CHEM-C2410: Materials Science from Microstructures to Properties Composites: basic principles

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1 CHEM-C2410: Materials Science from Microstructures to Properties Composites: basic principles Mark Hughes 14 th March 2017

2 Today s learning outcomes To understand the role of reinforcement, matrix and interface To understand the concept of volume fraction and the rule of mixtures To understand the principle of load sharing and reinforcement To become familiar with the effect of geometry on elastic stress transfer and reinforcement processes

3 Composite materials Composite materials are nowadays widely used by Humankind Many elegantly structured hierarchical composite have evolved in Nature. These are far more complex than any synthetic equivalents The properties of a composite are partly dependent on the properties of the constituents (parts) or phases that make them up One thing that is common to all natural composites and many synthetic composites is that they have very organised (micro)structures and this also partly explains the properties of the composite The properties of a composite are therefore controlled by both the constituent properties and the microstructure

4 Natural & synthetic composite microstructures Wood fibre Manmade laminates

5 From nano- or micro-structure to properties A composite is a material composed of two or more distinct constituents (or phases) separated by an identifiable interface Often there is a reinforcement phase of a stiff and strong material (frequently a fibre) embedded in a compliant and weak matrix (e.g. polymer) Because composites often have a very well-organised microstructure, many properties can be predicted from the volume weighted sum of the properties of the constituents. This is known as the general Rule of Mixtures Other properties are more difficult to predict and, as Aristotle said: the whole is greater than the sum of its parts

6 Example: toughening PLA with nanocellulose PLA is a rather brittle thermoplastic polymer The addition of small amounts of nanocellulose (1%, by weight) can result in an increase in the work of fracture of up to ten times

7 Mechanical properties For many real-life engineering applications it is often desirable to have a blend of properties: Good stiffness: resistance to deflection under short-term loading Adequate strength: how much force can be sustained before it breaks Toughness: the ability to resist the propagation of cracks (arguably the most important property of an engineering material)

8 Stress, strain, stiffness, strength (Source: Wikipedia) Stress: load/cross-sectional area Strain: extension/original length Poisson s ratio: ratio of transverse to axial strain Stiffness: Young s modulus, E, stress/strain (in linear elastic region Hooke s law) Strength: stress at ultimate load (tension or compression)

9 The range of properties that Nature can achieve (Source: J.E. Gordon: Structures )

10 Constituents: reinforcement, matrix and interface

11 Reinforcement Generally stronger and stiffer than the matrix The reinforcement provides the strength to the composite Reinforcement is mainly in the form of a fibre (glass, carbon, aramid, boron.) Fibres are good in tension (compare with rope), but poor in compression and shear, therefore need a matrix in which the fibre is embedded to support the fibre and to transfer externally applied loads to the reinforcement Fibre geometry as we shall see is important. Fibres may be short (i.e. a defined aspect ratio) or long (in effect infinitely long)

12 Flax fibre

13 Reinforcement properties Fibre type Density (g cm -3 ) Young s modulus (GPa) Tensile strength (MPa) Failure strain (%) Synthetic fibres E-glass high strength carbon Kevlar (aramid) boron Natural fibres flax hemp cotton cellulose

14 Matrices Can be metals, ceramics or, most commonly, polymers Most often weaker and less stiff than the reinforcement (especially if it is polymer) In addition to transferring externally applied loads to the reinforcement, the matrix protects the reinforcement from mechanical, physical, chemical (and biological) degradation, which would lead to a loss in performance

15 Some matrix properties (polymers) Polymer Density (g cm -3 ) Young s modulus (GPa) Tensile strength (MPa) Failure strain (%) Thermosets epoxy resins polyesters Thermoplastics Nylon polypropylene PEEK

16 Interface Interface (or interphase ), transmits the externally applied loads to the reinforcement via shear stresses at the interface The interface is analogous to a glue bond If there is no bonding (adhesion) between the matrix and the reinforcement, then stress transfer will be poor and it will lead to impaired composite properties On the other hand bonding may be too good! The interface is therefore a crucial factor in the short and long-term performance of composites Optimising the properties of the interface is a key step in the development of composites (Source: https://www.simm.espci.fr/spip.php?article772)

17 Microstructure

18 Microstructure: the reinforcement architecture The term reinforcement (fibre) architecture includes: The geometry of the reinforcement (aspect ratio, morphology) The volume fraction of the reinforcement The orientation of the reinforcement with respect to applied loads The packing arrangement of the reinforcement (also related to the orientation) woven, non-woven textiles, unidirectional fabrics Geometry, orientation, packing arrangement and volume fraction are all inter-dependent

19 Volume fraction V f = V fibre /V composite V f V fibre V composite = fibre volume fraction = volume of fibre in composite = volume of composite One of the most important concepts in composite science The volume fraction of the reinforcement, frequently referred to as the fibre volume fraction, strongly affects many composite properties Varies from a few per cent (<10%) to up to around 70% (above this value, the reinforcement will be in contact and so the matrix cannot completely surround the reinforcement)

20 Packing arrangement and volume fraction (de Morais et al, 2003) Circular cross-sectional fibres: - Upper limit of volume faction when fibres touch - Square or hexagonal array (Hull and Clyne 1992)

21 Effect of fibre architecture on volume fraction 3-D volumes do not pack to high volume fractions To obtain high volume fractions, organised packing arrangements are needed Computer model consisting of 150 fibres with an aspect ratio of 37. Volume fraction 8% (Source: ETH Zurich:

22 Rule of Mixtures The volume weighted average of the properties of each constituent comprising the composite can be used to describe a number of material properties In general terms, this relationship is known as the Rule of Mixtures and may be expressed as follows: X V X V X c f f m m X c X f X m V m is the composite property is the fibre property is the matrix property is the volume fraction of matrix. This is the volume of matrix in the composite as a fraction of the total volume of the composite. Assuming that the composite consists of two phases only (with no voids), V m may be expressed alternatively as 1 V f

23 Composite density Fibre density: 1500 kg/m 3 Polymer matrix density: 900 kg/m 3 V f : 0,45 Composite density: 1170 kg/m 3 If the composite density was found to be 1050 kg/m 3 what could this indicate?

24 Reinforcement processes: elastic stress transfer

25 Model composites The properties of a composite containing many fibres can sometimes be predicted from the properties of a composite consisting of one fibre This gives rise to concept of a model composite system consisting of a single fibre embedded in a matrix Tensile stress Key to the understanding of the mechanical behaviour of fibre reinforced composite materials is the concept of load sharing between fibre and matrix

26 Load sharing Whilst stress may vary sharply from point to point along the fibre (particularly in short fibres), the proportion of the external load carried by each of the individual constituents can be assessed by volume-averaging the loads associated within them. DoITPoMS, University of Cambridge

27 Load sharing V ( 1 V ) c f f f m c f m V f is the composite applied stress is the volume averaged fibre stress is the volume averaged matrix stress is the volume fraction of reinforcement. This is the volume of fibre present in the composite as a fraction of the total volume of the composite

28 Reinforcement principles For a two phase composite, a certain proportion of the load will be carried by the fibre and the remainder by the matrix The proportion of the load carried by each constituent will depend upon the microstructural arrangement (architecture) The reinforcement may be considered to be acting efficiently if it carries a relatively large proportion of the externally applied load A high reinforcing efficiency can lead to greater composite strength and stiffness, since the reinforcement is usually both stronger and stiffer than the matrix

29 Micromechanics The mechanical (and other) properties of a composite originate at the microstructural level, in other words at the level of the individual fibre and how it interacts with the matrix and with other fibres the micromechanics The ratio of length to diameter is known as the aspect ratio, s s = L/D Is a long fibre better than a short one?

30 Micromechanics Consider a simple, ideal composite (Fig. 1), consisting of a single element of reinforcement (fibre), of finite length, uniform geometry and having homogeneous properties embedded in a matrix material Single Filament/Fibre Composites (SFC) are often used in the study of composite micromechanics Tensile stress Fig. 1: Single filament composite

31 Reinforcement processes: stress transfer In order for the composite to support an externally applied load, it is a requirement that the loads are transmitted to the reinforcement This is achieved through shear stresses that operate at the interface Stress transfer is influenced by: The elastic properties (i.e. Young s modulus) of the constituents The geometry and orientation (relative to the applied stress) of the reinforcement A model proposed by Cox in 1952, known as the shear-lag model, is often used to describe composite micromechanical behaviour

32 Shear lag model: thought experiment! stiff reinforcement (Source: Hull & Clyne 1996) compliant matrix Distortion of compliant matrix around stiff reinforcement

33 Shear lag model In a photoelastic model shear stress can be visualised as the change in optical properties (Source: Hull & Clyne 1996) SSMG-ITALY - Laboratory for Physical Modelling of Structures and Photoelasticity (University of Trento, Italy) Distortion of compliant matrix around stiff reinforcement

34 Interfacial shear stresses i Interfacial shear stress ( ) operates at the interface, parallel to the fibre surface Using a force-balance approach it can be shown that: d dx f i 2 r Where: x is the axial distance from the fibre mid-point r is the fibre radius (Source: Hull & Clyne 1996)

35 Variation of fibre stress along the length It can be shown that the axial stress distribution, due to elastic stress transfer in a fibre, may be given by: f E 1 cosh nx / r sec h ns f 1 E f 1 s n is the fibre Young s modulus is the applied composite strain is the fibre aspect ratio, defined as L/r (where L is the fibre half length) is a dimensionless constant given by: 2E n E v V m 1 ln 1 f m f 1 2 E m v m is the matrix Young s modulus is the matrix Poisson s ratio

36 Effect of aspect ratio 250 s = 100 fibre axial stress (MN m -2 ) aspect ratio = 5 aspect ratio = 25 aspect ratio = 100 Reinforcement acts more effectively s = position along fibre (arbitary units) Assumptions: fibre modulus: 50 GPa; matrix modulus: 3.5 GPa; axial strain: 0.5%

37 Experimental validation Microdroplet test: hemp fibre embedded in epoxy (Source: Eichhorn and Young, 2004)

38 Experimental validation Axial stress along fibre, measured using Raman spectroscopy (Source: Eichhorn and Young, 2004)

39 Influence of aspect ratio on axial stiffness 160 s=1000 s=100 Stress (MN m -2 ) s=10 s= Strain (%)

40 Variation of interfacial shear stress It may be shown that the variation of shear stress along the fibre can be given by: i n 2 1 E f nx sinh sec h( ns) r

41 Shear stress distribution interfacial shear stress (MN m -2 ) aspect ratio = 5 aspect ratio = 25 aspect ratio = position along fibre (arbitary units) Assumptions: fibre modulus: 50 GPa; matrix modulus: 3.5 GPa; axial strain: 0.5%

42 Cox-type stress transfer As the aspect ratio increases, the efficiency of stress-transfer increases to a point where a plateau fibre stress is reached For a given set of fibre & matrix properties and applied strain, a maximum axial fibre stress and interfacial shear stress will be attained As aspect ratio increases no further axial stress in the fibre will be achieved, i.e. there is no stress transfer, except at the end of the fibre So, in long fibre composites, it can be assumed that fibre and matrix undergo equal strain, when a stress is applied parallel to the fibre axis

43 Literature Eichhorn, S.J. and Young, R.J. (2004). Composite micromechanics of hemp fibres and epoxy resin microdroplets. Composites Science and Technology 64, Hull, D. and Clyne, T.W. (1996). An Introduction to Composite Materials. Cambridge University Press, Cambridge, UK (Chapter 2: fibres and matrix; Chapter 6: reinforcement in short fibre composites) Piggott, M.R. Load bearing fibre composites. Pergamon Press (Chapter 5: reinforcement processes) Cox, H.L. (1952). The Elasticity and Strength of Paper and Other Fibrous Materials. Brit. J. Appl. Phys., 3: de Morais, W. A., J. R. M. d'almeida, L. B. Godefroid (2003). Effect of the fiber reinforcement on the low energy impact behavior of fabric reinforced resin matrix composite materials J. Braz. Soc. Mech. Sci. & Eng. 25(4) (http://dx.doi.org/ /s )

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