FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY Jörg Felhusen an Sivakumara K. Krishnamoorthy RWTH Aachen University, Chair an Insitute for Engineering Design (IKT) Steinbachstr. 54B, D-5074 Aachen e-mail: krishnamoorthy@ikt.rwth-aachen.e, webpage: www.ikt.rwth-aachen.e ABSTRACT This paper presents esign principles, tools, methos an experiments for joining sanwich materials. The connection technique presente here requires neither ahesive nor inserts for joining ifferent components an enables fast joining an repairing since stanar screw elements are use for connection. The novelty of the solution approach presente in this paper lies in its universal applicability for connecting ifferent materials in a T-, L- an V-joint joint connections without major changes in the calculation proceure. A new simplifie conservative-failure criterion for sanwich material is propose which can be use as a basis for FEM calculations at connection interfaces. For that, only experimental set ups are require to obtaine necessary material ata. Tools an methos of avoiing strength an stiffness iscontinuities are also iscusse.. INTRODUCTION There are several avantages of using sanwich material as a primary structural component in general mechanical engineering applications. Some avantages inclue light-weight esign, efficient energy absorption, increase mechanical amping an goo thermal an acoustic isolation. However, sanwich structures are sensitive to heat loas that often lea to elamination of the face sheet. Unexpecte local an impact loas may result in permanent eformation of the structure. These problems constrain the applicability of sanwich structures in general mechanical engineering. In such cases, techniques that allow fast joining an repairing of sanwich components can help to overcome this constraint. Kempf in his work [] has focuse exclusively on fining a variety of principle solutions to mechanically connect sanwich panels with in a plane. A principle solution usually emonstrates the physical effect (for ex. friction), effect carrier (material) an qualitative emboiment parameters (geometry) []. About 850 such principle solutions have been iscusse in his work for connecting two sanwich elements with in a plane. One such a principle solution is shown in Figure a). However, because of the lack of sanwich material ata, only functional moels were evelope earlier to emonstrate some principal solutions. Figure b) shows its functional moel. Figure : Principle solution an a functional moel
This paper escribes experiments, methos an tools that can be aopte for proper imensioning of sanwich materials, screw elements an sanwich connection elements as efine in Figure. Some reasons for the consieration of this connection technique in particular are: It allows joining an repairing with stanar mechanical elements. It requires less time to prepare sanwich materials an allows easy positioning. It nees comparatively lesser elements to transmit forces an moments. Furthermore, strength calculations of such screw elements are well known. Efficient application of such connection techniques for commercial purposes requires strength proofs of imensioning sanwich materials, screw element an connection element uner complex loaing conitions. This paper restrains itself proviing such proofs for sanwich materials with PUR-foam core materials separate by steel face sheets uner static loaing.. DIMENSIONING SANDWICH MATERIALS Literatures an stanars escribe a series of tests to etermine material parameters of sanwich materials. Performing most of these tests to etermine necessary material parameters woul be time an cost intensive because it requires a number test benches, test specimens of ifferent shapes an sizes, preparation time etc. The number of material parameters that have to be etermine epens on chosen failure criteria an moelling methos. Hence the failure criteria, moelling methos shoul be chosen in such a way that it allows goo usage of the sanwich material at less experimental cost. Also the test benches that shall be consiere shoul provie much information about sanwich materials. Hence this part escribes basic material information that shall be obtaine through a test series, for proper esigning of sanwich an sanwich connection elements. The change of strength characteristics of the material as a result of fatigue or impact loas is not consiere in this paper. The proceure suggeste here can also be applie for conservative imensioning of sanwich materials in general engineering applications. Since the face sheet of sanwich materials are usually mae of metallic materials, whose mechanical properties an failure criteria are well known, it is not consiere any further.. Failure criteria an moeling assumptions for sanwich materials The failure theories for composite materials can be in general classifie in three groups accoring to Daniel [3]. They are, the so calle non-interactive theories that suggests failure base on one stress value (ex. Maximum stress theory), the interactive theories that suggests failure base on interaction between two or more stress components (ex. Tsai-Hill, Tsai-Wu) an the theories that are purely base on moe of failure of the material. The choice of theory for any particular application epens on available ata, experimental facilities an conformity with experimental results. When experimental results of various failure criteria are compare in a plane-stress conition, Tsai-Wu criterion prove to have a relatively goo compliance in results. This compliance is also applicable to polymer foam core materials, which is use in the manufacture of sanwich materials [4]. Another important avantage of this failure criterion is that, it has been alreay implemente in commercial FE-Programs such as ANSYS TM an ABAQUS TM. Therefore, only this theory an the material parameters those are require for this theory is iscusse further.
Five failure parameters are essential to escribe Tsai-Wu criterion in a plane-stress conition an the etails are escribe for instance in literature [5]. They are tensile an compressive strengths of sanwich material in each irection of the consiere plane an the shear strength in this plane. One can make a further simplification by making an assumption that the foam core is macroscopically homogeneous. This assumption reuces the require parameters to three since compressive an tensile strengths in each irection are assume to be the same. In this paper, these parameters are ientifie by F (Tensile strength), F z (Compressive strength) an S (Shear strength). Such a erive-tsai-wu criterion can be written as: σ σ τ ( σ + σ ) + ( )( σ + σ ) + = () z z z S where, σ, σ an τ are the stress variable in plane stress conition. If these three parameters are known, the loa carrying capacity of sanwich core uner general forces (F x, F y un F z ) an moments (M x, M y an M z ) an at a ranom combination can be etermine easily using finite element simulation programs. Figure represents general forces an moments in the Cartesian coorinate system. Aitionally, simulation of a sanwich core in a FEM program requires at least two linear-elastic constants; for instance, Young s moulus (E), Poisson s ratio (υ) or shear moulus (G). Hence it can be sai that imensioning sanwich materials requires at least 5 material constants an of course the corresponing test benches to etermine these constants. Figure : Genaral forces an moments in a sanwich element. Choice of test benches In the iscussion above (See..), the strength properties of the glue material that connects the sanwich foam core with face sheets are not consiere. Strength proof of the complete sanwich element requires that the strength of the glue material is also consiere in the calculations. Hence it woul be ieal to choose test benches in such a way that it accounts for etermining the strength both glue an core materials an also enables etermining more than one necessary material constant. The tensile test benches as illustrate in DIN 539 or ASTM C97-6 an compressive test benches as illustrate in DIN 539 or ASTM C365, can be employe to obtain respective strength values (F t & F c ) an can be aitionally use to unerstan the strength properties of glue materials. One more avantage is that, it can be also use to etermine the linear-elastic constant Young s moulus (E). Shear testing fixture as illustrate in DIN 5394 or in ASME C73 can be preferre for obtaining other two constants (S & G). Hence it can be sai that at-least 3 test benches are require to obtain the necessary 5 constants.
Developing test benches for compression testing is much easier than eveloping test benches for tensile testing. If it is well-known that compressive strength of particular core materials is weaker than its tensile strength, further simplifications in the failure criteria can be mae by avoiing tensile testing. This is usually the case for most of the polymer foam core materials; PUR an PS as given by Zenkert [6]. Hence by making simplification F =F z, the formula can be written as: τ ( σ + σ σ σ ) + = () S But this further reuction in the number of parameters has a negative impact in calculations as illustrate further. To enable D illustration of failure criterion escribe by formula an formula, a constant K can be efine to relate shear stresses with shear strength as,τ = K S. Figure 3 emonstrates the ellipses escribe in formula (green otte) an formula (re straight) for a PUR foam with compressive strength of 0.4 MPa, tensile strength of 0.5 MPa an K=0.75. It can be clearly seen that this simplification results in uner-estimation of strength properties of the material in bi-axial compressive regions. This may lea to a catastrophic premature failure in commercial applications. Figure 3: D illustration of failure criteria- a comparison To enable a conservative-failure-criterion that lies within the erive-tsai-wu * criterion, a conservation shear strength value ( S ) shall be substitute in formula an can be written as:
τ ( σ + σ σ σ ) + = (3) S To etermine this value, an experiment must be so chosen, that the failure occurs uner biaxial compression an shear stresses. Four point bening test bench allows such a combine stress conition. Other avantages of four-point bening tests are its universally applicability in static an ynamic (fatigue) characterization of materials. Shear moulus can also be etermine by using formulas mentione in ASTM C393. Therefore, this test fixture is preferable to shear test benches escribe earlier. Bening tests shall be performe until core shear failure as illustrate in Figure 6c. With the help of four-point bening FE-Simulation, the tensor componentsσ, σ un τ at the corresponing failure region shall be etermine. By substituting these tensor * components in Formula 3, the conservative shear strength value ( S ) can be obtaine. Figure 4 shows failure ellipse accoring to erive-tsai-wu failure criterion having compressive strength of 0.4 MPa, tensile strength of 0.5 MPa an K=0.75. For the failure ellipse, the simplification with F = F z = 0.4 MPa is consiere. Instea of a FE-Simulation, the point (-9.4 MPa, -0.74 MPa) in biaxial compressive region is chosen from failure ellipse to etermine the conservative shear strength S *. Substituting these values along with formula 4, results in value of K* to 0.85. The failure ellipse represents the simplifie conservative-failure criterion which lies insie the failure ellipse. * * τ = K S (4) Figure 4: Simplifie conservative-failure criterion
.3 Result Hence it can be sai that by using four-point bening test benches an compressive test benches, two linear-elastic parameters (E & G) require for numerical simulation an * also two strength values ( S & F ) require for simplifie conservative-failure criterion can be obtaine. These values are goo enough to escribe the loa carrying capacity of sanwich beam uner combination of general force an moment components escribe in Figure. If aitional experimental facilities an time require to perform experiments an preparation of specimen are available, then other tests can also be one. 3. DIMENSIONING SCREW ELEMENTS A general methoology for imensioning screw elements, base on unerstaning its strength properties is given. To achieve this, the force transmission behavior from sanwich beam to the screw elements an its surrounings uner general forces an moments (F x, F y, F z, M x, M y an M z ) must be unerstoo. This can be one by making an assumption that sanwich an connection elements are rigi boies an the forces an moments they in-take are transmitte without any changes to the screw elements. Since this assumption is mae on safe sie basis, no negative influences in strength calculations of screw elements are expecte. This assumption enables to etermine the resultant force components transmitte to the most critically loae screw element as suggeste schematically in a functional black box (Figure 5). Figure 5: Black box Kempf in his work [] has provie such a calculation for imensioning screw elements for joining two sanwich materials with in a plane. The two formulas given below escribe axial an raial force components on a screw element for a worst-case scenario. The number of screws (n), the istance between them () an other necessary etails for esigning with screws can be taken irectly taken from VDI-Guieline 30 [7]. F F 3 ( ) F M M n M x t x z y = + + + Fz + ra (4) 3 axial n nt ( n n) t + ( n ) M x ( n ) Fy = + (5) t + ( n ) n n
Such an abstract escription of forces, efine through a function has several avantages. In particular, it enables calculation of transmitte forces an etaile esigning of screw elements for: - sanwich elements in a T-, L- an V-joint - sanwich elements with other structural components - sanwich elements with ifferent material properties without any change in the formulas 4 an 5. This can be emonstrate in Figure 6 in which a principle solution is given for connecting 3 ifferent sanwich materials in a T- Joint. The raial an axial components of forces on the screw element loae critically can be calculate using the same formula escribe above. Figure 5: Principle sketch of a T-joint connecting 3 ifferent sanwich materials 4. EXPERIMENTS, METHODS AND TOOLS FOR DIMENSIONING CONNECTION ELEMENTS Before imensioning connection elements for sanwich materials, it is important to know if it is absolutely essential to fin the optimum geometry of connection element for a given loa case. Fining a solution optimum usually consumes a lot of time, effort an resources. Other factors against such a consieration inclue; restrictions in manufacturability of specific shapes (raius, thickness of the tongue etc.), change of solution optimum ue to change in loaing conitions an spatial restrictions. So the aim of this part of this paper is not to fin the optimum imension of the connection element but to etermine a geometry that allows smooth transmission of forces an moments with minimize stiffness iscontinuities at sanwich interfaces. Therefore only the tools an methos that can be aapte to achieve this are iscusse here. This paper is restricte in etermining proper geometry of connection element joining two sanwich beams within a plane uner bening loaing conition. 4.. Experiments The suggeste two experiments in chapter are performe to etermine 4 necessary material parameters. Figure 6a) shows the four-point bening test fixture an figure 6b) shows compression testing. The etermine values are E= 4 MPa; G= 5.93 MPa; F ~0.3 MPa an S*= 0.8 MPa. It shall be note that, ifficulty may arise in etermining S* value, since the beam usually unergoes local failure an shear failure may not be realise easily for PUR foam core materials. During such circumstances, it is necessary to force the sanwich beam to fail preominantly uner shear as given in literature [8]. Figure 6c) shows such a force shear failure by aing aitional plates of mm thickness.
Figure 6a): four-point bening; Figure 6b): Compressive test; Figure 6c): Shear failure 4. Tools an Methos Basic profile imensions of connection element in form of I-, - or T-Profiles are to be obtaine base on bening stiffness of the sanwich beam. The emboiment parameters of I-profile for smooth transmission of forces in consiere further. The solution fiel is generally quite large to match the imensions of the I-profile in bening loa. The most efficient way of fining a solution is by following guielines for imensioning as suggeste in literature []. Once the basic imensions are chosen, FE-Simulation can be use to verify whether the stresses in sanwich beam an the I-profile satisfies their respective failure criterion. For sanwich beam, the simplifie conservative-failure criterion can be chosen an for I-profile which is in this case mae of steel, Von-Mises criterion shall be chosen. Differences in isplacement results at interfaces can be use to check stiffness iscontinuities. If geometrical solution is not satisfying for particular application an ifficulty persists in fining an appropriate solution, then proper geometry can be fin using shape optimization tools. In shape optimization, the outer bounary of the structure is moifie to solve the optimization problem. Using finite element moels, the shape is efine by the gri point locations. Hence, shape moifications change those locations [9]. D-Moelling an simulation will be the most appropriate metho for shape optimization since it requires simplifie moelling effort an reuce simulation time. Such moelling approach has conforming results with theory an 3D-moelling approaches [0]. Shape optimization for using commercial softwares such as Altair Optistruct allows change of shape of tongue of connection elements until specific stress criteria an eflection values are satisfie. Figure 7 shows such a connection element with minimize stress an stiffness iscontinuities at connection interfaces in a D finite element bening simulation. Figure 7: D simulation results of sanwich beam with I-profile
6. SUMMARY Design engineering methos, tools an experiments suggeste in this paper can be use for joining any polymer foam sanwich materials to its surrouning components an the proceure can be summarize as guielines given below: Designing connection technique for sanwich elements requires information about the loa carrying capacity of the sanwich material uner multi-axial loaing conitions. Using the test proceures suggeste here, the necessary material parameters can be etermine for the appropriate failure criterion. Application specific force an moment components ata shall be collecte base on homologation requirements of respective inustry (railway/aircraft construction) or using experiments an simulation. The number of screw elements an the istance between them is calculate base on the cross-sectional geometry of the sanwich material an conforming to suggestions of VDI-Guieline 30. Once the seconary an the primary variables as suggeste in chapter 3 are known, strength calculations for screw elements can be performe. The basic imensions of the connecting element can be chosen base on available profiles. D-FE simulation is one of the efficient tools to quantify the geometrical profile base on strength an stiffness continuity requirements. To achieve this appropriate failure criterion an isplacement requirement has to be satisfie. If necessary, shape optimization tools shall also be use. By employing extrusion profiles, the appropriate geometry requirement of the connection element can be satisfie. REFERENCES - Kempf A.: Entwicklung einer mechanischen Verbinungstechnik für Sanwichwerkstoffe, Doctoral Thesis, RWTH Aachen, 004 - Pahl G., Beitz J., Felhusen J., Grote K.H.: Engineering Design, A systematic approach, 3 r e., Springer 007 3- Daniel I. M.: Failure of composite materials, Northwestern university, http://ecf6.civil.uth.gr/menu/invitetalks/daniel.htm, website visite 30..006 4- Daniel I. M., Goutos, E.E., Wang, K.A., Abot, J.L.: Failure moes of composite sanwich beams, International journal of amage mechanics, Vol., Oct. 00 5- Felhusen J., Krishnamoorthy S. K., Beners M. J.: Test series for esign of sanwich components, Konstruktion, Springer 007, accepte for publication. 6- Zenkert, D. (E.): The hanbook of sanwich construction, Pages 3-34, Craley Heath, West Milans, EMAS 997 7- VDI-Guiline 30: Systematische Berechnunjg hochbeanspruchter Schraubenverbinungen, VDI Verlag 00 8- Felhusen J., Krishnamoorthy S. K., Beners M. J.: Shear strength characterization of PUR-Foam core by moifie 4-Point bening tests, 8 th international conference on sanwich structures, accepte for publication, 008 9- Altair Optistruct users guie, Shape Optimization, Altair Engineering Inc., 008 0- Ozare A. P.: Moelling an optimization of sanwich connector, Master Thesis, RWTH Aachen 006