Finite element analysis of composite structures

Transcription

1 Finite element analysis of composite structures Viktor Kulíšek CZCH TCHNICL UNIVRSITY IN PRU FCULTY OF MCHNICL NINRIN epartment of Production Machines and quipment PM Research Center of Manufacturing Technology RCMT

2 Overview F of composite structures 2 Introduction Typical composite applications Composite materials Fibre and matrix properties Fabrics and preforms Unidirectional composite Material properties Layered structures matrix and its implications F of composite structures lements for F of composites Stress and strength xamples

3 Introduction F of composite structures 3 Finite element analysis of composite structures The principle of F same as for the isotropic materials from the previous courses K. u = f K global stiffness matrix u global vector of nodal displacements f global vector of external equivalent nodal forces solution: u = K 1. f For composite structures more challenging in pre-processing of models and post-processing of results ue to orthotropic behaviour of material and other important parameters In this lecture, the basic approaches for modelling of long fibre reinforced plastics are discussed

4 Introduction F of composite structures 4 Important to know What are the demanded results of the simulation? (stress, displacement, natural frequencies, temperature distribution, crash behaviour, ) What is the demanded precision of results? What manufacturing technology and preforms are used for the structure? fabrics, prepregs, fibre tows unidirectional versus multidirectional preform abilities of manufacturing technology Important decisions lements type selection and geometry simplifications Modelling of composite structure full composite lay-up matrix properties homogenization

5 Introduction Composite structures - erospace 5 irbus 35XW, Premium ROTC

6 Introduction Composite structures - erospace 6

7 Introduction Composite structures - erospace 7

8 Introduction Composite structures - utomotive 8

9 Introduction Composite structures - utomotive 9

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11 Introduction Composite structures - Industry 11

12 Introduction Composite structures

13 Introduction 13 Short conclusions in terms of composite structures Usually thin components (thickness is significantly smaller than other 2 dimensions) Suitable for shell elements, beam elements Options for solid modelling limited Usually composite lay-up with layers with multiangle orientations, structures with only 1 orientation of fibres are rare Various semi-finished products used in the structures Fabrics, prepregs, rovings ifferent manufacturing technologies, different fibre volume fraction in the composite layer Various materials used in applications Fibres Matrices ll of the aforementioned influence the behaviour of the component and thereby the demands for its modelling

14 14 Composite materials emonstration layer of composite material Properties of layer is determined by type of fibre carbon, glass, boron, aramid type of matrix thermosets - epoxy, thermoplastics P, PK, PPS,... type of semi-finished product unidirectional multidirectional fibre volume fraction in the layer manufacturing technology

15 Composite materials - Fibres 15 Fibres carry the load; significantly defines the stiffness Overview of nominal properties of selected types of fibres L Youngs modulus in direction of fibre T Youngs modulus in direction perpendicular to fibre LT shear modulus of fibre s Lf tensile strength of fibre a L thermal expansion coefficient in direction of fibre l L thermal conductivity in direction of fibre lass isotropic fibre, Carbon strongly anisotropic r L L T f s Lf a L l Lf [kg.m -3 ] [Pa] [Pa] [Pa] [MPa] [K -1 ] [W.m -1.K -1 ] High-strength PN carbon ,38e-6 1 Ultra-high modulus PITCH carbon ,5e glass ,4e-6 1,35 S-glass ,6e-6 1,45 ramid ,4e-6,4

16 Composite materials - Fibres 16 IL - Mitsubishi Plastics Nippon raphite Fiber Corporation

17 Composite materials - Matrices 17 Matrix affects strength, fracture toughness affects other properties (flammability, conductivity, fatigue, biocompactibility, ) determines/restricts the manufacturing technologies Thermosets non-repeatable manufacturing process after curing no reshaping (nondestructively) longer time of curing (hours minutes) brittle materials Thermoplastics repeatable manufacturing process after heating matrix softening reshaping short time of processing (minutes) good fracture toughness

18 Composite materials - Matrices 18 Source: R, Chris. The Outlook for Thermoplastics in erospace Composites, In High- Performance Composites. Vol. 22, No. 5, 214.

19 Composite materials - Matrices 19 Matrix ensity [kg.m -3 ] [MPa] a [K -1 ] l [W/m/K] lass transition temp. [ C] poxy e-6,2,5 5 2 x Melting temp. [ C] Nonsaturated polyesters Phenolic resins e-6,3, x e-6,4,7 7 x PP e-6,17, P e-6,22, P e-6,22, PPS e-6 x PK e-6, PI 7 3 5e-6, x

20 2 Composite materials - semi-finished products Possible semi-finished products for composite applications fabrics prepregs, U tapes rovings / fibre tows chopped fibres Properties of semi-finished product influences the behavior of the unit and component (stiffness, strength) fibre orientation uni or bi-directional amount of fibres Type of semi-finished product affects the modelling approach fabrics prepregs rovings chopped fibres Source:

21 21 Composite materials - semi-finished products Fabrics plain worse drapability good strength, resistance against shift of fibres twill average drapability satin good drapability small resistance against shift of fibres

22 Composite materials - semi-finished products 22 Prepregs thermosets fabric or uni-directional and semi-cured matrix thermoplastics fabric or uni-directional and thermoplastic matrix Storage thermosets must be stored at approx. -18 C, limited lifetime thermoplastics can be stored at room temperature, without lifetime restrictions One of the highest-quality semi-finished product

23 Composite materials - semi-finished products 23 Rovings fibre tows notation 1k, 3k, 6k, k, 24k, 48k gives number of fibres in the tow (1k ~ 1 fibres) for filament winding, fibre placement, manufacturing of prepregs and fabricss

24 Composite materials 24 Short overview Internal structure of composite layer determines mechanical properties stiffness strength other From the F point of view Properties of layer described by material, thickness and orientation However, care must be taken when simplifying the semi-finished products like bi-directional fabrics into the layer properties asic unit for simulations Uni-directional layer of composite

25 25 asic computational element Properties determined by type of fibre type of matrix fibre volume fraction in the layer thickness of the layer / 1/ 1/ 1/ / / / 1/ / / / 1/ s s s s s s isotropic material / 1/ 1/ 1/ / / / 1/ / / / 1/ s s s s s s orthotropic material 1 2. Parameters:, n Parameters: x, y, z, xy, xz, yz, n xy, n xz, n yz j ji i ij Unidirectional layer of composite

26 26 Material properties must fulfil stability criterion / 1/ 1/ 1/ / / / 1/ / / / 1/ s s s s s s isotropic material / 1/ 1/ 1/ / / / 1/ / / / 1/ s s s s s s orthotropic material 1 2. Parameters:, n Parameters: x, y, z, xy, xz, yz, n xy, n xz, n yz j ji i ij j i ij >, > i >, ij > i,j=x,y,z 2 1 xz zy yz xz zx zy yz yx xy 1,5 Unidirectional layer of composite Conditions of stability

27 Unidirectional layer of composite Thin composite structures neglecting through thickness stresses plane stress model enable to simplify the model for composite laminates 27 orthotropic material model lamina material model (plane stress) 11 1/ 1 22 / / / 21 1/ 23 2 / 2 2 / / 3 3 / 3 1/ 1/ 13 1/ 23 s 11 s 22 s 33. s s 13 s / 1 2 / 1 / 21 1/ 2 2 1/ s 11 s 22 s Parameters: x, y, z, xy, xz, yz, n xy, n xz, n yz Parameters: x, y xy, n xy, ( xz, yz ) lthough 4 parameters are necessary ( x, y, xy, n xy ), the other two shear modules should be included as well due to low values of shear modulus of fibre composites to prevent unreasonable deformations of finite element model

28 28 Unidirectional layer of composite Modelling of U layer thickness material properties ( x, y, xy, n xy, xz, yz ) material orientation lements baqus orientation must be specified for not isotropic material; otherwise input will not pass solver check nsys PL if not specified, orientation is taken from the global coordinate system** Shell elements Solid elements (full orthotropic material model needed) be careful for the transverse shearing stresses eams In reality, most composite structures compose of layers (U or bi-directional) with various orientation ** for shell elements the situation is more complicated

29 Unidirectional layer of composite 29 Mechanical properties of layer Necessity to input x, y, xy, n xy, xz, yz How to get these constants? Issues From the manufacturer of semi-finished product (prepregs) From experimental measurements y computation from fibre and matrix properties and assumed fibre volume fraction (rule of mixture, micromechanics of composites) Parameters of fibres can be unknown (mostly parameters in transverse direction) Micromechanical model or rule of mixture might not correspond to the selected fibre ifferent models for isotropic fibres (glass) and orthotropic fibres Variation between the models and experimental behaviour Theoretical fibre volume fraction does not match with the fibre volume fraction of real composite component ifferent tensile and compressive modulus x of carbon fibre composites (approx. 1%)

30 Unidirectional layer of composite 3 Mechanical properties of layer Necessity to input x, y, xy, n xy, xz, yz xample of rule of mixture presented equations the most simple, not necessary the most accurate Longitudinal modulus of layer V 1V L f f f m In-plane Poisson number n Vn Vn LT f f m m Transverse modulus of layer T LT m 1V 1 f m 1V 1 f m f m f m 1 V In-plane Shear modulus m 1 V f f

31 Unidirectional layer of composite 31 Mechanical properties of layer Necessity to input x, y, xy, n xy, xz, yz Should the factors like the fibre properties be included in the selection of the mechanical model? Transverse modulus of layer* T = In-plane Shear modulus* LT = m 1 1 m ft. V f m 1 V f. 1 m flt Transverse modulus of layer T LT m 1V 1 f m 1V 1 f m f m f m 1 V In-plane Shear modulus m 1 V * quations Chamis model, CHMIS, Christos C. Simplified Composite Micromechanics quations for Strength, Fracture Toughness and nvironmental ffects. Houston, January Report No. NS TM National eronautics and Space dministration. f f

32 32 Unidirectional layer of composite Mechanical properties of layer x, y, xy, n xy, xz, yz How to calculate other parameters Z, n xz, n yz, xz, yz? yz, n yz quite problematic xy = xz = LT x = L y = z = T / 1 1 f m m V Chamis (): Tsai (): m f f f f f V V V V m f m m 4 1 / 4 3 Hashin f23 > m m m m K m m K m m K f V m f m f V m n n

33 33 Unidirectional layer of composite Mechanical properties of layer x, y, xy, n xy, xz, yz How to calculate other parameters Z, n xz, n yz, xz, yz? yz, n yz quite problematic xy = xz = LT x = L y = z = T / 1 1 f m m V Chamis (): Tsai (): m f f f f f V V V V m f m m 4 1 / 4 3 Hashin f23 > m m m m K m m K m m K f V m f m f V m n n

34 Unidirectional layer of composite 34 ffect of transverse shearing ending of rectangular beam u = F. L3 3 J bending + β. F. L transverse shearing eam of rectangular cross-section (J) modulus 1 () modulus 13 For orthotropic beam profile low stiffness in transverse shearing can be neglected when length/thickness ratio is 3 (2) and more increase of thickness not efficient, need to change material orientation Material r f [kg.m -3 ] 1 [Pa] steel [Pa] uhm/ (2 4) combination of layers and [45,-45]s

35 Layered structures & Laminates 35 Let s get to reality

36 Layered structures & Laminates 36 Real composite components composed of layers with different orientations Hand made laminates Laminates from prepregs RTM products (resin transfer moulding) Filament or tape winding products, braiding In comparison with isotropic F models Restriction of element types More time consuming preprocessing of the model More data consuming model Need to have clear idea what to do at the beginning of pre-processing Simplifications necessary, but might lead to fatal errors in modelling or postprocessing

37 Layered structures Laminate theory 37 Classical laminate theory relations between the load and deformations of the laminate plane stress state in the laminate neglecting transverse shear stresses thickness of layer is significantly smaller than other dimensions rigid interference between the layers N N N M M M x y xy x y xy xx yy xy k x k y k xy

38 38 Layered structures Laminate theory Properties of laminate can be described by matrix In general, matrix contains all components xy y x xy yy xx xy y x xy y x k k k M M M N N N k k n k k ij ij h h Q xy y x xy yy xx k xy yy xx k k k Q Q Q Q Q Q Q Q Q z Q Q Q Q Q Q Q Q Q s s s k k n k k ij ij h h Q 1 1 k k n k k ij ij h h Q

39 Layered structures matrix and its meaning 39 Full matrix 1 loading component leads to all deformation effects normal strains bending strains twisting strains shearing strains The coupled deformation effect might cause problems when simplifying modelling using the symmetry of models using the homogenized material constants N N N M M M x y xy x y xy xx yy xy k x k y k xy xx N 16 x N yy y N xy xy k M x x k M y y k M xy xy

40 Layered structures matrix and its meaning 4 ffect of composite lay-up on matrix Symmetric alanced Např.: S Symmetric balanced Např.: Např.: s Symmetric cross-ply O 66 Např.: ntisymmetric cross-ply O 66 Např.: 9 9 9

41 Layered structures first order shear theory 41 Classical laminate theory Kirchhoff First order shear theory with effect of transverse shearing N N N M M M x y xy x y xy k x k y k xx yy xy xy Nx xx N y yy N xy xy M x kx M y k y M xy kxy Q y F44 F 45 yz Qx F45 F55 xz

42 Layered structures first order shear theory 42 Transverse shearing can be neglected for very thin plates for composites, the length to thickness ratio, from which it is possible to neglect transverse shearing, is significantly higher than for isotropic materials F shells generally with FOST Nx xx N y yy N xy xy M x kx M y k y M xy kxy Q y F44 F 45 yz Qx F45 F55 xz sxx Q11 Q Q16 xx s Q Q Q yy yy s Q Q Q xy xy s yz C 44 C 45 yz s xz C k 54 C 55 xz F ij n C ij hk hk 1, i, j 4, 5 k 1 k

43 Layered structures homogenization 43 xx N 16 x N yy y N xy xy k M x x k M y y k M xy xy N. xx Nx yy xy k x k y k xy x x _ tah xx 11. Nx x _ tah t i Inverse matrix to can be used for determination of equivalent material properties of the laminate x, y, xy, n xy This approach leads to simplified modelling, but with reduced accuracy (missing the coupling between the deformations) Homogenized constants might violate the stability conditions of material model more precise xx yy xy k M x x k y k xy M x k. M o x 11 x x _ ohyb. J x_ohyb = t i 3

44 lements for F of composite structures 44 nsys F solver recommended elements layered shell elements (shell181, shell 281) layered solid-shell elements (solidshell 19) layered solid elements (solid185, solid186), beam elements 4-node layered shell element SHLL181 modelled on reference surface each node 3 translation OF and 3 rotation OF 8-node layered shell element SHLL281 (SHLL91, SHLL99)

45 lements for F of composite structures 45 nsys F solver recommended elements layered shell elements (shell181, shell 281) layered solid-shell elements (solidshell 19) layered solid elements (solid185, solid186), beam elements 8-node solid-shell element SOLSH19 Solid geometry, node 3 translation OFS ehaviour similar to shell elements It is necessary to have consistent orientation of element in thickness direction VORINT ORINT For thicker components more precise than classical shells, can be stacked through thickness In comparison with solids more precise in transverse sharing stresses

46 lements for F of composite structures 46 nsys F solver recommended elements layered shell elements (shell181, shell 281) layered solid-shell elements (solidshell 19) layered solid elements (solid185, solid186), beam elements 8-node layered solid element SOLI185 limited usage (free edge problems, ) 2-node layered solid element SOLI186

47 lements for F of composite structures 47 baqus & composites solid elements conventional shell elements continuum shell elements (solid-shell elements from previous slides) Source: baqus v6.1 ocumentation

48 lements for F of composite structures - Shells 48 Conventional shells The most common elements for modelling of components from fibre reinforced plastics Source baqus v6.1 ocumentation nable to easily define the material, orientation and thickness of every layer of lay-up Layers are modelled in the same order as were defined, stacking is in direction of shell normal the first layer is at the bottom of shell the last layer at the top surface of shell Results of shell in integration points, in every layer section points through thickness Shell are modelled on the reference surface Source Solidworks help Reference surface on midsurface Reference surface - offset from the midsurface enabling to model the ply-drops

49 lements for F of composite structures - Shells 49 asic assumptions for using shell elements each ply is modelled as homogenous, its thickness is significantly smaller in comparison with the other dimensions interface between the layers is ideally rigid, thin, the displacements of the layers through the interfaces are therefore continuous Kirchhof or First Order Shear Theory shell thickness does not change with deformation the ration of smallest dimension of shell surface to its thickness is larger than 1 stiffness of laminate in coordinates X, Y, Z of shell does not differ by more than 2 orders (might be violated in sandwich constructions) more: pdf

50 lements for F of composite structures - Shells 5 asic difference in comparison with modelling of isotropic materials Potential source of fatal errors if neglected Isotropic shells in commercial F solvers default: data stored in the top and bottom layer of the shell maximum of bending stresses safe for evaluation of strength Orthotropic shells when using default settings without enhancing the data storage to every layer layers with maximal loading might be not evaluated in terms of stress, strain and failure only top and bottom layer post-processed Works both for conventional and continuum shells If you need to investigate the stress loading of component and potential failure, you need to know the stress loading of every layer in critical area of components If deformations are needed only, this can be neglected

51 51 Strength evaluation Orthotropic materials strength differs for different modes of loading do not evaluate by isotropic approaches (von Mises stress, ) F of composite structure failure index for the first ply failure maximal stress or strain criterion Tsai-Wu, Tsai-Hill, PUCK, LRC3,LRC4 User defined criteria might be complicated to get all data of ply strengths for the criteria evaluation not every criteria is suitable for the loading mode (but still better to be used than to use von Mises stress) S4/ - glass/ V f [%] 6 62 X T [MPa] X c [MPa] Y T [MPa] Y c [MPa] S [MPa] T [%] 1,38 2,13 1C [%] 1,18 1,7 2T [%],44,2 2C [%] 2,,64 [%] 2 3,8

52 52 Strength evaluation Failure index f f<1 no first ply failure f=1 first ply failure o not forget to evaluate data through all the layers specified in the lay (i.e. not only from the top and bottom layer) solsh19, keyopt(8)= f TSIWU =,7 solsh19, keyopt(8)=1 f TSIWU =,2

53 53 Strength evaluation Options to model progressive damaging of composites Stiffness degradation due to damage initiation and growth baqus, nsys - Options for progressive damage implemented Source C ssociates Progressive amage of Fiber Reinforced Composites in nsys v15 Options to investigate the composites delamination Cohesive Zone Modelling Virtual Crack Closure Technique used also for simulations of debonding of adhesive joints between the components

54 Composite structures 54 Short conclusions in terms of modelling structural level Usually thin components (thickness is significantly smaller than other 2 dimensions) Suitable for shell elements, beam elements Options for solid modelling limited Usually composite lay-up with layers with multiangle orientations, structures with only 1 orientation of fibres are rare Conventional shell elements definition of full composite lay-up» material, thickness, orientation in respect to element normal specification by matrix» matrix, optionally with transverse shear stiffness specification by homogenized properties» modules of laminate

55 Composite structures 55 Short conclusions in terms of modelling structural level Usually thin components (thickness is significantly smaller than other 2 dimensions) Suitable for shell elements, beam elements Options for solid modelling limited Usually composite lay-up with layers with multiangle orientations, structures with only 1 orientation of fibres are rare Continuum shell elements definition of full composite lay-up» material, relative thickness, orientation in respect to element normal specification by homogenized properties» modules of laminate specification by matrix not applicable must be divided into sub-laminates if having more than 1 element through thickness

56 Composite structures 56 Short conclusions in terms of modelling structural level Usually thin components (thickness is significantly smaller than other 2 dimensions) Suitable for shell elements, beam elements Options for solid modelling limited Usually composite lay-up with layers with multiangle orientations, structures with only 1 orientation of fibres are rare Continuum shell elements definition of full composite lay-up» material, relative thickness, orientation in respect to element normal specification by homogenized properties» modules of laminate specification by matrix not applicable must be divided into sub-laminates if having more than 1 element through thickness

57 Composite structures 57 Lay-up specification baqus shell section composite lay-up manager (preferable)

58 Composite structures 58 Lay-up specification nsys shell section (Mechanical PL, Workbench through PL commands) nsys Composite Pre-Post graphical interface for composite materials additional plug-in to nsys, available to students of CTU in Prague! sect,1,shell,,navin1 secdata,.5,1,,3 secdata,.4,2,45,3 secdata,. 4,2,-45,3 secdata,.6,3,93 secdata,.4,2,-45,3 secdata,. 4,2,45,3 secdata,.5,2,,3! et,2,solsh19 emodif,all,type,2 emodif,all,esys,11 emodif,all,secnum,1

59 xample 1 59 Laminate beam Laminate from U prepregs imensions 7x7 mm Lay-up [, 45, -45, 9]s high-strength C/ high-modulus C/ material data from prepreg manufacturer sheets additional parameters from micromechanics

60 xample 1 6 Laminate beam Shell finite element model Full Lay-up specification

61 xample 1 61 Comparison with experimental results modal analysis mode shapes and its frequencies match between F and experiment acceptable Mode [-] xperiment [Hz] F [Hz] Mass [g]

62 xample 1 62 Comparison with experimental results laminate beam from HM/ U prepregs [, 45, -45, 9]s laminate modelled by 1 matrix homogenized x, y, xy, n xy, xz, yz of the lay-up 2 matrix with transverse shear stiffness (F) using first order shear theory with specified transverse stiffness most precise Mode [-] xp. [Hz] 1 [Hz] hom. const [Hz] F [Hz] bend bend tors bend bend tors

63 xample Unidirectional beam 63 Unidirectional thick-walled beam beam 74x3x2 material: ultra-high modulus carbon / epoxy composite modelled by solid elements C38I (baqus) material properties from fibre and matrix parameters, assumed fibre volume fraction estimation n23, 23 xperiment F [Hz] [Hz] first bending mode shapes with good precision; torsional mode more inaccurate

64 xample beam profile coupons 64 ffect of geometry mode shapes of free beam m1 m2 xperiment [Hz] Model 1 [Hz] Model 2 [Hz] #1 #2 #3 #4 due to the geometry simplifications, shell model or even continuum shell model with 1 element per thickness not working for the mode shapes and frequency prediction except the bending mode more detailed geometry from continuum shells in good relation with experiment both models work for the bending modes in a similar way

65 xample beam profile coupons 65 ffect of element selection important for hybrid composites with damping layers that have significantly higher compliance separation of elements for damping material necessary ~ 4 MPa x ~ 13 Pa, y,z ~ 5 Pa m1 m2 m3 xperiment [Hz] F solid shells [Hz] F one shell [Hz] MF solid shells, mat hom [Hz]

66 xample beam profile coupons 66 Spindle ram coupons comparison of steel, cast iron, CFRP plates assembly and profile by winding F models derived from the previous cases separation of elements for damping layers Cast iron Welded steel CFRP plates Filament winding F_1 [Hz] xp_1 [Hz] F_2 [Hz] xperiment to F deviation in bending bellow 1% xp_2 [Hz]

67 xample - hybrid spindle ram 67 Modelling of hybrid spindle ram and its composite reinforcement Combination of carbon/epoxy layers from PITCH and PN fibres, 1 integrated damping layer Solid shell model with element stacking For bending modes deviation between F and experiment bellow 5% For other modes deviation up to 2% and more Mode [-] f XP [Hz] f F [Hz] f F/XP [%] ,9 1 st bending , , , ,9 2 nd bending #1 #2 #3 #4

68 68 xample material degradation Crash absorbers simulation ability of progressive damaging of fibre composites to transform kinetic energy into the deformation energy in the safety element ii v bezpečnostním členu

69 69 Simulations of progressive damaging progressive damage implemented by failure criteria (Chang-Chang) element stiffness degradation in respect to achieving criterion after the set level of degradation element removal Chang-Chang failure criterion fibre failure in tension stiffness change of element for f ft =1 fibre failure in compression stiffness change of element for f fc =1 matrix failure in tension stiffness change of element for f mt =1 matrix failure in compression stiffness change of element for f mc =1 xample material degradation 1,, ˆ ˆ s s where S X f L T ft 11 = 22 = = ν = ν 21 =, ˆ 2 11 C fc X f s, ˆ ˆ L T mt S Y f s s. ˆ ˆ ˆ L C T C T mc S Y S Y S f s s s 11 = ν = ν 21 =, 22 = = ν 21 =, 22 = = ν = ν 21 =

70 7 xample material degradation Simulations of progressive damaging LS-yna: shell element with 1 element per the coupon thickness good match with experimental behaviour

71 xample material degradation 71 Simulations of progressive damaging

72 72 xample adhesive joints of components Simulation of adhesive joint failure in composite shafts with bonded metal endings prediction of the joint degradation cohesive elements damage initiation damage growth after the determined degradation element removal demonstration from the development of composite shafts for the machine tool industry dhesive joint model amage initiation and growth

73 73 xample adhesive joints of components Simulation of adhesive joint failure in composite shafts with bonded metal endings prediction of the joint degradation cohesive elements damage initiation damage growth after the determined degradation element removal demonstration from the development of composite shafts for the machine tool industry xperimental testing loading of shafts in torsion F model of the shaft ending green metal ending blue composite shaft

74 74 xample adhesive joints of components Simulation of adhesive joint failure in composite shafts with bonded metal endings Finite element simulation in comparison with experimental behaviour Comparison of reaction moment and rotation acceptable prediction of maximal loading moment

75 xample sandwich panels 75 Sandwich structures + low-weight design + high bending stiffness + high natural frequencies - low compressive strength - difficulty when joining 5 4 s [MPa] 3 2 1,2,4,6,8 [-]

76 xample sandwich panels 76 Necessary to include the effect of transverse shearing F due to transverse shearing, the normal to the reference surface rotates shell element cannot behave in this way with some exceptions (sandwich logic, balance of energy) nsys: Shell91 former element for sandwich simulations nowadays Shell181,281 - elements model the transverseshear deflection using an energy-equivalence method

77 xample sandwich panels 77 pproaches for F modelling of sandwich panels Shell elements - generally care must be taken as the approach of using 1 shell element for the sandwich structure might work only for specified shells in one F solver, but not in other solver - problematic behaviour of the core with larger compliance (stiffness is lower by 3 orders in comparison with skins does not meet the conditions for shells) Solid elements - core and skins modelled by solid elements, or solid-shell elements - might be problematic for composite skins Combination of solid and shell elements - core modelled by solid elements - skins modelled by shell or solid shell elements

78 xample sandwich panels models shell99 skins, solid95 core Comparison of 3point bending test deflection of the beam Skin Core Weight [kg] Mid Span eflection [mm] F results [mm] C/ C/ Roh71 c=3mm Roh71 c=5mm C/ Roh11 c=3mm, C/ Roh11 c=5mm *.5.44* C/ Roh11 c=5mm *.35.32* C/ l25 c=5mm Steel lporas23 c=5mm *.8.7* Steel lporas23 c=3mm *.13.* Steel l25 c=5mm *.8.6* C/ L honeycomb core,

79 79 xample sandwich panels F model 1: nsys skins: Shell99, 7 layers core: Solid95 Skins are at the top (bottom) surface of the solid core; with offset from the midsurface Nodes of the shell skins are shared with the nodes of the solid core surface F model 2: baqus skin: S4R core: C38i *Tie constraint between skin and shell xperimental modal analysis ifference between FM and experiment bellow 15% for the first bending frequency 3mm C/, 3mm PMI 3mm C/, 5mm PMI Mód f exp [Hz] f mkp1 [Hz] f mkp2 [Hz] f exp [Hz] f mkp1 [Hz] f mkp2 [Hz]

80 8 Thank you for your attention! Contact