failure mechanisms in twill-weave laminates: fem predictions vs. experiments by

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

Outline

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

• Introduction e motivation

• Related works

• Twill-weave laminate chacterization

• Finite element modeling

• Experimental observations and computational results

• Conclusions


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Motivation

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

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.

Related Modeling Work

• Analytical approach

T.W. Chu et al (1983 - )N.K. Naik et al (1991 - )


• 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.

• Finite element approach

J. Whitcomb et al. (1990-1998)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.

K. Schulte et al (1988 - )J.C. Abry et al. (1998)

Electrical resistance method applied to unidirectional composites


Related Experimental Work


Material and Experiments

Fiber: Toray T-300 carbon fibersFiber diameter: 7 μmFiber volume fraction Vf: 42%Density ρ: 1.76 g/cm2

Strength u3200 MPaElastic modulus E: 228 GPa

Matrix: Epoxy Hexcel 1990S

LaminateLay-up: 8-plyTexture: Twill-weaveYarns: 3k fibersWarp 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

0° direction


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 6.15All dimensions in mm

COMPTEST 2003 Chalons en Champaign G. Nicoletto & E. Riva

Tensile Tests and Evolution of Electrical Resistance

Strain

Norm. elect. resistance vs. strain

Stre

ss (

MP

a)

(R-R

0)/R

0

Stress vs. strain

Twill-weave laminates


Damage Observations

Fill yarn Tow yarn

Epoxy

Fiber fracture Fracture in yarn


Damage Mechanisms: a Summary

• 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

Inter-ply delamination

Crack in fill yarn

Delamination between orthogonal

yarns

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



Texture and Representative Volume RV

Material models:

• Yarn: transverse isotropic, linear elastic

• Matrix: linear elastic

RV

Twill-weave


Finite Element Modeling of RV

• Parametric geometrical model (I-DEAS)

• Finite element code (ABAQUS)

• Convergence study

• Optimized model: > 30000 elements

• Geometric nonlinearity included

• Progressive damage evolution routine in FORTRAN


Boundary conditions on RV

Post, Han and Ifju (1994)

)x(u~xExu)x(u 0

Carvelli & Poggi (2001)

where

u(x) is the displacement field in the RVu0 is a rigid displacement of the RV is a small rigid rotation of RVE is the average strain (macroscopic)

of RVũ(x) is a periodic displacement associated

to microscopic strain field within RV

Free surface

Damage Modes for Fiber Yarn


M. Zako et al (2003)


Modeling Damage Development

Blackketter et al (1993)Discount method

• 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.

Effect of Texture on Longitudinal Stiffness


• 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.

Plain weave

Twill weave

Lamina

Thick laminate


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.

Stresses and Damage


0

200

400

600

800

0 0.4 0.8 1.2 1.6

Strain (%)

Str

ess

(MP

a)

ab

cd 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.


0

200

400

600

800

0 0.4 0.8 1.2 1.6

Strain (%)

Str

ess

(MP

a)

ab

cd 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.

Stresses and Damage


0

200

400

600

800

0 0.4 0.8 1.2 1.6

Strain (%)

Str

ess

(MP

a)

ab

cd 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.

Stresses and Damage


0

200

400

600

800

0 0.4 0.8 1.2 1.6

Strain (%)

Str

ess

(MP

a)

ab

cd 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.

Stresses and Damage


Inter-ply delamination

Crack in fill yarn

Delamination between orthogonal

yarns

Qualitative Correlation

Experimental

Computational

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.

failure mechanisms in twill-weave laminates: fem predictions vs. experiments by

Documents

twill weave

twillweave laminates

plain weave

plainweave texture

stiffness of woven laminates

orthogonal yarns

direction texture

finite element method