MATERIAL EFFICIENCY AND COST EFFECTIVENESS

1

MATERIAL EFFICIENCY AND COST EFFECTIVENESSOF SANDWICH MATERIALS

Jochen Pflug, Bart Vangrimde, Ignaas VerpoestDepartment Metallurgy and Materials Engineering (MTM)

Katholieke Universiteit Leuven, Belgium

ABSTRACT

Sandwich constructions are used since may decades for lightweight structures. Theireconomical advantages are vital for their potential in many applications. This paper presentsan approach to compare sandwich material combinations based on their bending modulus,density and cost. The properties of sandwich material combinations are therefore shown inmaterials selection charts as a function of the ratio between skin thickness and sandwichheight t/h. This enables a graphical comparison of the material efficiency of solid materialsand different sandwich material options. Furthermore a technique to balance the major targetsof low cost and low weight is presented. For that purpose, the economical value of weightsaving for the target application is accounted for in the materials selection charts. This allowsto define besides the weight saving factors also cost saving factors, which are useful todetermine the economical advantage of a sandwich material combination. The necessary costeffectiveness of sandwich material production processes resulting in an economicaladvantage of sandwich panels can be calculated.

KEY WORDS: Sandwich Construction, Cost/Economics, Core Materials

1. INTRODUCTION

Lightweight sandwich constructions are used to increase the specific stiffness and strength ofstructures because of functional reasons and economical reasons. In aerospace engineering,challenging requirements already necessitated in the past to employ the latest technology, tocreate extreme lightweight constructions. But today, the exploitation of the economicaladvantages of weight reduction has become essential for many industries. The possible costreductions by use of sandwich design, due to lower weight and less raw material usage,interact and often contradict with the selection of a low cost material and a cost efficientproduction process. Sandwich constructions with low cost core materials can be not onlymore lightweight but also more cost effective, especially because the advancement andautomation of production processes results in a reduction of the production cost forlightweight sandwich panels.In the following materials selection charts, material efficiency and the value of weight savingare first briefly reviewed before those concepts are applied to sandwich constructions, withthe objective to provide a method to facilitate sandwich material selection for combineddemands of low weight and low cost.

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2. MATERIAL EFFICIENCY AND MATERIAL COST

The structural efficiency is defined as the capability of a structure to carry loads at aminimum weight. If geometry, loading and type of support are not changed (i.e. the structuralloading coefficient is constant) the structural efficiency becomes only dependent on thematerial efficiency. The material efficiency is usually defined as a mechanical performanceper weight. For buckling and bending stiffness of plates, the material efficiency per weight isE1/3/ρ and for tension and compression stiffness of plates it is E/ρ (with E the elastic modulusand ρ the material density). Materials selection charts [1] can be used to compare howefficient different materials fulfil a certain structural function. Those charts allow to select amaterial for bending as well as for tension and compression loads. However, since a maximaleconomical advantage is often targeted the optimisation of stiffness per weight or strength perweight should be part of a performance per cost optimisation. A general procedure for multi-objective optimisation based on cost value functions has been presented by Ashby in [2]. Tothe material cost, other cost factors need to be added as shown in equation (1). For structuraldesign, performance is primarily determined by the structural (mechanical) performance.Nevertheless, the non-structural performance, (i.e. physical-chemical properties like e.g.surface quality, sound absorption, wear, chemical resistance, flame-retardancy) and thereliability and maintainability can be important issues for structural parts as well.

(1)

The material selection and the production process selection determine usually a large part ofthe cost of a structure [4]. The operating cost, (e.g. of an aircraft) is often related to theweight of the structure. The weight also affects the ecological cost (e.g. recycling). Both areof increasing importance since many years. Maximisation of performance per cost forstructural parts requires thus to find the best compromise between (structural) performanceand material cost, production cost and weight. In table 1 material properties of some materialsare shown, e.g. woven glass fibre reinforced plastics (GFRPwoven), natural fibre matreinforced plastics (NFRPmat), polypropylene (PP). The material modulus E, the density ρ, thematerial cost Cw and Cv Mat of those examples are utilized and indicated further on in thematerials selection charts of this paper. The material cost per volume (Cv Mat) is calculatedfrom the material density information and the material cost per kg data. The values Cv Valueand Cv Sum will be defined in the following section 3.

materialsE

modulus[GPa]

ρdensity

[kg/dm³]

Cwmaterial cost

[€/kg]

Cv Matmaterial cost

[€/dm³]

Cv Value(with 2 €/kg)

[€/dm³]

Cv Sumtotal cost[€/dm³]

Steel 210 7.8 0.6 4.68 15.60 20.28Aluminium 72 2.7 2.0 5.40 5.40 10.80GFRPwoven 20 1.7 3.3 5.61 3.40 9.01NFRPmat 6 1.0 1.1 1.10 2.20 3.30PP 1.2 0.9 1.0 0.90 1.80 2.70Balsa wood 0.15 0.15 10.0 1.50 0.30 1.80PP honeycomb 0.03 0.08 4.0 0.32 0.16 0.48Paper honeycomb 0.02 0.08 2.0 0.16 0.16 0.32

Table 1: Properties of some example materials

skin

core

performance structural performance

cost material cost + production cost + operating cost + ecological cost≈

affected by weight

3

Materials selection charts provide basic data for the comparison towards minimal weight orminimal cost. However, an optimal balance between a low cost target and a low weight targetis often requested for sandwich material.

2.1. The value of weight saving Sandwich constructions may enable cost reductions dueto a reduction in material cost. However, additional cost savings, due to the effect of a weightreduction on the operating cost and where applicable on the ecological cost should beconsidered. To include those cost reductions into the comparison of the material efficiencyper cost, the benefit of weight savings CwValue in €/kg has to be determined. This value isdependent on the application area and may vary for different components. For example inautomotive applications the value of weight savings is dependent on the position of the partin the vehicle [5]. However, usually the value of a weight reduction can be easily estimated ifweight reduction is a requirement for a component. For automotive applications an estimationis shown in the appendix. In table 1 and in the later examples a CwValue = 2 €/kg is used. Thevalue of material savings per volume CvValue in €/dm³ can be calculated by multiplication withthe material density values. Those costs per volume are added to the material cost per volumeCv Mat and shown in equation (2) and in the column Cv Sum of table 1.

(2)

The total cost per volume Cv Sum combines thus the cost paid for the material and the costexpected due to the weight of a part during the full life cycle or just during the in-service lifeof the component. The value of weight saving may be established by a detailed life cycleanalysis or a designer may just use what a custom is willing to pay for a weight reduction.

3. SANDWICH CONSTRUCTIONS

Optimal structural performance may require the selection of material combinations, becausedifferent functions have to be fulfilled by the part. The composition can be most efficient ifeach component is optimised for a certain function. A sandwich construction combines thein-plane properties of a skin material with the out-of-plane properties of a core material.Since the sandwich concept finds applications in many industries, different terminology canbe found. The skin material is e.g. also called facing, face or liner. In the following theterminology shown in figure 1 will be used.

Figure 1: Sandwich constituents and constructions

The skins carry the in-plane tension/compression stresses and in-plane shear stresses. Theyare usually relatively thin and have a high stiffness and strength. Besides high mechanical in-plane properties per weight the skin material usually has to fulfil also other requirements like

upper skin

lower skinbondinglayers

core

sandwich constituents(core, skin and bonding layer)

sandwichmaterial

(with dimensionsthis is referred to asa sandwich panel)

sandwichpart

(panel withedge closures,inserts and/orcurvatures)

sandwichstructure

(assembly ofsandwich parts)

bonding /lamination forming assembling

core and skinproductionraw

materials(for core

and skins)

sandwich constructions

1 1 1 Cv Sum Cv Mat + Cv Value Cw ρ + Cw Value ρ

= =

4

low cost, high surface quality and good impact performance. Sandwich constructions use thefact that the core of a panel that is loaded in bending does not carry much in-plane stressesand does not provide the surface of the part. The core can thus be made from a different,more lightweight and/or less expensive material. In lightweight sandwich constructions thecore is usually relatively thick and has a much lower density compared to the skins. Theprimary mechanical requirement for the core is to prevent the movement of the skins relativeto each other in-plane (by sufficient out-of-plane shear properties) and out-of-plane (bysufficient out-of-plane compression properties). The core material can furthermore haveadditional functions e.g. thermal and acoustic isolation or energy absorption during impact.

4. CORE MATERIAL SELECTION

For the most economical selection of a core material, besides sufficient mechanical propertiesboth low density and low material cost are required. The thickness of a panel with a weightper unit area of 1 kg/m² can be calculated by dividing the weight per unit area by the densityρ. This thickness of 1 kg/m² panels can be shown as a function of the material cost (figure 2).

Figure 2: Sandwich core materials selection chart

Figure 2 shows how much thickness the different materials provide for the same cost andweight. The mechanical properties have to be considered as well, however figure 2 enables tofind from all materials with sufficient mechanical properties the most lightweight ones in the

0,1 1 10 1000,1

1

10

100

0,03 0,3 3 30

Thic

knes

s [m

m]

Cost [€/kg = €/m²]

Composites

Diamond(300.000 €/kg)

Low alloy steels

Concrete,Cement

Brick, Stone

AluminiumMetalsand alloys

Polymers

Foams

PVC foam

PU foam

OakPine

Paper

Balsa

CFRP

GFRP

PP PET

PA

Cast iron

High alloy steels

Stainless steel

NFRP mats

PE

thickness/cost [mm/(€/m²)] = 1/Cv Mat [dm³/€]

100 10 2 11

0.5

0.1

0.01

Paper honeycombs

PP honeycombs

Woods andwood products

Fibre boardMDF

PMI foam

PEI foam

PP foam

1/Cv sum [dm³/€](with Cw value = 2 €/kg)

Material cost Cw [€/kg = €/m²]

Thic

knes

s [m

m] =

1 [k

g/m

²] / ρ

[kg/

dm³]

0.03 0.1 0.30.1

5

uppermost part of the diagram while the materials with the lowest material cost in €/kg arefound at the left side of the diagram. If for an application both low cost and low weight aredesired, an optimal material selection can be made by including the value of weight saving.In the sandwich core material selection chart curves (dashed) are shown for the reciprocalsum of the material cost and the cost of the weight (1/Cv Sum). In figure 2 the curves are shownfor a value 1/Cv Sum of 0.5, 1 and 2 dm³/€ for a value of weight saving of 2 €/kg.The thickness and cost of 1 kg panels of 1 m² can be compared. For example a polypropylene(PP) panel of 1 m² and 1 kg weight is about 1.1 mm thick and the material cost is 1 €. Thecost of thicker or thinner panels from each material can be compared along the lines forequivalent thickness per cost (dotted lines). An equally thick sandwich core from a solid layerof polypropylene (PP) costs 60% of a balsa core, although the PP layer is 6 times heavier thanthe balsa core. If the lower weight in a certain application is valued with 2 €/kg the higherweight of the PP leads to 1.5 times higher cost (compare Cv Mat, ρ and Cv Sum in table 1).The materials selection chart in figure 2 allows to compare the weight and cost of differentcore materials. An optimal core material selection becomes possible if all alternatives whichfulfil the mechanical requirement of a specific application are pre-selected. Nevertheless, forthe comparison of sandwich panels the material properties need to be included.

5. SANDWICH MATERIAL EFFICIENCY

For sandwich constructions the material efficiency per weight in bending E1/3/ρ is especiallyimportant because the bending stiffness is the main advantage of the sandwich concept. Theperformance of different sandwich panels can be compared to each other and to solid panelsby calculating a material efficiency per weight coefficient for buckling and bending EH

1/3/ρHusing a homogenised bending modulus EH and a homogenised density ρH. The homogenisedbending stiffness of a sandwich material with total height h and thickness of the skins t isequal to the bending stiffness of a homogeneous material with the same height h and anelastic modulus EH given in equation (3) and density ρH, given in equation (4). In equation (3)all three components contributing to the bending stiffness of a symmetrical sandwich materialare used. In the following sandwich materials are assumed to be symmetrical. For non-symmetrical panels similar equations can be derived. The symbols Ec, ρc, Cwc and Es, ρs, Cwsare used for the elastic modulus, material density and material cost of the core and skins,while EH, ρH and CwH are used for the properties of sandwich materials.

(3) (4)

Equation (5) shows the bending stiffness per width of a homogenised sandwich D. Theweight per unit area W/A is equal to the homogenised sandwich density ρH times the height.

(5) (6)

In equation (6) the height h is expressed via the homogenised modulus and the bendingstiffness from (5). Equation (6) shows that, for an equal bending stiffness, the weight per unitarea W/A gets minimal if the material efficiency coefficient EH

1/3/ρH is maximised. Theoptimal ratio between the thickness of the skins and the sandwich height can be calculatedfrom the maximum of the material efficiency per weight coefficient with the help of theequations (3), (4) and (7).

(7)

6

The exact solution for the optimal thickness ratios t/h for a maximal material efficiency perweight for buckling and bending EH

1/3/ρH is given in equation (8).

(8)

Shear deformations of the core can be included into the optimisation of sandwichconstructions. Furthermore an optimisation towards a maximum bending strength, involvingdifferent failure modes, can be performed. Those optimisations have been discussed in detailin [1,6,7]. However, the inclusion of shear deformation and strength leads to a dependency ofthe optimum on the loading case and the span length. In the following out-of-plane sheardeformations as well as out-of-plane compression deformations and strength not be includedin order to enable a general bending stiffness efficiency based comparison of sandwichmaterials. The required mechanical properties for the core can be determined separately forthe specific loading and support conditions. After the pre-selection of sandwich cores andskin materials with sufficient properties, the optimal core/skin material combination and theoptimal sandwich thickness ratio can be obtained. The material efficiency coefficients can beshown graphically as a function of the thickness ratio t/h. In the following a sandwichmaterial combination with aluminium skins and a solid core layer from polypropylene withmaterial properties from table 1 is used as an example.

Figure 3: Material efficiency as a function of the thickness ratio (example for aluminium skins and polypropylene core)

Figure 3 shows the effect of the thickness ratio on the bending stiffness material efficiencyper weight MEW, defined in equation (9).

(9)

Materialefficiencies MEW MECM MEC

Thickness ratio t/hsolid panel fromthe core material solid panel from

the skin material

Material efficienciesMEW per weightMECM per material costMEC per total cost

7

The figure 3 shows furthermore the material efficiencies per material cost MECM and per totalcost MEC. The material efficiency based on material cost (i.e. material cost effectiveness) isdefined in equation (10).

(10)

The material cost for the homogenised sandwich material (CwH in €/kg) can be calculated viaequation (11).

(11)

The material efficiency based on total cost (i.e. total cost effectiveness) includes not onlymaterial cost and the value of weight saving but also the production cost (equation 12).The panel production cost CaPanelProd is the additional cost per unit area required to produce asandwich panel of the thickness h. This includes cost for producing layers of the requiredthickness from the core and the skin material plus cost of bonding the skins onto the core.Those costs usually depend on the panel surface area and are thus given in €/m².

(12)

In the following the panel production cost CaPanelProd will not be directly included. Acomparison of the sandwich material cost effectiveness MEC with CaPanelProd = 0 enables todetermine the allowable sandwich panel production cost.In table 2 the efficiencies of some materials are compared to the sandwich material withaluminium (Al) skins and a solid polypropylene (PP) core. The efficiency values for asandwich material with a thickness ratio of 0.052 are shown in table 2. This thickness ratio isclose to all three optima (see vertical line in figure 4).

panel materials E[GPa]

ρ[kg/dm³]

Cw[€/kg]

MEW= E1/3/ρ

[GPa1/3/(kg/dm³)]

MECM= E1/3/(Cw ρ)

[GPa1/3/(€/dm³)]

MEC (Cw Value = 2 €/kg)= E1/3/(Cw ρ + Cw Value ρ)

[GPa1/3/(€/dm³)]

Steel 210 7.8 0.6 0.76 1.27 0.293Aluminium 72 2.7 2.0 1.54 0.77 0.385GFRP 20 1.7 3.3 1.60 0.48 0.301Polypropylene PP 1.2 0.9 1.0 1.18 1.18 0.394Sandwich material example (with homogenised properties EH, ρH and CwH)Al / PP t/h = 0.052 21.1 1.09 1.26 2.54 2.01 0.777

Table 2: Material efficiency in bending of some panel materials

The material efficiency values for a solid aluminium panel and a solid PP panel can be foundat t/h = 0 and t/h = 0.5 in the diagram in figure 3. The ratios between the material efficiencyof a material option and efficiency of a reference material can be interpreted as savingfactors. Compared to the efficiency values those saving factors enable to determine directlythe potential weight savings and cost savings of different material options. To quantify theincrease of mechanical performance per weight due to structuring, e.g. in an I-beam, a shapefactor has been described by Ashby in [8]. This approach defines a ratio between the materialefficiency coefficient per weight of the structured material and the material efficiencycoefficient per weight of the same unstructured material. This can be applied to sandwich

8

materials if the saving factors is define as the ratio of the efficiencies of a sandwich materialcombination and a solid panel from the skin material. The skin material choice is oftenrestricted due to mechanical requirements (e.g. hardness) and/or optical requirements on theouter surface. The resulting weight shape factor ФW is the factor of weight saved due the useof a sandwich construction with the lightweight core material (equation 13). In addition amaterial cost saving factor ФCM and a total cost shape factor ФC can be calculated (equation14 and 15). Thus material cost savings, the value of weight saving as well as the productioncost for the sandwich panel CaPanelProd and a solid plate CaSolidProd can be included.

(13)

(14)

(15)

The efficiency factors of sandwich material combinations can be compared as a function ofthe thickness ratio in the full range from a solid panel of the core material (t/h = 0) to a solidpanel of the skin material (t/h = 0.5) (figure 4). The total cost factor is in the followingcalculated without the production cost (i.e. CaPanelProd = 0, CaSolidProd = 0).

Figure 4: Weight and cost saving factors as a function of the thickness ratio(example for aluminium skins and polypropylene core)

Factors ФW ФCM ФC

EH / Es ρH / ρsCvMat / Cvs

Saving factorsФW of weightФCM of material costФC of total cost

Thickness ratio t/hsolid panel fromthe core material solid panel from

the skin material

Property factorsEH / Es (modulus)ρH / ρs (density)CvMat / Cvs (cost per m³)

9

The graphs in figure 4 enable to directly assess reduction of weight savings and cost savingsdue to the selection of less optimal thickness ratios. Often a higher skin thickness needs to beselected because of strength requirements, dimpling or wrinkling failure modes, surfacequality requirements or production constraints. An optimal bending efficient sandwichmaterial has always a EH/ρH ratio which is equal to the tension/compression efficiency of theskin material. The intersection of the modulus ratio EH/Es with the density ratio ρH/ρs definesin figure 4 e.g. the thickness ratio for a maximal material efficiency per weight.

(16) (17) (18)

Equations (16), (17) and (18) describe the relation between the material properties for optimalthickness ratios. The concise equation (16) lead to the same optima as the equations (8).

6. SANDWICH MATERIAL SELECTION

The materials selection chart showing the modulus versus density can be used to selectmaterials for solid panels with the maximal bending efficiency per weight [3]. We propose todisplay homogenised properties of sandwich material combinations as a function of thethickness ratio t/h in this chart (figure 5) to facilitate the selection of sandwich materials.

Figure 5: Sandwich selection with the chart for modulus versus density

0,1 1 100,01

0,1

1

10

100

1000

0,03 0,3 3

Mod

ulus

E [G

Pa]

Density [kg/dm³]

E1/3/ρ [GPa1/3/(kg/dm3)]

E/ρ [GPa/(kg/dm3)]

100

33.3

10

3.33

1

10 4.64 2.15 1Diamond

Steels

Concrete,Cement

Brick, Stone

Aluminium

CompositesMetalsand alloys

Polymers

Foams

Woods andwood products

PP

LDPE

PET

PA

PP foam

PMI foam

PVC foam

Oak ||

Oak ⊥

Pine ||

Pine ⊥

Paper ⊥

Fibre boardMDF

Balsa ||

Balsa ⊥

PU foam

CFRP UD

CFRP woven

GFRP UD

GFRP woven

GFRP matsNFRP mats

PEI foam

HDPE

Paper ||

Paper honeycombs

PP honeycombs

Material efficiency in bending MEW

Mat

eria

l effi

cien

cy in

tens

ion

/ com

pres

sion

t/h = 0.005

t/h = 0.01

t/h = 0.02

t/h = 0.05t/h = 0.1

t/h = 0.2

t/h = 0.05

0.03 0.1 0.3

0.1

10

Figure 5 shows the curves for two sandwich material combinations (aluminium skins onpolypropylene core and steel skins on paper honeycomb core) and the properties of differentmaterials [3] (with additional data from [7]). The maximum material efficiency in bending isat high E1/3/ρ value in the upper left corner of the diagram. The tension/compression materialefficiency lines E/ρ are also shown. In accordance with equation (16) the optimal thicknessratio is obtained where a parallel line from the skin materials properties Es and ρs intersectsthe curve of the sandwich material properties EH and ρH. It has to be kept in mind that thedisplayed modulus for the sandwich material combinations is a homogenised bendingmodulus. Thus EH/ρH is not the tension/compression material efficiency of the sandwichmaterial.Figure 6 presents the materials selection chart for optimal total cost effectiveness. Thehomogenised bending modulus and the total cost of sandwich material combinations areagain displayed as a function of the thickness ratio t/h. Like in figure 5 the thickness ratiosequal to 0.005 ; 0.01 ; 0.02 ; 0.05 ; 0.1 ; 0.2 are marked with small crosses.

Figure 6: Materials selection chart for modulus versus cost per m³with 2 €/kg weight penalty cost (value of weight saving)

The total cost Cv Sum have been calculated with equation (2) from the material cost and a value ofweight saving. The optimal material combination and the best thickness ratio for combined weightand cost objectives can be found with the help of the lines for equivalent material efficiencyper total cost (MEC = E1/3/Cv Sum).

1 10 1000,01

0,1

1

10

100

1000

0,3 3 30

Mod

ulus

E [G

Pa]

Cost [€/dm³] (with 2 €/kg value of weight saving)

Composites

Low alloy steels

Concrete,Cement

Brick, Stone

Metalsand alloys

Polymers

Aluminium

Woods andwood products

Balsa ⊥

Oak ||

Oak ⊥

Pine ||

Pine ⊥

Fibre board MDF

Balsa ||

CFRP UD

GFRP UD

GFRP woven

GFRP mats

PP

LDPE

PET

PA

Cast iron

High alloy steelsStainless steel

CFRP woven

NFRP mats

HDPE

E1/3/Cv Sum [GPa1/3/(€/dm³)]

E/Cv Sum [GPa/(€/dm³)]

10 1 0.110

1

0.1

Paper ⊥

Paper ||

FoamsPP foam

PMI foam

PVC foam

PU foam

PEI foamPaperhoneycombs

PP honeycombs

Material efficiencyin bending MEC

Mat

eria

l effi

cien

cy in

tens

ion

/ com

pres

sion

t/h = 0.05

0.3

0.1

0.01

Cost Cv Sum [€/dm³] (with 2 €/kg value of weight saving)

11

In [2] value functions are used to combine multiple objectives. In this general terminology1/MEC (= 1/MECM + CwValue/MEW) is the value function for cost and weight optimisation.Figure 7 shows the curves for the efficiencies of the used sandwich examples as a function ofthickness ratio in the trade-off diagram proposed in [2].

Figure 7: Material efficiencies per weight and per cost (adapted from [2])

The thickness ratios 0.005 ; 0.01 ; 0.02 ; 0.05 ; 0.1 ; 0.2 are again marked with small crosses.Although the graph allows to read out the combined material efficiencies per weight and permaterial cost, the identification of minimal 1/MEC values is more difficult than in figure 6.The curves of equivalent 1/MEC values shown in figure 7 become here in a logarithmic plothyperbolic functions. Furthermore, in figure 6 the effect of selecting a different skin or corematerial on the curves of the homogeneous sandwich properties can be concluded from thepositions of the materials in the diagram, while this is not obvious in figure 7. It is thussuggested to use the modulus versus density or modulus versus cost diagrams for thesandwich material selection.

7. CONCLUSION

The material efficiency per weight and per material cost of a sandwich panel material can becompared to solid panels and to other sandwich material options using the material efficiencyparameters MEW, MECM and the saving factors ΦW, ΦCM. The total cost effectiveness MEC

0,1 1

0,1

1

10

100

0,5 2

1/M

Ecm

= (C

ost*

Den

sity)

/E^(

1/3)

[€/d

m³/G

Pa^(

1/3)

]

1/MEw = Density/E^(1/3) [kg/dm³/GPa^(1/3)]

Composites

Concrete,Cement

Brick,Stone

Metalsand alloys

Polymers

Woods andwood products

PMI foam

PVC foam

Balsa || PET

PEI foam

Lowalloysteels

High alloy steels

StainlesssteelPA

CFRP UD CFRP woven

Balsa ⊥

Aluminium

GFRP UDGFRP woven

GFRP mats

NFRP mats

Fibre boardMDF

PPPP foam

Paper ⊥

Paper ||

Pine ||

Pine ⊥

LDPE

HDPE

Oak ||

Oak ⊥

Cast iron

Paper honeycombs

PP honeycombs

PU foam

0.1 0.5

0.1

1/MEW [(kg/dm³)/GPa1/3]

1/M

E CM

[(€

/dm

³)/G

Pa1/

3 ] 1 / MEC

1

2

4

Trade-offsurface

12

and the total cost saving factor ΦC provide the possibility to compare and select materials forapplications requiring both low weight and low cost. The loading conditions, strength criteriaand surface requirements of a specific application demand often a larger then optimal skinthickness. In most cases a rather slow decrease of the material efficiency close to theoptimum allows to increase the thickness ratio t/h slightly without a large penalty. Theproposed sandwich selection diagrams allow to assess the effects of non-optimal thicknessratios.

ACKNOWLEDGMENTS

The authors acknowledge the Flemish Institute for the Promotion of Scientific andTechnological Research in Industry (IWT) for its financial support to the EUREKA projectsThermHex and TorHex. The Belgian program on Interuniversity Poles of Attraction, initiatedby the Belgian State, Prime Minister's Office, Science Policy Programming is acknowledgedfor the general support of the department MTM. The authors gratefully acknowledgefurthermore the contribution and financial support of all project partners.

REFERENCES

1. Ashby, M. F.,Gibson, L. J., Cellular Solids, Cambridge University Press, Cambridge, 1997

2. Ashby, M. F., Multi-Objective optimization in Material Design and Selection, ActaMetall. Mater., vol. 48/1, pp. 359-369, 2000

3. Granta Design, Material data from Cambridge Engineering Selector, Interactive materialselection charts, 2002

4. Beukers, A., Cost effective composite plate and shell structures for transports, Proc. ofEuropean SAMPE Conference, Hamburg, ed. Brandt et al., 1992, p.495-506

5. Haldenwanger, H.-G., Komplexität des Leichtbaus im Pkw, Conference proceedings of the7. Rudolstädter Kunststofftag, TITK Rudolstadt, 2001

6. Wiedemann, J., Leichtbau Konstruktion, vol. 2, Springer-Verlag, Berlin, 1997

7. Zenkert, D., The handbook of sandwich construction, Chameleon Press Ltd., London, 1997

8. Ashby, M. F., Materials and Shape, Acta Metall. Mater., vol. 39/6, pp. 1025-1039, 1991

9. Pehnt, Ökologische Nachhaltigkeitspotenziale von Verkehrsmitteln und Kraftstoffen, DLRAbt. Systemanalyse und Technikbewertung, STB-Bericht Nr.24, pp. 86-104, 2001

13

APPENDIX

As an example the value of weight saving is in the following estimated for automotiveapplications, using the value of the saved fuel. Apart from the fuel saving the dynamics of thecar need to be considered. The control of the car during emergency braking requires a certainweight on the rear axis, thus a weight saving in the back of the car is less desirable, as shownin figure 8.

Figure 8: Value of weight reductions in automotive applications (adapted from [5])

For this example other costs, e.g. for recycling are neglected. This leads to equation (19)where the fuel price Cfuel is multiplied by the depreciation mileage Dkm and the fuelconsumption reduction Lsaved per km and per kg weight reduction. The fuel cost is assumed tobe Cfuel = 1 €/liter. For the depreciation mileage 45.000 km (three leasing years of 15.000 km)is supposed [5]. The reduction in fuel consumption Lsaved depends on the weight and type ofthe car as well as on the type of engine. The fuel consumption reduction for a weight savingof 100 kg can vary from 0.2 to 0.6 liters per 100 km [9], which leads to a weight saving valueof CwValue = 0.9 to 2.7 €/kg.

CwValue = Cfuel Dkm Lsaved (19)

If a value Lsaved = 0.4 liter / 100 km / 100 kg is assumed, a CwValue of 1.8 €/kg results.Multiplication with the position factor Fc pos leads to a maximal value of 3 €/kg in the front ofthe car. For a sports car a high acceleration and thus a low weight are more important. Thusfor some sports cars a CwValue of up to 5 €/kg is rewarded for parts in front of the front axis[5]. A value of 2 €/kg is for automotive applications a suitable average.

Zones for lightweight design

four wheel drive

rear wheel drive

front wheel drive

Posi

tion

fact

or F

c po

s

fron

t cra

sh z

one

rear

cra

sh z

one

centre of gravity

centre of gravitywith driver

1.0

1.671.39

0.5

rear axis front axis