Materials for engineering, 3rd Edition - (Malestrom)

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Determination of mechanical properties 49 σ 2c σ 2.9 Crack in plate of unit thickness. + U s = 4cγ Energy C* 1 / 2 crack length – 2.10 Change in energy with crack length. U v = π c 2 σ 2 /E the diagram of free energy change versus embryo size in the theory of nucleation of phase transformations (Fig. 1.4). The critical crack size c* is thus when:
50 Materials for engineering d/dc (4cγ – πc 2 σ 2 /E) = 0 i.e. 2γ = πc*σ 2 /E so σ = (2Eγ/πc*) 1/2 [2.12] which is the well-known Griffith equation. At stress σ, cracks of length below 2c* will tend to close and those greater than 2c* will grow. Thus, at a given stress level, there is a critical flaw size which will lead to fracture and, conversely, for a crack of a given length, a critical threshold stress is required to propagate it. Under conditions of plane strain, [2.12] becomes: σ = [2Eγ /π(1 – ν 2 )c*] 1/2 [2.13] where ν is the Poisson ratio for the material. In considering real materials, rather than an ideal elastic solid, the work required to create new crack surfaces is more than just the thermodynamic surface energy, 2γ. Other energy absorbing processes, such as plastic deformation, need to be included and these are taken into account by using the toughness, G c , to replace 2γ in equations [2.12] and [2.13] giving a fracture stress σ F : σ F = (E G c /απc) 2 [2.14] where α = unity in plane stress, and (1 – ν 2 ) in plane strain. A related measure of toughness is the fracture toughness, K c , which is related to G c by: Gc = α Kc 2 / E [2.15] From equation [2.14] this may be written: K c = σ F (πc) 2 [2.16] The fracture toughness is measured by loading a sample containing a deliberately introduced crack of length 2c, recording the tensile stress σ c at which the crack propagates. This is known crack opening, or mode I testing. The toughness K c is then calculated from K c = Yσ c (πc) 2 [2.17] where Y is a geometric factor, near unity, which depends on the details of the sample geometry. The toughness can then be obtained by using equation [2.15]. This approach gives well-defined values for K c and G c for brittle materials (ceramics, glasses and many polymers), but, in ductile metals, a plastic zone develops at the crack tip. The linear elastic stress analysis we have assumed so far can be applied only if the extent of plasticity is small compared with the specimen dimensions. Additionally, the testpiece must be sufficiently
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Materials for engineering Third edi
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Related titles: Solving tribology p
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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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Preface to the first edition This t
Page 17 and 18: xvi Introduction Young’s modulus,
Page 20 and 21: 1 Structure of engineering material
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Appendix I Useful constants Symbol
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234 Appendix II Fracture toughness
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Appendix IV Sources of material pro
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Sources of material property data 2
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Index acrylics 160 adhesives 121 ad
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Index 245 smart fibre 189 stiffness
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Index 247 GPC (gel permeation chrom
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Index 251 nitriding 83-4 normalisin
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Materials for engineering, 3rd Edition - (Malestrom)

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