SANDWICH BEAMS AHD PANELS UNDER BENDING AND BUCKLING LOADS by Abid Ali

378 Pages·2014·8.35 MB·English

SANDWICH BEAMS AHD PANELS UNDER BENDING
AND BUCKLING LOADS
by
A.W.P.
Abid Ali Muhammad Sayigh, B.Sc.(Eng.),
Thesis submitted in fulfilment of the requirements
for the Diploma of Membership of Imperial College
of Science and Technology, and the Degree clf...-Dbotor
of Philosophy of the University of London.
'Work carried out in the Department of Mechanical
Engineering, City and Guilds College
IMPERIAL COLLEGE OP SCIENCE AND' TECHNOLOGY
1966
I
SUMMARY
Sandwich structures have become increasingly important during
the past two decades. Because of their strength, low costs of
production and light weight, they have become widely used particularly
in the aviation field.
The object of this investigation was to obtain experimental
evidence of the behaviour of plastic sandwich composites subjected to
bending and buckling loads, and to establish a reliable theoretical
basis for the calculation of deflections, stresses, strains and
failing loads in such sandwich constructions.
The skin and core of sandwich structure components were tested
in tension, compression, shear and plane strain compression.to obtain
basic material datareithe limitations and difficulties of each method
being discussed in each case. Several types of adhesives were also
tested for their suitability and reliability in bonding the skin to
the core materials forming the sandwich composite.
The sandwich panels were then cut into beams and panels of the
required size and tested under three-point bending, four-point bending
and uniformly distributed loads. In these tests all the beams and
A
panels were simply supported. The experimental values of the maximum
hu4
deflections,Ftrains R$40649tbeempe of the core and the skin materials
were compared with those calculated using a method established by March
and Smith of the U.S. Forest Products Laboratory and using a new
theoretical approach to the bending problem of beams under uniformly
II
distributed loads established by the author.
Because of the weakness of cellular plastic taterials, the local
deformation due to concentrated loads were also studied, and three
different possible approaches were discussed.
Most plastic materials are creep dependent and since'a number
of sandwich beams made of plastic were tested here a complete study
of the components of the sandwich beam in creep was carried out with
the aid of 4ke computer. The creep property of the composites was
analysed by using the components' creep.
Finally the buckling of sandwich beams and panels under edgewise
compression loads was studied. Four modes of failure were established
experimentally and for each mode the experimental results of buckling
loads and lateral deflections were compared with those calculated
following existing theories.
III
Page
Summary
List of Figures VI
List of Tables XVIII
Acknowledgements XIX
Notation XX
Chapter Is Introduction 1
Chapter II: Testinr: of the Component Materials 6
2.1 The Skins or Faces of Sandwich Structures 6
2.2 Tension Tests of Skin Materials 7
23
2.3 Plane..Strain Compression Tents
2.4 Determination of Modulus of Rigidity (G) 30
2.5 Determination of Poisson's Ratio 37
2.6 Core Materials 39
2.7 Tension Tests of Polyurethane Foam 41
2.8 Compression Tests 46
2.9 Determination of the Modulus of Rigidity (Shear Modulus)
46
2.10 Evaluation of Poisson's Ratio 57
2.11 Tension Tests of Expanded P.V.C. 59
2.12 Compression Tests 60
2.13 Determination of Modulus of Rigidity (Shear Modulus) 65
2.14 Determination of Poisson's Ratio 65
2.15 Conclusions 67
Iv
Pac-e
Chapter III: Preparation of the Sandwich Panels 71
Chapter IV: Beams and Panels Under Bending Loads 74
4.1 Centrally Loaded, Simply Supported-Sandwich Beams'
and Panels 74
4.2 Derivation of Stresses and Strains 85
4.3 Experimental Data for Centrally Loaded, Simply
Supported Sandwich Beams and. Panels 88
Chapter V: Pure Bending of Sandwich Beams and Panels 111
5.1 Four-Point Bending of Sandwich Beams and Panels 111
5.2 Determination of Stresses and Strains 113
5.3 Experimental Data for Four-Point Bending of
Sandwich Beams and Panels 114
Chapter VI: Simply Supported Beams With Uniformly
Distributed Load 128
6.1 Theoretical Analysis of Simply Supported
Sandwich Beans Under Uniformly Distributed Load 128
6.2 Derivation of Stresses and Strains 140
6.3 -Experimental Data 143
Chapter VII: Local Deformation 152
7.1 Stress Function Method 153
7.2 Elastic Foundation Method 164
7.3 Semi-Empirical Method 172
7.4 Maximum Load Applied in Three-Point Bending 174
V
Chapter VIII: Creep Properties of Sandwich Beams 178
8.1 Creep Experiments 179
8.2 Experimental Results 181
a)T ension Test 181
b)P oisson's Ratio Test 191
c)S hearer Creep 198
8.3 Creep Moduli 198
8.4 Creep Deflection of Sandwich Beams 208
a)C reep Interpolation of Sandwich Beam 211
b)C omparison Between Experimental and Computer
Results 222
Chapter IX: Conclusions 232
Chapter X: Buoklins of Beamn and Panels Under
Axial Loads 239,
10.1 General Buckling of Sandwich Beams and Panels 242r
10.2 Face Wrinkling of Sandwich Beams and Panels 251
10.3 Shear Crimping of the Core Material 265
10.4 Face Dimpling of Sandwich Beams and Panels 266
10.5 Experimental Procedure and Results 271
10.6 Conclusions 307
References 317
Appendix 322
4.
VI
FIGURES
Figure SSuubbjject
Number
1 Photograph of the Tension Test Mnchine . 9
2 - 5 Graph of Tension Tests of P.V.C.-skin 12 - 15
6 Graph of Probabilit- of r.v.c. Tmgent Modulus
Being in the Range (.415 - .425)
6
x 10 lbs/in2 17
7 A Histogram of P.V.C. Tangent Modulus 18
0.
3 Photograph of fhe Specimen Attachment to
the Instron Machine 19
9 Tension Tests of P.V.C.-skin at Eight
Different Strain Rates 21
10 Tension Tests of P.V.C.-skin at Eight
Different Strain Rates, Superimposed on
Each Other 22
11 Tension Test of AL-skin 24
12 Sub-press Used in Plane-Strain Compression
Tests 26
tiazd
13 XY-PlotterAin Conjunction with the Instron
Machine 27
14 Graph of Plane-Strain Compression Test for
P.V. C. -skin 28

15 Graphs of Plane-Strain Compression Tests of
P.V.C.-skin at Seven Different. Sirain:Rates 29 .
•
. • •
VII
Firrure Sub eat Pam
Number
16 Anti-olastio Bending of the Plate 32
far
17 The Set-up #1 Twisting of the Plate 33
18 Graph of Twisting of AL-Plate 35
19 Five Tests of TrAsting of P.V.C.-Plates 36
20 Two Tests to Determine Poisson's Ratio
for P.V.C.-skin 38
21 S-;ecimens Used in Tests 42
22 Tension Tests ih XX-Direction of PU-
Form 43
23 Tension Tests in YY-Direction of PU-
Poem 44
24 Tension Tests in ZZ-Direction of PU-
POP]; 45
25 Compression Tests of PU-Foe in XX-
Direction 47
26 Compression Tests of PU-Foam in YY-
' Direction 48
27 Compression Tests of FU-Four in ZZ-
Direction 49
28Modes of Shear Deformation 51
29A Photograph of Single-Block Shear Test 53
29 Shear Tests of PU-Foam in LX-Direction 54
30 Sheer Tests of PU-Foam in YY-Direction 55
31 Shear Tests of PU-Foam in ZZ-Direction 56
VIII
Figure Sub1 291
Number
32 Tension Tests of Expanded P.V.C. in XX-
II
Direotion 61
33 Tension Tests of Expanded P.V.C. in tY-
Direction 62
34 Tension Tests of Expanded P.V.C. in ZZ-
Direction 63
35 Compression Tests of Expanded P.V.C. in Three
Orthogonal Directions 64
36 Shear Tests of Expanded P.V.C. in Three
Orthogonal Directions 66
37 Photograph of Adhesion of Skins to Core 73
38 46104.0011044041107, Sketch of Centrally Loaded,
Simply Supported Sandwich Beam 76
39 Block Diagram for Centrally Loaded, Simply
Supported Sandwich Beams 87
40 Photograph of Three-Point Bending Testis 89
41 Deflection of Centrally Loaded, Simply
Supported Sandwich Beams with P.V.C.-skins
and PU-cores 90
42 Longitudinal Strain of P.V.C.-okins in
P.V.C.-PU Sandwich Beams Simply Supported
and Centrally Loaded 92
43 Longitudinal Strain of P.V.C.-skins in
P.V.C.-PU Sandwich Beams at Quarter Span
When Simply -Supported and Centrally Loaded 93
IX
Fitmre Subject Page
Number
44 Deflection of Centrally Loaded, Simply
Supported Sandwich Beams of AL-skins and
PU-cores 94
45 Longitudinal Strain of AL-skins in AL-PU
Sandwich Beams Simply Supported and
Centrally Loaded
95
46 Deflection of Centrally Loaded, Simply
Supported Sandwich Beams with AL-skins and
PU-cores 96
47 Longitudinal Strain of AL-skins in AL-P.V.C.
Sandwich Beams Simply Supported and Centrally
Loaded 97
• 48 DefiEction of Centrally Loaded, Simply
Supported P.V.C.-P.V.C. Sandwich Beams 98
49 Longitudinal Strain of P.V.C.-skins in
Sandwich Beams Centrally Loaded and
Simply Supported 99
50 Deflection of Centrally Loaded, Simply
Supported Sandwich Beams and Panels with
P.V.C.-skins and PU-cores 100
51 Longitudiani Strain of P.V.C.-skins in P.V.C.-
PU Sandwich Beams and Panels Simply Supported
and Centrally Loaded ----.102