Materials selection for mechanical design 1, Schemes and Mind Maps of Design

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Materials selection for mechanical design 1 • Breaking down a design problem • Identifying function, objectives, constraints • Optimizing performance • Ashby plots • Mechanical response: how does a material respond to loads? • Elastic deformation • strain: unitless change in dimension • stress: force per area • elastic deformation is reversible upon release of applied forces • Plastic deformation • permanent deformation is what’s left over • response depends on material history (microstructure) • Fracture • preexisting cracks/flaws in material, propagate under applied stress • catastrophic failure of material • Creep • time-dependent permanent deformation to time-independent load • thermally activated response • Fatigue • fracture response to time-dependent cyclic loading • cycling promotes crack nucleation and growth; catastrophic failure Mechanical response of materials 2 ! Rupture occurs along a cone-shaped surface that forms an angle of approximately 45° with the original surface of the specimen (“cup-cone” shape) ! Shear is primarily responsible for failure in ductile materials ! Axial loading: maximum shear stress occurs at 45o Necking Rupture 5Stress-strain diagram: ductile materials Ashby plots Materials selection for mechanical design: choose best material among competing properties Our goal: understanding mechanisms responsible for behavior M. Ashby “Materials Selection in Mechanical Design” 6 PM(M)PG(G) Materials selection Design concerns function - what a component does constraints - what must/must not occur objective - what is maximized/minimized M. Ashby, “Materials Selection in Mechanical Design” function constraint objective Example: tie-rod stretches to carry load, must not yield, and be lightweight Rank different designs performance as a function P(F, G, M): functional needs (F) geometry (G) material properties (M) We assume a separable form: P(F, G, M) = PF(F) PG(G) PM(M) so that material choice can be optimized independent of design specifics, with flexibility The goal: optimize performance pmax = 2 ↵⇡r · 0 BBBB@ K2 Ic YS 1 CCCCA Ex: maximum pressure in cylindrical vessel to leak, but not fracture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elative (raw) abundances from U.S. Geological Survey Nucleosynthesis (stellar fusion processes) determines what “raw” materials we have available. 10 Materials properties and selection Material properties mechanical: modulus, yield stress, fracture toughness, ... transport/thermal: heat capacity, thermal expansion, resistivity economic: density, cost/mass price includes: cost to extract, cost/energy to process, cost/energy to form, cost of disposal, regulation cost Materials selection involves 1. determining combination of properties to maximize (function, constraint, and objective) 2. selecting material/material class to fill that need M. Ashby, “Materials Selection in Mechanical Design” We do selection via an “Ashby plot”: log-log plot of two material properties PM(M) =M↵1 1 ·M ↵2 2 · · · log PM(M) = ↵1 log M1 + ↵2 log M2 + · · · Why log-log? Constant (equal) performance is a straight line on an Ashby plot 11 Light, strong tie-rod 12 A tie-rod carries load along its length. We want it to carry the load without yielding, and if it’s in a vehicle, we want a low mass. First: what is the function? A. low mass B. low area C. carry load D. long length E. not yield Light, strong tie-rod 15 A tie-rod carries load along its length: • Functional needs: carry load F • Geometry: length L, area A • Constants? F, L • Variables? area A, material • Constraint? stress below yield stress • Performance? mass m Light, strong tie-rod 16 A tie-rod carries load along its length: • Functional needs: carry load F • Geometry: length L, area A • Constants? F, L • Variables? area A, material • Constraint? stress below yield stress • Performance? mass m m = SLF ρ σYS Yield strength vs. density M. Ashby, “Materials Selection in Mechanical Design” 17 Yield strength vs. density M. Ashby, “Materials Selection in Mechanical Design” increasing YS/density 20 Light, stiff tie-rod 21 A tie-rod carries load along its length. We want it to carry the load without extending more than length δ, and if it’s in a vehicle, we want a low mass. • Functional needs: carry load F • Geometry: length L, area A • Constants? F, L • Variables? area A, material • Constraint? extension below δ • Performance? mass m Light, stiff tie-rod 22 A tie-rod carries load along its length. We want it to carry the load without extending more than length δ, and if it’s in a vehicle, we want a low mass. • Functional needs: carry load F • Geometry: length L, area A • Constants? F, L • Variables? area A, material • Constraint? extension below δ • Performance? mass m m = SFL2 δ ρ E Light, strong cantilever 25 A cantilever is fixed at one end, and carries load perpendicular to its length. We want it to carry the load without yielding, we want a low mass. • Functional needs: carry load W • Geometry: length L, diameter d • Constants? W, L • Variables? diameter d, material • Constraint? stress below yield • Performance? mass m Light, strong cantilever 26 A cantilever is fixed at one end, and carries load perpendicular to its length. We want it to carry the load without yielding, we want a low mass. • Functional needs: carry load W • Geometry: length L, diameter d • Constants? W, L • Variables? diameter d, material • Constraint? stress below yield • Performance? mass m m ∝ ρ σ2/3 YS Yield strength vs. density M. Ashby, “Materials Selection in Mechanical Design” 27 Young’s modulus vs. cost increasing E/cost M. Ashby, “Materials Selection in Mechanical Design” 30 Young’s modulus vs. cost increasing E1/2/cost M. Ashby, “Materials Selection in Mechanical Design” 31 • External load does work on a body: change in internal energy • Work = integral of force × distance • Force = (stress) × (area) • Distance = (strain) × (length) • stress × strain → energy/volume • If the deformation is recoverable then so is the energy. Strain energy density 32 W = Z F · dr = Z (A0)(L0 d✏) = V0 Z d✏ Elastic energy storage density: modulus of resilience Total strain energy density from fracture: modulus of toughness ur = 1 2 pl✏pl = 1 2 2 pl E Pressure tanks 35 A pressure tank holds a fluid at pressure, and carries load perpendicular to its thickness. We want it to carry the load to yield before fracture, and so that the critical flaw size is larger than the thickness (leak before fracture). • Functional needs: hold pressure p • Geometry: wall thickness t, diameter d • Constants? d • Variables? thickness t, material • Constraint? stress below yield, flaw size above t • Performance? pressure p Fracture toughness vs. yield strength increasing KIc/YS increasing YS M. Ashby, “Materials Selection in Mechanical Design” 36 Fracture toughness vs. yield strength M. Ashby, “Materials Selection in Mechanical Design” 37