i induced streess. If the buckling b occcurs, the energy e releaased due too buckling must be t taken into considerationn in the calcculation of interfacial i t toughness. Fig. 4.13: Plane F P view of the intterfacial craack pattern by SEM*: (a) BD film with t thickness off 200 nm; (b) ( BD film m with thick kness of 5000 nm. Interffacial crack k front is t taken as beffore the cracck kinks intto the film and a toward film f surfacee [1]. The FESEM pllane view image of a wedge indeentation im mpression is used to d determine thhe curvature of a delam mination craack front. The T followinng approach hes have b been appliedd. First, a trransparent grid g paper is used to obbtain the cooordinates along a the f front of the delaminatioon crack (byy defining the t origin of the coordiinates at thee middle o the wedgge indentatioon impressiion); then a commerciaal software (Origin Pro of o 7.5) is u used to fit thhe delaminaation crack front with a ninth-ordeer polynomiial function n, f(x), as s shown in Fig.4.14. Thhe curvaturee of interfaccial crack front, f κ, forr different BD B film t thickness caan then be determined d u using Eq.(4.9) and the function f(xx) as κ= * f ''( x) ⎡1 + ( f '( x) )2 ⎤ ⎦ ⎣ 3/ . (4.9) Courtesy of o Ms. Jiangg Haiyan, M.Sc. M studen nt of Associiate Prof. Drr. Zeng Kaiyang 89 Chapter C Fig. 4.14: FESEM F F planne-view imaage of delam minated area on 500nm m BD film. A nintho order polynnomial funcction is fittted to the crack fronnt in orderr to determ mine the c curvature off the crack front f [2]. Fig. 4.15: Curvature F C fr determ mined for tthe BD film ms with of interfaciial crack front t thickness raanging from m 100 to 10000nm [2]. 90 Chapter C Fig. 4.16: FESEM planne-view imaages of the wedge F w indenntation sitess and the associated i interfacial c crack front on o (a) the 1000 nm BD film: f a straigght crack frront; (b) thee 300 nm B film: a slightly currved crack front; BD f (c) th he 500 nm BD B film: a curved cracck front, a (d) the 1000 nm BD and D film: alm most circularr delaminatiion [2]. To determine the curvatuure of the delaminatiion crack ffront, at leeast five m measuremen nts are madde for eachh BD film thickness (100nm, 3000nm, 500n nm, and 1000nm). Fig.4.15 show ws the relattionship bettween the cuurvature off crack frontt and the f film thickneess. As cann be seen in i Fig.4.16((a), for a BD B film ≤ 100 nm th hick, the i interfacial c crack front is very straaight and th he curvature is closed to zero (Fiig.4.15); t suggestts that the critical this c buckkling stress should folloow the straight-sided buckling b m mode, and the plane strain conddition is fu ulfilled. In contrast, w when the BD B film t thickness is increased to t about 5000 nm or morre (Fig.4.166(c) and 4.16(d)), the cu urvature r reaches a pllateau at abbout 0.51 µm m-1 (Fig.4.1 15), and thee delaminatiion shape iss almost c circular; thuus the circullar bucklingg mode should be adoppted. For thhe 300 nm th hick BD f film, the craack front is slightly cuurved (Fig.4 4.16(b)); hennce the critical bucklin ng stress 91 . M c curs, the e c ulation of i t erfacial cr a m with thic k t o the film a mage of a m ination cr a g rid paper i y defining t i on); then a front with a e of interfa c u sing Eq.(4 . rele a i nterfacial t a ck pattern k ness of 50 0 a nd toward f wedge ind e a ck front. T s used to o b t he origin o a commerci a a ninth-ord e c ial crack f .9) and the n t of Assoc i a sed due t o t oughness 0.51 µ m l ar bucklin g slightly c u a ges of the w 0 0 nm BD f f ront; (c) t h m ost circula r u re of the h BD fil m t ionship b e t i n Fig.4. 16 ( a ight and t h k ling stress d ition is