Material Indicies

8/9/2019 Material Indicies

1/8

Material Performance indices (taken from CES disc)

Introduction

The performance, p, of a component is measured by a performance equation. Theperformance equation contains groups of material properties. These groups arethe material indices. Sometimes the "group" is a single property; thus if theperformance of a beam is measured by its stiffness, the performance equationcontains only one property, the elastic modulus E. It is the material index for this

problem. More commonly the performance equation contains a group of two ormore properties. amiliar examples are the specific stiffness, E !, and the specificstrength, #y !, $where E is %oung&s modulus, #y is the yield strength or elasticlimit, and is the density', but there are many others. They are a (ey to theoptimal selection of materials.

Uses of Material Indices

Material Selection. )omponents ha*e functions+ to carry loads safely, totransmit heat, to store energy, to insulate, and so forth. ach function has anassociated material index. Materials with high *alues of the appropriate indexmaximi-e that aspect of the performance of the component. The material index isgenerally independent of the details of the design. Thus the indices for beams inthe tables which follow are independent of the detailed shape of the beam; thatfor minimi-ing thermal distortion of precision instruments is independent of theconfiguration of the instrument. This gi*es them great generality.

Material Deployment or Substitution. new material will ha*e potentialapplication in functions for which its indices ha*e unusually high *alues. ruitfulapplications for a new material can be identified by e*aluating its indices andcomparing these with them of incumbent materials. Similar reasoning points theway to identifying *iable substitutes for an incumbent material in an establishedapplication.

Shape classification as defined by CES (for use in process selection)


2/8

Stiffness-limited desin at minimum mass (cost! enery!

en"ironmental impact)

#U$C%I&$ '$D C&$S%'I$%S M'IMISE

%IE (tensile strut)

stiffness, length specified; section area free E !

S*'#% (loaded in torsion)

stiffness, length, shape specified, section area free G/!0 !

stiffness, length, outer radius specified; wall thic(ness free G !

stiffness, length, wall1thic(ness specified; outer radius free G/!2 !

+E'M (loaded in bendin)

stiffness, length, shape specified; section area free E/!0 !

stiffness, length, height specified; width free E !

stiffness, length, width specified; height free E/!2 !

C&,UM$ (compression strut! failure by elastic bucklin)

buc(ling load, length, shape specified; section area free E/!0

!

P'$E, (flat plate! loaded in bendin)

stiffness, length, width specified, thic(ness free E/!2 !

P,'%E (flat plate! compressed in-plane! bucklin failure)

collapse load, length and width specified, thic(ness free E/!2 !

C,I$DE I%* I$%E$', PESSUE

elastic distortion, pressure and radius specified; wall thic(ness free E !

SP*EIC', S*E,, I%* I$%E$', PESSUE

elastic distortion, pressure and radius specified, wall thic(ness free E ! $/13'


3/8

/. To minimi-e cost, use the abo*e criteria for minimum weight, replacingdensity by Cm, where Cm is the material cost per (g. To minimi-eenergy content, use the abo*e criteria for minimum mass replacingdensity by q where q is the energy content per (g. To minimi-e

environmental impact , replace density by Ie instead, where Ie is theeco1indicator *alue for the material

0. E 4 %oung&s modulus for tension, the flexural modulus for bending orbuc(ling; G 4 shear modulus; 4 density, q 4 energy content!(g;Ie 4 eco1indicator *alue!(g.

Strent/-limited desin at minimum mass (cost! enery!

en"ironmental impact)


%IE (tensile strut)

stiffness, length specified; section area free #f !

S*'#% (loaded in torsion)

load, length, shape specified, section area free #f 0!2 !

load, length, outer radius specified; wall thic(ness free #f ! load, length, wall1thic(ness specified; outer radius free #f /!0 !

+E'M (loaded in bendin)

load, length, shape specified; section area free #f 0!2 !

load length, height specified; width free #f !

load, length, width specified; height free #f /!0 !

C&,UM$ (compression strut)

load, length, shape specified; section area free #f !

P'$E, (flat plate! loaded in bendin)

stiffness, length, width specified, thic(ness free #f /!0 !

P,'%E (flat plate! compressed in-plane! bucklin failure)

collapse load, length and width specified, thic(ness free #f /!0 !


4/8

C,I$DE I%* I$%E$', PESSUE

elastic distortion, pressure and radius specified, wall thic(ness free #f !

SP*EIC', S*E,, I%* I$%E$', PESSUE

elastic distortion, pressure and radius specified, wall thic(ness free #f !

#,*EE,S! &%'%I$0 DIS1S

maximum energy storage per unit *olume; gi*en *elocity

maximum energy storage per unit mass; no failure #f !

/. To minimi-e cost , use the abo*e criteria for minimum mass, replacingdensity by Cm, where Cm is the material cost per (g. To minimi-e

energy content , use the abo*e criteria for minimum weight replacingdensity by q where q is the energy content per (g. To minimi-eenvironmental impact , replace density by Ie instead, where Ie is theeco1indicator *alue for the material

0. #f 4 failure strength $the yield strength for metals and ductile polymers,the tensile strength for ceramics, glasses and brittle polymers loaded intension; the flexural strength or modulus of rupture for materials loadedin bending'; 4 density.

2. or design for infinite fatigue life, replace #f by the fatigue strength$endurance limit' #e.

Strent/-limited desin for ma2imum performancesprins! /ines etc.


SPI$0S

maximum stored elastic energy per unit *olume; no failure #f 0 ! E

maximum stored elastic energy per unit mass; no failure #f 0 ! E

E,'S%IC *I$0ES

radius of bend to be minimi-ed $max flexibility without failure' #f ! E

1$I#E ED0ES! PI3&%S

minimum contact area, maximum bearing load #f 2

! E0

and H


5/8

C&MPESSI&$ SE',S '$D 0'S1E%S

maximum conformability; limit on contact pressure #f 2!0 ! E and / ! E

DI'P*'0MS

maximum deflection under specified pressure or force #f 2!0 ! E

&%'%I$0 DUMS '$D CE$%I#U0ES

maximum angular *elocity; radius fixed; wall thic(ness free #f !

/. To minimi-e cost , use the abo*e criteria for minimum weight, replacingdensity by Cm, where Cm is the material cost per (g. To minimi-eenergy content, use the abo*e criteria for minimum weight replacingdensity by q where q is the energy content per (g. To minimi-eenvironmental impact , replace density by Ie instead, where Ie is theeco1indicator *alue for the material

0. #f 4 failure strength $the yield strength for metals and ductile polymers,the tensile strength for ceramics, glasses and brittle polymers loaded intension; the flexural strength or modulus of rupture for materials loadedin bending'; 4 density; H 4 hardness.

2. or design for infinite fatigue life, replace #f by the fatigue strength$endurance limit' #e.

3ibration-limited desin


%IES! C&,UM$S

maximum longitudinal *ibration frequencies E !

+E'MS! all dimensions prescribed

maximum flexural *ibration frequencies E !

+E'MS! lent/ and stiffness prescribed

maximum flexural *ibration frequencies E/!0 !

P'$E,S! all dimensions prescribed

maximum flexural *ibration frequencies E !

P'$E,S! lent/! 4idt/ and stiffness prescribed

maximum flexural *ibration frequencies E/!2 !


6/8

%IES! C&,UM$S! +E'MS! P'$E,S! stiffness prescribed

minimum longitudinal excitation from external dri*ers, ties 5 E !

minimum flexural excitation from external dri*ers, beams 5 E/!0 !

minimum flexural excitation from external dri*ers, panels 5 E/!2 !

/. E 4 %oung&s modulus for tension, the flexural modulus for bending;G 4 shear modulus; 4 density; 5 4 damping coefficient $mechanicalloss coefficient'.

Damae-tolerant Desin


%IES (tensile member)

Maximi-e flaw tolerance and strength, load1controlled design K IC and #f

Maximi-e flaw tolerance and strength, displacement1control K IC ! E and #f

Maximi-e flaw tolerance and strength, energy1control K IC0 ! E and #f

S*'#%S (loaded in torsion)




+E'MS (loaded in bendin)




PESSUE 3ESSE,

%ield1before1brea( K IC ! #f

6ea(1before1brea( K IC0 ! #f

/. K IC 4 fracture toughness; E 4 %oung&s modulus; #f 4 failure strength$the yield strength for metals and ductile polymers, the tensile strengthfor ceramics, glasses and brittle polymers loaded in tension; the flexuralstrength or modulus of rupture for materials loaded in bending'.


7/8

%/ermal and %/ermo-mec/anical Desin


%*EM', I$SU,'%I&$ M'%EI',S

minimum heat flux at steady state; thic(ness specified / ! 7

minimum temp rise in specified time; thic(ness specified / ! a 4 C p ! 7

minimi-e total energy consumed in thermal cycle $(ilns,etc'

$8a' ! 7 4 8$/ ! 7 C p'

%*EM', S%&'0E M'%EI',S

maximum energy stored ! unit material cost $storageheaters'

C p ! Cm

maximi-e energy stored for gi*en temperature rise andtime

7 ! $8a' 4 8$7 C p'

PECISI&$ DE3ICES

minimi-e thermal distortion for gi*en heat flux 7 ! 9

%*EM', S*&C1 ESIS%'$CE

maximum change in surface temperature; no failure #f ! E 9

*E'% SI$1S

maximum heat flux per unit *olume; expansion limited 7 ! :9

maximum heat flux per unit mass; expansion limited 7 ! :9

*E'% EC*'$0ES (pressure-limited)


8/8

maximum heat flux per unit area; no failure under : p 7 #f

maximum heat flux per unit mass; no failure under : p 7 #f !

/. 7 4 thermal conducti*ity; a 4 thermal diffusi*ity;C p 4 specific heat capacity; Cm 4 material cost !(g;Tmax 4 maximum ser*ice temperature; 9 4 thermal expansion coeff;E 4 %oung&s modulus; 4 density; #f 4 failure strength $the yieldstrength for metals and ductile polymers, the tensile strength forceramics, glasses and brittle polymers'

Electro-mec/anical Desin


+US +'S

minimum life1cost; high current conductor / ! e Cm

E,EC%&-M'0$E% I$DI$0S

maximum short1pulse field; no mechanical failure #y

maximi-e field and pulse1length, limit on temperature rise C p ! e

I$DI$0S! *I0*-SPEED E,EC%IC M&%&S

maximum rotational speed; no fatigue failure #e ! e

minimum ohmic losses; no fatigue failure / ! e

E,' 'MS

minimum response time; no fatigue failure #e ! E e

minimum ohmic losses; no fatigue failure #e0 ! E e

/. Cm 4 material cost !(g; E 4 %oung&s modulus; 4 density;e 4 electrical resisti*ity; #y 4 yield strength; #e 4 fatigue strength

$endurance limit'.

Documents

Material Indicies