HW8+solutions (1) - MechEng 382 Winter 2010 Homework #8...

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MechEng 382 Winter 2010 Homework #8 Solutions 1. Dowling 8.1 (a) Fracture toughness for: 800 MPa 185 1600 MPa 40 (b) Transition crack length, (Pg. 12-13 Data handbook) For , a t = 17.02 mm For , a t = 0.20 mm For low fracture toughness and high yield strength, failure is likely to be dominated by fracture rather than yielding since the transition crack length decreases by orders of magnitude. Thus, for such cases, it is essential to employ fracture mechanics in design.
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MechEng 382 Winter 2010 Homework#8 Solutions 2 2. Dowling 8.4 (a) Material K IC ( ) ς o or equivalent (MPa) a t (mm) AISI 1144 66 540 4.75 ASTM A517 187 760 19.27 300-M (650°C temper) 152 1070 6.42 300-M (300°C temper) 65 1740 0.44 2219-T851 36 350 3.37 7075-T651 29 505 1.05 ABS 3.0 34-50 2.48-1.15 Epoxy 0.6 28-90 0.15-0.01 Soda-lime glass 0.76 50 0.07 Si 3 N 4 5.6 450 0.05 (b) For metals, transition crack lengths are on the mm scale. In the case of low-temperature tempering, there is a large decrease in fracture toughness, hence a sub-mm size crack will result in fast fracture. Soda-lime glass and Si 3 N 4 are highly susceptible to fracture with a crack length on the order of 50-70μm. ABS and epoxy appear to have a wide range of strengths indicating that there might be internal flaws leading to a statistical distribution of the strength.
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MechEng 382 Winter 2010 Homework#8 Solutions 3 3. Dowling 8.8 Dowling Fig 8.12(c) OR case (c) from Pg 13. Data Handbook (a) For α = a/b = 18/120 = 0.15 > 0.13, F = 1.2826 (Pg13. Data Handbook) (Pg13. Data Handbook) Given that KIC = 80 , using a safety factor of X k = 3, = 87.4 MPa But, where Area = b x t So, Force, P = ς x area = 87.4 x 120 x 12 = 125.9 kN (b) For fully plastic yielding to occur, Ref: Example A.1, Dowling for derivation Therefore P o = 1335 kN
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This note was uploaded on 05/12/2010 for the course MECHENG 382 taught by Professor Thouless during the Winter '08 term at University of Michigan.

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HW8+solutions (1) - MechEng 382 Winter 2010 Homework #8...

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