2K16-MSE Lec-6 Behavior of Materials PDF

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Lecture-06 Materials Science & Engineering (ME 202) References:Mechanical Behavior of Materials; William F. Hosford; University of Michigan; Cambridge University Press 2005 Chapter -8, An Introduction To Materials Science and Engineering; 8th Edition; By William D.Callister, Jr. & David G. Rethwisch 5-Minute Metallurgy Lesson; What is the difference between strength and toughness? ;Michael Pfeifer, Ph.D., P.E. President, Industrial Metallurgists, LLC; [email protected] 1

MATERIAL SCIENCE AND ENGINEERING Today’s Topic

Mechanical Behavior of Materials

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Catastrophic Failure – Example 1 Brittle Failure Of A Ship

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Oil tanker struck under sea causing growth of a small crack resulting in brittle failure

Catastrophic Failure - Example-2

Failure Of Plane In Coastal Humid And Salty Environment

An explosive decompression and structural failure on April 28, 1988 in Boeing 737-200 commercial aircraft (Aloha Airlines 4 flight 243) – Fatigue failure due to compression – decompression

Behavior of Materials  Response of materials to  Forces  Temperature  Chemicals  Electric field  Magnetic field  Light energy  Behavior of a material is studied to assess its availability for intended purposes  Inability to perform intended purpose is termed as failure 5

Behavior of Materials

Materials Response to Forces  Stress and Strain  Elastic deformation  Isotropic Elasticity  Anisotropic Elasticity  Plastic deformation  Already discussed in detail in lecture-5  Fracture  Brittle – No plastic deformation  Ductile – Extensive plastic deformation  Fatigue

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Behavior of Materials

Materials Response to Forces Stress and Strain Stress Intensity of force at a point, σ = ∂F/∂A……… ∂A→0 points σ = F/A For same state of stress at all points, Normal Stress (Compressive or Tensile) Force is normal to area on which it acts Shear Stress Force is parallel to area on which it acts 7

Behavior of Materials

Materials Response to Forces Stress and Strain  Strain  Change of length, L, of a line on the surface of the material  Infinitesimal normal strain, ϵ = dL/L (L→Lo)  Integrating from Lo to L, ϵ =

= ln (L/Lo )

 ln(L/Lo) = True Strain, Natural or Logarithmic Strain  Engineering or normal strain, e=ΔL / Lo (ΔL=L-Lo)  For small strains, engineering strain ≈ true strain

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Behavior of Materials

Materials Response to Forces Stress and Strain

Behavior of Materials

Materials Response to Forces Elastic Deformation Isotropic Elasticity Same property in all directions direction, For uniaxial tension in xx-direction ex = σx/E , where E is Young's Modulus Lateral strains, ey = ez = -ѵ ex , where ѵ is Poisson’s ratio Generalized Hook’s law ex = 1/E {σx – ѵ (σy + σz )}

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Behavior of Materials

Materials Response to Forces Elastic Deformation Shear strain, γyz = τyz / G Summarizing:ex = (1/E)[σx − υ(σy + σz)]; γ yz = τyz/G ey = (1/E)[σy − υ(σz + σx )]; γzx = τzx/G ez = (1/E)[σz − υ(σx + σy)]; γxy = τxy/G Poisson's ratio is the ratio of transverse strain to axial strain in the direction of stretching force. 11 ѵ = -ϵtrans /ϵaxial

Behavior of Materials

Materials Response to Forces Elastic Deformation Example Problem-11.3:- A wide sheet of steel (1 mm thick) is bent elastically to a constant radius of curvature, ρ = 50 cm, measured from the axis of bending to the center of the sheet, as shown in opposite figure. Find the stress in the surface E = 208 GPa, and υ = 0.29 for steel. Assume no net force in the plane of the sheet.

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Behavior of Materials

Materials Response to Forces Elastic Deformation Stress normal to a free surface, σz = 0 The sheet is wide relative to its thickness => ey = 0 0 001 Geometrically ex = (t/2)/ρ = (1/2)/500 = 0.001 Geometrically, Substituting into Hooke’s laws, ey = 0 = (1/E)[σy − υ(σx + 0)] => σy = υσx ex = t/(2ρ) = (1/E)[σx − υ(σy + 0)] = (1/E)(σx − υ2σx) = σx(1− υ2)/E σx = [t/(2ρ)]E/(1− υ2)] = (0.001)(208 × 109)/(1 − 0.292) = 227 Mpa and σy = υσx = 0.29 (227 ) = 65.8 MPa

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Behavior of Materials

Materials Response to Forces Elastic Deformation The Elastic behavior of polymers The elastic strains - largely by straightening of polymer chains by rotation of bonds rather than by bond stretching Young’s moduli generally lower than those of metals and ceramics Stretching of covalent bonds in highly oriented polymers - comparable with metals and ceramics

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Behavior of Materials

Materials Response to Forces Isotropic thermal expansion Fractional change in length due to change in temperature Thermal Strains, ΔL/L = αΔT ;(α = Coefficient of Thermal Expansion) Generalization of Hook’s law to include thermal strain, ex = (1/E)[σx − υ(σy + σz)] + αΔT

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Behavior of Materials

Materials Response to Forces Isotropic thermal expansion

Elastic constants and thermal expansion coefficients for various materials Note:- Bimetallic strips used for sensing temperature depend on the differences of 16 the thermal expansion of the two materials

Behavior of Materials

Materials Response to Forces Anisotropic elasticity  Materials are generally assumed isotropic, whereas,  In single crystals, elastic properties vary with crystallographic direction  In poly crystals  Preferred growth directions during solidification  Lattice rotation during deformation  Re-crystallization - the grains orientation changes but does not eliminate 17

Behavior of Materials

Materials Response to Forces Fracture

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Behavior of Materials

Materials Response to Forces Ductile Fracture vs Brittle Fracture Ductile

Brittle

Slow crack propagation and Rapid and spontaneous crack responds on increase in applied propagation not requiring load increase in applied load Plastic deformation gives warning Occurs suddenly that failure is imminent, allowing catastrophically without preventive measures to be taken warning

and any

More strain energy is required to Less strain energy is required to induce ductile fracture induce brittle fracture Most of the metal alloys are Ceramics are generally brittle ductile 19 Ductile Materials Are Generally Preferred Over Brittle Materials

Behavior of Materials

Materials Response to Forces Fracture Highly Ductile Materials  100% RA at fracture  Examples: Pure metals including Gold, Lead, Aluminum, Copper and iron at room temperature and polymers including polyethylene, polytetraflouroethylene (PTFE, Teflon) at room temperature

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Behavior of Mate Moderately Ductile Materials 25% RA at fracture Examples: Aluminum alloys, Copper alloys and Titanium alloys, Nylon and Polycarbonate etc

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Behavior of Materials

Materials Response to Forces Fracture

Brittle Materials No RA Examples: NaCl, MgO, Al2O3, ZrO2 , glass, chalk, concrete, diamond, germanium and silicon 22

Behavior of Materials

Materials Response to Forces Stages of Ductile Fracture

Initial Necking

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Behavior of Materials

Materials Response to Forces Stages of Ductile Fracture

Formation of Small cavities, or microvoids

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Behavior of Materials

Materials Response to Forces Stages of Ductile Fracture

Enlargement of microvoids  l coalesce to fform an elliptical crack Long axis perpendicular to the stress direction

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Behavior of Materials

Materials Response to Forces Stages of Ductile Fracture

Rapid propagation of crack resulting in fracture

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Behavior of Materials

Materials Response to Forces Stages of Ductile Fracture

Final shear fracture at 45° angle (at max shear stress) relative to the tensile direction

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Behavior of Materials

Materials Response to Forces Fractured Shapes Brittle fracture in a mild steel

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Behavior of Materials

Materials Response to Forces Fractured Shapes Ductile fracture in Aluminum (Cup and cone fracture)

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Behavior of Materials

Materials Response to Forces Transgranular Fracture

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Behavior of Materials

Materials Response to Forces Intergranular Fracture

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Behavior of Materials

Materials Response to Forces Principles of Fracture Mechanics  The critical stress σc for crack propagation in a brittle material

where E = γs = a =

Modulus of elasticity Specific surface energy* One-half the length of an internal crack

*Specific surface energy, also known as surface free energy, is the increase in 32 free energy when the area of a surface increases by every unit area.

Behavior of Materials

Materials Response to Forces Principles of Fracture Mechanics

Equation mentioned in a previous slide shall be used here. Rearrangement

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Behavior of Materials

Materials Response to Forces Principles of Fracture Mechanics Modes of Cracked Surface Displacement

Mode I, opening or tensile mode

Mode II, sliding mode

Mode III, tearing mode

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Behavior of Materials

Materials Response to Forces Principles of Fracture Mechanics Determining Fracture Toughness of a Material  Critical stress for crack propagation (σc) and crack length (a) determine fracture toughness of the material as

Where, Kc is the fracture toughness Y is a dimensionless parameter, depends on both crack, specimen size, geometry and the manner of load application

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Behavior of Materials

Materials Response to Forces Principles of Fracture Mechanics Ductile to Brittle Transition Temperature (DBTT)

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An Example of Improving The Material Behavior Heat Treatment of Steel

Steel properties are improved through heattreatment, which involves Heating to a suitable temperature Soaking Cooling rate Essential heat treatment processes are briefly discussed in following slides

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An Example of Improving The Material Behavior Heat Treatment of Steel – Annealing The material is exposed to an elevated temperature for an extended time period then slowly cooled Ordinarily, annealing is carried out to Relieve stresses Increasing softness, ductility, and toughness Produce a specific microstructure A variety of annealing heat treatments are possible; depending upon desired microstructure and physical properties 38

An Example of Improving The Material Behavior Heat Treatment of Steel – Normalizing

Steel is heated above upper transformation temperature and is cooled in still air The purposes of normalizing are To relieve internal stresses caused by forging, bending, machining, etc. To produce a uniform grain structure in the metal Steel that has been normalized is soft and ductile but harder than steel that has been fully annealed Normalizing is sometimes followed by tempering, particularly in the case of certain steels that tend to become brittle when normalized 39

An Example of Improving The Material Behavior Heat Treatment of Steel – Quenching

Heating above upper transformation temperature Soaking Rapidly cooling Final structure produced in the steel is very hard, known as martensite Cutting tools, chisels, twist drills, etc must be hardened to retain cutting edges. Surfaces of roller bearings, and armor plate etc must be hardened to prevent wear and penetration

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An Example of Improving The Material Behavior Heat Treatment of Steel – Tempering

Tempering is done to reduce brittleness and relieve internal stresses developed normally during hardening the steel It involves heating steel below the lower transformation point and then slowly cooling in still air

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An Example of Improving The Material Behavior Heat Treatment of Steel – Case Hardening

A process by which steel can be given a hard, wear-resistant surface while retaining a softer but tougher interior than would be possible if the whole piece were hardened Steels may be case hardened by Carburizing Cyaniding Nitriding

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An Example of Improving The Material Behavior Heat Treatment of Steel – Case Hardening (Carburizing) Carbon is introduced into the surface layer of the steel by following process Steel is heated in contact with a substance that has a high carbon content  Held H ld att a temperature t t above b th upper transformation the t f ti temperature for a suitable length of time Quenched rapidly to produce a hardened outer layer or “case” over a softer, tougher core As a rough indication, a carburized depth of about 0.030 to 0.050 inch can be obtained in about 4 hours at 1,700°F, depending upon the type of carburizing agent, which may be a solid, liquid, or gas 43

An Example of Improving The Material Behavior Heat Treatment of Steel – Case Hardening (Cyaniding) Carbon and nitrogen both are introduced into the surface layers of the low-carbon steel by following process: Steel is heated in a molten bath of cyanide carbonatechloride salts Quenched in brine, water, or mineral oil Temperature of operation is generally within the range of 1,550° to 1,600°F The depth of the case is a function of time, temperature, and composition of the cyanide bath The time of immersion usually varies from 15 minutes to 2 hours The maximum case depth is rarely more than about 0.020 inch and the average depth is considerably less 44

An Example of Improving The Material Behavior Heat Treatment of Steel – Case Hardening (Nitriding) Nitrogen is introduced into the surface of the steel through following process The piece is heated between 950° and 1,200°F and, at the same time, is exposed to ammonia gas The heat of the furnace causes the ammonia to break down into nitrogen and hydrogen Some of the nitrogen combines with the elements in the steel to form chemical compounds called nitrides in the outer layer of the steel Nitriding makes the steel surface hard and wear resistant 45

MATERIAL SCIENCE AND ENGINEERING Next Topic (Tentative)

Ceramic Materials

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