做波纹梁数值模拟的关键论文.pdf

American Institute of Aeronautics and Astronautics 1 SIMULATING COMPOSITES CRUSH FROM THE COUPON LEVEL TO FULL VEHICLE CRASHWORTHINESS Kyle C Indermuehle1 and Vladimir S Sokolinsky 2 Dassault Syst mes SIMULIA Corp Providence RI 02909 USA and Graham Barnes 3 Engenuity Limited West Sussex RH17 5HF United Kingdom The initial usage of composites in the aerospace automotive and other industries was for the primary benefits of their high strength to weight ratios the ability to mold complex shapes and reduction in manufacturing time Today composites are also being utilized to take advantage of their excellent performance related to energy absorption during impact and crash events Advances in commercial Finite Element Analysis FEA software have enabled engineers to accurately simulate the performance of composite structures in these high speed highly nonlinear events Different methodologies and modeling approaches are needed for simulating composites crush at the coupon level versus simulating the full vehicle crash event This paper presents new FEA technology and damage models related to composites crush analysis together with methodologies for performing physics based simulations at the coupon level phenomenological simulations at the full vehicle level and for applying the two levels of modeling together A discussion of the technology is illustrated by several examples I Introduction omposite materials are increasingly prevalent in many industries and have become the dominant material in many aerospace vehicles Today in contrast to their earlier days composite materials are used in critical load bearing and energy absorbing structural components There are many well known benefits to using composites but there are also some challenges One of the most significant design difficulties is the ability to reliably simulate how the composite part will perform during an impact event due to the various complex failure modes that composites have Numerous papers describe these failure modes and discuss simulation methodologies and technologies for analyzing them The crushing of a composite as a result of impact may cause simultaneous matrix failure fiber breakage and delamination Figure 1 shows coupon testing of a composite panel that underwent a crush event It can be clearly seen in the figure that the composite experiences fracture and delamination and that pulverization of the material also takes place In this paper a new finite element analysis technology related to composites crush analysis together with 1 Aerospace Lead SIMULIA 166 Valley St Providence RI 02909 2 Engineering Specialist SIMULIA 166 Valley St Providence RI 02909 3 Director Engenuity Ltd The Old Hospital Ardingly Road Cuckfield West Sussex RH17 5HF C Figure 1 Composite coupon subject to crushing 52nd AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference 19th 4 7 April 2011 Denver Colorado AIAA 2011 1735 Copyright 2011 by Dassault Systemes SIMULIA Corp Published by the American Institute of Aeronautics and Astronautics Inc with permission American Institute of Aeronautics and Astronautics 2 methodologies for performing simulations at the coupon level and a different methodology for simulations at the full vehicle level are discussed A way of using the two levels of modeling together to analyze real structural parts is also outlined In what follows the geometry and lay up of the corrugated test specimen are presented first Then a new finite element analysis technology for physics based simulations at the coupon level is described followed by a description of a phenomenological approach to simulations at the full vehicle level The numerical results obtained using both approaches are compared with the experimental data and conclusions are presented II Description of the Specimen used in Physical Coupon Testing The Composite Material Handbook CMH 17 group conducted a round robin effort during which crush tests on corrugated plate specimens were performed and published the test results 1 The test panel was made of a carbon epoxy TORAYCA fabric It consisted of 8 plies 0 90 2S and was 0 079 inches thick To facilitate stable crushing a 45 degree chamfer was located at the bottom to act as a crush initiator The testing was performed at a quasi static speed 2 in min A cross section of a corrugated panel is shown in Figure 2 III Physics based Simulation at the Coupon Level The first goal is to model and analyze the crush event At this level both in plane and out of plane delamination failure behaviors should be considered to model accurately the real physics of composites crushing The in plane failure response of the coupon is modeled using the Abaqus fabric damage model described below whereas delamination is simulated through the Abaqus surface based cohesive contact capability This is a very detailed model with a large number of degrees of freedom It requires long simulation run times on a compute cluster using the Abaqus Explicit software A Constitutive Model for Fabric reinforced Composites A new constitutive model for fabric reinforced composites has been released in Abaqus Version 6 10 for the Abaqus Explicit solver 2 The fabric reinforced ply is modeled as a homogeneous orthotropic elastic material with the potential to sustain progressive stiffness degradation due to fiber matrix cracking and plastic deformation under shear loading Therefore this model is suitable for the simulation of composites crush events A schematic representation of the geometry of the woven fabric reinforcement considered in the constitutive model is shown in Figure 3 The fiber directions are assumed to be orthogonal The constitutive stress strain relations are formulated in a local Cartesian coordinate system with base vectors aligned with the fiber directions as shown in the figure The in plane elastic stress strain relations are based on orthotropic damaged elasticity where the damage parameters are associated with stiffness degradation caused by microdamage in the material The damage variables are assumed to be the functions of the effective stresses which are directly related to the thermodynamic forces The formulation of the damage evolution law ensures that the damage variables are monotonically increasing quantities and that the correct amount of energy is dissipated when the lamina is subjected to uniaxial loading along the fiber directions The formulation imposes an upper bound on the characteristic element length of the finite element mesh that is given by the ratio of the fracture energy per unit area under uniaxial tensile or compressive loading to the elastic energy density at the point of damage initiation The in plane shear response is dominated by the non linear behavior of the matrix that exhibits both stiffness degradation due to material microcracking and plasticity Extensive cracking or plasticity in the matrix leads to permanent deformation in the ply upon unloading This behavior is accounted for by using a classical plasticity model with an elastic domain function and a hardening law which is applied to the effective stresses in the damaged material Figure 2 Schematic of a corrugated fabric panel Figure 3 Schematic representation of woven fabric American Institute of Aeronautics and Astronautics 3 The mathematical formalism of this damage model is not discussed here but the required material properties for the utilization of the model will be presented and discussed in the next section B Detailed Finite Element Model The finite element model FEM of the corrugated composite fabric plate was created in Abaqus CAE 2 Each ply of the coupon was uniformly meshed using continuum shell elements SC8R Continuum shell elements in Abaqus have the geometry of a 3D solid element but their kinematic and constitutive behaviors are similar to those of conventional shell elements This type of element allows for the accurate modeling of stacked composite plies A cohesive surface definition was used between the adjacent ply layers to account for the adhesive bond between the plies and to enable delamination to occur during the analysis The FEM of the composite coupon is shown in Figure 4 There are several aspects to the definition of the composite material properties These aspects or domains include a the definition of the basic material properties like modulus and strength properties b shear damage parameters c compressive and tensile fracture energies along the fiber directions d shear hardening properties e definition of the damage limit at which point the element is deleted from the simulation and f definition of the cohesive properties related to delamination between the plies The composite material and damage properties used for this analysis are shown in Table 1 Table 1 Material and Damage Properties Used for Crush Simulation Description Variable Value Material properties of the TORAYCA T700 2510 fabric Longitudinal modulus GPa E11 55 9 Transverse moduli GPa E22 E33 54 4 Principal Poisson s ratio 12 0 042 Shear moduli GPa G12 G23 G31 4 2 Longitudinal tensile strength MPa X1 911 3 Longitudinal compressive strength MPa X1 704 0 Transverse tensile strength MPa Y2 770 1 Transverse compressive strength MPa Y2 698 2 In plane shear strength MPa S 131 6 Critical fracture energies per unit area along the fiber directions Tensile fracture along fiber direction 1 kJ m2 125 Compressive fracture along fiber direction 1 kJ m2 250 Tensile fracture along fiber direction 2 kJ m2 95 Compressive fracture along fiber direction 2 kJ m2 245 Interface damage initiation properties Maximum nominal stress in the normal only mode MPa 54 Maximum nominal stress in the first or second shear direction for a mode that involves separation only in one direction MPa 70 Critical interface fracture energies Mode I fracture toughness kJ m2 GIC 0 504 Mode II fracture toughness kJ m2 GIIC 1 566 The material properties of the TORAYCA fabric and critical interface fracture energies were obtained directly from Ref 1 without any further adjustments The critical fracture energies along the fiber directions were taken as average values for similar material systems from Ref 3 The interface damage initiation properties are usually difficult to determine experimentally with good accuracy therefore they can be used as calibration parameters if required In the present work the variation of the damage initiation parameters within 15 from the typical values given in Table 1 did not influence the analysis results Figure 4 Finite element model of the corrugated fabric coupon American Institute of Aeronautics and Astronautics 4 The material and damage properties are obtained through various standard coupon level testing It should be noted that all of these material properties and all of the testing is done at the lamina level and thus can be used to construct any type of composite layup or geometry for the crush specimen A detailed mesh is needed for this type of analysis and for the sine wave specimen the FEM consisted of approximately 0 5 million degrees of freedom C Simulation Results The crushing load was applied to the composite plate through a rigid steel plate moving with a constant velocity of 470 in min This loading rate is higher than the maximum quasi static test speed of 2 in min used in the experimental study of the Composite Material Handbook CMH 17 group and was used to achieve a reasonable run time for the explicit dynamic analysis This artificial increase of the loading velocity has little effect on the analysis results because according to the experimental work in Ref 4 dynamic effects become significant beyond 1200 2400 in min As the simulation progresses the development of in plane damage in individual elements is evaluated using the fabric damage model which was described previously If an element fails it is deleted from the simulation Along with this the development of the out of plane damage delamination between the plies of the coupon is tracked by the surface based cohesive behavior capability After the debonding of the adjacent plies takes place a contact definition is automatically created between them Figures 5 and 6 show the deformed shape of the coupon at the end of the crushing simulation From these figures it is clearly seen that composite undergoes damage and failure pieces of the material breaks off and delamination between the plies takes place The physics of the crush event is captured properly Figure 7 shows the comparison between the experimental Ref 1 and simulated load displacement curves Both the test data and the simulation results have been filtered with a SAE filter to reduce high frequency noise in the results The peak and the average crush forces correlate very well between the test and analysis As can be seen from the figure the height of the crushed coupon at the end of the analysis was reduced by half with respect to its undeformed configuration As mentioned previously this is a very detailed model that requires significant computational power the simulation ran 9 hours of wall time on a 16 core Linux cluster Figure 5 Deformed shapes of the fabric coupon at the end of the Abaqus simulation American Institute of Aeronautics and Astronautics 5 Figure 6 Isometric view of the deformed fabric coupon at the end of the Abaqus simulation Figure 7 A comparison between the experimental and numerical load displacement curves for the corrugated fabric coupon American Institute of Aeronautics and Astronautics 6 IV Simulation at the Full Vehicle Level The previous section presented the methodology and modeling technique for the simulation of composites crush at the coupon level It has been demonstrated that using Abaqus it is possible to obtain accurate results at this level but the computational cost is fairly high Expanding this technique to a full vehicle analysis is currently prohibitive because the simulation time would be too long to accomplish any meaningful design For full vehicle simulation there is an alternative and preferred approach Although this approach does not explicitly account for the physics of composites response matrix cracking fiber breakage and delamination it does represent the forces generated by the phenomenon of composites crush For this modeling the CZone for Abaqus CZA software code is utilized A Coupon Level Model CZone technology has been developed by Engenuity Limited as a way to enable robust simulation of composites crushing so that simulation based design of composite structures for crashworthiness can be carried out with a similar level of predictability as is presently possible for metallic structures The basis of CZone recognizes crush or crush stress as a distinctive mechanical property of a composite material Crush is essentially defined as the ability of a material to progressively absorb energy through destruction and disintegration CZone technology is being made available commercially within the Abaqus finite element software suite The advantage of CZone is that the simulation uses a much simpler shell element model A schematic of the FEM of the corrugated fabric specimen with only 1000 degrees of freedom is shown in Figure 8 The key to the CZone model is the accurate definition of the crush stress material property The crush stress is defined as the ratio of the average crush force to the cross sectional area In the CZone model this property can be defined as having velocity and angle dependencies The cross sectional area is simple enough to calculate for any geometry and the only additional material property that is required by CZone is the average crush force This average crush force can be obtained in two ways namely by performing a test on a coupon sample or carrying out a detailed simulation like that presented in Section III of this paper For example based on the data in Figure 7 the average crush force is 3 800 lbf Dividing this crush force by a cross sectional area of 0 195 in2 produces the crush stress of the corrugated specimen as 19 487 lbf in2 Besides the basic material properties of the corrugated fabric specimen first section of Table 1 this is the only additional material input required for the CZone simulations B Simulation Results at the Coupon Level The result of the CZone crush simulation for the corrugated fabric coupon is shown in Figure 9 As can be seen from the figure a constant crushing load of 3 800 lbf is predicted This result may appear trivial because a response is predetermined by the crush material property that has been defined earlier as input However in fact it is a very non trivial simulation where all the physical features characteristic of the composites crush are taken into account The difference between the physics based and CZone approaches is that the former accounts for the main features of composites crush through an appropriate in plane fiber breakage and matrix microcracking and plasticity and out of plane delamination damage models whereas the latter combines all of those effects into a single material damage property called crush stress By using CZone based on accurately determined crush stress property the crushing behavior of the corrugated fabric coupon can be simulated with high fidelity Figure 9 Figure 8 Schematic of the FEM of the corrugated fabric coupon used by CZone for Abaqus American Institute of Aeronautics and Astronautics 7 C Composites Crush at the Full Vehicle Level The modeling approach used by CZone significantly reduces simulation times compared to more detailed modeling approaches for crush analysis For the detailed Abaqus simulation presented in Section III the computation time was 9 hours of wall time running on 16 cores of a Linux cluster The simulation time for the same coupon using CZone was less than 20 minutes running on a single CPU laptop Because of this larger models at the sub component level and full vehicle level can be analyzed in a feasible amount of time To illustrate this point the next