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Q1:Suppose that you want to investigate the factors that potentially affect cooking rice. a. What would you use as a response variable that could impact the response? b. List all of the potential sources of variability that could impact the response? c. Complete the first 3 steps of the guidelines (State Problem, Identify Response, Choice of Factor) for designing experiments (from section 1.4).See Answer
Q2:What is replication? Why do we need replication in an experiment? Present an example that illustrates the differences between replication and repeated measures.See Answer
Q3:Why is randomization important in an experiment?See Answer
Q4:UNIVERSITY OF LIVERPOOL 1 Aim & Objectives The aim of this lab is to develop an appreciation of the principles of mechanical testing, in particular uniaxial tensile testing of metals and polymers, and how it is used to measure mechanical properties of materials. Upon successful completion of this lab, you will be able to: Undertake tensile testing to measure mechanical properties associated with elastic and plastic deformation; ● ● TT Lab Script // MATS105 ● ● Describe and explain qualitative aspects of mechanical properties and mechanical testing Record and present experimental data Plot graphs, and extract values. Improve technical reporting skills. The technical objective of this lab is to determine the tensile deformation behaviour of two metal samples and two polymer samples (steel, aluminium, polypropylene and Perspex acrylic) using an Instron tensile tester, and compare the mechanical properties measured with "text-book" values./n2 Introduction The uniaxial Tensile Test is a common, standard mechanical test, and is widely used in engineering. The objective of the tensile test is to measure specific mechanical properties of structural materials so that their strength, ductility, Young's modulus etc. may be compared. The mechanical properties measured by this test are often required by engineering designers undertaking various stress calculations, therefore the reliability and standardization of the measurement process is essential. In this experiment you will test four common engineering materials using an industry standard "Instron" testing machine: . . UNIVERSITY OF LIVERPOOL ● a steel, an aluminium alloy, polypropylene, and Perspex acrylic. Note acrylic is a commonly used name for polymethyl pethacrylate (PMMA) polymer. Perspex® acrylic is a tradename of Lucite International and is a premium acrylic. There are British Standard (nowadays also European Standard, or "EN") procedures which specify the precise procedure that must be adopted for tensile testing. One example is EN 10002-1 for metallic materials which says it must be undertaken at an ambient temperature between 10 °C and 35 °C, normally at a controlled temperature of 23 °C ±5 °C, and defines how the mechanical properties should be determined. This standard defines the principle of the test as "straining a test piece in tension, generally to fracture, for the purpose of determining one or more of the mechanical properties". Definitions of some material mechanical properties have been (or will be) provided to you in your lecture notes. You will also have the tensile test explained in detail at some point during lectures. But resources are also provided in case you are undertaking the lab before this time. In this TT experiment you will gradually strain (elongate) each sample incrementally, recording the sample's elongation and applied load (force) required. You will then/nSome of these mechanical property measurements are shown in the schematic strass vs strain curve in Figure 1. Stress a Yield stress 0.1% offset strain Modulus of Elasticity 0.1% proof stress E Strain Ultimate Tensile Strength Ao Ac Failing i Stress Failing Strain Figure 1: Schematic of the stress vs strain curve showing various mechanical properties that can be extracted using data obtained from tensile testing. 2.1 Apparatus You will be using an Instron testing machine. The load (force applied) is accurately measured using a load cell attached to one of the sample grips as you manually extend the samples, and displayed on the PC in Newtons. When undertaking tensile testing in industry, the strain would normally be measured very accurately using a strain gauge glued to the test sample surface (https://en.wikipedia.org/wiki/Strain gauge), or a "clip-on" or "digital sensor arm" extensometer attached to the sample being tested https://en.wikipedia.org/wiki/Extensometer. However in this lab you will not have strain gauges or extensometers available, you so will be making a much more inaccurate measurement of the strain by simply measuring the elongation of the whole test sample (the increase in separation of the grips holding each end of the test sample) and dividing that by the original gauge length of the test sample. This tends to result in measurements of strain greater than the correct value due to various reasons (sample slippage in the grips, tensioning of the joints in the system etc), particularly at the start of the test. A consequence can be that the values of Young's modulus that you obtain from your stress vs. strain curves may be up to an order of magnitude too low, whist your values of yield stress and ultimate tensile stress can be very accurate, and you will investigate this as part of the practical./nTT Lab Script // MATS105 UNIVERSITY OF LIVERPOOL 3 Health & Safety You must always have a screen between you and the test samples during testing. It is possible that the samples could fail suddenly, which can be associated with a loud noise and some fragments may fly off. The apparatus also contains moving parts. You should carefully follow the instructions given by the laboratory teaching assistants for loading the test samples, and follow the standard testing procedure which will be explained to you. Students are reminded that they are required by law to comply with the School's rules of lab safety. 4 Experimental Procedure Each group will be given one specimen of each of the four samples: mild steel, an aluminium alloy, a polypropylene, and Perspex acrylic. You should record by hand the readings of load and elongation in the tables in your own lab script as the test proceeds. You will eventually have to photograph these tables and upload them into your technical note, so ensure accurate recording and that your hand- writing is clear. For each specimen in turn: Measure the starting width and thickness of the original gauge length region of the sample be tested, using the micrometre or callipers provided. Determine the original cross-sectional area (which you will need to convert applied load to engineering stress). Record these values in Table 1a & 2a. a. b. Measure (approximately) the original gauge length of the test sample. This is the length of the narrow central parallel region of the test sample over which most of the displacement/ elongation takes place. You will need this to convert measured elongation to engineering strain. Record the value in Table 1a & 2a. C. Remove any surface cover sheet from the Perspex acrylic samples. d. Carefully mount the sample vertically and securely in the grips of the tensile testing machine, following the instructions provided. If you don't tighten the grips sufficiently, your sample may slip in the grips and you will have to repeat the test. Zero the load and displacement measurements, and set the manual cross-head speed (rate of elongation) to its minimum value. Make sure the screen is in place. Follow the instructions and guidance of the teaching assistants at all times, and ask them if you are unsure about anything. e. Using the manual jog control, elongate the sample in initial increments (steps) of about 0.1mm, increasing the increments gradually as per the elongation values given in Table 1b & 2b. Record in Table 1b & 2b the actual elongation (in mm) and the load (in N) on the specimen after each elongation step, using the values displayed in the Bluehill software on the Instron's PC screen. Record your data carefully and neatly in this lab script. (You will notice that the ad record the valuo faicho/n4. 3. Ultimate Tensile Strength the maximum engineering stress recorded. 1. 2. UNIVERSITY OF LIVERPOOL Strain at failure a measure of the material's ductility. Note that strain is sometimes expressed as a % rather than a fraction (a factor of 100 different!). 5 Technical Note Instructions You will complete a Technical Note using the template provided in Canvas, and submit this in Canvas for marking. The assessment of this practical is mainly an assessment of the quality of the presentation of your results and their interpretation. The technical note contains the following sections, each worth the percentages indicated: TT Lab Script // MATS105 Abstract Write a paragraph about what you did, why you did it, how you did it, the results and what you concluded (roughly 250 words) Results Images of original data recorded by hand during the practical in the lab script. Images of the excel spreadsheet, showing data from both metals and from both polymers. Image of two excel stress-strain graphs, each containing data from two materials i.e. showing two stress-strain curves. Completed tables with values obtained from the stress-strain graphs Discussion The quality of technical writing is important - good English without any grammatical errors Conclusions Submission instructions: 10% 60% 20% 10% Download the Technical Note Template from the Submission folder in the TT: Tensile Test section of the Year 1 Labs Canvas site. Complete the Technical Note Template by following the instructions and answering the questions. If you are having difficulty please contact the teaching assistants by email for help./nRepeat for each of the four samples. You have now completed the practical part of the experiment. // MATS100 For the mild steel sample, transcribe your recorded elongation and load data into two adjacent columns in an excel spreadsheet, and generate stress (in MPa) and strain values in two columns immediately to the right. Hence you should have four columns of data for each sample. The top row (row 1) should have merged cells across all four columns and state the name of the sample material (e.g. "Mild steel"). The second row (row 2) will contain the column header i.e. "Elongation (mm)", "Load (N)", "Stress (MPa)" and "Strain" respectively. The rows below these will be filled with transcribed and calculated data. Add a border around all the cells in the four columns containing data for the sample. For the aluminium alloy sample data, leave a blank column to the right of the steel sample's data and then repeat as for steel, entering the aluminium data into the next four columns to the right starting again with the name of the material ("Aluminium alloy") in row 1. It is important to use this layout so that you can produce a single image of all the data for both metals to upload into your technical note. Open a new sheet in excel, and repeat the data entry for the polypropylene and Perspex acrylic sample data. In the sheet containing metal data, create a single stress v strain scatter graph (called scatter chart in excel) showing both mild steel and aluminium alloy curves on a single graph. To create a single stress v strain scatter graph showing both mild steel and aluminium alloy data on a single graph, you need to plot two sets of x and y data on common axes. There are various ways to do this in excel, which will require you to re-arrange the data in your excel spreadsheet slightly. If you search the internet using a search term like "excel plot two sets of x and y data on common axes" you will find out how to do it. Repeat for the polypropylene and Perspex acrylic data in the other sheet. Make sure the axes are correctly labelled and with easy-to-read axis values. Use a different data marker shape for each material (one square and one circle is sensible) and make sure that a legend clearly identifies the material corresponding to each set of data. Then manually add a straight line to give a reasonable fit to the initial linear region of each stress-strain curve where elastic-only deformation is taking place, and estimate Young's modulus from the gradient of this line (normally expressed in GPa). Do not use excel's trend-lines for this just use your best judgement to fit a straight line (you may need to ignore the first two or three data values). Ensure all the data points and labels are clearly visible as you will have to paste images of these graphs into your technical note. For each material, obtain the following mechanical properties from the stress-strain graphs: Young's Modulus (Modulus of Elasticity)-the gradient of the linear initial region of the stress strain graph. Yield stress (Limit of Proportionality) - the stress at which there is a change from elastic (linear) to plastic (non-linear) deformation. For mild steel you may also be able to see an Upper and Lower Yield Stress, but they are not always clearly visible - if you can see it, use the lower yield stress. Note that if the yield stress is not clear because of a very gradual transition from linear to non-linear behaviour, it is customary to use the 0.1% Proof Stress to define the transition to plastic deformation (see previous figure). However this is not necessary in this practical. Ultimate Tensile Strength - the maximum engineering stress recorded./nUNIVERSITY OF LIVERPOOL Table 2a: Initial Test Sample Measurements Thickness of gauge length (mm) Width of gauge length (mm) Original Cross-section Area (mm²) Length of gauge length (mm) Table 2b: Elongation and load data during tensile test Indicative elongation (mm) 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Results tables for polypropylene and Perspex acrylic 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.5 4 4.5 5 POLYPROPYLENE Actual elongation (mm) 0 Measured load (N) 0 Polypropylene PERSPEX ACRYLIC Actual elongation (mm) 0 O 013 016 TT Lab Script // MATS105 0,7 0,7 1/1 1,1 \/\ \r\ 115 115 117 211 2,1 211 211 Perspex acrylic 2,5 1212 80 Measured load (N) die 0 10 11,96 15,3 15,225 3814 164 267 394 550 636 753 869 976 1088 1190 1275/nTadic 19.1 Thickness of gauge length (mm) Width of gauge length (mm) Original Cross-section Area (mm²) Length of gauge length (mm) Indicative elongation (mm) 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.25 1.5 1.75 2.0 2.25 2.5 2.75 3.0 3.5 4 4.5 5 10 Table 1b: Elongation and load data during tensile test 15 20 imple ivice 25 30 35 40 45 50 ements MILD STEEL Actual elongation (mm) 0 Mild Steel Measured load (N) 0 0 0 O O O Actual elongation (mm) O O 0 013 0,3 03 113 115 118 2,2 21 2 215 2,6 26 4,0 7,9 Aluminium 1,4 ALUMINIUM 99.5 Measured load (N) 0 11,6 25,5 158,0 314 722 1146 1532 1911 2144 2224 2268 2310 2337 2360 2364 2385 2365 2300 2355 2373See Answer

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