Measuring the Creep of Lead

This laboratory explores the phenomenon of front crawl. fawn is a slow continuous optical aberration within a material in response to increasing time, a constant utilize seek and an elevation temperature. Here in this laboratory lead is chosen as the try metal as it is shown to have poor resistance to loony and withal has a relatively low melting temperature.ApplicationsEngineers argon interested in the bootlick properties and stability of materials when roleing specific parts and assemblies. Creep gondolas such(prenominal) as the one utilise in the laboratory are use by Engineers to determine these material properties.Creep causes many problems to the Engineer in design. They need to determine that the materials they use impart stay within the call for move limits for the lifetime of the cistron.Creep is peculiarly important in the design components that need to withstand superior temperatures. Creep ordain pass off in metals at a faster place as the temperat ure developments. These design considerations inclination into four diametrical applications1Displacement limited applications are where dimensions must be precise with small clearances and little error. The small clearances must be maintained at high temperatures. An example of this type of application is in the turbine rotors of greens engines.Rupture limited applications are where precise dimensions are not particularly essential. However it is essential that fracture stick outnot occur to the material. An example of this is the need for high pressure steam tubes and pipes to withstand any break in their structure. emphasis relaxation limited applications are needed where the initial tension in component relaxes with time. An example of where this application occurs is in the pretensioning of cables on bridges or in the pretensioning of bolts.Buckling limited applications of quail are needed in slight columns or panels which carry compressive charge ups. An example of th is type of application would be in a structural steel range that is exposed to fire.ObjectivesThe objective is to witness the snarf properties in lead. To achieve this spook tests are performed on lead ideals. Three fawn tests are carried out using three different lead exemplars. The load is varied in each of the three tests and observations are made on the results.TheoryCreepCreep is a time dep balanceent deformation that occurs under a constant utilize load and temperature. The vagabond of cower is influenced by temperature and shade generally occurs at a high temperature. Creep then is a function of stress, time and temperature.The lowest temperature at which snarf foundation occur in a given material is generally , where Tm is the melting temperature of the material in degrees Kelvin.Total engineering creep human body preempt be expressed by the following linguistic ruleWhere is the theoretical stress, is the change in the materials length and is the materials or iginal length.The demarcation rate describes the rate of change in the strain of a material with compliancy to time.Where is the strain rate is the change in strain and is the change in time.The rate of deformation caused by creep is called the creep rate. The creep rate for a material with a constant stress and constant temperature stool be calculated using the following formulaSteady defer Creep tellWhere Q is the activation energy n is the stress counselor A is a material constant R it the universal accelerator constant and T is the temperature in degrees Kelvin.The activation energy Q can be determined try outally, by plotting the natural put down of creep rate against the interactional of temperature. The gradient of the subsequent dispose is equal to.Fig. 1 Natural pound of strain rate against reciprocal of temperature. 2For this try out we are using a constant temperature for the three specimens. The Arrhenius equality can then be simplify to give a power law r elationshipWhere A is a constant that depends on the given material.Rearranging this equation the material constant A can be foundThe value of A can excessively be found by plotting the natural log of the strain order against the natural log of the applied stress values. Here the value of A is equal to the forceial of the intercept of the bourne created by this plot.The stress exponent n can be determined by plotting the natural log of the strain rate against the natural log of the applied stress. The gradient of this cant over is equal to the stress exponent n.Fig. 2 Natural log of strain rate against natural of applied stress 2The stress component n is defined by the following equationStages of CreepPrimary creep occurs at the initial bes of creep. In this tier the strain rate is relatively higher and then begins to gradually strike.Secondary creep is likewise called the perk up nominate creep point. This occurs after the primary creep stage and the creep rate changes to a constant. In this stage there is no increase or decrease in the creep rate.Tertiary creep is the finale stage of creep. The creep rate moves from the brace state of the secondary stage to a continuous increase. The creep rate progressively increases until the material reaches its pause point and it shoots.MaterialsFig. 3 Analogue Creep Testing Machine not used in experiment 3* Lever-arm creep scrutiny machine.* Various dead-weight quite a little. For this experiment there were 1.0, 1.2 and 1.4 kg masses.* Various lead creep specimens compatible with the creep scrutiny machine. Similar to that in Fig. 4.* Linear Variable Displacement Transducer in finish off with the open up.* Analogue to Digital convertor in the form of a PCI card.* Data logging computer program.* Computer.Because the creep testing machine uses a lever similar to that in Fig. 3, a mechanical advantage takes place. This inevitably to be taken into consideration when analysing the results. The lever in the creep testing machine in the experiment has an 81 mechanical advantage.The machine pictured in Fig. 3 uses an analogue dial for evidenceing displacement. The creep testing machine used in this experiment uses an LVDT transducer. This is in contact with the lever and sends displacement info to the A/D card in the form of electrical signals.Fig. 4 Lead Creep Specimen 4 regularity* The three lead specimens are measured for their length and cross sectional area. For the first of the three tests, a 1kg load level is selected.* The top end of the first specimen is installed in the top grip of the creep testing machine.* The bottom end of the specimen is installed in the lower grip of the creep testing machine.* The creep testing machine is zeroed. In this experiment zeroing wasnt possible so the recorded displacement results were offset by 6.039. This was remedied by adding 6.039 to all recorded displacements.* The data logger program is started while choosing an admit file na me. For this experiment data1.txt was chosen for the first specimen.* The load is now applied to the specimen in the creep machine. The data logger go away record the elapsing time and the deformation in the specimen.* The specimen will eventually rupture payable to the increasing creep and at this stage pressing furlough in the program will end the logging.* For the second specimen a load of 1.2kg is selected. A different filename is chosen in the data logger program. For this experiment data2.txt was chosen for the second specimen.* The process is repeated until the specimen fails.* For the third and last specimen a 1.4 kg load is chosen. once more a different filename is selected in the data logger program. For this experiment data3.txt was chosen for the third specimen.* The process is repeated for the last time until the specimen fails.* The results are then analysed as described below.ResultsFig. 5 Specimen 1 product line against condemnation with 1kgFig. 6 Specimen 2 Strain against Time with 1.2kgFig. 7 Specimen 3 Strain against Time with 1.4kgFig. 8- Specimen 1 Strain Rate against Time with 1kgFig. 9 Specimen 2 Strain Rate against Time with 1.2kgFig. 10 Specimen 3 Strain Rate against Time with 1.4kgFig. 11 Table of Values Calculated from Experimental ResultsFig. 12 Natural log of strain rate against natural of applied stress 3 specimens(a)Estimationis made of the maximum applied stress that the material can withstand considering creep of less than 1% per year.Assuming 31,536,000 seconds in a yearThe angle of the line in Fig. 12 gives the value for n. The exponential of the intercept of the line in Fig. 12 gives the value for A. Subbing for A and n and rearranging(b)Estimation is made for the maximum applied stress considering a total time to failure of more than 10 years.Again an assurance of 31,536,000 seconds in a year is taken. For the strain at failure an medium was taken from the data for specimens 1 and 2, giving 13.134.Sub bing in for A and n and rearrangingDiscussionFrom looking at the strain against time graphs, Fig. 5, 6, & 7, the different stages of creep can clearly be seen. In the primary stage the strain rate is relatively high and this can be seen visually by the steeper slope at this section on the graph. The slope in the primary stage then begins to decline indicating a decrease in the strain rate. This is despite the applied stress and temperature remaining constant. This can be explained by strain hardening occurring in the lead cod to dislocations in the crystalline structure.Looking at these graphs it can be seen that their slopes edit further to a minimum and for a time stay intimately constant. This is a visual indication of the secondary stage in the creep process where the strain rate becomes nearly constant. Here there is a recovery process in the lead collect to thermal softening. The recovery balances the effect of the strain hardening causing the strain to reach its steady s tate.At the beneficial get through side of the same graphs it can be seen that the slope increases. In Fig. 6 and Fig. 7 this is shown more clearly where the slope increases exponentially. This increase in slope after the steady state is a visual indication of the tertiary stage in creep. The increased strain rate, as visualised by the increasing slope, is caused by necking. The necking begins due to local variations in stress concentrations in the specimen due to microscopic differences, defects or impurities. After the necking the cross-sectional area of the specimen decreases resulting in rapidly increasing stress concentrations. This increases the strain rate exponentially principal to fracture.In figures 8, 9 and 10 where the strain rate is graphed against time, the secondary creep stage can be seen more clearly. Here the steady state creep rate is visualised by a straight line with a value of y = 0. In the same graphs the secondary stage is bordered by two spikes in the st rain rate. The left hand side has a smaller spike due to no work hardening having occurred and the specimens reacting to the applied load. The strain rate then decreases as discussed earlier. The right hand side shows a much larger spike due to the exponentially increasing strain rate caused by the necking.The stress component n is defined by the following equationThe stress component is then found by calculating the slope of against as seen in Fig.12. The material constant A can be found on the same graph by calculating the exponential of the intercept. Alternatively A can be found rearranging the power law equationFig. 14 Theoretical values for A against the experimental value.In Fig. 14 it can be seen the values for A when using the power law equation compared against the value of found from Fig. 12. The differences are negligible and can be explained by errors as discussed below. The results of the experiment then confirms the steady state creep law.ErrorsIf the masses are appl ied suddenly to the machine it will have a higher resulting stress on the specimen compared to a mass applied more gently. This is due to impact loading and will cause a higher deformation and creep in the specimen.The precision of the machine used in the experiment will have a result on the error. Also over time a machine needs to be calibrated. In this experiment it was not possible to calibrate the machine so this needed to be compensated in calculation later.Any vibrations on the machine or the LVDT will impact on the readings. This can occur through impact loading resulting in cyclical loading vibrations or it might be outside forces such as a put off being moved.As discussed earlier, the creep rate is impacted by temperature. Changes in temperature due to draft or other influences could result in a change in the creep rate.No two lead specimens are exactly the same. There will be minor differences due to impurities in the metal or small defects such as notches caused by wear. referable to the manufacturing of the specimens there could be minor differences in their shape and area. All of these differences will have an impact on the results.Friction in the creep testing machine will resist the stresses caused by the dead-weight masses. Ideally this friction will be at a minimum, however some friction will always still remain and this will be a root system of error. Most of this friction will be concentrated at the fulcrum of the lever arm on the creep testing machine.Electromagnetic interference in the electrical circuitry can impact on the recordings from the LVDT. Also any mould components in the system such as parasitic capacitances will also cause some interference.Rounding errors in the software or algorithmic rule or later by the user will result in cumulative errors.