Why model single fibre tests?

Transcription

1 Finite Element Modelling of Tensile Tests of Geometrically Well Characterized Single Wood Fibres Kristofer Gamstedt, KTH Fibre and Polymer Technology Dennis Wilhelmsson, Semcon Cristian Neagu, EPFL Laboratory of Polymer and Composite Technology Stig Bardage, SLU Department of Forest Products Why model single fibre tests? How can modelling be of assistance in analysis of data from single fibre tests? Data reduction from structural behaviour to material (cell wall) properties p Compare bottom up simulations with experimental results 1

2 Structurevs. material properties Geometry dependency! Careful data reduction Hull and Clyne, An Introduction to Composite Materials, 1996 Uniform stress state: Load displacement stress strain Bottom up simulations for deeper understanding 1. MD simulations of wood polymers. Micromechanics, homogenization 3. Numerical simulation of fibre 4. Comparison with experimental tests Burgert et al. (005)

3 Hierarchical structure of wood Cell wall model Brändström (00) Chemical constituents Panshin and de Zeeuw (1980) Microscopy and 3D reconstruction Longitudinal tracheids in softwood Stig Bardage (001) 3

4 Parameterization and 3D reconstruction: 3 examples of Norway spruce latewood Segment 1 60 µm Segment 380 µm Segment 3 80 µm Elastic properties of the cell wall layers Cellulose Hemicellulose Lignin Plausible elastic properties and volume fractions Micromechanical model (Hashin 1979) Equivalent elastic properties for each layer S1 layer: E 11 = 31.7 GPa E = E 33 = 4.1 GPa S and S3 layers: E 11 = 7.5 GPa E = E 33 = 6.4 GPa 4

5 Elastic properties of the cell wall layers S S1 S3 Thickness fractions: S1 = 6.8 % S = 90.9 % S3 =.3 % The finite element models Shell Solid Sub 5

6 The finite element shell model Thickness definition with script on an element to element basis The shell model Material orientation 6

7 The solid model Volume regions (S) Meshing Offset meshing S1, S3 7

8 The solid model Material orientation S1 = 80 S = 0 S3 = 50 Elastic properties at tensile loading Comparison shell / solid elements Tensile stiffness as load at 1% axial strain Two different boundary conditions: free & constrained rotation Parametric studies with MFA 0 45 in S Comparison with an analyticalmodel 8

9 Animation MFA 10 free Animation MFA 10 constrained 9

10 Analytical modelling (Tarn and Wang, 001) Assumptions Fiber as an assembly of coaxial ilhollow orthotropic t cylinders MFA is constant though the thickness of any one layer of the fibre cell wall Same input data as in finite element model Dimensions averaged from geometrical data INPUT DATA CONSTITUENT S3,S,S1 CELL WALL Cellulose Hemicellulose Lignin C H L E 11 (GPa) E (GPa) Homogenization L H C Analytical G 1 (GPa) ν 1 (-) ν 3 (-) β 11 (-) β (-) Sakurada et al. (196) Cousins (1976,1978) Tashiro and Kobayashi (1991) Nakamura et al. (004) Cave (1978) Volume C H L fraction S3, S S Layer MFA ( ) Thickness fraction S S +(0-50) 87 S Persson (000) Fengel and Stoll (1973) Brändström (00) Brändström et al. (003) Abe et al. (199) Bergander et al. (00) 10

11 Stiffness analytical model Page et al. (1977) Wood Composite Paper Stiffness of segment 1 Segment 1 11

12 Stiffness of segment Segment Stiffness of segment 3 Segment 3 1

13 Difference between analytical and FE modelling results Stress analysis and failure prediction Submodelling technique Stress distributions in three cross sections (TFS1) Stresses in the fibril direction Tsai Hill Failure criterion Parametric studiesfor both loadcases cases, MFA 0 40 Animation stress field in a tensile loaded fibre 13

14 From solid to solid submodel 10 µm long subsegment 14

15 Tsai Hill failure criteria σ ˆ σ σ1σ ˆ σ σ + ˆ σ τ + ˆ τ 1 1 = Stress analysis and failure criterion Page et al. (1973) Axial: σ 3u = 1.64 GPa Transverse: σ u = 144 MPa Shear: τ 3u = 91 MPa Failure initation? 15

16 Tsai Hill failure criterion, MFA 10 The effect of structural inhomogeneities The effect of circular pits Comparison with an analytical model 16

17 TFS Submodelling Stress distribution in an infinite orthotropic plate with a circular opening (Lekhnitskii) E σθ = p E + θ 1 ( [ cos ϕ + ( k + n)sin ϕ] [(1 + n)cos ϕ k sin ϕ] sin θ n(1 + k + n)sinϕ cosϕ sinθ cosθ k cos θ ) P P Polar plot of the stress concentration factor 17

18 Stresses in the fibril direction (σ 11 )MFA 30 P K FEM = 5.3 P K analyt = 6.0 Concluding remarks Modelling of single fibre testing can be useful to. quantify effects of structural inhomogeneity accurately estimate cell wall properties from tensile test data bottom up modelling to connect molecular dynamic simulations with micromechanically measureable properties Features addressed by modelling related to single fibre testing: effects of rotational constraint stress analysis for failure prediction stress concentation from bordered pits 18

19 Materials design on various length scales Polymer Species Earlywood Interfacial bonding Latewood Defibration Impregnation Fibre orientation Aspect ratio Delignification Wood mechanics in an engineering context Hot pressing 3D form Flat Parametric design models Microfibril angle Modification Models at macroscale (continuum) FEEDBACK Models at nano and microscale (micromechanics) Welcome the Working Group Discussion on Modelling (WG3) Today in place How could modelling be of best use? Forum for relevant and focussed discussions 19