Certification of Discontinuous Composite Material Forms for Aircraft Structures Paolo Feraboli (UWAA), Mark Tuttle (UW), Larry Ilcewicz (FAA), Bill Avery (Boeing), Bruno Boursier, Dave Barr (Hexcel) JAMS 2011 The Joint Advanced Materials and Structures Center of Excellence
Aluminum Clamps Strain Gage Wiring to Data Acquisition System Top Load Point Tuttle and Shifman Steel Linkages Angle beams with 3 different flange lengths were tested: 3.5 inch (Large Angle Beam, 4 plies) 2.5 inch (Medium Angle Beam, 4 plies) 1.75 inch (Small Angle Beam, 2 plies) Four point bending loads were applied to the composite beams with the test fixture shown. Tests were conducted in 6 different beam orientations. 8x1 in. strain gages were bonded to each of the three angle beam sizes in order to monitor Bottom Load Point Test 1: 0 strain +z +y 2 +z +y 5,6 3 2 7,8 1,4 Test 4: 90 +z +y +y Test 2: 135 (unsymmetric) +z +y Test 5: 90 HexMC Angle Test 3: 45 (unsymmetric) +z +y Test 6: 180 Pivots +z
Beam Theory z (major principal centroidal axis) Distances from centroid to extremities of angle beam and moments of inertia: a y (minor principal centroidal axis) zc t yc T M Normalized strain as defined by Shifman & Tuttle 3
Shell elements with MPC Centroidal axis M z y M x Section at C1 & C2 4
Longitudinal Strain (x-direction) FEM Analysis (Orthotropic/ Quasi-Isotropic Tape) Orthotropic mechanical properties: 5.97 0.28 1.8 Average values for & based on experiment Typical Strain behavior showing match between model & beam theory with an approximated percentage error of 0.65% (comparison based on maximum strain in the x-direction) 5
Typical Plot of Results Normalized Strain Curves EMAX=8.68 EAVG=5.97 EMAX EAVG EMIN Highlighted region is admissible for HexMC based on modulus variability EMIN=4.12,, : three different values for based on experiment 1. 8.68 2. 5.97 3. 4.12 Normalized strain is a function of 1/E, hence non linear, 1 Modulus for each angle beam is determined by averaging slope values of trendline curves obtained from experimental data for each geometry configuration and angle beam orientation 6
Comparison between Experiment and Simulation (Large Angle Beams, 0 degree) EMAX EAVG E BEST FIT EMIN # data points in this quadrant (5) 1. 8.68 2. 5.97 3. 4.12 4. 4.93 7
Comparison between Experiment and Simulation (Large Angle Beams, 180 degree) EMIN E BEST FIT EAVG EMAX # data points in this quadrant (6) 1. 8.68 2. 5.97 3. 4.12 4. 4.89 8
Comparison between Experiment and Simulation (Large Angle Beams,90 degree) EMAX EMIN E BEST FIT EAVG # data points in this quadrant (7) 1. 8.68 2. 5.97 3. 4.12 4. 5.41 9
Comparison between Experiment and Simulation (Large Angle Beams, -90 degree) EAVG E BEST FIT EMIN EMAX # data points in this quadrant (7) 1. 8.68 2. 5.97 3. 4.12 4. 5.48 10
Comparison between Experiment and Simulation (Large Angle Beams, -45 degree) EMIN EAVG E BEST FIT EMAX # data points in this quadrant (6) 1. 8.68 2. 5.97 3. 4.12 4. 6.17 11
Comparison between Experiment and Simulation (Large Angle Beams,-135 degree) E BEST FIT EMIN EAVG EMAX # data points in this quadrant (7) 1. 8.68 2. 5.97 3. 4.12 4. 5.13 12
Comparison between Experiment and Simulation (Medium Angle Beams, 0 degree) EMIN E BEST FIT EAVG EMAX # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 5.71 13
Comparison between Experiment and Simulation (Medium Angle Beams,180 degree) EMAX EAVG E BEST FIT EMIN # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 5.62 14
Comparison between Experiment and Simulation (Medium Angle Beams,90 degree) EMAX EMIN E BEST FIT EAVG # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 5.87 15
Comparison between Experiment and Simulation (Medium Angle Beams,-90 degree) E BEST FIT EAVG EMIN EMAX # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 6.07 16
Comparison between Experiment and Simulation (Medium Angle Beams, -45 degree) EMAX EAVG EMIN E BEST FIT # data points in this quadrant (3) 1. 8.68 2. 5.97 3. 4.12 4. 5.52 17
Comparison between Experiment and Simulation (Medium Angle Beams, -135 degree) EMIN EAVG E BEST FIT EMAX # data points in this quadrant (5) 1. 8.68 2. 5.97 3. 4.12 4. 6.61 18
Comparison between Experiment and Simulation (Small Angle Beams, 0 degree) EMIN EAVG EMAX EBEST FIT # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 11.9 19
Comparison between Experiment and Simulation (Small Angle Beams, 180 degree) EBEST FIT EMAX EAVG EMIN # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 12.1 20
Comparison between Experiment and Simulation (Small Angle Beams, 90 degree) EBEST FIT EMIN EAVG EMAX # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 11.2 21
Comparison between Experiment and Simulation (Small Angle Beams, -90 degree) EMAX EAVG EMIN EBEST FIT # data points in this quadrant (4) 1. 8.68 2. 5.97 3. 4.12 4. 11.5 22
Comparison between Experiment and Simulation (Small Angle Beams, -45 degree) EAVG EMIN EMAX EBEST FIT # data points in this quadrant (5) 1. 8.68 2. 5.97 3. 4.12 4. 11.8 23
Comparison between Experiment and Simulation (Small Angle Beams, -135 degree) EAVG EMIN EMAX EBEST FIT # data points in this quadrant (5) 1. 8.68 2. 5.97 3. 4.12 4. 12.4 24
Modulus Best Fit Angle [ ] Modulus [Msi] (Large Angle Beam) Modulus [Msi] (Medium Angle Beam) Modulus [Msi] (Small Angle Beam) 0 4.93 5.71 11.9 180 4.89 5.62 12.1 90 5.41 5.87 11.2-90 5.48 6.07 11.5-45 6.17 5.52 11.8-135 5.13 6.61 12.4 AVG 5.33 5.90 11.8 CoV 9% 7% 4% From experimental coupon-level data: 8.68, 5.97, 4.12 with average 0.64 0.07 5.83 25
FEM Analysis (Randomized Orthotropic) The models were discretized in: - 312 RRVE for the large angle beam - 216 RRVE for the medium angle beam - 168 RRVE for the small angle beam Each RRVE has elastic orthotropic material properties assigned independently from the neighboring ones and generated by running the stochastic laminate analogy code in Matlab. The discretization of the specimen into RRVE s has no relation with the mesh size. The nodes of neighboring RRVE s are merged to ensure displacement compatibility. For each geometry (large, medium, small): 30 FEM runs 1 fixed angle beam orientation (0 degree shown) 8 strain gage locations After FEM run, data is reduced: obtain value of normal strain at SG location Of the 30 values generated, only the MAX, AVG, MIN are reported Longitudinal Strain (x-direction) 26
Modulus: Global Properties & Distribution Overall Modulus MAX [Msi] AVG [Msi] MIN [Msi] 9.18 6.34 3.96 x-x y-y Global properties same as orthotropic with EAVG RRVE # Section Modulus Modulus at Section x-x [Msi] Modulus at Section y-y [Msi] 1 6.57 6.64 2 6.63 5.15 x-x 1 2 3 4 3 6.44 5.44 4 5.92 6.77 5 5 5.16 4.33 y-y 6 7 8 9 10 6 5.99 5.52 7 6.10 6.69 Modulus distribution also important 11 12 RRVE # 8 6.03 4.75 9 5.71 4.81 10 9.24 7.57 11 7.29 6.63 12 5.69 5.99 27
Large Angle Beam: Max, Avg, Min @ SG #1 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MIN predicted modulus) NOTE: Experimental strain value falls OUTSIDE of range of random prediction 1 data point only 28
Large Angle Beam: Max, Avg, Min @ SG #2 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MIN predicted modulus) NOTE: Experimental strain value falls OUTSIDE of range of random prediction 1 data point only 29
Large Angle Beam: Max, Avg, Min @ SG #3 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 30
Large Angle Beam: Max, Avg, Min @ SG #4 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls OUTSIDE of range of random prediction 1 data point only 31
Large Angle Beam: Max, Avg, Min @ SG #5 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 32
Large Angle Beam: Max, Avg, Min @ SG#6 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 33
Medium Angle Beam: Max, Avg, Min @ SG#1 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 34
Medium Angle Beam: Max, Avg, Min @ SG#2 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 35
Medium Angle Beam: Max, Avg, Min @ SG#3 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 36
Medium Angle Beam: Max, Avg, Min @ SG#4 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls OUTSIDE of range of random prediction 1 data point only 37
Medium Angle Beam: Max, Avg, Min @ SG#5 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 38
Medium Angle Beam: Max, Avg, Min @ SG#6 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 39
Medium Angle Beam: Max, Avg, Min @ SG#7 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls INSIDE of range of random prediction 1 data point only 40
Medium Angle Beam: Max, Avg, Min @ SG#8 (0 degree) with stochastic approach (MIN, AVG, MAX over 30 runs) with QI Tape approach (MIN, AVG, MAX predicted modulus) NOTE: Experimental strain value falls OUTSIDE of range of random prediction 1 data point only 41
Conclusions Prediction based on orthotropic (quasi isotropic) layered with E 1 =E 2 =E AVGEXPER are not sufficient All data points fit in the admissible region for the large & medium beams. Small beams fall outside region. Admissible region based on EMAX, EAVG, EMIN obtained from experiments E BESTFIT shows non negligible error in prediction of elastic response if using E AVGEXPER Need to define a suitable E for the material (statistical B-basis value?) For small beams (2 plies), predictions are too off to be due to normal variability. Different explanations exist, confirmation will follow. If multiple beams of same size are tested, different results are expected. So far only 1 beam per geometry and orientation has been strain gaged & tested. Not possible to measure the variability of the same location strain over multiple specimens. For stochastic approach proposed previously, some agreement (40%) but in others (60%) experimental data falls outside of predicted range. Explanations: 30 runs not sufficient Number of RRVE in each model (312 to 168 depending on size) is not sufficient for convergence 1000 is the suitable value demonstrated previously 42
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