Robust/realistic simulation of coupon tests: ⢠Plain tension/compression. ⢠Open-hole tension/compression. ⢠Filled-hole tension. ⢠Bolt bearing. ⢠Drop-weight ...
A VIRTUAL TEST LAB FOR UNIDIRECTIONAL COMPOSITE COUPONS Olben Falcó1, Bas Tijs2, Brendan Romano2, Cláudio S. Lopes1 1IMDEA 2GKN
Materials Institute, Getafe, Madrid, Spain Aerospace: Fokker, Papendrecht, The Netherlands
THE CASE FOR VIRTUAL TESTING
Building block certification
VIRTUAL TESTING
C.S. Lopes, C. González, O. Falcó, F. Naya, J. Llorca, B. Tijs, Multiscale virtual testing: the roadmap to efficient design of composites for damage resistance and tolerance, CEAS Aeronautical Journal (2016) 7: 607-619.
THE CASE FOR VIRTUAL TESTING Challenge: towards simulation-based material certification Robust/realistic simulation of coupon tests: • Plain tension/compression • Open-hole tension/compression • Filled-hole tension • Bolt bearing • Drop-weight impact • Compression after impact • Etc….
Approach: Virtual Test Lab Framework: • Commercially-available explicit FE solver (ABAQUS/Explicit) • 3D damage model for FRP plies enforcing crackband erosion (user subroutine) • Surface-based cohesive-frictional model for ply interfaces (ABAQUS native) • Purpose-built automated ABAQUS plug-in (Python scrip + GUI), to model laminated coupons using regularized meshes
FRP PLY FAILURE Ply Properties:
Unidirectional characterization tests Computational micromechanics
Constituents characterized by means of micromechanical testing (nanoindentation, push-in, single fibre, etc.)
F. Naya et al., Composites: Part A 92 (2017)
FRP PLY FAILURE 3D Failure Criteria Transversely-dominated modes Mixed-mode transverse crack opening: 𝝓𝑴𝑻 =
𝑡𝑁 𝑆𝑇𝑖𝑠
2
+
2
𝑡𝐿
+
𝑆𝐿𝑖𝑠
2
𝑡𝑇
+𝜆
𝑆𝑇𝑖𝑠
2
𝑡𝑁 𝑆𝑇𝑖𝑠
𝑡𝐿 𝑆𝐿𝑖𝑠
2
+𝜅
𝑡𝑁
2
𝑆𝑇𝑖𝑠 2
𝜅=
Transverse compressive shear banding: 𝝓𝑴𝑪 =
2
𝑡𝐿
+
𝑆𝐿𝑖𝑠 − 𝜂𝐿 𝑡𝑁
𝑆𝑇𝑖𝑠 − 𝑌𝑇𝑖𝑠 𝑆𝑇𝑖𝑠 𝑌𝑇𝑖𝑠
2
𝜆=
2𝜂𝐿 𝑆𝑇𝑖𝑠 𝑆𝑇𝑖𝑠
−𝜅
2
𝑡𝑇 𝑆𝑇𝑖𝑠 − 𝜂𝑇 𝑡𝑁
Longitudinally-dominated modes Brittle longitudinal failure: 𝝓𝑳𝑻 =
𝜀11 𝜀1𝑇
Fibre kinking (under compression and shear): (𝜑) 2
𝝓𝑲𝑴𝑻 =
𝑡𝑁
(𝜑) 2
𝑡𝐿
+
𝑆𝑇𝑖𝑠
𝝓𝑲𝑴𝑪 =
+
𝑆𝐿𝑖𝑠 2
(𝜑)
𝑡𝐿
(𝜑)
𝑆𝐿𝑖𝑠 − 𝜂𝐿 𝑡𝑁
(𝜑) 2
𝑡𝑇
𝑆𝑇𝑖𝑠
(𝜑) 2
+𝜆
+
𝑆𝑇𝑖𝑠
(𝜑) 2
𝑡𝐿
𝑆𝐿𝑖𝑠
+𝜅
𝑡𝑁
2
𝑆𝑇𝑖𝑠
2
(𝜑)
𝑡𝑇
𝑡𝑁
(𝜑)
𝑆𝑇𝑖𝑠 − 𝜂 𝑇 𝑡𝑁
Catalanotti et al. Composite Structures 95 (2013) 63–79
FRP PLY FAILURE 3D Continuum Damage Behavior 1 1 d E 1 1 1 12 E1 1 2 13 E1 3 23 0 31 12 0 0
21
31
32
0
0
0
1 1 d3 3 E3
0
0
0
0
1 1 d 4 23 G23
0
0
0
0
1 1 d5 13 G31
0
0
0
0
1 1 d 2 2 E2
0
E2
23 E2
Longitudinal tension/compression:
E3 E3
0 1 2 0 3 23 0 31 12 0 1 1 d 6 12 G12 0
Transverse tension/compression:
FRP PLY FAILURE 3D Continuum Damage Behavior 1 1 d E 1 1 1 12 E1 1 2 13 E1 3 23 0 31 12 0 0
In-plane shear (12):
d6
21
31
32
0
0
0
1 1 d3 3 E3
0
0
0
0
1 1 d 4 23 G23
0
0
0
0
1 1 d5 13 G31
0
0
0
0
1 1 d 2 2 E2
0
E2
23 E2
E3 E3
Out-of-plane shear (23)
0 1 2 0 3 23 0 31 12 0 1 1 d 6 12 G12 0
Out-of-plane shear (13)
d4
Non-linear shear laws, type Ramberg-Osgood : Out-of-plane tension/compression: Linear elastic behaviour, d3=0 - all out-of-plane softening lumped at the interface
d5
MESH ALIGNEMENT, BIASING AND EROSION
van de Meer and Sluys, 2009
The microstructure constraint to the crack path is lost in the ply-level homogenization
Mesh-alignment and mesh biasing reintroduce the constraint Material-aligned biased mesh:
l*trans
Non-aligned mesh:
E G l * min 2 M 2 M , M 1, 2,6 XM Bažant and Oh, 1983
* l long 2
l*long
E1G1 * E2G2 G12G6 l min 2 ,2 2 X T2 trans is 2 YT SLis
* * ltrans f llong
MESH ALIGNEMENT, BIASING AND EROSION 10o Tensile Test P
q10o
P
Non-aligned mesh: • Non-physical crack paths • Crack bifurcation • Wrong energy dissipation
Material-aligned mesh: • Physical crack paths • Crack bifurcation • Wrong energy dissipation
Mesh-alignment and biasing: • Physical crack paths • No crack bifurcation • Correct energy dissipation
PLY INTERFACE FAILURE Frictional-Cohesive Surface Contact
Damage initiation
Damage evolution (Benzeggah-Kenane criterion)
MODELLING STRATEGY DEMONSTRATION In-Plane Shear (IPS) Test [+-45]2s
X-Ray Tomography
Matrix Cracking
Delamination
Matrix Cracking
Simulation (incl. residual thermal stresses)
NOTCHED/UN-NOTCHED TENSION/COMPRESSION
Material: AS4/8552 Ply elastic and strength properties characterized by GKN Fokker Ply fracture energies characterized by IMDEA (and from literature)
Configurations (limits of the design space): • ´Hard´ - (50/40/10) - [0/45/0/90/0/-45/0/45/0/-45]s • Quasi-isotropic – (25/50/25) - [-45/0/45/90]2s • ´Soft (10/80/10) - [45/-45/0/45/-45/90/45/-45/45/-45]s Tests: • Unnotched tension/compression • Open-hole tension/compression Correlation with two databases: • GKN Fokker • NCAMP (National Center for Advanced Materials Performance, 2011)
O. Falcó, R. L. Ávila, B. Tijs, C.S. Lopes, Modelling and simulation methodology for unidirectional composite laminates in a Virtual Test Lab framework, Composite Structures, 190 (2018) 137–159
NOTCHED/UN-NOTCHED TENSION/COMPRESSION
• • •
Strength results within experimental scatter (in general) Batter match to Fokker results in tension tests (properties from Fokker material batches) Better match to NCAMP results in compression tests (different test methods)
OPEN-HOLE TENSION ´Hard´ (50/40/10) laminates Simulation
Experimental
BRITTLE FAILURE
Strength correlation
OPEN-HOLE TENSION Quasi-isotropic (25/50/25) laminates
Strength correlation
‘SEMI’- BRITTLE FAILURE
OPEN-HOLE TENSION ´Soft´ (10/80/10) laminates
Strength correlation
‘DUCTILE’ FAILURE
OPEN-HOLE COMPRESSION
e.g. quasi-isotropic (25/50/25)
Strength correlation
BOLT BEARING Test stand.: AITM 1-0009 Mat: AS4/8552 Lam: [±45/0/90/0/±45/90]s
simulation
Empirical Torque – Clamping Pressure relationship:
modelling
experimental
* not same material
BOLT BEARING Bearing load behavior
Hole deformation
Critical delamination size (wider than washer) fibre damage
matrix damage
delamination
Qualitative Experimental (X-ray)
Influence of clamping pressure Bearing hole deformation 0.005D (0.5%) 0.02D (2%) 0.04D (4%) 0.06D (6%) Ultimate stress
Test result [MPa] 747.0 894.0 975.0 989.0 1006.0
Simulation result [MPa] Bolt torque: 1.3Nm 594.7 734.6 821.0 883.8 >20% 964.4 error
Simulation result [MPa] Bolt torque: 5.4Nm 727.2 885.1 952.2
