a basic understanding of materials
TRANSCRIPT
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Materials Review
Class Notes
AISI/SAE steel numbers are indicated below.
Example AISI/SAE No. 1020
the first digit indicates that this is plain carbon steel.
the second digit indicates there are no alloying elements
the last two digits indicates that the steel contains approximately 0.20 percent carbon
Example AISI/SAE No. 4340
the first two digits indicates a Nickel-Chromium-Molybdenum alloy steel
the last two digits indicates carbon content roughly 0.4 percent
10XX
Carbon steels
Plain carbon, Mn 1.00% max
11XX Resulfurized free machining
12XX Resulfurized / rephosphorized free machining
15XX Plain carbon, Mn 1.00-1.65%
13XX Manganese steel Mn 1.75%
23XX
Nickel steels
Ni 3.50%
25XX Ni 5.00%
31XX
Nickel-chromium steels
Ni 1.25%, Cr 0.65-0.80%
32XX Ni 1.75%, Cr 1.07%
33XX Ni 3.50%, Cr 1.50-1.57%
34XX Ni 3.00%, Cr 0.77%
40XX
Molybdenum steels
Mo 0.20-0.25%
44XX Mo 0.40-0.52%
41XX Chromium-molybdenum steels Cr 0.50-0.95%, Mo 0.12-0.30%
43XX Nickel-chromium-molybdenum steels Ni 1.82%, Cr 0.50-0.80%, Mo 0.25%
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47XX Ni 1.05%, Cr 0.45%, Mo 0.20-0.35%
46XX
Nickel-molybdenum steels
Ni 0.85-1.82%, Mo 0.20-0.25%
48XX Ni 3.50%, Mo 0.25%
50XX
Chromium steels
Cr 0.27-0.65%
51XX Cr 0.80-1.05%
50XXX Cr 0.50%, C 1.00% min
51XXX Cr 1.02%, C 1.00% min
52XXX Cr 1.45%, C 1.00% min
61XX Chromium-vanadium steels Cr 0.60-0.95%, V 0.10-0.15%
72XX Tungsten-chromium steels W 1.75%, Cr 0.75%
81XX
Nickel-chromium-molybdenum steels
Ni .30%, Cr 0.40%, Mo 0.12%
86XX Ni .55%, Cr 0.50%, Mo 0.20%
87XX Ni .55%, Cr 0.50%, Mo 0.25%
88XX Ni .55%, Cr 0.50%, Mo 0.35%
92XX Silicon-manganese steels Si 1.40-2.00%, Mn 0.65-0.85%, Cr 0-0.65%
93XX
Nickel-chromium-molybdenum steels
Ni 3.25%, Cr 1.20%, Mo 0.12%
94XX Ni 0.45%, Cr 0.40%, Mo 0.12%
97XX Ni 0.55%, Cr 0.20%, Mo 0.20%
98XX Ni 1.00%, Cr 0.80%, Mo 0.25%
Instructions: The UNS number (short for "Unified Numbering System for Metals and Alloys") is a systematic scheme in which each metal is
designated by a letter followed by five numbers. It is a composition-based system of commercial materials and does not guarantee any
performance specifications or exact composition with impurity limits. Other nomenclature systems have been incorporated into the UNS
numbering system to minimize confusion. For example, Aluminum 6061 (AA6061) is assigned UNS A96061. Likewise AISI 1018 steel becomesUNS G10180.
Overview of the UNS system
This is an overview of the UNS system, with special emphasis on common commercial alloys. As with any system, there are ambiguities such as
the distinction between a nickel-based superalloy and a high-nickel stainless steel.
Axxxxx- Aluminum Alloys
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Cxxxxx- Copper Alloys, including Brass and Bronze
Fxxxxx- Iron, including Ductile Irons and Cast Irons
Gxxxxx- Carbon and Alloy Steels
Hxxxxx- Steels - AISI H Steels
Jxxxxx- Steels - Cast
Kxxxxx- Steels, including Maraging, Stainless Steel, HSLA, Iron-Base Superalloys
L5xxxx- Lead Alloys, including Babbit Alloys and Solder Alloys M1xxxx- Magnesium Alloys
Nxxxxx- Nickel Alloys
Rxxxxx- Refractory Alloyso R03xxx- Molybdenum Alloyso R04xxx- Niobium (Columbium) Alloyso R05xxx- Tantalum Alloyso R3xxxx- Cobalt Alloyso R5xxxx- Titanium Alloyso R6xxxx- Zirconium Alloys
Sxxxxx- Stainless Steels, including Precipitation Hardening Stainless Steel and Iron-Based Superalloys
Txxxxx- Tool Steels
Zxxxxx- Zinc Alloys
Class examples
AISI UNS
1020 G10200 Other alloys
4340 G43400 No Alloys added
12L40 Lead Alloy G12404 Lead Alloy
50B40 Boron Alloy G50401 Boron Alloy
Slide Summary
INTRODUCTION
What is manufacturing(1.1)?
Manufacturing is concerned with making products. Vast majority of objects around us consists of
numerous individual pieces that are build and assembled by a combination of processes called
manufacturing.
Product Design and Concurrent Engineering(1.2)(Fig 1.2 pg8)
Product design involves the creative and systematic prescription of the shape and characteristics
of an artifact to achieve specified objectives while simultaneously satisfying several constraints. 80% of the cost of product development and manufacture is determined by the decisions made
in the initial stages of design.
Strong interaction between manufacturing and design activities.
Traditional design and manufacturing activities have taken place in sequence.
Methodology may appear straight forward and logical, however, it is a waste of resources.
Concurrent engineering is also called as simultaneous engineering.
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From the earlier stage of product design and engineering, all relevant disciplines are now
simultaneously involved.
Driven primarily by consumer electronic industry where continuous trend is taking place to bring
products to the market as rapidly as possible.
Green Design and Manufacturing (1.4)
Common in all industrial activities, with major emphasis on design for environment(DFE), which
considers environmental impact of materials and manufacturing processes and taken into
account at earliest stage of design and production.
Design for recycling (DFR) involves the Biological and Industrial cyle
Cradle-to-Cradle Production (C2C) takes responsibility of resources from raw materials to
recycling
Cradle-to-grave (womb-to-tomb) is similar but doesnt take responsibility for recycling.
Selection of Materials (1.5)
MaterialsPoints to be considered while selecting materials
Material properties and manufacturing characteristics
Advantages and limitations
Material and production costs
Consumer and industrial application
Availability, service life, green design (design for the environment)
Mechanical Properties
Strength: Ability of a material to withstand an applied load without failure
Ductility: The extent of plastic deformation that the material undergoes before fracture
Hardness: Resistance to permanent indentation (Steel is harder than aluminum)
Toughness: Resistance to fracture
Stiffness: Resistance of an elastic body to deformation by an applied force
Fatigue: Ability to withstand rapidly fluctuating loads (crack grows with every stress cycle)
Creep: Creep is a permanent elongation of a component under a static load maintained for a
period of time.
Physical Properties
Density: Mass per unit volume
Melting point: Energy required to separate its atoms
Specific heat: Is the energy required to raise the temperature of a unit mass by 1 degree
Thermal conductivity: Indicates the rate at which heat flows within and through a material
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Selection of Manufacturing Processes (1.6)
There is often more than a method that can be employed to produce a component for a product
from a given material.
Selection of particular manufacturing process or more often sequence of process depends on
o Geometric features
o Material properties
o Dimensional tolerance
o Net-shape or near-net-shape
o Ultra-precision manufacturing
o Types of production
o Job shop: typically less than 100 parts
o Small-batch: 10-100 parts
o
Batch production: 100-5000 partso Mass production: 100,000 parts
Processes
Casting
Forming and shaping: Rolling, forging, extrusion, drawing, sheet forming, powder metallurgy and
molding
Machining: Turning, boring, drilling, milling, shaping, grinding, chemical, electric and
electrochemical machining etc.
Joining: Welding, brazing, soldering, adhesive bonding, and mechanical joining
Finishing: Polishing, grinding, surface treatment, coating, and plating
Microfabrication and nanofabrication: Technology that are capable of producing parts with
dimensions at the micro (MEMS) and nano levels (NEMS).
Casting: Casting is a process in which molten metal flows by gravity or other forces into a mold cavity
where it solidifies in the shape of the mold cavity. Metal casting is the oldest manufacturing technique
Arrows
Jewelry
Advantages:
Complex shapes can be made
Can create both external and internal shapes
Flexibility of size and weight
Simple and inexpensive tools
Variety of metals (Ferrous and Nonferrous)
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Wastage of raw material is less
Mass production
Disadvantages:
Poor accuracy(need to carry machining process)
Labor intensive process
Poor surface finish (Improved by Investment casting, Shell molding process)
Internal defects
THE STRUCTURE OF METALS
Introduction (1.1)
P)The atomic weight of copper is 63.55, meaning that 6.023 X 1023 atoms weigh 63.55 grams. The
density of copper is 8970 kg/m3, and pure copper forms fcc crystals. Estimate the diameter of a copper
atom.
The face of the FCC unit cell consists of a right triangle with side length a and hypotenuse 4r. From the
Pythagorean Theorem we know a=4r/Sqrt2. Therefore the volume (V) of the unit cell can be
represented as:
V=a^3=(4r/aqrt2)^3=22.63r^3
Each FCC unit cell has four atoms and each atom has a mass represented as
Mass= 63.55g/6.023 x 10^23= 1.055 x 10^-22
So that density inside the FCC unit cell is
P =M/V=8970 kg/m^3= 4(1.055 x 10-22/22.63r^3
Solving for r =1.27 x 10^-10m and d=2r
P) Suppose we count 16 grains/square inch in a photomicrograph taken at magnification X250. What is
the ASTM grain size number?
Actual area of 1in^2 at 250x = 1/250x250 = 0.16 x^-4 in^2
Actual are of 1 in^2 at 100x = 1/100x100 = 10^-4 in^2
N= 2^n-1 n=grain size # N= #grains/in^2 at 100x
100= 2^n-1
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log(100)= (n-1)log(2)
n= 7.64
P) Determine the ASTM grain size number if 25 grains/square inch are observed at a magnification of 50.
N=(50/100)^2(25)= 100 grains/in^2=2^n-1
log(6.25)=(n-1)log(2)
.79588= (n-1)(.301)
n=3.644
***Mechanical Behavior, Testing and Manufacturing Properties of Materials***
Types of testing
Tension
Compression- specimen subjected to compressive forces and estimates forces and power
requirements in proceses
Torsion- determine properties of materials in shear
Bending- test method for brittle materials(three and four-point bending). Modulus of
rupture(transverse rupture strength) is stress fracture at bending point.
Hardness test- (fig 2.13 for diff types)
Fatigue- most failures in mechanical components. Testing specimens under various states of
stress in tension and bending.
Creep- permanent deformation of a component under a static load maintained for a period of
time. At elevated temperatures is attributed to grain-boundary sliding.
Tension (2.2)
Tensile test is the most common method for determining Strength, ductility, toughness, elastic modulus,
and strain-hardening capability.
Ductility- The extent of plastic deformation that the material undergo before fracture.
2 common measures of Ductility:
Elongation = (lf-lo/lo)x100 Reduction of Area= (Ao-Af/Ao)x100
Two Types of Failure:
Buckling
Fracture
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Schematic illustration of types of failures in materials: (a) necking and fracture of ductile materials;
(b)buckling of ductile materials under a compressive load; (c) fracture of brittle materials in
compression; (d)cracking on the barreled surface of ductile materials in compression.
Ductile Fracture : plastic deformation
Brittle Fracture: Brittle failure occurs with little or no gross plastic deformation. Example: Chalk, Graycast iron, Concrete
Defects: An important factor in fracture is the presence of defects such as Scratches, flaws, preexisting
external or internal cracks
Fatigue Fracture: Typically occurs in brittle material Minute external or internal cracks develop at pre-
existing flaws or defects in the material; these cracks propagate over time and eventually lead to total
failure.
fracture in tension: (a) brittle fracture in polycrystalline metals; (b) shear fracture in ductile single (c)
ductile cupand- cone fracture in polycrystalline metals; (d) complete ductile fracture in polycrystalline
metals, with 100%reduction of area.
Residual Stresses- Stresses that remain within the part after it has been formed and all the external
forces are removed. Caused by Plastic deformation (not uniform throughout the part), Temperature
gradient (Cooling of a casting/forging). Reduced by Stress-relief annealing (Heated to around 6000C and
held for extended time), Further deformation, Diminish over a period of time.
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Metal Alloys: Their Structure and Strengthening by Heat Treatment
Two-phase Systems (4.2.3)
Phase: Defined as a physically distinct and homogeneous portion in a material Each phase is a
homogeneous part of a total mass and has its own characteristics and properties. Example: Sand
+ Water; Ice + Sand
Two-Phase System: Most alloys consist of two or more solid phases and may be regarded as
mechanical mixtures; two solid phases
Two-Phase Metal: Lead added in copper in the molten state
Second phase particles provide obstacles to dislocate movement and thus increase strength
(a) Schematic illustration of grains, grain boundaries, and particles dispersed throughout the structure of
a two-phase system, such as a leadcopper alloy. The grains represent lead in solid solution in copper,
and the particles are lead as a second phase. (b) Schematic illustration of a two phase system consisting
of two sets of grains: dark and light. The green and white grains have separate compositions and
properties.
Phase Diagrams (4.3)
Shows graphically the various phases that develop as a function of alloy composition and temperature.
(a) Cooling curve for the solidification of pure metals. Note that freezing takes place at a
constant temperature; during freezing, the latent heat of solidification is given off. (b)
Change in density during cooling of pure metals.
***UNDERSTAND HOW TO READ PHASE DIAGRAMS FOR DIFFERENT ALLOYS AND SYSTEMS***
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Iron-Carbon System (4.4)
Alpha Ferrite:
Is the stable form of iron at temperatures below 912OC
Alpha ferrite is a solid solution of bcc iron.
Alpha ferrite has a max solubility of 0.002%
Ferrite is relatively soft and ductile.
Although very little carbon can dissolve interstitially in bcc iron, the amount of carbon can
significantly affect the mechanical properties of ferrite
Delta ferrite is another form that is stable only at very high temperatures
Upon further cooling to 768OC, iron undergoes a transition from nonmagnetic to magnetic.
Austenite:
Within certain temperature range iron undergo polymorphic transformation from bbc to fcc.
Solid solubility of 2.11% C at 1148 C because of fcc.
Denser than ferrite
Exhibits high formability that is characteristic of the face-centered-cubic structure and is capable
of dissolving more than 2% Carbon in single phase solid solution
Most of the heat treatment of steel begins by forming the high-temperature austenite structure
Cementite:
Very hard and brittle intermetallic compound and has a significant influence on steel .
Care should be exercised in controlling the structures in which it occurs.
Alloys with excessive amount of cementite, or cementite in undesirable form, tends to havebrittle characteristics.
Cementite is also called carbide.
Heat Treatment of Ferrous Alloys (4.7)
Heat treatment: Modifies microstructure, Induces phase transformation (influence mechanical
properties such as hardness, strength, ductility, toughness etc.)
Heat treatment processes:
Quenching (rapid cooling in water, oil etc.) Tempering (reheating and controlled cooling, to reduce hardness and improve ductility)
Annealing (slow cooling in air)
Effect of heat treatment depends on:
Particular alloy
Composition and microstructure
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Degree of prior cold work
Rate of heating and cooling during heat treatment
Hardenability of Ferrous Alloys (4.8)
Hardenability: The capacity of an alloy to be hardened by heat treatment. It is a measure of the depth of
hardness that can be obtained by heating and subsequent quenching.
Hardness: Resistance of a material to indentation or scratching.
Hardenability of ferrous alloys depends on:
Carbon content
Grain size of the austenite
Alloy elements present in the material
Cooling rate
Quenching Media:
Fluid used for quenching the heated alloy effects hardenabiity
Quenching may be carried out in water, oils, molten salt, air, polymer solution etc.
Water is a common medium for rapid cooling
Rate of cooling is different because of the difference in thermal conductivity, specific heat of
vaporization.
Agitation effects cooling rate (vigorous agitation higher rate of cooling)
Heat Treatment of Nonferrous Alloys and Stainless Steels (4.9)
Nonferrous alloys do not undergo phase transformation like those in steels.
The hardening and strengthening mechanisms for these alloys are fundamentally different.
Heat-treatable aluminum alloys, copper alloys etc. are hardened and strengthened by a process
called precipitation hardening
Precipitation Hardening: Is a technique in which small particles of different phase, called precipitates,are
uniformly dispersed in the matrix of the original phase.
Case Hardening (4.10)- Component is heated in an atmosphere containing elements that alter thecompositions, microstructure, and properties of surfaces. (processes Table 4.1)
Annealing (4.11)- Term used to describe the restoration of a cold-worked or heat treated alloys to its
original properties, used to relieve residual stress.
The annealing process consists of the following steps:
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Heating the workpiece to a specific range of temperature in a furnace
Holding it at that temperature for a period of time
Cooling the workpiece, in air or in a furnace.
Production of Iron and Steel (5.2)
Raw materials for Iron:
Iron ore- Principal Iron Ores are Toconite (black flint like rock),Hematite (Iron Oxide minerals),
Limonite (Iron Oxide containing water)
Limestone- To remove impurities from molten iron. Limestone combines with impurities and
forms slag
Coke- To generate high level of heat required for chemical reaction. To produce carbon
monoxide to reduce iron oxide to iron.
Steel Production- Steel making process is essentially one of refining the pig iron by reducing the
percentages of manganese, silicon, carbon, and other elements and by controlling the composition of
the output through the addition of various elements. Three processes are:
Open-hearth-
o shallow hearth that is open directly to the flames that melt the metal. Replaced by
electric.
Electric furnace
o Heat is generated by continuous electric arc that is formed between the electrodes andthe charged metal
o Temperatures as high as 1925OC are generated
o The quality of steel produces is better than that from either the open-heart or the basic-
oxygen process
o Electric furnace capacity range from 60 to 90 tons of steel per day
o For small quantities, electric furnace can be of induction type
Vacuum furnace
o Melted in induction furnaces where air removed and cooling through injecting an iner
gas(argon) at high pressure
Basic-oxygen furnaceo Is the fastest and by far the most common steelmaking furnace
o Typically, 200 tons of molten pig iron and 90 tons of scrap are charged into a vessel,
some units can hold as much as 350 tons.
Casting of Ingots (5.3)
Reactions during Solidification of Ingot:
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Significant amount of oxygen and other gases are present in molten metal during steel making
As the temperature decreases, solubility of gases decreases and hence rejected during
solidification
Rejected oxygen combines with carbon to form carbon monoxide, which causes porosity in the
solidification ingot
Depending on the amount of gas evolved during solidification:
Killed Steel (deoxidized steel, oxygen is removed and the associated porosity eliminated, pipe at
the top(due to shrinkage))
Semikilled Steel (partially deoxidized steel, some porosity, no pipe, no scrap)
Rimmed Steel (low carbon content and hence gases are partially killed , produce holes along the
outer rim of the ingot)
Continuous Casting (5.4)
(a) The continuous-casting process for steel. Typically, the solidified metal descends at a speed of
25 mm/s(1 in./s); note that the platform is about 20 m (65 ft) above ground level.Source: Figure
adapted from Metalcasters Reference and Guide (c. 1989, p. 41), American Foundrymens
Society. (b) Continuous casting using support or guide rollers to allow transition from a vertical
pour zone to horizontal conveyors. (c) Continuous strip casting of nonferrous metal strip.
Carbon and Alloy Steels (5.5)
Effects of elements in Steel
Antimony/arsenic-cause temper embrittlement
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Hydrogen-severely embrittles, but heating during processing drives out hydrogen
Nitrogen-improves strength, hardness and machinability.
Oxygen- improves strength of rimmed steels, severely reduces toughness
Tin- causes hot shortness and temper embrittlement.
Designations for Steel
G- AISI/SAE carbon and alloy steels
J- Cast steels
K-misc steels andferrous alloys
S-stainless steels and superalloys
T-tool steels
Carbon Steels
Low-Carbon Steel (Mild Steel)
Contains less than 0.3% C
Used for machine components that do not require high strength (bolts, nuts, sheets, plates, and
tubes)
Medium-Carbon Steel
Has 0.3% - 0.6% C
Used in applications that require higher strength (gears, axles,connecting rods, crankshafts)
High-Carbon Steel
Has more than 0.6% C
Used for applications require strength, hardness, and wear resistance (cutting tools, cable wire,
springs and cutlery)
The parts are usually heat treated and tempered
High-Strength Low-alloy Steels
To improve strength-to-weight ratio
Typically produced in sheet forms by microalloying followed by controlled hot rolling
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Contains less than 0.3% C (microstructure consists of fine grains of ferrite as one phase and a
hard second phase of martensite and austenite)
Have high yield strength and energy absorption capacity compared to conventional steel
The ductility, formability, and weldability of HSLA steels, are generally inferior to those of
conventional low-alloy steels.
Applications: Automobile bodies, mining, agricultural, and various other industrial applications. Plates
are used in Ships, bridges, building construction (I-beams).
BH: Bake-hardenable
HSLA: High-strength low-alloy
DP: Dual-phase
TRIP: Transformation-induced plasticity
TWIP: Twinning-induced plasticity
MART: MartensiticCP: Complex phase
Ultra-high-strength Steels
Ultra-high-strength steel are defined by AISI as those with an ultimate tensile strength higher
than 700 MPa (100 ksi)
There are five types: Dual-phase, Transformation-induced plasticity, twinning-induced plasticity,
Martensitic, Complex phase
o Dual Phase
Mixture of ferrite (matrix, week and ductile) and martensite (islands of high-
strength, high hardness, and high carbon content)
Have high work hardening, which improves ductility and formability with no loss
in weldability
o Transformation-induced plasticity(TRIP)
Consists of ferrite-bainite matrix and 5-20% retained austenite
Have both excellent ductility because of austenite and high strength after
forming
o Complex-phase grades
Very fine grained microstructures of ferrite and a high volume fraction of hard
phases (martensite and bainite)
Can provide ultimate tensile strength as high as 800 MPa.
o Twinning-induced plasticity(TWIP)
High strain hardening and avoiding thinning during processing
Combine high strength with high formability
o Martensitic
High fractions of martensite to attain tensile strengths up to 15ppMPa.
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HOMEWORK
Grain-crystalline structure grown from crystals found when molten metal begins to solidify
Grain boundary- the interfaces that separates the individual grains
Grain size-Grain size effects properties. Large grains are generally associated with low strength, low
harness, and low ductility.
Grain growth- temperature rises and grains grow to exceed original size.
Isotropy- properties do not vary with direction.
Anisotropy- crystal exhibits different properties when tested in different directions.
Deformation and strength of single crystals (1.4)
If the force on the crystal structure is increased sufficiently, the crystal undergoes plastic
deformation or permanent deformation.
Two mechanisms by which plastic deformation takes place in crystals
o Slipping of one plane of atoms slipping over an adjacent plane under shear stress
(critical shear stress)
o Twinning: A portion of the crystal forms a mirror image of itself across the plane of
twinning.
Mechanical behavior, testing and manufacturing properties of materials (see Chapter 2 slide notes)
Cast Iron(4.6)- refers to ferrous alloys composed of iron, carbon (2.11-4.5%) and silicon (up to 3.5%).
Classified according to solidification morphology from eutectic temperature. Are liquid at temperatures
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lower than steel, thus are cast at lower temperatures. Cementite is not completely stable(meta-stable),
with low decomposition rate. Formation of graphite can be controlled, promoted and accelerated by
modifying composition, the rate of cooking and addition of silicon. Types are:
Gray Cast Iron- graphite exists in flake form and acts as stress raisers, results in negligible
ductility, weak in tension and strong in compression. Flakes gives capacity to dampen vibrationsby internal friction. Commonly used for constructing machine-tool bases and machinery
structures. 3 types are ferritic(fully gray), perlitic(brittle but stronger than ferritic) and
martensitic(austenitize pearlitic then quench rapidly; very hard).
Ductile(Nodular) Iron- somewhat ductile and shock resistant. Made feritic or pearlitic by heat
treatment.
White Cast Iron- very hard, wear resistant and brittle because of large amounts iron
carbide(instead of graphite).
Malleable Iron- obtained by annealing white. Good ductility, strength and shock resistant.
Compacted-graphite Iron- properties intermediate between flake and nodular graphite cast
irons.
Heat-treatment furnaces and equipments(4.12)-Two furnaces used for heat treating: batch furnaces
and continuous furnaces. Either fuelled by gas/oil(introduces combustion products into furnace) or
electric (slower start-up time and more difficult to adjust and control)
Types of furnaces
Batch Furnaces- heat treatment in batches. Has insulating chamber, heating system and acces
doors. Types include
o Box furnace- horizontal chamber with up to 2 access doors
o Pit furnace- vertical pit below ground level parts are lowered into
o Bell furnace- round/rectangular box without bottom. Suitable for coils of wire, rods and
sheet metal
o Elevator furnace- parts loaded onto car platform, rolled into position and raised into
furnace
Continuous furnaces- parts move continuously through furnace on conveyors of various designs
Salt-bath furnaces- salt baths with high heating rates and better control of temp uniformity are
ideal for nonferrious strip wire. Heating rates are higher because of thermal conductivity of
liquid salts.
Fluidized beds- uses dry fine and loose solid particles(Al) that are heated and suspended in achamber by upward flow of hot gas at various speeds
Induction Heating- part headed rapidly by electromagnetic field from induction coil. Coil shaped
to fit contour of part, made of copper and water cooled.
Furnace atmospheres- atmospheres controlled to avoid oxidation, tarnishing and
decarburization of ferrous alloys heated to elevated temperatures. Water vapor causes
oxidation of steels, resulting in blue colour(bluing).
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Stainless Steels (5.6)
Characterized by corrosion resistance, high strength, and ductility
In air develop thin, hard and adherent film of chromium oxide that protects the metal from
corrosion.
Higher the carbon content, lower the corrosion resistance Applications include cutlery, kitchen equipment, health care, surgical equipment and
applications in chemical, food-processing and petroleum industries.
Stainless steels are divided into 5 types:
Austenitic(200/300 series)-non magnetic and good corrosion resistance. Stess-corosion cracking
can occur. Most ductile and formed easily. Wide variety of apps(kitchen, fittings, weld constr,
transportation eqp, furnace/heat exchanger parts and components for severe chemical envts)
Ferritic(400)-magnetic and good corrosion resistance, but lower ductility. Used for nonstruct
apps(kitch and auto)
Martensitic(400/500)-no nickel and hardenable by heat treatment. Magnetic and high strength,
hardness, fatigue resistance, good ductility and moderate corrosion resistance. Used for cutlery,
surgical tools, instruments, valves and springs.
Precipitation-Hardening(PH)- good corrosion resistance, ductility, high strength at elevated
temp. Aircraft and aerospace uses.
Duplex structure- mixture austenite and ferrite. Good strength and higher resistance to
corrosion and stress-corrosion cracking than 300 series. Used in water treatment plants and
heat exchanger components.
Tool and Die Steel (5.7)- specially alloyed steels that are high strength, impact tough, wear resistant for
tool and die requirements. Used for forming and machining metals.
High-speed steel-most highly alloyed. Maintain hardness and strength at elevated temp. 2
types:
o M-series-higher abrasion resistance, undergo less distortion in heat treatment and less
expensive. 95% of all high-speed tools produces.
o T-series-
Die steels
o Hot-work steels(H-series) used at elevated temp, have high toughness and resistance to
wear and cracking.
o Cold-work steels(A, D, O-series) used for cold-working operations, have high resistance
to wear and cracking and available as oil hardening or air hardening types.
o Shock-resisting steels(S-series) designed for impact toughness and used in header dies,
punches and chisels.
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09 Oct 13
Rule of Mixture
Assumptions
Fibers are uniformly distributed
Perfect bonding between fibres and resin,
No voids
Applied loads are either parallel/perpendicular to the fibre direction
No residual stresses
Linear elastic constituents
(Andrew Vaz part starts here)
Chapter 6 Nonferrous metals and Alloys
Nonferrous alloys do not undergo phase transformation like those in steels.
The hardening and strengthening mechanisms for these alloys are fundamentallydifferent.
Heat-treatable aluminum alloys, copper alloys etc. are hardened andstrengthened by a process called precipitation hardening .
Precipitation Hardening:Is a technique in which small particles of different phase, called precipitates, areuniformly dispersed in the matrix of the original phase.
Heat Treatment of Nonferrous Alloys and Stainless Steels(Look at lecture 7 slide 6 for diagram)
Production of Iron:The raw materials are: Iron ore, Limestone, and Coke.
Iron ore elements: (Purpose of the elements)
Principal Iron Ores: Toconite(black flint like rock), Hematite (Iron Oxide minerals),
Limonite (Iron Oxide containing water)
Limestone:To remove impurities from molten iron. Limestone combines with impuritiesand forms slag
Coke: To generate high level of heat required for chemical reaction. To produce carbon
monoxide to reduce iron oxide to iron.
Procedure to create iron
1. Take iron ore and put it through a machine to make pellets or sinter.
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2. Crush the limestone
3. Put coke in the coke oven
4. Then put the materials in right quantity in a blast furnace to produce molten iron.
5. Separate the slag from the molten iron and then put the molten iron in the mold
to produce the iron bars.
Production of steel
Steel making process is essentially one of refining the pig iron by reducing thepercentages of manganese, silicon, carbon, and other elements and by controlling thecomposition of the output through the addition of various elements.
Steel producing methods:
1. Open-Hearth 2. Electric Furnace 3. Basic-Oxygen Furnace
Heat is generated by continuous electric arc that is formed between the electrodes and
the charged metal!
Temperatures as high as 1925 degree Celsius are generated!
The quality of steel produces is better than that from either the open-heart or the basic-
oxygen process!
Electric furnace capacity range from 60 to 90 tons of steel per day!
For small quantities, electric furnace can be of induction type
Basic-Oxygen Furnace
Is the fastest and by far the most common steelmaking furnace!
Typically, 200 tons of molten pig iron and 90 tons of scrap are charged into a vessel,some units can hold as much as 350 tons.
Casting of Ingots
Reactions during Solidification of Ingot: !
Significant amount of oxygen and other gases are present in molten metal during
steel making! As the temperature decreases, solubility of gases decreases and hence rejected
during solidification !
Rejected oxygen combines with carbon to form carbon monoxide, which causesporosity in the solidification ingot
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Depending on the amount of gas evolved during solidification:
Killed Steel (deoxidized steel, oxygen is removed and the associated porosityeliminated, pipe at the top(due to shrinkage)) !
Semi-killed Steel (partially deoxidized steel, some porosity, no pipe, no scrap)!
Rimmed Steel (low carbon content and hence gases are partially killed , produceholes along the outer rim of the ingot)
Some metals and characteristics to know:
Nonferrous alloys- wide range of mechanical, physical, and electrical properties; goodcorrosion resistance; high temperature applicationsAluminum- high strength-to-weight ratio; high thermal and electrical conductivity; goodcorrosion resistance; good manufacturing properties.Magnesium- Lightest metal; good strength-to-weight ratio.Copper- High electrical and thermal conductivity; good corrosion resistance; goodmanufacturing properties.Super alloys- Good strength and resistance to corrosion at elevated temperatures; canbe iron, cobalt, and nickel based alloys.
Low carbon steelhas less than 0.3% C. Used for machine parts that do not requirehigh strength.Medium carbon steelis from 0.3 0.6% C. used for application that require higherstrength.High carbon steelhas more than 0.6% C. Parts are usually heat treated. Used forapplications that require high strength, hardness, and wear resistance.
Carbon Fibre and Resin
Composite on composite
Ceramic- matrix composite
https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=9https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=14https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=13https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=12https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=11https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=10https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=9https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=8https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=7https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=6https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=5https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=4https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=3https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=2 -
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Polymer-matrix composite
Learn how to use the composite formula which were used in the assignment. (If you do not have
formulas or the example get it off someone)
Glass fibre
The composite material is called glass-fibre reinforced plastic and may contain 30% to 60% glass
fibre. There are 3 types:
1. E-type: a calcium aluminoborosilicate glass, the type most commonly used.
2. S-type: a magnesia aluminosilicate glass, offering higher strength and stiffness, but at a
higher cost.
3. E-CR-type: a high-performance glass fibre, with higher resistance to elevated
temperatures and acid corrosion than does the E-glass.
https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=15https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=24https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=23https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=22https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=21https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=20https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=19https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=18https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=17https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=16https://d2l.laurentian.ca/content/enforced/49934-ENGR_3536EL_01_2013F/Lecture%207.pdf?rnum=173&d2l_body_type=4#page=15 -
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Vacuum Bagging Process
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Also the Boeing 787 is made from carbon fibre.
Method to make a composite material:
1. Have a mold of the material you want to create it could be made fromfoam, fibre glass.
2. Add a layer of the of a unique wax on the mold so that the carbon fibre
does not stick to the mold and apply it so that there is a nice layer of it on
the mold.
3. Then add resin and wait until it gets tacky and then apply carbon fibre and
then cover it with resin and another layer of carbon fibre and continue
process until you desire.
4. For the resin try to dab it on the carbon fibre so that it gets applied equally
to the fibre
5. Then use a process like vacuum bagging to remove excess resin from the
fibre.
Metal Casting
Metal Casting process (Also have to take into consideration
about shrinkage)
1. Mold Preparation2. Metal Heating3. Pouring4. Solidification5. Part Removal
Patterns can be made from :Wood , metal , wax , plaster, sand. And foam.
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Advantages:
Complex shapes can be made
Can create both external and internal shapes
Flexibility of size and weightSimple and inexpensive tools
Variety of metals (Ferrous and Nonferrous)
Wastage of raw material is less
Mass production
Disadvantages:
Poor accuracy (need to carry machining process)
Labour intensive process
Poor surface finish (Improved by Investment casting, Shell molding process)
Internal defects
Casting NomenclatureFlask:Metal or wood frame in which mold is formedTwo-piece molds consists of a cope on top and a drag on the bottom
Pour ing Basin :In to which the molten metal is pouredSprue:Through which the molten metal flows downwardRunner:Which has channels that carry the molten metal from thesprue to the mold cavityRiser:Which supply additional molten metal to the casting as it shrinksduring solidification (Reservoir)Core:Which are inserts made from sand. They are placed in the mold toform hollow regions or otherwise define the interior surface of the castingVents:Which are placed in molds to carry off gases produced when themolten metal comes into contact with the sand in the mold and the coreRunn er Gate:A channel through which molten metal enters the moldcavity
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Various Metal Casting Processes
Important considerations in casting operations:
Flow of the molten metal into the cavity
Solidification and cooling of the metal in the mold
Influence of the type of mold material
Events affect the size, shape, uniformity and chemical
composition of grain
Factors affecting these events:
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Type of metals
Thermal properties of both metal and the mold
Geometric relationship between the volume and surface area of thecasting and the shape of mold
Solidification of metals
Freezing range: TLTS
TLTemperature of molten liquid
TS - Temperature of solid metal
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Fluid Flow for Casting
F= to friction loss
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Sand Casting
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Forming Processes
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Metal rolling Process
Metal Rolling Process and Equipment
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Formulas for rolling
Geometric Consideration
So in rolling the shape of the metal piece has to be taken into consideration. Because roll forces
tend to elastically bend the rolls during rolling. This leads to the issue that the centre is ticker
than the edges which is known as crown. To reduce deflection the rolls can be subjected to
external bending.
Vibration and Chatter
So vibration and chatter has significant adverse effects on product quality and productivity in
manufacturing operations. If chatter occurs then there will be variations in thickness of the
sheet. Chatter can be reduced by:
1. Increasing the distance between the stands of the rolling mill
2. Increasing the roll radius
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3. Decreasing the reduction per pass
4. Increasing the roll radius
5. Increasing the strip-roll friction
6. Incorporating external dampers in the rolling supports
Flat-rolling process
1. Cold rollingis carried out at room temperature
2. Pack rolling is a flat rolling operation in which two or more layers of the sheet are rolled
together, thus increasing productivity
3. Rolled mild steel , when subsequently stretched during sheet- forming operations,
undergoes yieldpoint elongation.
Defects in rolling
1. Wavy edges are due to roll bending2. Cracks are usually the result of low material ductility at the rolling temperature.
Various rolling process and mills
Shape rolling
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Friction Hill
P= Ye2(r(outer)-r)/h
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Various Forging operations
1. Coininga closed die forging process used to create coins medallions and
jewellery. Marking can be done with this process as well.
2. HeadingAlso called upset forging. An upsetting operation performed on
the end of a rod or wire in order to increase the cross section. Products are
nails, bolt heads, screws, rivets, and various other fasteners.
3. Piercing- This process of indenting(but not breaking through)the surface of
a work piece with a punch, in order to produce a cavity or an impression.
4. OrbitalIn this process, the upper die moves along an orbital path and
forms the part incrementally, an operation that is similar to the action of a
mortar and pestle, used for crushing herbs and seeds.
5. Incremental- In this process, a tool forges a blank into a particular shapein
several small steps.
6. Isothermal- Also known as hot-die forging, the dies in this process are
heated to the same temperature as that of the hot work piece.
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7. Rotary Swaging- In this process, also known as radial forging, rotary
forging, or simply swaging, a solid rod or tube is subjected to radial impact
forces using a set of reciprocating dies.
8. Tube Swaging- In this process, the internal diameter and/or the thickness
of the tube is reduced, with or without the use of the internal mandrels.
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Drawing Defects
1. Center cracking
2. Seams which are longitudinal scratches or folds in the drawn product.
Fundamentals of Machining
Introduction
1. Turningin which the work piece is rotated and a cutting tool removes a
layer of material as the tool moves along its length.
2. Cutting off- in which the tool moves radially inward, and separates the
piece on the right in from the blank
3. Slab milling- in which a rotating cutting tool removes a layer of material
from the surface of the work piece.
4. End milling- in which a rotating cutter travels along a certain depth in the
work piece and produces a cavity.
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Mechanics of cutting
Parameter Influence and interrelationship
Cutting speed
,depth of cut,
Feed, cutting
fluids
Forces, power, temperature rise, tool life, type of chip, surface
finish, and integrity.
Tool angles As above, influence on the chip flow direction; resistance to tool
wear and chipping.
Continuous
chip
Good surface finish; steady cutting forces; undesirable, especially
in modern machine tools
Built-up edge
chip
Poor surface finish and integrity; if thin and stable, edge can
protect tool surfaces
Discontinuouschip
Desirable for ease of chip disposal; fluctuating cutting forces; canaffect surface finish and cause vibration and chatter.
Temperature
rise
Influences tool life, particularly crater wear and dimensional
accuracy of work piece; may cause thermal damage to work piece
surface
Tool wear Influences surface finish and integrity, dimensional accuracy,
temperature rise, forces and power.
Machinability Related to tool life, surface finish, forces and power, and type of
chip produced.
Major independent variables are:
1. Tool material and coatings
2. If any tool shape, surface finish, and sharpness
3. Work piece material and its processing history.
4. Cutting speed, feed, and depth of cut.
5. Cutting fluids, if any.
6. Characteristics of the machine tool
7. The type of work-holding device and fixturing.
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Dependent variables are:
1. Type of chip produced
2. Force and energy dissipated during cutting
3. Temperature rise in the work piece, the tool, and the chip.4. Tool wear and failure
5. Surface finish and surface integrity of the work piece.
(From the textbook seventh edition there are formulas for cutting ratio, shear
strain, and velocities in the cutting zone pages 569-570)
Types of chips produced in Metal cutting
Four main types and they are: Continuous, Built- up edge, Serrated or segmented,
and discontinuous.
Continuous chips usually are formed with ductile materials, and this type of chip
may develop a secondary shear zone.
Built-up edge consists of layers of materials from the work piece that gradually
are deposited on the tool tip and BUE dulls the cutting tool. This can be reduced
by increasing the cutting speed, decrease the depth of cut, increase the rake
angle, use a cutting tool that has lower chemical affinity for the work piecematerial or use a sharp tool, and use an effective cutting fluid.
Serrated chips also known as segmented or nonhomogeneous chips, these are
semi continuous chips with large zones of low shear strain and small zones of high
shear strain, hence the latter zone is called shear localization. The chips have a
saw tooth-like appearance.
Discontinuous chips consist of segments, attached either firmly or loosely to each
other.
Chip curl this occurs in all operations on metals and non-metallic materials, chip
develop a curvature (chip curl) as they leave the work piece surface.
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Temperature in cutting
1. Excessive temperature lowers the strength, hardness, stiffness, and wear
resistance of the cutting tool; tools also may soften and undergo plastic
deformation, thus altering the tool shape.2. Increased heat causes uneven dimensional changes in the part being
machined, depending on the physical properties of the material, thus
making it difficult to control its dimensional accuracy and tolerances.
3. An excessive temperature rise can induce thermal damage and
metallurgical changes (chapter 4) in the machined surface, adversely
affecting its properties.
(Two temperature formulas in the book on pages 580 -581 for the formula
sheet from seventh edition)
Surface finish and integrity
The surface finish influences not only the dimensional accuracy of the
machined part but also their properties and their performance in service. The
term surface finish describes geometric features and surface integrity pertains
to material properties, like fatigue life, and corrosion resistance.
Surface roughness equation:
Rt=f2/8R f- is feed R- tool-nose radius Rt- roughness height
Cutting tool Materials and cutting fluids (chapter 22)
Tool materials General
Characteristics
Modes of tool
wear or failure
Limitations
High-speed steels High toughness,
resistance to
fracture ,widerange of roughing
and finishing cuts,
good for
interrupted cuts
Flank wear, crater
wear
Low hot
hardness, limited
hardenability, andlimited wear
resistance
Uncoated High hardness Flank wear, crater Cannot use at low
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carbides over a wide range
of temperatures,
toughness, wear
resistance
versatile, widerange of
applications
wear speeds because
of cold welding of
chips and micro
chipping
Coated carbide Improved wear
resistance over
uncoated
carbides, better
frictional and
thermal
properties
Flank wear, crater
wear
Cannot use at low
speeds because
of cold welding of
chips and micro
chipping
Ceramics High hardness at
elevated
temperatures,
high abrasive
wear resistance
Depth of cutline
notching, micro
chipping, gross
fracture
Low strength and
low thermo
mechanical
fatigue strength
Polycrystalline
cubic boron
nitride(cBN)
High hot
hardness,
toughness,
cutting edgestrength
Depth of cutline
notching,
chipping,
oxidation,graphitization
Low strength, and
lower chemical
stability than
ceramics athigher
temperature
Diamond High hardness
and toughness,
abrasive wear
resistance
Chipping,
oxidation,
graphitization
Low strength, and
low chemical
stability at higher
temperatures
Inserts have a huge application when it comes to tools because tools and beeasily repaired because by taking out the old insert and putting in a new one
and it is more economical when it comes to tools.
Coated tools have a lot of advantages:
1. Lower friction
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2. Higher resistance to wear and cracking
3. Higher hot hardness and impact resistance
4. Acting as a diffusion barrier between the tool and the chip
5. Coated tools can last 10 times longer than uncoated tools.
Multiphase Coating advantages:
1. High-speed, continuous cutting: TiC/Al2O3
2. Heavy-duty, continuous cutting: TiC/Al2O3/TiN
3. Light, interrupted cutting: TiC/TiC+TiN/TiN
Ion Implantation
Ions are introduced to the surface of the cutting tool and this helps with a better
surface properties. Right Nitrogen-ion tools are being used and Xeon-ion tools are
under development.
Machining Processes: Turning and hole making (chapter 23)
Some machines to know are the Lathe, mill, Band saw, and CNC machine.
Turningis used to produce straight ,conical, curved, or grooved work pieces such
as shafts , spindles, and pins.
Facingused to produce flat surface at the end of the part and it is perpendicular
to its axis. Can do face grooving for applications as O-ring seats.
Cutting with form tools used to produce various axisymmetric shapes for
functional or for aesthetic purposes
Boringused to enlarge a hole or cylindrical cavity made by a previous process or
to produce circular internal grooves.
Drillingused to make holes and may be used after boring to improve dimensional
accuracy and surface finishing
Parting or Cutting offused to remove a piece
Threadingused to produce external or internal threads
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Knurlingto produce a regularly shaped roughness on cylindrical surfaces, as
making knobs and handles.
Tool geometry
Rake angle-Is important in controlling both the direction of chip flow and the
strength of the tool tip.
Side rake angle-is more important than the back rake angle, which usually
controls the direction of chip flow; these angles typically are in the range from -5
to 5 degrees.
Cutting edge angle- affects tool formation, tool strength, and cutting forces to
various degrees.
Relief angle- controls interference and rubbing at the tool-work piece interface.
Relief angle is typically 5 degree.
Nose radiusaffects surface finish and tool tip strength.
(Copy the formulas from page 630 0f the seventh edition textbook and list of
what the variable means are on page 631)
Rough cuts done at high speed and finishing cuts done at low speeds
Chips from any material should be properly collected and disposed of properly
so that it does not harm the environment.
Machining Processes: Milling, Broaching, Sawing, Filing and Gear Manufacturing
(Chapter 24)
(Should know about the mill from the lab )
Formulas
V=DN tc=2f(sqrt(d/D) f=v/Nn
t=l+lc/v MRR(material removable rate)=lwd/t=wdv
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N= Rotational speed of the milling cutter, rpm
F=feed mm/tooth or inch/tooth
D= cutter diameter, mm or inches
n= number of teeth or cutter
v = linear speed of the work piece or feed rate , mm/min or inches/min
V = Surface speed of cutter, m/min or ft/min
f = feed per tooth, mm/tooth or in./tooth
l = length of cut, mm or in.
t= cutting time, s or min
MRR = mm3/min or in
3/min
Torque= N-m or lb-ft = FcD/2
Power = kw or hp (curved w)= 2N (unit is radians/min)
Broaching and Broaching Machines
A tool which remove a lot of material and one large broach can remove material
as deep as 38mm (1.5in) in one stroke.
Formula to obtain the pitch for a broach to cut surface of length is :
Pitch = k(sqrt(l)) l = L
K is a constant and in when L is in mm k = 1.76 and when L is in inches k= 0.35
L is the length
Another tool is the saw which has a series of small teeth which removes small