Validity check of an analytical dimensioning approach for potted insert load introductions in honeycomb sandwich panels

Accepted Manuscript Validity check of an analytical dimensioning approach for potted insert load introductions in honeycomb sandwich panels Johannes Wolff, Marco Brysch, Christian Hühne PII: DOI: Reference:

S0263-8223(18)30217-4 https://doi.org/10.1016/j.compstruct.2018.05.105 COST 9744

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

15 January 2018 17 May 2018 18 May 2018

Please cite this article as: Wolff, J., Brysch, M., Hühne, C., Validity check of an analytical dimensioning approach for potted insert load introductions in honeycomb sandwich panels, Composite Structures (2018), doi: https:// doi.org/10.1016/j.compstruct.2018.05.105

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

12th International Conference on Composite Structures (ICCS20)

Paris - France, 04–07 September 2017

VALIDITY CHECK OF AN ANALYTICAL DIMENSIONING APPROACH FOR POTTED INSERT LOAD INTRODUCTIONS IN HONEYCOMB SANDWICH PANELS Johannes Wolff1, Marco Brysch2 and Prof. Dr. Ing. Christian Hühne3 1

2

Institute of Composite Structures and Adaptive Systems, DLR, Braunschweig, Germany. [email protected] Institute of Adaptronics and Function Integration, Technische Universität Braunschweig. [email protected] 3 Institute of Composite Structures and Adaptive Systems, DLR, Braunschweig, Germany. [email protected]

ABSTRACT An easy to handle mechanical-analytical dimensioning approach for insert load introductions on sandwich panels with honeycomb cores is of great value, since remarkable weight reductions can be achieved if the diameters of all inserts in a structure are reduced to their inevitable minimum. This is of special interest for mass critical structures of e. g. satellites, airplanes or race cars. For these structures, a combination of core connected (i. e. potted), through-the-thickness inserts in sandwich panels with fiber reinforced face sheets and aluminum honeycomb core material is frequently in use, since it offers an outstand lightweight performance. Unfortunately, a straight forward, mechanical-analytical dimensioning approach, especially for this particular insert-sandwich combination, is still missing. An analytical-mechanical model, basing on the higher order sandwich theory, was developed by Ericksen in 1953 for inserts without a connection to the core (i. e. clamped between the face sheets). In 1981, Hertel modified Ericksen’s model in order to achieve more convenient to use solution equations. However, Hertel used his modified model also for strength predictions of core connected inserts, although the core shear stress progression, decisive for the strength of an insert, differs highly from clamped inserts. However, since Hertel did not validate his extension of the modified Ericksen model onto core-connected inserts in any way, the authors suspect a misunderstanding. Unfortunately, the model was used frequently for core connected inserts afterwards and is even cited in a standard reference published by ESA and ECSS. To address this uncertainty, the authors carried out a comparison of experimental results to the predictions of the modified Ericksen model for core connected inserts within this work. Therefore, initially a cumulated overview of the Ericksen model and Hertel’s modifications is provided, since this is not available in literature. Included are current approaches for the homogenization of the anisotropic FRP- and honeycomb material properties in order to receive moat precise results. The comparison of experimental and analytical results offers mostly a poor correspondence in terms of the strength of an core connected insert. This, on one hand, reveals that the modified Ericksen formulation is not applicable on core connected inserts without significant restrictions in contrast to Hertel’s assumption. Moreover, it also becomes apparent that the various state-of-the-art test data interpretations deliver widely diverging results for the strength of an insert load introduction. Consequently, the analytical dimensioning of core connected inserts remains unreliable. Yet, this investigation derives useful improvement measures on both, theoretical and practical side.

1

INTRODUCTION 1.1

Motivation

The major requirement for aerospace and ground vehicle structures is an efficient lightweight design, expressed by a high stiffness-to-mass-ratio. Sandwich elements offer excellent specific bending and shear stiffness ratios and therefore are frequently used in primary structures of e. g. satellites and monocoques of race and sports cars. Yet, concerning airliners and passenger trains, sandwich elements can be found mostly only in secondary structures like interior applications, Fig. 1, Fig. 23.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Fig. 1: Examples of primary (Philae Lander) and secondary (airliner galley) sandwich structures, [1], [2].

The combination of carbon fiber reinforced plastic (CFRP) face sheets and aluminium honeycomb core material delivers sandwich elements with outstanding specific bending and shear stiffness. In accordance, this work focuses on this material configuration. A further essential requirement for most technical structures is its disassembling ability to serve assembly, rework, maintenance, repair and recycling purposes. Accordingly, removable connections between sandwich elements are often inevitable. Since bolting is the common way to generate detachable joints, it is exclusively regarded herein. Additionally, a tendency to functional integration into sandwich elements (e. g. structural supports, cables, pipes, antennas, grounding and health monitoring systems, [3], [4]) can be observed. This suggests a further increase of removable joints to ensure a quick replacement in case of malfunctions. Typical sandwich core materials provide only a low resistance against local compression due to their small volumetric density. Therefore, the clamping force, necessary for the function of a bolted connection, can crush the core easily, Fig. 2. For prevention, local, cylindrical core supporting elements, so called “inserts”, are popular for a local stabilization as well as for a smooth transfer of structural loads into the sandwich structure, Fig. 3.

Fig. 2: Core damage due to clamping force of a screw.

Fig. 3: Local core reinforcement by an insert element.

Fig. 4: Elements of an insert load introduction in a honeycomb sandwich panel.

If huge numbers of such inserts are demanded, they add a remarkable mass proportion to the overall weight of a sandwich structure and cost a severe decrease in its payload capability. Since sandwich structures

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

of communication satellites can contain numerous inserts (up to 25.000, [5]) and space vehicle launching costs can reach , [6], [7], [8], a mass minimization of all insert load introductions is absolutely worthwhile. Considering typical insert load introductions, both, insert element and screw, add the highest proportions to its total mass. Accordingly, dimensioning efforts should primarily concentrate on these two elements. Since screws can be sized with e. g. the help of the guideline VDI 2230, [9], [10], this work focusses on developing an dimensioning approach for the minimization of the diameter of insert elements, , under a given external load , Fig. 4. Existing insert dimensioning approaches can be categorized into finite element, [11] - [13], mechanical-analytical, [12], [14] - [19] and empirical (i. e. iterative testing) methods, [12], [20] - [22].

1.2

Objective

Yet, empirical and FE- methods require sophisticated efforts for every individual insert with its own, local load, material and geometrical conditions. Especially for projects with small monetary and computational resources as well as for sandwich structures with huge insert numbers, an individual dimensioning of every insert cannot be justified neither by time and material consuming testing nor by high fidelity finite modelling. Consequently, only a simple to use, mathematical dimensioning approach is suitable for the dimensioning of huge insert numbers in a fast and convenient way, especially when provided as computational routine. Ideally, the dimensioning approach comes in analytically closed form and depends only on the acting external force and on the geometry and material properties of the sandwich element to prevent extensive iterative solving cycles.

1.3

Basic conditions for an analytical-mechanical insert dimensioning model

As basic conditions for such a mechanical-analytical dimensioning approach, the relevant insert type, load type and –direction, damage type as well as all (anisotropic) material properties have to be defined. Regarding [16], [23] and [24], through-the-thickness, core connected (e. g. potted) insert elements offer the best specific mechanical performance (load-to-mass ratio) of all insert types, Table 1, bottom row. Therefore, this insert type is widely used in structural applications and is exclusively regarded within this work. Table 1: Spectrum of insert types. Moment of installation

Height of insert

Inserted before closing the face sheets, “hot Inserted in the sandwich plate, “cold bonded”. bonded”. Smaller than or equal to Thicker than sandwich Sandwich thickness. core height. height, protruding.

Partial potted

Fully potted Through-the-thickness insert, clamped resp. not core connected. Through-the-thickness insert, core connected with potting compound.

Since insert load introductions are notoriously weak in withstanding bending and torque loads, they have to be avoided by constructive measures, Fig. 5.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Fig. 5: Constructive measures to avoid bending and torque loads on insert load introductions, [23].

Fig. 6: Higher sensitivity of inserts to normal than to plane parallel loads, [23].

Considering the remaining bidirectional force , almost all insert-sandwich configurations offer a much superior resilience against its plane parallel proportion, , than against its plane normal one, , [23], [25], Fig. 6, Eq. (1. (1) In consequence, becomes the design load, i. e. the exclusively relevant load for the dimensioning of the insert, Fig. 4. In accordance to specification CS-25 [9], primary structures of aerospace vehicles must stay completely undamaged when they are exposed to their maximal load during operation, respectively to their limit load . Consequently, any deformation in any part of the structure, which cause a decrease in either stiffness or stability until , must be completely precluded by a proper design. Accordingly, the failure strength of any insert, , must exceed its local equivalent force when the total structure is exposed to . With an additional safety factor , is defined as Eq. (2. (2) Hertel and ECSS suggest the initial deformation of an insert load introduction to be an elastic (i. e. reversible) shear buckling at an angle of degrees of some of the cell walls in the honeycomb core adjacent to the potting of the insert at a load state of , [23], [25]. With increasing force, , these buckled cell walls get stretched beyond their elastic limit. These plastic deformations remain after unloading, Fig. 7, red arrow. Typical honeycomb materials exhibit cell walls with single and double thickness due to their manufacturing process (see also section 2.2). It is noticeable that only the cell walls with single thickness are generating shear buckles, while the cell walls with double thickness remain undeformed due to their higher shear strength, Fig. 7, blue arrows, [25]. With a further load increase, , the shear buckle plastification continues on the cell walls further away from the insert, starting always from the lower face sheet, Fig. 7, yellow arrows.

Fig. 7: Plastification of shear deformed cell walls adjacent to the insert (red arrows), specimen Al-02.

With higher loads, , tensional fractures occur in some of the stretched cell walls next to the insert, transversely orientated to the direction of the shear buckles, Fig. 8, orange arrows. In addition, the potting detaches from the face sheets, Fig. 8, white arrows. This is often followed by cracks in the upper face sheet. Finally, the insert is ripped through the upper face sheet. Depending on the geometrical and

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

material configuration of the insert-sandwich system, these damage types can occur in different sequence and on various load stages.

Fig. 8: Additional damage types with increasing load, specimen Al-01.

A typical curve of a load-deflection progression corresponding to the described damage process is displayed in Fig. 9, blue curve.

Fig. 9: Load-displacement and stiffness progressions of inserts loaded once until (insert Al-01) and two times until (insert Al-02). The range of 2 – 6 mm is compacted for better visibility of the leading sector.

When an insert (e. g. ) is loaded the first time beyond ( ), the stiffness, represented by the derivation , decreases after the point “maximal stiffness”, Fig. 9. This may indicates first cell walls to buckle plastically and the point “maximal stiffness”, e. g. the load to correspond to . Therefore, strictly following the standard CS-25, must become since any permanent deformation is permitted, Table 2, Eq. (3. Yet, after loading a similar insert (herein ) twice far beyond , the resulting stiffness curve, , reveals a stable, more even stiffness plateau which ends at point “end of stiffness plateau” at a much higher load , Fig. 9. When accepting the amount of plastification of some cell walls until does not generate a crucial decrease in stiffness, suggested by the authors for

, Table 2, Eq. (4.

in contradiction to CS-25 since it may correspond to

and is additionally

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Table 2: Different strength( respectively design load) definitions for insert load introductions Condition

Equation

(3) (4)

In strictly accordance to standard CS-25 If a slight permanent deformation is acceptable

Unfortunately, the state-of-art suggest additional, divergent characteristics of the load-displacement progression curve to correspond to . There is an allocation to the first peak of the load-displacement curve, [1], [6], [20], [21], [26] - [30], intersection points with 2%- and 5%-regression lines, [22], [31], [32] as well as the load level corresponding to the first hysteresis curve in repetitiv tests, [11], [33]. Consequently, all test data interpretations have to be considered furthermore.

2 STATE OF THE ART OF MECHANICAL-ANALYTICAL INSERT-SANDWICH MODELS The basic mechanical model for an insert-sandwich system is derived in regard of the damage process of through-the-thickness, core connected inserts in honeycomb sandwich panels in accordance to Hertel [25].

2.1

Basic mechanical-analytical insert-sandwich model

For closer distances towards the insert’s center, the available shear area in the core, Consequently, the core shear stress increases, Fig. 10, black vector fields, Eq. (5.

, decreases.

(5) According to ECSS, the increase of the core shear stress towards an insert is a function of the inverse of the distance , , [6]. Therefore, the maximal shear stress in the honeycomb core material is located directly in the junction between potting and core material at the middle of the sandwich height, [16], [23], Fig. 11, Eq. (6. (6)

Fig. 10: Decreasing core shear area the insert.

towards

Fig. 11: Shear stress progression in the core elements around an insert.

Regarding ECSS and Hertel, the plastification of the shear deformed single cell walls starts when the elastic shear strength of the honeycomb core material, , is reached, [23], [25]. To avoid any plastic deformation of core cells in accordance to specification CS-25, the highest shear stress in the core, , shall not exceed . Consequently, the minimal radius of the insert load introduction (inclusive potting), , is found when is decreased until equals , Fig. 11, Eq. (7.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

The core shear stress and related core shear area

(7) can also be described as the quotient of the internal core shear force in accordance to the general definition of stresses in materials, [23], Eq. (8. (8)

The core shear area multiplied by the core height

is defined as product of the circumferential length of a circle with radius , , Eq. (9. (9)

In regard of Eq. (7 and Eq. (8, also the core shear force

is maxed out at

, Eq. (10.

(10) Eq. (8 substituted with Eq. (9 and Eq. (10 at the potting-honeycomb core junction results in Eq. (11. (11) Rearranging formula (11, a relation of the minimal potting diameter force and the shear strength of the core material is found, Eq. (12.

to the internal maximal shear (12)

2.2

Effective potting diameter, potting to insert relation

To obtain the minimal insert diameter from Eq. (12, the empirical relationship between and for honeycomb materials, , has to be integrated. For sandwich panels with homogenous, closesurfaced core materials like foam, wood or cork, the trivial relationship between potting and insert diameter is valid. However, this does not apply to honeycomb materials. Typical insert installation methods have in common that the exact position of the insert in the honeycomb grid is unknown. That provokes an uncertain cut into the honeycomb core, causing an unknown number of truncated, e. g. affected cells . The result is a wide variety of different, partly irregular potting shapes and quantities , above all for small insert-diameter-to-cell-size ratios , Fig. 12, left side. With increasing -ratio, the asymmetry of the irregular potting shapes decrease, Fig. 12, right side.

Minimal number of filled cells, point sym. shape.

Min. number of filled cells, line sym. Shape.

Maximal number of filled cells, line symmetric shape.

Max. number of filled cells, assymetric shape.

Fig. 12: Different potting shapes of inserts in honeycomb cores with different insert diameter-to-cell-size ratios.

Since Eq. (12 demands a single, explicit value for the potting diameter shape has to be “smoothed” to an effective quantity.

, the real, irregular potting

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Analytical formulations provided by Hertel in 1981 and ECSS in 2011 allow to calculate such an effective circular potting diameter , Fig. 13, [23], [25].

Fig. 13: Definition of the effective potting diameter

by Hertel, [25].

For the calculation of , the vectors , spanning from the borehole center to each corner node of all potting filled cells or, if existing, to the outer edges of adjacent double cell walls (see also section 1.3) are taken into account, Fig. 13, middle. The effective potting radius is defined as the sum of all vector lengths divided by their total number , Eq. (13. (13) With the help of Eq. (13, Hertel generated an analytic formulation to predict average values of different -ratios with a-coefficients depending on according to Table 3, Eq. (14.

for (14)

Hertel and ECSS provide divergent a-coefficients suiting Eq. (14. Unfortunately, both do not provide any information of how they determined their particular a-coefficients. While Hertel only provides a-coefficients for average effective potting diameters, , ECSS published also a-coefficients for maximal potting diameters , yet not for the minimal ones, . Furthermore, the a-coefficients by Hertel and ECCS lack from precision since they address all typical cell sizes at once, Table 3. Table 3: a-coefficients according to Hertel, ECSS and Wolff –Brysch for perforated honeycomb material. Source

a-coefficients

Hertel 1981 [25], valid for all cell sizes

ECSS 2011 [23], valid for all cell sizes Cell size

WolffBrysch 2016 [34]

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Thus, Wolff and Brysch initiated an approach to generate own a-coefficients for every typical cell size , covering the whole range of possible effective potting diameters from to , [34]. Therefore, Wolff and Brysch analyzed huge numbers of random placed inserts in a honeycomb grid with the help of a stochastic simulation model regarding Eq. (13 for a range of with insert diameters . Since the minimal possible potting diameter is the worst case scenario, it becomes the design case herein, . In this regard, only the -coefficients by Wolff and Brysch are used for the insert dimensioning approach furthermore. When Eq. (14 is set into Eq. (12, Eq. (15 results. (15) Rearranging Eq. (15 to yields Eq. (16, which now provides a direct relationship of the maximal internal shear force to the minimal insert diameter . (16) The anisotropic behavior of honeycomb core materials has to be regarded in the insert dimensioning approach also, since it has crucial influence on the minimal insert diameter. Common honeycomb material contains single and double cell walls due to its manufacturing method, Fig. 14 and Fig. 15.

Fig. 14: Typical manufacturing processes for honeycomb material with small (upper picture) and big cell sizes (lower picture), [35].

Fig. 15: Resulting cell walls with double and single thickness causing anisotropic structural properties in WT- and LT-plane.

While the minimal shear strength of common honeycomb materials matches with the WTplane, the maximal value occurs in LT-plane, while the relation is about according to [25] and [23], Eq. (17. (17) To generate and from shear strength values provided in data sheets, the dependence of the shear strength on the thickness of the honeycomb material has to be regarded. According to Hexcel Company, the average shear strength of honeycomb material increase with smaller thickness and decreases otherwise, [35]. With smaller honeycomb thicknesses, the fillets of the core-face-sheet adhesive layer support the shear strength of the honeycomb cell walls. For large thicknesses in contrast, the shear strength is decreased since a mix of shear and tensional stresses occur, leading to deformations at lower load states. Therefore, shear strength data, e. g. determined with the test standard ASTM C 273, demand corrections when differs from the common thickness the honeycomb material was tested with, , Fig. 16. Hexcel provides a diagram, allowing to determine the correct honeycomb shear strength in graphical way, [35], Fig. 17.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Fig. 16: Shear test setup ASTM C 273, [35], [36].

Fig. 17: Correction factor K for shear strength results of test ASTM C 273, [35].

The graphical data of Fig. 17 can be converted into a potency function, allowing to compute the correction factor for thicknesses diverging from , Eq. (18. (18) For metallic honeycomb material like used herein, Eq. (19 results for

. (19)

Since Eq. (16 demands a single value for the shear strength of the core material , the different shear strengths in W- and L-direction need to be homogenized to a single, effective shear strength , Eq. (20. (20) To generate “smear”) factors

, Hertel as well as Rodriguez suggest semi-analytical based homogenization (or , Eq. (21, Table 4. (21) Table 4: Homogenization factors for the critical shear strength of honeycomb material.

Reference

Homogenization factor

Hertel 1981 [25], ECSS [23]

(22)

Rodriguez 2017 [37]

(23)

Inserting Eq. (21 into Eq. (16 yields a formulation containing the corrected, homogenized, critical honeycomb shear strength, Eq. (24. (24) In regard of Eq. (20, Eq. (24 is shortened to Eq. (25. (25)

2.1

Core shear load proportion in dependence of the sandwich configuration

In a last step, the relation of has to be integrated into Eq. (25 to achieve the aspired analytical insert dimensioning approach. Yet, an analytical description for the relation of the external load

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

and the core shear force is complex, since either the material properties as well as the geometrical configuration of the sandwich element must be regarded. Depending on the sandwich configuration, the main proportion of the internal shear force, relevant for the strength of an insert load introduction, is transferred either by the core or the face sheets, Table 5. Table 5: Influence of geometry and material of sandwich elements on the distribution of the internal loads.

Configuration A

Configuration B

Sandwich element with thin (= flexible) face sheets, high core thickness, core material with high shear stiffness.

The main proportion of the internal shear load transferred by the core.

is

Sandwich element with thick (= bending stiff) face sheets, small core thickness, core material with low shear stiffness.

The main proportion of the internal shear load transferred by the face sheets.

is

The equilibrium of forces in z-direction for the free cuts shown in Table 5 is given by Eq. (26. (26) Considering configuration A, the major proportion of the internal shear force is transferred by the honeycomb core. Therefore, the simplification according Eq. (27 is valid and results in Eq. (29. (27) With configuration B in contrast, the face sheets transfer the major proportion of the internal loads due to their high bending resistance. In consequence, the shear load proportion in the core is reduced, Eq. (28, resulting in a divergent definition for , Eq. (30. (28) Table 6: Minimal potting diameter formulations in dependence of the sandwich configuration.

Sandwich configuration

Valid formula for

A

(29)

B

(30)

Since the core shear force and the core shear stress are related, Eq. (8, the core shear stress of configuration B is decreased in comparison to configuration A, e. g. by at , Eq. (31, Fig. 18. (31)

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

In consequence, also the position of core shear stress to equal the critical shear strength is reached at a smaller distance for configuration B than for configuration A, e. g. by at , Eq. (32, Fig. 18. (32)

Fig. 18: Individual minimal potting diameters in dependence of the sandwich configuration.

Depending on the insert-sandwich configuration, can vary widely and therefore must be addressed in a proper insert dimensioning approach. To describe the distribution between the shear force proportions in core and face sheets, Youngquist introduced a core shear reduction factor in 1955, called “ ”, [38], or “ ”, [39], herein called , describing the relation between the external force and the core shear force , Eq. (33. (33) At the relevant insert-core junction

,

becomes Eq. (34 according to Eq. (33. (34)

With Eq. (33, Eq. (30 can be written as Eq. (35. (35) Youngquist also introduced the factor “ ” to distinguish whether the shear loads in the face sheets can be neglected (configuration A) or have to be considered (configuration B), Table 7. Table 7: Minimal potting diameter formulations with respect to .

Sandwich configuration -factor -value Formula for

Configuration A

Configuration B (36)

(37)

(38)

(39)

(40)

(41)

Within , the effective elastic modulus and effective Poisson ratio of the face sheets, the effective shear modulus of the core material as well as the geometrical configuration of the sandwich panel are set into relation, Eq. (42. (42)

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

The moments of inertia (

),

and

are defined according to Table 8.

Table 8: Relevant moments of inertia of a symmetrical sandwich element for a determination of , [14], [38], [39].

Description

Formulas

MoI of each individual face sheet.

(43)

Parallel axis theorem resp. Steiner Share of the face sheets at their distance in the sandwich panel, valid for symmetrical sandwich elements. MoI of the face sheets in the sandwich element.

(44) (45)

ECSS suggested an alternative, simplified notation in 2008, valid for sandwich elements with symmetrical face sheets, Eq. (46, [23]. (46) Several references provide similar factors, [19], [23], [40]. Yet, since Youngquist’s -factor is also useful for a graphical determination of , it is used herein exclusively. To obtain the effective values and from the anisotropic properties of core and face sheet materials, several approaches are provided by literature, Table 9 and Eq. (51, [23]. Table 9: Homogenization formulations for the anisotropic shear moduli of honeycomb materials.

Reference

Homogenization formulation

Kaechele 1957, [41]

(47)

Hertel 1981, [25]

(48)

Thomsen 1994, [16]

(49)

ECSS 2011, [23], Hertel 1981 [25]

(50)

(51) Since the divergent definitions of yield a difference over 200%, the respected definitions of strongly justifies a deeper investigation.

2.2

Higher order sandwich theory HSAPT

For the calculation of for a certain insert-sandwich system, the classical (or also called “antiplane”) sandwich theory is not suitable, since core and face sheets are mechanically seen as one, incompressible element e. g. cannot be differentiated, which yet is crucial to describe locally limited problems like insert elements. In contrast, the so called “higher order sandwich theory” considers face sheets, core material and insert as individual mechanical elements which are connected by transition conditions. While the face sheets are seen as e. g. Kirchhoff or Mindlin-Reissner plate elements, [16], [42], the honeycomb material is considered as e. g. transversally isotropic solid, [24]. To solve the higher order sandwich theory, the equilibria of forces and moments (in analogy to Eq. (26), the stress- strain as well as displacement relations are considered within infinitesimal 2D- or 3D-sections of the different elements, Fig. 19. The higher order sandwich theory is frequently used to describe two-dimensional sandwich beams (HSABT) as well as three-dimensional sandwich plates (HSAPT) by several authors, [42], [43], [44], [45], [46]. Since the HSABT lags of precision for circular problems like insert load introductions since it neglects of tangential forces, only the HSAPT, basing on the cylindrical coordinate system, is considered furthermore, Fig. 20.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Fig. 19: Loads and stresses on infinitesimal sections of a sandwich beam, [15].

Fig. 20: HSAPT insert-sandwich model by Thomsen, [16].

From mechanical point of view, insert-sandwich systems are statically overdetermined. Herein, the degrees of freedom of the mechanical elements differ from the sum of external, boundary and transitional forces. To achieve a solution nevertheless, additional independent boundary conditions, delivered by e. g. the energy method (like e. g. the principle of virtual work), [15], [17], or the Bessel differential equation, [14], are implemented into the HSAPT. Also a computer-assisted, numerical calculation was performed by [16]. Famous insert-sandwich models derived from the HSAPT were published by Ericksen in 1953, [14], and Thomsen in 1998, [16]. These models differ in number of connections between insert and surrounding elements, boundary conditions and mechanical complexity, Table 10. Table 10: Mechanical-mathematical insert-sandwich models basing on the HSAPT. Ericksen 1953 [14]

Thomsen 1994 [16]

Scope ublication

Mechanical model

Model

Dimensions, element type

3D, circular plate

3D, circular plate

Insert type

Through-the-thickness, core levelled

Through-the-thickness, face sheet levelled

Insert-core interaction

Not connected

Connected

Potting

/ (non-existent)

isotropic material

Insert

infinite rigid element

infinite rigid element

Type of sandwich element support

Fully clamped or simply supported

Simply supported

Considered external loads

Only plane normal force

Plane normal, plane parallel forces, bending and torque moments

Variation of parameters?

yes, by [38] and [39]

yes, by [16] and [47]

Sensitivity analysis?

yes, by [23]

no

Analytical or graphical solution provided?

yes, by [38] and [39]

no

Although the Thomsen-model addresses the relevant, core connected, through-the-thickness insert type, concerning literature lags from easy to handle analytical solution formulations for . In contrast, such solution formulations are provided in analytical and graphical form for the Ericksen model by [10], [23], [25], [38] and [39], Fig. 22. Unfortunately, the original Ericksen model is only intended for

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

through-the-thickness inserts without a connection to the core. Thus, the Ericksen model is not applicable for the core connected insert types which are addressed herein. Yet, Hertel suggested a modified version of the Ericksen model (further on called “Ericksen-Hertel model”) also to be applicable on potted, e. g. core connected inserts like regarded in this work. Therefore, it will be used herein furthermore in absence of a more suitable alternative. The development of the Ericksen-Hertel model is presented here in a cumulated overview, since this cannot be found in literature.

2.3

Ericksen’s insert-sandwich model

Ericksen’s basic model is a cylindrical insert without connection to the core (respectively clamped) in a circular, simply supported sandwich plate with isotropic core and face sheet materials, Table 10, Fig. 21. Ericksen transformed the equilibrium of stresses for the core element, which he received from the HSAPT, into a so called “modified Bessel differential equation”, Eq. (52, [14]. (52) The modified Bessel differential equation is a linear, ordinary differential function of second order. It is popular for analytical descriptions of signal proceeding, acoustic membranes and electromagnetic wave distribution problems, [48]. As differential equation of second order, the Bessel differential equation has to linear independent solutions, denoted as and . For typical values of , the Bessel solution functions can be denoted as Euler functions, Eq. (53 and Eq. (54. (53)

(54)

With and , Ericksen obtained Eq. (55 as solution formulation for the relation of core shear stress progression in dependence of the external force around an insert. Herein, represents the diameter of the circular support of the sandwich element, and , Fig. 21.

(55)

With the help of Eq. (55, the progression as well as the maximum of the core shear of insert-sandwichsystems with non-core-connected inserts can be calculated, Fig. 21.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Fig. 21: Core shear stress progressions as solution of the Ericksen model for clamped inserts in a simple supported sandwich element with .

With the help of parameter studies carried out by [10], [38] and [39], diagrams were performed, allowing the derivation of particular in graphical way, Fig. 22.

Fig. 22: Graphical derivation of

2.4

as result of a parameter variation of Eq. (55, [39].

Modifications to the Ericksen model by Hertel

To find a more convenient to use analytical solution formulation, Hertel used alternative notations for the Bessel functions and , Eq. (56 and Eq. (57.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

(56)

(57)

According to Hertel, Eq. (58 results as solution for the core shear stress progression by a substitution of the alternative Bessel functions Eq. (56 and Eq. (57 into Eq. (55. (58) Herein, Hertel obtained the factor

, which depends only on ,

and

anymore, Eq. (59. (59)

Therefore, Hertel claimed Eq. (58 to be also suitable for the dimensioning of core connected inserts. Considering the -denotation according to Eq. (35, the relation to yields Eq. (60. (60) To achieve a formulation for the minimal potting diameter, Eq. (60 is inserted into Eq. (35 with resulting in Eq. (61.

, (61)

Inserting the relation of

according to Eq. (16 into Eq. (61 yields Eq. (62.

(62)

Eq. (62 has to be solved with alternating -values in iterative order, since an equilibrium is obtained. A rearrangement of Eq. (62 to also allows a strength prediction for an existing insert load introduction with a given insert diameter , Eq. (63. (63) Hertel as well as other authors used Eq. (63 (or simplified versions) to calculate the strength of core connected inserts, [25], [26], [49], [50], [51].

3

PROBLEM DESCRIPTION

However, Hertel neither motivated nor validated his application of the Ericksen-Hertel model onto core connected insert types. In this regard, the authors distrust Hertel’s action and suspect a misunderstanding. In consequence, the applicability of the Ericksen-Hertel model onto core connected inserts has to be proven. For this, a validity check is performed for core connected inserts in honeycomb sandwich panels herein by a comparison of the theoretical results of the Ericksen-Hertel-model to experimental outcomes.

4

CASE STUDY

For the announced validation of the Ericksen-Hertel model, insert load introductions in the sandwich monocoque of the race car LR16 (Formula Student, Lions Racing Team, Brunswick) are used as case study. Herein, inserts, attaching the driver harness to the back resting plate of the sandwich monocoque, are addressed, Fig. 23 and Fig. 24.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Fig. 23: Bolted connection between harness bracket and sandwich monocoque.

Fig. 24: Load introduction in the sandwich monocoque by four through-the-thickness, core connected (potted) inserts

All necessary geometrical and material properties are given in Table 11. Table 11: Mechanical properties of sandwich and insert elements of the LR16 harness sandwich plate.

Face sheets Manufacturer Prepreg materials Fiber type Weave style Resin system Curing thickness Stacking

SGL Group Sigratex Prepreg CE 8201–200–45S Sigratex Prepreg CR 1007–150–38 Carbon fibre T700 HT/HTS, Toho Tenax Fabric, twill 2/2 unidirectional Epoxide based (“201”) Epoxide based (“022”) 5 layers, [0°/90°fb, 0°ud, +/-45°fb, 0°ud, 0°/90°fb]

Property

Variable

Value, Unit

Source / reference

Nominal overall thickness

[52]

Elastic modulus, direction 1 Elastic modulus, direction 2 Poisson ratio 12 Poisson ratio 21 Honeycomb core Manufacturer Raw material

Plascore GmbH & Co. KG Aluminium 5056 Property

Designation Variable

PAMG-XR1-4.5-1/8-10-P-5056 Value, Unit

Source / reference

Height Cell size, nominal Foil thickness, nominal

[53]

Average volumetric density, nominal Average shear modulus, WT, nominal WT-shear strength according ASTM C 273 at RT, .

[54] [53] [54]

Adhesive layers between face sheets and core Manufacturer

SHD Composites

Designation

VTFA400 (DF034)

Inserts Material designation

Aluminium AlMg3

Property

Variable

Value, Unit

Source / reference

Center borehole diameter Potting compound Manufacturer Curing cycle

3M™ ScotchWeld™ 2 hours at 65 °C or 7 days at 23°C

Designation

2K Epoxide Adhesive DP490 [55]

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

4.1

Calculation of theoretical minimal insert diameter

Regarding the Formula Student regulations, the harness attachment has to withstand a force of , acting normal to the surface of the sandwich panel, without any damage respectively loss in stiffness. Considering the design of the harness attachment bracket, Fig. 24, four inserts have to deal with the external force . Regarding Eq. (2, the safety margin is chosen to be , resulting in the critical load per insert , Eq. (64. (64) Since the beelonging -factors according Eq. (46 exceed the minimal value , Table 7, the influence of the sandwich configuration (respectively face sheet bending stiffness) onto the core shear force is negligible and the load distribution factor becomes . Therefore, the calculation of the minimal insert diameter is performed according to the “simple” formulation Eq. (35 ( ) as well as with the solution equation of the Ericksen-Hertel model, Eq. (62 ( ) provided in Table 12. Since divergent formulations are state of the art for e. g. and , a range of outcomes results for . Provided are the minimal (emphasized with “ ”), the maximal ( of the complete range of results.

) as well as the average outcomes (“ ”)

Table 12: Results for the minimal insert diameter of the harness attachment brackets in the LR16’s sandwich backrest panel.

Variable

Eq.

Critical design load per insert

Designation

Output, unit

Eq. (64

Eff. Young’s modulus

Eq. (51

Eff. Poisson ratio

Eq. (51

[1]

-factors

Effective shear moduli

Eq. (48 Eq. (49 Eq. (50

Moments of Inertia

Load distribution factor

Minimal insert diameter

Eq. (47

MoI Face sheets

Eq. (43

Steiner share

Eq. (44

MoI of face sheets, incl. distance

Eq. (45

Eq. (46

Eff. shear strength

Eq. (40 Correction factor

1 [1]

Fig. 17 Eq. (21

Eq. (35

Eq. (62

For the LR 16 harness attachment, a fairly conservative insert diameter of is chosen, since the results obtained from the Ericksen-Hertel model is distrusted according to section 3. Subsequently, the theoretical, critical load levels are calculated with the “simple” solution, Eq. (35 with ,

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

, as well as with the Ericksen-Hertel model solution, Eq. (63, . Due to the different definitions of some of the input values, a range of outcomes result. The provided results, Table 12, represent the maximal, minimal and average values of this range of resulting theoretical strength values, Table 13. Table 13: Theoretical predictions for the insert strength with

Eq. (35 Designation

5

.

Eq. (63 Output, unit

Designation

Output, unit

PILOT TESTING 5.1

Test specimen configuration, manufacturing

The dimensions of both test specimen are . The insert element is a cylindrical element made of aluminium with a diameter of according to the results provided in Table 12. The position of the insert element towards the honeycomb grit is intentionally random. The inserts provide central through-holes with a diameter of , Fig. 25.

Fig. 25: Built up and dimensions of the LR16 insert test specimen Al-01 and Al-02.

The insert is applied using the “hot bond” procedure, where the insert is installed into the honeycomb core before it is enclosed by the face sheets. Herein, the truncated cells around the machined hole in the honeycomb grit were filled with potting compound DP 490 by hand, Fig. 26. Afterwards, the insert element, raked with potting compound, is applied. Remaining gaps between insert and honeycomb core were refilled.

Fig. 26: Refilling of cells with compound DP490, application of the insert, film adhesive and face sheet layers.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

For the attachment of the face sheets, the film adhesive VTFA400 is applied onto the honeycomb core. The prepreg-layers of the face sheets were aligned following the staking order provided in Table 11. The face sheet lay-ups were applied on both sides of the honeycomb core in a symmetrical orientation. The layers were secured with a hand held roller press and completed with a top peel ply layer. After the vacuum bag is applied and evacuated, the sandwich plate was fabricated by co-curing of the epoxy resin in the face sheets as well as the film adhesive with elevated pressure and temperature in an autoclave process according to Fig. 27. After curing, the vacuum bagging and peel ply layer are removed and holes were drilled through the face sheets. In a last step, the test specimens were cut square with a circular saw.

Fig. 27: Vacuum built-up, temperature-pressure progression of autoclave process, [52].

5.2

Test preparation and procedure

Since no general testing standard for pull-testing of insert load introduction exist, different references used various test rig arrangements, ranging from rigs with two-sided, straight lined supports, [1], [2], to circular bearing supports with divergent diameters, , [6], [11], [21], [22], [26] - [29], [31], [33], [56]. Herein, a circular support with a diameter of is used, Fig. 28. The test specimen and the pull-out plate are connected by a cylinder head screw, , . A torque of is applied to ensure a reliable connection between test specimens and pull-out plate. The connection to the testing machine is done with pin connections to provide a balancing of moments.

Fig. 28: Insert test rig with circular support, test rig installed into loading press test machine.

The insert pull tests were performed with a Zwick/Roell BZ1 loading press testing machine. The machine is equipped with a load cell, type Z0 WN 812616. Deflection data was recorded from the machine displacement output, while the load data was recorded from the calibrated load cell. The load and crosshead signals were recorded at a rate of with the data program TestExpert II, provided by Zwick/Roell. The testing was conducted at room temperature at a constant sampling rate of . The actual tests are

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

performed after a preload of , which was reduced to before testing to avoid settling effects of both, specimen and test rig. Since the first specimen ( ) was tested until the total failure of the insertsandwich connection, test specimen was unloaded after reaching 88% ( ) of the first peak load level of specimen ( ) and then reloaded until 96% ( ) of the first peak load of , Fig. 9. To have a better visibility onto the damages in the honeycomb core around the insert element, both samples are cut vertical with a band saw, Fig. 7 and Fig. 8.

5.3

Interpretation of test data

Considering the different insert strength interpretation methods from test data presented in Fig. 9, the following range for experimental obtained strength levels result, Table 14. Table 14: Results for different interpretations approaches for the critical force level

Al-01

from raw test data.

Al-02

First peak value

-*

Intersection with 2% regression line Intersection with 5% regression line Load to maximal stiffness Load at end of stiffness plateau after second test run *)= Specimen

-**

was loaded only below the first peak load level; **)= No second test run performed with specimen Al-01.

Although specimen is subjected only to load levels below the first peak load level, it also reveals plastic deformations in the cell walls adjacent to the insert. Therefore, the “first peak” interpretation can be disproved as indicator of initial irreversible damages. Since no hysteresis tests were generated, no results are available in this regard.

6

COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS

The experimental results are not statistically relevant due to the small number of tested specimen. Therefore, it is impossible to tell whether theoretical or experimental results have a better reliability and therefore should serve as basis for this comparison. In this regard, only a direct comparison between theoretical and experimental results can be performed like displayed in Fig. 29 in accordance to Table 13 and Table 14.

Fig. 29: Comparison of theoretical vs. test results for the insert strength load level.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Considering the theoretical strength values , the bandwidth lasts from 3,77kN to 5,45kN (according to Eq. (35) respectively 4,24kN to 5,64kN (according to Eq. (63), corresponding to ranges of 31% and 25%. Both analytical approaches produce quite similar results, the average strength values only differs by 5%. Concerning the experimental results, much wider ranges result, since for the specimen , and differ by 75%. It is noticeable that the force level regarding the 2%- and 5%-regression line interpretations deliver almost similar results for , yet are very divergent for . The experimental strength interpretations of the “2%-regression line” of and “maximal stiffness” of come closest to the theortical results with an divergence of . All other experimental results, especially the “first peak” interpretation, reveal much larger differences of to the theoretical predictions. Hence, the range of theoretical results fits completely between the experimental “maximal stiffness” and the “2%-regression line” interpretation strength values of test specimen Al-01. Assuming an insert dimensioning strictly following the standard CS-25, , Eq. (3, would lead to a critical overestimation of the load carrying capability of an insert load introduction. If all other interpretation approaches are put in charge, the analytical models highly underestimate the experimental results and therefore deliver highly oversized insert elements. Respecting the high divergences of experimental and theoretical results, the analytical predictions neither by the simple, nor by Ericksen-Hertel model seems to be useful for a dimensioning of core connected, through the thickness inserts without severe modifications. Although, on experimental side, a testing standard as well as the validation of one of the diverse interpretation approaches is demanded. Therefore, the most important step is a precise determination the strength level precisely corresponding to the first irreversible damage in the insert load introduction, best with the help of hysteresis tests and cutting samples in a statistically suitable number. In a second step, a significant characteristic of the load-deflection and stiffness progressions has to be allocated to this first damage load level.

7

CONCLUSIONS

With the mechanical-analytical Ericksen-Hertel model, the minimal diameter for insert load introductions in a sandwich monocoque of a race car were calculated and checked against experimental results. The theoretical and experimental results offer mostly unacceptable differences. Therefore, the Ericksen-Hertel model inhibits an effective dimensioning of core connected, through-the-thickness inserts at its current state. This is caused mainly by three reasons, concerning both, the analytical model as well as the interpretation of experimental data. Firstly, the extension of validity of the Ericksen-Hertel model on core connected insert types like performed by Hertel is highly doubtable, since neither motivated nor validated by any means. Therefore, the Ericksen-model demands a new derivation, taking the correct boundary- and transitional conditions for core connected inserts into account. Secondly, the different (semi-)analytical homogenization formulations for material properties of honeycomb materials deliver widely varying outcomes and demand further development. Thirdly, on experimental side, the different current test data interpretation methods deliver widely diverging strength values since they associate the relevant initial damage of the honeycomb core to different load levels. This is caused by the poor understanding of the real failure process of the core cell walls around the insert load introduction. Neither the initial type of deformation, nor belonging phenomena in the load-deflection progression are clearly understood currently. In this regard, hysteresis experiments have to be performed, allowing a precise allocation of the first irreversible damage to the regarding load level in the insert load introduction.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

8

AKNOWLEDGEMENTS

The work is financed by the German Aerospace Center DLR within the help of the base funded project Next Generation Train III.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

9

NOTATION Unit

Explanation

Latin symbols Area Shear area in the core of a sandwich Radius of the bearing support of the sandwich element, a-coefficients for the calculation of

Bending stiffness

[1]

Farthest radius of all elements of an insert load introduction, Ericksen model: , Ericksen-Hertel model: Outer insert diameter Outer diameter of the potting of an insert load introduction Diameter of circular bearing support or the smallest distance to the next “disturbance” in the sandwich plate, whether it is an edge or another (insert) load introduction. Young’s modulus of a material Force Function of Shear modulus of a material Typical thickness of honeycomb material tested with the test standard ASTM 273 Core thickness of the sandwich element First solution function of first order of the modified Bessel differential equation Moment of Inertia of the face sheets in the sandwich element. Moment of Inertia of each individual face sheets. Parallel axis theorem resp. Steiner Share of the face sheets at their distance in the sandwich panel, valid for symmetrical sandwich elements. Second solution function of first order of the modified Bessel differential equation Core thickness correction factor Factor to obtain an homogenized, single shear strength for honeycomb materials, provided by Hertel Factor to obtain an homogenized, single shear strength for honeycomb materials, provided by Rodriguez External bending moment External torsional moment; torque Internal normal force Number of truncated cells around a borehole in a sandwich element Progression of the internal shear force in the face sheets of the sandwich element Progression of the internal shear force in the core of the sandwich element Radius Radius around an insert, where the shear strength of the core material and the local shear stress in the core are equal. Safety margin Cell size of a honeycomb grid Deflection distance in a tensional test Thickness of face sheets of a sandwich element Foil thickness of honeycomb material

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

Unit

Explanation

Greek symbols Ratio of stiffness between core and face sheets according to Youngquist Factor for the distribution of the internal core shear force proportions in core and face sheets Poissons’s ratio of a material Average, nominal volumetric density of honeycomb material Tension Shear stress progression in the rz-plane of the sandwich core Shear strength of the core material in WT-plane Shear strength of the core material in rz-plane

Subscripts Value related to sandwich configuration A Average or typical value Value related to sandwich configuration B Bore hole According to test standard ASTM C 273 Related to the core of the sandwich critical; e. g. critical load level = sizing load level Ericksen, Hertel; according to the Ericksen-Hertel model Effective or homogenized value At the end of the stiffness plateau of the stiffness progression curve Experimental; value is generated with the help of an experiment At the first peak of the force-deflection progression curve Insert Plane in honeycomb material in LT-direction (T: plane normal direction, L: orthogonal to the expansion direction) Limit load on a structure Maximal value Minimal value At the maximal stiffness point of the stiffness progression curve In normal direction, orthogonal to the surface of an sandwich Nominal value Parallel; in parallel direction to the surface Potting At intersection of force-deflection curve with a 2% regression line At intersection of force-deflection curve with a 5% regression line Simple; according to the simple equation Bearing support According to the insert test theoretical; value is generated with the help of an theoretical method Plane in honeycomb material in WT-direction (T: plane normal direction, W: expansion direction) First surface parallel direction of a fiber reinforced laminate Second surface parallel direction of a fiber reinforced laminate Plane with directions 1 an 2 in fibre reinforced laminate Special symbols Maximal value, e. g. the highest core shear stress occurring in the neutral axis of a sandwich beam. Average value Minimal value

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

10 REFERENCES [1] J. Block, M. Brander, J. Lyytinen, K. Marjoniemi, R. Schütze and L. Syvänen, Carbon Fibre Tube Inserts - A light Fastening Concept with high Load Carrying Capacity, DLR, ESA, European Conference on Spacecraft Structures, Materials & Mechanical Testing (ECSSMET 2005), 2005. [2] J. Wolff, A. Pototzky, D. Holzhüter and C. Hühne, Abschlussbericht zum Teilprojekt des DLR im Verbund, Project InGa (Innovative Galley), DLR, Institute of Composite Structures and Adaptive Systems, 2016, p. 192. [3] A. Zinno, A. Prota, E. Di Maio und C. E. Bakis, Experimental characterization of phenolicimpregnated honeycomb sandwich structures for transportation vehicles, Composite Structures 93, 2011, p. 2910–2924. [4] J. Wolff, Nutzung gefalteter Sandwichstrukturen als tragendes Bauteil mit integrierter Medienführung, Bachelor Thesis, Fachgebiet für Kraftfahrzeuge, TU Berlin, Stuttgart, 2007. [5] RUAG Schweiz AG, Automating inserts for sandwich panels, Composites World Vol. 9, RUAG Space, 2015, p. 12. [6] B. J. Kim und D. G. Lee, Characteristics of joining inserts for composite sandwich panels, Composite Structures 86, 2008, p. 55–60. [7] B. J. Kim und D. G. Lee, Development of a satellite structure with the sandwich T-joint, Composite Structures 92, 2009, p. 460-468. [8] D. Brosius, Outer space: The “final frontier” is exciting again!, Composites World 9, 2015, p. 6. [9] VDI-Gesellschaft Entwicklung Konstruktion Vertrieb, VDI 2230: Systematic Calculation of high duty bolted Joints - Joints with one cylindrical Bolt, vol. Part 1, Beuth Verlag GmbH, 2003. [10] J. Wolff und J. Skibbe, Optimierung innovativer Sandwich-Verbindungselementgeometrien, project report NGT III, Institute of Composite Structures and Adaptive Systems, 2016. [11] P. Bunyawanichakul, B. Castanié and J.-J. Barrau, Non-linear finite Element Analysis of Inserts in composite Sandwich Structures, Composites Part B 39, 2008. [12] E. Bozhevolnaya, A. Lyckegaar, O. Thomsen and V. Skvortsov, Local Effects in the Vicinity of Inserts in Sandwich Panels, Composites Part B, vol. 35, 2004, p. 9. [13] C. Burchardt, Fatigue of Sandwich Structures with Inserts, Composite Structures 40, 1998, pp. 201 211. [14] W. S. Ericksen, The Bending of circular Sandwich Plate under normal Load, Report, US Department of Agriculture, 1953, p. 35. [15] Y. Frostig, M. Baruch, O. Vilnay and I. Sheinman, High Order Theory for Sandwich-Beam Behaviour with transversally flexible Core, Journal of Engineering Mechanics 118, 1992, p. 1026 - 1043. [16] O. T. Thomsen, Analysis of Sandwich Panels with through-the-thickness Inserts using a higher-order Sandwich Plate Theory, ESA, 1994. [17] V. Skvortsov and O. T. Thomsen, Analytical Estimates for the Stresses in Face Sheets of Sandwich Panels at Junctions between different Core Materials, Conference on Sandwich Structures, 2002, p. 551 - 559. [18] E. Bozhevolnaya and A. Lyckegaard, Local Effects at Core Junctions of Sandwich Structures under different Types of Loads, Composite Structures 73, 2006, p. 24 - 32. [19] E. Bozhevolnaya, O. T. Thomsen, A. Kildegaard and V. Skvortsov, Local Effects across Core Junctions in Sandwich Panels, Composite Structures, 2003, p. 509-517. [20] K.-I. Song, C. Ji-Young, K. Jin-Hwe, C. Jin-Ho and K. Kwang-Soo, An experimental Study of the Insert Joint Strength of composite Sandwich Structures, Composite Structures 86, 2008, p. 107–113. [21] J. W. Lim and D. G. Lee, Development of the hybrid Insert for composite Sandwich Satellite Structures, Composites Part A 42, 2011, p. 1040-1048. [22] R. Seemann and D. Krause, Virtual Testing of Nomex Honeycomb Sandwich Panel Inserts, 20th International Conference on Composite Materials (ICCM 20), 2015. [23] ECSS European Cooperation for Space Standardization, Space Engineering Insert Design Handbook, ECSS-E-HB-32-22A, ESA-ESTEC, 2011. [24] O. T. Thomsen et al., Analysis and Design of Sandwich Plates with Inserts - a high-order Sandwich Plate Theory Approach, Composites Part B 29B, 1998, pp. 795-807. [25] W. Hertel, W. Paul and D. Wagner, Standardisation Programme on Design Analysis and Testing of Inserts, Final Report, ESTEC, 1981, p. 426. [26] S. Heimbs and M. Pein, Failure Behaviour of Honeycomb Sandwich Corner Joints and Inserts, Composite Structures 89, 2009.

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

[27]

G. Bianchi, G. S. Aglietti and G. Richardson, Optimization of bolted Joints connecting

Honeycomb Panels, School of Engineering Sciences, University of Southampton, 2006. [28] K.-H. Nguyen, Y.-B. Park, J.-H. Kweon and J.-H. Choi, Failure Behaviour of Foam-based Sandwich Joints under pull-out Testing, Composite Structures 94, 2012, p. 617 - 624. [29] Y.-B. Park, J.-H. Kweon and J.-H. Choi, Failure characteristics of carbon/BMI-Nomex sandwich joints in various hygrothermal conditions, Composites Part B 60, 2014, p. 213–221. [30] J. Block, Study on Carbon Fibre Tube Inserts, Summary report, DLR, Institute of Composite Structures and Adaptive Systems, ESTEC /Contract No. 16822/02/ NL/PA, 2004 [31] R. Roy, K. Nguyen, Y. Park, J. Kweon and J. Choi, Testing and modeling of Nomex™ Honeycomb Sandwich Panels with bolt Insert, Composites: Part B 56, 2014, p. 762 – 769. [32] J. Block, Technical Note 4, Test Report, Deutsches Zentrum für Luft- und Raumfahrt DLR, Report., Braunschweig, 2007, p. 1 - 49. [33] P. Bunyawanichakul, B. Castanie and J.-J. Barrau, Experimental and numerical Analysis of Inserts in Sandwich Structures, Applied Composite Materials 12, 2005, p. 177-191. [34] J. Wolff, M. Brysch and C. Hühne, Pilot Study on an analytic Sizing Tool Approach for Insert Load Introductions in Sandwich Elements, ECCM17, DLR, 2016, p. 1 - 12. [35] Hexcel Corporation, HexWeb Honeycomb Attributes and Properties, P. C. Hexcel Corporation, 1999, p. 40. [36] ASTM International, Standard Test Method for Shear Properties of Sandwich Core Materials C 273/C 273M – 07, ASTM International, license by Beuth Verlag. [37] J. D. D. Rodriguez Ramirez, Shear Testing of Honeycomb Cores for Inserts, Institute Clément Ader (ICA), International Conference on Composite Structures (ICCS20), 2017. [38] W. G. Youngquist and E. W. Kuenzi, Stresses induced in a Sandwich Panel by Load applied at an Insert, US Department of Agriculture, Wood Engineering Research, Forest Service, 1955, p. 27. [39] H. M. Montrey, Bending of a circular Sandwich Plate by Load applied through an Insert, Report, US Department of Agriculture, 1973, p. 31. [40] Department of Defense USA, Structural Sandwich Composites, MIL-HDBK-23A, 1968, p. 491. [41] L. E. Kaechele, Minimum-Weight Design of Sandwich Panels, US Force, The Rand Corporation, 1957. [42] Y. Frostig und M. Baruch, Bending of Sandwich Beams with Transversely Flexible Core, AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics, and Materials Conference, Williamsburg, 1988, p. 8. [43] Y. Frostig and M. Baruch, Bending of Sandwich Beams with Transversely Flexible Core,

29th Structures, Structural Dynamics and Materials Conference, Williamsburg, 1988, p. 8. [44] E. Bozhevolnaya and Y. Frostig, Nonlinear closed-form high-order analysis of curved sandwich panels, Composite structures No. 1-4, 1997, pp. 383-394. [45] S. Karczmarzyk, Static Transverse Bending Problem for the Static Transverse Bending Problem for a Sandwich Strip with Realistic Clampings of the Edges, 20th International Conference on Composite Materials, 2004, pp. 7-39. [46] S. J. Salami, M. Sadigh and M. Shakeri, Improved extended High Order Analysis of Sandwich Beams with a bilinear Core Shear Behaviour, Journal of Sandwich Structures & Materials, Sage Publications, 2014, pp. 1-36. [47] B. Banerjee and B. Smith, The Thomsen model of inserts in sandwich composites: An evaluation, Industrial research New Zeeland, Auckland, 2010 [48] W. Rehwald, Elementare Einführung in die Bessel-, Neumann- und Hankel-Funktionen, S. Hirzel Verlag, Stuttgart , 1959, p. 1-52. [49] L. Syvänen, K. Marjoniemi, A. Ripatti und M. Pykäläinen, Analysis models for insert design rules in sandwich panels with CFRP facings, Patria Finaviacomp, 2003. [50] G. Bianchi and G. S. Aglietti, Static Performance of hot bonded and cold bonded Inserts in Honeycomb Panels, Journal of Sandwich Structures and Materials, 2010, p. 1099-6362. [51] V. Bardet, Automation of Inserts-Checking on an Aluminium Sandwich Structure, KTH, School of Engineering Sciences (SCI), Kopenhagen, 2013, p. 14. [52] M. Bröker, J. Wolff, Massereduzierung einer Lasteinleitung im LR16-Sandwichmonocoque durch Optimierung des Insertelements, Bachelor Thesis, Technical University Braunschweig, 2016, p. 78. [53] Plascore Incorporated, Data sheet of PAMG-XR1 5056 Aluminium Honeycomb, www.plascore.com, 2014 [Accessed 15.01.2018].

Johannes Wolff, Marco Brysch and Prof. Dr. Christian Hühne

[54] Plascore GmbH & Co. KG, Test Certificate 41137-123366-1, Plascore GmbH & Co. KG, 2016. [55] 3M Scotch-Weld, Technical Data Sheet for Structural Adhesive 9300 B/A FST, https://multimedia.3m.com/mws/media/749734O/3mtm-scotch-weldtm-9300-b-a-fst-two-part-structuraladhesive.pdf, 2011 [Accessed 15.01.2018].