Analysis of Failure in Textile Composites via Meso- Damage Mechanics: Effect of lay-up Dmitry S. IVANOV, Stepan V. LOMOV, Ignaas VERPOEST Katholieke Universiteit Leuven, Belgium Department of Metallurgy and Materials Engineering Composite Materials Group 1 28.07.2009 ICCM 2009
Outline � Introduction Textile composites – Multi-scale concept – Problem statement – � Mechanical insight Deformation mechanisms in textile laminates – Energy-based scaling procedure for boundary conditions for unit – cell in N-ply laminate cell in N-ply laminate Modelling of delaminations via new BC’s – Damage modelling: ERR model + Zinoviev’s assumptions – � Examples: experiments and FEA 1-ply and multi-ply composites – Plain weave and 3D composites – Triaxial braided composites – � Conclusions 2
Diversity of textile structures Patterns 3D woven Woven Braided Knitted Non crimp Laminated Sheared Stitched 3 Diversity = Architectures* Patterns*Lay-ups*Geometry*Textile deformations*…
Design concept: Meso-scale Patterns 3D woven Woven UD fibre bundle Braided Knitted Non crimp Laminated Sheared Stitched 4 Meso scale → → → Properties of UD and Matrix + Internal geometry + → Boundary conditions
Outline Introduction � Textile composites – Multi-scale concept – Problem statement – Mechanical insight � Deformation mechanisms in textile laminates – Energy-based scaling procedure for novel boundary conditions for unit cell – in N-ply laminate Modelling of delaminations via new BC’s Modelling of delaminations via new BC’s – – Damage modelling: ERR model + Zinoviev’s assumptions – Examples: 2D and 3D glass-epoxy composites � Comparison: 1-ply and multi-ply composites – Comparison: plain weave and 3D composites – FEA vs. experiments: local strain distribution – FEA vs. experiment: stress-strain diagrams – Conclusions � 5
Through-the-thickness non- homogeneity Reference problem 6
Reasons: (1) The moment caused by force misbalance is compensated by the stress distribution in the outer plies ∆ ∆ ∆ ∆ F (2) A high inter-0 ° (2) A high inter-0 ° ° -yarn shear ° ° ° -yarn shear ° ° stress S is zeroed at the surface ε σ + τ γ eff 11 11 12 12 ≈ E 1 2 ε 11 Effective E-modulus 7
Deflection profiles ~ = − ε u u x 2 2 22 2 ~ µ u , m 2 The less plies are in the laminate the higher The deflection for all the plies in the deflection the laminate is nearly the same The deflections of N-ply laminates are proportional to each other 8
New BC’s Outer and inner unit cells Energy of effective medium ( ) = σ ε + − σ ε E 2 N 2 11 11 11 11 E outer outer inner inner Energy of heterogeneous medium ( ) = σ ε + − σ ε E 2 N 2 H ij ij ij ij outer inner Deviation from the balance ( ) ∆ λ = − E E E H E Minimisation of the deviation Optimum scaling coefficients Number of the plies, N 2 3 4 5 6 Reference solutions 1.725 1.383 1.273 1.210 1.160 9 Numerical procedure 1.709 1.375 1.253 1.190 1.153
Analysis of the results 10
3D test problem: twill woven FE models are generated by MeshTex software, Osaka University, based on WiseTex geometry Displacement profiles: the same as 2D ⇒ ⇒ ⇒ new BC’s can be used ⇒ 11
Laminates with a ply shift “Step” “Stairs” Can one unit cell be representative in the case of laminates with an arbitrary ply shift? Which BC to apply? 12
Stress in laminate with an different ply shifts Stress along the loading directions “Periodic stacking” “Step” “Stairs” -2.5 ÷ ÷ ÷ ÷ 126.9 -2.3 ÷ ÷ ÷ ÷ 149.6 -4.0 ÷ ÷ 160.1 ÷ ÷ Surface strain map -0.02 ÷ ÷ ÷ 0.33 % ÷ -0.08 ÷ ÷ ÷ ÷ 0.28 % 0.02 ÷ ÷ ÷ ÷ 0.24 % Average surface strain 13 0.1002 % 0.1002 % 0.1003 %
Superposition of periodic profiles To set the correct boundary conditions we have to predict the laminate deformed shape “Step” ~ ∞ u Periodic profile. Ply 1 z ~ ∞ u Periodic profile. Ply 2 z Superimposed profile � ~ ( ) ∞ + + u x shift z 1 � ~ ~ ( ) ∞ ∞ + + + u x shift max( u ) 1 ~ z 2 z = u � z ~ ~ ( ) ∞ ∞ N + + + u x shift 2 max( u ) Deformed profile of a textile laminate z 3 z ... can be presented as a superposition of periodic profiles for each of the plies 14
Superposition of periodic profiles To set the correct boundary conditions we have to predict the laminate deformed shape “Stairs” ~ ∞ u Periodic profile. Ply 1 z ~ ∞ u Periodic profile. Ply 2 z Superimposed profile � ~ ( ) ∞ + + u x shift z 1 � ~ ~ ( ) ∞ ∞ + + + u x shift max( u ) 1 ~ z 2 z = u � z ~ ~ ( ) ∞ ∞ N + + + u x shift 2 max( u ) Deformed profile of a textile laminate z 3 z ... can be presented as a superposition of periodic profiles for each of the plies 15
Actual and predicted profiles Superimposed/predicted ~ profile u z µ , m “Step”-wise shift x , mm 1 Profiles along the inter-layer boundaries Average profile in the laminate Predicted and average profiles are proportional ⇒ Energy-based scaling is also applicable here ⇒ ⇒ ⇒ 16 The scatter of the profiles is bigger than in the periodic stacking
Actual and predicted profiles Superimposed/predicted profile ~ u z µ , m “Stair”-wise shift x , mm 1 Profiles along the inter-layer boundaries Average profile in the laminate Predicted and average profiles are proportional ⇒ Energy-based scaling is also applicable here ⇒ ⇒ ⇒ 17 The scatter of the profiles is bigger than in the periodic stacking
Outline Introduction � Textile composites – Multi-scale concept – Problem statement – Mechanical insight � Deformation mechanisms in textile laminates – Energy-based scaling procedure for novel boundary conditions for unit cell – in N-ply laminate Modelling of delaminations via new BC’s Modelling of delaminations via new BC’s – – Damage modelling: ERR model + Zinoviev’s assumptions – Examples: 2D and 3D glass-epoxy composites � Comparison: 1-ply and multi-ply composites – Comparison: plain weave and 3D composites – FEA vs. experiments: local strain distribution – FEA vs. experiment: stress-strain diagrams – Conclusions � 18
Modelling of delaminations via novel BC’s Delamination can be modelled by “releasing” the interlayer boundary of single UC from the prescribed BC’s “Step” ~ ∞ Zero-traction surface u Periodic profile. Ply 1 z ~ ∞ u Periodic profile. Ply 2 z Superimposed profile Delamination Thus, 1-ply solution can be effective for No need to insert the the modelling delamination in the cohesive elements entire laminate 19
Outline Introduction � Textile composites – Multi-scale concept – Problem statement – Mechanical insight � Deformation mechanisms in textile laminates – Energy-based scaling procedure for novel boundary conditions for unit cell – in N-ply laminate Modelling of delaminations via new BC’s Modelling of delaminations via new BC’s – – Damage modelling: ERR model + Zinoviev’s assumptions – Examples � 1-ply and multi-ply plain weave composites – 3D composites – Triaxail braided composite – Conclusions � 20
Damage modelling � 1) Elementary damaged entity: segment Yarn segment: fibre orientation is constant � 2) Orientation of the failure plane: Mohr-Hashin-Puck concept Crack plane defines the orientation of degradation � 3) Degradation scheme of Murakami-Ohno � 3) Degradation scheme of Murakami-Ohno d 2 0 0 2 = − = − − − E E ( 1 d ) G G ( 1 d ) 2 ( 1 1 d ) 2 2 2 12 12 12 12 = d 2 − − 0 ( 2 1 d ) = − 0 v v ( 1 d ) = − v v ( 1 d ) 12 12 12 2 23 23 2 d � 4) Damage evolution law: 12 Y = d d Damage ↔ energy release rate Y 0 5) Combination: micro/plasticity and � damage 21
Damage evolution law σ x , MPa � ± 60 Damage Damage 0 Y onset ( ) 12 onset γ = − d 1 12 12 ε , % Y x 12 ∂ d 1 ( ) ( ) ( ) ( ) 2 0 0 0 0 2 0 2 = − ε ε − + ε + ε + γ + γ Y 1 d C 1 d C C G G 12 2 22 22 22 2 11 12 33 13 12 12 23 23 ∂ d 2 12 In line with the assumptions of Zinoviev 22
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