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**Failure Mechanisms in Twill-weave Laminates: **

FEM Predictions vs. Experiments by Gianni Nicoletto and Enrica Riva Dipartimento di Ingegneria Industriale Università di Parma Parma, Italy COMPTEST 2003 Chalons en Champagne, France Jan. 28, 2003

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**Outline Introduction e motivation Related works**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Outline Introduction e motivation Related works Twill-weave laminate chacterization Finite element modeling Experimental observations and computational results Conclusions

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**Motivation Cooperation with Dallara Automobili F3 racing car**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Motivation Cooperation with Dallara Automobili F3 racing car IRL racing car Infinity Pro CFRP Chassis

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**Woven Composites Definitions Advantages**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Woven Composites Definitions Yarns: bundle of thousands fibers Warp yarns: parallel to load direction Fill yarns: perpendicular to load direction Texture: plain weave, twill weave, etc. Crimp ratio: degree of yarn curvature Advantages With respect to unidirectional laminates: Easier handling and shaping Improved impact resistance Superior out-of-plane stiffness Balanced in-plane mechanical properties Cost competitive yarn

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**COMPTEST 2003 Chalons en Champagne G. Nicoletto & E. Riva**

Objectives of the work Develop a finite element-based modeling approach to the mechanics of woven laminate composites. Compare modeling results and experimental observations. Analyze the role of texture on mechanical performance. Develop tools for monitoring damage development in woven laminates.

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**Related Modeling Work Analytical approach T.W. Chu et al (1983 - )**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Related Modeling Work Analytical approach T.W. Chu et al ( ) N.K. Naik et al ( ) Models, such as mosaic, crimp and bridging models subjected to iso-strain or iso- stress conditions, predict adequately the stiffness of woven laminates. These models are less satisfactory for strength prediction and micromechanical stress determination. Convenient approach for texture design. The plain-weave texture has been mainly considered.

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**Finite element approach V. Carvelli and C. Poggi (2001)**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Finite element approach J. Whitcomb et al. ( ) V. Carvelli and C. Poggi (2001) D. Blackketter et al. (1993) Computational prediction of the mechanics of woven laminate composites. The finite element method is used to geometrically model an elementary cell of the woven laminate. Boundary conditions enforcing stress and strain periodicity are imposed to the representative volume (RV) . Stress-based damage and stiffness discount technique to model damage progression. Most studies deal with the plain-weave texture.

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**Electrical resistance method applied to unidirectional composites**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Related Experimental Work K. Schulte et al ( ) J.C. Abry et al. (1998) Electrical resistance method applied to unidirectional composites

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**Material and Experiments**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Material and Experiments 0° direction Fiber: Toray T-300 carbon fibers Fiber diameter: 7 μm Fiber volume fraction Vf: 42% Density ρ: 1.76 g/cm2 Strength su= 3200 MPa Elastic modulus E: 228 GPa Matrix: Epoxy Hexcel 1990S Laminate Lay-up: 8-ply Texture: Twill-weave Yarns: 3k fibers Warp and fill yarns: Identical Laminate thickness: 2.4 mm Tensile tests according to: ASTM D3039 Servo-hydraulic testing machine: MTS 810 Resistance strain gages & Extensometer Electric resistance measuring apparatus

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**Geometrical Characterization of Twill-weave Texture**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Geometrical Characterization of Twill-weave Texture Yarn shape: circular arcs Ply stacking: random a b g RT RL 2.04 0.17 1.13 6.11 6.15 All dimensions in mm

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**Tensile Tests and Evolution of Electrical Resistance**

COMPTEST Chalons en Champaign G. Nicoletto & E. Riva Tensile Tests and Evolution of Electrical Resistance Strain Norm. elect. resistance vs. strain Stress (MPa) (R-R0)/R0 Stress vs. strain Twill-weave laminates

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**Damage Observations Fill yarn Tow yarn Epoxy Fiber fracture**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Damage Observations Fill yarn Tow yarn Epoxy Fiber fracture Fracture in yarn

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**Inter-ply delamination Delamination between orthogonal yarns**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Damage Mechanisms: a Summary Inter-ply delamination Crack in fill yarn Delamination between orthogonal yarns Final longitudinal fiber fracture is preceeded by a number of mechanisms. Matrix cracks develop in fill yarns. Delamination occurs between orthogonal yarns. Inter-ply delamination is observed

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**Homogeneization Method for Composite Materials**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Homogeneization Method for Composite Materials Assumption of periodic microstructures which can be represented by unit cells Asymptotic expansion of all variables and the average technique to determine the homogeneized (macroscopic) material properties and constitutive relations of composite materials Prediction of microscopic fields of deformation inside the unit cell through the localization process

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**Texture and Representative Volume RV**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Texture and Representative Volume RV Material models: Yarn: transverse isotropic, linear elastic Matrix: linear elastic Twill-weave RV

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**Finite Element Modeling of RV**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Finite Element Modeling of RV Parametric geometrical model (I-DEAS) Finite element code (ABAQUS) Convergence study Optimized model: > elements Geometric nonlinearity included Progressive damage evolution routine in FORTRAN

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**Boundary conditions on RV**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Boundary conditions on RV Free surface Carvelli & Poggi (2001) where u(x) is the displacement field in the RV u0 is a rigid displacement of the RV W is a small rigid rotation of RV E is the average strain (macroscopic) of RV ũ(x) is a periodic displacement associated to microscopic strain field within RV Post, Han and Ifju (1994)

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**Damage Modes for Fiber Yarn**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Damage Modes for Fiber Yarn M. Zako et al (2003)

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**Modeling Damage Development**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Modeling Damage Development Discount method Blackketter et al (1993) Iterative procedure. Evaluation at each integration point. Normal stress criterion for failure. Elastic modulus is reduced to 1/10 of its initial value. Role of time step and mesh size.

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**Effect of Texture on Longitudinal Stiffness**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Effect of Texture on Longitudinal Stiffness Plain weave Twill weave Lamina Thick laminate Strong influence of crimp ratio on stiffness. Good correlation with experimental results. A thick laminate is stiffer than a single lamina. At high crimp ratios the twill-weave is stiffer than the plain- weave.

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**Effect of Crimp Ratio on Stress-Strain Curve**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Effect of Crimp Ratio on Stress-Strain Curve Strong influence of crimp ratio on stress-strain curve. Good correlation with experimental results. Low crimp ratio shows a trend linear to failure. Influence of computational parameters.

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**Stresses and Damage Step a a d c b**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Stresses and Damage a b c d Step a The critical stress is perpendicular to the fill yarn surface. The wedge elements of the straight portion of the fill yarns fail first. Initial damage occurs near the fill yarns. The critical stress is representative of damage initiation in the matrix.

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**Stresses and Damage Step b b d c a**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Stresses and Damage a b c d Step b The critical stress direction does not change. It is perpendicular to the fill yarn surface. Damage continues in the fill yarns. Damage now involves the brick elements next to the wedge elements. The damage spreads into the matrix.

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**Stresses and Damage Step c c d b a**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Stresses and Damage a b c d Step c The wedge elements, where the two perpendicular yarns are close to each other, fail. Fiber failure occurs in the fill yarn. Failure occurs where the yarn is curved to the maximum.

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**Stresses and Damage Step d d c b a**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Stresses and Damage a b c d Step d Failure extends to the neighboring brick elements up to final catastrophic collapse. In this final stage different failure modes are activated such as transverse and longitudinal shear, and transverse direct stress.

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**Inter-ply delamination Delamination between orthogonal yarns**

COMPTEST Chalons en Champagne G. Nicoletto & E. Riva Qualitative Correlation Experimental Inter-ply delamination Crack in fill yarn Delamination between orthogonal yarns Computational

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**COMPTEST 2003 Chalons en Champagne G. Nicoletto & E. Riva**

Conclusions Optical inspection of a twill-weave laminate during tensile testing showed different damage mechanisms. Finite element modelling of an appropriate RV provided the macroscopic stress-strain relation of a woven laminate that were compared to experimental results. The finite element model of the RV provided the microscopic stresses and strains within matrix and reinforcements. An iterative procedure based on a damage routine has been developed to simulate damage evolution. A first correlation between experimental observations and computed damage evolution in a twill-weave laminate is encouraging.

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