# Methods to Analyse Adhesive Properties of Fibre/ Matrix in Composite Reinforced Scaffold

The fibre reinforced composites consist of two phases: matrix phase and fibre phase. The adhesive strength of the composite mainly depends on characteristics of these materials. Fibres are divided into three groups based on their diameter and character, that is namely (i) whiskers, (ii) fibres and (iii) wires. Whiskers are very thin single crystals with large length-to-diameter ratio, and considered as the strongest materials due to their high strength and flaw free nature. However, whiskers are not widely used as a reinforcement medium due to high cost and practically not possible to include into a matrix. Materials like silicon nitride, graphite, silicon carbide and aluminium oxide can be included in the whisker group. Generally fibres are polycrystalline or amorphous materials with small diameter fibrous material. Polymer aramids, carbon, glass are classed within the fibre group. Finally, wires have relatively large diameter, typical materials include steel, molybdenum and tungsten and are considered most useful in the automotive industry.

The matrix phase mainly binds the fibres together and distributes the external applied stress to the fibres. A small amount of an applied load is sustained by the matrix phase. Moreover, the matrix phase should be ductile and protect individual fibres from surface damage due to mechanical abrasion or chemical reactions with the environment to avoid surface flaws capable of forming cracks, which may lead to failure at low tensile stress levels. Most importantly, the matrix phase acts as a barrier for crack propagation. It is essential that the adhesive bonding forces between fibre and matrix are high to minimise fibre pull-out. Also, adequate bonding helps to maximise the stress transmittance from weak matrix to the strong fibres. So choice of fibre-matrix combination dictates the bond strength of composite.

Fibre-matrix adhesion is crucial for competitive mechanical properties of natural fibre reinforced composites. The most commonly used test method to determine the fibre strength and adhesion is the single fibre fragmentation test (SFFT), which yields fibre break number as a function of the applied strain for a fibre embedded in matrix [149]. The adhesion between the reinforcing fibres and the matrix in composite materials determines the reinforcement efficiency as the stress transfers between the fibres and matrix. The mechanical adhesion of reinforcing fibres characterised by the interfacial shear strength (ISS) using various test methods such as the fibre pull-out, micro-debond test, fibre fragmentation test methods. The shear strength of fibre/polymer interface was evaluated using the SFFT method. The ISS, t, is estimated as:

Where d is the fibre diameter, lc is the critical length related to the average fibre length at saturation of the fragmentation process, {l}, as:

and {c} is the average fibre strength at critical length [150].

Some polymers like phenol-formaldehyde resins form chemical bond with natural fibres and modification of the fibre or matrix is needed to improve adhesion for other polymer matrices. In the case of flax fibres, several papers have been published in terms of the adhesion achieved [151-154].

Moreover, the mechanical properties of the composite depends on fibres orientation within the matrix and also the concentration and distribution. Basically two types of fibre orientations (i.e. parallel alignment and random alignment) influence

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**Fig. 3.9 ****Schematic representation of continuous fibre composite with different types of loads**

the mechanical properties of the composite. Normally continuous fibres are aligned whereas discontinuous fibres may be aligned or randomly oriented.

For continuously aligned fibre composites, the mechanical properties depend on various factors such as stress vs. strain of fibre and matrix, volume fraction, distribution and the direction in which load is applied (longitudinal or transverse) (Fig. 3.9). Also, the properties of fibre aligned composites are highly anisotropic. When fibres are aligned in the loaded longitudinal direction, the strength is normally taken as the maximum stress on the stress vs. strain curve and is considered as fibre fracture or onset of composite failure. These types of composite failure depend on fibre-matrix properties, nature and strength of the fibre-matrix interfacial bond. In such composites, fibre fracture strain (e_{f}) is less than the matrix fracture strain (e_{m}) because when the fibre is fractured, the majority of the load transferred is to the matrix. This being the case, the longitudinal strength of the composite (o_{cl}) can be calculated using following equation.

Here c_{m} is the stress in the matrix at fibre failure and o_{f} is the fibre tensile strength.

Unidirectional fibrous composites are normally designed to be loaded along high strength, longitudinal direction. However, during in-service applications transverse tensile loads may also be present. Transverse strength is extremely low and below the tensile strength of the matrix. Influence of various factors includes the properties of the fibre and the matrix, the fibre-matrix bond strength, and the presence of voids (Table 3.2).

Discontinuous aligned fibres composites are gaining interest in the commercial market such as chopped glass fibres, carbon fibres and aramid fibres. The reinforcement efficiency for such composite systems is less than for aligned continuous fibre composites. The longitudinal strength (o_{cd}) of discontinuous aligned fibre composites with uniform distribution of fibres and in which fibre length (l) is greater than critical fibre length (l_{c}) can be calculated using following equation:

**Table 3.2 **Longitudinal and transverse tensile strengths of unidirectional fibre-reinforced composites

Material |
Longitudinal tensile strength (MPa) |
Transverse tensile strength (MPa) |

Glass-polyester |
700 |
20 |

Carbon-epoxy |
1000 |
35 |

Kevlarâ„˘-epoxy |
1200 |
20 |

Source: D. Hull and T.W. Clyne, An Introduction to composite Materials, 2nd edition, Cambridge University Press, 1996, p. 179

Where c_{f} denotes fracture strength of the fibre and o_{m} represents the and the stress in the matrix when the composite fails.

If *l _{c} < l* then the longitudinal strength o

_{cd}is given by:

Where *d* is the fibre diameter and t_{c} is the smaller of either the fibre-matrix bond strength or the matrix shear yield strength.