Experiment 1,The measurement ofelastic modulus by tensile method1Experiment 1. The measurement of elastic modulus bystretching methodIntroductionAny object under the action of external forceoccur deformation,when thedeformation doesnot exceed a certain limit,deformation candisappear after thewithdrawal of external force, and this deformation is called elastic deformation.Whenthematerial deformselastically,the internal forcewill beproducedwithinthematerial which tend to bring the material back to its original shape.Themodulus ofelasticity commonly used in engineering technology is a physical quantity thatdescribes the degree of materials deformation and internal force density,which is ameasure of material's ability to resist elastic deformation.In this experiment we willmeasure the elastic modulus by stretching method.ExperimentalObjectives(1) Determine the elastic modulus of metal wire by stretching method.(2) Understand the principle of small length changes measurement by optical levermirror method, try to learn the specific measuring technique.(3) Learn how to process experimental data by least square method.Experimental InstrumentsElastic modulus stretcher (steel wire, optical lever apparatus composed by scale,mirror, optical lever mirror and telescope, digital tension meter, and etc.), tape,micrometer caliper and vernier caliperElastic modulus stretcher shown in fig1 was mainly composed by mounting frame,telescope system, digital tension meter and measuring tools
Experiment 1. The measurement of elastic modulus by tensile method 1 Experiment 1. The measurement of elastic modulus by stretching method Introduction Any object under the action of external force occur deformation, when the deformation does not exceed a certain limit, deformation can disappear after the withdrawal of external force, and this deformation is called elastic deformation. When the material deforms elastically, the internal force will be produced within the material which tend to bring the material back to its original shape. The modulus of elasticity commonly used in engineering technology is a physical quantity that describes the degree of materials deformation and internal force density, which is a measure of material’s ability to resist elastic deformation. In this experiment we will measure the elastic modulus by stretching method. Experimental Objectives (1) Determine the elastic modulus of metal wire by stretching method. (2) Understand the principle of small length changes measurement by optical lever mirror method, try to learn the specific measuring technique. (3) Learn how to process experimental data by least square method. Experimental Instruments Elastic modulus stretcher (steel wire, optical lever apparatus composed by scale, mirror, optical lever mirror and telescope, digital tension meter, and etc.), tape, micrometer caliper and vernier caliper. Elastic modulus stretcher shown in fig1 was mainly composed by mounting frame, telescope system, digital tension meter and measuring tools
Experiment I, The measurement of elastic modulus by tensile method2UpperclampingheadScaleSteel wireVerniercalipeMicrometereaCtapeOptical leverTelescopeDigital tensionmeterTension sensForce nutFig1-1Schematic diagramofelastic modulus system1.ExperimentalframeTheexperimental frameisthemainplatformformeasuringtheelasticmodulusofthetested wire. The wire is connected to the tension sensor through a clamping head, andthe force is applied by the rotation of force nut. The signal output of tension sensorthat represents thetension value of the wire is displayed via a digital tension meterThe pivot support of reflecting mirror of optical lever is fixed to a plate, and the reartoe is freely placed on the surface ofthe clamping head.2.TelescopeThe telescope system consists of a telescope bracket and a telescope. The telescopebracket can fine tune the telescope by adjusting the screw. The telescope has amagnification of 12 and a closest line of sight of 0.3 m. It contains eye-crossing lines(vertical andhorizontal).ThetelescopeisshowninFigure2
Experiment 1. The measurement of elastic modulus by tensile method 2 Fig 1-1 Schematic diagram of elastic modulus system 1. Experimental frame The experimental frame is the main platform for measuring the elastic modulus of the tested wire. The wire is connected to the tension sensor through a clamping head, and the force is applied by the rotation of force nut. The signal output of tension sensor that represents the tension value of the wire is displayed via a digital tension meter. The pivot support of reflecting mirror of optical lever is fixed to a plate, and the rear toe is freely placed on the surface of the clamping head. 2. Telescope The telescope system consists of a telescope bracket and a telescope. The telescope bracket can fine tune the telescope by adjusting the screw. The telescope has a magnification of 12 and a closest line of sight of 0.3 m. It contains eye-crossing lines (vertical and horizontal). The telescope is shown in Figure 2. Tension sensor Force nut Upper clamping head Optical lever Steel wire Digital tension meter Scale Telescope Vernier caliper Micrometer caliper tape
Experiment I, The measurement of elastic modulus by tensile method31. Blister mirror132. Round blister3. Round blister adiustment4. Horizontal micro adiustment5.Base106. Foot screw hand wheel7. Focusing hand wheel8. DialCrossing lines9. Objective lens10. Dial indicator11.Eyepiece12. Dust cover13. Sighting devicesFig1-2 Schematicdiagram oftelescope (Telescope appearance, cross lines, components)3.DigitaltensionmeterPowersupply:AC220V±10%，50HzDisplay range: 0~±19.99kgResolution:0.001kgZero cleaning function (Short press the clear button for zero cleaning)ContainsDCpoweroutputinterface:OutputDCpowerforpoweringthebacklightThepanel of digitaltensionmeter:ZI中数字拉力计清零传感器背光源02.86Kg120102四川世纪中科光电技术有限公司Fig1-3Thepanel of digital tensionmeterExperimental principle1. Elastic modulusAn even thickness metal wire with length I, and cross section S, and fasten its upperend, m isthe weight exerted on the lower end of the wire.Thus, F=mg is the forceexerted on the wire when it is extended by /. The force per unit area F/S is referred
Experiment 1. The measurement of elastic modulus by tensile method 3 Fig 1-2 Schematic diagram of telescope (Telescope appearance, cross lines, components) 3. Digital tension meter Power supply：AC220V±10%，50Hz Display range：0~±19.99kg Resolution：0.001kg Zero cleaning function（Short press the clear button for zero cleaning）. Contains DC power output interface: Output DC power for powering the backlight. The panel of digital tension meter： Fig 1-3 The panel of digital tension meter Experimental principle 1. Elastic modulus An even thickness metal wire with length l, and cross section S, and fasten its upper end, m is the weight exerted on the lower end of the wire. Thus, F=mg is the force exerted on the wire when it is extended by Δl. The force per unit area F/S is referred 1. Blister mirror 2. Round blister 3. Round blister adjustment 4. Horizontal micro adjustment 5. Base 6. Foot screw hand wheel 7. Focusing hand wheel 8. Dial 9. Objective lens 10. Dial indicator 11. Eyepiece 12. Dust cover 13. Sighting devices Crossing lines
Experiment 1,The measurement ofelastic modulus by tensile method4to as stress, the elongation per unit length l/l is referred to as strain. The stress F/Sis proportional to strain i/l within elastic limits. HenceF-EN(1-1)s-1This principle is known as Hooke's law, the proportional constant in this formula isreferred as elastic modulus of this material.E-F/S(1-2)/1The experiment has proven that the elastic modulus E is only depend on the materialof metal wire, which is independent of the external force, length of object I and crosssection S.According to equation (1-2), we could calculate the elastic modulus if all thequantities on the right side of the equation has been measured. The external forceapplied on the metal wire, the original length of metal wire and the cross-sectionalarea could be measured by common methods. The main problem in this experiment isthat the length change is so small, usually at the magnitude of 10-' mm, which is quitedifficult to realize the accurate measurement. In this experiment, we will measure thesmall variation of length relatively accurately via optical lever method.2.Theprincipleofoptical leverAt the beginning we assume that the scale no on the scale is imaged on the alignmentline of the telescope reticle. When the wire is stretched by Al, the rear leg of theoptical lever falls subsequntally by l, which will drive the plane mirror to rotate by, at this position, the value on the scale is imaged on the alignment line, the changein scale value n = n1 - no is proportional to l, when Al < H, is very small.ThereforeN_ An/2(1-3)b-H
Experiment 1. The measurement of elastic modulus by tensile method 4 to as stress, the elongation per unit length ∆𝑙/𝑙 is referred to as strain. The stress F/S is proportional to strain ∆𝑙/𝑙 within elastic limits. Hence l l E S F = (1-1) This principle is known as Hooke's law; the proportional constant in this formula is referred as elastic modulus of this material. l l F S E = (1-2) The experiment has proven that the elastic modulus E is only depend on the material of metal wire, which is independent of the external force, length of object l and cross section S. According to equation (1-2), we could calculate the elastic modulus if all the quantities on the right side of the equation has been measured. The external force applied on the metal wire, the original length of metal wire and the cross-sectional area could be measured by common methods. The main problem in this experiment is that the length change is so small, usually at the magnitude of 10-1 mm, which is quite difficult to realize the accurate measurement. In this experiment, we will measure the small variation of length relatively accurately via optical lever method. 2. The principle of optical lever At the beginning we assume that the scale n0 on the scale is imaged on the alignment line of the telescope reticle. When the wire is stretched by ∆𝑙, the rear leg of the optical lever falls subsequntally by ∆𝑙, which will drive the plane mirror to rotate by 𝜃, at this position, the value on the scale is imaged on the alignment line, the change in scale value ∆𝑛 = 𝑛1 − 𝑛0 is proportional to ∆𝑙, when ∆𝑙 ≪ 𝐻, 𝜃 is very small. Therefore H n b l 2 = (1-3)
Experiment I, The measurement of elastic modulus by tensile method5AnScaleLnnoHRear feetTelescopeALReflectingmirrorFigure1-4Theprinciple of optical leverWhere H is the distance between optical lever mirror and scale, b is vertical distancebetween the rear leg of the mirror and twofront legs,b is called optical lever constant,thenbN/ =(1-4).An2HSubstitute formula (1-4) into formula (1-2), we get2FIHE=(1-5)SbAnSubstut the cross-sectional area SDofthesteelwire(Disthediameterof4steelwire),thentheelasticmodulusis8FIHE=(1-6)元DbnIf the force applied on the steel wire is Fi, the corresponding readings of the scale is ni,then,81H(1-7)n,F + ng元D"bEn, is proportional to Fi, the elastic modulus E can be derived from straight line's slopethat obtained by the least squares method.Experimental Procedure1)Turn on the digital dynamometerpower switchand preheatfor10minutes.The
Experiment 1. The measurement of elastic modulus by tensile method 5 n0 H O n1 θ θ 2θ b Δl Δn N Nn Reflecting mirror Telescope Scale Rear feet Figure 1-4 The principle of optical lever Where H is the distance between optical lever mirror and scale, b is vertical distance between the rear leg of the mirror and two front legs, b is called optical lever constant, then n H b l = 2 (1-4) Substitute formula (1-4) into formula (1-2), we get Sb n FlH E = 2 (1-5) Substitute the cross-sectional area 4 2 D S = of the steel wire（D is the diameter of steel wire）, then the elastic modulus is D b n FlH E = 2 8 (1-6) If the force applied on the steel wire is Fi , the corresponding readings of the scale is ni, then, 2 0 8 F n D bE lH ni = i + (1-7) ni is proportional to Fi, the elastic modulus E can be derived from straight line's slope that obtained by the least squares method. Experimental Procedure 1）Turn on the digital dynamometer power switch and preheat for 10 minutes. The