Lab 4 Report Kai Henderson

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University of Toronto *

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270

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Mechanical Engineering

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Jan 9, 2024

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Material Selection Lap Report MIE270 Kai Henderson 1008990790 E2 Lab TA: Naghmeh Safaie Lab 4 Material Selection Abstract: Engineers are often presented with an array of candidate material for a design, that may posses many design considerations. Often engineers utilize the Cambridge Engineering Selector program as to readily find the optimum candidate materials based on the design considerations and candidate material presented. In Lab 4 students were tasked with using the CES software to find different mechanical properties of a variety of specified materials. Student were then tasked with tabulating different mechanical properties as to complete comparative analysis between 3 candidate materials for the design of a brewery pressure vessel. Based on the data calculated students then justified which of the candidate materials was optimum for the design, based on a list of criteria. This was done with the intent of familiarizing students with material selection process through the CES software.

Introduction 1.0 In materials science of engineering, understanding the properties of a material and how comparative analysis between materials is crucially important in material selection. There exists a myriad a of characteristics that may influence a materials viability within a design, and plethora of candidate material’s that may suit designs need. For engineers to effectively select materials from this immense selection pool, Material Science Engineering (MSE) programs are utilized. The Cambridge Engineering Selector (CES) is one popular MSE application that functions as repository for material data and conducts comparative analysis between materials based specified parameters. This allows engineers to effectively choose viable material that meet design specification and are compliant with safety standards. The objective of Lab 4 was to familiarize students with the CES software and its features, as to become more oriented with the process of material selection. This objective would be achieved by conducting stress, tensile and cost analyses between materials as to meet as set of prescribed engineering specifications. The methodology by which this was achieved is outlined in the procedure section. Procedure 2.0 This section details the steps taken by students when conducting the labs as attain the data necessary for the answer the questions in the discussion sections. Students were required to the CES software to find the specified the data on certain materials. 1) Student opened the CES software and created a new level one project file 2) Student then collected the thermal conductivity and cost/kg data of materials outlined in the discussion questions 3.1 and 3.2. This was achieved by searching each material on the CES database and manually copying the wanted data. 3) Student were then tasked with deriving the MPI stiffness formula given as set complementary relation and formulas as to answer discussion question 3.3 4) An analysis of the of various materials was then conducted by students using the program view graph feature, with a y-axis of fracture toughness and an x-axis of tensile strength. Two lines of best fit were created on the graph using values by the lab TA as to filter for possible candidate materials for question 3.4. 5) The rest of the lab consisted of conducting a comparative analysis between the filtered materials, Stainless steel, CFRP epoxy matrix and titanium alloy. The criteria for this analysis consisted of the materials relative cost per kg and toughness, as this related to the design specifications of a brewery’s spherical pressure vessel. Both the minimum and maximum values for each material’s density, volume, and cost, were used and tabulate 2 data table of each materials information.

Discussion 3.0 Question 3.1 The thermal conductivity range of brick, high carbon steel and polyester were given by the CES program in units of Materials Minimum Thermal Conductivity Maximum Thermal Conductivity Brick 0.46 0.76 Polyester 1.51e3 1.53e3 High Carbon Steel 47 53 (Table.1 Thermal Conductivity ranges of specified materials as given by the CES program) Question 3.2 The per kilogram price of Silicon, Aluminum alloy and Zinc alloy was provided data sheet given by CES, in USD currency. To convert to British pounds a conversion rate 1 USD to 0.82 British Pounds Sterling was used, to find each materials approximate £/kg cost. Materials Minimum £/kg cost Maximum £/kg cost Silicon 7.48 12.38 Aluminum alloy 1.63 1.75 Zinc Alloy 1.89 2.62 (Table.2 £/kg cost of each specified materials as given by the CES program) Question 3.3 The following outlines the method by which MPI stiffness of a beam was derived, as given the equations for deflection, moment of inertia relating to rectangular bar, mass and the MPI proportion. (1) Deflection equation: (2) Moment of inertia equation for rectangular beam: (3) Mass Density equation: or (4) Mass proportionality: (5) MPI proportionality: • The moment of inertia equation (1) was substituted into the deflection equation (2) as I correspond to the moment of inertia of the beam.

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• The deflection equation was then rearranged for height as this represents our free variable within the MPI calculations. • This equation was substituted into the mass density equation (3) as to attain the general equation for mass that relates to the other known variables. • Using the mass proportionality equation (4) and condensing our constants into our unknowns of Youngs Modulus ( E ), we rewrote out previous equation into the form below. • Taking the MPI proportionality equation, in which mass is inversely proportional to MPI, the above equation was rearranged as to give the final derivation for MPI stiffness. Question 3.4 A) Student were required to construct a view graph of the material listed within the CES data bases and filter based on brewery’s spherical pressure vessels’ design specifications. These specifications included a material having MPI stiffness within the range of 0.02027 MPa to 0.2569MPa, and minimum tensile and elastic limits of 600 MPa and 800 MPa respectively. Based on this filtering process the CES program displayed the following materials graphically. (Figure.1 Graph outline the materials Nickle Alloys, Titanium Alloys, Tungsten Alloys, Epoxy Matrix CFRP, High Carbon Steel, Low Carbon Steel, Medium Carbon Steel, Stainless Steel)

B) This section details the comparative analysis between the materials stainless steel, titanium alloys and epoxy matrix, and the procedure by which these values were attained. The toughness and density values of each material were provided by the CES program in terms of a range, while the rest of value were derived using the following procedure. Stress equations Volume of shell equation Mass equation • The constant S and P were provided and had values of 2 and 5 respectively. The stress equation was rearranged for t representing thickness, as this would help determine the pressure vessels volume. The stress would be represented by the toughness value provided by the CES program. • This equation was substituted into the volume equation, which was subsequently substituted into the volume equation as to the total mass of material required to construct the pressure vessel. • This provided student with a mean which by approximate the cost of the materials required to construct the pressure vessel. Materials Toughness MPa Density g/cm 3 Volume Mass Min Cost / kg Max cost / kg Minium Price Maximum price Epoxy Matrix 550 1500 0.11 171 37.4 41.6 $6,409 $7,128 Stainless Steel 480 7600 0.13 995 5.68 5.95 5,651 5,919

Titanium Alloys 300 4400 0.21 922 20.9 21.5 19,260 19,813 (Table 3. Data sheet on the relative price of constructing the spherical pressure chamber using specified material while considering their minimum toughness and density values) Materials Toughness MPa Density g/cm 3 Volume Mass Min Cost / kg Max cost / kg Minium Price Maximum price Epoxy Matrix 1050 1600 0.06 96 37.4 41.6 3,581 3,983 Stainless Steel 2240 8100 0.03 227 5.68 5.95 1,291 1,352 Titanium Alloys 1630 4800 0.04 185 20.9 21.5 3,867 3,978 (Table 4. Data sheet on the relative price of constructing the spherical pressure chamber using specified material while considering their maximum toughness and density values) Based on the data calculated and provided by the CES program, stainless steel represents the optimum candidate material based on the pressure vessel’s design requirements. This statement is justified by stainless steel’s mechanical properties, of corrosion resistance and high ductility relative to other metals, which are emphasized pressure vessels design requirements. Furthermore, the high toughness values of stainless steel make it ideal for handling the stresses that pressure vessel will be subjected while being utilized, as its values are well within the design limits (Table.4). Comparing the relative costs of each material, stainless steel represents the most cost-effective option, as its relatively low cost per kilogram makes it economically completive for the pressure vessel. Given this data stainless steel represents the definitively most optimal material option to construct the pressure vessel (Table.3,4). Conclusion 4.0 In conclusion he CES program is a useful engineering tool that allows engineers to access repository of material data and compare data such against other material relatively easily. This is vital in martial selection as engineers are often presented with a wide array of candidate materials for design the have numerous design constraints based on material properties and cost. Through this lab student were familiarized with some of these metrics such MPI, thermal conductivity and cost per kilogram, serving to teach more about the material selection process.

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