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Mechanics Research Communications 39 (2012) 35– 43

Contents lists available at SciVerse ScienceDirect

Mechanics Research Communications

j o ur nal homep age: www.elsev ier .com/ locate /mechrescom

ultifunctional thermal barrier coating in aerospace sandwich panels

ody H. Nguyena, K. Chandrashekharab, Victor Birmanb,c,∗

Boeing, 163J.S. McDonnell Blvd., St. Louis, MO 63042, United StatesDepartment of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409, United StatesEngineering Education Center, Missouri University of Science and Technology, One University Blvd., St. Louis, MO 63121, United States

r t i c l e i n f o

rticle history:eceived 28 July 2011eceived in revised form 13 October 2011vailable online 29 October 2011

eywords:

a b s t r a c t

The paper is concerned with the effectiveness of multifunctional thermal barrier coatings employed insandwich panels with a dual objective, i.e. slowing heat transfer from the surface exposed to thermalload and improvements in the thermomechanical response, including higher strength and stiffness. Thesolution is obtained for a typical aerospace panel mimicking thermal loading at a supersonic high-altitudeflight. The analysis is conducted numerically as dictated by the necessity to account for temperature-

andwich panelhermal barrier coatingtrengthtiffnesseat transfer

dependent material properties. The results illustrate that the introduction of thermal barrier coatingsbetween the facings and core of the panel may result in a significant reduction of temperature at the inner(colder) surface of the panel in both transient and steady-state phases. It has also been demonstrated thatbesides an improved heat transfer behavior, modified panels with thermal barrier coatings have lowerstresses and higher stiffness (higher stability and fundamental frequencies). The objectives considered

ed wi

in the paper were achiev

. Introduction

The concept of a multifunctional thermal barrier coating (TBC)n sandwich panels explored in the paper is concerned with twossues: delaying heat propagation to the interior behind the panelnd enhancing structural response of the panel. These goals areursued subject to a weight constraint. The multidiscipline prob-

em that has to be addressed involves the solutions of the heatransfer and structural response problems, accounting for the effectf temperature on the properties of the materials constituting theandwich panel. The latter effect makes the analytical solution ofhe heat transfer problem impossible (or impractical), althoughhe structural problem may still be analyzed for a limited class ofoundary conditions. Numerical solutions presented in the paperemonstrate the feasibility of the proposed concept.

Sandwich structures employed in aerospace applications areften exposed to thermal loading. The effects of such exposurenclude a degradation of the materials of facings and core, thermallynduced stresses or instability, and reduced damage tolerance.ctive and passive cooling, as well as functional grading are among

he methods of enhancement of the response of structures sub-ect to thermal loads. In particular, functionally graded sandwichtructures were considered both for an enhancement of their

∗ Corresponding author at: Missouri University of Science and Technology Engi-eering Education Center One University Blvd., St. Louis, MO 63121, United States.el.: +1 314 516 5436, fax: +1 314 516 5434.

E-mail address: vbirman@mst.edu (V. Birman).

093-6413/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.mechrescom.2011.10.003

th the minimum weight penalty.© 2011 Elsevier Ltd. All rights reserved.

thermomechanical response as well as in such problems as low-velocity impact (e.g., Birman and Byrd, 2007; Kirugulige et al., 2005;Apetre et al., 2006). While most studies of functionally gradedsandwich structures concentrate on grading of either the core orfacing-to-core interface, the effects of in-plane grading of facingsand variations in the thickness of facings in sandwich panels havealso been considered (Birman et al., 2008; Nguyen et al., 2011a,2011b).

Thermal barrier coatings have been extensively investigated(e.g., Evans et al., 2001; Abdul-Aziz et al., 2002; Cao et al., 2004).While their studies are often concerned with preventing debond-ing from the substrate, a possible contribution of the coating tomechanical response of the structure is seldom a major considera-tion. However, if the coating possesses high stiffness and strength, itmay effectively enhance structural response, in addition to improv-ing thermal characteristics. We explore such possibility in thispaper adding very thin thermal barrier coating layers to a typi-cal aerospace sandwich structure and monitoring their effect onthrough-the-thickness heat transfer as well as the thermomechan-ical stress distribution and stiffness (stability and fundamentalfrequencies). The main objective of the concept considered in thispaper is to delay heating of the inner surface of the sandwichpanel, possibly avoiding a need in active cooling and reducingtemperature of the interior compartment under the panel. Thesecond objective is improving the load-carrying capacity and ther-

momechanical response of the panel. We attempt to achieve bothobjectives without a significant increase in the weight of the panel.

Baseline panels considered in this study have metallic fac-ings and core. In particular, metallic cores have been extensively

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6 C.H. Nguyen et al. / Mechanics R

mployed in aerospace applications as is evidenced from a numberf previously published papers (Bart-Smith et al., 2002; Villanuevand Cantwell, 2004; Rakow and Waas, 2007). While the materialsf facings and core are retained in modified panels, thin ceramicayers are added between facings and core to reduce heat transfers well as increase the stiffness and reduce stresses throughout theanel.

. Analysis

The problem analyzed in the paper is depicted in Fig. 1. A sand-ich panel is subject to thermal load at one surface as a result of

irflow. The baseline panel that is constructed of identical 0.102 cmhick titanium alloy (Ti–6Al–4V) facings and a titanium alloyTi–6Al–4V) 2.337 cm thick foam core is replaced with a modifiedounterpart that employs the same material of facings and core. Inhe modified panel the thickness of the core is reduced to 2.311 cmo allow for two symmetric 0.0127 cm thick TBC between each fac-ng and the core (the effect of TBCs of different thicknesses was alsoonsidered in Fig. 6). The material of TBC is barium strontium alu-inosilicate (BSAS) that has a low density (3.183 g/cm3), a broad

ange of operating temperatures allowing operations up to 1386 ◦Cnd a low thermal conductivity equal to 2.0 W/m ◦C at room tem-erature (Patent US 7579085B2, August 25, 2009). Note that bariumtrontium aluminosilicate is a brittle material and it has a relativelyow flexural strength of an order of 130 MPa, for a monolithic mate-ial, (Unal and Bansal, 2000). In case of a deposited coating, thistrength may be smaller, possibly limiting the applicability of theonsidered design. While the increase in weight remains very small,BCs both delay heat transfer to the colder surface and increasehe strength and stiffness of the original design. The properties ofacings, core and TBC employed in the following analysis were spec-fied using data from Military Handbook (2001), Harris (2000), andbdul-Aziz and Bhatt (2009) and Abdul-Aziz et al. (2002), respec-

ively. A sample of the properties used in this study are shown inable 1 (E = modulus of elasticity, v = Poisson’s ratio, ̨ = coefficientf thermal expansion, k = thermal conductivity).

.1. Transient thermal problem

Thermal loading was determined for the flight at the supersonicpeed (Mach number equal to 3.88) at the altitude of 21.34 km,t the ambient temperature of −55 ◦C (Fogiek, 1996). A turbulentirflow was assumed over the panel. Under these conditions, thediabatic wall temperature (Taw) of the panel surface exposed tohe airflow was determined from (Ozisik, 1985):

aw = Ta + rV2

2Cp(1)

here Ta is the ambient temperature, Cp is specific heat of air, V ishe air speed, and the recovery factor r = Pr1/3, Pr being the Prandtlumber.

The initial exposed surface temperature found under such con-itions was 524 ◦C, but it slowly decreased with time as a result ofhe change in thermal conductivity of the exposed facing affectedy temperature and the corresponding change in the Prandtl num-er. Temperature of the air outside the colder (inner) surface of theandwich panel was sustained at 21 ◦C (room temperature). Theominant thermal boundary condition for the inner surface wasonvection.

The thermal flow was one-dimensional by assumption thathe boundaries of the panel do not serve as heat sinks (a possi-

le reference to heat-sink boundaries can be incorporated in theumerical solution, if necessary). However, even a one-dimensionaleat transfer problem does not typically have an analytical solution,s long as one takes into account the effect of local temperature

h Communications 39 (2012) 35– 43

on material properties of the facings and core. Although, analyti-cal models of material properties as functions of temperature havebeen suggested (e.g., Touloukian, 1967; Tanigawa et al., 1996),such models result in a differential equation of heat transfer withvariable coefficients that has analytical solutions only in simplestsuperficial cases. For example, the properties of materials subject toan elevated temperature can be represented in a polynomial form(Touloukian, 1967):

P = P0(P−1T−1 + 1 + P1T + P2T2 + P3T3) (2)

where P is a property, Pi (i = −1, 0, 1, 2, 3) are material constantsand T is temperature.

The one-dimensional dynamic heat conduction equation for anisotropic material is (Mills, 1995):

d

dz

[k(z)

dT

dz

]= �c

dT

dt(3)

where z is a coordinate (in this case, this would be a coordinatein the thickness direction), k(z,t) is a thermal conductivity, � isdensity, and c(z,t) is specific heat. If the conductivity and specificheat are functions of temperature resembling (2), the analyticalsolution of Eq. (3) becomes impractical. Accordingly, the follow-ing analysis was conducted numerically using Nastran-2004 andthree-dimensional solid elements (the modeling scheme is shownin Fig. 2 that also lists nodal surface temperatures corresponding tothe initial exposure time).

The general equation considered in transient analysis is (MSCNastran, 2004)

[B]{

du

dt

}+ [K]{u} + [R]{u + TABS}4 = {P} + {N} (4)

where [B] = heat capacity matrix, [K] = heat conduction matrix,[R] = radiation matrix, {P} = vector of applied heat flows that areeither constant or functions of time, {N} = vector of nonlinear heatflows that depend on temperature, {u} = grid point temperatureand TABS = absolute temperature scale factor.

The MSC/NATRAN analyzer solves differential Eq. (4) with initialthermal boundary condition specified in Fig. 2 using the one-stepintegration scheme. The time step employed in calculations waschosen �t = 0.01 s.

An example of the through-the-thickness temperature distri-bution after a 3-h exposure to thermal loading is demonstrated inFig. 3. As follows from this figure, the presence of TBCs changesboth the thermal gradient through the thickness as well as thetemperature on the exposed and inner surfaces of the panel. Thetemperature of the exposed surface is actually a little higher in themodified panel reflecting a low thermal conductivity of TBC layers.However, as a result of these layers, the temperature of the innersurface remains much lower in the modified panel, even after a 3-hexposure. A distribution of temperature through the thickness dur-ing the initial 30 min of flight is illustrated in Fig. 4 (baseline panel)and Fig. 5 (modified panel).

An interesting observation available from the comparison ofFigs. 4 and 5 is that even though the conductivities of the panelmaterials depend on temperature, the temperature distributionthrough the thickness of each facing and core of the sandwich panelremains nearly linear. As the time of exposure elapses, the distribu-tion of temperature through the thickness becomes more uniform,as anticipated. A sharp change in temperature between the fac-ings and core observed in the modified panel is explained by thepresence of very thin TBC layers that have a low conductivity.

The principal objective of the concept considered in the paper

is to slow the process of heating of the inner surface of the panel.The effectiveness of the modified panel in addressing this objec-tive is illustrated in Fig. 6. As follows from this figure, in both thebaseline and modified panels the temperature of the inner surface

C.H. Nguyen et al. / Mechanics Research Communications 39 (2012) 35– 43 37

Fig. 1. Concept of sandwich panel with multifunctional TBC. The baseline sandwich panel is on the left and the modified panel with TBCs between the facings and core is onthe right.

Table 1Properties of materials of the sandwich panel.

Property Face sheet Foam core (Ashby et al., 2000) Thermal barrier coating

21.11 ◦C 537.78 ◦C 21.11 ◦C 537.78 ◦C 25 ◦C 1386 ◦C

E (GPa) 110.32 55.16 0.75 0.37 95 95� 0.31 0.31 0.33 0.33 0.19 0.19˛ (1/◦C) 8.73 × 10−6 1.01 × 10−5 8.73 × 10−6 1.01 × 10−5 5.60 × 10−6 5.60 × 10−6

k (W/m ◦C) 7.30 13.30 5.00 5.00 2.00 0.50Density (gm/cm3) 4.43 4.43 1.10 1.10 3.20 3.20

Note: Properties of facing and core materials are shown for sample temperatures of 21.11 ◦C and 537.78 ◦C. For intermediate temperature values, the properties were generatedusing the methodology in Military Handbook (2001) and Harris (2000). The properties of TBC are shown for two sample temperatures. These properties were insensitive totemperature variations (Cao et al., 2004).

Fig. 2. The finite element model of the baseline panel is shown on the left. The modified panel is on the right: the only difference is the added thermal barrier coating layersbetween the facings and core.

Fig. 3. An example of temperature distribution after a 3-h exposure to thermal loading. The baseline panel is shown on the left; the modified panel is on the right. Thenumbers in color bars refer to ◦R (Rankine degrees). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

38 C.H. Nguyen et al. / Mechanics Research Communications 39 (2012) 35– 43

Fa

iasiotttbFst

cotf

the thickness introduces a peculiar element in the analysis if the

ig. 4. A distribution of temperature through the thickness of the baseline panelfter 10, 20 and 30 min of exposure to thermal loading.

ncreases with time, but this increase slows with time of exposurend eventually, temperature approaches a steady state level. Theteady state temperature of the inner surface is significantly smallern the modified panel. Furthermore, even prior to the achievementf the steady state level, at any time instant, the temperature ofhe inner surface of the modified panel remains much lower thanhat in the baseline design. As an example, after a 0.78 h exposure,he temperature of the inner surface is equal to 481.11 ◦C in theaseline panel and only 356.11 ◦C in the modified panel (case 6 inig. 6). These observations reflect on the efficiency of TBC layers inandwich panels where the task is to slow the process of heating ofhe inner surface and reduce its steady state temperature.

A decrease of the temperature of the inner facing can signifi-antly improve the response of the panel, even if this decrease is

nly of an order of 100 ◦C. For example, the modulus of elasticity ofhe facing decreases by a factor of 1.5 if temperature is increasedrom 400 ◦C to 500 ◦C.

Fig. 6. Temperature of the inner (colder) surface of the sandwich pan

Fig. 5. A distribution of temperature through the thickness of the modified panelafter 10, 20 and 30 min of exposure to thermal loading.

The results and conclusions regarding the efficiency of TBC insandwich panels obtained in this section are not affected by theboundary conditions along the edges of the panel (except for theabove-stated assumption that the edges do not serve as heat sinks)or by in-plane dimensions. However, the boundary conditions anddimensions affect the stress, stability and dynamics of the panel.Some of these issues are discussed below.

2.2. Static and dynamic response and merit of the modified panel

The evaluation of a thermomechanical response of a sandwichor laminated structure where temperature is nonuniform through

effect of temperature on the material properties is accounted for.The structure that is typically designed symmetric with respectto the middle surface exhibits asymmetry due to a nonuniform

el as a function of time for the baseline and modified designs.

esearch Communications 39 (2012) 35– 43 39

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2p3bAdmftwsspiaiafjfttw

fsuottta

ariiriwvitttnFq

Table 2Weights of the baseline and modified sandwich panels with various thicknesses ofTBC layers.

Baseline panelweight (kg)

Modified panelweight (kg)

TBC thickness (cm)

13.993 14.039 0.002513.993 14.080 0.005113.993 14.120 0.007613.993 14.166 0.010213.993 14.207 0.0127

Table 3Fundamental frequencies of baseline and modified simply supported panels subjectto thermal loading.

Case Baseline panelfrequency (Hz)

Modified panelfrequency (Hz)

Room temperature 213 21910 min exposure 188 201

results shown here we have to conclude that if the goal of the mod-ification is a higher fundamental frequency, adding TBCs appearsto be ineffective.

Table 4Fundamental frequencies of baseline and modified clamped panels subject to ther-mal loading.

Case Baseline panelfrequency (Hz)

Modified panelfrequency (Hz)

C.H. Nguyen et al. / Mechanics R

egradation of properties. For example, in the present case, thetiffnesses of the exposed facing is smaller than that of the inneracing. The same asymmetric change in the stiffness is observedor the sections of core adjacent to the exposed and inner fac-ngs (the properties of the coatings are practically unaffected byemperature considered in examples). As a result, the structurehat was designed symmetric about the middle surface acquiresoupling stiffnesses, exhibiting bending-stretching coupling. Ana-ytical solutions for shear-deformable sandwich structures withending-stretching coupling are available for a limited numberf boundary conditions. Besides the limitations introduced byoundary conditions, the temperature distribution through thehickness varies with time implying a need in a continuous updatef the stiffness of the panel. Thus, the analysis is conductedumerically. For additional discussion on the effect of temperature-ependent properties on the response of structures, see Birman2011).

The NASTRAN finite-element computer program (MSC Nastran,004) was used in the thermomechanical analysis of the sandwichanels. The sandwich panel (face sheets and core) was modeled by-D brick elements. The model consists of 255,000 nodes, 60,000rick elements and 400 Rigid Body Element (RBE) joint locations.s follows from our analysis, increasing the number of elementsoes not result in a higher accuracy of either thermal or thermo-echanical analyses. The panel was simply supported, so that while

our edges could not move in the x-, y- or z-directions, their rota-ion was unconstrained. Such boundaries are encountered in caseshere the edges are supported by stringers or frames of a low tor-

ional stiffness but high bending stiffness that can be modeled asimple support. In-plane displacements along the edge are usuallyrevented by high axial stiffness of the supporting structure, while

n-plane displacements in the direction perpendicular to the edgere absent due to the presence of adjacent panels possessing highn-plane stiffness. To simulate the boundary condition describedbove, RBEs were attached to the panel edges connecting the twoace sheets as shown in Fig. 7. The midpoint of these RBEs was pin-ointed and prevented against the motion in the x- and y- directionor the edges x = constant and y = constant, respectively. In addi-ion, vibrations of the panels were considered for the case wherehe edges were clamped (in-plane displacements of clamped panelsere also prevented).

The length and width of the panel were equal to 63.5 cm, exceptor the buckling problem discussed below. The loading was repre-ented by the thermal load described in the previous section and aniform pressure equal to 317.16 kPa applied to the exposed facingf the panel. The chosen value of pressure is quite high being equalo 1/3 the yield stress of the titanium facing. Thus, we can monitorhe response of the panel operating close to the failure load. The dis-ribution of temperature being variable with time, thermal load andccordingly, the stresses in the panel were also time-dependent.

Deflections of the panels subject to thermomechanical loadingre shown in Fig. 8. It is observed that the deflection is significantlyeduced in the modified design as could be anticipated consider-ng high stiffness of TBC and their location adjacent to the facing,.e. at a large distance from the middle plane. A valid concern iselated to the weight penalty associated with such improvementn the stiffness. This concern is addressed in Table 2 that presents a

eight comparison between the baseline and modified panels witharious thicknesses of TBCs. Notably, even if the thickness of TBCs increased to 0.0127 cm resulting in a very large enhancement ofhe stiffness (the examples considered in this paper consider onlyhis thickness, except for Fig. 6), the weight increase compared to

he baseline design is limited to 1.5%. The enhancement of the stiff-ess resulting in a significant reduction of deflections as shown inig. 8 also produces an increase of stability and the fundamental fre-uency of the panel. The resistance against such local failure modes

20 min exposure 185 19730 min exposure 185 194

as wrinkling and kinking would also be improved (the analysis ofthese modes is outside the scope of the paper).

Consider an increase in the fundamental frequency of the paneldue to the introduction of TBC. Such increase is sometimes requiredin engineering applications where the goal is to “shift” the natu-ral frequencies from the spectrum of possible driving frequenciesavoiding resonance.

The frequencies vary with the time of exposure to thermal load-ing reflecting the process of heat transfer, changes in the thermalprofile through the thickness and related changes in the mate-rial properties affected by local temperature. This is illustrated inTables 3 and 4 (simply supported and clamped panels with iden-tical in-plane boundary conditions, respectively). In both casesthe increase in the fundamental frequency remained quite smallreflecting the fact that natural frequencies are roughly propor-tional to a square root of the stiffness. The relative increase in thebuckling load that is roughly proportional to the stiffness is muchhigher as shown below. The frequencies decrease with the timeof exposure to thermal loading for both boundary conditions con-sidered in Tables 3 and 4. This occurs as a result of the change ofthe thermal profile through the thickness of the panel as well asthermally induced compressive stress resultants (thermal couplesthat are also present have a minimal effect on the frequencies sincesandwich panels considered in examples are predominantly geo-metrically linear systems). As the exposure time increases and theheat transfer approaches steady state, the frequencies stabilize. Themode shapes of both baseline and modified vibrating panels vibrat-ing at their fundamental frequencies are identical as shown in Fig. 9.A similar pattern, i.e. insensitivity of the mode shape to the modifi-cation of the panel adding TBCs, was observed during the exposureto thermal loading for clamped boundary conditions. Based on the

Room temperature 336 34210 min exposure 300 31720 min exposure 295 31130 min exposure 295 307

40 C.H. Nguyen et al. / Mechanics Research Communications 39 (2012) 35– 43

Fig. 7. Thermomechanical loading and boundary conditions of a sandwich panel.

F olor bi

asTci

Fbl

ig. 8. Deflections of the baseline and modified sandwich panels. The numbers in cn this figure legend, the reader is referred to the web version of the article.)

In the present study, we also consider the stability problem for square panel with the thickness-to-side ratio of 1/100 and the

ame through-the-thickness dimensions as previously discussed.he change in the in-plane dimensions compared to the previousase was due to the necessity to avoid local buckling of the fac-ngs (wrinkling occurred prior to global instability if the panels

ig. 9. Mode shapes of baseline (left) and modified (right) simply supported panels vibars reflect a relative deflection only (output from Nastran, without a reference to absolu

egend, the reader is referred to the web version of the article.)

ars refer to inches (actual deflections). (For interpretation of the references to color

had smaller in-plane dimensions resulting in a higher overallstiffness and buckling load). The panel was clamped around the

boundary and subject to uniaxial compression. The uniaxial buck-ling stress resultants evaluated at the room temperature wereequal to 4.16 × 106 N/m for the baseline panel and 4.97 × 106 N/mfor the modified panel. This presents a 19% improvement in the

rating with their respective fundamental frequencies at room temperature. Colorte values of deflections). (For interpretation of the references to color in this figure

C.H. Nguyen et al. / Mechanics Research Communications 39 (2012) 35– 43 41

Fig. 10. Buckling mode shape of clamped square baseline (left) and modified (right) panels. Color bars reflect a relative deflection only (output from Nastran, without areference to absolute values of deflections). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

F adingt readet .)

bobi

ppmtd

Fr

ig. 11. Stress distribution in the exposed facing after 10 min exposure to thermal loo stress (psi). (For interpretation of the references to color in this figure legend, theo color in this figure legend, the reader is referred to the web version of the article

uckling load, further illustrating a possible multifunctional usef TBCs in sandwich panels. The mode shapes of buckling of theaseline and modified panels were nearly identical, as evidenced

n Fig. 10.Stress analysis represents significant interest for sandwich

anels considered in relevant applications. As follows from the

revious discussion, both the thermal profiles as well as ther-ally induced stresses vary with time. Moreover, the properties of

he panel materials, including their stiffness, being temperature-ependent, mechanically induced stresses also change with time.

ig. 12. Stress distribution in the exposed facing after 20 min exposure to thermal loadiefer to stress (psi). (For interpretation of the references to color in this figure legend, the

(the load includes both temperature and pressure). The numbers in color bars referr is referred to the web version of the article.) (For interpretation of the references

As an example, we illustrate the von Mises stresses in the exposedfacing of the baseline and modified panels 10, 20 and 30 min afterthe exposure to thermal load (besides thermally induced contribu-tions, the stresses in the panel are affected by uniform pressure of317.62 kPa (46 psi) applied to the panel). The stresses in TBCs, thefacing adjacent to the inner surface and in the core were also eval-

uated and found less dangerous than those in the exposed facing.

The stresses in the exposed facing shown in Figs. 11–13increased with time of exposure approaching the yield stress oftitanium (126 ksi). The reason is evident from the previous section

ng (the load includes both temperature and pressure). The numbers in color bars reader is referred to the web version of the article.)

42 C.H. Nguyen et al. / Mechanics Research Communications 39 (2012) 35– 43

F l loadir d, the

witco(m

iirrc

M

rfsimtbt

erncl

3

riatwmriIpt

ig. 13. Stress distribution in the exposed facing after 30 min exposure to thermaefer to stress (psi). (For interpretation of the references to color in this figure legen

here it was shown that temperature in the panel also graduallyncreases with time resulting in a degradation of the properties ofhe facing and core (TBC material was insensitive to temperatureonsidered in examples). Notably, the stresses in the exposed facingf the baseline panel approach the yield limit after 30 min exposureFig. 13). However, the stresses in the modified panel remained

uch lower than the yield stress, even after such exposure.The efficiency of the proposed concept in its aspect related the

ncreased load-carrying capacity has to be considered against anncrease in the weight of the panel. As has already been discussed inegards to Table 2, such increase remains small, even for panels withelatively thick TBCs. Here we define a measure of the efficiency,alled a merit factor (M), as follows

= (�/W)base

(�/W)mod(5)

In (5), the ratios in the numerator and in the denominator rep-esent the von Mises stress in the panel divided by the panel weightor the baseline and modified designs, respectively. The von Misestress is determined in the element of the panel where such stresss the closest to the allowable or yield stress of the corresponding

aterial. In the examples considered in the paper, the critical loca-ion was the center of the exposed facing. The merit factor definedy (5) reflects the improvement in the strength of the panel, subjecto the constraint on its weight.

The merit factor of panels decreased with exposure time, beingqual to 1.17, 1.11 and 1.08 after 10, 20 and 30 min exposure,espectively. Thus, the reduction in the stresses is particularly sig-ificant in the initial phase of thermal loading suggesting that theoncept considered here may be particularly effective in case of aimited-time exposure.

. Conclusions

The paper illustrates the concept of multifunctional thermal bar-ier coatings in sandwich panels. The multifunctionality is reflectedn both the control of heat transfer through the panel as well asn improvement in the strength and stiffness. It is demonstratedhat an improved performance can be achieved without a note-orthy weight penalty using currently available TBC materials. Aajor potential complication introducing the proposed design is

elated to manufacturing complications. The relevant manufactur-

ng issues will be the proper bonding of the face sheet to the core.f the bond is weak, then delamination will occur. Also, there is aossibility of face sheet blow-up due to hot air from the core. Thus,he fabrication process has to be closely monitored.

ng (the load includes both temperature and pressure). The numbers in color bars reader is referred to the web version of the article.)

The panel considered in the examples was subject to thermalloading for a representative high altitude supersonic flight. The heattransfer analysis was conducted by the finite element method sincetemperature-dependence of the conductivity results in a differen-tial heat conduction equation with variable coefficients making ananalytical solution impossible. It was shown that the temperatureof the inner surface of the modified panel with TBCs remains sig-nificantly lower than that in the baseline panel throughout theentire time of exposure to thermal loading. After the initial tran-sient period, the temperature of the inner surface stabilizes; thecorresponding stable temperature of the modified panel is muchlower than its counterpart in the baseline panel. This representsan important improvement in applications where it is necessary toshield the interior from elevated temperatures.

Besides the improvement in thermal behavior, the strength andstiffness of the representative panel were noticeably increased asa result of the introduction of TBC layers. The improvement in thestrength constituted by reduced stresses was particularly notice-able in the initial transient period of the exposure to thermalloading. A higher stiffness of the modified panel resulted in a smallincrease of the fundamental frequency and a larger enhancementof stability. The improvements in both the thermal performance aswell as in the strength and stiffness were achieved at the cost of aminimal increase in weight. Accordingly, it is concluded that cur-rently available materials make the application of multifunctionalTBCs in sandwich panels both feasible and attractive.

Acknowledgement

This research was supported by Boeing that provided necessarytechnical and computational resources.

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esearc

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