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Steel XY Curve Analysis
- 9. 038.57E+027.31E-038.58E+027.32E-038.59E+027.32E- 038.60E+027.32E-038.61E+027.32E-038.62E+027.32E- 038.63E+027.32E-038.64E+027.32E-038.65E+027.32E- 038.66E+027.33E-038.67E+027.33E-038.68E+027.33E- 038.69E+027.33E-038.70E+027.33E-038.71E+027.33E- 038.72E+027.33E-038.73E+027.32E-038.74E+027.33E- 038.75E+027.32E-038.76E+027.31E-038.77E+027.29E- 038.78E+027.31E-038.79E+027.32E-038.80E+027.31E- 038.81E+027.31E-038.82E+027.31E-038.83E+027.29E- 038.84E+027.29E-038.85E+027.26E-038.86E+027.22E- 038.87E+027.26E-038.88E+027.30E-038.89E+027.30E- 038.90E+027.31E-038.91E+027.31E-038.92E+027.30E- 038.93E+027.31E-038.94E+027.31E-038.95E+027.31E- 038.96E+027.31E-038.97E+027.31E-038.98E+027.30E- 038.99E+027.31E-039.00E+027.31E-03 Sheet2 Sheet3 Case Study: Weight: 10% Gang Aft Agley, a manufacturing company, faces the aggregate planning problem shown in the table below. Cost of regular production is $5 per unit, the cost of producing the same unit on overtime is $7.50, the cost of subcontracting is $9 per unit, and the cost of carrying a unit in inventory from one month to the next is $2. The labor contract at the plant prohibits overtime output to exceed 300 units in any five month window (that is the entire time horizon being considered); likewise, subcontracting output also can’t exceed 300 units in any five month window. The plant capacity is 600 units per month (during regular time) produced using two shifts, regardless of the number of days in a month. By policy, management wants to avoid stockouts. Formulate the aggregate plan considering regular time costs, overtime costs, subcontracted production costs, inventory costs and the necessary constraints using linear programming and
- 10. solve it using Excel Solver for obtaining the optimum minimum cost for the 5-month horizon. Your case study report must contain A.Objective function B.Constraints C.Excel Solver output (if you don’t attach Excel output with your report you will be awarded ‘0’ for the case) Case study is an individual assignment; please note that cheating on the assignment will not be tolerated. All the students whose reports look similar will be awarded ‘0’; Repeat violators will be reported to the Dean of Students. NO EXCEPTIONS. Month Units produced during Regular time Units produced during Overtime Subcontracted Priduction Inventory at the end of the time period Demand 0100 1
- 38. Experiment #9- Corrosion of Metals Abstract: Studying the corrosion of materials and applying the prevention of corrosion is important and can help aid the economy. If used properly, inhibitors can help reduce the rate of corrosion on materials. This experiment is designed to help determine how inhibitors make a difference in corrosion rates by using two types of metals. Corrosion has been at fault in many accidents involving bridges, highways, and structures seen in everyday life. By having a little knowledge of material behavior and corrosion it is possible to help save large amounts of waste and accidents due to corrosion. Tests for corrosion are made in order to come up with a corrosion resistant material and better inhibitors. the use of a EG&G Versa Stat machine is made in order to determine how long a certain material will last under a corrosive environment. The machine will also help in determining the rate of corrosion with and without an inhibitor, while also determining the degree of effectiveness of the inhibitor. The samples used for this specific experiment are 1018 steel and brass. Description of Work: The experiment is started by preparing the samples of 1018 steel and brass by polishing them using different weight polishing compounds. The samples are then taken after completion of polishing and placed under a microscope in order to ensure proper polishing and to take initial photographs. The dimensions of the samples are then measured and their cross sectional areas are then calculated. A 3.5% saline solution is poured into the electrochemical cell. The first specimen is then connected to the colmel standard reference electrode and counter electrode while making sure that the counter electrode
- 39. and the surface of the sample are parallel. The wiring is as follows: the green wire connects to the working electrode, the red wire connects to the counter electrode, and the white wire connects to the reference electrode. The computer on the EG&G Versa Stat machine is then set up according to the parameters of the material being used in the experiment. Once the test is complete the data must be saved on a disk and verified on another computer in order to ensure proper storage of the data. An image of the corroded sample is then taken in order to be compared to the initial photograph of the uncorroded sample. The sample is then taken and polished once again to remove all of the corrosion accumulated on it’s surface from the previous test. The test is then run once again, but with antifreeze as the inhibitor mixed with the saline solution. Photographs must be once again taken after the corrosion test has been completed. The same procedure must be repeated for the other sample once the first in complete. This data is to be collected to determine the corrosion rate of the metals and degree of effectiveness of the inhibitor. Results: Based on the data collected it is apparent that the samples placed in the saline solution had much more corrosion and had corroded at a higher rate than the samples with the inhibitor. The samples in the saline solution corroded at an increasing rate, while the samples in the saline solution with an inhibitor corroded at a decreasing rate, showing how the inhibitor proved useful. The brass corroded at at rate of approximately 18.0mpy in the saline solution and at approximately 14.5mpy in the solution with an inhibitor. The steel sample corroded at a rate of approximately 10.0mpy in the saline solution, and at a rate of approximately 0.7 mpy in the solution with the inhibitor. As one can see from these results, it is made apparent that the use of an inhibitor is extremely important in reducing rates of corrosion. Both of the samples used proved to have good resistance to
- 40. corrosion signifying a good use in industry. The sources of error in this experiment could have come been attributed to many factors. Some being as follows: There could have been under- polished samples that had initial corrosion that attributed to an increase in corrosion rate, the area measurements used in the calibration of the machine could have been incorrect, the position of the sample in the solution could have been incorrect, The wiring could have been incorrect, and the Parameters set on the computer could have been incorrect leading to incorrect readings. EXPERIMENT #9 CORROSION OF METALS Objective The objective of this experiment is to measure the corrosion rate of two different metals and to show the effectiveness of the use of inhibitors to protect metals from corrosion. Background The importance of corrosion can be seen in daily life. Corrosion causes accidents in industry, on highways, and in homes. It is wasteful financially, costing industrialized nations 4-5% of their gross domestic products annually. A little knowledge of electrochemistry, material science and corrosion could save nations some 25% of this loss. Corrosion engineering is the application of science and art to prevent or control corrosion damage in a safe and economical manner. To perform this
- 41. function properly, the corrosion engineer must rely on experimental research. This is because the major aspects of corrosion engineering are largely empirical in nature. A body of theory exists that can be very helpful in solving corrosion problems, but in the final analysis, most decisions are based on the results of empirical tests. Corrosion tests are conducted for a number of reasons including: 1. Establishing corrosion mechanisms. 2. Defining corrosion resistance of materials and how to develop new corrosion resistant alloys. 3. Estimating service life of equipment. 4. Developing corrosion protection processes. 5. Defining the critical potential values for materials in various environments. Theory Anodes and Cathodes: In analyzing corrosion, the first thing that must be determined is whether a metal reacts with its environment. If so, the nature of the reaction must be understood. It is generally accepted that corrosion processes are caused by the formation of electrochemical cells. The electrochemical reactions in these cells can be divided into two reactions: 1. Anodic reactions 2. Cathodic reactions where each reaction is called a half-cell reaction. In the anodic
- 42. reaction, metal goes into solution as an ion. The reaction is generally written as: M --> Mn+ + ne- where M is a metallic element, e- is an electron and n is the valence of the metal as an ion. An example of this is Zinc where: Zn --> Zn2+ + 2e- In the cathodic reaction, electrons provided by the anode, flow through the metal until they reach the cathode where they can be combined with positively charged ions. In acidic solutions this reaction is: 2H+ + 2e- --> 2H --> H2(gas) and in neutral solutions the reaction is: O2 + 2H2O + 4e - --> 4OH- Both the anodic and cathodic reactions must occur simultaneously for a corrosion process to proceed. If both reactions are not occurring then a charge builds up and the corrosion process stops. The anodic reaction is generally the simple case of a metal going into solution. However a variety of cathodic reactions are encountered depending on the conditions of the process involved. Table 1 shows several examples of different
- 43. cathodic reactions. Note that in all of the cathodic reaction electrons are absorbed. Table 1 - POSSIBLE CATHODE REACTIONS IN DIFFERENT GALVANIC CELLS ––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––– Cathode Reaction Example 2H+ + 2e- --> 2H Acid Solution s O2 + 2H2O + 4e - --> 4OH- Neutral and alkaline solutions O2 + 4H + + 4e- --> 2H2O Using both O2 and H + in acid solutions M3+ + e- --> M2+ When Ferric ions are reduced to ferrous
- 44. M2+ + 2e- --> MO When iron is placed in a Cu salt solution the electron from solution of the iron reduces Cu ions to metallic Cu ––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––– The electrode potential in the electrochemical cell When an ideal metal is placed in an electrolyte, an electrode potential develops that is related to the tendency of the material to give up electrons. To measure this tendency, we measure the potential difference between the metal and a standard electrode using a half-cell. The standard reference electrode is a half cell with a known constant potential. Different standard reference electrodes are used depending on the solution environment. Some standard electrodes are the standard hydrogen electrode (SHE) and the saturated calomel electrode (SCE).
- 45. Standard expressions for corrosion rate In most cases, aside from contamination problems, the primary concern where corrosion is present, is the life (usually in years) of metals in question. A good corrosion rate experiment should include: 1. Familiar units. 2. Easy calculations with a minimum opportunity for errors. 3. Ready conversion of data to life in years. 4. Penetration. 5. Whole numbers without cumbersome decimals. Mils penetration per year (mpy) is the most commonly used corrosion rate expression in the United States. One formula used to calculate the corrosion rate is: 534 x W mpy = –––––––– D x A x T
- 46. where, W = weight loss (gms) D = density of the specimen, g/cm3 A = area of specimen, sq. in. T = exposure time, hr. The corrosion rates of resistant materials generally range between 1 and 200 mpy. The relative corrosion resistance of a material can be evaluated using the following criteria: Relative Corrosion Resistance mpy outstanding <1 excellent 1-5 good 5-20 fair 20-50 poor 50-200 unacceptable >200 Consider a car engine block with and without the addition of antifreeze, as an example of a corrosion rate problem. Engine blocks are generally made from low carbon steel that corrodes when exposed to tap water. This is the brown rust that is often seen in cooling
- 47. systems containing water only. The corrosion reactions for low carbon steel are: Fe --> Fe2+ + 2e- Fe2+ --> Fe3+ + e- O2 + 2H2O + e - --> 4OH- 2Fe + 2H2O + O2 --> 2Fe 2+ + 2OH- --> 2Fe(OH)2 2Fe(OH)2 + H2O + 1/2 O2 --> 2Fe(OH)3 (rust) The electrochemical technique is used to study the corrosion rate of low carbon steel in tap water instead of using the weight loss technique. This is because the former is a very rapid method of obtaining data while the latter technique is a very
- 48. lengthy process. In the electrochemical process the corrosion rate is measured by measuring the current density, J: I J = –– A where I is the current in microamps (µA) and A is the area in cm2. The corrosion rate can be calculated from this using the relationship: 1 mpy = (1/n ) J where n is the valence of the metal involved (M --> Mn+ + ne-). PROCEDURE CAUTION: BE SURE YOU UNDERSTAND HOW TO OPERATE THE EQUIPMENT BEFORE BEGINNING THE EXPERIMENT If you are not familiar with the equipment ask for help from your instructor. DO NOT START INDISCRIMINATELY MAKING ADJUSTMENTS TO
- 49. THE EQUIPMENT. Your group will be provided with samples of 1018 steel and brass. Prepare the sample (metal exposed side) for metallographic observation (polish/grind using 400 grit, 600 grit sandpaper and 1 micron powder). Check the specimens under the microscope to be sure that they are well polished. Observe the surface of each specimen before and after corrosion takes place. Take photos. CAUTION: The equipment used to measure corrosion rates is very delicate. Use extreme care when handling. Pour about 400cc tap water (room temperature) into the beaker that makes up the electrochemical cell and add approximately one teaspoon of salt to form a solution. Then place one prepared (steel or brass) specimen in the cell setup with the calomel standard reference electrode and the counter electrode. Check to be sure that the counter electrode and the sample surface are parallel (not touching).
- 50. Connect the leads from the EG&G VersaStat to the electrochemical cell. The Green wire attaches to the working electrode (the sample), the Red wire attaches to the counter electrode, and the White wire attaches to the reference electrode. If the machine is not already on, boot up the computer and at the DOS C:> prompt type: corr [ENTER]. When the title screen comes up hit any key to display the Main menu. Pick “SetUp“ from the main menu to display the Set up menu. Pick “Get Set Up”. You will then be asked to “Enter setup filename for recall.” Type: 227L [ENTER]. The screen will now display the test parameters to be used for your experiment. Your group will have to enter the correct sample area and specimen density in their respective fields on
- 51. the test Setup Screen. Once the correct test parameters have been entered for your specimen, your group is ready to run a test. Choose the Run command from the menu and turn the Cell Switch located on the front of the EG&G Versa Stat to the ON position. A plot of your test will appear on the computer screen once the test begins. The test runs for 15 minutes. When the test stops, turn the Cell Switch to the OFF position. Save your data to a 3.5” floppy before beginning any further tests. Put a 3.5” floppy disk into the A drive. To save your data first save your data on the C drive using the “Save” command in the “File” menu. Next recall your data using the “Get Data” command in the “File” menu. Finally, transfer the data to your diskette in the A drive by choosing the “Export Data” from the “File” menu. Type in a file name for your data including an A drive path. (For example, you can type: a:steel).
- 52. Repeat this procedure for the other metal (steel or brass) sample. Next put about 400cc of the prepared antifreeze/water mixture (50% ethylene glycol) into the electrochemical cell and repeat the experiment for the remaining samples. Note the corrosion inhibiting effect of the antifreeze. Normally, when antifreeze is added in small concentrations to an environment, the corrosion rate decreases. In a sense, an inhibitor can be considered a retarding catalyst. The effectiveness of an inhibitor can be measured based on: Corrosion rate without inhibitor Degree of effectiveness of inhibitor = –––––––––––––––––––– –––––– Corrosion rate with inhibitor when a rate is determined using the mpy equation once the rate has plateaued. Glossary of Terms
- 53. Understanding the following terms will help in understanding this experiment. Anode. The electrode in an electrochemical cell that oxidizes, giving up electrons to an external circuit and ions into solution during corrosion. Anodic reaction. The oxidation reaction occurring at the anode in an electrochemical cell. Aqueous corrosion. Dissolution of a metal into a water-based environment. Cathode. The electrode in an electrochemical cell that accepts electrons from an external circuit and where a by-product is produced during corrosion. Cathodic reaction. The reduction reaction occurring at the cathode in an electrochemical cell. Composition cells. Electrochemical corrosion cells produced between two materials having a
- 54. different composition. Also known as a galvanic cell. Corrode. Lose material to a surrounding solution in an electrochemical process. Electrochemical cell. A cell in which electrons and ions can flow by separate paths between two materials (a cathode and an anode), producing a current which in turn leads to corrosion or plating. Electrochemical corrosion. Corrosion produced by the development of a current in an electrochemical cell which removes ions from the material. Electrode potential. Related to the tendency of a material to corrode. The potential is the voltage produced between the material and a standard electrode. Electrolyte. The conductive medium through which ions move to carry current in an electrochemical cell. Electromotive force series. The arrangement of elements according to their electrode potential, or their tendency to corrode. A listing of half cell reaction
- 55. voltages. Galvanic corrosion. Corrosion produced by the electromotive force associated with two dissimilar metals. Galvanic series. The arrangement of alloys according to their tendency to corrode in a particular aqueous environment. Inhibitors. Additions to the electrolyte that preferentially migrate to the anode or cathode, cause polarization, and reduce the rate of corrosion. Oxidation reaction. The anode reaction, by which electrons are given up to the electrochemical cell. Oxygen electrode. The cathode reaction by which electrons and ions combine to produce OH- ion groups in the electrolyte. Passivation. Producing strong anodic polarization by causing a protective coating to form on the anode surface and interrupt the electric circuit.
- 56. Reduction reaction. The cathode reaction, by which electrons are accepted from the electrochemical cell. Water electrode. The cathode reaction by which electrons and ions combine to produce water in the electrolyte. Write Up Write a memo report including the rate of corrosion for all samples in mpy (once the specimen's rate levels off), and the degree of effectiveness of the inhibitor. Graph the current density versus time. Discuss the sources of error in this experiment. MSE 227L Name ________________________ Corrosion of Metals Poor Fair Average Good Excellent Memorandum Format Used 1 2 3 4 5
- 57. Spelling, grammar, & punctuation correct 1 2 3 4 5 Report includes: Poor Fair Average Good Excellent Discuss rate of corrosion for all samples in mpy (once the specimen's corrosion rate levels off). Discuss current density vs. time. Show calculation for mpy. 1 2 3 4 5 Discuss the degree of effectiveness of the inhibitor. Show calculations. 1 2 3 4 5 Graph the current density versus time. Overlay graphs for comparison. Include more than 1 graph. 4 8 12 16 20 Include table of results, measurements, significant parameters obtained or used in this lab. (relevant information)
- 58. 1 2 3 4 5 Discuss sources of error in this experiment. 1 2 3 4 5 Attach photos of steel and brass samples (comparison of before and after testing in saltwater and antifreeze solution) 1 2 3 4 5 Column Subtotals Poor Fair Average Good Excellent Overall level of effort apparent 1 2 3 4 5 Quality of graphs 1 2 3 4 5 Quality of abstract 1 2 3 4 5 Quality of work description 1 2 3 4 5 Quality of conclusions 1 2 3 4 5 Column Subtotals