1ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldMicrostructure-Properties: IMaterials Properties:Strength, Ductility27-301Lecture 3Fall, 2007Profs. A. D. Rollett,M. de GraefMicrostructure PropertiesProcessingPerformance2ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldObjective• The objective of this lecture is to remind you of what amaterial property is.• Strength and ductility are defined and used to illustrate therelationship between materials properties and microstructure.• The measurement of a “stress-strain” curve is described.• More specifically, this lecture explains the “Taylor Equation”that relates yield strength to dislocation content of a material(and other obstacles to dislocation flow): σy = M α G b √ρLook at www.steeluniversity.org, orhttp://www.steeluniversity.org/content/html/eng/default.asp?catid=1&pageid=1016899460,and specifically “Tensile Test”, “Hardness Test”, for self-learning guides3ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldNotationL, l := specimen lengthε := strainG (or µ) := shear modulusb := Burgers vectorr := Particle size (radius)f ≡VV(α) := volume fraction (of precipitates)σ := stress (macroscopic)τ := shear stress (critical value, in some cases)u := displacementA := area (cross section of specimen)α := geometrical constant (~1)φ := angle between dislocation and line perpendicular to the obstacle line<L3> := mean intercept length (of precipitates)λ := mean spacing (of dislocations, precipitates)F := forceA := area (cross section of specimen)m := Schmid factorM := Taylor factor∆2 := nearest neighbor distanceλ, φ := angles between tensile axis and slip direction, slip plane normal,respectively4ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldKey Concepts• Stress, yield strength, typical values, extreme values• Strain, engineering versus logarithmic strain• Stress-strain curves• Ductility, necking limit, relationship to hardening parameters,Considère’s Criterion• Dislocation loops, obstacle spacings• Critical resolved shear stress, relationship to shear modulus• Schmid factors, average Taylor factor for polyxtal5ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldWhat is a Material Property?• A Material Property is some quantifiable behavior ofa material.• For a property to be a material property, it shouldbe a characteristic of the material, not theconfiguration in which it is used.• Example: the load carrying capacity of a beamdepends on the cross-section of the beam,therefore is not a material property.• The yield strength is a material property because itis the same no matter how the material is tested.6ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldProperties & Microstructure• Why are [some] properties dependent on microstructure?• Many properties are controlled by the propagation of defectswithin the material.• The defect propagation is an example of a mechanism thatcontrols the property.• Example: yield strength measures the resistance to plasticflow, which is controlled by the mechanism of dislocationmotion. Dislocations are line defects whose motion is moresensitive to precipitates, grain boundaries etc. than to thelattice. The latter constitutes microstructure, as previouslydiscussed.7ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldIssues, new ideas, so far• The following new ideas or concepts have beenintroduced.1. Strength2. Hardness3. Ductility4. Military non-diffusional transformations5. Martensite (a lower symmetry crystal structure,formed as a result of a military transformation)6. The Fe-C phase diagram (not completely new)7. Diffusional transformations, decomposition8. Pearlite (a two-phase structure, formed as a resultof a diffusional transformation)9. TemperingPropertiesProcesses8ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldStrength• Strength is very basic to the value of a structural material. Wemeasure it in terms of force per unit area: σ = F/A• Strength means resistance to irreversible deformation or, ifyou prefer, the upper limit of elastic stress that is safe to applyto a material.• Strength is highly dependent on microstructure because it isproportional to the difficulty of moving dislocations through(and between) the grains.• Typical values? Most useful structural metals have strengthsin the range 100-1000 MPa; ultra-high strength steel wire canbe produced up to 5,500 MPa!• Engineers are often taught strength as being related to(chemical) composition. Materials engineers studystrengthening mechanisms and therefore understand how tocontrol strength.• Strength is typically measured in a tension test, but we willalso examine this test when we discuss ductility.9ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldComparisons••SOFTSOFT: Lead piping(Roman!)• HARD: Comparison of highstrength (pearlitic) steels,used for bridges, tyre cord“Processing and mechanical behaviorof hypereutectoid steel wires, D.Lesuer et al., Metallurgy, Processingand Applications of Metal Wires, TMS,1996.http://www.time-travellers.org/Historian/Rome2001/romephotos.html www.www.brantacanbrantacan.co..co.ukuk/ suspension./ suspension.htmhtm10ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldTypes of Strength• Later in the course, we will study stress and strength as tensorquantities. For now, we will treat them as scalar quantities,i.e. a single number.• There are different modes of loading materials:– Yield Strength: ambient conditions, low strain rate– Dynamic Strength: ambient conditions, high strain rate– Creep Strength: high temperature strength, low strain rate– Torsion Strength: strength in twisting– Fatigue Strength: alternating stresses• The strength value is highly dependent on the loading mode.• Each type of strength is controlled by a variety ofstrengthening mechanisms.11ObjectiveExampleStrengthHardnessDuctilityOrowanBowingSingleCrystalYieldPolyxtalYieldYield strength• A yield strength is boundary between elastic andplastic flow.σ=0 σelasticplasticExample: tensile stressσ=