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Page Materials Selection Lecture #10: Materials Selection Charts Monday October 3, 2005

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Page 2 Common wisdom : Material properties limit performance. Performance can be maximized by comparing and selecting the appropriate material. Always consider a wide range of materials.

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Page 3 Range of material properties :

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Page 4 Simple solution : List in rank order and choose cut-off point. Steel210 GPa Glass 80 GPa Al 69 GPa Wood 8 GPa

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Page 5 However... Often must consider more that one property. I.e. space structures must be light and stiff !!! Can take ratios : specific modulus E / = … specific strength failure / = …

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Page 6 Ratios of properties : Relative importance depends on design criteria !!!

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Page 7 Plate deflection : = 0.67 Mga 2 E t 3 Mass = a 2 t solve for t and substitute: M = (0.67g / ) 1/2 a 4 ( / E 1/3 ) 3/2 M 1 = ( / E 1/3 ) 2a t W=mg

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Page 8 Beam deflections : Square beam of length L : = 4 L 3 F / E t 4 M = L t 2 Solve and substitute: M = (4L 5 F / ) 1/2 ( / E 1/2 ) M 2 = ( / E 1/2 ) F L

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Page 9 Beam buckling : ? Post of length L : m = r 2 l P crit = 2 EI = 3 Er 4 l 2 4l 2 Solve and substitute: M = (4L 5 F / ) 1/2 ( 2 / E) 1/2 M 2 = ( / E 1/2 )

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Page 10 The Ashby solution : Materials Selection Charts Property #2 Property #1 lo,lo hi,hi lo,hi hi,lo

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Page 11 The Ashby solution : Materials Selection Charts Property #2 Property #1 lo,lolo,hi hi,lo subrange

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Page 12 Examples of MS charts : Materials Selection, Ch. 4 Modulus - Density (p 37) Strength - Density (p 39) Modulus - Strength (p 42) Loss coefficient - Modulus (p 48) Conductivity - Diffusivity (p 49) Expansion - Modulus (p 52) Modulus - Cost (p 57) etc.

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Page 13 Material grouping into classes : Fig. 4.2 in Materials Selection (p 34) Density (g / cm 3 ) Modulus (E) (GPa) alloys ceramics composites woods polymers elastomers foams

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Page 14 Adding contours to the plots : From wave equation we know : vel = (E / ) 1/2 take log and rearranging gives: log (E) = log ( ) + 2 log (vel) slope of log-log plot is: d log (E) / d log ( ) = 1 (for const. vel) intercept of log-log plot is: related to vel.

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Page 15 Contour plots : Fig. 4.2 in Materials Selection (p 34) Density (g / cm 3 ) Modulus (E) (GPa) alloys ceramics composites woods polymers elastomersfoams 10 4 m/s 10 3 m/s

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Page 16 Adding contours to the plots : From beam buckling we get : E 1/2 / = const. take log and rearranging gives: log (E) = 2 log ( ) + 2 log (const.) slope of log-log plot is: d log (E) / d log ( ) = 2 intercept of log-log plot is: related to const.

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Page 17 Adding contours to the plots : From plate deflection we get : E 1/3 / = const. take log and rearranging gives: log (E) = 3 log ( ) + 3 log (const.) slope of log-log plot is: d log (E) / d log ( ) = 3 intercept of log-log plot is: related to const.

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Page 18 Contours : * see Fig. 4.3 in Materials Selection (p 37)

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Page 19 Can use both to compare : Property #2 Property #1 m A B

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