Impact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics

Impact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics Dr. A. Johnson DLR Dr. A. K. Pickett ESI GmbH EURO-PAM 99

Impact and Crash Modelling of Composite Structures: A Challenge for Damage Mechanics Alastair Johnson (DLR) e-mail: alastair.johnson@dlr.de Anthony Pickett Engineering Systems International GmbH Eschborn e-mail: akp@esigmbh.de ABSTRACT The paper describes recent progress on the materials modelling and numerical simulation of the crash and impact response of fibre reinforced composite structures. Composite materials are now being used in primary aircraft structures, particularly in helicopters, light aircraft, commuter planes and sailplanes, because of numerous advantages including low weight, high static and fatigue strength and the possibility to manufacture large integral shell structures. Materials such as carbon fibre/epoxy are inherently brittle and usually exhibit a linear elastic response up to failure with little or no plasticity. Thus composite structures are vulnerable to impact damage and have to satisfy certification procedures for high velocity impact from runway debris or bird strike. Conventional metallic structures absorb impact and crash energy through plastic deformation and folding. Modern explicit FE codes such as PAM-CRASH are able to model these effects and are being successfully applied to simulate the collapse of metallic aircraft and automotive structures. This paper is concerned with the further development and improvement of such codes for modelling the response of composite structures under crash and impact loads. This topic is being studied in some detail within a CEC funded research project on 'High velocity impact of composite aircraft structures' HICAS [1]. This project includes an extensive composites materials and structures test programme, composites modelling developments, FE code implementation and impact simulations. Two important aspects of impact modelling are delamination, which is important in lower energy impacts and in failure initiation, and in-plane ply failure which controls ultimate failure and penetration in the structure. This paper summarises some of the modelling developments being carried out within the HICAS project on in-plane damage models for both unidirectional (UD) and fabric reinforced composite plies. Emphasis is given to composite materials models suitable for implementation into explicit FE codes, which can adequately characterise the nonlinear damage progression and different failure modes that occur in composites. A continuum damage mechanics model for composite plies under in-plane loads is presented. It is based on methods developed for UD ply materials in [2], which are generalised to fabric reinforcements. This model has a number of features not included in the existing 'bi-phase' model. It allows damage parameters for in-plane and through-thickness shear failure modes, as well as failures along and transverse to the fibre directions. Delamination models and strain rate dependence may also be incorporated in the damage mechanics framework. The model contains elastic damage in the fibre directions, with an elastic-plastic model for inelastic shear

effects. A novel approach is being developed for delamination modelling based on laminates modelled numerically as stacked plies, with a new sliding interface whose failure properties are consistent with the fracture mechanics of composite delamination. The models are currently being implemented into PAM-CRASH and preliminary results are presented on simulations of impacted composite plates and progressive delamination. REFERENCES [1] HICAS High Velocity Impact of Composite Aircraft Structures, CEC DG XII BRITE- EURAM Project BE 96-4238 (1998). [2] P. Ladeveze, E. Le Dantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, 43, 257-267 (1992).

Two important aspects of impact modelling are delamination, which is important in lower energy impacts and in failure initiation, and in-plane ply failure which controls ultimate failure and penetration in the structure. This paper summarises some of the modelling developments being carried out within the HICAS project on in-plane damage models for both unidirectional (UD) and fabric reinforced composite plies. Emphasis is given to composite materials models suitable for implementation into explicit FE codes, which can adequately characterise the nonlinear damage progression and different failure modes that occur in composites. A continuum damage mechanics model for composite plies under in-plane loads is presented. It is based on methods developed for UD ply materials in [2], which are generalised to fabric reinforcements. This model has a number of features not included in the existing bi-phase model. It allows damage parameters for in-plane and through-thickness shear failure modes, as well as failures along and transverse to the fibre directions. Delamination models and strain rate dependence may also be incorporated in the damage mechanics framework. The model contains elastic damage in the fibre directions, with an elastic-plastic model for inelastic shear effects. A novel approach is being developed for delamination modelling based on laminates modelled numerically as stacked plies, with a new sliding interface whose failure properties are consistent with the fracture mechanics of composite delamination. The models are currently being implemented into PAM-CRASH and preliminary results are presented on simulations of impacted composite plates and progressive delamination. REFERENCES [1] HICAS High Velocity Impact of Composite Aircraft Structures, CEC DG XII BRITE- EURAM Project BE 96-4238 (1998). [2] P. Ladeveze, E. Le Dantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, 43, 257-267 (1992). 2

List of Slides Slide 1. Title and authors. Slide 2. Outline of presentation. Slide 3. Composites in PAM-CRASH: Overview of the existing PAM-CRASH Bi-Phase model for UD composites, explanation of the damage function and methods used to calibrate this parameter. Slide 4. Improved composites models under development: Review of the status of the existing Bi-Phase model and a summary of the principle features of the new Ladeveze model being implemented within the HICAS project are given. Slide 5. Composites materials damage models: Gives an introduction of a more general damage model for composites with independen t damage modes d1(fibre), d2(transverse) and d12(shear). Slide 6. Damage evolution equations based on Ladeveze model: Introduction of the concept of conjugate damage (driving) forces (derived from additional state variables and thermodynamics considerations) and the corresponding damage parameters. Expressions giving the relationship between the driving forces and damage parameters (and their interaction) are presented. Slide 7. Generalised fabric damage model (elastic-plastic in shear): Gives details of the elasto-plastic model aused to model the permanent plastic strains that occur under shear loading. Slide 8. Determination of fabric model parameters in shear: Example test data is presented for the cyclic tensile loading of a ±45 coupon specimen. Methods to identify the permanent plastic and damage contributions is shown. Slide 9. Trial simulation with fabric ply model: A first simulation is shown of an impactor striking a GF/epoxy plate at 3.13m/s. The plate is modelled using a first version of the Ladeveze law. Slide 10. Composite tube crushing using a detailed solid model: This simulation shows the current capabilities and limitations for modelling composites delamination using PAM-CRASH.. The detailed (computationally expensive) nature of the required mesh is shown. Slide 11. Options for delamination modelling: Summarises the various options available to model delamination in the current code. Slide 12. Stacked shell interface model: This shows some details of the PAM-CRASH type 32 tied contact algorithm. The new relationship between normal (mode I) and shear (mode II) stresses and nodal deformations is shown. Slide 13. Failure Criteria and delamination model: The new material model and the interaction failure model is shown. Slide 14. Some first results for the failure prediction of a DCB test are shown. Slide 15. Conclusions and outlook 3

Impact and Crash Modelling of Composite Structures: A Challenge for Damage mechanics Alastair Johnson DLR Institute of Structures and Design Stuttgart, Germany Anthony Pickett Engineering Systems International GmbH Eschborn, Germany 4

Outline Composites models in explicit FE code PAM-CRASH Simulation of composites structures with existing models crash response of helicopter subfloor elements impact behaviour of wing access panel Improved composites models under development damage mechanics models for ply in-plane properties interlaminar failure models Conclusions and outlook 5

Composites models in PAM-CRASH -PAM-CRASH contains a bi-phase model for UD plies, in which fibres and matrix are both assigned elastic and stiffness degradation properties - difficult to calibrate with tests - the 'degenerate bi-phase model' is simplified model for orthotropic elastic damaging material Idealised model for elastic damaging material True Stress [MPa] 800 - model has single damage function d which is assumed here to be a bi-linear function of 2nd strain invariant IIe 700 600 500 400 300 Aramid Ply (STRAFIL AT285/M10) Carbon Ply (VICOTEX G803/M10) - damage parameters determined from stressstrain data -d1 gives initial modulus reduction -du controls reduction from peak to residual stress level 200 100 0 0 1.0 2.0 3.0 4.0 5.0 True Strain [%] Typical 0 -compressive stress-strain response of fabric composite ply material used in FE simulations - this simplified model with shear damage used for the simulations in this paper - suitable for quasi-isotropic layups - an approximation for orthotropic fabric plies 6

Improved composites models under development Status of existing composites models - bi-phase composites model in PAM-CRASH is stable and efficient - model parameters determined from standard stress-strain curves - FE crash and impact simulations on composite structural elements predict well observed failure modes - simulated impact loads and energy absorbed often much lower than structural test results - valuable as preliminary design tool for ranking structural concepts - improvements required for better quantitative predictions Further composites developments - damage mechanics based model for in-plane properties which includes elastic damage evolution and inelastic effects - implementation of Ladeveze UD ply model and extension to fabric plies - development of interlaminar failure models for stacked shell elements - tied slidelines used with fracture mechanics based failure criteria - code implementation and validation being carried out with partners in CEC BRITE/EURAM Project HICAS 7

Composite materials damage model Composites with fabric reinforcement modelled as elastic damaging materials in fibre directions, with elastic-plastic shear behaviour Materials are initially elastic but degraded by microcracks before failure. Stiffness degradation modelled by scalar damage parameters d i, 0< di < 1 Orthotropic stress-strain relation for elastic strains has form ε = S σ The compliance matrix for shell elements has general form: S = 1/ E 1( 1 d 1) ν12 / E 1 0 ν12 / E 1 1/ E 2( 1 d 2 ) 0 0 0 1/ G12( 1 d 12 ) Model has 4 undamaged elastic constants: E 1 E 2 G 12 ν 12. 3 scalar damage parameters d 1 d 2 d 12 - may be measured from modulus reduction in stress-strain curves damage mechanics theory gives evolution equations for the damage parameters - framework for modelling damage interaction, multiaxial failure and rate dependence 8

Damage evolution equations - based on Ladeveze model For elastic damaging materials conjugate damage forces are introduced : Y 1 = σ 2 11 / (2E 1 (1-d 1 ) 2 ) Y 2 = σ 2 22 / (2E 2 (1-d 2 ) 2 ) Y 12 = σ 2 12 / (2G 12 (1-d 12 ) 2 ) corresponding to damage parameters d 1, d 2 and d 12 respectively. The general form of the damage evolution equations is: d 1 = f 1 (Y 1, Y 2, Y 12 ) d 2 = f 2 (Y 1, Y 2, Y 12 ) d 12 = f 12 (Y 1, Y 2, Y 12 ). The evolution functions f 1, f 2, f 12 determine damage failure surfaces coupling between damage and failure modes require determination from materials test data Fabric composites model assume 2 independent damage modes fibre dominated d 1 and d 2 for tension/compression matrix dominated d 12 for in-plane shear d 1 = f 1 (Y 1 ) d 2 = f 1 (Y 2 ) d 12 = f 12 (Y 12 ) Measured stress-strain curves for glass fabric/epoxy lead to evolution equations in form: d 1 = 0, Y 1 < Y 10 d 1 = α 1 (Y 1 - Y 10 ) for Y 10 < Y 1 < Y 1f d 12 = 0, Y 12 < Y 12 d 12 = α 12 (ln Y 12 - ln Y 120 ) for Y 120 < Y 12 < Y 12f where Y 1 (t) = max { Y 1 (τ) }, Y 2 (t) = max { Y 2 (τ) }, Y 12 (t) = max { Y 12 (τ) }, τ t 9

Generalised fabric damage model: elastic-plastic in shear In-plane shear failure is matrix controlled at large shear strains inelastic damage is observed extend model to include elastic-plastic behaviour in shear Assume the plastic strains: ε 11 p = ε 22 p = 0, ε 12 p 0 following the UD Ladeveze model we introduce an elastic domain function F F = σ 12 /(1-d 12 ) - R(p) - R o where R(p) is a plastic hardening function and p is the accumulated effective plastic strain : p ε12 p = ( 1 d ) 0 12 dε p 12 The hardening function is determined from cyclic shear tests. Data on glass fabric/epoxy fit the general form R(p) = β p m The model then requires only 3 parameters R o, β and m to characterise the plastic response. 10

Determination of fabric model parameters in shear Evolution eqn. - elastic shear Glass fabric/epoxy. cyclic shear stress-strain curve 0.8 0.7 0.6 0.5 Shear stress s12 Mpa d12 0.4 0.3 d12 Logarithmisch (d12) 0.2 0.1 0 0 0.02 0.04 0.06 0.08 0.1 0.12 e12pl e12el Total shear strain e12 Cyclic shear stress-strain curve Cyclic shear stress-strain curve for GF/epoxy 700 R(p) : comparison test data and power law model -0.1 -- sq rt Y12 Elastic damage evolution curve 600 500 400 - cyclic shear stress-strain curves show significant inelasticstrains - elastic evolution equation for d 12 is nonlinear R(p) 300 200 100 s12/(1-d12)-q0 R(p) - hardening function R(p) modelled by power law 0-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-100 p Plastic hardening function R(p) 11

Trial simulation with fabric ply model GF/epoxy plate impact simulation after 4 ms - (V 0 = 3.13 m/s, M = 21 kg) with contours of: (a) fibre strains (b) plastic shear strains - elastic-plastic fabric ply model tested in plate impact simulation - rigid impactor penetrates the plate - model shows fibre damage, fibre failure and matrix shear plasticity during impact, allowing damage progression to be modelled 12

Composite Tube Crushing using detailed solid modelling Fine solid model to individually model plies and interlaminar resin layers Bi-Phase damage model for fibre-matrix failure prediction Elasto-plastic damage model for resin interface elements Rigid wall 5mm trigger 0 90 +45-45... Matrix interlaminar 22.5 section 15mm length 13

Options for delamination modelling Fine solid models CPU expensive Impractical for large-scale structures Multilayered shell models Elements unable to represent interply shear deformation modes Inter-ply deformation energies must be calibrated using questionable test programs Stacked shell elements New approach that could resolve CPU problems and provide realistic engineering solutions Each ply is modelled using one layer of shell elements The plies are tied using interface conditions that damage during delamination 14

Stacked shell interface model 1) A tied slideline connects the shells (plies). Adjacent elements (slave and master segments) are identified and traction forces applied. 2) For each slave node the displacement components in modes 1 and 2 (relative to their original position) is computed. 3) Elastic, or elastic-damaging stresses are computed and imposed in modes 1 and 2. Deformed position Slave segment Slave node δ I Undeformed position L O δ II Master segment E I G II σ I = E I * δ I / L O τ II = G S * δ II / L O where, E I is the equivalent ply and resin tensile modulus (mode I) G S is the equivalent ply and resin shear modulus (mode II) 15

Failure criteria and delamination model Coupled (mode 1 and Mode 2) strain energy failure criterion G G I IC m G + G II IIC n = e D ed < 1 no failure ed 1 failure (mode 1 and mode 2) Elastic-damaging stress-strain behaviour: Damage D is a function of GI and GII. σ (stress) σ max Area = G C(I,II) unload/ reload σ = σ I σ II = [ I D] E O ε I ε II δ (crack opening) δ o δ max 16

Simulation of delamination (Mode 1) Damaging normal stress versus crack opening displacement for the interply resin Example: Delamination (Mode 1) for a composite DCB test Time history of crack opening force measured at free end 17

Conclusions and outlook FE simulations with bi-phase model predict well observed failure modes of composite elements under crash and impact loads helicopter EA floor beam structures wing access panel under high velocity impact For complex crush and delamination failure modes, simulated loads and EA levels do not agree quantitatively with test results further improvements required in materials and numerical modelling Improved composites models under development in HICAS damage mechanics models for UD and fabric ply in-plane properties interlaminar failure models based on fracture mechanics inclusion of strain rate dependence First trials with code implementations in PAM-CRASH look promising fabric ply damage model implemented and tested stacked shell elements with slide lines tested in mode I failure. Acknowledgements: Some of the work presented here was developed in the EU project HICAS. The Acknowledgements: financial contribution from the CEC and technical input from the partners is acknowledged. 18