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Materials - Mech 2 Materials Formula and Data Sheet Stress...

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Mech 2 Materials Formula and Data Sheet Stress, Strain, Poisson’s ratio, elastic moduli: A F = σ , A F s = τ , A F p = , strain tensile strain lateral = ν l u n = ε , l w = γ , V V = n E ε σ = , γ τ G = , = K p F ( F s ) = normal (shear) component of force; A = area; u ( w ) = normal (shear) component of displacement; σ ( ε n ) = true tensile stress (nominal tensile strain); τ ( γ ) = true shear stress (engineering shear strain); p ( ) = external pressure (dilation); ν = Poisson’s ratio; E = Young’s modulus; G = shear modulus; K = bulk modulus. Bonding: ) ( n m r B r A Fdr U n m r < + = = ; U = potential energy, r = distance between the atoms, A , B , m , n = constants Composites: Loading parallel to fibres (upper bound) : m f f f V V σ σ σ ) 1 ( + = ; m f f f composite E V E V E ) 1 ( + = Loading perpendicular to fibres (lower bound): nm f nf f n V V ε ε ε ) 1 ( + = ; + = m f f f composite E V E V E ) 1 ( 1 V = volume fraction, f = fibre, m = matrix Nominal/true stress/strain: o n A F = σ ; A F = σ ; o o o n l l l l u = = ε ;
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