7 Optimal Materials Selection in Mechanical Design
7.5 TOOLS FOR SELECTION OF PROPERTIES
In.dealing.with.the.best.selection.only.on.the.basis.of.properties.of.materials,.it.is.necessary.to.
interpret.the.requirements.linked.to.the.functions.needed.and.any.other.constraints,.as.indications.
of.what.properties.a.material.ought.to.have.
A.ranking.of.materials.can.be.made.based.on.two.different.criteria,.depending.on.how.materials.
and.constraints.are.referable.to.their.properties:
•. If.they.just.identify.properties.coming.into.play,.it.is.possible.to.make.a.choice.selecting.
those.materials.that.feature.the.most.suitable.values.of.these.properties.(higher.or.lower,.
depending.on.the.property).
•. If.requirements.and.constraints.are.expressed.by.minimum.or.maximum.limits.to.impose.
on.some.properties,.or.by.specific.values.these.properties.are.to.have,.the.choice.can.be.
made.ranking.materials.on.the.basis.of.their.compliance.with.these.limit.values.
7.5.1 stanDarD anD weighteD ProPerties MethoD
The.first.case.is.typical.of.a.preliminary.search.for.materials,.when.the.design.process.is.still.tak-ing. the. first. steps,. and. very. little. information. is. known,. beThe.first.case.is.typical.of.a.preliminary.search.for.materials,.when.the.design.process.is.still.tak-ing. limited. to. primary. requirements..
Continue.to.consider.a.pressure.tank.(Figure.7.1),.imagine.making.a.pre-survey.of.materials.to.make.
a.compressed-air.tank.that.can.withstand.a.maximum.service.pressure.of.1.5.MPa.(15.bars),.with.
temperatures.up.to.100°C,.perhaps.with.the.presence.of.water.
As.requirements.and.constraints.related.to.other.variables.are.not.considered.in.this.preliminary.
phase.(tank.capacity,.shape,.bulk,.and.geometric.parameters.such.as.length,.diameter,.wall.thick-ness).the.problem.involves.the.following.set.of.requirements,.each.referable.to.specific.properties.
of.the.material:
•. Resistance.to.load.due.to.pressure.(yield.point)
•. Rigidity.(Young’s.modulus)
•. Resistance.to.breakage.(tenacity)
•. Stability.at.maximum.working.temperature.(service.temperature,.thermal.expansion)
•. Stability.and.endurance.at.service.environment.conditions.(water.resistance)
Additional.requirements,.generally.considered.in.accordance.with.efficiency.and.on.economic.
grounds,.can.also.include.the.following:
•. Weight.reduction.(density)
•. Cost.containment.(cost.per.unit)
σz σr σt
t
Pressure p 2R
L
FIGURE 7.1 Example:.pressure.vessel.
Some.of.these.requirements.become.primary.constraints.for.the.initial.step.of.screening.of.mate-rials. to. be. selected:. the. top. service. temperature. of. the. material. must. have. a. minimum. value. of.
100°C;.the.material.must.be.water.resistant.
are.very.different.from.one.other..If.a.set.of.nM.materials.{Mi}i.=.1,…,nPM.is.to.be.compared.to.a.set.
of.nPM.properties.for.the.{PMj}j.=.1,…,.nPM.ranking,.standardization.can.be.obtained.by.the.following.
expressions: where.Vij.is.the.quantity.of.the.j-th.property.for.the.i-th.material.and.Nij .is.the.corresponding.stan-dard.value..Equation.7.1.is.used.for.properties.to.maximize,.and.Equation.7.2.for.those.to.minimize..
where.αj.are.the.weight.coefficients.(Σαj .=.1).that.quantify.the.importance.of.each.property.com-pared. to. the. others.. In. this. way,. it. is. possible. to. associate. each. material. to. a. unique.γi. index of weighed properties,.which.depends.on.the.importance.given.to.the.various.properties.at.stake..The.
material.with.the.highest.index.is.that.which.best.responds.to.requirements.
Table.7.2.shows.the.values.of.γi,.for.the.five.materials.examined,.calculated.for.a.specific.set.of.
weight.coefficients.(α1.=.0.25,.α2.=.0.15,.α3.=.0.15,.α4.=.0.10,.α5.=.0.15,.α6.=.0.20)..In.this.case,.too,.
the.carbon.steel.solution.appears.the.most.interesting.
The.index.of.weighed.properties.can.also.be.used.in.the.following.form:
. γʹ =i γi/Cρ,. (7.4)
relating.γi.to.cost.and.density.product,.as.previously.described..It.is.a.simple.way.to.emphasize.the.
economic.factor,.which.is.no.longer.considered.as.an.element.to.evaluate.when.the.efficiency.of.
TABLE 7.2 Properties Method: Materials Comparison Materials Material PropertiesPerformance Metrics Yield Strength [MPa]Young Modulus [GPa]Toughness [MPa.m½]
Thermal Expansion [𝛍strain/∙C]Density [kg/m3]Cost [€/kg]𝛄𝛚𝛒∙𝛔s [kg/MPa.m3]Cm 𝛒/𝛔s [[€//MPa.m3] Carbon.steel29021060127700.0.6074.90.5226.515.9 Stainless.steel31020095107400.1.5070.30.5723.935.8 Aluminum.alloy240.7035242500.1.6048.50.4310.416.6 GFRP150.2016211600.3.1036.40.4610.733.2 CFRP25011018.5150016.0056.60.99.6.096.0
materials.is.assessed,.but.as.a.primary.factor..The.cost.of.materials.is.therefore.ruled.out.here.from.
the.preliminary.calculation.of.γi.in.accordance.with.Equation.7.3.
This.estimate.and.classification.procedure.of.components.can.be.used.even.when.dealing.with.
non-numerically.quantifiable.properties,.provided.they.are.not.quality.properties.and.are.correctly.
standardized.numerically.
7.5.2 MethoD of liMits anD objectives on ProPerties
The. main. shortcoming. of. the. standard. and. weighted. properties. method. is. that. classification. of.
materials.is.not.made.just.based.on.a.criterion.of.efficiency,.as.most.efficient.materials.indiscrimi-nately.maximize.or.minimize.the.properties.to.be.detected.
A. more. effective. classification. is. feasible. in. the. second. case,. that. is,. when. requirements. and.
constraints.are.expressible.by.maximum.or.minimum.limits.and.also.by.the.specific.values.these.
can.be.assessed.by.simple.expressions.of.σr,.σt,.σz,.radial,.tangential,.and.longitudinal.tensions.as.in.
the.note.in.Figure.7.1.(see.Pipes.and.Vessels,.Chapter.17):
Density Density
Thermal
Yield strength Yield strength
Cost Carboon steel
Stainless steel
Aluminum alloy CFRP
FIGURE 7.2 Properties.method:.graphic.materials.comparison.
. σr= p σt= pR σz=
t pR
t
2 2 .. (7.7)
.Tensile.stress.on.the.spherical.caps.is.given.by.the.same.σr.of.the.cyclindrical.section.and.by.
tangential.tensions.equal.to.σz .in.the.same.area..Most.critical.stress.conditions.occur.in.the.cylindri-cal.section.of.the.tank,.and.depend.on.the.wall.thickness..Assuming.t.=.3.mm,.a.peak.of.tension.
σt.=.60.MPa.results,.as.well.as.an.ideal.tension.according.to.von.Mises.of.σid.=.52.MPa.(see.Failure.
Theories,.Chapter.8).
The.other.{PMj}.properties.are.handled.with.maximum.or.minimum.limit.conditions:
•. Young’s.modulus.≥.20.GPa
•. Resistance.to.fracture.≥.10.MPa.m1./.2
•. Thermal.expansion.≤.50.×.10–6.1/°C
•. Density.≤.7000.kg/m3
•. Cost.≤.5.00.€/kg
These.conditions.could.be.used.for.the.initial.screening.of.materials,.to.rule.out.those.that.do.not.
After.defining.objective.values.and.maximum.and.minimum.limits,.a.ωi.index,.called.a.merit parameter,.can.be.calculated.for.each.material,.from.the.expression:
.
ω= α ⋅ − + α ⋅ + α ⋅
= = =
∑
nrOBT1 r OVrr 1∑
nsINF1 s VLss∑
ntSUP1 t VLtt,. (7.8)where. nOBT,. nINF,. and. nSUP. are,. respectively,. the. number. of. objective. properties,. of. inferior. and.
superior.limits;.αr,.αs,.and.αt.are.the.weight.coefficients.of.objective-properties,.of.those.subject.to.
inferior.limits,.other.and.superior.limits;.Vr,.Vs,.and.Vt.are.the.values.of.tested.materials.compared.
to.the.objective.properties,.to.those.subject.to.inferior.limits,.and.other.to.superior.limits;.Or.are.the.
values.fixed.for.objective.properties,.Ls.and.Lt.are.the.values.of.inferior.and.superior.limits.
The.material.with.the.lowest.merit.parameter.turns.out.to.be.the.most.effective..In.detail,.giving.
more.importance.to.objective.properties.than.to.those.subject.to.limits,.defines.that.material.as.the.
one.with.the.objective.properties.closest.to.fixed.values.
In.Table.7.2.are.the.ωi,.values.for.the.five.materials.tested,.calculated.for.the.same.set.of.weight.
coefficients.used.for.calculating.γi..As.can.be.seen,.the.aluminum.alloy.solution.represents.the.best.
compromise.between.objective.and.imposed.limits..The.Glass.Fiber.Reinforced.Polymer.composite.
solution,.according.to.γi.parameters.the.least.effective,.reveals.itself.the.second.most.efficient,.as.out.
of.all.the.others.it.best.satisfies.the.objective.property.(yield.point.target.value).