Modeling Formation and Bonding of Wood Composites

Transcription

1 Modeling Formation and Bonding of Wood Composites Chunping Dai FPInnovations Forintek Division Vancouver, Canada October, 2007

2 Empirical Approach vs Modeling Trial-and-Error Approach Advantages: - Simple - Direct Disadvantages: - Time consuming - Expensive - Lack of fundamental understanding Modeling offers a new approach to advancing the science of wood composites, by applying mathematics, physics, mechanics and computer simulation to the field of wood science.

3 Objectives To develop basic theories and models for wood composites, particularly: - Mat formation, - Mat consolidation, - Hot pressing, and - Bonding.

4 Model Development: Theory and Methodology

5 Mathematical Modeling ρ 1. Rectangular Strand Shape 2. Layered Structure: 2D Model Legend Void area 1-strand area 2-strand area 3. Random Formation 3-strand area Strand crossing length Theories: Geometric Probability and Statistics, Material Science, Physics, Mechanics and Thermal Dynamics.

6 Computer Simulation 1. Irregularity of Strands 2. Strand Orientation Machine Direction 3. Machine Induced Non-Randomness Methodology: Discrete Object Simulation, Monte Carlo Simulation, FD/FE Method, Computer Graphics and Programming

7 Key Results: Fundamentals of Composite Manufacturing

8 Mat Formation: A Stochastic Network of Wood Strands p( i) a A e n n i! i i = = and n = C T r r

9 Mat Formation: Horizontal Density Distribution # of Overlaps Dˆ a a 2a 2 D Var( Dˆ ) = η( r; λ, ω) n 0 p( r, a) dr

10 Mat Formation: Size Effect on Variability Density (g/cm 3 ) Maximum, ˆD max Average, D Minimum, ˆD min Experiment Simulation Specimen size, a (mm) Theoretical basis for analyzing mat formation uniformity

11 Mat Consolidation: Compression Mechanics of Wood and Porous Strand Structure stress (x1000 psi) σ = ϕ( ε )Eε Wood Strand i -n n σ n = E e ϕ( ε i ) ε i i=t/ τ i! strain Mat f(t, MC) Theoretical basis for modeling pressing and vertical density profile stress (MPa)

12 Mat Consolidation: Porosity Variations Total Void Inside-strand Void Between-strand Void Porosity φ i t = 1 t ρ ρ φ = φ φ φ = f ρ / ρ ; λ, ω, τ ) b ( m w m c b Mat Density (kg/m 3 )

13 Mat Consolidation: Inter-element Contact Development Relative Contact Area Math model Computer Simulation Mat Density (kg/m 3 ) 100 x 25 x 0.75 (mm) mm

14 Mat Consolidation: Permeability (k) Thickness k Tortuosity = c τ 2 e φ 3 b ( 1 φb ) 2 Porosity f(d; λ, ω, τ) Theoretical basis for linking strand dimensions to hot pressing

15 Computer Simulation of Hot Pressing: Temperature

16 Computer Simulation of Hot Pressing: Moisture Content

17 Computer Simulation of Hot Pressing: Gas Pressure

18 Computer Simulation of Hot Pressing: Vertical Density Profile

19 Modeling Wood Composite Bonding [σ] IB E, σ, [σ] A Spring Field Model iτ β i R a Surface Contact Resin Coverage Spring Element E i, σ i, [σ] i a i Localized Strand Column E i, σ i, [σ] i Inter-strand Bonding [σ] w Wood Strength

20 Resin Distribution: Resin Coverage Content Relationship Ideal Resin Area Coverage, R a (%) R i a = 2 (1 + τρsrc MC) τ ρ R r r solid R r a = 1 Loss to overlap exp( R i a ) Real Resin Content, R c (%) 15 20

21 Bonding Strength between Two Wood Strands 2.5 Bonding strength (MPa) IB (MPa) Model Experiment Compaction ra tio

22 Internal Bond (IB) Strength of OSB Internal Bond (IB) Strength (MPa) Model Prediction Experimental Data Panel Density (g/cm3)

23 Predicted Effect of Strand Thickness on IB IB Strength, [σ] IB (MPa) Strand Thickness, τ 0 (mm) Panel Density (kg/m 3 )

24 Predicted Effect of Wood Density on IB IB strength, [σ] IB (MPa) Wood Density, ρ w (kg/m 3 ) Panel Density (kg/m 3 )

25 Summary Analytical and computer simulation models are developed which can predict: mat formation, consolidation, hot pressing and bonding of wood composites. The results improve the fundamental understanding of processing characteristics and performance of wood composites. The proposed theories and methodologies open a new path for research and education in wood composites.

26 References He, G., Yu, C., Dai, C Theoretical modeling of bonding characteristics and performance of wood composites. Part 3: Bonding strength between two wood elements. Wood and fiber science. 39(4): Dai C. Yu C. and Zhou, C Theoretical modeling of bonding characteristics and performance of wood composites: Part 1. Inter-element contact. Wood and Fiber Science. 39(1): Dai C., Yu C, Groves K. and Lohrasebi H Theoretical modeling of bonding characteristics and performance of wood composites: Part 2. Resin distribution. Wood and Fiber Science. 39(1): Dai, C. C. Yu, C. Xu and G. He Heat and mass transfer in wood composite panels during hot pressing: Part IV. Experimental investigation and model validation. Holzforschung. 61(1): Dai, C., Yu, C. and Zhou, X Heat and mass transfer in wood composite panels during hot pressing: Part 2. Modeling void formation and mat permeability. Wood and Fiber Science. 37(2): Dai, C. and C. Yu Heat and mass transfer in wood composite panels during hot pressing: Part 1. A physical-mathematical model. Wood and Fibre Science. 36(34): Dai, C Viscoelastic behaviour of wood composite mats during consolidation. Wood and Fibre Science. Vol.33, No.3: Dai, C. and Steiner, P.R On horizontal density variations in randomly-formed short-fibre wood composite boards. Composites Part A. 28(A): Dai, C. and Steiner, P.R Spatial structure of wood composites in relation to processing and performance characteristics. Part III. Modelling and simulation of a random multi-layered flake mat. Wood Science and Technology. Vol.28, No.3: Dai, C. and Steiner, P.R Compression behaviour of randomly-formed wood flake mats. Wood and Fibre Science. Vol.25, No.4: