Material Selection in Mechanical Design Indiana FIRST / Purdue FIRST Forums October 24, 2015 Matthew Prall School of Mechanical Engineering, Purdue University

Overview Product Analysis Key Concepts Stress and Strain Bending and Torsion Material Selection

Product Analysis For a system: For each part of a system: What does it do? How does it do it? Where does it do it? Who uses it? What should it cost? For each part of a system: What is the function? What does the geometry look like? How many are going to be made? How is it going to be manufactured? Before making any design decisions, determine the function of the product and each part

Product Analysis What is important? Functionality Material properties Mechanical, physical, electrical, ect… Geometry Manufacturability Cost Determine the function of the product

Product Analysis 3 main factors: Loads Material Geometry Know 2, solve for the 3rd! (usually an iterative approach) Determine the function of the product

Most important for robot design: Key Concepts How strong is a material? Toughness Strength Stiffness Resilience All are different, important, and RELATED terms! Most important for robot design: Strength Stiffness

Key Concepts Strength versus toughness Stiffness versus resilience Strength - the resistance of a material to failure due to an applied stress Toughness - a material’s ability to absorb energy and plastically deform without fracturing Stiffness versus resilience Stiffness - the resistance of a material to deflection or deformation due to an applied force Resilience - a material’s ability to absorb energy when it is deformed elastically and release that energy upon unloading Strength - http://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/strength-toughness/basic.html Stiffness - http://www.engineeringtoolbox.com/stiffness-d_1396.html Toughness – a material’s ability to absorb energy and plastically deform without fracturing [2] Resilience – a material’s ability to absorb energy when it is deformed elastically, and release that energy upon unloading [3]

Material properties are independent of geometry! Key Concepts Important Material Properties: Strength Yield (Tensile/Compressive) Ultimate Fatigue Flexural Modulus Young’s Modulus Poisson's Ratio Material properties are independent of geometry! Flexural modulus – tendency for a material to bend Young’s modulus – linear strain of a material Poisson’s Ratio – negative ratio of transverse to axial strain

Key Concepts Material Terminology: Alloy Brittle versus ductile A metallic material consisting of two or more elements that cannot be readily separated e.g. Steel (iron and carbon) Brittle versus ductile Brittle materials – little plastic deformation and low energy absorption before fracture Ductile materials – extensive plastic deformation and energy absorption before fracture Alloy: http://www.eurometaux.org/metalstoday/metalsfaqs/whatarealloys.aspx Brittle vs Ductile: http://people.virginia.edu/~lz2n/mse209/Chapter8.pdf

Stress and Strain Stress: force, or load, per unit area (Pa, psi) Can come from: compression (pushing), tension (pulling), shear, bending, torsion (twisting), etc. Image: Wikimedia Commons

Stress and Strain Strain: how much a material deforms Variation: normal strain (tension/compression) But what are all these letters? Force (P), length (L), area (A) Stress (σ), strain (є), deformation (δ) Young’s modulus (E) [material dependent] Hooke’s Law

Stress and Strain Stress versus Strain Diagram

Bending and Torsion Bending The letters never stop Moment / torque (M), height in beam (y) Curvature (C), radius of bend (R) Young’s Modulus (E) [material] Moment of Inertia (I) [geometry] *Sign convention: tension is positive, compression is negative Image: Wikimedia Commons

Bending and Torsion Torsion A veritable alphabet soup Hooke’s Law Radius (r), angle (θ), length (L), torque / moment (T) Shearing strain (γ), shearing stress (τ) Modulus of rigidity (G) [material] Polar moment of inertia (J) [geometry] Hooke’s Law Image: Wikimedia Commons

Bending and Torsion Moments of inertia (I and J) Essentially, resistance to rotation / bending about a given axis A cautionary note: There are two types of moment of inertia: area and mass [we’re concerned with area] For a Rectangle:

Mechanical Loads Tension: Structures stretch under tension Dependent on material and area It doesn’t matter what shape Commonly use cables Compression: Squeeze under compression Dependent on material, length, and geometry Shape matters! Want large value for I Short sections for compression loads (buckling)

Mechanical Loads Bending: Torques / moments can also bend Dependent on geometry, material Shape still matters, want large I Max stress near top (tension) and bottom (compression) Torsion: Torques / moments can twist Dependent on length, geometry, material Again, shape matters! Want large J Shorter members better resist twisting Stress concentrated near outside (shear)

Material Selection Common FIRST Materials Aluminium Steel Plastics Composites

Principal Alloying Element Material Selection Aluminium Common alloys 2024 5052 6061/6063 7068 7075 Can be heat treated or annealed Strength and price vary Common structural components Alloy Series Principal Alloying Element 1xxx 99.000% Minimum Aluminum 2xxx Copper 3xxx Manganese 4xxx Silicon 5xxx Magnesium 6xxx Magnesium and Silicon 7xxx Zinc 8xxx Other Elements Table: http://www.esab.ca/ca/en/education/blog/understanding-the-aluminum-alloy-designation-system.cfm Al info: http://www.aircraftspruce.com/catalog/mepages/aluminfo.php

Material Selection Aluminum comparison 2024-T4 5052-H32 6063-T6 Density (g/cc) 2.78 2.68 2.70 2.69 2.81 Modulus of Elasticity (GPa) 73.1 70.3 68.9 69.0 71.7 Tensile Yield Strength (MPa) 324 193 214 260 503 Fatigue Strength (MPa) 138 117 95 159 Poisson’s Ratio 0.33 Properties: ASM Square tubing: 6061/6063

Material Selection Steel Categories Commonly used for gears, fasteners Carbon Steel (low, medium, high) Alloy Steel Stainless Steel Tool Steel Commonly used for gears, fasteners

Material Selection Aluminium versus steel Cost Steel generally cheaper per pound (prices vary) Strength Steel is much stronger, but cannot be formed or machined as easily Weight Aluminium is much lighter Strength to weight ratio Aluminum has a higher ratio http://www.wenzelmetalspinning.com/steel-vs-aluminum.html

Material Selection Plastics Common plastics Much lighter than metals ABS Polycarbonate Acrylic Much lighter than metals Lower strength Non-conductive

Material Selection Composites A combination of two (or more) different materials that produces a material of superior performance than the components Fiber and matrix components High strength to weight ratio Tailor strength in specific directions

Material Selection Where to find information: Textbooks Databooks Manufacturer’s literature Internet Sites

Material Selection cost versus performance Summary: 1. Determine functionality and design requirements 2. Calculate loads and geometry 3. Choose suitable materials 4. Iterate 2 and 3 if necessary Don’t forget the big picture: cost versus performance

Concluding Thoughts Balance of cost and performance Loads, material, geometry Mechanical properties are independent of geometry Each material has advantages and disadvantages

Thank you! Questions?

References [1] Stuart, Jeff. “Designing for Strength and Durability”. School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN. October 2015. [2] NDT Resource Center. “Toughness”. The Collaboration for NDT Education, Iowa State University. October 2015. https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/Toughness.htm [3] Campbell, Flake C. Elements of Metallurgy and Engineering Alloys. ASM International. p. 206. ISBN 9780871708670. [4] Engineering and Materials Education Research Group. “Materials Selection for Engineering Design”. University of Liverpool. www.materials.ac.uk/resources/fe/materialsselection.ppt