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Chap 7_2pages_solutions

Chap 7_2pages_solutions - the size of the flaw that...

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A ceramic matrix composite contains internal flaws as large as 0.001 cm in length. The plane strain fracture toughness of the composite is 4i tcal6' and the tensile shength is 550 MPa. will the flaw cause the composite to fail before thi tensile strength is reached?Assume that/= 1. since the crack is internal , ?n = 0.001 cm = 0.00001 m. Therefore e = 0.000005 m Kn=fq^lfi or c-KuIf"ha or = ( sMParffi-) l (r)@ = n,3s4MPa The $clence and Englneerlng of Materlals Instructor,s soluilons Manual 1+ ) -4 The applied shess rcquired for the qack to cause failure is much larger than the tensile snength of 550 Mpa, Any failure of the ceramic should be expected due to the massive overload, not because ofthe presence of the flaws. An aluminum alloy that has a plane srain fracture toughness of 25,000 psi6 fails when a stess of 42,000 psi is applied. Observation of the fracture surface indi- , cates that fracture began at the surface of the part. Estimate
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Unformatted text preview: the size of the flaw that initiated fracture. Assume thatl- l.l. Sofution: Kr = fa,,lE or a = (t t n)lK6 | falz a = (l I x)[2S,ONpsi6 [email protected],OWpsi)]2 = 0.093in. c. 7-3 ,t' el r{u 7:2il The high-strength steel in Figure 7-21 is subjected to a stress alternating at20O revolutions per minute between 600 MPa and 200 MPa (both tension). Calculate the growth rate of a surface crack when it reaches a length of 0.2 mm in both m/cycle and m/s. Assume mxf = lX Sotutlon: For the steel, C = L .62 x l0-t2 and n = 3.2.'l\e change in the stess intensity factor AK is b,DZ AK - ttt^,I *= qiFfooor"rPa - 200MPa\fifr-oooz tnl =t!llMPa.6-il The crack growth rate is dntdN=r.62x 10-r'\W;; z,yq N6t-q dnldN = !.62x 10-r2(ffi)3'2 - ffi m/cycle The Sclence and Englneerlng of Materlals 'lnstructor,s Soluflons Manual z.fl fuldt= (€ x lOa m/cycle[20O cycleVmin/ 60 Vmin datdt=E&b ?"b3XtE,-? n lS ? q t . - a . q . I...
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  • Spring '08
  • snively
  • Tensile strength, Fracture toughness, The Flaws, strain fracture toughness, srain fracture toughness, initiatedfracture. ssumethatl- l.l

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Chap 7_2pages_solutions - the size of the flaw that...

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