機(jī)翼機(jī)身對(duì)接結(jié)構(gòu)三維斷裂分析【含圖紙、說(shuō)明書】,含圖紙、說(shuō)明書,機(jī)翼,機(jī)身,對(duì)接,結(jié)構(gòu),三維,斷裂,分析,圖紙,說(shuō)明書,仿單 畢 業(yè) 設(shè) 計(jì)（論 文）任 務(wù) 書 ?? 設(shè)計(jì)（論文）題目： 機(jī)翼機(jī)身對(duì)接結(jié)構(gòu)三維斷裂分析 ? 學(xué)生姓名： 張嘉歡 學(xué)??號(hào)： 1204201026 專????業(yè)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 所在學(xué)院： 機(jī)電工程學(xué)院 指導(dǎo)教師： 王芳麗 職????稱： 發(fā)任務(wù)書日期：年月日 任務(wù)書填寫要求 1．畢業(yè)設(shè)計(jì)（論文）任務(wù)書由指導(dǎo)教師根據(jù)各課題的具體情況填寫，經(jīng)學(xué)生所在專業(yè)的負(fù)責(zé)人審查、系（院）領(lǐng)導(dǎo)簽字后生效。此任務(wù)書應(yīng)在畢業(yè)設(shè)計(jì)（論文）開(kāi)始前一周內(nèi)填好并發(fā)給學(xué)生。 2．任務(wù)書內(nèi)容必須用黑墨水筆工整書寫，不得涂改或潦草書寫；或者按教務(wù)處統(tǒng)一設(shè)計(jì)的電子文檔標(biāo)準(zhǔn)格式（可從教務(wù)處網(wǎng)頁(yè)上下載）打印，要求正文小4號(hào)宋體，1.5倍行距，禁止打印在其它紙上剪貼。 3．任務(wù)書內(nèi)填寫的內(nèi)容，必須和學(xué)生畢業(yè)設(shè)計(jì)（論文）完成的情況相一致，若有變更，應(yīng)當(dāng)經(jīng)過(guò)所在專業(yè)及系（院）主管領(lǐng)導(dǎo)審批后方可重新填寫。 4．任務(wù)書內(nèi)有關(guān)“學(xué)院”、“專業(yè)”等名稱的填寫，應(yīng)寫中文全稱，不能寫數(shù)字代碼。學(xué)生的“學(xué)號(hào)”要寫全號(hào)，不能只寫最后2位或1位數(shù)字。 5．任務(wù)書內(nèi)“主要參考文獻(xiàn)”的填寫，應(yīng)按照《金陵科技學(xué)院本科畢業(yè)設(shè)計(jì)（論文）撰寫規(guī)范》的要求書寫。 ?6．有關(guān)年月日等日期的填寫，應(yīng)當(dāng)按照國(guó)標(biāo)GB/T 7408—94《數(shù)據(jù)元和交換格式、信息交換、日期和時(shí)間表示法》規(guī)定的要求，一律用阿拉伯?dāng)?shù)字書寫。如“2002年4月2日”或“2002-04-02”。 畢 業(yè) 設(shè) 計(jì)（論 文）任 務(wù) 書 1．本畢業(yè)設(shè)計(jì)（論文）課題應(yīng)達(dá)到的目的： ? 本畢業(yè)設(shè)計(jì)課題的主要目的是培養(yǎng)學(xué)生綜合運(yùn)用所學(xué)的基礎(chǔ)理論、專業(yè)知識(shí)和專業(yè)基本技能分析和解決實(shí)際問(wèn)題，訓(xùn)練應(yīng)用ANSYS軟件對(duì)機(jī)翼與機(jī)身對(duì)接機(jī)構(gòu)進(jìn)行有限元建模和三維斷裂分析的能力，主要包括以下幾個(gè)方面： 1．調(diào)查研究、中外文獻(xiàn)檢索、閱讀與翻譯的能力； 2．綜合運(yùn)用基礎(chǔ)理論、專業(yè)理論和知識(shí)分析解決實(shí)際問(wèn)題的能力； 3．查閱和使用專業(yè)設(shè)計(jì)手冊(cè)的能力； 4．應(yīng)用catia軟件和ANSYS軟件進(jìn)行建模和有限元分析的能力； 5．撰寫設(shè)計(jì)說(shuō)明書（論文）的能力。 2．本畢業(yè)設(shè)計(jì)（論文）課題任務(wù)的內(nèi)容和要求（包括原始數(shù)據(jù)、技術(shù)要求、工作要求等）： ? （1） 熟悉并理解機(jī)翼機(jī)身對(duì)接結(jié)構(gòu)與受力特點(diǎn)；（2） 熟悉和掌握三維斷裂理論知識(shí)；（3） 應(yīng)用ANSYS軟件對(duì)機(jī)翼機(jī)身對(duì)接結(jié)構(gòu)進(jìn)行三維建模和斷裂分析。 畢 業(yè) 設(shè) 計(jì)（論 文）任 務(wù) 書 3．對(duì)本畢業(yè)設(shè)計(jì)（論文）課題成果的要求〔包括圖表、實(shí)物等硬件要求〕： 1.外文參考資料及譯文（附原文）； 2.畢業(yè)設(shè)計(jì)開(kāi)題報(bào)告一份； 3.有限元分析結(jié)果分析說(shuō)明一份； 4．主要參考文獻(xiàn)： [1] 吳相憲，王正為，黃玉堂主編.實(shí)用機(jī)械設(shè)計(jì)手冊(cè).中國(guó)礦業(yè)大學(xué)出版社，1993. [2] 王洪欣，李木，劉秉忠主編.機(jī)械設(shè)計(jì)工程學(xué)[M].中國(guó)礦業(yè)大學(xué)出版社，2001. [3] 唐大放，馮曉寧，楊現(xiàn)卿主編.機(jī)械設(shè)計(jì)工程學(xué)[M].中國(guó)礦業(yè)大學(xué)出版社，2001. [4] 中國(guó)紡織大學(xué)工程圖學(xué)教研室等編.畫法幾何及工程制圖.上?？茖W(xué)技術(shù)出版社，1997. [5] 史美堂主編.金屬材料及熱處理.上海科學(xué)技術(shù)出版社，1983. [6] 蘇翼林主編.材料力學(xué).高等教育出版社，1980. [7] 顧崇銜主編.機(jī)械制造工藝學(xué).陜西科學(xué)技術(shù)出版社，1999. [8] 詹熙達(dá)主編.CATIA V5R20曲面設(shè)計(jì)教程. 北京：機(jī)械工業(yè)出版社,2013. [9] 詹熙達(dá)主編.CATIA V5R20快速入門教程. 北京：機(jī)械工業(yè)出版社,2011. [10] 劉文珽，羅毅，童明波．概率損傷容限分析模型研究[J]．航空學(xué)報(bào)，1993，14（3）：136-139． [11] 劉文珽等．概率斷裂力學(xué)與概率損傷容限/耐久性[M]．北京航空航天大學(xué)出版社，1998. [12] 羅毅，黃培彥，劉文珽．裂紋擴(kuò)展壽命安全可靠性分析模型研究[J]．北京航空航天大學(xué)學(xué)報(bào)，2002，28（1）：113-115. [13] 杜永恩．概率損傷容限分析體系及其關(guān)鍵技術(shù)的研究[D]．西安：西北工業(yè)大學(xué)，2014. [14] K.Y. Lin and A.V. Styuart. Probabilistic approach to damage tolerance design of aircraft composite structures [J]. Journal of Aircraft, 2007,44(4):1309-1317. [15] Spencer B F，Tang J. Markov Model for fatigue crack growth [J]. Journal of Engineering Mechanics，1998,114:2134-2157. 畢 業(yè) 設(shè) 計(jì)（論 文）任 務(wù) 書 5．本畢業(yè)設(shè)計(jì)（論文）課題工作進(jìn)度計(jì)劃： 2015.12.16-2.16.3.9 畢業(yè)實(shí)習(xí)調(diào)研，完成開(kāi)題報(bào)告、中英文翻譯、論文大綱 2016.3.19-2016.4.25 提交論文草稿，4月中旬中期檢查 2016.4.26-2016.5.6 提交論文定稿 2016.5.6-2016.5.13 準(zhǔn)備答辯 2016.5.13-2016.5.26 答辯，成績(jī)?cè)u(píng)定，修改完成最終稿 所在專業(yè)審查意見(jiàn)： ?通過(guò)? 負(fù)責(zé)人： ??????????? ?2016? 年??? 1 ?月???18 ?日 畢 業(yè) 設(shè) 計(jì)（論 文）開(kāi) 題 報(bào) 告 設(shè)計(jì)（論文）題目： 機(jī)翼機(jī)身對(duì)接結(jié)構(gòu)三維斷裂分析 ? 學(xué)生姓名： 張嘉歡 學(xué)??號(hào)： 1204201026 專????業(yè)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 所在學(xué)院： 機(jī)電工程學(xué)院 指導(dǎo)教師： 王芳麗 職????稱： ? ?年? ?月??日 ? 開(kāi)題報(bào)告填寫要求 ? 1．開(kāi)題報(bào)告（含“文獻(xiàn)綜述”）作為畢業(yè)設(shè)計(jì)（論文）答辯委員會(huì)對(duì)學(xué)生答辯資格審查的依據(jù)材料之一。此報(bào)告應(yīng)在指導(dǎo)教師指導(dǎo)下，由學(xué)生在畢業(yè)設(shè)計(jì)（論文）工作前期內(nèi)完成，經(jīng)指導(dǎo)教師簽署意見(jiàn)及所在專業(yè)審查后生效； 2．開(kāi)題報(bào)告內(nèi)容必須用黑墨水筆工整書寫或按教務(wù)處統(tǒng)一設(shè)計(jì)的電子文檔標(biāo)準(zhǔn)格式打印，禁止打印在其它紙上后剪貼，完成后應(yīng)及時(shí)交給指導(dǎo)教師簽署意見(jiàn)； 3．“文獻(xiàn)綜述”應(yīng)按論文的框架成文，并直接書寫（或打?。┰诒鹃_(kāi)題報(bào)告第一欄目?jī)?nèi)，學(xué)生寫文獻(xiàn)綜述的參考文獻(xiàn)應(yīng)不少于15篇（不包括辭典、手冊(cè)）； 4．有關(guān)年月日等日期的填寫，應(yīng)當(dāng)按照國(guó)標(biāo)GB/T 7408—94《數(shù)據(jù)元和交換格式、信息交換、日期和時(shí)間表示法》規(guī)定的要求，一律用阿拉伯?dāng)?shù)字書寫。如“2004年4月26日”或“2004-04-26”。 5、開(kāi)題報(bào)告（文獻(xiàn)綜述）字體請(qǐng)按宋體、小四號(hào)書寫，行間距1.5倍。 ? 畢 業(yè) 設(shè) 計(jì)（論文） 開(kāi) 題 報(bào) 告 1．結(jié)合畢業(yè)設(shè)計(jì)（論文）課題情況，根據(jù)所查閱的文獻(xiàn)資料，每人撰寫不少于1000字左右的文獻(xiàn)綜述： 機(jī)翼機(jī)身對(duì)接接頭設(shè)計(jì)是飛機(jī)結(jié)構(gòu)設(shè)計(jì)的一個(gè)重要環(huán)節(jié)，其設(shè)計(jì)的好壞嚴(yán)重關(guān)系到飛機(jī)的飛行性能和使用安全，本文詳細(xì)地闡述了飛機(jī)結(jié)構(gòu)設(shè)計(jì)載荷系數(shù)的產(chǎn)生和發(fā)展，提出在飛機(jī)結(jié)構(gòu)設(shè)計(jì)中用可靠性安全系數(shù)替代傳統(tǒng)安全系數(shù)的觀點(diǎn)。介紹分析了機(jī)翼機(jī)身對(duì)接設(shè)計(jì)思想和接頭耳片受力特性，提出了改善機(jī)翼機(jī)身對(duì)接區(qū)域傳力特性的設(shè)計(jì)方法。 現(xiàn)代超音速戰(zhàn)斗機(jī)常采用中單翼布置，受機(jī)身部位安排的限制，不能有中央翼通過(guò)機(jī)身，此時(shí)機(jī)翼通過(guò)幾個(gè)集中接頭與機(jī)身在側(cè)邊相連，機(jī)翼彎矩要作用于翼身對(duì)接框上，從而機(jī)身框結(jié)構(gòu)要加強(qiáng)，結(jié)構(gòu)重量加大。我們知道現(xiàn)代超音速戰(zhàn)斗機(jī)的機(jī)翼很薄，機(jī)翼的相對(duì)厚度約為4％，隨著機(jī)翼面積的增加，機(jī)翼載荷大幅度上升，翼梁承擔(dān)和傳遞的載荷越來(lái)越大，機(jī)翼載荷完全由接頭耳片及連接螺栓傳遞到機(jī)身對(duì)接框，因此若直接將如此結(jié)構(gòu)高度的翼梁連接到加強(qiáng)框上，機(jī)翼機(jī)身對(duì)接接頭耳片、連接螺栓及加強(qiáng)框受力都是比較嚴(yán)重的。由此，現(xiàn)代先進(jìn)戰(zhàn)斗機(jī)在總體設(shè)計(jì)時(shí)，結(jié)合總體氣動(dòng)布局、機(jī)翼機(jī)身部位安排的要求采用了多種設(shè)計(jì)方法來(lái)改善對(duì)接接頭區(qū)域的傳力特性。 目前對(duì)接頭問(wèn)題的研究有很多，孫庚茂、丁惠粱等采用釘“超元”模擬復(fù)合材料的連接，宋恩鵬等采用梁元和彈簧元分別模擬螺栓連接，張永杰等采用體單元對(duì)螺栓連接進(jìn)行剛度分析。采用螺栓、彈簧元或釘元模擬螺栓連接都是從整體結(jié)構(gòu)承載出發(fā)，給出了有限元仿真中螺栓連接的簡(jiǎn)化方法，但不能解決螺栓的預(yù)緊力、孔邊接觸應(yīng)力、接頭的屈服極限等方面的問(wèn)題。而大部分接頭的出現(xiàn)都會(huì)伴隨著孔結(jié)構(gòu)的產(chǎn)生．孔邊的受力由于要考慮摩擦和接觸問(wèn)題，使結(jié)構(gòu)孔邊周圍呈現(xiàn)出非線性特征，有時(shí)為了更大的挖掘接頭結(jié)構(gòu)的承載能力，甚至還要考慮結(jié)構(gòu)局部進(jìn)入塑性區(qū)應(yīng)力分布．這就更增加了非線性程度以及求解接頭接觸問(wèn)題的復(fù)雜性。隨著有限元軟件的發(fā)展，接觸問(wèn)題的數(shù)值方法得到了很大的提高，通過(guò)不斷細(xì)化網(wǎng)格可以得到逼近精確解的數(shù)值解。 本次設(shè)計(jì)的主要研究工作是探討傳統(tǒng)安全系數(shù)的發(fā)生和發(fā)展，分析傳統(tǒng)安全系數(shù)的利弊，建立可靠性安全系數(shù)觀念；對(duì)機(jī)翼機(jī)身對(duì)接接頭形式和布局以及接頭耳片的構(gòu)型和受力特性進(jìn)行分析和研究；對(duì)原型飛機(jī)橫梁結(jié)構(gòu)受力特性進(jìn)行有限元應(yīng)力分析；根據(jù)大改飛機(jī)設(shè)計(jì)要求，優(yōu)化結(jié)構(gòu)設(shè)計(jì)參數(shù)，給出接頭加強(qiáng)型和改進(jìn)型設(shè)計(jì)方案；對(duì)橫梁結(jié)構(gòu)疲勞危險(xiǎn)部位進(jìn)行損傷容限評(píng)定。 本次設(shè)計(jì)采用實(shí)體建模三維有限元方法，對(duì)飛機(jī)、翼身對(duì)接主承力接頭進(jìn)行傳力特性分析，對(duì)機(jī)身半框模型、機(jī)翼主梁一機(jī)身橫梁組合模型在CATIA和ANSYS下計(jì)算結(jié)果進(jìn)行了評(píng)價(jià)。根據(jù)結(jié)構(gòu)設(shè)計(jì)要求和結(jié)構(gòu)限制條件，優(yōu)化結(jié)構(gòu)設(shè)計(jì)參數(shù)，給出了飛機(jī)機(jī)翼機(jī)身對(duì)接主承力接頭的加強(qiáng)型和改進(jìn)型設(shè)計(jì)方案。從結(jié)構(gòu)尺寸、重量、疲勞危險(xiǎn)部位應(yīng)力水平、對(duì)氣動(dòng)力的影響以及裝配工藝性等方面對(duì)加強(qiáng)型和改進(jìn)型設(shè)計(jì)方案進(jìn)行了比較分析。疲勞斷裂起始于結(jié)構(gòu)細(xì)節(jié)，對(duì)疲勞危險(xiǎn)關(guān)鍵部位進(jìn)行了損傷容限評(píng)定，提出了提高結(jié)構(gòu)抗疲勞斷裂能力的措施。 畢 業(yè) 設(shè) 計(jì)（論文） 開(kāi) 題 報(bào) 告 2．本課題要研究或解決的問(wèn)題和擬采用的研究手段（途徑）： 本課題所要研究及解決的問(wèn)題： 本課題是機(jī)翼機(jī)身對(duì)接結(jié)構(gòu)三維斷裂分析，需要在給出和查閱到的設(shè)計(jì)基本資料上完成該裝置需要的結(jié)構(gòu)布置，需要研究及解決的問(wèn)題如下： （1）在了解現(xiàn)有幾種三維斷裂的原因，需要應(yīng)用有限元分析軟件對(duì)斷裂原因進(jìn)行仿真計(jì)算； （2）需要利用有限元軟件研究分析初始裂紋尺寸的變化，裂紋擴(kuò)展速率，無(wú)損檢查，飛行載荷和使用頻譜。 擬采用的研究手段（途徑）： 1、文獻(xiàn)收集 廣泛收集與永磁磁懸浮技術(shù)相關(guān)的資料； 2、實(shí)踐與實(shí)習(xí) 通過(guò)實(shí)驗(yàn)室內(nèi)建設(shè)基本模型進(jìn)行測(cè)試分析，通過(guò)大量的數(shù)據(jù)來(lái)進(jìn)行設(shè)置的計(jì)算機(jī)控制系統(tǒng)建立。 3、運(yùn)用CATIA和ANSYS設(shè)計(jì)軟件進(jìn)行三維分析； 4、結(jié)合指導(dǎo)老師的指點(diǎn)，分進(jìn)度，分階段實(shí)施，并對(duì)相關(guān)問(wèn)題展開(kāi)研究。 畢 業(yè) 設(shè) 計(jì)（論文） 開(kāi) 題 報(bào) 告 指導(dǎo)教師意見(jiàn)： 1．對(duì)“文獻(xiàn)綜述”的評(píng)語(yǔ)： 通過(guò)文獻(xiàn)綜述，該生對(duì)機(jī)身機(jī)翼對(duì)接接頭三維斷裂國(guó)內(nèi)外研究現(xiàn)狀有了較清晰的認(rèn)識(shí)，下一步可以通過(guò)Ansys軟件對(duì)對(duì)接接頭進(jìn)行有限元建模和三維斷裂分析研究。 ? ? ? ? 2．對(duì)本課題的深度、廣度及工作量的意見(jiàn)和對(duì)設(shè)計(jì)（論文）結(jié)果的預(yù)測(cè)： 本課題深度和工作量適中，具有一定的工程應(yīng)用價(jià)值，相信通過(guò)該生對(duì)各種機(jī)身機(jī)翼對(duì)接接頭三維斷裂的研究，在飛機(jī)設(shè)計(jì)時(shí)對(duì)對(duì)接接頭設(shè)計(jì)時(shí)具有一定的參考價(jià)值。 ? ? ? ? 3.是否同意開(kāi)題：√ 同意 □ 不同意 ? ???????????????????????????????????? ??指導(dǎo)教師：?????????????? ???????????????????????????????????????? 2016 年?? 03 月?? 08 日 所在專業(yè)審查意見(jiàn)： 同意 ???????????????????????????????????????? 負(fù)責(zé)人：?????????????? ?????????????????????????????????????????? 2016 年??? 03 月?? 09 日 26th ICAF Symposium – Montreal, 1-3 June 2011 *Challenges in Damage Tolerance Approach for Dynamic Loaded Rotorcraft Components – From Risk Assessment to Optimal Inspection Planning Jack Zhao1 and David Adams2 1 Structural Methods and Prognostics 2 Ground Test Sikorsky Aircraft Corporation Stratford, CT 06516 USA jzhao@sikorsky.com Abstract. The use of Crack Growth Damage Tolerance as a substantiation methodology for helicopter dynamic components is receiving increased attention as a logical and viable improvement in fatigue reliability and structural integrity. It has seen only limited use in helicopters because the addition of difficult periodic inspections was seen as a significant burden to the operator. However the certifying agencies are moving towards the simultaneous use of both Safe-Life and Damage Tolerance methodologies on each component. In order to mitigate the cost issue, a means to optimize the inspection protocol using a risk-informed damage tolerance based fatigue reliability model and maintenance optimization tool is evaluated in this paper. It was desired to maintain the same “6-9’s” level of structural reliability for Damage Tolerance that is now the standard practice for safe-life substantiations. The newly developed fatigue reliability methodology incorporates the variabilities in initial crack size, crack growth rate, nondestructive inspections, flight loads, and the usage spectrum. The reliability model is further integrated with optimization technique for inspection planning. An example case using the crack propagation test result from a helicopter main rotor spindle is evaluated with the reliability model. The concept of DT risk assessment and optimal inspection planning, impact of NDI detection capability and repair quality on risk reduction, and importance of incorporating CBM logistic requirement are demonstrated. It is concluded that a fatigue reliability model for Damage Tolerance was successfully demonstrated and that it can be used to determine an optimized inspection protocol that reduces the operator’s inspection burden while providing the required 6-9’s level of fatigue reliability. 1 Introduction Damage Tolerance, specifically Crack Growth Damage Tolerance, has been successfully applied in a limited number of helicopter fatigue substantiations for * Oral presentation. 928 J. Zhao and D. Adams more than 50 years, although it was originally called “Fail-Safe” methodology. The number of applications is now increasing, driven by an increased emphasis on Damage Tolerance by civil and military certifying agencies. The FAA’s Amendment 28 to FAR 29.571 in 1989 provided that Fail-Safety (Damage Tolerance) was an equal-choice option to Safe Life as a substantiation methodology. And a pending new 29.571 will require implementation of both methods on every substantiated component. Damage Tolerance methodology relies on the assumption that the component exhibits some initial damage that subsequently grows progressively over a period of time prior to catastrophic failure. A successful damage tolerance design must be capable of: 1) predicting crack initiation; 2) accurate modelling of subsequent crack growth; and 3) adequate NDI methodology with suitable inspection schedule. The advantage of a Crack Growth Damage Tolerance method over Safe Life is that the cause of an initial crack or damage does not matter since the inspection program will detect the presence of whatever crack occurs before it becomes catastrophic, with a significant safety margin. The disadvantage is the cost of the inspection program in terms of the intrusive down time, man-hours, training, and equipment required. Damage Tolerance will not be accepted as a viable and desirable methodology unless its benefits are perceived to be worth its cost. There is, therefore, an opportunity to employ a reliability approach to determine an optimum inspection methodology – one that provides a required level of structural reliability but does not require unnecessary or too-frequent inspections. Conventional Approach to Crack Growth Substantiations Sikorsky’s methodology for the substantiation of flight-critical fatigue-loaded components is entirely empirical and was initially developed in the early 1960’s for aluminium spar main rotor blades. This substantiation, called “Blade Inspection Method”, or BIM, is still in use today on thousands of rotor blades. It is based on sensing a loss of internal gas pressure in the event of a spar crack, with the inspection interval based on a full-scale fatigue test program that fully characterized the crack growth behaviour under conservative maximum flight loads and severe usage. Sensing of the pressure loss is done by a special visual indicator at the blade root. The inspection interval is essentially a pre-flight visual inspection that was set at minimum 3 to 1 reduction in the test crack growth time from detection to failure. Inspections start at zero time. This method – conservative full-scale test determination of crack growth, demonstration of a field inspection method, determination of a failure point, and an inspection interval based on a fraction of the test time – is still in use today with a few developments. We now require a static test demonstration for critical crack size, we avoid the inclusion of any blunting effect in metals due to high fatigue test loads, we have employed the method in composites, and we have standard methodology for number of fatigue test specimens and the inspection interval reduction factor. The basic method is accepted by all of our civil and military certifying agencies as illustrated in the figure below from the FAA’s AC 29-2C MG-11. Damage Tolerance Approach for Dynamic Loaded Rotorcraft Components 929 Fig. 1 Potential-to-Functional Failure Curve from NAVAIR 25-403. A reliability determination has not been part of the current crack growth damage tolerance method. Because of the conservative treatments of the flight loads, the usage, and the test-based crack growth characteristics in the substantiation, the current method meets the generic requirement that failure is “extremely remote”, and this criteria has been achieved in 50 years of service. There has been a methodology development, Reference [3], called “Empirical Damage Tolerance”, which allows the determination of an inspection interval for a different load spectrum than was applied in the full-scale test program. This development is also useful in the reliability studies that follow and is described in more detail later. Reliability-Based Approach to Helicopter Damage Tolerance The work done to show the reliability of a Damage Tolerant approach for helicopter dynamic component fatigue is not extensive. One early effort did show that a 6-9’s level of reliability was achieved for a multiple load path case, Reference [9]. However a good starting point for reliability-based approach is Reliability-Centered Maintenance (RCM) as described in NAVAIR 25-403, Reference [5]. The figure below illustrates the key points of RCM. This is a much more general methodology, referring to the decline in a functional capability to the point where the functionality is declared failed. The figure is generally known as a P-F curve. The P-F interval is the age interval (in flight hours, cycles, or calendar time) between the Potential Failure (some loss of functionality) becoming detectable (P) to the point of the defined functional failure (F). The inspection interval (I) is a defined fraction of the PF interval. 930 J. Zhao and D. Adams Fig. 2 Potential-to-Functional Failure Curve from NAVAIR 25-403. A reliability-based optimal inspection interval would provide a required predetermined level of structural reliability while minimizing the cost of conducting inspections too frequently. One simplified approach to the reliability is discussed in NAVAIR 25-403, where the Inspection Interval was initially determined by requiring that the projected probability of failure be reduced to less than or equal to the acceptable probability of failure. The interval of on-condition task, denoted as I, can be estimated by: where PF is the Potential-to-Functional failure interval and n denotes the number of inspections during P-F interval. In general, n can be determined by either safety requirements or cost optimization. For flight-critical components, the total risk considering the inspections shall not exceed the maximum acceptable risk, Therefore, where acc P is the maximum acceptable level of probability of function failure and is probability of detecting a potential failure in one inspection assuming it exists. The equation above implicitly assumes the failure will always occur in the P-F interval and a constant detectability which is independent to the size of damage. The extreme condition satisfying the risk constraint occurs if the total risk equals to the maximum acceptable level. Accordingly, the number of inspections can be determined by Damage Tolerance Approach for Dynamic Loaded Rotorcraft Components 931 The approach outlined in Eq. 1-3 is based on assumption that a potential failure always exists within the P-F interval and is independent between inspections. As a result, the inspection interval may be too conservative, meaning too-frequent inspections, which does not meet our minimized cost objective. The basic RCM approach does not consider the failure mechanics or the scatter of failure progression. Often, the potential failure mode under consideration exhibits inherent randomness. This is particularly important for the failure modes associated with progressive damage accumulation such as crack initiation and growth, corrosion, and mechanical wear. To effectively address variability and uncertainty of damage progression and understand their impact on P-F interval, it is highly desirable to incorporate stochastic characterization of failure progression into the RCM process. In this paper, a new approach is proposed to establish a risk-based interval for on- condition tasks by incorporating a baseline probability of failure and a characteristic detectability for inspection capability. Generally, the probability of failure for a component under scheduled inspections can be expressed as the probability of a sequence of events, such as: Where, pF0 is the probability of failure before the first inspection due to excessive damage progression; G i p is the probability that damage will grow to a detectable limit right before the ith inspection (i =1,2,??, n); ND i p is the conditional probability that inspection will not be able to detect damage at the ith inspection given that damage exists, and F i p is the conditional probability that un-detected damage at the ith inspection will further grow to failure before the next inspection [(i+1)th] or end of intended service life. Clearly, the probability of failure of these events depends on the probability of damage progress, inspection capability, the timing of inspection, and the number of inspections. Therefore, a more rigorous risk assessment of inspection planning requires comprehensive understanding of the physics of damage initiation, progression and associated randomness, as well as the mathematical model representing inspection capability, and advanced probabilistic methodology capable of performing complicated numerical simulation and assessment. Due to its simplicity for further implementation, the concept of P-F interval and procedure outlined in NAVAIR 00-25-403 serve as a good starting point for establishing a rough estimate of inspection interval. For the purpose of addressing inherent randomness of failure progression and to further facilitate quantitative risk assessment and management for CBM, a more rigorous approach incorporating physics-based damage accumulation model, inspection capability, and advanced probabilistic methodology is needed urgently.932 J. Zhao and D. Adams 2 Challenges in a Damage Tolerance Approach In damage tolerance approach, structural integrity is ensured through a predictive crack growth model representing the true nature of damage progression, nondestructive inspections to eliminate excessive damaging, and proper repair and maintenance actions. Many factors affects the effectiveness, robustness, an accuracy of the damage tolerance approach, including validation of crack growth model, qualify capability of desirable NDI methods, developing optimal inspection plan, establishing repair limits and criteria for proper maintenance actions, and setting up rational level of target reliability for risk management. This paper discusses some of the aforementioned technical challenges associated with rotorcraft components and presents a stochastic methodology for predicting rotorcraft component fatigue lifetimes and optimal inspection intervals and assessing underlying risk. Prediction of fatigue crack growth behaviour Damage tolerance approach relies heavily on capability of a fracture mechanics (FM) model to accurately predict potential damage progression initiated at preidentified locations. Several commonly used FM software packages are available for such purpose, including NASGRO, AFGRO, and FASTRAN. They are developed based on linear elastic fracture mechanics and possess a rich library of stress intensity solutions for the commonly encountered structural configuration and geometric profile for anticipated crack growth. From time to time, more advanced fracture mechanics may be employed for more complicated crack growth behaviour, structural layups, and loading, if there is the stress intensity solutions do not exist. These advanced fracture mechanics tools, such as BEASY and FRANC-3D, engage boundary element based numerical procedure and simulation. Occasionally, the crack behaviour will also be observed and derived directly from crack growth testing at full component level, such as the empirical damage tolerance approach reported in Reference [3]. These approaches represent various levels of modelling and numerical simulation efforts to ensure adequacy of the fracture mechanics model building and accuracy of the predictive capability. For the purpose of qualifying a crack growth model for further DT application, model validation is critical important. There are several ways to achieve the goal. One engages seeded fault testing and the other is to compare the predicted results against the fielded cracking data for further correlation. Uncertainty modeling and quantification for DT approach Primarily, probabilistic uncertainty analysis and risk assessment involves modeling all of the fundamental quantities entering the problem, and also all uncertainties that arise from lack of knowledge in these quantities, which may affect failure of the component or system. These terms are referred to as basic variables including quantities of structural dimensions and material properties, yield stress and other ultimate response limitations, operating conditions and degradations, environmental and loading factors, etc. The sources of uncertainty in Damage Tolerance Approach for Dynamic Loaded Rotorcraft Components 933 probabilistic analysis can be mainly classified into two categories as aleatory and epistemic uncertainties. Aleatory uncertainties refer to the natural randomness associated with an uncertain quantity, which is inherent in time, in space and measurements. This kind of uncertainty is quantified through the collection and analysis of data to fit to theoretical distributions and, since it is inherent, it cannot be reduced. Epistemic uncertainties reflect a lack of knowledge or information about a quantity, which can be considered in either model or statistical uncertainty-subdivisions. Modal uncertainties arise from simplifications and idealizations that are necessary to model the behavior in a reliability analysis, or from an inadequate understanding of the physical causes and effects. Statistical uncertainties are only due to a shortage of information, and originate from a lack of sufficiently large samples of input data. Statistical uncertainties can be reflected through either parameters of a distribution with a limited set of data or the type of a theoretical distribution to be chosen to fit to data. Since epistemic uncertainty is associated with a lack of knowledge and/or information it follows that it can be reduced through an increase in knowledge by gathering data for a longer period, taking more measurements or carrying out further tests, doing research, and by expert judgment. In order to consider these uncertainties in a structural analysis, appropriate uncertainty models are essential for performing reliability methods to estimate the probability of failure. As one of the key building blocks of a damage tolerance risk assessment and design process, all the sources of uncertainty and their statistical characteristics related to the key design variables must be identified, quantified and further integrated into probabilistic damage tolerance design system. It is well recognized that fatigue initiation and its subsequent crack growth is a random phenomenon. As depicted in Figure 3, various sources of uncertainties contribute to random fatigue and fracture process, including fatigue initiation time, micro-crack initiation and propagation, stress intensity threshold, crack growth rate, usage and loads, and inspection capability for product/in-service inspection. Fig. 3 Uncertainty Identification for Damage Tolerance Approach. It is beyond the scope of this paper to provide comprehensive review of the statistical procedure for modelling of aforementioned sources of variability associated with DT assessment, details of statistical procedure, methodologies, and practices for DT uncertainty identification and modelling can be found in reference [10]. 934 J. Zhao and D. Adams Probabilistic risk assessment methodology Probabilistic methodologies have been widely applied for uncertainty quantification and associated risk assessment. Among the procedures developed for structural reliability assessment and failure probability prediction, a prominent position is held by simulation methods. The Monte Carlo simulation technique, as the basis of all simulation-based techniques, is the most widely applied numerical tool in probabilistic analysis. The convergent rate of the Monte Carlo estimator is appropriately measured by the coefficient of variation of the estimated probability of failure. In general, the basic Monte Carlo technique requires a large sample size to achieve accurate estimate of probability of failure. This becomes a major limitation for the practical application of basic Monte Carlo simulation in structural reliability applications involved in a small probability of failure. To address the challenge, the Importance Sampling technique has been developed and becomes the most prevalent approaches in the context of simulation-based methods for probabilistic analysis. In importance sampling scheme, instead of drawing random samples arbitrarily as the way implemented in a basic Monte Carlo simulation, the majority of the random samples are drawn from the region that contributes the most for the probability of failure. Several approaches can be employed to identify the important region; including 1) MPP obtained through first order reliability methods (FORM) or second order reliability methods (SORM) solution; 2) a priori estimate from pre-sampling; and 3) Markov Chain Monte Carlo simulation. In general, the efficiency of the Importance Sampling technique improves significantly with a large reduction of the variance of estimator, once the appropriate Importance Sampling density function is identified. In general, DT risk assessment requires generating and repeatable drawings of short-life samples. This requirement dictates the utilization of sampling based methodology in risk a