded Ceramics (cement & concrete)
(c).Polymers: e.g. Plastics, Liquid Crystals, Adhesives
(d). Electronic Materials: e.g. Silicon, Germanium, Photonic materials (solid-state lasers,
(e). Composites: e.g. Particulate composites (small particles embedded in a different
material), Laminate composites (golf club shafts, tennis rackets), Fiber reinforced composites
(f). Biomaterials: e.g. Man-made proteins (artificial bacterium), Biosensors, etc
(g). Advanced / Smart Materials: e.g. materials in computers (VCRs, CD Players, etc),
fibreoptic systems, spacecrafts, aircrafts, rockets, shape-memory alloys, piezoelectric
ceramics, magnetostrictive materials, optical fibres, microelectromechanical (MEMs)
devices, electrorheological / magnetorheological fluids, Nanomaterials, etc
3. According to Applications
(a). Electrical Materials: e.g. conductors, insulators, dielectrics, etc
(b). Electronic Materials: e.g. conductors, semi-conductors, etc
(c). Magnetic Materials: e.g. ferromagnetic, paramagnetic & diamagnetic materials, etc
(d). Optical Materials: e.g. glass, quartz, etc
(e). Bio Materials: e.g. man-made proteins, artificial bacterium
Cast Iron
Carbon Steels
Alloy Steels
Shape-Memory Alloys
Piezoelectric Ceramics
Magnetostrictive Materials
Optical Fibres
Electrorheological Fluids
/ Smart
Difference between Metals & Non-Metals
Generally solids at room temp.
Gaseous & solid at ordinary
Metallic luster
No metallic luster (except
iodine & graphite)
Good conductors
Not malleable
Not ductile
Generally hard
Hardness varies
Form anions
Form anioins
Excitation of
electron by
Bad conductors
1. Material Properties •
Physical: e.g. appearance, shape, weight, boiling point, melting point, freezing point,
density, glass transition temperature, permeability
Mechanical: e.g. strength (tensile, compressive, shear, torsion, bending), elasticity,
plasticity, ductility, malleability, rigidity, toughness, hardness, brittleness, impact,
fatigue, creep, strain hardening, Bauschinger effect, strain rate effect, vibration
resistance, wear
Thermal: e.g. thermal conductivity, expansion coefficient, resistivity, thermal shock
resistance, thermal diffusivity
Types of Force / Stress System
Electrical: e.g. conductivity, resistivity, dielectric strength, thermoelectricity,
superconductivity, electric hysteresis
Magnetic: e.g. ferromagnetism, paramagnetism, diamagnetism, magnetic
permeability, coercive force, curie temperature, magnetic hysteresis
Chemical: e.g. reactivity, corrosion resistance, polymerization, composition, acidity,
Optical: e.g. reflectivity, refractivity, absorptivity, transparency, opaqueness, color,
Metallurgical: e.g. grain size, heat treatment done / required, anisotropy, hardenability
Imperfections in Crystals
Introduction to Crystal Geometry
¾ Materials may be classified as Crystalline or Non-Crystalline structures
¾ Crystalline solid can be either Single Crystal Solid (crystal lattice of entire sample is
continuous and unbroken to edges of sample with no grain boundary) or Poly Crystal
Solid (aggregate of many crystals separated by well-defined boundaries)
¾ Cluster of crystals with identical structure (same crystallographic planes & directions)
are known as Grains separated by Grain Boundaries
¾ X-ray diffraction analysis shows that atoms in metal crystal are arranged in a regular,
repeated 3-D Pattern known as CrystallineStructure
Ceramic: Inorganic non-metallic crystalline (regular internal Structure) materials
Glass: Inorganic non-metallic non-crystalline / amorphous (completely disordered
form) material
¾ Arrangement of atoms can be most simply portrayed by Crystal Lattice, in which
atoms are visualized as, Hard Balls located at particular locations
¾ Space Lattice / Lattice: Periodic arrangement of points in space with respect to three
dimensional network of lines
¾ Each atom in lattice when replaced by a point is called Lattice Point, which are the
intersections of above network of lines
¾ Arrangement of such points in 3-D space is called Lattice Array and 3-D space is
called Lattice Space
¾ Tiny block formed by arrangement of small group of atoms is called Unit Cell. It is
chosen to represent the symmetry of crystal structure, and may be defined as:
Finite representation of infinite lattice
Small repeat entity
Basic structural unit
Building block of crystal structure
Can generate entire crystal by translation
Lattice Parameters
¾ Six lattice parameters a, b, c, α, β, γ
¾ Typically in the order of few Angstroms (few tenths of nanometer)
¾ Example: Cubic structure has following lattice parameters:
a = b = c and α = β = γ = 90o
Types of Crystal
Cubic, Monoclinic, Triclinic, Tetragonal, Orthorhombic, Rhombohedral and Hexagonal
Crystal Type
Lattice Parameters
a = b = c, α = β = γ = 90
a = b ≠ c, α = γ = 90 = β
a ≠ b ≠ c, α = γ = β = 90
a = b = c, α = β = γ ≠ 90
a = b ≠ c, α = β = 90 , γ = 120
a ≠ b ≠ c, α = γ = 90 ≠ β
a ≠ b ≠ c, α ≠ γ ≠ β ≠ 90
Fluorite, Garnet, Pyrite
Principal Metal Crystal Structures
¾ Simple Cubic Lattice Structure
¾ Body Centered Cubic (BCC) Structure
¾ Face Centered Cubic (FCC) Structure
Simple Cubic Lattice
¾ Most elementary crystal structure with three mutually perpendicular axes arbitrarily
placed through one of the corners of a cell
¾ Each corners occupied with one atom
¾ Example: alpha polonium
SC Structure (i). Aggregate of atoms (ii). Hard Sphere Unit Cell Body Centered Cubic (BCC) Structure
¾ BCC cell has an atom at each corner and another atom at body center of cube
¾ Each atom at corner is surrounded by eight adjacent atoms
¾ Example: alpha iron, chromium, molybdenum & tungsten
BCC Structure i). Aggregate of atoms
(ii). Hard Sphere Unit Cell
Face Centered Cubic (FCC) Structure
¾ Atoms at each corner of cube, and in addition there is an atom at the center of each
cube’s face
¾ Example: aluminium, copper, gold, lead, silver and nickel
FCC Structure
(i). Aggregate of atoms (ii). Hard Sphere Unit Cell Hexagonal Close-packed (HCP) Structure
¾ Unit cell has an atom at each of twelve corners of hexagonal prism, with one atom at
centre of each of two hexagonal faces and three atoms in body of cell
¾ Example: zinc, lithium, magnesium, beryllium
Comparison Sl.
APF (Atomic Packing
(Ratio of vol . of atoms in
unit cell to unit cell vol.)
Co-ordination Number
(No. of nearest
neighbor atoms)
Close-Packed Structures
¾ How can metal atoms be stacked to fill empty spaces in the lattice?
¾ Can these 2-D layers be stacked to make 3-D structures
Example: Close-Packed FCC Structure
ABC Stacking Sequence
Example: Close-Packed HCP Structure
AB Stacking Sequence ABC Stacking Sequence Crystallographic Planes & Directions
¾ Crystallographic Planes &Directions are specified with respect to the reference axes
in terms of ‘Miller Indices’, which is the system of notation of planes within a crystal
of space lattice
¾ Example: SC structure is chosen for understanding
¾ Crystallographic Plane is specified in terms of length of its intercepts on three mutually perpendicular axes. To simplify it, reciprocals of these intercepts reduced to lowest common denominator (LCM) are used as miller indices, e.g. plane ABCD in figure is parallel to x and z axes and intersects y-axis
at one interatomic distance ‘a0’, therefore miller indices of the plane are 1/∞, 1/ a0, 1/∞ or
(hkl) = (010)
¾ Plane EBCF is designated as ( 00) plane, where bar indicates that plane intersects the
axis in negative direction
¾ Crystallographic Directions are indicated by integers in brackets like [uvw], where
reciprocals are never used, e.g. direction ‘FD’ is obtained by moving out from origin,
a distance ‘a0’ along positive x-axis and moving same distance along positive y-axis
also, therefore, the crystallographic direction will be given as [110]
¾ Example: Ionic crystals like NaCl, LiF (not for metals)
Note: For simple cubic lattice only, direction is always perpendicular the plane having same
Index system for crystal directions and planes
Crystal directions:
The direction is specified by the three integers [n1n2n3]. If the numbers n1n2n3 have a common
factor, this factor is
removed. For example, [111] is used rather than [222], or [100], rather than [400]. When we
about directions, we mean a whole set of parallel lines, which are equivalent due to
symmetry. Opposite orientation is denoted by the negative sign over a number. For example:
Crystal planes: The orientation of a plane in a lattice is specified by Miller indices. They are
defined as follows. We find intercept of the plane with the axes along the primitive
vectors a1, a2 and a3. Let’s these intercepts be x, y, and z, so that x is fractional multiple of a1,
y is a
fractional multiple of a2 and z is a fractional multiple of a3. Therefore we can measure x, y,
and z in
units a1, a2 and a3 respectively. We have then a triplet of integers (x y z). Then we invert it
(1/x 1/y
1/z) and reduce this set to a similar one having the smallest integers by multiplying by a
factor. This set is called Miller indices of the plane (hkl). For example, if the plane intercepts
x, y,
and z in points 1, 3, and 1, the index of this plane will be (313).
The orientation of a crystal plane is determined by three points in the plane, provided they are
collinear. If each point lay on a different crystal axis, the plane could be specified by giving
the coordinates
of the points in terms of the lattice constants a, b, c. A notation conventionally used to
describe lattice points (sites), directions and planes is known as Miller Indices.
A crystal lattice may be considered as an assembly of equidistant parallel planes passing
through the
lattice points and are called lattice planes. In order to specify the orientation one employs the
called Miller indices.
Crystal direction is the direction (line) of axes or line from the origin and denoted as [111],
[010] etc.
How to find Miller Indices:
To determine the indices for the plane p in Figure 2,
-first we have to find the intercepts with the axes along the basis vector
be x, y, z. We form the fractional triplet Let these intercepts
-Take reciprocal to this set.
-Then reduce this set to a similar one having the smallest integers multiplying by common
To determine the Miller indices:
(i) Find the intercepts on the axes along the basis vector
cba ,, in terms of the lattice constants a,b
and c. The axes may be those of a primitive or nonprimitive cell.
Let these intercepts be x, y, z. We form the fractional triplet
(ii) Take the reciprocals of these numbers.
(iii) Reduce the numbers to three smallest integers by multiplying the numbers with the same
integral multipliers.
This last set is enclosed in parentheses (h k l), is called the index of the plane or Miller
The Miller indices specify not just one plane but an infinite set of equivalent planes. Note that
cubic crystals the direction [hkl] is perpendicular to a plane (hkl) having the same indices, but
this is
not generally true for other crystal systems. Examples of the planes in a cubic
Allotropy / Polymorphism
¾ Two or more distinct crystal structures for the same material at different temperature
& pressure
¾ Examples: iron (α-iron &γ-iron), carbon (graphite & diamond), tin (α-tin &β-tin)
Imperfection / Defects In Crystals In actual crystals, imperfection or defects are always present, which are important to
understand, as they influence the properties of material
Classifications of Defects
(i). Point Defects (Zero Dimensional Defects)
(a). Vacancy
(b). Schottky Imperfections
(c). Interstitialcy
(d). Frenkel Defect
(e). Compositional Defect
Substitutional Defect
Interstitial Impurity
(f). Electronic Defect
(ii). Line Defects / Dislocations (One Dimensional Defects)
(a). Edge Dislocations
(b). Screw Dislocations
(iii). Surface / Plane Defects (Two Dimensional Defects)
(a). External Defects
(b). Internal Defects
Grain Boundary Defect
Tilt Boundary Defect
Twin Boundary Defect
Stacking Fault
(iv). Volume Defects (Three Dimensional Defects
(I). Point Defects (Zero Dimensional Defects)
¾ Imperfect point like regions in crystal (size is one or two atomic diameter)
¾ Completely local in effect, i.e. vacant lattice site
¾ Always present in crystals
¾ Created by thermal fluctuations, quenching (high rate of cooling), severe deformation
of crystal lattice (hammering or rolling) or external bombardment by atoms / high
energy particles
(a). Vacancy ¾ Simplest type of point defect involving a missing atom within crystal lattice of metal, which results due to imperfect packing during original crystallization process or by thermal vibrations of atoms at very high temperature (b). Schottky Imperfections
Involve vacancies in pair of ions having opposite charges and are found in compounds, which
maintain charge balance, e.g. alkali halides
(C). Interstitialcy
Addition of an extra atom in the crystal lattice, when atomic packing density / factor
is low and the foreign atom may be an impurity or alloying atom (generally very less in
number as additional energy is required to force atom / ion to occupy new position)
(d). Frenkel Defect Ion dislodged from its crystal lattice into an interstitial site (generally very less in number as
additional energy is required to force the atom / ion to occupy the new position)
(e). Compositional Defect
Arises due to presence of impurity atom in crystal lattice of metal during original
crystallization process (responsible for functioning of semi-conductor devices)
¾ Substitutional Defect:Original parent atom from its lattice is replaced
¾ Interstitial Impurity:Small impurity occupies interstitial spaces in lattice
(f). Electronic Defect
Errors in charge distribution in solids, e.g. diodes and transistors devices, where
charges diffuse in opposite regions leading to change of their concentration in that region
Substitutional Defect
Interstitial Defect
(ii). Line Defects (One Dimensional Defects) ¾ Linear disturbance of atomic arrangement, which can move very easily on slip plane
through crystal
¾ Occurs during recrystallization process or during slip
¾ Created along a line, which is also boundary between slipped and unslipped regions of
¾ Defect is known as ‘dislocation’ and boundary is known as ‘Dislocation Line’
¾ Region near dislocation, where distortion is extremely large is called ‘Core of
Dislocation’ (very high local strain)
(a). Edge Dislocation
¾ Any extra plane of atoms within a crystal structure is edge dislocation
¾ Accompanied by zones of compression and tension and there is a net increase in
energy along dislocation
¾ Displacement distance for atoms around dislocation is called ‘Burger Vector’, which
is at right angle to edge dislocation
¾ Berger vector is determined by drawing a rectangle in region by connecting an equal
number of atoms on opposite sides (circuit fails to complete), i.e. PP’ as shown in
Edge Dislocation
(b). Screw Dislocation ¾ Originate from partial slipping of a section of crystal plane
¾ Shear stresses are associated with adjacent atoms and extra energy is involved along
the dislocation
¾ Successive atom planes are transformed into the Surface of Helix of Screw (plane is
distorted), which accounts for its name as screw dislocation
¾ Displacement vector is parallel to the line defect
Comparison EdgeDislocation
Arise due to introduction or elimination of an extra Arise due to partial slipping of section of crysta
where planes of atoms are transformed into sur
row of atoms
helix of screw
Tensile, compressive or shear stress field may be Only shear stress field is present
Lattice disturbance extends along an edge inside Lattice disturbance extends into two separate
at right angles to each other
Burger’s vector is always perpendicular to dislocation Burger’s vector is parallel to dislocation line
Dislocations can climb and glide
Dislocation can only glide
Force required is less as compared to that for screw Force required is more as compared to that o
Edge Dislocation
Screw Dislocation
Geometry of Dislocation
Edge Dislocation
Burger’s Vector
Edge Dislocation
Screw Dislocation
Formation of Step on Crystal Surface
(iii). Surface / Plane Defects (Two Dimensional Defects) ¾ Two-dimensional regions in crystal and arise from change in stacking of atomic
planes on or across boundary
(a). External Defects
¾ Defects or imperfections represented by a boundary
¾ External surface of material itself is an imperfection because atomic bonds do not
extend beyond it
¾ Surface atoms do not have neighboring atoms on one side (as compared to atoms
inside the material) and thus, have high energy (in the order of 1 J/m2)
(b). Internal Defects
Grain Boundary Defect
¾ Imperfections, which separate crystals or grains of different orientation in
polycrystalline aggregation during nucleation or crystallization
¾ Individual crystals with different orientation are called as ‘Grains’, and boundary
separating grains are called as ‘Interface / Interface Boundary’
Example: copper metal
¾ Atoms within a grain are arranged with one orientation and pattern, which does not
aligns with orientation of atoms in neighboring grains
¾ Misalignment between adjacent grains may be of various degrees (small or high angle
grain boundaries)
¾ Always a transition zones between two neighboring grains
¾ Leads to less efficient packing of atoms at boundary and thus, atoms at boundary have
higher energy as compared to those at inside of grain boundaries
Grain Boundary Defect
Tilt Boundary Defect ¾ Series of aligned dislocations, which tend to anchor (fasten) dislocation movements
normally contributing to plastic deformation
¾ Associated with little energy
¾ Orientation difference between two neighboring grains is less than 100, thus, it may be
called as small / low angle grain boundary
Tilt Boundary Defect
Twin Boundary Defect ¾ Special type of grain boundary across which, there is specific mirror lattice of
symmetry, i.e. atoms on one side of boundary are located in mirror-image positions of
atoms on other side
¾ Region of material between these boundaries is called as ‘Twin’, which results due to
Stacking Fault ¾ Arise due to stacking of one atomic plane out of sequence on another, while lattice on
either side of fault is perfect, i.e. one or more than one atomic plane may be missing
from usual conventional style of stacking
(iv). Volume Defects (Three Dimensional Defects)
¾ Bulk defects, which includes pores, cracks, foreign inclusions or other phases
Slip by Dislocation Motion ¾ Slip is plastic deformation process produced by dislocation motion (Note:
Dislocations Can Move)
¾ Dislocation motion is analogous to the mode of locomotion employed by caterpillar
¾ Caterpillar forms a hump near its posterior (later) end by pulling in its pair of legs unit
leg distance and then this hump is propelled forward by repeating lifting and shifting
of leg pairs
¾ When a hump moves forward, entire caterpillar moves forward by leg separation
distance corresponding to extra half plane of atoms in its dislocation model of plastic
Analogy between Caterpillar & Dislocation
Concept of Elastic & Plastic Deformation
¾ Change in dimensions of material under action of applied forces
¾ Caused by mechanical action or by various physical and physio-chemical processes
¾ Deformed components are superior to cast components in performance
¾ Types: Elastic & Plastic deformations
Classification of Deformation Viscoelasticity
Elastic Deformation ¾ Disappears, when load is removed & takes place before plastic deformation
¾ Strain is proportional to stress (Hooke’sLaw)
¾ Ratio of stress to strain is Young’sModulusofElasticity (E), which is a material
characteristic (magnitude depends upon force of attraction between atoms of metal)
¾ Shear stress produces shear strains and ratio of shear stress to shear strain is Shear
Modulus of Rigidity (G)
¾ Ratio of volumetric stress to volumetric stain is Bulk Modulus of Elasticity (K)
¾ Perfect elastic material is one which regains back its original shape and size
completely, after deforming force is removed
¾ During elastic deformation, material stores energy (strain or elastic energy), which is
recovered, when load is removed
¾ Elastic strain energy is area under stress-strain curve (up to elastic limit)
¾ Materials subjected to tension shrink laterally & those subjected to compression,
¾ Ratio of lateral and axial strains is called the Poisson's ratio (ν), which is a
dimensionless quantity (sign shows that lateral strain is in opposite sense to
longitudinal strain)
¾ Theoretical value is 0.25 & maximum value is 0.50 (typical value lies in between 0.24
to 0.30
Plastic Deformation ¾ Permanent deformation, which persists even when deforming load is removed
(function of stress, temperature & rate of straining)
¾ Caused by loads exceeding elastic limit & occurs after elastic deformation
¾ Non-linear relation between stress and strain (nature varies with material &
deformation condition)
¾ Exhibit yield point phenomenon (yield stress)
¾ Continued plastic deformation leads to fracture (instantaneous fracture for brittle
material & necking followed by fracture for ductile material)
Yield Point Phenomenon
¾ Yielding starts at 1st higher point known as UpperYieldPointand 2nd lower point is
known as LowerYieldPoint
¾ Stress required to deform metal after yield point is always higher due to strain
hardening, which causes curve to gradually rise upwards uptill ultimate tensile point
(corresponding stress known as Ultimate Tensile Strength). After this specimen fails
by fracture
Stress-Strain curve for Mild Steel
True & Engineering Stress-Strain
Strain Hardening
¾ Increase in yield stress of material when loaded subsequently in same direction again
and again below recrystallization temperature
¾ When material is loaded in any direction (say tensile direction), it experiences linear
elastic deformation till elastic limit. If load is removed, material comes back to its
original shape and size and curve will retrace back loading path
¾ If material is further loaded (beyond yield stress ‘σ0’), slight plastic deformation
occurs leading to small permanent deformation. Now, if load is removed, material
will retail this small plastic / permanent deformation and curve will not retrace
original path, but will follow path parallel to original loading path
Strain Hardening
¾ If same material is loaded in same (tensile) direction again, it will start yielding at
new yield stress ‘σ0/’, which will be higher than initial yield stress of material ‘σ0’.
¾ This is because material becomes harder during plastic deformation by storing strain
energy (some % of total deformation energy)
¾ Reduces ductility and plasticity of material
¾ At micro level, dislocation piles up during plastic deformation at slip planes, which
interact with each other and create barriers to further motion / movement of
dislocations through crystal lattice
BauschingerEffect / Elastic Hysteresis
¾ Decrease in yield stress of material when loaded initially in one direction (tensile) and
then subsequently in opposite direction (compressive) below recrystallization
¾ When a material is loaded in any direction (say tensile direction), it experiences linear
elastic deformation till elastic limit. If it is further loaded (beyond yield stress ‘σ0’),
slight plastic deformation will occur leading to small permanent deformation
¾ Now, even if load is removed, material will retail this small plastic / permanent
deformation and curve will not retrace original path, but will follow path parallel to
original loading path
Bauschinger Effect
¾ Further, loaded in opposite direction (compressive), it will start yielding at new yield
stress ‘σ0/’, which will be very less than initial yield stress of material ‘σ0’.
¾ This is because residual tensile stress stored in material during tensile loading need to
be removed / compensated before elastic deformation in reversal (compressive)
direction starts
¾ At micro level, dislocations piles up during tensile loading along at slip planes, which
can be easily moved in opposite direction (compressive loading) by residual stresses
Anelasticity: Time‐dependent, recoverable low strain with linear behavior and relatively low damping Viscoelasticity: Time‐dependent, recoverable higher strains with nonlinear behavior and higher damping Viscoplasticity: Time‐dependent, non‐recoverable strain with nonlinear behavior and higher damping 
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