A basic understanding of materials

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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

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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