Composite Structures 70 (2005) 1–11

www.elsevier.com/locate/compstruct

Structurally graded core junctions in sandwich beams: quasistatic loading conditions

Elena Bozhevolnaya *, Ole Thybo Thomsen

Institute of Mechanical Engineering, Aalborg University, Pontoppidanstræde 101, 9220 Aalborg East, Denmark

Available online 30 September 2004

Abstract

The paper addresses the problem of sandwich beams/panels with junctions between different core materials. The physics of the

impairing local effects induced by a mismatch of the elastic material properties at core junctions is discussed, and the results of an

experimental investigation concerning the quasi-static failure behavior of sandwich beams with conventional butt and ‘‘structurally

graded’’ core junctions is discussed. The term ‘‘structurally graded’’ core junctions include scarf junctions and junctions provided

with local reinforcing patches of the faces. The influence of the junction interface geometry on the quasi-static deformation, failure

initiation and crack patterns are studied experimentally for sandwich beams loaded in the three-point bending. It is shown that

‘‘structurally graded’’ core junctions perform better than conventional butt junctions, and thus improve the strength of the structure.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Sandwich; Junction; Design; Critical load

1. Introduction

Sandwich elements formed by two thin stiff faces sep-

arated by a thick compliant core find numerous applica-tions in the spacecraft, aircraft, automotive, marine and

building industries. The significant resistance of the

faces to external bending loads, and the capability of

the core to withstand substantial but smoothly varying

external shear loads, provide for high structural per-

formance of sandwich panels [1,2]. However, for practi-

cal as well as structural reasons the use of sandwich

structures frequently involves the use of different coresin the same sandwich element [3–5]. Various core inserts

(stiffeners, backing plates, etc.), which substitute a part

of the original core in sandwich panels, are also used

often in sandwich structures, where they serve mainly

to introduce fasteners for attachment or rigging purposes

0263-8223/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2004.08.030

* Corresponding author. Tel.: +45 96 35 93 23; fax: +45 98 15 16 75.

E-mail address: eb@ime.aau.dk (E. Bozhevolnaya).

[6–8]. Both core/core and the core/insert junctions are

characterized by having interfaces of dissimilar materials

with elastic properties that may be rather different.

A conventional core butt junction [9] presents astraight interface between two adjoining cores as shown

in Fig. 1(a). The interface plane terminates with an angle

of 90� relative to the sandwich faces. It was perceived

very early [3,10,11], that the mere presence of core joints

in a sandwich structure can be a source of severe stress

concentrations, which may trigger a failure of the whole

structure. A recently developed analytical model of the

local effects across junctions between different cores[12] has shown that the local effects cause the induce-

ment of a significant rise of the normal stresses in the

sandwich faces, as well as a considerable variation of

the shear and normal bending stresses, in the near vicin-

ity of the core junctions. The analysis demonstrates that

the intensity of the local effects is proportional to the

shear stress resultant at the junction as well as to the

ratio of the shear moduli of the two adjoined core mate-rials (i.e. proportional to the degree of dissimilarity of

Fig. 1. Sandwich beams with different types of core junctions. (a)

Beam with butt junctions. (b) Beam with scarf junctions and an obtuse

angle of 135� of the soft core insert. (c) Beam with scarf junctions and a

sharp angle of 45� of the soft core insert. The junctions are also

provided with reinforcing patches. (d) Zoom on the beam diaphragm.

(e) Zoom on the local reinforcement. All dimensions are given in mm.

The material data of the beam constituents are given in Table 1.

2 E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11

the cores). An experimental verification of the analytical

results for the case of sandwich beams with dissimilar

cores, and a generalization for the case of in-plane core

inserts in sandwich panels, were subsequently performed

in [13] and [14], respectively.

The geometry of the junctions in sandwich panelsplays an essential role in the strength of the local effects.

The stress concentrations at butt joints between two dif-

ferent materials were investigated by Ribeiro-Ayeh and

Hallstrom [15,16], in which the failure of bi-material

interfaces in beams assembled from PVC foam and alu-

minium/plexiglas was studied experimentally and on the

basis of FE calculations. The tested beams were loaded

in four-point bending, which provided a constant bend-ing moment across the joints. Strength predictions for

different interfaces were made using a point-stress crite-

rion reformulated for the first principal stress, and ap-

plied at some characteristic distance away from the

joint wedge. It was found that both a joint induced fail-

ure or a global failure may occur depending on the joint

angle and the elastic properties of the joined materials.

In this study, the beams were not provided with face,and thus cannot be classified as sandwich structures.

The edges of sandwich beams and panels inherently

include a significant degree of material property mis-

match. The design of rigid edge inserts for composite

sandwich beams suggested in [17] comprises V-shaped

rather than straight interfaces between the rigid edge

material and the soft core of the sandwich beam itself.

This design, which was based on geometrical optimiza-

tion, was proven effective in minimizing the stress con-

centrations that develop across material boundaries at

the sandwich beam edges.

A similar structural approach leads to the concept

of so-called ‘‘functionally graded’’ cores, where themechanical properties of the functionally graded cores

vary gradually with the location within the material,

with the objective of diminishing the local effects as dis-

cussed above. Until now, the through-the-thickness var-

iation of the elasto-mechanic properties of sandwich

cores was studied in [18–20]. However, the design or tai-

loring of core properties (for instance, variation of the

core properties in a longitudinal direction) and the sub-sequent practical implementation/realization are im-

peded by the obvious manufacturing challenges in this

type of sandwich structures [21].

The possible failure modes of sandwich structures are

numerous, which is due to the presence of different

materials joined together, as well as the notorious sensi-

tivity to concentrated loads exhibited by these struc-

tures. The classical work of Triantafillou and Gibson[22] distinguishes between yield of the sandwich faces,

failure of the core in tension/compression and failure

of the core in shear. Further exploration of this field

[2,23–26] uncovers other possible failure modes like

local face wrinkling, delamination, interaction of shear

and normal stresses in the core, etc.

The most probable failure modes for core junctions

are local yield/buckling of the faces, as well as a corefailure by way of shear or compression/tension in the

vicinity of the core junctions.

All of the quoted references, in one way or the other,

lead to the question about how to properly design core

junctions in sandwich beams/panels. In the work pre-

sented herein both conventional butt core junctions as

well as scarf core junctions (with boundaries terminated

at an angle different from the right angle) are consid-ered. A novel design, which includes a local reinforce-

ment of the faces at the butt and scarf junctions, is

also investigated.

The paper presents an experimental study of the

deformation, failure initiation and crack patterns of

sandwich beams with core junctions subjected to

quasi-static loading. The obtained results clearly indi-

cate that the novel design of core junctions providesenhanced performance of sandwich beam subjected to

quasi-static loading.

2. Local effects in the vicinity of butt junctions

The physics of the local effects is discussed with refer-

ence to the problem of a sandwich beam with two typesof core materials loaded in three-point bending, as

shown in Fig. 1(a). The bending moment increases from

Fig. 2. Stress distribution in the lower face of the sandwich beam

across the core junction. The beam is loaded in three-point bending as

shown in Fig. 1(a). The dashed line shows the normal stress along the

neutral axis of the face due to bending only, while the solid lines show

the real global level of stresses in the face. The material data of the

sandwich beam constituents are given in Table 1.

E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11 3

the supports to the centre of the beam, and normal

bending stresses are induced in the sandwich faces.

The stress distribution in the lower face along the beamspan is depicted in Fig. 2. The dashed line here repre-

sents the stresses along the neutral axis of the lower face,

which is in a state of tension. Notice that the left core

junction (Fig. 1(a)) is situated 120mm from the left sup-

port. From ordinary/classical first-order theory solution

[1,2] a pure bending stress of rbendingf ¼ 78MPa (tensile)

should be expected when a central load of 1800N is ap-

plied. According to the more advanced analytical modeldeveloped for butt core junctions [12], the locally in-

duced stresses in the faces emerge exactly at the core

junctions, and their maximum may be estimated as

rloc;maxf � Q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Ef

2Gc comphfhcð1� gÞc

sð1Þ

Here, Q is the shear resultant at the junction (which is

equal to P/2 for the case of a central point load P shown

in Fig. 1(a)), and the main parameters of the model are

as follows:

Table 1

Mechanical properties of the constituents of the sandwich beams

Modulus of elasticity (MPa) Shear modu

Faces

Aluminium 7075-T6 Ef = 72,000 –

Compliant core

PVC foam Divinycell H60 Ec comp = 60a Gc comp = 22

Stiff core

PVC foam Divinycell H200 Ec stif = 310a Gc stif = 90

Reinforcing patch

Araldite� 2022 Ep = 2600 –

Central diaphragm

Araldite� 1011 Ed = 2600 –

a Compressive modulus.b Shear strength might vary according to data sheet [28].

g ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiGc comp

Gc stif

r; c ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 2l

1þ lð1þ g1=4Þ

s

l ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikGc comphcðhf þ hcÞ2

Efh3f

s;

k ¼0:13 plane stress

0:17 plane strain

(ð2Þ

The two parameters g and l in Eq. (2) are of special

importance. The parameter g defines the quantitative

magnitude/amplitude of all the local effects, i.e. the lar-

ger the disagreement between the elastic properties of

the adjoining materials is the larger the locally induced

stresses will be. The second important model parameteris the decay parameter l that characterizes the in-plane

extension of the local effects (or the bending boundary

layer).

The definition of all other parameters are found in

Fig. 1(a) and Table 1.

For the case of a sandwich beam in the three-point

bending, the net bending stress is estimated as follows:

rmaxf ¼ rbending

f þ rloc;maxf

� PðL� aÞ4bhfðhf þ hcÞ

� P2b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Ef

2Gc1hfhc

sð1� gÞc ð3Þ

where ‘‘+’’ and ‘‘�’’ correspond to outer and inner sur-

faces of the sandwich beam face, respectively. The lo-cally induced stress is added to the bending stress at

the outer surface of the face, and subtracted from the

bending stress of the same face at the face/core interface

as illustrated in Fig. 2. This stress distribution is ob-

tained with the help of the analytical model [12,13],

but the local maximum rfloc,max = 68 MPa can always

easily be estimated using Eq. (1). Fig. 2 shows that a sig-

nificant variation of the stresses is induced in the vicinityof the core junction (across the junction). This variation

lus (MPa) Yield strength (MPa) Shear yield strength (MPa)

rYf = 450 –

rcomprYc ¼ 0:8, rtens

Yc ¼ 1:4 sYc = 0.7(0.6)b

rcomprYc ¼ 4:5, rtens

Yc ¼ 4:8 sYc = 3.3

– sYp = 23

rcomprYd ¼ 140, rtens

Yd ¼ 60 –

4 E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11

displays an almost complete decay within a distance of

less than two core thicknesses away from the junction.

This variation of the stresses, and the associated stress

peaks, may lead to failure of one of the sandwich faces

due to yielding, non-ductile compressive material failure

or local buckling, depending on the material propertiesof the face and the underlying core. The danger of local

failure of the faces might be severe, especially for the

case of the carbon fibre reinforced faces, which are

known to be weak in compression compared to their

strength in tension [27].

A numerical solution for the stress variation in the

core along the lower face/core interface is presented in

Fig. 3. The dashed line represents the results obtainedusing a classical first-order theory solution, which im-

plies that the core carries the entire shear load. Accord-

ing to classical theory, the shear stress sclasc ¼ P=ð2bhcÞ ¼0:65MPa is constant across the beam junction (if the

shear resultant is constant, which is the case here).

The solid lines represent the solutions according to the

2-D elasticity model [12]. This refined solution predicts

a very distinctive variation of the shear stress sc, andquite importantly predicts the presence of tensile trans-

verse normal core stresses rc of significant magnitude

at the lower face/core interface. The peak of the normal

stress rc (Fig. 3) may lead to a delamination between

the core and the face. At the upper interface (the same

data as in Fig. 3, but with the reverse sign for rc) the

transverse normal core stress will be a ‘‘crack closing’’

compressive stress. The value of rc in the compliantcore at the interface is modest, rc = 0.38MPa. However,

this together with the shear stress at the junction,

sc = 0.55MPa, may effectively cause a rise of the ‘‘effec-

tive’’ stress above the predicted ‘‘classical’’ shear stress

sclasc ¼ 0:65MPa, and more importantly above the

strength level of the compliant core (Table 1). It should

be noticed that the stiffer core may be the first to fail,

Fig. 3. Stress distribution in the core of the sandwich beam along the

lower face/core interface. The beam is loaded in three-point bending

as presented in Fig. 1(a). The dashed line shows the ‘‘classical’’ shear

stress due to a constant shear resultant, while the solid lines describe

the stress distributions in the core, when the local effects are taken in

to account. The material data of the beam constituents are given in

Table 1.

since the locally induced normal stress is extremely high

here.

A question still exists about the accuracy/reliability of

the 2-D elasticity solution discussed above [12], when the

stress concentrations are of concern. Analysis methods

based on strain energy release rate considerations (e.g.fracture mechanics) may be applied to further elucidate

this issue. Nevertheless, the model [12] gives some pre-

liminary estimates of the core stresses, and draws atten-

tion to the fact that additional normal stress appears at

a junction between two different core materials due to

the mere existence of the junction itself (and the presence

of the shear stress resultant). Thus, the sheer existence of

core junction in a sandwich structure may trigger failureof the core or the faces in the vicinity of the junctions

much earlier than predicted by conventional/classical

sandwich theories.

3. Scarf junctions and junctions with reinforcing

patches

Scarf inserts in sandwich panels (with bias, inclined

junctions) have been shown to induce local stresses of

lower magnitude than conventional ‘‘butt’’ inserts. This

was shown both experimentally and using finite element

analysis in [13,14]. Accordingly, it is proposed to use a

similar scarf design also for core junctions. Thus, the

new design suggests an angle of termination between

two different core materials in the sandwich beam/panelto be different from the right angle of 90� shown in Fig.

1(b) and (c). Such a design increases the transition zone,

where the bordering sandwich cores change their elastic

properties, and this effectively smoothens the stress con-

centrations in the adjacent materials. In composite

materials technology, this shape of core boundaries is

traditionally referred to as a scarf junction [7,9], and this

terminology is maintained herein.The analysis results shown in Fig. 2 reveal that signif-

icant local bending of the faces takes place exactly at the

core junctions. This implies that a local reinforcement of

the faces at the junction will locally increase the face

flexural rigidity. This will reduce the local face bending,

and thereby also reduce the accompanying deformation

and stress concentrations in the joined cores. A possible

design of reinforcing patches in the form of circular seg-ments is shown in Fig. 1(c) and (e) for the scarf junc-

tions, but any reasonably smooth shape of the patch

may be acceptable. Reinforcing patches are almost

effortlessly manufactured by machining grooves along

the core junctions, and subsequently filling them with

an appropriate adhesive/material before assembling the

core with the faces. Alternatively, for a sandwich panel

manufactured using vacuum infusion techniques, thegrooves will be filled automatically when the resin is

infused.

E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11 5

4. Experimental set-up and test specimens

To demonstrate the efficiency of the proposed core

junction design, sandwich beams with butt and scarf

core junctions, schematically shown in Fig. 1(a)–(c),

were studied. The sandwich beams were equipped withaluminium 7075-T6 faces (Aluminium Company of

America) and Divinycell H-grade PVC core (DIAB

AB Group). The compliant core constituted the central

part of the beams, while the stiff core made up the outer

edges of the beams. All the beam constituents were

joined using an epoxy resin, Araldite� 2022 (Huntsman

Adv. Materials). The geometrical parameters of the

sandwich beams are also shown in Fig. 1, and themechanical properties of the beam constituents are given

in Table 1 according to [28].

A series of eight sandwich beams with butt and scarf

junctions, with and without reinforcing patches at the

junctions, were manufactured and subsequently studied

experimentally. The reinforcing patches were achieved

by the machining of circular segment grooves across

the junctions (Fig. 1(c)). These grooves were then filledwith the adhesive (Araldite� 2022) when applying the

faces onto the core. A zoom of the local reinforcement

of a scarf junction is seen in Fig. 1(e).

The stated objective of the experimental work was to

uncover the nature of the local effects in the vicinity of

junctions between different core materials, as well as

the core failure modes when the sandwich beams were

loaded up to failure. In order to eliminate undesired fail-ure modes, special care was given to the design of the

beams. The preliminary design analysis was based on

the estimates of the critical loads corresponding to the

major failure modes for a sandwich beam loaded in

three-point bending as shown in Fig. 1(a). The calcula-

tions of the critical loads were carried out according to

[25,26], and with the help of the model [12,13]. The re-

sults are presented in Table 2. The notation used in

Table 2

Critical failure loads for sandwich beam loaded in three-point bending

Failure mode Estimation formulae after [25,26]

Face yielda P 1 ¼ rYfL

4tf ðtfþtc Þþ6

4t2fb

b;b ¼ 3Ec

Ef t3f tc

� �1=4

Face wrinkling P 2 ¼ 2tf ðtfþtcÞbL EfEcGcð Þ1=3

Core shear yield P3 = 2sYc(tf + tc)b

Core compressived yield P 4 ¼ 2rYc

b b; b ¼ 3Ec

Ef t3f tc

� �1=4

Face yield at junction P 5 ¼ rYfðL�aÞ

4hf ðhfþhcÞ þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Ef ð1�gÞ2c28Gc comphfhc

r� ��

Core yielde at junction

a P1 includes both global bending stress and local indentation stress. Theb P1_H200 is estimated for the stiffer core at the edges of the beam, and only

here.c P3_H60 calculated for the given range of the core shear strength sYc = 0.d P4 originates from the Winkler foundation model.e Numerical estimates are available according to [12], and P6 6 P3 is reco

the formulae of Table 2 is explained in Fig. 1 and Table

1. The failure load corresponding to face/core interface

delamination is not included in Table 2, since this load

is expected to be larger than the critical load for core

shear yielding P3, assuming that the interface shear

strength is not smaller than the core shear strength.Considering the data in Table 2 it is concluded that

the smallest minimal ‘‘critical’’ (or failure) load,

P4_H60 = 933 N, would cause compressive yield of the

compliant core under the applied concentrated load.

Thus, the Divinycell H60 core is the limiting factor in

the applied beam design and loading set-up. The next

(in ascending order) ‘‘critical’’ load, P1_H60 = 1520 N,

would lead to face yielding in the vicinity of the centralloading point. To prevent these undesired modes of

failure, a rigid diaphragm was introduced in the centre

of all tested beams, as shown in Fig. 1. The diaphragm

of thickness 4 mm was moulded from Araldite� 1011

epoxy resin in a separate process, and was subsequently

glued into a rectangular groove machined in the com-

pliant core prior to the application of the second face.

A zoom on the diaphragm is presented in Fig. 1(d).The use of the rigid diaphragm not only eliminated

the possible occurrence of failure modes 1 and 4

(according to Table 2) in the central part of the beam,

but also provided a balanced transmission of the

central load to both faces, and established a smoother

variation of the shear stress resultant at the beam

centre.

The next probable failure mode is core yield at thecore junction (cf. Table 2), which occurs due to an inter-

ference of the shear and tension stresses in the corner of

the softer core. The critical load was estimated to

P6 6 P3 = 1728 � 2017 N. Thus, the most probable fail-

ure mode of the sandwich beam was found to be core

yield at the junction. This is consistent with the overall

goal of the experiment, which was defined as the study

of the local effects at the core junctions.

and [12,13] Critical loads, N

P1_H60 = 1520, P1_H200 = 4032b

P2_H60 = 2830, P2_H200 = 7826

P3_H60 = 1728 � 2017,c P3_H200 = 9604

P4_H60 = 933, P4_H200 = 3484

1

b P5 = 5710

P6 6 (1728 � 2017)

latter is modelled with the help of the Winkler foundation model.

the indentation stress is taken into account since no bending is present

6 � 0.7MPa (cf. Table 1).

mmended for practical purpose.

Table 3

Inventory of the experimentally investigated beams

Beam number (video footage) Type of junction Critical load Pcr (N) Average Pcr (N) Crack pattern

1 (Fig. 8) Butt 1825

1803

2 Butt 1782

3 (Fig. 9) Scarf 1819

1843

4 Scarf 1874

6E.Bozhevolnaya,O.T.Thomsen

/Composite

Structures70(2005)1–11

5 (Fig. 10) Reinforced butt 2026

1974

6 Reinforced butt 1923

7 (Fig. 11) Reinforced scarf 2008

1935

8 Reinforced scarf 1862

E.Bozhevolnaya,O.T.Thomsen

/Composite

Structures70(2005)1–11

7

8 E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11

It should be noticed that the beam overhangs were

only 20mm long, which is less than the value recom-

mended in the standard methods for three-point bend-

ing testing of sandwich beams [29]. Short sandwich

beam overhangs have been used successfully previously

[30], and their usage in the present study is believed tobe completely justified by the fact that not a single of

the investigated beams experienced any damage near

the ends during the experiments. Furthermore, cracks

never initiated at the point of the load application in

the beam centre. Delamination always started/ended at

some considerable distance away from the central dia-

phragm and the supports (as it is shown in the figures

in Table 3).When all the design precautions described above were

taken into consideration, the choice of the three-point

bending scheme seems reasonable. It is known that the

four-point bending loading scheme used in many similar

tests does not exclude the possibility of severe indenta-

tions of the faces [31]. In the three-point bending set-

up, the local effects in the sandwich beam may originate

due to: (1) the centrally applied load; (2) the presence ofthe supports; (3) the presence of the core junctions. The

first cause of failure was eliminated by introducing a stiff

diaphragm, the second one was not crucial due the pres-

ence of the stiff core (Divinycell H-200) at the beam

edges (cf. P1_H200, P2_H200, P3_H200, P4_H200 in Table

2). Thus, the core junctions were left to be the most

probable causes of failure. It should be added that the

three-point bending load scheme enables the distancebetween the zones of the three local effects listed above

to be increased by a sufficient amount, such that interac-

tions between the different local effects may be avoided.

Consequently, the different failure modes (should they

occur) may be clearly separated and recognized.

The testing rig for the three-point bending loading

was built on the basis of a servo hydraulic universal

Fig. 4. Sandwich beam loaded in the three-point bending test rig—

SCHENK Hydropuls� PSB.

testing machine, SCHENK Hydropuls� PSB, as illus-

trated in Fig. 4. Computer data acquisition of the loads

and the corresponding displacements as well as video

recording of the beam deformations, were performed

simultaneously.

5. Experimental procedure and data

A list of the experimental test samples is given in

Table 3. Four different core junctions were considered,

and two beams of each type were manufactured and

investigated as depicted in Table 3. The photo of each

beam (half of the beam) with the appropriate fracturepattern is also included into the table. It should be

noticed that beams 5–8 were furnished with reinforcing

patches in the core at the junctions, and these patches

were adjoined to the lower faces. This is due to the fact

that in the chosen three-point bending load scheme, the

transverse normal stress emerging in the core is com-

pressive at the upper face-core interface [12], which pre-

vents visible crack formation and propagation. At thesame time, the locally induced transverse normal stress

in the core at the lower interface is tensile. This addi-

tional ‘‘opening’’ stress together with the shear stress

present in the core enhances the possibility of crack ini-

tiation at the junctions adjoined to the lower face.

Each beam was centrally loaded until final failure of

the beam occurred. The rate of deformation (deforma-

tion control) was 0.05mm/s. The load and the cross headdisplacement were monitored and video images were re-

corded simultaneously with 25 frames per second.

The experimentally measured critical (failure) loads

were identified as the maximum loads recorded, and

they are given in Table 3. Typical load–displacement

curves for the sandwich beams with butt and scarf junc-

tions are presented in Fig. 5. It is seen that the stiffness

of the sandwich beam, which is characterized by the ini-tial tangent of the load–displacement curves, is nearly

unaffected by the design of the core junctions. There is

Fig. 5. Load versus displacement curves for sandwich beams with two

types of junctions. The legend numbers refer to the beam numbers in

Table 3.

E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11 9

a scatter in the values of the maximum critical loads,

though the average critical load for the beams with

scarf junctions is somewhat larger than the average crit-

ical load for beams with conventional butt junctions

(Table 3).

Figs. 6 and 7 illustrate the comparative load–dis-placement curves for beams with butt and scarf junc-

tions provided with reinforcing patches (see Fig. 1(e)).

It is observed that an increase of the critical failure loads

for this type of beams is obtained (Table 3).

The overall behavior displayed by the curves in Figs.

5–7 confirms the findings in [32], which demonstrated

that Divinycell-H60, as other cross-linked PVC foams,

fails in a brittle manner.It should be noticed that the obtained data for the

critical loads lies mainly within the interval of

P6 = (1728 � 2017) N estimated earlier in Table 2. The

failure modes of all the tested beams were solely due

to yielding of the softer core, as clearly demonstrated

in the pictures of the crack patterns in Table 3.

Although the speed of the video recorder (25 frames

per second) was not sufficiently high to capture all thedetails of the crack development, it was sufficient to dis-

close the major features of the crack initiation in the

tested sandwich beams. The video footages of beams

Fig. 6. Load versus displacement curves for sandwich beams with butt

and reinforced butt junctions. The legend numbers refer to the beam

numbers in Table 3.

Fig. 7. Load versus displacement curves for the sandwich beams with

scarf and reinforced scarf junctions. The legend numbers refer to the

beam numbers in Table 3.

with butt junctions clearly prove that the crack initiated

at the corner of the softer core as it is clearly seen in Fig.

8. Notice how a shadow of the sheared/stretched core

originates from the lower corner of the left junction in

frame 1 of Fig. 8. Here in the junction corners, the stress

concentrations in the compliant material were largest asexpected according to the theoretical model [12].

The failure in the sandwich beams with scarf junc-

tions may also start in the corner of the compliant core

itself. However, the subsequent crack propagation pat-

tern is somewhat different, since a delamination of the

face and the core at the lower face/core interface takes

place first, which then moves the shear kinking away

from the junction as shown in Fig. 9. Obviously, stressconcentrations are also present in the cores of scarf junc-

tions, but their magnitude is lower than this/similar

effect in butt junctions. There is no video recording

available of the crack initiation for scarf junctions with

the sharp angle, but the after crack pattern of beam 4

(Table 3) shows that this type of scarf junction is more

effective to move the crack initiation into the bulk of

the softer core, than the scarf junctions with obtuseangles.

To compare the strength of scarf junctions with ob-

tuse (Fig. 1(b)) and sharp (Fig. 1(c)) angles of the soft

core at the lower core/face interface, attention should

be given to sandwich beams 3 and 4 in Table 3. The

critical (failure) load for beam 4 is larger than this

for beam 3, which is in accordance with the findings

of the numerical and experimental analyses performedearlier [13]. It was shown in this study, that the stress

induced locally in the faces at the junctions is always

smaller, where a sharp angle in softer core is found,

Fig. 8. Crack initiation and final rupture at butt junction in sandwich

beam 1 (see Table 3). The time interval between two consecutive video

frames 1 and 2 equals to 1/25s.

Fig. 11. Crack initiation and final rupture at reinforced scarf junction

in sandwich beam 7 (see Table 3). The time interval between the two

consecutive video frames 1 and 2 equals to 1/25s.

Fig. 9. Crack initiation and final rupture at scarf junctions with obtuse

angle in sandwich beam 3 (see Table 3). The time interval between the

two consecutive video frames 1 and 2 equals to 1/25s.

10 E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11

i.e. sharp angles provide lesser stress concentrations inthe adjacent cores.

The use of reinforcing patches in the sandwich beams

with butt and scarf junctions led to the same positive ef-

fect, i.e. they move the crack start/initiation away from

the junctions. This is illustrated in Fig. 10, where an

arrow indicates the emanation of the crack in the soft

core. Fig. 11 shows the crack initiation in a sandwich

beam with reinforced scarf junctions. There are indi-cations that the soft core yields first, and that this is

Fig. 10. Crack initiation and final rupture at reinforced butt junction

in sandwich beam 5 (see Table 3). The time interval between the two

consecutive video frames 1 and 2 equals to 1/25s.

followed by delamination of the lower core/face interface.Subsequently, a shear crack propagates through the core

at an angle of 45�, and finally a delamination of upper

core/face interface takes place.

There is a certain scatter in the values of the critical

(failure) loads obtained for the various designs of the

core junctions (Table 3), but this may be explained by

the scatter of the strength properties of the softer core.

6. Conclusions

Sandwich beams/panels with junctions between dif-

ferent core materials were considered, where a mismatch

of the elastic properties of the adjoined cores leads to

damaging local effects in the vicinity of the core junc-

tions subjected to shear loading. These effects displaythemselves by an a substantial increase of the normal

bending stresses in the beam faces, a significant varia-

tion of the core shear stress across the junctions, and

finally in the inducement of severe transverse normal

stresses in the core. The latter would be absent in the

case of a homogeneous sandwich core. Interference be-

tween the locally induced core stresses is estimated to

be the most probable cause of failure of the entire sand-wich assembly.

It has been shown that the geometry of the core inter-

faces determines the magnitude of the local effects at the

core junctions. Sandwich beams with conventional butt

junctions and structurally graded core junctions, that in-

cluded scarf junctions and junctions provided with local

reinforcing patches of the faces, were manufactured and

experimentally investigated in three-point bending load-

E. Bozhevolnaya, O.T. Thomsen / Composite Structures 70 (2005) 1–11 11

ing. The experiments were designed such that all other

possible failure modes except failures initiated at the

junctions were excluded. The load–displacement curves,

failure initiation and crack propagations patterns were

studied experimentally.

All the investigated beams failed due to crack initia-tion in the soft core near the core junctions. The exper-

imental data clearly demonstrated that the proposed

novel design of the core junctions, i.e. the structurally

graded core junctions, improves the structural perform-

ance of the sandwich beams. The sandwich beam with

scarf junctions and junctions supplemented with rein-

forcing patches displayed higher failure loads than sand-

wich beams with conventional butt core junctions did.Moreover, the new type of junctions helped to change

the crack initiation pattern.

Acknowledgments

The PVC foam core materials used for the experimen-

tal investigations presented herein were kindly suppliedby DIAB ApS, Denmark. The authors acknowledge

with gratitude the support received.

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