(Manufacturing) will carry the remaining 50%. Please ensure that you retain a duplicate of your assignment. We are required to send samples of student work to the external examiners for moderation purposes. It will also safeguard in the unlikely event of your work going astray. IMPORTANT INFORMATION You are required to submit your work within the bounds of the University Infringement of Assessment Regulations (see your Programme Guide). Plagiarism, paraphrasing and downloading large amounts of information from external sources, will not be tolerated and will be dealt with severely. Although you should make full use of any source material, which would normally be an occasional sentence and/or paragraph (referenced) followed by your own critical analysis/evaluation. You will receive no marks for work that is not your own. Your work may be subject to checks for originality which can include use of an electronic plagiarism detection service. Where you are asked to submit an individual piece of work, the work must be entirely your own. The safety of your assessments is your responsibility. You must not permit another student access to your work. Where referencing is required, unless otherwise stated, the Harvard referencing system must be used (see your Programme Guide). Submission Date and Time 14th December 2016 Submission Location Online via Sunspace EAT104: COURSEWORK 2016/2017 SESSION: MATERIALS ASSIGNMENT Materials Properties and Materials Selection Introduction Engineers design and make things. Let's assume we're talking about engineering components. These components are made of MATERIALS (metal, plastic, ceramic, composite etc.). The best material from which to make any given component depends on a number of factors (e.g. mechanical, thermal or electrical properties, density, cost, environmental impact etc.) and the process by which the final material is chosen is MATERIALS SELECTION. In this module we use a well-established graphical methodology for materials selection based on quantitative measures of performance called PERFORMANCE INDICES. This methodology is the one employed within the CES 2016 software - and part of the aim of this assignment is that you become familiar with the use of this software. You will be using it in all 3 years of your degree. 1. Materials Selection Charts A materials selection chart is a 2-D plot of one material property (or combination of properties) against another. A simple example might be a plot of Young's Modulus (y-axis) v Density (x-axis). Such a plot can be generated via CES (Figure 1): Figure 1. Young's Modulus -v- Density Materials Selection Chart. Any given unique material would occupy a single point on the above chart. Because a material such as cast iron or PVC is, in reality, a family of materials, then it occupies a "bubble" or "island" on the chart as indicated in Figure 1 above. Density (kg/m^3) 10 100 1000 10000 Young's modulus (GPa) 1e-4 0.001 0.01 0.1 1 10 100 1000 Rigid Polymer Foam (MD) Softwood: pine, along grain CFRP, epoxy matrix (isotropic) Polyvinylchloride (tpPVC) Cast iron, gray Young's Modulus v Density (Level 2 Database) TASK 1 Using CES software (using Level 2 Database, Edu Level 2 Materials subset), prepare the following materials selection charts (y-axis variable listed first): 1.1 Yield Strength -v- Density: (σy -v- ρ) 1.2 Yield Strength -v- (Price x Density): (σy -v- Cm ρ) 1.3 (Young's Modulus)1/2 / Density -v- (Yield Strength)2/3 / Density: [(E1/2/ρ) -v- (σy 2/3/ρ)] Copy/Paste your charts from CES into your report. Label and format the charts in your chosen style. Give a full commentary on your work. 2. Performance Indices In order to be able to select the "best" or "optimum" material for a particular component we need to understand what we're trying to optimise. Essentially, what is needed is a material which will meet all of the mechanical / electrical / thermal requirements of the component. These requirements are COMPULSORY and are called CONSTRAINTS. The best material is the one which meets all of these compulsory needs at (say) minimum mass, minimum cost or minimum environmental impact. This optimisation is termed the OBJECTIVE. The constraint and objective factors dictate the selection methodology. Hence we find materials which are capable of meeting all compulsory performance requirements and then find the one that achieves this at (e.g.) minimum mass. This selection methodology should be quantitative to work effectively. A quantitative measure will allow us to shortlist materials and then rank them from best (lightest component) to worst (heaviest component). This ranking is done via the PERFORMANCE INDEX. Here are some common performance indices (Table 1): Typical Application/Function Performance Index for Stiffness-Critical Applications Performance Index for Strength-Critical Applications Rods in Tension E / ρ σy / ρ Beams in Bending E 1/2 / ρ or E1/3 / ρ σy 2/3 / ρ or σy 1/2 / ρ Panels in Bending E 1/3 / ρ σy 1/2 / ρ Plates/Panels in Compressive Buckling E 1/3 / ρ - Columns in Compressive Buckling E 1/2 / ρ - Shafts in Torsion G / ρ , G1/2 / ρ or G1/3 / ρ σy / ρ, σy 2/3 / ρ or σy 1/2 / ρ Table 1: Some common performance indices for minimum weight design. In class you have learned to take a given performance index (M) and use this: (i) to plot the appropriate selection chart, and (ii) apply a selection line of given gradient to allow the selection process to proceed [In essence, if a performance index, M, is given by: M = Y 1 n X ......then the correct selection chart is log Y -v- log X and the correct selection line will possess a gradient of n.] TASK 2 Using the 2 charts you have already prepared in Task 1.1 and 1.2, insert an appropriate selection line and thereby determine a shortlist of the best 10-15 materials for each of the following (2.1 and 2.2). 2.1 A strong circular cross-section beam in bending with minimum mass (M = σy 2/3 / ρ). 2.2 A strong circular cross-section beam in bending with minimum cost (M = σy 2/3 / Cm ρ). Now perform the following task: 2.3 Determine if there is any overlap between your lists of lightest and cheapest materials from 2.1 and 2.2 respectively (you may need to expand either or both of your shortlists slightly). Comment on your findings. Finally, answer the following: 2.4 From a materials selection point of view, how would you use the chart you prepared in task 1.3? What does it show? Where appropriate, Copy/Paste all of your CES charts and constructions to support your answers. Again, label and annotate your charts in an appropriate manner. 3. Objectives in Conflict The exercise done in tasks 2.1 and 2.2 is one in which the objectives of the materials selection are "in conflict". Task 2.1 requires you to find the lowest mass materials solutions for the component. Task 2.2 requires you to find the lowest cost materials solutions for the component. The problem is that high performance lightweight materials tend to be expensive (think of carbon fibre), while cheap materials tend not to have excellent mechanical properties. Hence lightweight solutions tend to be expensive. Conversely, cheap solutions will tend to weigh more. This is what we mean by "objectives in conflict". Such a situation can be illustrated by using CES. Suppose we are searching for LIGHTWEIGHT and CHEAP aerospace materials for a stiffness-critical (also called deflection-critical) beam. The relevant performance indices are: For either of these, the higher the index gets, the resulting beam will be lighter or cheaper. Hence, as the ratio (M1 = E 1/2 / ρ) gets bigger, the mass of the component made from it gets smaller. Similarly, as the ratio (M2 = E 1/2 / Cm ρ) gets bigger, the cost of the component made from it gets lower. For the sake of the next graph, we are going to turn this argument around and turn the ratios upside down. From what we've said above, if we invert the ratios, then as the inverted ratios get bigger the mass or cost must also get bigger (instead of smaller). We'll call the new ratios the Relative Mass Index and the Relative Cost Index. Now, the bigger M3 gets, the heavier the component and the bigger M4 gets, the more expensive the component. TASK 3 Using CES with the Level 3 Aerospace Database, Aerospace Materials subset, prepare the following: 3.1 A selection chart of M3 = ρ E 1 2 (y-axis) -v- M4 = Cm ρ E 1 2 (x-axis) 3.2 Draw in a "trade-off surface" line for "non-dominated" material solutions. 3.3 Discuss the significance of your results. 4. Manipulating Material Properties Plastic materials (polymers) are very versatile, but from a mechanical viewpoint they suffer from having low stiffness and strength. It is possible to increase both the stiffness (Young's modulus) and strength (tensile strength and/or yield strength) by mixing them with stiff, strong materials such as glass fibre or carbon fibre. One such polymer is polypropylene (often abbreviated to "PP"). Polypropylene is available with a wide range of glass fibre contents ranging from 0% to 50% by weight. TASK 4 Your task here is to use CES to investigate how the addition of glass fibre affects the properties of polypropylene. To achieve this, complete the following tasks.: Minimum Mass Index: M1 = E 1 2 ρ Minimum Cost Index: M2 = E 1 2 Cmρ Relative Mass Index: M3 = ρ E 1 2 Relative Cost Index: M4 = Cmρ E 1 2 4.1 Use the CES "Browse" function (Follow the route , , , ) to determine the Young's modulus (E), and Yield Strength (Elastic Limit) (σy ) of each of the following materials:  PP Homopolymer (High Flow Grade) – i.e. 0% Glass Fibre  PP Homopolymer + 10% Glass Fibre  PP Homopolymer + 20% Glass Fibre  PP Homopolymer + 30% Glass Fibre  PP Homopolymer + 40% Glass Fibre Because CES always gives a RANGE for any given property, it is suggested you use the UPPER value of the range for your plots. 4.2 Use Excel to plot and label graphs of (i) Young's Modulus -v- Fibre Content (i.e. 0% to 40% weight fraction) and (ii) Yield Strength -v- Fibre Content (i.e. 0% to 40% weight fraction). The glass content figures used above (i.e. the 10%, 20% 30% and 40% figures) refer to WEIGHT FRACTION of glass. In reality, a better value to use for analysis purposes is the VOLUME FRACTION. You can convert weight fractions to volume fractions as long as you know the densities of the individual components (i.e. the densities of PP and Glass). In composite analysis, we call the PP the MATRIX and the glass is the FIBRE. We use the subscripts "m" and "c" to refer to matrix and fibre respectively. We use the symbols ρ, V and W to refer to density, volume fraction and weight fraction respectively. Hence: ρf = Density of Fibre (Glass) = 2.54 g/cm3 = 2540 kg/m 3 ρm = Density of Matrix (PP) = 0.903 g/cm3 = 903 kg/m 3 Vf = Volume fraction of Fibre Vm = Volume fraction of Matrix (where Vm = 1 - Vf) Wf = Weight fraction of Fibre Wm = Weight fraction of Matrix (where Wm = 1 - Wf) The conversion from weight fraction to volume fraction is given by the equation: Vf = Wf ρm (Wf ρm + Wm ρf ) Substituting in the values for density: Vf = 903 Wf (903 Wf + 2540 Wm ) [Note: As long as the units for density are consistent you'll get the correct answer - just don't mix g/cm3 values and kg/m 3 values. Similarly, remember that a weight fraction of 20% is Wf = 0.2 etc. This is the value you should enter in your formula]. 4.3 Convert your weight fractions to volume fractions and re-plot your graphs from Task 4.2, but this time with fibre content represented by volume fraction rather than weight fraction. 4.4 Discuss how the addition of glass fibre to PP affects its mechanical properties.