INFL??NC? T?? L?CATI?N ANDCRACK ANGL??N T?? STR?SS INT?NSITY FACT?RNaja? R?st?m M??sin Abstract: T?ispap?r d?als ?it?t?? ?ff?ct ?f crack ?bliq?? and its l?cati?n ?n t?? str?ss int?nsity fact?r m?d? I (KI) and II (K11) f?r a finit? plat? s?bj?ct?d t? ?niaxialt?nsi?n str?ss.

T?? pr?bl?m is s?lv?d n?m?rically ?singfinit? ?l?m?nt s?ft?ar? ANSYS R15 and t???r?tically ?singmat??matically ?q?ati?ns.A g??d agr??m?nt is ?bs?rv?d b?t???n t?? t???r?tical andn?m?rical s?l?ti?ns in all st?di?d cas?s. ?? s??? t?at incr?asing t?? crackangl? f l?ads t? d?cr?asing t?? val?? ?f K1andt?? maxim?m val?? ?f K11 ?cc?rs at f=45?.

F?rt??rm?r?, K11 ?q?al t? z?r? at f= 0? and 90? ??il? K1?q?al t? z?r? at f= 90?. ????v?r, t??r? is n? s?nsitiv? ?ff?ct t? t?? crack l?cati?n??il? t??r? is a c?nsid?rabl? ?ff?ct ?f t?? crack ?bliq??.K?y ??rds: Crack,angl?, l?cati?n, t?nsi?n, KI, K11, ANSYS R15.I. INTR?D?CTI?NFract?r?can b? d?fin?d as t?? pr?c?ss ?f fragm?ntati?n ?f a s?lid int? t?? ?r m?r?parts ?nd?r t?? str?ss?s acti?n. Fract?r? analysis d?als ?it? t?? c?mp?tati?n ?fparam?t?rs t?at ??lp t? d?sign a str?ct?r? ?it?in t?? limits ?f catastr?p?icfail?r?.

It ass?m?s t?? pr?s?nc? ?f a crack in t?? str?ct?r?. T?? st?dy ?f crackb??avi?r in a plat? is a c?nsid?rabl? imp?rtanc? in t?? d?sign t? av?id t??fail?r? t?? Str?ss int?nsity fact?r inv?lv?d in fract?r? m?c?anics t? d?scrib?t?? ?lastic str?ss fi?ld s?rr??nding a crack tip.?as?b?and In??ara 1 analyz?d t?? r?lati?ns b?t???n t?? str?ss int?nsity fact?rs andt?? angl? ?f t?? ?bliq?? ?dg? crack f?r a s?mi-infinit? plat?. T???carisand Papad?p??l?s 2 ?s?d t?? ?xp?rim?ntal m?t??d ?f r?fl?ct?d ca?stics t? st?dyt?? infl??nc? ?f t?? g??m?try ?f an ?dg?-crack?d plat? ?n str?ss int?nsityfact?rs K1and Kn. Kim and L?? 3 st?di?d K1and K11 f?r an ?bliq??crack ?nd?r n?rmal and s??ar tracti?n and r?m?t? ?xt?nsi?n l?ads ?sing ABAQ?S s?ft?ar?and analytical appr?ac? a s?mi-infinit? plan? ?it? an ?bliq?? ?dg? crack and anint?rnal crack act?d ?n by a pair ?f c?nc?ntrat?d f?rc?s at arbitrary p?siti?nis st?di?d by Qian and ?as?b? 4.

Kim?ra and Sat? 5 calc?lat?d K1and K11 ?ft?? ?bliq?? crack initiat?d ?nd?r fr?? ing fatig?? c?nditi?ns. F?? and Rizzi 6 d?scrib?d t?? str?ss int?nsityfact?rs ?nd?r vari??s crack s?rfac? tracti?ns ?sing an ?bliq?? crack in a s?mi-infinit?b?dy. C??i 7 st?di?d t?? ?ff?ct ?f crack ?ri?ntati?n angl? f?r vari??s mat?rialand g??m?tric c?mbinati?ns ?f t?? c?ating/s?bstrat? syst?m ?it? t?? grad?d int?rfacialz?n?. G?k?l ?t al 8 calc?lat?d t?? str?ss int?nsity fact?r ?f m?ltipl? straig?tand ?bliq?? cracks in a riv?t ??l?.

K??lil ?t al 9 ?val?at?d K1n?m?rically ?singlin? strain m?t??d and t???r?tically. R?c?ntllty, M??sin 10 and 11 st?di?d t???r?ticallyand n?m?rically t?? str?ss int?nsity fact?rs m?d? I f?r c?nt?r, singl? ?dg? andd??bl? ?dg? crack?d finit? plat? s?bj?ct?d t? t?nsi?n str?ss .Patr iciand Ma? ??ij 12 m?nti?n?d t?at, ?? can disting?is? s?v?ral mann?rs in ??ic? af?rc? may b? appli?d t? t?? plat? ??ic? mig?t ?nabl? t?? crack t? pr?pagat?. Ir?inpr?p?s?d a classificati?n c?rr?sp?nding t? t?? t?r?? sit?ati?ns r?pr?s?nt?d in Fig.1.

Acc?rdingly, ?? c?nsid?r t?r?? distinct m?d?s: m?d? I, m?d? II and m?d? III. Int?? m?d? I, ?r ?p?ning m?d?, t?? b?dy is l?ad?d by t?nsil? f?rc?s, s?c? t?at t??crack s?rfac?s ar? p?ll?d apart in t?? y dir?cti?n. T?? m?d? II , ?r sliding m?d?,t?? b?dy is l?ad?d by ?rc?s parall?l t? t?? crack s?rfac?s, ??ic? slid? ?v?r ?ac??t??r in t?? x dir?cti?n. Finally, in t?? m?d? III , ?r t?aring m?d?, t?? b?dyis l?ad?d by s??ar f?rc?s parall?l t? t?? crack fr?nt t?? crack s?rfac?s, and t??crack s?rfac?s slid? ?v?r ?ac? ?t??r in t?? z dir?cti?n. str?ss fi?lds a??ad ?f a crack tip (Fig.2) f?rm?d? I and m?d? II in a lin?ar ?lastic, is?tr?pic mat?rial ar?as in t?? f?ll??, And?rs?n 13 In many sit?ati?ns, a crack is s?bj?ct t? a c?mbinati?n?f t?? t?r?? diff?r?nt m?d?s ?f l?ading, I, II and III. A simpl? ?xampl? is acrack l?cat?d at an angl? ?t??r t?an 90° t? a t?nsil? l?ad: t?? t?nsil? l?ad C?, is r?s?lv?d int? t?? c?mp?n?nt p?rp?ndic?lart? t?? crack, m?d? I, and parall?l t? t?? crack, m?d? II as s???n in Fig.

3. T??str?ss int?nsity at t?? tip can t??n b? ass?ss?d f?r ?ac? m?d? ?sing t?? appr?priat??q?ati?ns, Ra? 14, Str?ss int?nsity s?l?ti?ns ar? giv?n in a vari?ty?f f?rms, K can al?ays b? r?lat?d t? t?? t?r??g? crack t?r??g? t?? appr?priat?c?rr?cti?n fact?r, And?rs?n 13 ???r? ?: c?aract?ristic str?ss, a: c?aract?risticcrack dim?nsi?n and Y: dim?nsi?nl?ss c?nstant t?at d?p?nds ?n t?? g??m?try andt?? m?d? ?f l?ading.?? can g?n?raliz?t?? angl?d t?r??g?-t?ickn?ss crack ?f Fig.4 t? any planar crack ?ri?nt?d 90° -p fr?m t?? appli?d n?rmal str?ss. F?r ?niaxial l?ading, t?? str?ss int?nsityfact?rs f?r m?d? I and m?d? II ar? giv?n by K1= ???r? KI0 is t?? m?d?I str?ss int?nsity ???n ? = 0.

T?? crack-tip str?ss fi?lds (in p?lar c??rdinat?s)f?r t?? m?d? I p?rti?n ?f t?? l?ading ar? giv?n by II. Mat?rials and M?t??dsBas?d ?nt?? ass?mpti?ns ?f Lin?ar ?lastic Fract?r? M?c?anics L?FM and plan? strain pr?bl?m,K1and K11 t? a finit? crack?d plat? f?r diff?r?nt angl?s and l?cati?ns ?nd?r ?niaxialt?nsi?n str?ss?s ar? st?di?d n?m?rically and t???r?tically.A. Sp?cim?ns Mat?rialT?? plat?sp?cim?n mat?rial is St??l (str?ct?ral) ?it? m?d?l?s ?f ?lasticity 2.

07?5 Mpaand p?is?n’s rati? 0.29, Y??ng and B?dynas 15. T?? m?d?ls ?f plat? sp?cim?ns ?it?dim?nsi?ns ar? s???n in Fig.5. B. T???r?tical S?l?ti?nVal??s ?fK1and K11 ar? t???r?tically calc?lat?d bas?d ?n t?? f?ll??ing pr?c?d?r? 1)D?t?rminati?n?f t?? KI? (K1???np = 0) bas?d ?n (7), ???r? (Tada ?t al 16 ) 2) Calc?lating K1and K11 t? any plan?r crack ?ri?nt?d(P) fr?m t?? appli?d n?rmal str?ss ?sing (8) and (9).

C. N?m?rical S?l?ti?nK1and K11 ar? calc?lat?d n?m?rically ?singfinit? ?l?m?nt s?ft?ar? ANSYS R15 ?it? PLAN?183 ?l?m?nt as a discr?tizati?n ?l?m?nt.ANSYS m?d?ls at P=0? ar? s???n in Fig.6 ?it? t?? m?s?, ?l?m?nts andb??ndary c?nditi?ns.

D. PLAN?183 D?scripti?nPLAN?183 is ?s?d in t?is pap?r as a discr?tizati?n?l?m?nt ?it? q?adrilat?ral s?ap?, plan? strain b??avi?r and p?r? displac?m?nt f?rm?lati?n.PLAN?183 ?l?m?nt typ? is d?fin?d by 8 n?d?s ( I, J, K, L, M, N, ?, P ) ?r 6 n?d?s( I, J, K, L, M, N) f?r q?adrilat?ral and triangl? ?l?m?nt, r?sp?ctiv?ly ?avingt?? d?gr??s ?f fr??d?m (?x , ?y) at ?ac? n?d? (translati?ns in t?? n?dal X andY dir?cti?ns) 17. T?? g??m?try, n?d? l?cati?ns, and t?? c??rdinat? syst?m f?rt?is ?l?m?nt ar? s???n in Fig.7. E.

T?? St?di?d Cas?sT? ?xplaint?? ?ff?ct ?f crack ?bliq?? and its l?cati?n ?n t?? K1and K11, many cas?s (r?p?rt?din Tabl? 1) ar? st?di?d t???r?tically and n?m?rically. III. R?s?ltsand Disc?ssi?nsK1and K11 val??s ar? t???r?tically calc?lat?d by (7 – 10) and n?m?rically ?singANSYS R15 ?it? t?r?? cas?s ass???n in Tabl? 1.A.

Cas? St?dy IFigs. 8a, b, c, d, ?, f, g, ? and i ?xplain t??n?m?rical and t???r?tical variati?ns ?f K1and K11 ?it? diff?r?ntval??s ?f a/b rati? ???n ? = 0?, 15?, 30?, 40?, 45?, 50?, 60?, 70? and 75?, r?sp?ctiv?ly.Fr?m t??s? Figs., it is t???asy t? s?? t?at t?? K1> K11 ???n ? < 45? ??il? K1 45? and K1? K11at ? = 45?. B. Cas? St?dyIIA c?mpr?ssi?nb?t???n K1and K11 val??s f?r diff?r?nt crack l?cati?ns (m?d?ls b, ? and ?) atp=30?, 45? and 60? ?it? variati?ns ?f a/b rati?ar? s???n in Figs. 9a, b, c, d, ?, f, g, ? and i.

Fr?m t??s? Figs., it is cl?art?at t?? crack angl? ?as a c?nsid?rabl? ?ff?ct ?n t?? K1and K11 val??s b?t t?? ?ff?ct?f crack l?cati?n is insignificant. Fig.9: Varia ti?n ?f K1N?m., K1T?.

, K11 N?m. and K11 T?. ?it? t?? variati?n ?f a / b f?r b, ? and ? m?d?l at P = 30, 45 and 60.

C. Cas? St?dyIIIFigs.10a, b, c and d ?xplain t?? variati?ns ?f K1and K11 ?it? t?? crack angl? P = 0?,15?, 30?, 45?, 60?, 75? and90? f?r m?d?ls b, ? and ?.

Fr?m t??s? Figs., ?? s??? t?at t?? maxim?mK1and K11 val??s app?ar at P=0? and P=45?, r?sp?ctiv?ly.F?rt??rm?r?, K11 ?q?al t? z?r? at P = 0? and P = 90?. G?n?rally,t?? maxim?m val??s ?f t?? n?rmal and s??ar str?ss?s ?cc?r ?n s?rfac?s ???r? t??P=0? and P=45?, r?sp?ctiv?ly. Fr?m all Figs.

, it can b? s??n t?at t??r? is n?significant diff?r?nc? b?t???n t?? t???r?tical and n?m?rical s?l?ti?ns. F?rt??rm?r?,Figs. 11 and 12 ar? grap?ically ill?strat?d V?n._Mis?s str?ss?s c??nt?r pl?ts ?it?t?? variati?n ?f l?cati?n and angl? ?f t?? crack, r?sp?ctiv?ly.

Fr?m t??s? Figs.,it is cl?ar t?at t?? ?ff?ct ?f crack angl? and t?? ?ff?ct ?f crack l?cati?n ar?inc?mparabl?. Fig.12: C?? nt?r pl?ts ?f V?n._Mis?s str?ss ?it? t?? variati?n ?f crack angl? at sp? cific l?cat i?n.

IV. C?ncl?si?ns1) A g??d agr??m?nt is ?bs?rv?d b?t???n t?? t???r?ticaland n?m?rical s?l?ti?ns in all st?di?d cas?s.2) Incr?asing t?? crack angl? p l?ads t? d?cr?as?t?? val?? ?f K1and t?? maxim?m val?? ?f K11 ?cc?rs at p=45.3) K11 vanis??d at p = 0? and 90???il? K1vanis??d at p = 90?.4) T??r? is n? ?bvi??s ?ff?ct t? t?? crack l?cati?nb?t t??r? is a c?nsid?rabl? ?ff?ct ?f t?? crack ?bliq??.

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