Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells Numerical simulation of composites using commercial FE softwares
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 3 Numerical simulation of composites using commercial FE softwares
Overview of Composites Composites are hybrid materials in which two or more substances with very different physical and chemical properties, are combined to achieve a new superior material. Heterogeneous Composition Unlimited possibilities Why we use them? Any characteristic material behaviour 4 - High specific strength - Increased toughness - Material can be tailored - Excellent chemical and weather resistance - Modified electric, thermal, optical and magnetic behaviour. - Cost effectiveness - repairability - etc
Types of Composites - Natural Composites: Wood, bones, stones etc - Man-made Composites: - Fibre reinforced composites, particle reinforced composites (particulate composites). Example: CFRP, GFRP - polymer matrix composites (or polymer composites), metal matrix composites and ceramic matrix composites - Laminated composites, sandwich Structures 5
Applications of Composites - should have low density and, at the same time, should be very stiff and strong Aerospace Applications Structural Marine and Mechanical Sports 6
The topics covered include: Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 7 Numerical simulation of composites using commercial FE softwares
Micromechanics vs. Macromechanics Micromechanics Predicting mechanical behaviour of a composite material in terms of its constituent materials Macromechanics Predicting mechanical behaviour of a composite material considering it to be a homogenized material 8
Micromechanics Theory Composites Matrix +Fibres (Constituent materials) Properties mechanical and hygrothermal properties Properties RVE Mathematical Analyses -Rule of Mixtures Properties of Composites 9 Theoretical Prediction of Behaviour of Composites
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 10 Numerical simulation of composites using commercial FE softwares
Properties of Composites (Micromechanics Theory) General properties of Unidirectional Composites Longitudinal modulus, E 1 Major Poisson's ratio, ν 1 Transverse modulus, E Shear modulus, G 1 Coefficients of thermal expansion (CTE) Moisture Expansion (MTE) Matrix Fibre Matrix Constituent Materials: Fiber (Graphite, boron, Silicon): E f, ν 1, G f, and V f 11 Matrix (Resin): E m, ν m, G m,v m Assumptions in Micromechanics of Composites?
Properties of Composites (Micromechanics Theory) What we know... (properties of individual fibres and matrix) Elastic Modulus Volume fractions 1 1 What is the elastic modulus of the composite?
Representative volume element (RVE): Model RVE Simplified model t t t 1=V f + V m V f, V m : fiber and matrix volume fraction
Properties of Composites Matrix Fibre Matrix Fibre 14 Rule of Mixtures
Strength Properties of Composites - level of stress at which failure occurs - material constant We know strength properties of fibres and matrix. What about the composites? x x x 1 X' 11t = X' 11f V f + X' 11m V m X c 1 / ( V V / )( V / 3V ) 11 f m m f f f m m x x x 1 15 t X [ 1 ( V V )(1 / )] X f f m f t m c X [ 1 ( V V )(1 / )] X f f m f c m
Hygrothermal Properties The change in properties due to moisture absorption and temperature change 1 We know hygrothermal properties of fibres and matrix. What about the composites? Longitudinal moisture diffusion coefficient of the composite d' 11 = d ' 11f V f + d' 11m V m Transverse moisture diffusion coefficient of the composite d d m [( d [( d f f d d m m ) ) ( d ( d f f d d m m ) V ) V f f ] ] Thermal expansion coefficients 16 11 11 f 11 f 11 f V V f f 11 m 11 m V 11 m m V m [ V V ] 33 1 f f 1 m m 11 f 11 f 11 f V V f f 11 m 11 m V 11 m m V m
Particulate and Short fibre composites Micromechanics Theory? 17
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 18 Numerical simulation of composites using commercial FE softwares
Macromechanical behaviour of composites Predicting mechanical behaviour of a composite material considering it to be a homogenized material Design of Composites! Constitutive Relations: 19
Isotropic composites Example: particle composite layer Characteristic: same material properties in all directions E, x 1 x x 3 Effective properties: 0 Elastic: E, Thermal expansion coefficient: Strength value: s u, t u
Orthotropic composites Example: unidirectional fiber composite layer The fibers are oriented in two mutually perpendicular directions x 1 x x 3 Effective properties (plane stress): Elastic: E 1, E, G 1, 1 1 Thermal expansion coefficient: 1, Strength value: s u 1, s u, t u 1
Anisotropic composites Example: short fibre composite layer, The fibres are oriented randomly or aligned in two non-orthogonal directions x 1 x x 3 Effective properties (plane stress): Elastic: : D 11, D, D 33, D 1, D 13, D 3 Thermal expansion coefficient: 1,, 1 Strength value: s u 1, s u, t u 1
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 3 Numerical simulation of composites using commercial FE softwares
Composite Laminate: DEFINITION A fibre composite laminate consists of thin, parallel, unidirectionally reinforced layers, which are firmly bounded together Each layer is usually represented as homogeneous anisotropic with effective properties of unidirectional material Composite Laminates are typically defined using: nr of layers, thickness, fibre orientation and layer material Heterogeneity is produced by the different orientations of the layers Fibres are no longer aligned with the applied stress!!! 4
GENERAL LAMINATES Constitutive Equation describes the stiffness matrix of a laminate 1 6 1 6 A A A B B B 11 1 16 11 1 16 A A A B B B 1 6 1 6 A A A B B B 16 6 66 16 6 66 B B B D D D 11 1 16 11 1 16 B B B D D D 1 6 1 6 B B B D D D 16 6 66 16 6 66 k k k 0 1 0 0 6 1 6 5 inplane, extension bending coupling and bending stiffness n ( Q ) ( z z ) ij ij k k k 1 k 1 1 B ( Q ) ( z z ) n ij ij k k k 1 k 1 1 D ( Q ) ( z z ) n 3 3 ij ij k k k 1 3 k 1
SANDWICH STRUCTURE: A composite construction, where a relatively thick core layer of low strength, stiffness and density is sandwiched between two thin, face layers of strong and dense materials face core 6 face adhesives
, Vibration and buckling analysis of laminated plates (7.65) Cross-ply laminations of stacking sequence [0/90] n 0 0 0 11 1,11 66 1, 1 66,1 11,111 A u A u ( A A ) u B w 0 0 0 0 1 66 1,1 66,11, 11, ( A A ) u A u A u B w 0 0 0 11,1111, 1 66,11 11 1,111, D ( w w ) ( D D ) w B ( u u ) q [ N ( w pw ) pw],11, 0 m x nx 1 A cos sin 1 mn u e a b 0 m x nx 1 u B sin cos e mn a b m x nx i w W sin 1 sin e mn a b i mnt i mnt mnt Governing Equations 7 4 m D m 11 4 D D m n 1 66 k pn n m n m n 4 D D D a b 6 3 3 3 6 6 B m H m n F n E 11 m n m n m n 4 D ( ) E H F m n m n m n 4 p b mn Nb mn 4 D k mn, D
, Vibration and buckling analysis of laminated plates Angle-ply laminations Governing Equations 4 m D m D D m n 11 1 66 4 k pn n m n m n 4 D D D 1 m m m N D D mn L M m n m n B 3B n 3 16 6 n B B n 16 6 k mn Nb D, 11 66 16 6 L ( m A n )( B m 3 B n ) mn mn p 4 mn D b 4 1 66 16 6 n ( )(3 B m B n ) 8 66 16 6 M ( m A n )(3 B m B n ) mn 1 66 16 6 m ( )( B m 3 B n ) a b mn mn mn mn N E H F
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 9 Numerical simulation of composites using commercial FE softwares
Laminates damage Laminate composite structure develop Matrix cracks Fibre-matrix debonds Fibre fractures Delaminations loss of stiffness and strength of the material! 30 Once the mechanical properties of the layers are known, the initial failure of a layers within a laminate or structure can be predicted by applying an appropiate failure criterion Failure criterion is used only to check whether allowables are exceeded
Composite (anisotropic ) failure criterion Layer failure index (F>1) Maximum stress criterion Maximum strain criterion Tsai-Hill anisotropic criterion: Bonding failure index 31 Global final failure index for composite element Maximum of all computed layer and bonding failure indices
Buckling Sudden large out-of-plane displacements occur when the critical value of the load is reached. Compressed bar Compressed isotropic plate b s c =KE(h/b) Linear Buckling Analysis (K-K G )U = 0 : smallest positive eigenvalue is associated with buckling, cr. K: Stiffness matrix, K G : geometric stiffness matrix 3 P cr = cr P ref Critical or buckling load
Delamination buckling Local delamination can be seen as a crack in the bond. Laminated plastic material possess fairly low bonding low velocity impacts and defects in manufacturing lead to local delamination 33 Delamination buckling can be considered as a classical linear problem of buckling of a strip with fixed ends
The topics covered include: OUTLINE Overview of composites and their applications Micromechanics theory for analysis of composites Properties (elastic properties, strength properties and hygrothermal properties) in (i) unidirectional composites and (ii) particulate and short fibre composites Macromechanical behaviour of composites Definition of composite laminates and sandwich structures; vibration and buckling analysis of laminated plates Laminate damage and failure criteria in composites Finite Element (FE) analysis for composites; Bending and vibration of Composites Shells 34 Numerical simulation of composites using commercial FE softwares
Finite Element (FE) Analysis Consider: an arbitrary plate geometry with complicated loading and boundary conditions Analytical Technique Numerical analysis technique Finite Element Method 35 [K e ] {d e } ={P e } Meshing of joint plates FE of train nose section
Overview - Example What do we know: We have a plate We know how it is supported We know what composite material it is made of We know what the loading is What would we like to know? 36 Displacements Strains Stresses Delamination Fracture
37 Bending and vibration of Composites Shells Finite Elements Approach 0 ] [ ] [ M K mn [K] {d} = {P} 1 ] ][ [ ] [ ] [ dx dx B D B K T e 0 5 0 4 6 1 0 6 0 0 1 5 4 6 1 6 1 0 0 0 0 K K K S K D B B A Q Q ij ij ij ij ij ij 1 ] ][ [ ] [ ] [ dx dx T e 1 } { ] [ } { dx dx q P T e Vibration Equation Bending Equation The stress resultants on a composite shell : Element mass matrix : Element stiffness matrix : Element load vector
Finite Element (FE) softwares used for Composites Analysis ABAQUS, ALTAIR HYPERWORKS, ANSYS and NASTRAN Common characteristics: FE solvers for solids, fluids, thermal, acoustic, electromagnetic and/or multiphysics problems Robust and reliable meshing tools Several optimization methods: topological, size and shape Combination of performance data management, process automation and good data exchange facilities for the solution of large scale optimization problems 38
Steps in a FE software Geometry definition: CAD, drawing facilities Element definition & FE mesh construction D Application of constraints and loads Selection of the type of Material Element properties definition Type of problem: Static, dynamic Run the program 39 Analysis of results: Displacements, stresses, etc
Analysis Steps in Hyperworks Geometrical Model Finite Element Model 40 Post Analysis Model Deformation in Hyperview courtesy
FE Solver & DYNAMIC (CRUSH) ANALYSIS 41 courtesy
Topology Optimisation of Composites -PCOMP -HyperLaminate Composite Cantilever Plate 4 courtesy
Composite Aircraft Structure FE Model 43 courtesy
Thank You