Macro-Scale Modeling For Structural Analysis

Plain weaves stitched composites as explained on section 4.2 have been considered at macro-scale. Laminates with stitch along longitudinal and transverse direction are modelled with solid shell elements for structural-macroscopic analysis. During the macroscopic modeling, it is impractical to model microscopic details as shown in fig.

4.4 using unit cell modeling. However, a single micro-block configuration can be used

65

as an assembling unit for different types of the macroblock patterns and the macro-block to represent the laminate structure⁶¹. A macro-block, which represents the majority of

the structure, is used to represent woven characteristics. Straight cross ply micro-block, which represent majority of the structure has been modelled considering woven characteristic. Thus, a single solid through-thickness element has been adopted that represents the warp and weft yarn. These elements have been so arranged at 0° and 90°

so that the internal orientation will represent the combined overall effect of the lamina.

Additionally, certain assumptions have been made to cope with the complexity of architecture:

• The plain weave woven fabrics are assumed to be balanced; i.e., the woven fabric unit cell, fiber volume fraction and mechanical properties along the warp direction are identical to those in the weft direction.

• The warp and weft tows are packed perfectly, and the void of resin and nesting resin on the interlacing areas between warp and weft tows are ignored.

Fig 4. 4 Schematic of plain weave woven composite laminates (i) warp and weft tows

arrangement (ii) cross-section of unit cell (iii) micro-structures of unit cell (a) void/pure resin (b) undulated (c) straight cross ply

(iii) (a)

(b)

(c)

(ii) (i)

66

• The macro-structure of woven fabric is orthotropic and homogeneous.

• All lamina undergo the same deformation.

3D structural modeling and finite element analysis have been carried out for stitched laminates because of their capability to achieve realistic physical representation and in-plane and out-of-plane laminate behavior analysis. A detail modeling approach with stitching has been incorporated because the idealized model has been reported to overestimate the strength^{1, 2}. Puck‟s failure theory has been incorporated into the failure analysis.

The finite element model of unstitched, transversely and longitudinally stitched open-hole laminates with pertinent boundary condition to experimental condition with a fine mesh after convergence is as shown in fig 4.5. Specimen was grip at 50mm on either ends, thus it has been represented by constraining translation on y and z direction and constraining rotation on x, y & z. Tensile forces have been applied at the end of the structure along x direction. Open-hole laminates consists of maximum element number of 115120 and node number of 158562.

F

Grip (Constrain on 2,3,4,5,6)

Grip (Constrain on 2,3,4,5,6)

Grip (Constrain on 2,3,4,5,6)

Grip (Constrain on 2,3,4,5,6)

F

Grip (Constrain on 2,3,4,5,6)

F

Loading Direction

F

F

Loading Direction

Loading Di ection Grip (Constrain on 2,3,4,5,6)

F

Fig 4. 5 Loading and boundary conditions for open-hole laminates x

y

67

The commercial MSC Nastran/Patran has been incorporated for the analysis with user

subroutine. During this analysis, a single element per lamina has been employed, in contrast to defining a laminate stacking sequence in a single element through the

thickness. In this formulation, lamina properties have been assigned separately in a layer-by-layer manner. The user interface can be used to define the stacking sequence of all lamina of the laminate in a single element with the relevant material properties. The multi-layered material definition for each lamina is shown in Table 4.1 and Table 4.2.

This approach transfers the laminate definition based on the material properties to the lamina geometric orientation defined by the stacking sequence. Nodes between the lamina are shared. It is to be noted that for the computational ease laminates has been modeled and analyzed with half-symmetry on xy in-plane axis as in fig.4.5. This modeling is limited to plain weave woven composites.

Kevlar-29 T300-3k Table 4. 1 Material properties

Volume fraction (%) - 59

Longitudinal Modulus (GPa) E_x 70.5 139.18

Transverse Modulus (GPa) Ey 2.59 9.71

Out-of-plane Modulus (GPa) Ez 2.59 9.71

In-plane Shear Modulus (GPa) G_xy 2.17 5.58

Out-of-plane Shear Modulus (GPa) Gxz 2.17 5.58

Out-of-plane Shear Modulus (GPa) G_yz 2.17 3.76

Poisson's ratio ϑxy 0.36 0.29

Poisson's ratio ϑxz 0.0132 0.02

Poisson's ratio ϑyz 0.36 0.40

68

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 fiber layers¹⁹. Henceforth, stitching and laminates are discretized in the model.

Stitches are represented by a homogeneous solid element. Interfaces between matrix and stitch yarns are assumed to be perfectly glued and are modeled by the type of contact capability. The node-to-surface definition 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. Fig. 4.6 shows the finite element modelling of stitch on open-hole stitched laminate with contact.

Fig 4. 6 Stitch modelling on open-hole laminates

69

The finite element formulation for separation and sliding on contact of finite amplitude between three dimensional deforming bodies are based on penalty method. Fig 4.7 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 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.

Fig 4. 7 Stitch and composite modelling by contact

70

User Defined Subroutine for Open-hole Stitched Laminates

$ Direct Text Input for Nastran System Cell Section NASTRAN SYSTEM(316)=19

SOL 400 CEND

BCONTACT = 0 SUBCASE 1 STEP 1

SUBTITLE=0penholecontact ANALYSIS = NLSTATIC NLSTEP = 1

BCONTACT = 1 SPC = 2 LOAD = 2

DISPLACEMENT(SORT1,REAL)=ALL

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

NLSTRESS(SORT1)=ALL BOUTPUT(SORT1,REAL)=ALL

BEGIN BULK

PARAM PRTMAXIM YES

BCPARA 0 NLGLUE 1 IBSEP 3 FTYPE 6 PARAM LGDISP 1

NLSTEP 1 1.

GENERAL 10 1 10

ADAPT .1 1.-5 .5 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 BCTABL1 1 8001

$ Deform Body Contact LBC set: composite

BCBODY1 1 5001 3D DEFORM 5 BCBDPRP 5001 FRIC .3

$ Deform Body Contact LBC set: stitch

BCBODY1 2 5002 3D DEFORM 6 BCBDPRP 5002 FRIC .3

ENDDATA

71

4.4 Result and Discussions