Presentation on theme: "Chapter 6. Mechanical Behavior"— Presentation transcript:
1 Chapter 6. Mechanical Behavior Stress versus StrainElastic DeformationPlastic DeformationHardnessCreep and Stress RelaxationViscoelastic Deformation
2 Stress versus Strain Mechanical Properties Deal directly with behavior of materials under applied forces.Properties are described by applied stress and resulting strain, or applied strain and resulting stress.Example: 100 lb force applies to end of a rod results in a stress applied to the end of the rod causing it to stretch or elongate, which is measured as strain.Strength: ability of material to resist application of load without rupture.Ultimate strength- maximum force per cross section area.Yield strength- force at yield point per cross section area.Other strengths include rupture strength, proportional strength, etc.Stiffness: resistance of material to deform under load while in elastic state.Stiffness is usually measured by the Modulus of Elasticity (Stress/strain)Steel is stiff (tough to bend). Some beds are stiff, some are soft (compliant)
3 Testing Procedures Primary types of tests Mechanical Testing Properties that deal with elastic or inelastic behavior of a material under loadPrimary measurements involved are load applied and effects of load applicationTwo classification of tests; method of loading and the condition of the specimen during the testPrimary types of testsTensileCompressionShearTorsionFlexure
4 Mechanical Test Considerations Principle factors are in three main areasmanner in which the load is appliedcondition of material specimen at time of testsurrounding conditions (environment) during testingTests classification- load applicationkind of stress induced. Single load or Multiple loadsrate at which stress is developed: static versus dynamicnumber of cycles of load application: single versus fatiguePrimary types of loadingshearcompressiontensiontorsionflexure
5 Standardized Testing Conditions Moisture100F, 100% R.H.1 Day, 7 Days, 14 DaysTemperatureRoom Temperature: Most commonElevated Temperature: Rocket enginesLow Temperature: Automotive impactSalt spray for corrosionRocker Arms on cars subject to immersion in NaCl solution for 1 Day and 7 Days at Room Temperature and 140 F.Acid or Caustic environmentsTensile tests on samples after immersion in acid/alkaline baths.
6 StressStress: Intensity of the internally distributed forces or component of forces that resist a change in the form of a body.Tension, Compression, Shear, Torsion, FlexureStress calculated by force per unit area. Applied force divided by the cross sectional area of the specimen.Stress unitsPascals = Pa = Newtons/m2Pounds per square inch = Psi Note: 1MPa = 1 x106 Pa = 145 psiExampleWire 12 in long is tied vertically. The wire has a diameter of in and supports 100 lbs. What is the stress that is developed?Stress = F/A = F/r2 = 100/( * )= 12,739 psi = MPa
7 Stress10in1 in0.1 inExampleTensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the stress that is developed? What is the Load?Stress = F/A = F/(width*thickness) = 100lbs/(1in*.1in )= 1,000 psi = 1000 psi/145psi = MpaLoad = 100 lbsBlock is 10 cm x 1 cm x 5 cm is mounted on its side in a test machine. The block is pulled with 100 N on both sides. What is the stress that is developed? What is the Load?Stress = F/A = F/(width*thickness) = 100N/(.01m * .10m )= 100,000 N/m2 = 100,000 Pa = 0.1 MPa= 0.1 MPa *145psi/MPa = 14.5 psiLoad = 100 N100 lbs1 cm10cm5cm
8 Strain % Elongation = strain x 100% lF l0 Strain: Physical change in the dimensions of a specimen that results from applying a load to the test specimen.Strain calculated by the ratio of the change in length and the original length. (Deformation)Strain units (Dimensionless)When units are given they usually are in/in or mm/mm. (Change in dimension divided by original length)% Elongation = strain x 100%l0lF
9 Strain10in1 in0.1 inExampleTensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the strain that is developed if the bar grows to 10.2in? What is % Elongation?Strain = (lf - l0)/l0 = ( )/(10) = 0.02 in/inPercent Elongation = 0.02 * 100 = 2%Block is 10 cm x 1 cm x 5 cm is mounted on its side in a test machine. The block is pulled with 1000 kN on bone side. If the material elongation at yield is 1.5%, how far will it grow at yield?Strain = Percent Elongation /100 = 1.5%/100 = cm /cmStrain = (lf - l0)/l0 = (lf -5)/(5) = cm/cmGrowth = 5 * = cmFinal Length = cm100 lbs1 cm10cm5cm
10 Strain Lateral Strain Axial Strain Permanent set is a change in form of a specimen once the stress ends.Axial strain is the strain that occurs in the same direction as the applied stress.Lateral strain is the strain that occurs perpendicular to the direction of the applied stress.Poisson’s ratio is ratio of lateral strain to axial strain. Poisson’s ratio = lateral strainaxial strainExampleCalculate the Poisson’s ratio of a material with lateral strain of and an axial strain of 0.006Poisson’s ratio = 0.002/0.006 = 0.333LateralStrainAxialStrainNote: For most materials, Poisson’s ratio is between 0.25 and 0.5Metals: 0.29 (304 SS) to 0.3 (1040 steel) to 0.35 (Mg)Ceramics and Glasses: 0.19 (TiC) to 0.26 (BeO) to 0.31 (Cordierite)Plastics: 0.35 (Acetals) to 0.41 (Nylons)
11 Stress-Strain Diagrams EquipmentStrainometers: measures dimensional changes that occur during testingextensometers, deflectometers, and compressometers measure changes in linear dimensions.load cells measure loaddata is recorded at several readings and the results averaged, e.g., 10 samples per second during the test.
12 Stress-Strain Diagrams Stress-strain diagrams is a plot of stress with the corresponding strain produced.Stress is the y-axisStrain is the x-axisStressStrainLinear(Hookean)Non-Linear(non-Hookean)
13 StiffnessStiffness is a measure of the materials ability to resist deformation under load as measured in stress.Stiffness is measures as the slope of the stress-strain curveHookean solid: (like a spring) linear slopesteelaluminumironcopperAll solids (Hookean and viscoelastic)metalsplasticscompositesceramics
14 ModulusModulus of Elasticity (E) or Young’s Modulus is the ratio of stress to corresponding strain (within specified limits).A measure of stiffnessStainless Steel E= 28.5 million psi (196.5 GPa)Aluminum E= 10 million psiBrass E= 16 million psiCopper E= 16 million psiMolybdenum E= 50 million psiNickel E= 30 million psiTitanium E= 15.5 million psiTungsten E= 59 million psiCarbon fiber E= 40 million psiGlass E= 10.4 million psiComposites E= 1 to 3 million psiPlastics E= 0.2 to 0.7 million psi
15 Modulus Types Modulus: Slope of the stress-strain curve Initial Modulus: slope of the curve drawn at the origin.Tangent Modulus: slope of the curve drawn at the tangent of the curve at some point.Secant Modulus: Ratio of stress to strain at any point on curve in a stress-strain diagram. It is the slope of a line from the origin to any point on a stress-strain curve.StressStrainInitial ModulusTangent ModulusSecant Modulus
16 Compression Testing Principles Universal test machine (UTM) Stress l0 Compression results from forces that push toward each other.Specimens are short and large diameter.Circular cross section is recommended.Length to diameter ratio is important considerationUniversal test machine (UTM)Size and load of compression machine are specially built.Load and compression amount are measured.StressForce per unit area. Applied force divided by the cross sectional area of the specimen.Strain calculated by the ratio of the change in length and the original length. (Deformation)lFl0
17 Expected Results Similar Stress-strain curve as tensile testing Stress
18 Shear Testing Principles Direct shear occurs when parallel forces are applied in the opposite direction.Single shear occurs on a single plane.Double shear occurs on two planes simultaneously.
19 Shear Testing Principles Universal test machine (UTM) Torsional shearing forces occur when the forces applied lie in parallel but opposite directions. Twisting motion.Torsional forces developed in a material are the result of an applied torque.Torque is Forces x distance..Universal test machine (UTM)Special fixtures are needed to hold the specimen.One end of the specimen is placed in a fixture that applies torsional load and the other end is connected to a tropometer, which measures the detrusion (load and deflection or twist)
20 Expected Results Similar Stress-strain curve as tensile testing Stress
21 Bend of Flexure Testing PrinciplesBending forces occur when load is applied to a beam or rod that involves compression forces on one side of a beam and tensile forces on the other side.Deflection of a beam is the displacement of a point on a neutral surface of a beam from its original position under action of applied loads.Flexure is the bending of a material specimen under load.Strength that material exhibits is a function of the flexural modulus of the material and the cross-sectional geometry.Example, rectangular beam of 1” x 4” (W) will exhibit higher flexural strength than a 2” by 2” square beam of the same material modulus.Properties are the same as in tensile testing.Strength, deflection, modulus, ultimate strength, etc.Specimen is loaded in a 3-point bending testbottom goes in tension and the top goes in compression.Failure analysis can provide information as the type of failure,either tension or compression failure,buckle prior to failure,condition of fracture, e.e., rough, jagged, or smooth.
22 Equipment Universal test machine (UTM) Special fixtures are needed to hold the specimen.PrecautionsSpecimen length should be 6 to 12 times the width to avoid shear failure or buckling.Areas of contact with the material under test should be such that unduly high stress concentrations are avoided.Longitudinal adjustments are necessary for the supports.Lateral rotational adjustments should be provided to prevent torsional stresses.The parts should be arranged to be stable under load.
23 Expected Results Similar Stress-strain curve as tensile testing Stress
24 Impact Testing Principles Materials exhibit different properties depending on the rate at which a load is applied and the resulting strain that occurs.If a load is applied over a long period of time (static test)the material can withstand greater loads than if the test is applied rapidly (dynamic).Properties of materials are stain dependent.Standardized tests are used to determine the amount of energy required to break a material in impact tests.Outcome of impact tests is to determine the amount of energy needed to break a sample.
25 Impact Testing Principles Energy absorbed in several ways Elastic deformation of the members or parts of a system.Plastic deformation.Hysteresis effects.Frictional actioneffects of inertia on moving parts.Energy is defined as the ability to do work. E =W = F*DWork is Force times distance moved.Energy of a dropped object hitting a specimen isE = w*h Energy is weight times height dropped.E = m*g*h (metric) Energy is mass times gravity acceleration times height.
26 Equipment Impact Testing Equipment Izod and Charpy are the most common tests.Both employ a swinging pendulum and conducted on small notched specimens. The notch concentrated the load at a point causing failure. Other wise without the notch the specimen will plastically deform throughout.They are different in the design of the test specimen and the velocity at which the pendulum strikes the specimen.Charpy: the specimen is supported as a single beam and held horizontally. Impacted at the back face of the specimen.Izod: the specimen is supported as a cantilever and help vertically. Impacted at front face of the specimen.Figure 19-1
27 Impact TestIn standard testing, such as tensile and flexural testing, the material absorbs energy slowly.In real life, materials often absorb applied forces very quickly: falling objects, blows, collisions, drops, etc.A product is more likely to fail when it is subjected to an impact blow, in comparison to the same force being applied more slowly.The purpose of impact testing is to simulate these conditions.
28 Impact TestImpact testing is testing an object's ability to resist high-rate loading.An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocity.Most of us think of it as one object striking another object at a relatively high speed.Impact resistance is one of the most important properties for a part designer to consider, and without question the most difficult to quantify.The impact resistance of a part is, in many applications, a critical measure of service life. More importantly these days, it involves the perplexing problem of product safety and liability.One must determine:1.the impact energies the part can be expected to see in its lifetime, the type of impact that will deliver that energy, and then select a material that will resist such assaults over the projected life span.Molded-in stresses, polymer orientation, weak spots (e.g. weld lines or gate areas), and part geometry will affect impact performance.Impact properties also change when additives, e.g. coloring agents, are added to plastics.
29 Impact TestMost real world impacts are biaxial rather than unidirectional.Plastics, being anisotropic, cooperate by divulging the easiest route to failure.Complicated choice of failure modes: Ductile or brittle.Brittle materials take little energy to start a crack, little more to propagate it to a shattering climax.Highly ductile materials fail by puncture in drop weight testing and require a high energy load to initiate and propagate the crack.Many materials are capable of either ductile or brittle failure, depending upon the type of test and rate and temperature conditions.They possess a ductile/brittle transition that actually shifts according to these variables.For example, some plastic food containers are fine when dropped onto the floor at room temperature but a frozen one can crack when dropped.
30 Expected Results Charpy Test Procedure Capacity of 220 ft-lb for metals and 4 ft-lbs for plasticsPendulum swings at 17.5 ft/sec.Specimen dimensions are 10 x 10 x 55 mm, notched on one side.ProcedurePendulum is set to angle, , and swings through specimen and reaches the final angel, . If no energy given then = .Energy is
31 Expected Results Izod Test Procedure Capacity of 120 ft-lb for metals and 4 ft-lbs for plasticsImpacted at the front face of the specimen.Specimen dimensions are 10 x 10 x 75 mm, notched on one side.ProcedurePendulum is set to angle, , and swings through specimen and reaches the final angel, . If no energy given then = .Energy is
32 Fundamentals of Hardness Hardness is thought of as the resistance to penetration by an object or the solidity or firmness of an objectResistance to permanent indentation under static or dynamic loadsEnergy absorption under impact loads (rebound hardness)Resistance toe scratching (scratch hardness)Resistance to abrasion (abrasion hardness)Resistance to cutting or drilling (machinability)Principles of hardness (resistance to indentation)indenter: ball or plain or truncated cone or pyramid made of hard steel or diamondLoad measured that yields a given depthIndentation measured that comes from a specified loadRebound height measured in rebound test after a dynamic load is dropped onto a surface
33 Hardness Mechanical Tests Brinell Test MethodOne of the oldest testsStatic test that involves pressing a hardened steel ball (10mm) into a test specimen while under a load of3000 kg load for hard metals,1500 kg load for intermediate hardness metals500 kg load for soft materialsVarious types of BrinellMethod of load application:oil pressure, gear-driven screw, or weights with a leverMethod of operation: hand or electric powerMethod of measuring load: piston with weights, bourdon gage, dynamoeter, or weights with a leverSize of machine: stationary (large) or portable (hand-held)
34 Brinell Test Conditions Brinell Test Method (continued)MethodSpecimen is placed on the anvil and raised to contact the ballLoad is applied by forcing the main piston down and presses the ball into the specimenA Bourbon gage is used to indicate the applied loadWhen the desired load is applied, the balance weight on top of the machine is lifted to prevent an overload on the ballThe diameter of the ball indentation is measured with a micrometer microscope, which has a transparent engraved scale in the field of view
35 Brinell Test Example Brinell Test Method (continued) Units: pressure per unit areaBrinell Hardness Number (BHN) = applied load divided by area of the surface indenterWhere: BHN = Brinell Hardness NumberL = applied load (kg)D = diameter of the ball (10 mm)d = diameter of indentation (in mm)Example: What is the Brinell hardness for a specimen with an indentation of 5 mm is produced with a 3000 kg applied load.Ans:
36 Brinell Test Method (continued) Range of Brinell Numbers90 to 360 values with higher number indicating higher hardnessThe deeper the penetration the higher the numberBrinell numbers greater than 650 should not be trusted because the diameter of the indentation is too small to be measured accurately and the ball penetrator may flatten out.Rules of thumb3000 kg load should be used for a BHN of 150 and above1500 kg load should be used for a BHN between 75 and 300500 kg load should be used for a BHN less than 100The material’s thickness should not be less than 10 times the depth of the indentation
37 Advantages & Disadvantages of the Brinell Hardness Test Well known throughout industry with well accepted resultsTests are run quickly (within 2 minutes)Test inexpensive to run once the machine is purchasedInsensitive to imperfections (hard spot or crater) in the materialLimitationsNot well adapted for very hard materials, wherein the ball deforms excessivelyNot well adapted for thin piecesNot well adapted for case-hardened materialsHeavy and more expensive than other tests ($5,000)
38 Rockwell TestHardness is a function of the degree of indentation of the test piece by action of an indenter under a given static load (similar to the Brinell test)Rockwell test has a choice of 3 different loads and three different indentersThe loads are smaller and the indentation is shallower than the Brinell testRockwell test is applicable to testing materials beyond the scope of the Brinell testRockwell test is faster because it gives readings that do not require calculations and whose values can be compared to tables of results (ASTM E 18)
39 Rockwell Test Description Specially designed machine that applies load through a system of weights and leversIndenter can be 1/16 in hardened steel ball, 1/8 in steel ball, or 120° diamond cone with a somewhat rounded point (brale)Hardness number is an arbitrary value that is inversely related to the depth of indentationScale used is a function of load applied and the indenterRockwell B- 1/16in ball with a 100 kg loadRockwell C- Brale is used with the 150 kg loadOperationMinor load is applied (10 kg) to set the indenter in materialDial is set and the major load applied (60 to 100 kg)Hardness reading is measuredRockwell hardness includes the value and the scale letter
40 Rockwell ValuesB Scale: Materials of medium hardness (0 to 100HRB) Most CommonC Scale: Materials of harder materials (> 100HRB) Most CommonRockwell scales divided into 100 divisions with each division (point of hardness) equal to 0.002mm in indentation. Thus difference between a HRB51 and HRB54 is 3 x mm mm indentationThe higher the number the harder the number
41 Rockwell and Brinell Conversion For a Rockwell C values between -20 and 40, the Brinell hardness is calculated byFor HRC values greater than 40, useFor HRB values between 35 and 100 use
42 Rockwell and Brinell Conversion For a Rockwell C values, HRC, values greater than 40,Example,Convert the Rockwell hardness number HRc 60 to BHN
43 Form of Polymers Melt Temp Rubbery Increasing Temp Glassy Polymer Form Thermoplastic Material: A material that is solid, that possesses significant elasticity at room temperature and turns into a viscous liquid-like material at some higher temperature. The process is reversiblePolymer Form as a function of temperatureGlassy: Solid-like form, rigid, and hardRubbery: Soft solid form, flexible, and elasticMelt: Liquid-like form, fluid, elasticTempGlassyRubberyMeltPolymerFormIncreasing TempTmTg
44 Glass Transition Temperature, Tg Glass Transition Temperature, Tg: The temperature by which:Below the temperature the material is in an immobile (rigid) configurationAbove the temperature the material is in a mobile (flexible) configurationTransition is called “Glass Transition” because the properties below it are similar to ordinary glass.Transition range is not one temperature but a range over a relatively narrow range (10 degrees). Tg is not precisely measured, but is a very important characteristic.Tg applies to all polymers (amorphous, crystalline, rubbers, thermosets, fibers, etc.)
45 Glass Transition Temperature, Tg Glass Transition Temperature, Tg: Defined asthe temperature wherein a significant the loss of modulus (or stiffness) occursthe temperature at which significant loss of volume occursModulus(Pa)or(psi)Temperature-50C50C100C150C200C250CTgTemperature-50C50C100C150C200C250CAmorphousCrystallineTgVol.
46 Crystalline Polymers: Tm MeltTm: Melting TemperatureT > Tm, The order of the molecules is random (amorphous)Tm >T >Tg, Crystallization begins at various nuclei and the order of the molecules is a mixture of crystals and random polymers (amorphous). Crystallization continues as T drops until maximum crystallinity is achieved. The amorphous regions are rubbery and don’t contribute to the stiffness. The crystalline regions are unaffected by temperature and are glassy and rigid.T < Tg, The amorphous regions gain stiffness and become glassyTmTempRubberyDecreasing TempTgGlassyPolymer Form
48 Temperature Effects on Specific Volume T > Tm, The amorphous polymer’s volume decreases linearly with T.Tm > T >Tg, As crystals form the volume drops since the crystals are significantly denser than the amorphous material.T < Tg, the amorphous regions contracts linearly and causes a change in slope-50C50C100C150C200C250CAmorphousCrystallineTgSpecificVolumeTemperature
49 ElastomersElastomers are rubber like polymers that are thermoset or thermoplasticbutyl rubber: natural rubberthermoset: polyurethane, siliconethermoplastic: thermoplastic urethanes (TPU), thermoplastic elastomers (TPE), thermoplastic olefins (TPO), thermoplastic rubbers (TPR)Elastomers exhibit more elastic properties versus plastics which plastically deform and have a lower elastic limit.Rubbers have the distinction of being stretched 200% and returned to original shape. Elastic limit is 200%
50 RubbersRubbers have the distinction of being stretched 200% and returned to original shape. Elastic limit is 200%Natural rubber (isoprene) is produced from gum resin of certain trees and plants that grow in southeast Asia, Ceylon, Liberia, and the Congo.The sap is an emulsion containing 40% water & 60% rubber particlesVulcanization occurs with the addition of sulfur (4%).Sulfur produces cross-links to make the rubber stiffer and harder.The cross-linkages reduce the slippage between chains and results in higher elasticity.Some of the double covalent bonds between molecules are broken, allowing the sulfur atoms to form cross-links.Soft rubber has 4% sulfur and is 10% cross-linked.Hard rubber (ebonite) has 45% sulfur and is highly cross-linked.
51 Vulcanizable Rubber Typical tire tread Typical shoe sole compound Natural rubber smoked sheet (100),sulfur (2.5) sulfenamide (0.5), MBTS (0.1), strearic acid (3), zinc oxide (3), PNBA (2), HAF carbon black (45), and mineral oil (3)Typical shoe sole compoundSBR (styrene-butadiene-rubber) (100) and clay (90)Typical electrical cable coverpolychloroprene (100), kaolin (120), FEF carbon black (15) and mineral oil (12), vulcanization agent
52 Thermoplastic Elastomers PolyurethanesHave a hard block segment and soft block segmentSoft block corresponds to polyol involved in polymerization in ether basedHard blocks involve the isocyanates and chain extendersPolyesters are etheresters or copolyester thermoplastic elastomerSoft blocks contain ether groups are amorpous and flexibleHard blocks can consist of polybutylene terephthalate (PBT)Polyertheramide or polyetherblockamide elastomerHard blocks consits of a crystallizing polyamideSoftHard
53 Testing Elastomers Modulus is low for elastomers and rubbers Fig 6-47, 6-48, 6-50Modulus depends uponCrosslinking = modulusTemp = modulusRubbers havelarge rubber regionLarge elastic componentCan test over and over againWith same resultsModulus(Pa)or(psi)Temperature-50C50C100C150C200C250CHeavy crosslinkingMedium crosslinkingLow crosslinkingTgTmModulus(Pa)or(psi)Rubbery RegionTmTgTroomStress(Pa)or(psi)StrainHigh modulusLow modulus
54 Glasses and Ceramics Thermal Viscosity- materials resistance to flowViscosity of glasses are between 50 and 500 P, whereas viscosity of water and liquid metals are 0.01pViscosity of soda-lime glass from 25C to 1500C. (Fig 6-42)Melting range is between 1200 and 1500CWorking range is between 700 and 900 CAnnealing PointInternal stresses can be relievedSoftening point at 700CViscosity = PGlass transitionOccurs around annealing pointTemperature, CLogViscosity(poise)500100015002015105Annealing PointAnnealing RangeWorking RangeMelting Range
55 Glasses and Ceramics Stresses Thermal stresses occur during production of tempered glass.Fig 6-43High breaking strength of product is due to residual compressive stress at the material surfaces.Above TgNo tension or compressionAir quenched surface below TgCompression on surface tension on the bottomSlow cool to room temperatureSurface compression forces on tension inside.
56 Long Term Static Loading: Creep Measures the effects of long-term application of loads that are below the elastic limit if the material being tested.Creep is the plastic deformation resulting from the application of a long-term load.Creep is affected by temperatureCreep procedureHold a specimen at a constant elevated temperature under a fixed applied stress and observe the strain produced.Test that extend beyond 10% of the life expectancy of the material in service are preferred.Mark the sample in two locations for a length dimension.Apply a loadMeasure the marks over a time period and record deformation.
57 Creep Results Creep versus time Fixed lF l0 Tertiary Creep Constant LoadFixedCreep(in/in)Time (hours)Primary CreepSecondary CreepTertiary Creep
58 Short Term Conventional Testing TearFlexible plastics and elastomers often fail in a tearing mode and their resistance to tearing is often inadequately reflected in tensile strengthStandard tear tests involve a variety of test specimen geometries (angle tear, trouser tear, etc.) Figure 4.12Conducted on a Universal testing machine or specialized equipInvolve a cut, slit, or nick which is made before the test.Biaxial stressDeveloped when a circular diaphragm, pipe, or container is subjected to pressure (Fig 4.13)Basis for quick-burst tests.The pressure at failure (rupture), or the stress is measured
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