A 3D Discrete Damage Modeling Methodology for Abaqus for Fatigue Damage Evaluation in Bolted Composite Joints Eugene Fang 1, Ling Liu 1, Michael Stuebner 1, Jim Lua 1 1 Global Engineering and Materials, Inc. Endel V. Iarve 2, Michael Swindeman 2 2 University of Dayton Research Institute April 23, 2012 1
Introduction to the R&D Team at GEM (www.gem-innovation.com) Overview and Capabilities Founded in 2001 as an engineering service and software development company Specialized in R&D consulting for DoD, Marine & Aerospace; Technology transfer from research labs to industries Developing analysis/design tools for advanced materials/structures; Strategic Alliance and Business Partnership Business partnership and collaboration with SIMULIA (Abaqus), Marine and Aerospace industries Jointly exploring business opportunities within government agencies and commercial industries
Outline Background on tool development Introduction of key solution moudules Implementation in Abaqus Application examples Summary and conclusions 3
(Hallet & Wisnom, 2007) Challenges in Progressive Damage Analysis Discrete Damage Interaction Analyses demonstrate that fracture is dominated by interactions between transverse matrix cracks and delaminations How to define such critical crack patterns a priori? Develop methods to model arbitrary cracking! 4
Regularized X-FEM X-FEM/Phantom Discrete Crack Network (DCN) Module for Abaqus for Residual Strength and Life Prediction of Bolted Composite Joint Application Simulation
Discrete Damage Modeling Goal: Discrete Modeling of Matrix Cracking and Delamination Networks General approach based on X-FEM ideas Must accommodate cracking & delamination interaction Kinematic Description of a Discrete Crack 1.0 0.0 X-FEM Displacement Jump Rx-FEM Crack Location
Crack description: X-FEM and RX-FEM f ( x) sign( n( x)( x x))min x x x x t on t Standard FE Jump function introduction u( x) X i( x) u ii ii / J i u( x) X ( x) u H( f ( x)) X ( x) u (1) i i j j jj 1 H( f ( x)) X ( x) u jj j (2) j u x on u Standard X-FEM Regularized X-FEM 1 x 0 H( x) 0 x 0 H( x) X i( x) hi i h i 1 X i( x) f ( x) dv 1 V 2 X i( ) f ( ) dv x x V Endel Iarve. Mesh independent modelling of cracks by using higher order shape functions. IJNME, 56(6), 2003: 869:882 7
VCCT Based G Extraction: Matrix Cracking VCCT based G extraction Crack propagation New virtual crack extension New crack tip Crack growth Original virtual crack extension Original crack tip Original crack cos 2 4 2 2 1 3KII KI 8KI KII 2 2 KI 9K II
Crack Front Tracking and Extraction of SERR via Spring Model: Delamination Geometric Tracking of Arbitrary Delamination Front 9
Merging of Delamination Fronts Merging Fronts Merging Front with Boundary Front 1 Front 2 Front Geometric Boundary Delaminated Area 2 Delaminated Area 1 Merged Front Physical Delaminated Area Virtual Delaminate d Area 10
Turon s Cohesive Damage Accumulation ModelFor Delamination Fatigue Prediction Damaged area Cracked area da coh coh coh coh coh Damaged area ratio Paris law Energy dissipation ratio x 0 ( ( x)) ( x) x Damage variable dn G cm, mm, Gthm, Gcm dd Cycle number Load level Output: damage evolution A. Turon, J. Costa, P.P. Camanho, C.G. Davila. Simulation of delamination in composites under high-cycle fatigue. Composites A: applied science and manufacturing. 38, 2007:2270-2282 Input: fatigue loading & Material properties 11
Fatigue Delamination Initiation Characterization Quasi-static analysis Cohesive elements Cohesive elements break S-N curve to get damaged strength Damaged cohesive constitution law Stress level Cycle number Damage accumlation Cohesive strength & toughness degradation The strategy can be summarized as follows: (1) Determination of cohesive stress via a quasi-static analysis; (2) Degradation of both cohesive strength and toughness under cyclic load based on an S-N curve; and (3) Crack initiation via monitoring cohesive elements with traction-free displacement jump 12
Phantom-Paired X-FEM for Residual Strength Prediction Initial stress External loading Failure reached? Y Matrix crack injection 0 Gc c ( ) d 0 back to the beginning with evolved structure K 0 G d * * (, ( )) Update cohesion status K (1 d ) K 0 0 * Cohesive law c 13
constant amplitude Co-Simulation of Matrix Cracking and Delamination Growth F max (1) F max varied amplitude F ( n) max F min (1) F min F ( n) min Maximum load Initial stress Minimum load S-N based damage accumulation Coupled balance analysis Failure reached? Y Delamination mode Matrix crack injection G G G max min G G G max min 0 Gc c ( ) d 0 allowed dd f1 d A/ d N K 0 * * (, ( )) G d K (1 d ) K 0 allowed dd f2 G 0 * c computed fatigue dd i dn min dn, dn crack max Coupled fatigue evolution delamination max computed fatigue dd i update matrix cracks damage back to the beginning with evolved structure update delamination damage 14
Implementation of Rx-FEM within Abaqus via Its User-Defined Subroutines Rx-FEM Routines ABAQUS Abaqus Start of Analysis (LOP = 0) Start of Increment (LOP = 1) UEXTERNALDB (LOP = 0) (LOP = 1) (LOP = 2) Read Rx Data Set up External Database Create Elements Update Internal Variables Equilibrium Iterations UEL Current DOF Check Failure Criteria Write to Database End of Increment (LOP = 2) Element Tangent Stiffness Matrix Load Residuals Check for Cracks Adjust Elements for Cracks Calculate Damage Generate Cohesive Stiffness Matrix 15
Summary of X-FEM for Abaqus Solution Modules Composite Laminate Simulation system Fatigue solution module Residual strength prediction module Cohesive damage accumulation (Turon s model) Front tracking (VCCT) Cohesive approach S-N based matrix properties damage Turon s fatigue cohesive law S-N based matrix properties damage S-N based Cohesive strength and toughness damage Matrix crackiing Delamination propagation Failure criteria Cohesive crack injection Failure criteria Cohesive crack injection VCCT based spring injection Critical initial delamination size reached VCCT based spring injection Failure criteria Crack injection Cohesive law Cohesive element approach Critical initial matrix crack size reached Not implemented yet Notes: Need to be enhanced and validated further 16 Long term work
RX-FEM Example: DCB Crack Propagation E11 (GPa) E22 = E33 (GPa) G12 = G13 (GPa) G23 (GPa) 150.0 11.0 6.0 3.7 v12 = v13 v23 GIc (N/mm) 0 (MPa) 0.25 0.45 0.352 60.0 (a) Michael Swindeman. A regularized extended finite element method for modeling the coupled crack and delamination of composite materials [D]. UDRI, Dayton, 2011.
RX-FEM Example: Strength and Damage Prediction of Composite Laminate Endel V. Iarve1,Mark R. Gurvich, David H. Mollenhauer, et al. Mesh-independent matrix cracking and delamination modelling in laminated composites. IJNME, 88, 2011: 749-773
RX-FEM Example: Damage Pattern Comparison with Experimental Observation Load Step N +45 /90 Ply Interface 90 /-45 Ply Interface -45 /0 Ply Interface
P, kn F/b, N/mm X-FEM Capability Illustration of Residual Prediction Module 14 12 10 theoretical case1 8 6 4 2 25 0 0 2 4 6 8 10 12 20 delta, mm 15 10 5 Abaqus, pre-existing crack XFEM, phtantom pair 0 0 0.2 0.4 0.6 0.8 1 1.2 displacement, mm 20
K I, N/mm X-FEM Capability Illustration for Fatigue Crack Propagation 100 MPa clamping zone 75 mm 250 mm (initial crack 10 mm) 600 mm 2500 2000 1500 1000 XFEM ASPAN clamping zone 75 mm 500 500 mm 0 0 50 100 150 200 250 300 Crack length(2a ), mm
Capability Illustration for Mesh Independent Fatigue Crack Propagation within Interface W = 25.4 mm L = 101.6 mm bolt w = 25.4 mm t = 2.236 mm, max = 80 Mpa [45 4 /-45 4 ] min = 0 MPa s N = 6 N = 74 Initial delamination front 25 20 D 0 = 5.425 mm 15 R 0 = 3.175 mm 10 N = 11 N = 104 5 10 15 20 25 30 35 40 N = 39 N = 175 22
Parameter Analysis for Fatigue Delamination Propagation through thickness direction = +(45±1)º = -(45±1)º = -(45±1)º = +(45±1)º interface interface symmetric surface t = 2.336 mm M 44 45 46 a i = 2 mm R i = 5.175 mm R 0 = 3.175 mm a i = 2.25 mm a i = 2.5 mm case C ai theta 1 3.13E-08 2 44 2 3.76E-08 2 44 3 4.10E-08 2 44 4 3.13E-08 2.25 44 5 3.76E-08 2.25 44 6 4.10E-08 2.25 44 7 3.13E-08 2.5 44 8 3.76E-08 2.5 44 9 4.10E-08 2.5 44 10 3.13E-08 2 45 11 3.76E-08 2 45 12 4.10E-08 2 45 13 3.13E-08 2.25 45 14 3.76E-08 2.25 45 15 4.10E-08 2.25 45 16 3.13E-08 2.5 45 17 3.76E-08 2.5 45 18 4.10E-08 2.5 45 19 3.13E-08 2 46 20 3.76E-08 2 46 21 4.10E-08 2 46 22 3.13E-08 2.25 46 23 3.76E-08 2.25 46 24 4.10E-08 2.25 46 25 3.13E-08 2.5 46 26 3.76E-08 2.5 46 27 4.10E-08 2.5 46 C does not affect the damage patterns 101.6 mm
dl (mm) Fatigue Delamination Propagation Process A B C D A B C D 10 A A B Case 21 B C Case 4 D C D 1 1 10 100 1000 10000 100000 1000000 0.1 N (cycle)
Stress, MPa Capability Illustration of Continuum Based X-FEM for Fatigue Life Prediction 40 35 30 Crack injection RF force decreases after crack injection 25 20 15 10 5 0 S-N based fatigue damage accumulation of strength Turon s fatigue cohesive model 1 10 100 1000 10000 100000 1000000 Cycle K (N/mm 3 ) n (N/mm 2 ) s (N/mm 2 ) G Ic (N/mm) G IIc (N/mm) h R E3 (N/mm 2 ) 1.00E+06 60 90 0.2 1 2.239 0 11380 C I C II m I m II G th-i (N/mm) G th-ii (N/mm) h 2 0.0616 0.0616 4.5 4.5 0 0 2.239
1.75 inch Demonstration of Fatigue Damage Accumulation of Laminated Plate [60 2 /-60 2 ] s ply thickness 0.005 inc Material: T300/976 u1 = 0.5 mm 6 inch K (N/mm 3 ) n (N/mm 2 ) s (N/mm 2 ) G Ic (N/mm) G IIc (N/mm) h R E3 (N/mm 2 ) 1.00E+06 60 90 0.2 1 2.239 0 11380 C I C II m I m II G th-i (N/mm) G th-ii (N/mm) h 2 0.0616 0.0616 4.5 4.5 0 0 2.239 0 N = 15,470 N = 58,249 N = 61,165 N = 76,721 N = 85,966 N = 88,704
Problem Statement Capability Illustration for a 2-Ply Plate with a Bolt/Nut Connection and an Interface Bonding (Mixed UEL and Abaqus Elements) Effective Stress Distribution at Ply Interface e 11 in 0 o -ply e 22 in 90 o -ply 27
Summary and Conclusions Implementation both standard X-FEM and RX-FEM with Abaqus for discrete crack description of matrix cracking and delamination. Development of VCCT-based delamination propagtion model under fatigue loading. Implementation of fatigue crack initiation and the fatigue cohesive model for both matrix crack and delamination under cyclic loading. Developed a mesh independent crack front tracking via a spring model. Constructed the co-simulation framework for matrix cracking and delamination evolution in laminated composites. Final goal: an efficient analysis module for failure process simulation of composite laminates under monotonic/cyclic loadings. Future investigation of convergence issue associated with user-defined elements under monotonic load. 28