Theoretical estimation of fracture toughness of fibrous composites

A method of estimating the fracture surface energy of fibre-reinforced materials is discussed. The surface work is shown to increase with increasing fibre content, strength and diameter, and decrease with increasing fibre modulus and matrix flow stress (or hardness).Relatively short fibres should be used if high toughness is required, and the maximum toughness that can be achieved is limited by the amount of crack opening that can be permitted. Under certain conditions, incorporation of fibres into a material can lead to embrittlement.Symbols used c half length of crack - d fibre diameter - D average separation of nearest neighbour fibres - E Young's modulus - G shear modulus of matrix - K fracture toughness - L length of fibre on either side of crack - n number of fibres per unit area - P force on fibre - R pressure exerted by matrix on fibres - u displacement - U work - x distance Greek symbols 8 G/d ² E _fr log(2/p 3) - surface energy or work - tensile strain - _fm E _mr/E_fr R - tensile stress - shear stress - coefficient of friction - Poisson's ratio Suffixes c composite - e elastic - f fibre - m matrix