2 lecture 4 - Failure Predictors and Safety Factors - slide

E u distortion u distortion yield 2 2 2 2 1 1

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Unformatted text preview: 2 Ⱥ 1 + µ Ⱥ Sy − 0 + 0 − 0 + 0 − Sy u (distortion, yield) = 3E Ⱥ 2 Ⱥ ( 1+ µ = Sy 3E () )( 2 )( ) 2 Ⱥ Ⱥ Ⱥ Ⱥ Mechanical Design Failure Predictors Distortion energy failure predictor Good design practice requires that the stresses in the designed component are always less than the limiting value of strength, i.e. u (distortion) ≤ u (distortion, yield) 2 2 2 2 1+ µ 1 + µ Ⱥ (σ 1 − σ 2 ) + (σ 2 − σ 3 ) + (σ 3 − σ 1 ) Ⱥ Ⱥ (Sy ) ≥ 3E Ⱥ 3E 2 Ⱥ Ⱥ Ⱥ Ⱥ € σ vM = (σ 2 1 2 )( )( − σ 2 + σ 2 − σ 3 + σ 3 − σ1 2 ) 2 Sy ≤ Fd E = Young’s modulus µ = Poisson’s ratio vM = von Mises What is Fd ??? Mechanical Design Failure Predictors Three main failure predictors for stress: Maximum Principal Stress Typically for brittle materials only Maximum Shear Stress (Tresca) ductile materials a conservative failure estimate Distortion Energy (von Mises) ductile materials more accurate failure estimate Mechanical Design Failure Predictors – summary X X(σ1, σ2, σ3) X(σ1 = S, 0, 0) σ1 = σ1 X(σ1 = SU, 0, 0) = SU τMAX = (σ1 – σ3) / 2 = Sys = Sy / 2 u(distortion) 2 2...
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