Macroscale Finite Element Modeling Approach

A detailed 3D structural modeling was carried out because of its capability of realistic physical representation and in-plane, out-of-plane laminates behavior analysis. Total number of element of 131840 and 637608 for moderately dense and highly dense stitched laminates are meshed after convergence check. The finite element model of highly dense stitched and moderately densely stitched laminates with pertinent boundary condition is shown in fig. 3.4. Laminates grip has been represented by constraining the specimen in y and z direction and its rotational directions. Force has been applied on x-directions.

Moreover, modeling with stitch has been given importance in this analysis to study the effect of the stitch on laminates. Interfaces between matrix and stitch yarns are modeled

y

x

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by contact capabilities. Together with 3D modeling, Puck‟s failure theory can incorporate post-failure analysis. In this analysis, post failure analysis has been carried out to quantization of transverse crack density.

The commercial MSC Nastran/Patran has been incorporated for the analysis with user defined subroutine. Laminate finite element modeling technique imbedded has been customized to model the laminate ply-by-ply, so as to obtain global and localized stress-strain distribution. On the conventional process laminate formulation, different stacking sequences are defined within a single element through thickness. The user interface facilitates to define stacking sequence of each individual lamina of the laminate in a single element with material properties. While in this formulation, each lamina in laminates is modeled with single element through thickness. In this formulation, lamina properties have been assigned separately layer-by-layer.

Multilayered laminates have been modeled with orthotropic material definitions for each lamina. Material properties for composites are illustrated on Table 3.1. Fiber and epoxy properties have been illustrated on Table 3.2. This approach transfers laminate definition based on material properties to lamina geometric orientation defined by

Fig 3. 4 Load and boundary condition of 6x6 Stitched and 3x3 stitched laminates

F

F

F

F

Constrain 2,3,4,5,6 Constrain 2,3,4,5,6

Constrain 2,3,4,5,6

Constrain 2,3,4,5,6

y

x

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stacking sequence; while nodes in between lamina have been shared. The solid shell element has been generated for composite laminate and stitches individually. Staking sequence of [+45/90/-45/02/+45/902/-45/0]s has been defined layer by layer of the laminate. It is to be noted that for the computational ease laminates has been modeled and analyzed with half-symmetry through the laminate thickness.

Unstitched 6x6 Stitched 3x3 Stitched Vectran 200d

(Homogeneous) (Homogeneous)

Table 3. 1 Material Properties T800SC-24k

Volume fraction (%) 45 47 49 -

Longitudinal Modulus (GPa) Ex 133.9 53.46 55.34 75

Transverse Modulus (GPa) E_y 8.389 53.46 55.11 3

Out-of-plane Modulus (GPa) Ez 8.431 18.01 17.25 3

In-plane Shear Modulus (GPa) G_xy 9.879 14.52 16.23 5 Out-of-plane Shear Modulus (GPa) Gxz 9.902 6.94 6.99 5 Out-of-plane Shear Modulus (GPa) Gyz 4.790 6.94 7.04 5

Poisson's ratio ϑxy 0.347 0.151 0.182 0.3

Poisson's ratio ϑxz 0.329 0.205 0.202 0.012

Poisson's ratio ϑyz 0.472 0.205 0.201 0.3

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Table 3. 2 Material Properties T800SC-24kf and Epoxy XNR

Fiber Tensile Strength (MPa) 5490

Fiber Compressive Strength (MPa) 2600

Matrix Tensile Strength (MPa) 0.8

Matrix Compressive Strength (MPa) 0.5

For the modeling of stitches, the emphasis has been placed on properly characterizing the stitching process. The stitching process consists of inserting a needle and carrying a stitch thread through a stack of fabric layers. Fibers are arranged along two axial lines, and a series of stitch yarn with predefined pitch are thrust into the fiber layers¹⁹. During the stitch modelling it has been idealized. Stitch fiber on z-direction has been modelled.

Stitch knot and bobbin thread has been ignored for the computational ease. Fig 3.5 illustrates the finite element modelling of the stitch thread on stitched laminates.

Bobbin Thread Stitch Knot

Needle Thread

x z y

Stitching

Fig 3. 5 Stitch modelling

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Further, stitch and laminates are discretized in the model. Vectran stitch has been represented by homogeneous solid element. Interfaces between matrix and stitch yarns are assumed to be perfectly glued and are modeled by the type of contact capability.

Subroutine has been defined for the definition of the contacts in between the stitch element and composite in-plane elements. The node-to-surface algorithm of contact detection is adopted to represent contact on the deformable body. Contact is assumed to occur when the element surface penetrates one of the target segment elements on the specified target surface. The finite element formulation for separation and sliding on contact of finite amplitude between three dimensional deforming bodies are based on penalty method.

Fig 3.6 defines the contact between the stitch nodes and composite elements. Stitch elements have finer mesh than the composite mesh. These stitch outer element nodes are in contact with the composite element surface. During subroutine definition stitch nodes

Fig 3. 6 Stitch and composite modelling by contact

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are defined as slave and composite nodes as master elements. The gap between these nodes and surface are assumed to be 0.5 mm. Subroutine for stitched laminates are highlighted as below.

User Defined Subroutine for Varied Density Stitched Laminates

$ Direct Text Input for Nastran System Cell Section NASTRAN SYSTEM(151)=1

NASTRAN SYSTEM(316)=19 SOL 400

CEND

BCONTACT = 0 SUBCASE 1

STEP 1

SUBTITLE=Stitchcontact ANALYSIS = NLSTATIC NLSTEP = 1

BCONTACT = 1 SPC = 2

LOAD = 1

DISPLACEMENT(PLOT,SORT1,REAL)=ALL

STRAIN(PLOT,SORT1,REAL,VONMISES,STRCUR,BILIN)=ALL STRESS(PLOT,SORT1,REAL,VONMISES,BILIN)=ALL

NLSTRESS(PLOT,SORT1)=ALL BOUTPUT(SORT1,REAL)=ALL BEGIN BULK

PARAM PRTMAXIM YES

BCPARA 0 NLGLUE 1 IBSEP 1 FTYPE 6 PARAM LGDISP 1

NLSTEP 1 1.

GENERAL 10 1 10

ADAPT .05 1.-5 .05 4 1.2 0 6 2.-4 MECH PV PFNT .2 BCTABL1 0 8001

BCONECT 8001 3001 2 1

BCONPRG 3001 IGLUE 2 ISEARCH 1

$ Deform Body Contact LBC set: composite

BCBODY1 1 5001 3D DEFORM 18 BCBDPRP 5001 FRIC .3

$ Deform Body Contact LBC set: sttitch

BCBODY1 2 5002 3D DEFORM 19 BCBDPRP 5002 FRIC .3

BCPROP 19 11 ENDDATA

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3.4. Results and Discussions