Materials for engineering, 3rd Edition - (Malestrom)

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Composite materials 205 σ f * σ = σ f + σ (1 – f ) c * f * f m ’ f Stress σ m * * σ = σ (1 – f ) m * f 0 f min f crit f f 1.0 6.14 Variation of fracture stress of composite with volume fraction of fibres when ε > ε . m * f * shown in the model in Fig. 6.15, in which a thin fibre is embedded to a depth x in a medium which adheres to it. If the fibre is pulled, the adhesion between the fibre and the matrix produces a shear stress τ parallel to the surface of the fibre. The total force on the fibre is 2πrxτ due to this shear stress. Suppose the maximum value of shear stress which this interface can withstand is τ max , and the breaking stress of the fibre is σ f * : if we require that as we increase the pull on the fibre, the fibre breaks before it pulls out of the matrix, we must have i.e. πr 2 σ < 2πrxτ [6.9] f * σ 4τ f* max < x d max The ratio x/d is called the aspect ratio of the embedded part of the fibre and, in order to fulfil this condition, it is clear that the fibre has to be sufficiently long and thin. Let us now consider a ‘unit cell’ (Fig. 6.16) of matrix containing a representative short fibre of length l. If a tensile load P is applied to each end of the unit cell, the load is transferred into the fibre from both ends by shear forces at the fibre/matrix interface. Consider an element of fibre at a distance x from one end, Fig. 6.17, balancing the loads on the element we have: P – dP + 2πr dx τ = P
206 Materials for engineering d = 2r x 6.15 Model of fibre embedded in an adherent medium. P dx x P I 6.16 Element of matrix containing a fibre. i.e. dP/dx = 2πrτ Therefore P = 2πrτx If the applied stress upon the element is σ, πr 2 σ = 2πrτx, i.e. σ = 2τ/rx
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Materials for engineering Third edi
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Woodhead Publishing Limited and Man
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vi Contents 3.4 Degradation of meta
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Preface to the third edition The cr
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xvi Introduction Young’s modulus,
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1 Structure of engineering material
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Structure of engineering materials
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Page 248: Appendix I Useful constants Symbol
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Page 256: Sources of material property data 2
Page 260 and 261: Index acrylics 160 adhesives 121 ad
Page 262 and 263: Index 245 smart fibre 189 stiffness
Page 264 and 265: Index 247 GPC (gel permeation chrom
Page 266 and 267: Index 249 offset yield strength 39
Page 268 and 269: Index 251 nitriding 83-4 normalisin
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Materials for engineering, 3rd Edition - (Malestrom)

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