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IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi*, C. Davila** *Dipartimento Ingegneria Aerospaziale,

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Presentation on theme: "IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi*, C. Davila** *Dipartimento Ingegneria Aerospaziale,"— Presentation transcript:

1 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi*, C. Davila** *Dipartimento Ingegneria Aerospaziale, Politecnico di Milano **NASA Langley Research Center COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011

2 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila  Introduction & Motivation  experiments and numerical model  Superposed cohesive laws approach for bridging  Numerical identification  Conclusions CONTENTS oCohesive zone models and fibre bridging oDCB tests on fiberglass specimens and numerical model oSuperposition of cohesive elements and analytical identification of material parameters oResponse surface and optimization approaches to material parameter identification

3 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila INTRODUCTION AND MOTIVATION Bi-linear cohesive laws can be successfully in FE models of delaminations They are adequate when toughness is constant with crack length. Characterisation Material model Analysis of crack growth in curved fabric laminates Application Verification

4 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila INTRODUCTION AND MOTIVATION The crack growth resistance can significantly increase in the presence of fibre bridging In large scale fibre bridging a very long process zone develops before toughness reaches a steady level G C Cohesive laws with linear softening are inadequate to model the G-a curve effect.

5 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila INTRODUCTION AND MOTIVATION The measurement of bridging tractions in the wake of crack confirms that they do not have a linear softening (Sorensen et al. 2008). The superposition of two linear softening laws has been proposed for intralaminar fracture (Davila et. Al 2009). Other shapes must be employed for the softening law It can be considered an appealing practical approach (conventional cohesive elements can be used)

6 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila INTRODUCTION AND MOTIVATION Objectives: oApply the superposed element approach to model the R-a curve effects in interlaminar fracture in glass fiber reinforced laminates oDevelop an analytical approach for the calibration of material parameters from the experimental R-a curve oApply numerical techniques for the automatic identification of such parameters based on the force vs. displacement response of DCB tests

7 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila EXPERIMENTS AND NUMERICAL MODEL DCB tests have been performed on [0] 48 laminates of S2 Glass fibre reinforced tape with an Epoxy Cycom SP250 matrix (5 Tests)  Crack advance monitored by dye penetrant inspection.  Pre-crack has been obtained by means of a PTFE insert  Pre-opening test were performed  Subsequent opening tests

8 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila EXPERIMENTS AND NUMERICAL MODEL Four data reduction techniques: Beam Theory (BT), Compliance Calibration (CC), Modified Beam Theory (MBT), Modified Compliance Calibration (MCC) Large scale fibre bridging and a marked G-a curve effect. The length of the process zone (LPZ) is approximately 80 mm

9 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila EXPERIMENTS AND NUMERICAL MODEL A 2 mm wide strip of the specimen has been analysed in Abaqus Standard Incompatible modes C3D8I elements  0.5 mm equispaced grid COH3D8 cohesive elements Material stiffness from previous characterisation and transverse isotropy assumptions E a (MPa)45670G ta (MPa)5900v ta 0.257 E t (MPa)13600G t (MPa)5230vtvt 0.3 Imposed displacement

10 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila EXPERIMENTS AND NUMERICAL MODEL ocohesive law with linear softening oG IC = 1.0 KJ/m 2 o  0 =20 MPa and  0 =50 MPa Preliminary numerical evaluation: Bi-linear cohesive law largely overestimates the force in DCB tests Peel strength has a little influence on DCB response as expected

11 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila SUPERPOSED COHESIVE LAWS APPROACH  the complete cohesive law is approximated by means of two superimposed cohesive laws . In the presence of bridging, the softening law is non-linear

12 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila SUPERPOSED COHESIVE LAWS APPROACH reference length of the process zone Linearised expression of the G-a curve by Davila et al. 2009 G1G1 GcGc Parameter m is G 1 /G c n is obtained by imposing G R = G C in correspondance of the experimental

13 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila SUPERPOSED COHESIVE LAWS APPROACH The previous formulation has been applied and verified for a compact tension specimen (Davila et al. 2009) Turon et al. (2008) suggested a correction of reference process zone based on an undetermined factor H A refined model using a single cohesive (linear softening law) has been used to asses an appropriate expression of reference LPZ In DCB test adherends are thin and LPZ becomes much shorter than

14 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila SUPERPOSED COHESIVE LAWS APPROACH FEM 2D Two corrections are considered:  The errors in the uncorrected l c are very large when LPZ is long  For large LPZ a correction factor with the additional parameter  provides the best results   is set to 0.48 for best correlation LPZ 1 LPZ 2 LPZ 1 LPZ 2

15 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila Using and m=2 Sigma (MPa) 152535 n0.98000.99280.9963 LPZ and Force vs. Displacement curves captured for Sigma = 15 and 25 MPa superposed cohesive elements model: Numerical G(  a) SUPERPOSED COHESIVE LAWS APPROACH

16 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION The presented model proved effective to accurately capture the forces and the process zone lenght for moderate values of peel strength Analytical calibration of material parameters requires the knowledge of the G-a curve An alternative strategy is explored, based on a numerical identification technique The objective is the identification of material parameters considering the Force vs. Displacement curve  A cost function is defined  response surfaces techniques is applied to explore the feasibility of the approach  Optimization procedures is applied to minimize the error

17 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Cost Functions d1d1 d2d2 d3d3 d4d4 Mean Square Error between numerical and average test Average MSE values in 4 selected zones Global error index

18 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Implementation Ichrome/NEXUS Optimisation Suite variables Abaqus runs Matlab post- processing Error zones EiEi Total error

19 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Response surface techniques Response surfaces have been built by means of a Kriging approximation (second order polynomial + local gauss functions) The surface has been created by allocating 300 points within the domain minmax Sigma(MPa)1550 m0.0000.500 n 0.999 Steady state toughness has been set at 1.0 kJ/m 2 The database allows the creation of different surfaces of the cost function in the space m-n at a given value of peel strength (Sigma)

20 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Response surface for Sigma = 15 MPa Minimum of cost function is found along a valley for high values of n An interval 0.05 < m < 0. 2 can be identified along the valley

21 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Response surface for Sigma = 25 MPa As Sigma is increased optimal n slightly moves towards 1.0 optimal m seems to be lower than m=0.2, but derivatives are small in such direction

22 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Response surface for Sigma = 35 MPa For Sigma = 35 MPa qualitative tendencies are confirmed. Overall minimum values of cost function are about 20 N.

23 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Following the meta-model indications three solutions have been selected Meta-model allows identifying acceptable approximations Sigma (MPa)mnCost (N)LPZ (mm) 150.190.98516.4074 250.140.98517.1276 350.110.99021.1473

24 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Optimization: Gradient-based method Sigma = 15 Mpa, Gc = 1 kJ/m 2 Initial guess m=0.3, n=0.7 (meta-model indications ignored) mnCost (N)LPZ (mm) 0.1690.97715.6167 Optimized Solution Evolution of m,n, Objective

25 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION For Sigma =25 and 35 MPa meta-model indication have been used as initial guess for a gradient based method The application of different weights to error indices in the different zones of the curve has been investigated Initial Guess Interesting results have been found by increasing the weights in the first 2 zones of the domain

26 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila NUMERICAL IDENTIFICATION Sigma = 25 Mpa mn Initial0.1400.985 optim0.1520.986 m n Initial0.1100.990 optim0.1460.991 minimization of cost function lead to increase m Sigma = 35 Mpa Improvement of Force-displacement and G-a correlation in the initial part of the response Final G C is almost unchanged (imposed value of 1 kJ/m 2 )

27 COMPTEST 2011 – Ecole Polytechnique Fédérale de Lausanne (EPFL) Switzerland – February 14 th 16 th, 2011 IDENTIFICATION OF MATERIAL PARAMETERS FOR MODELLING DELAMINATION IN THE PRESENCE OF FIBRE BRIDGING A. Airoldi, C. Davila CONCLUSIONS  Bi-linear softening laws can model delamination processes in the presence of fibre bridging  An analytical calibration procedure of the model has been assessed for moderate values of peel strength (more refined models could be required for higher values)  Numerical identification (response surface/optimization) can obtain approximate solutions without requiring the knowledge of the G-a curve  Numerical procedures can be extended to multi-linear softening laws which could be more flexible for capturing both force response, G-a curve and process zone lengths

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