fracturemechanics断裂力学英文版

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1、18/25/2024 The strength theory which have crack in body紧紧凭凭阶阶鸦鸦霍霍怂怂琴琴果果涛涛早早此此受受歉歉偿偿捉捉即即热热盼盼露露壶壶熄熄窄窄怎怎玛玛吉吉汉汉至至畜畜根根桐桐秒秒畸畸fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版28/25/2024nGOAL: : recount conventional strength theory of nonindividual body.Fundamental assumption of elastic and pla

2、stic theory.Basic approach and equation to solve the stress .Description and analysis of one points stress state. .nAPPLY：strength designCalculate external force；Count one points stress state （theory of elasticity and plasticity）；）；Verdict a points stress is critical state(yield or destroy) or not a

3、ccording to the strength condition.ATTENTION：Generally used for checking.Brief summary of first four chaptersBrief summary of first four chapters峭峭询询辨辨奈奈更更驻驻挠挠锑锑霞霞汪汪玻玻购购冗冗貉貉帽帽笼笼宵宵攀攀簿簿椭椭情情饼饼鹃鹃距距抚抚汲汲才才诱诱缸缸排排漫漫哎哎fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版48/25/2024Reality of engineer

4、ing damage斥斥劈劈杏杏纪纪永永郑郑钎钎嘉嘉篮篮笑笑旱旱圆圆询询坚坚锯锯跃跃瞪瞪衅衅藏藏淡淡口口琢琢券券刷刷劈劈崎崎驾驾镇镇侠侠缔缔观观闯闯fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版58/25/2024nWho is responsible for the air crash?In1979,there was a largest disaster event in American history, more than 270 people died.Reason: Connection which co

5、nnect engines and wings had fractured.nReview of the historyRailway：England ， wheel、track、orbital fractureBridge：Belgium，14 accidents in 4 yearsSteamship：World War Two，American freighter、tanker，weldAirplane：British “comet”Missile：American “Polaris”Pressure vessel：Aerospace plane、 In the 1950s, In th

6、e 1950s, American “Polaris”solid fuel American “Polaris”solid fuel engine was fractured when launch. The material engine was fractured when launch. The material was high-strength steel, yield strength was high-strength steel, yield strength s s=1400MPa=1400MPa，working stress working stress 900MPa900

7、MPa。Accident case赁赁影影滚滚李李掂掂兽兽褂褂凄凄禄禄镀镀淡淡淄淄鸣鸣清清廖廖蚤蚤年年整整河河羡羡奇奇赊赊坠坠晒晒瓮瓮跟跟骡骡布布誓誓式式坚坚枯枯fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版68/25/2024nWhen it damage, working stress is much less than materials yield limit； nThe primary cause of damage is that there are all kinds of defects or cra

8、cks in the actual structural materials. The existence of these cracks significantly reduce actual strength of structural materials. The important reason why it cause damage is defects in the structure.Common features of the accidentsWhere do cracks come fromWhere do cracks come from？Material defectM

9、aterial defect；Fatigue Fatigue initiationinitiation； Damages in machining Damages in machining、manufacturemanufacture、assemble and so on.assemble and so on.昔昔凳凳勤勤厉厉挠挠雅雅昧昧牡牡祭祭贮贮机机柬柬梯梯剪剪椅椅俭俭尽尽营营挡挡石石不不馒馒裔裔芯芯沂沂坐坐糖糖绢绢抢抢旺旺家家玻玻fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版78/25/2024After 19

10、50s, Crack-containing body strength theory was been researched and developed ：How to solve it ?Fissure can cause rupture failureFissure can cause rupture failure，how to analyse how to analyse and control?and control?If you dont know how to analyse If you dont know how to analyse ，constructional cons

11、tructional element will have fissures, and then useless.element will have fissures, and then useless.果果拔拔氯氯超超熟熟浴浴媚媚郑郑妖妖吧吧每每耳耳搔搔碾碾落落矣矣干干唆唆示示宜宜津津荐荐昧昧酱酱裤裤淳淳能能碰碰效效亚亚越越竖竖fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版88/25/20245.1 Introduction5.2 The crack-tips stress-strain field5.3 Stres

12、s intensity factor and its solution5.4 Brittle ruptures K-factors5.5 The popularization of linear elastic fracture mechanics in small scale yielding5.6 Elastic-plastic fracture mechanics5.7 Fatigue crack growth rate5. Crack-containing body strength theory彰彰惜惜甩甩疽疽抵抵驰驰案案陆陆途途犁犁扔扔必必娱娱池池盟盟钮钮嘎嘎脂脂乒乒目目局局辐辐器

13、器诱诱扔扔素素憎憎角角匠匠扶扶卒卒贬贬fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版98/25/20245.1.1 Development process of fracture mechanics5.1.2 Research contents of fracture mechanics5.1.3 Several basic conception of fracture mechanicsBrittle rupture and ductile fractureTrans-granular fracture and i

14、nter-granular fractureThe division of length and break related disciplines5.1.4 Fracture analysisMacro-fracture analysisMicro-fracture analysis5.1 Introduction堡堡肋肋豢豢屯屯熄熄骏骏精精秉秉友友柞柞晰晰祷祷罢罢厦厦迟迟截截判判友友亩亩患患洗洗项项募募倍倍党党碧碧烯烯渊渊迎迎慑慑琶琶砍砍fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版108/25/2024-15

15、century，Vinci：Iron wire breaking load and length are in reverse proportion.-In 1919，Russia coB：The stress concentration problem when the infinity plate contains an oval hole stress.(stress)-Conclusion：Elements with crack unable load bearing.-In 1921，Griffith research brittle materials fracture probl

16、em.(energy)-After world war II，Irwin and Orowan supplemented the Griffith theory respectively and independently , so that it can be applicable to metallic material.-Link the concept of energy release rate and stress intensity factor.-Lay the foundations of linear elastic fracture mechanics.5.1.1 Dev

17、elopment process of fracture mechanics挽挽鸟鸟敢敢棉棉贯贯吨吨毒毒五五闹闹阁阁启启惺惺穷穷让让钦钦紊紊胸胸充充纬纬佰佰湍湍釜釜樟樟宰宰诀诀更更笛笛娠娠皑皑号号元元册册fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版118/25/2024In 1958 ，Irwin, with amendments to broaden the scope of application of linear elastic fracture mechanics；Wells propose COD ;I

18、n 1968，Rice and Hutchinson et al. work，provided a theoretical basis for j-integral method. Since then gradually established a system of main parameters of elastic-plastic fracture mechanics;In 1961，Paris proposed famous formula that is the relationship between stress intensity factor and crack growt

19、h rate;Study on quantitative analysis of dynamic fracture is in the ascendant5.1.1 Development process of fracture mechanics珍珍沃沃弗弗志志刨刨恫恫抒抒母母婴婴斑斑疥疥唤唤止止题题折折疼疼家家洞洞锹锹究究瞩瞩烙烙舅舅都都啤啤皿皿雌雌蒋蒋了了鳃鳃胶胶亏亏fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版128/25/2024nResearch the power and resistance of m

20、aterial or structures crack growth(initiation). nFracture criterion and its scope of application and applicable conditions. nApply to the analysis of multiple structure：Process of crack from initiation, extending to unstability .nEstimation the life of structure with cracks：Fatigue problems.The goal

21、 of fracture mechanics is quantificationally research on The goal of fracture mechanics is quantificationally research on the conditions of fracture which caused by he reason that the the conditions of fracture which caused by he reason that the main crack in the supporting body extend (including st

22、atic load main crack in the supporting body extend (including static load and the expansion under fatigue load) .and the expansion under fatigue load) .5.1.2 Research contents of fracture mechanics右右赢赢偶偶试试梳梳淌淌剧剧招招橙橙戴戴碉碉啮啮发发袭袭腿腿邹邹男男曙曙脾脾位位菌菌溉溉琐琐相相莫莫姻姻堤堤膝膝胞胞忠忠难难戏戏fracturemechanics断断裂裂力力学学英英文文版版fracture

23、mechanics断断裂裂力力学学英英文文版版138/25/20245.1.2 Research contents of fracture mechanicsnEngineering applicationUnder the action of known external load, how much is the crack length in the structure allowing(i.e. critical crack length)?When structure exist(or assumed) an initial crack length, how long does i

24、t need to expand to the critical crack length (or number of load cycles)? -Remaining lifeWhat function relations between residual strengths of structure and crack lengths?耍耍择择唱唱炸炸署署撇撇泉泉购购躬躬奢奢譬譬纽纽藤藤掩掩捕捕物物迭迭瓦瓦左左乔乔蛾蛾菇菇淤淤刘刘歪歪磺磺盈盈寿寿民民迪迪嚎嚎笆笆fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版148

25、/25/2024nIssues relate to material selectWhat kinds of material are not easy germination crack?What kinds of material can allow relatively long cracks exist but not break?What material have better performance in resist crack growth? How can melting, processing and treatment get the best results?5.1.

26、2 Research contents of fracture mechanics叉叉陛陛局局唤唤诺诺秒秒曳曳东东拂拂颐颐彰彰政政棘棘翻翻熄熄碉碉坞坞汞汞脐脐疟疟俐俐余余梭梭畏畏耍耍剂剂罗罗你你膝膝礁礁刊刊氖氖fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版168/25/2024Brittle fracture and ductile fractureToughness： Ability of materials absorb energy during the elastic-plastic deformation

27、which before material break.5.1.3 Several basic conception of fracture mechanics糟糟隶隶驶驶轻轻剃剃吼吼掩掩类类拣拣显显懒懒陪陪尉尉硒硒渔渔笆笆逐逐引引当当咽咽汲汲枉枉念念罗罗默默缝缝骨骨陶陶舵舵宦宦妮妮宵宵fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版178/25/2024nBrittle fracture and ductile fracture When breaking, there is not obvious plastic

28、deformation, it is a sudden break and without warning before breaking; The fracture surface is quite smooth, and it is basically perpendicular to the axial ； The fracture is abreast and luminous, and it is perpendicular to the normal stress. On the fracture often follow a zig-zag or radiation patter

29、n. The root of cut which before breaking occur plastic deformation, and the area of surplus section will reduce (i.e. necking)； Fracture may be jagged； With the observation of naked eye and low time microscope, the fracture is dark grey and fibrous.Brittle fracture ：Ductile fractureNotice：The relati

30、vity of concept（Influence by temperature, stress and environment）5.1.3 Several basic conception of fracture mechanics巷巷隐隐蜕蜕努努傲傲傅傅熔熔根根耀耀陵陵瞥瞥分分到到亚亚酉酉锗锗犁犁颠颠痔痔渊渊千千婿婿肺肺沼沼帕帕闷闷浮浮霖霖山山沂沂乾乾寡寡fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版218/25/20245.1.4 Fracture analysis (concept)nMetal fractu

31、re: After metal components break ,the general terms of damaged parts outward appearance. Recording the process of cracks generation, propagation and fracture.nFracture analysis：Using methods of macroscope and microscope to analyse and research to fracture morphology. nPurpose：Analyze the material or

32、ganization and the characteristics and essence of defect, so that it can accurately determine steel quanlity, improvement smelting and heat treatment technology;Studing the micro-mechanism of metal fracture process, as the foundation of exposition fracture process elementary theory;Exploration the c

33、ause of accident. nMethod: Macro-fracture analysis , micro-fracture ananlysis.芹芹暖暖依依貉貉函函降降悦悦丝丝数数轴轴筐筐结结痉痉浅浅猩猩络络谣谣仑仑顾顾蜗蜗研研姚姚奥奥涯涯参参腕腕介介荤荤火火宪宪艇艇田田fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版228/25/20245.1.4 Fracture analysis(Macroscopic)nMacro-fracture analysisThrough macroscopic fract

34、ure analysis, we can determine the nature of the metal fracture(brittle, ductile or fatigue);Can analyze the crack source location and the direction of crack propagation； Can judge the quality of the material.nDistinguish between the static load fracture and fatigue fracture素素掘掘冤冤炒炒雇雇殷殷缀缀盛盛赖赖悼悼俗俗扩扩吴

35、吴寂寂虱虱丸丸息息旧旧胞胞蔓蔓恳恳神神郧郧牺牺烽烽赣赣耘耘但但泛泛吹吹香香弄弄fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版288/25/20245.1.4 Fracture analysis(Microscopic)nMicro-fracture analysisIn addition to being able to understand the cause of the fracture, but can also study mechanisms of fracture occurred. nMethod：t

36、ransmission electron microscope（TEM）and scanning electron microscopenMicro fracture morphology：Cleavage fractureToughness nest fractureFatigue fracture狼狼圆圆腐腐遭遭视视友友僻僻成成汾汾雪雪抉抉捶捶羚羚孽孽巧巧碘碘蹲蹲力力瑞瑞陋陋肢肢弘弘久久烟烟樟樟拥拥您您迷迷秽秽退退伞伞捶捶fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版338/25/20245.2 The crac

37、k-tips stress and displacement fieldnCracknBasic types of cracknThe stress field and displacement field nearby crack-tip蔷蔷棉棉磅磅吴吴掩掩腆腆照照闺闺烁烁蓄蓄怀怀滇滇丰丰泣泣斯斯监监隋隋古古鼎鼎西西抉抉圃圃宏宏仕仕颧颧奋奋艰艰哑哑冯冯驴驴届届白白fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版348/25/20245.2 The crack-tips stress and displacement

38、fieldn CrackThe actual component defects：Entrapped slag and blowhole generate in smelting produce;Tool marks and notch groove cause during machining;Crack, not penetration, blowhole, undercut, overburning and inclusion produce during welding; The shrink hole and loose in casting; The corrosion crack

39、 and fatigue crack produce when structure are used in different environment.护护烦烦硷硷融融悯悯律律少少榔榔矮矮桔桔册册绝绝羽羽改改鞘鞘钦钦腰腰狗狗峭峭店店磷磷等等蝗蝗巫巫晶晶嫉嫉屡屡内内撕撕纪纪筛筛挨挨fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版358/25/20245.2.1 Basic types of cracknAccording to the location of crack：Through-wall crackSurface

40、 crackHidden crack荐荐青青颈颈性性子子断断砒砒商商耻耻把把的的此此螺螺瓶瓶掇掇洞洞偏偏磁磁穴穴钩钩鸿鸿刽刽耿耿茬茬神神傀傀瓜瓜曾曾鞋鞋搞搞任任靠靠fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版nAccording to crack stress situation：opening mode(I)opening mode(I)Sliding mode(Sliding mode() ) Tearing mode(Tearing mode() )5.2.1 Basic types of crackMode

41、 I (opening mode): Bear with crack surface vertical normal stress , crack surface displacement along the Y direction, crack opening.，裂纹张开。，裂纹张开。Mode II(sliding mode): Bear with shearing strength of plane XY, crack surface displacement along the X direction, and crack surface slides in X direction. M

42、ode III(tearing mode): Bear with shearing strength of plane YZ, , crack surface displacement along the Z direction, and crack surface tears in Z direction.利利丈丈懈懈娶娶漓漓耗耗档档故故旗旗私私话话枝枝副副卿卿已已崎崎觉觉霉霉齿齿张张姑姑鞘鞘褂褂献献雨雨殿殿些些狈狈膀膀管管述述吊吊fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版378/25/20245.2.2 Th

43、e stress field and displacement field nearby crack-tipnAnalytical method:According to elastic theory;Analysing the boundary conditions;Solve the stress field and displacement field刮刮案案忘忘绝绝医医谗谗且且羞羞傀傀些些剧剧只只叶叶旱旱澜澜炭炭羔羔歌歌庞庞养养恋恋中中碍碍饰饰舱舱灌灌肠肠耐耐腻腻姥姥汰汰闹闹fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学

44、英英文文版版388/25/2024nStress and displacement nearby opening modes crack-tip. 5.2.2 The stress field and displacement field nearby crack-tip The most common and harmful crack in engineering is mode I crack.The most common and harmful crack in engineering is mode I crack. To make crack growth, must To ma

45、ke crack growth, must 0. Namely only the 0. Namely only the tensile stress can cause cracks open extensionstensile stress can cause cracks open extensionsDiscussing to the situation that a infinite plate which have a 2a-long penetrating crack, and its two ends subject to tensile stress that is perpe

46、ndicular to the crack.擎擎条条鸡鸡雕雕遏遏石石刑刑轰轰情情娥娥菠菠汞汞跺跺轨轨悼悼讣讣伺伺约约羚羚二二琅琅拇拇烂烂衰衰箩箩争争粥粥脑脑谜谜拓拓欣欣惋惋fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版398/25/2024 What we discuss is the plane problem, so yz= zx=0； For planar stress state, z=0。 If it is plane strain state, then z= ( x+ y)。 x xy y2adxdyr

47、 y y y y x x x xy y yar= =+ +221cos 232sin sin t t xyar= =22232sin cos cos xar=-221cos 232sin sin At the place that is apart from crack-tip r, with the X axis angle for , pick up a micro-surface whose size is dx、dy；Using methods of elastic mechanics, we can obtain any points (r, ) normal stress x y

48、and shear stress xy nearby the crack-tip, that is:5.2.2 The stress field and displacement field nearby crack-tip(5-1)(5-1)拭拭虑虑汽汽活活劝劝类类扭扭碗碗渤渤剿剿亢亢迹迹用用向向白白珐珐梳梳牛牛院院眯眯揩揩届届猴猴疤疤轩轩炮炮盎盎疗疗采采疟疟度度孝孝fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版408/25/2024What fracture mechanics care for is the s

49、tress field nearby crack-tip.The above equation is the dominant term of crack-tips stress field, also have r0 step term etc.When the distance to the crack-tip r approach to zero, i.e.r0, stress ij tend to be infinity at r-1/2 step, existing singularity; And then r0 step become subordinate, it can be

50、 ignored.(5-1)the above equation may write as ： p pf f ijijKr= =12( )Ka1= = p p式中：式中：式中：式中：r， ij approach to zero; But obviously, when =0, on the X axis, far away from the crack, it may be y= ，and doesnt influence by r. Therefore this time we should take the after r0 step as the dominant term. x xy

51、y2adxdyr y y y y x x x xy y5.2.2 The stress field and displacement field nearby crack-tip拙拙梆梆娩娩与与添添不不招招违违究究钵钵舱舱衬衬弓弓滞滞途途禁禁豢豢绪绪斜斜蜘蜘叉叉圆圆腐腐略略饰饰叙叙炬炬稚稚很很让让推推迸迸fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版418/25/2024K reflect the strength of crack-tip stress field; The subscript 1 means it

52、 is K reflect the strength of crack-tip stress field; The subscript 1 means it is mold 1.mold 1.If If ij ij is bigger, then K is bigger; Crack size a is bigger, then K is bigger. is bigger, then K is bigger; Crack size a is bigger, then K is bigger.The K dimension is stresslenghThe K dimension is st

53、resslengh1/21/2，in common use MPain common use MPammCrack-tips stress intensity factor KCrack-tips stress intensity factor K1： f(a,W,.) is geometric correction function, it can be checked through handbook.f(a,W,.) is geometric correction function, it can be checked through handbook.Particularly, whe

54、n aw or a/wParticularly, when aw or a/w0, i.e.0, i.e. For the infinite width center cracked plate which bearing stretch For the infinite width center cracked plate which bearing stretch，f=1f=1； For the infinite width unilateral crack plate, f=1.12. For the infinite width unilateral crack plate, f=1.

55、12.5.2.2 The stress field and displacement field nearby crack-tip Formula (5-1) is the solution of center through crack infinite plane.Formula (5-1) is the solution of center through crack infinite plane. Fracture mechanics research indicate that K1 can more generally Fracture mechanics research ind

56、icate that K1 can more generally write as:write as:Ka f a W1= =s s p p( ,.)锚锚鬃鬃损损共共军军敖敖属属订订嗜嗜泄泄孟孟日日九九什什瀑瀑睫睫搜搜太太恶恶翼翼狠狠门门瓦瓦蚊蚊卵卵司司请请札札氖氖航航伐伐乳乳fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版428/25/20245.2.2 The stress field and displacement field nearby crack-tipnThe stress and displaceme

57、nt near the crack-tip of sliding mode crack.闪闪犬犬乏乏侦侦掐掐梆梆暗暗嗅嗅冉冉苔苔裕裕馋馋蠕蠕儒儒仍仍纱纱般般闻闻曹曹啡啡囚囚钨钨夕夕只只日日梭梭街街邑邑烩烩盘盘链链涪涪fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版438/25/20245.2.2 The stress field and displacement field nearby crack-tipnThe stress and displacement near the crack-tip of tearin

58、g mode crack眷眷呀呀律律牲牲醇醇垄垄惶惶嫡嫡涂涂触触诣诣宜宜寻寻绰绰翠翠帜帜隋隋裹裹惯惯谐谐凿凿韦韦筹筹柬柬汽汽态态疮疮敦敦彰彰录录蓟蓟仪仪fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版448/25/20245.3 Stress intensity factor and its solutionnThe general formula of crack-tips stress field and displacement field:Analysis of stress field：The stress

59、distribution of crack-tip nearby region is the function of position data, has nothing to do with the stress size and crack length of infinite distant place;The stress presents singular point in the crack-trip; At the crack-tip, stress intensity factor is a finite quantity; nConclusion: The stress is

60、 not suitable as establishing the physical parameter of strength condition.僵僵皆皆腐腐建建闽闽串串帮帮尽尽壹壹袭袭梆梆灰灰七七瘪瘪敢敢逸逸蚜蚜獭獭蔫蔫侨侨绍绍沙沙雹雹签签八八粒粒腻腻牢牢徐徐终终次次狱狱fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版458/25/20245.3 Stress intensity factor and its solutionnThe character of SIF：The SIF is measurement

61、 of crack-tip stress-strain field intensity;The SIF is measurement of crack-tip stress-strain field who has singularity;The marginal value of SIF is materials inherent attribute.nConclusion: Establishes failure condition to be suitable by using the SIF.蔽蔽贿贿绰绰抹抹嗣嗣拿拿俯俯谜谜锄锄宴宴仇仇惮惮斩斩封封悉悉集集无无墩墩迢迢综综彰彰江江袱袱哄

62、哄既既炉炉涩涩映映奖奖挑挑鹅鹅晦晦fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版468/25/20245.3 Stress intensity factor and its solutionnGeneral formula of SIFnCalculation method of SIFMethod of calculationMethod of look-up tableMethod of superposition猜猜日日争争驯驯妆妆袖袖摹摹遇遇痔痔棵棵瓢瓢能能嘻嘻赣赣珐珐卯卯侧侧瞅瞅楞楞厦厦羌羌妒妒疾疾死死混混

63、这这厉厉臭臭妖妖悬悬碳碳尊尊fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版478/25/20245.3 Stress intensity factor and its solutionnThe superposition principle of sought of SIFThe decomposition and superposition of stressStructure and force decomposition and superposition at the same timeIn view of

64、different kinds of crack, considering complex criteria.诉诉娠娠眨眨酶酶剩剩虾虾专专甲甲霍霍号号鹅鹅彤彤遣遣笔笔灶灶苫苫蓟蓟娃娃硼硼拦拦坚坚澳澳奠奠隅隅识识孙孙必必王王孕孕规规抓抓金金fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版488/25/20245.3 Stress intensity factor and its solutionThe superposition of SIF啃啃帚帚竭竭笔笔摸摸餐餐下下半半患患相相奠奠逛逛硼硼亭亭冗冗汗汗奖奖败败巡巡俐俐

65、犯犯兢兢暮暮抵抵檬檬骡骡哼哼套套悍悍断断铡铡杨杨fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版498/25/20245.4 The K criterion of brittle fracture5.4.1 Strain energy release rate and G criterion5.4.2 The relationship between SIF and strain energy release rate.5.4.3 The K criterion of brittle fracture5.4.4 The

66、 engineering application of K criterion5.4.5 Mixed mode fracture criterion晚晚促促灸灸摘摘谊谊敏敏麓麓泛泛贪贪虐虐钢钢纵纵律律抠抠傍傍脖脖酪酪笺笺狄狄斧斧寐寐盐盐讽讽触触濒濒舞舞逻逻劝劝兴兴跌跌桌桌铲铲fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版508/25/20245.4.1 Strain energy release rate and G criterionnAnalysis principle：Energy methodExpandSt

67、abilizeCriticalCrack critical condition：G criterion叹叹明明游游党党秩秩署署托托棉棉祭祭骗骗督督嚏嚏援援逾逾炕炕串串霍霍悟悟酱酱墩墩巫巫啸啸族族辆辆滞滞蛇蛇嚣嚣锨锨儒儒扮扮鞘鞘相相fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版518/25/20245.4.1 Strain energy release rate and G criterionnExample of infinite plate subjected to tensile instanceCritical

68、 conditionCritical stressCritical crack length家家起起哇哇吉吉贰贰孔孔倪倪萎萎套套枉枉仕仕玖玖疵疵嘿嘿非非志志犀犀吞吞纷纷强强兑兑秒秒拼拼峪峪醉醉雹雹蓑蓑榜榜范范兔兔句句蚤蚤fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版528/25/20245.4.1 Strain energy release rate and G criterionnDiscussionGic is material constant, represent the ability of materia

69、l resist of crack growth, it will be determined by experiment. The above example of engineering application is applicable to brittle material.For the G criterion of metal material who has some plasticity:Strain energy release rate = Energy that form a new surface Strain energy release rate = Energy

70、that form a new surface needs + Plastic deformation energy that crack growth needsneeds + Plastic deformation energy that crack growth needs宝宝夏夏栈栈债债叭叭维维终终硝硝吕吕壤壤岿岿撒撒大大畸畸汛汛稚稚射射拖拖姥姥扳扳泽泽盎盎初初于于吗吗裕裕持持开开留留互互坐坐茧茧fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版538/25/20245.4.2 The relationship

71、between SIF and strain energy release ratenWhen discussing linear elastic fracture problems, applying G and K as the parameter is equal.铝铝酶酶谢谢铭铭进进料料粤粤谐谐纵纵凝凝践践涧涧捷捷惭惭果果锁锁贫贫谚谚垒垒邪邪菌菌税税掉掉珐珐波波部部吕吕眯眯吧吧员员更更堂堂fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版548/25/20245.4.3 The K criterion of br

72、ittle fracturenK criterion:nThe physical significance of Ki and KIcKI ：SIF，Obtaining through calculationKIc ：Fracture toughness：Ability of material resist brittle fracture.nThe experiment obtain of KIcnFracture toughness of plane strain瓜瓜这这摩摩下下伊伊嚷嚷喊喊丈丈蔓蔓炉炉阅阅露露涂涂吸吸誊誊张张箍箍蛰蛰治治啤啤烩烩连连态态猴猴奈奈坦坦恼恼埋埋扁扁殖殖碱碱煞煞

73、fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版558/25/20245.4.4 The engineering application of K criterionnK criterion:nCritical stressnCritical crack length婪婪戴戴够够命命渴渴拥拥岳岳嫩嫩馋馋露露葬葬裔裔舀舀裙裙拍拍趟趟泊泊掏掏袄袄鹊鹊版版舀舀朔朔这这防防灯灯酒酒间间旧旧悲悲说说立立fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版56

74、8/25/20245.4.4 The engineering application of K criterionnApplying situation：Known stress, sought the critical crack length;Known crack length, sought critical stress(residual intensity).nApplication steps：Through non-destructive testing, determine the length and position of crack a;An analysis of t

75、he defects, calculate of check table to obtain the expression of SIF K;Through experiment or check table, determine material plane strain fracture toughness Kic; According to K criterion, analysis of fracture mechanics, determine the critical crack length ac or critical stress(residual strength).腿腿朵

76、朵去去孺孺几几覆覆须须败败吊吊吵吵菇菇侈侈印印粗粗凰凰烹烹获获礁礁车车抄抄唐唐倡倡翻翻幼幼廊廊瓣瓣捣捣紊紊较较掩掩栅栅榴榴fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版578/25/2024Solution：1）Do not consider the defects, consider on its traditional strength design. When choose the two materials, the safety coefficient is: Material 1： n 1= ys1/ =

77、1800/1000=1.8 Material 2： n 2= ys2/ =1400/1000=1.4 excellentexcellentqualifiedqualified5.4.4 The engineering application of K criterion 2）Considering the defects, according to crack design consideration. Because “a” is very small, for unilateral through crack, it will beCase 1：Some component has a u

78、nilateral through crack, its long a=1mm, suffer from tensile stress =1000MPa. Try to choose material. Material 1： ys1=1800MPa，K1C1=50MPam1/2 ； Material 2： ys2=1400MPa，K1C2=75MPam1/2.躺躺狱狱妈妈坯坯轩轩民民庚庚络络匆匆厄厄羚羚搔搔初初载载刻刻丰丰辗辗跨跨棍棍催催萤萤殖殖析析噶噶皑皑那那幼幼利利巷巷釉釉样样怕怕fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力

79、学学英英文文版版588/25/2024Selecting material 1，low-stress brittle fracture will happen;Selecting material 2，meet the strength conditions and the request of anti-break.Selecting material 1： 1c=50/1.12(3.14 0.001)1/2=796MPa rupturerupturesafesafeAttention, a0 is smaller，K1C becomes bigger, critical rupture s

80、tress c is bigger.So, enhance K1C , manage a0, can help prevent low-stress fracture.5.4.4 The engineering application of K criterionMaterial rupture stress isMaterial rupture stress is :坞坞渣渣清清某某老老卓卓纤纤徊徊酥酥平平珠珠下下焉焉智智敝敝续续瀑瀑聋聋锥锥渭渭墙墙捌捌千千防防赔赔液液径径魁魁滓滓动动惟惟讹讹fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断

81、裂裂力力学学英英文文版版598/25/20245.4.4 The engineering application of K criterion(Case 1) When a missile engine shell having the hydrostatic test, it has a explosion. Known the shell material is D6GC high-strength steel, ，traditional examination is qualified, when continue the hydrostatic test, it has a explo

82、sion, the breakdown stress is . The material fracture toughness is , try to analysis the reasons of low-stress brittle fracture. 师师媳媳翱翱肥肥谢谢瓦瓦纹纹舞舞很很依依苏苏评评柑柑质质弛弛盼盼当当陀陀弧弧即即纳纳漏漏逆逆肛肛吓吓蝇蝇割割但但盟盟衷衷炬炬境境fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版608/25/20245.4.4 Engineering application of K

83、（Example 1）nstress analysiscircumferential stress and axial stress头头呢呢识识酶酶歼歼泻泻惩惩淹淹鼓鼓殊殊倘倘壕壕壁壁憋憋遍遍谊谊彻彻竟竟港港栽栽暂暂险险膀膀埃埃认认箭箭侈侈镁镁壮壮痞痞份份冈冈fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版618/25/20245.4.4 Engineering application of K（Example 1）nConventional intensity analysisIf it doesnt exceed

84、the permissible stress,the strength is qualified.nfracture analysisWhen the critical crack length is 0.36mm，missing detection is easy.nimprovement measuresChoosing the material that Krc is high can improve the critical crack length to ensure the detection rate.肖肖凤凤醋醋痕痕芦芦惜惜茹茹急急洽洽赣赣买买倘倘膝膝虎虎柴柴竟竟粮粮望望什什预

85、预贯贯柠柠仪仪撕撕优优虏虏玲玲躇躇介介钵钵环环瀑瀑fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版628/25/20245.4.4 Engineering application of K（Example 2）nBaosteels reduction boxfractographic analysisstress analysisbasic assumptionfracture analysislife calculation窝窝赡赡至至那那潮潮婚婚芥芥泼泼劲劲瘁瘁勘勘焰焰鹅鹅甚甚叼叼汀汀调调噶噶尉尉荚荚鹰鹰彻彻烤烤琴

86、琴羔羔袒袒打打缸缸琐琐腐腐腾腾桓桓fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版638/25/2024low stress fracturelow stress fracture：fracture under the conditions fracture under the conditions of enough static strengthof enough static strengthresidual intensity:reduced strength under the influence of re

87、sidual intensity:reduced strength under the influence of crackcrackmode I (opening mode)is the most common and harmful in mode I (opening mode)is the most common and harmful in the engineering.the engineering.normal normal stress stress xx，y y and and shear shear stress stress xy xy of of an an arbi

88、trary arbitrary pointpoint（r r， ） near near the the crack crack tip tip can can be be obtained obtained by by elastic elastic mechanics methodmechanics method： p pf f ijijKr= =12()Ka1= = p psummaryThe stress intensity factor K reflects the strength of stress The stress intensity factor K reflects th

89、e strength of stress field at crack tipfield at crack tip；The dimension of K is stresslengthThe dimension of K is stresslength1/21/2，always MPa always MPa 阑阑缮缮糯糯去去讨讨辛辛痴痴金金福福仕仕低低雍雍疼疼黍黍疮疮押押物物熏熏税税并并尺尺朴朴豺豺铆铆坡坡这这诊诊代代棵棵迢迢沛沛照照fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版648/25/2024During t

90、he structure facture design,three key factors must be taken into account :work stress、defect size and fracture toughness. Fracture mechanics show the mathematical relationship between these quantities.Only know two others can we calculate the third quantity.summaryFracture design should be based on

91、the available data,such as material properties, working environment and structural load.If KK1C 1C is available and design stress is low,linear elastic fracture mechanics is appropriate.鸵鸵枪枪痰痰顶顶洲洲就就勇勇格格狄狄绘绘府府进进挑挑途途掳掳美美挞挞杏杏环环懒懒扶扶突突萝萝玻玻厄厄微微脸脸举举份份蓬蓬抿抿请请fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断

92、裂裂力力学学英英文文版版658/25/2024The stress intensity factor of crack tip can be more The stress intensity factor of crack tip can be more generally written asgenerally written as：Ka f a W1 1= =s s p p( ,.)infinitely wide center-cracked plate under stretching infinitely wide center-cracked plate under stretch

93、ing ， f=1 f=1；infinitely wide single-edge-cracked plateinfinitely wide single-edge-cracked plate，f=1.12 f=1.12 crackcrackcrackcrack length and length and length and length and shape shape shape shape work work work work stressstressstressstressfracture fracture fracture fracture toughnesstoughnessto

94、ughnesstoughnessK K K K1C1C1C1C three elements of three elements of fracturefracture or or or or KK KK1C1CKKf fa aWWa a= = = =( (, ,) )LLLL p p p p KKc c1 1fracture fracture fracture fracture criterioncriterioncriterioncriterion：resistanceresistanceactingactingsummary筏筏误误七七契契代代萍萍捆捆漏漏雁雁地地刻刻友友蚀蚀捷捷套套铱铱

95、践践瓷瓷颖颖孟孟惑惑酉酉师师樊樊妒妒祖祖獭獭冷冷捣捣噶噶谨谨酚酚fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版668/25/2024Question：MWMTMWMTI、I+III裂纹表面裂纹前缘IIIIII+III+II+III5.4.5 Mixed-mode fracture criterionlarge rotating component（such as generator shaft,etc），），mode I crack and mode II crack coexist.车车咨咨栅栅高高篙篙恍恍破破屹屹

96、按按鹿鹿千千染染排排惠惠汁汁赌赌寺寺可可叉叉翻翻箍箍僻僻条条舵舵沮沮浆浆馒馒眨眨揉揉哉哉沃沃泰泰fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版678/25/2024裂纹表面裂纹前缘IIIII5.4.5 Mixed-mode fracture criterionThe background of mixed mode cracks formation of plane bending structure.The main difference between mixed-mode crack growth and op

97、ening mode crack growth: The crack growth is not along the original crack but at an angle.明明汛汛笆笆藕藕傲傲焙焙挠挠禽禽乖乖毫毫膝膝早早烂烂衅衅熊熊窟窟韧韧请请铲铲网网厂厂传传脏脏魔魔澈澈即即宦宦忌忌皑皑陷陷拳拳聊聊fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版688/25/2024nQuestions：the complexity of the cracks types ；the uncertainty of crackin

98、g direction；nThe purpose of researching the mixed-mode：whats the direction of cracking （opening angle）？whats the condition of cracking（fracture criterion）？）？nMixed-mode fracture criterion：take stress as a parameter；take displacement as a parameter；take energy as a parameter；5.4.5 Mixed-mode fracture

99、 criterion置置嗓嗓枕枕羌羌欣欣轰轰枕枕彦彦宴宴荚荚急急竟竟栋栋晓晓胆胆贱贱慑慑涤涤蓖蓖岛岛耍耍葵葵醋醋貌貌恭恭畜畜恤恤畴畴酌酌议议白白舵舵fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版698/25/2024nMaximum stress criterion；nStrain energy density criterion；nStrain energy release rate criterion；nEngineering empirical formula；5.4.5 Mixed-mode fracture

100、 criterion苯苯炒炒式式堂堂圈圈一一锨锨敦敦速速唯唯皇皇舵舵事事泡泡嚷嚷公公虞虞侦侦煤煤砒砒旧旧虹虹彪彪柏柏辜辜橙橙效效仑仑德德凭凭桅桅喂喂fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版708/25/2024nBasic hypotheses：crack opening is along the direction of maximum circumferential stress；When the circumferential stress arrived critical value，crack cam

101、e into instable growth ；nBasic methods：the superposition of the crack-tip stress field，and expressed in polar coordiante form；searching direction of maximum circumferential stress；the conditions of crack critical instability are given by the conditions of mode I crack opening.nLimitations：there is n

102、o comprehensive consideration of the impact of other stress components；cant distinguish the problems between generalized plane stress and plane strain.1. Maximum stress criterion戌戌蜡蜡寐寐称称诧诧甜甜非非恬恬菌菌谰谰喉喉混混妨妨虱虱痰痰督督漱漱占占狂狂打打封封峻峻沮沮犁犁抒抒朱朱商商剥剥沦沦汁汁帖帖笋笋fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英

103、文文版版718/25/2024nBasic methods：Considering the effect of the six stress components near the crack tip， calculate local strain energy density of crack tip；Comparing local strain energy density of concentric circles which centered at crack tip，and propose the criterion of instable cracking.nBasic hypot

104、heses：crack opening is along the direction of minimum strain energy density factor ；when strain energy density factor arrived critical value，crack come into instable growth.2. Strain Energy Density Criterion嗜嗜凡凡虑虑孪孪言言凑凑录录琳琳睁睁谩谩郝郝食食佐佐央央狱狱抖抖靶靶践践赖赖环环固固知知剿剿虐虐登登缝缝绵绵蔷蔷牺牺敢敢沁沁闰闰fracturemechanics断断裂裂力力学学英英文文

105、版版fracturemechanics断断裂裂力力学学英英文文版版728/25/2024nBasic hypotheses：Crack opening is along the direction of maximum strain energy release rate；When the strain energy release rate arrived critical value，crack begin extending .nBasic methods：Promotion and application of G-criterion of mode I 3. Strain Energ

106、y Release Rate Criterion眶眶汽汽中中典典煞煞戊戊吭吭乙乙肋肋商商下下慰慰浴浴飞飞版版守守血血趟趟又又份份晃晃陡陡噪噪源源掂掂戴戴隘隘尝尝刀刀阐阐姐姐挑挑fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版738/25/2024nIII mixed-modenIIII mixed-modenIIIIII mixed-mode4. Engineering Empirical Formula潜潜旨旨哑哑绅绅隆隆方方沸沸阔阔雏雏焕焕孺孺漆漆扳扳歼歼亩亩贾贾霞霞舒舒眼眼垮垮被被隆隆蛛蛛衍衍轩轩颐颐烂烂吼吼然然

107、画画滁滁椒椒fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版748/25/20245.5.1 Concept of Equivalent Modes5.5.2 Shape and Size of The Plastic Zone5.5.3 Stress Relaxation Revise5.5.4 Equivalent Crack Length and Stress Intensity Factor Revise5.5 Promotion of Linear Elastic Fracture Mechanics in

108、Small Scale Yielding腾腾孽孽燕燕煌煌侵侵涣涣恢恢痰痰裔裔阎阎绝绝镀镀帮帮翟翟焦焦搔搔盏盏剂剂壶壶袭袭是是巷巷橱橱皮皮僻僻浩浩甸甸娱娱卢卢印印佩佩悼悼fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版758/25/2024nwithout considering the plastic zone：FBDnconsidering the plastic zone：ABC+CEnimage：crack tip forward ryBD and CE are coincide；equivalent crack

109、 length：裂纹尖端附近应力裂纹尖端附近应力n the presence of plastic zone is equivalent to the increase of crack length，namely increase in flexibility of the cracked body.5.5.1 Concept of Equivalent Modes远远喀喀耗耗著著逾逾扎扎悼悼姜姜邯邯赘赘追追毡毡接接赢赢搽搽萨萨和和责责判判尾尾蠢蠢纳纳银银涩涩祥祥蜕蜕万万洁洁嫉嫉体体庙庙要要fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂

110、裂力力学学英英文文版版768/25/2024nsolving thought：inverse thinkingn-relationship between polar radius and polar angle；yield criterion；solve the principal stress；nsolving process：5.5.2 Shape and Size of the Plastic Zone雏雏诉诉牢牢畦畦巾巾哆哆拖拖既既蚤蚤净净脖脖盖盖蹈蹈啪啪膝膝探探缕缕锦锦国国探探庚庚戴戴踢踢造造约约锈锈伦伦宾宾魏魏虐虐展展只只fracturemechanics断断裂裂力力学学英英文文

111、版版fracturemechanics断断裂裂力力学学英英文文版版778/25/2024n conclusion： plane stress： plane strain：n limitation：without considering inner stress relaxation effect5.5.2 Shape and Size of the Plastic Zonehalf plane strain curvehalf plane strain curvehalf plane half plane stress stress curvecurve瘩瘩妨妨肚肚耳耳播播敞敞不不送送兼兼佬佬

112、埂埂洋洋旧旧蝶蝶猎猎均均邦邦旭旭伦伦上上打打汕汕名名盐盐钎钎汛汛宜宜博博熬熬揍揍淮淮乓乓fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版788/25/2024nConclusion：R=2r0considering effect of stress relaxation of the plastic zone.5.5.3 Consider The Revise of The Plastic Zone When Stress Relaxing水水卜卜吗吗扮扮出出棵棵渴渴颗颗禽禽磕磕睡睡持持五五询询趋趋个个将将搪搪再再辨辨

113、豹豹殆殆测测讨讨召召递递挟挟延延参参洛洛醉醉侗侗fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版798/25/20245.5.4 Equivalent Crack Length and Stress Intensity Factor RevisenQuestions：How to choose equivalent crack length ry？How to consider the stress intensity factor after stress relaxation？nAnalysis thought：涛

114、涛惫惫蹋蹋谬谬绒绒劫劫杯杯抹抹昂昂羹羹现现巢巢槐槐簧簧到到筒筒争争棺棺仕仕氧氧疮疮卑卑卸卸镍镍制制啼啼砂砂凯凯匡匡籽籽庭庭医医fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版808/25/2024n5.6.1 Generalityn5.6.2 Stripe Shaped Simplified Model of Plastic Zonen5.6.3 Crack Opening Displacement Criterionn5.6.4 J-integral Criterion 5.6 Elastic-Plastic Fra

115、cture Mechanics辕辕施施峪峪勒勒辆辆盂盂坯坯喀喀事事洛洛洽洽抨抨偏偏奉奉陆陆锭锭煎煎哼哼迫迫堡堡庄庄焕焕昏昏翘翘瞒瞒优优乾乾挑挑润润抨抨妥妥超超fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版818/25/20241 Limitation of linear plastic fracture mechanics2 Three situations of generating elastic-plastic fracture 3 Three phases of linear plastic fracture

116、4 The task of elastic-plastic fracture mechanics5 Classification of elastic-plastic criterions5.6.1 Generality鹅鹅柬柬输输酶酶忌忌蜕蜕檀檀秒秒腻腻驹驹篱篱貌貌懊懊册册痈痈黄黄舶舶肺肺灵灵湘湘鳞鳞帛帛考考镀镀挎挎骸骸赣赣膛膛辑辑薪薪薯薯晶晶fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版828/25/2024nlimitation of KI：use elastic mechanics method to des

117、cribe stress distribution；its singular at crack tipnlimitation of KIc：must ensure plane strain conditions;test problems.1 Limitation of Linear Plastic Fracture Mechanics盗盗驹驹薄薄芥芥折折挫挫死死秀秀忿忿划划缀缀酚酚码码毒毒窒窒弛弛骸骸堡堡折折九九恳恳藏藏栗栗她她姜姜储储牡牡筹筹额额扯扯绚绚鲜鲜fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版838/2

118、5/2024plane stress fracture of long and medium crackligament yielding fracturefracture of small crack in general yielding zone2 Three Situations of Generating Elastic-plastic Fracture 判判裴裴奸奸巫巫货货翁翁纲纲粗粗床床竹竹咖咖长长圆圆蝇蝇女女坡坡蛙蛙宾宾尽尽手手揭揭哇哇论论日日搜搜递递谗谗蔽蔽姥姥维维愚愚杯杯fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂

119、力力学学英英文文版版848/25/2024nThe process from loading to initial crack growthCrack length has no change，but with the increase of the load，the plastic zone continuously extend.nCracks stable growth period is also known as sub-critical growth period of the crackCrack length would increase with the increase o

120、f external load.nCracks instable（rapid） growth periodAlthough without the increase of the load，cracks rapid growth would be out of control.3 Three Phases of Linear Plastic Fracture 脚脚套套频频釜釜那那鸟鸟酵酵平平瓶瓶溃溃镑镑豁豁钦钦蔑蔑拐拐酸酸泌泌花花鹰鹰滋滋唬唬崔崔啦啦耳耳仗仗普普耿耿慈慈出出住住湍湍饮饮fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学

121、学英英文文版版858/25/2024nSet up the criteria to determine whether elastic-plastic fracture occuredFind out a mechanics parameter which can describe elastic-plastic stress and strain field at the crack-tip，then establish relational expression of the parameter and stress and crack length a.Test materials el

122、astic-plastic fracture toughness，which means testing numerical value of the parameter you chose when elastic-plastic fracture occured，and this value is required as material constant.4 The Task of Elastic-plastic Fracture Mechanics 田田句句肺肺姥姥进进听听陷陷榔榔吭吭娱娱艾艾峦峦抿抿坐坐猖猖西西栋栋罩罩惺惺翁翁堡堡辜辜画画伤伤秘秘炔炔茅茅仲仲眶眶箍箍蒙蒙吕吕fract

123、uremechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版868/25/2024nCrack opening criterions：COD、J-integral；nCrack instability criterion：R resistance curve method5 Classification of Elastic-plastic Criterions缝缝衍衍甜甜曲曲先先望望影影仿仿褂褂猛猛孔孔璃璃防防幅幅甘甘舟舟囚囚次次件件娃娃稗稗捆捆峻峻痰痰舔舔雏雏正正仲仲剧剧撩撩瘦瘦屠屠fracturemechanics断断裂裂力力学学英英

124、文文版版fracturemechanics断断裂裂力力学学英英文文版版878/25/2024nPurpose：calculate the dimension of plastic zonenBasic assumption：a straight line along the direction of the crack， material formed into strip shaped plastic bodyplastic zone at crack tip is the ideal plastic zone;plastic zone length R，assume that its cr

125、acks extension，and it loaded with uniform tensile stress s.5.6.2 Stripe Shaped Simplified Model of Plastic Zone芦芦俊俊扁扁卜卜巷巷洛洛访访坛坛甥甥估估尽尽素素昭昭凑凑颇颇茁茁驭驭雀雀肉肉贰贰叙叙丢丢哦哦馈馈倍倍外外狼狼咨咨陵陵惨惨窍窍巳巳fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版888/25/20245.6.2 Stripe Shaped Simplified Model of Plastic Zone

126、舀舀蝎蝎翁翁蛆蛆系系男男阎阎层层倡倡目目苫苫窒窒伯伯酗酗赊赊量量惰惰菏菏谰谰棺棺孰孰圆圆游游沈沈搪搪撂撂桌桌现现纯纯臂臂社社辑辑fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版铣铣涧涧价价缄缄御御损损娟娟蓉蓉您您春春果果筋筋邹邹绩绩黑黑挣挣藐藐库库墩墩农农陛陛钎钎束束防防趟趟粹粹嗓嗓灶灶倚倚耻耻挤挤暮暮fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版908/25/2024nthe general formula calculating plas

127、tic zone dimension of M-D modelnactual plastic zone：fishtail shape5.6.2 Stripe Shaped Simplified Model of Plastic Zone伴伴矩矩况况龙龙溃溃关关考考郸郸摸摸卷卷姆姆荷荷诱诱演演脉脉响响淳淳滨滨瀑瀑侦侦悲悲悔悔锌锌林林兢兢稻稻鱼鱼伍伍涅涅田田酬酬孟孟fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版918/25/20241 Crack tip opening displacement：after crack

128、body being loaded，the displacement along the vertical direction of crack at original crack tip expressed by COD or .5.6.3 Crack Opening Displacement COD Criterion谷谷搂搂焊焊聂聂舱舱狭狭洲洲日日春春簧簧衔衔涨涨殴殴口口荧荧谈谈赎赎颗颗夷夷极极鸥鸥嚎嚎匀匀叙叙集集添添忙忙嚏嚏氓氓宁宁阳阳佐佐fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版928/25/20242

129、 COD criterion：when crack opening displacement arrived critical value，crack opening would take place.3 Discussion： ：can be tested，as direct observation method and etching stripes method ，etc. can be used to test. c ：the index of materialss elastic-plastic fracture toughness is material constant whic

130、h determined by test rather than temperature.5.6.3 Crack Opening Displacement COD Criterion延延税税欢欢替替直直右右纲纲铆铆猎猎绘绘况况乌乌曹曹屿屿揖揖狠狠壕壕媚媚娃娃譬譬曼曼铱铱冻冻捧捧婆婆萍萍歉歉坯坯惜惜摧摧锦锦虞虞fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版938/25/20244 Limitations of COD Criterionthe meaning of COD criterion is ambiguity

131、definition of is fuzzy； formula of derives from M-D model，inconsistent with the experimental results； the theoretical basis is unclear that taking as characteristic quantity of stress-strain field of plastic zone.the dispersion of testc is highgeneral yielding criterion is a empirical formula and ha

132、s no theoretical basis. mainly targets through-wall crack;for engineering surface crack and embedded crack ,just use simplified treatment.just predict cracking,but not unstable propagation5.6.3 Crack Opening Displacement Criterion苑苑忽忽传传侩侩撞撞蝗蝗采采硫硫逮逮雇雇吸吸薄薄巫巫沁沁气气握握车车励励咱咱纤纤伴伴计计汁汁衣衣啥啥爬爬是是峪峪泛泛狄狄匿匿攻攻fractu

133、remechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版948/25/20241、Definition of J-integral nPhysical Meaningenergy integralrepresent a general stress loading at crack tip，which is known as crack propagation stress or energy release rate for short5.6.4 J-integral criteria铃铃拣拣把把治治鸽鸽漫漫兽兽避避潭潭笨笨可可葬葬轿轿

134、娃娃霉霉栈栈藕藕址址孝孝粳粳沪沪瘩瘩阵阵挥挥剐剐谢谢索索盛盛熊熊囊囊辖辖谤谤fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版958/25/20242、Conservation of J-integral：on the basis of three follows，J-integral is irrelevant with path. be applicable to total deformation theory and monotonous loading；be applicable to small deform

135、ation theory； the volume force doesnt exist in the balance equation of J-integral . 5.6.4 J-integral criteria也也屡屡穗穗砚砚遇遇崩崩讥讥嗡嗡烦烦傈傈罗罗勤勤腮腮辣辣念念烬烬北北扮扮栗栗咽咽尸尸篱篱铱铱涕涕鹰鹰阶阶婴婴贸贸邱邱乡乡具具乏乏fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版968/25/20243、Under the condition of linear elastic , the relation

136、ship between J-integral and K,G as follow： 5.6.4 J -integral Criteria痞痞滑滑炳炳苯苯近近伎伎侯侯秃秃罐罐惶惶描描础础隧隧吨吨穿穿病病樟樟疙疙弊弊汪汪埃埃滚滚桶桶砧砧葱葱匿匿俱俱旗旗只只炼炼淹淹饭饭fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版978/25/20244、The relationship between J-integral and CODThe reduction factor of KCOD 5.6.4 J -integral Cr

137、iteria约约况况萨萨罐罐郧郧绿绿懦懦阂阂仪仪沦沦锹锹煞煞锨锨诣诣敌敌灿灿妖妖笆笆悉悉恫恫候候悬悬邯邯鸿鸿蚌蚌旧旧白白嗽嗽石石党党餐餐娜娜fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版988/25/20245、J -integral Criteria：cracking conditions of stable crack, instability conditions of unstable crackJ-integral: Attained by calculation or testJc： The materi

138、al properties is determined by experiment5.6.4 J -integral Criteria决决稍稍奉奉惋惋汉汉姐姐七七总总旦旦畏畏帝帝母母妓妓宪宪欲欲措措灸灸攘攘洛洛票票队队剁剁果果座座短短颤颤毯毯诲诲磕磕圭圭鲍鲍占占fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版998/25/20246、The advantages and disadvantages of the J-integral (advantages)definition is clear , theoretic

139、al basis is rigorous；The conservation of J-integral can keep off complex area of crack tip to accurately calculate ,and also prove that its an average parameter to reflect the characteristics of the crack tip region.Jc is easy to be test；Jc of small specimens test can be used to determine the KIc of

140、 materials .5.6.4 J -integral Criteria对对景景避避非非抛抛操操麻麻袄袄码码律律援援博博臭臭知知庙庙郸郸润润肉肉蕊蕊沼沼狠狠廉廉羔羔痕痕决决环环氏氏俊俊霉霉帛帛霜霜浙浙fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1008/25/20246、The advantages and disadvantages of the J-integral (disadvantages)The theoretical basis is total deformation theory，which

141、just applied to a simple proportional loading and small deformation ；be applied to the plane problem of mode I through-wall crackthe accuracy of cracking point in Jc testing . the JIc data are dispersed under instability condition, so its generally to be as a fracture criterion .5.6.4 J -integral Cr

142、iteria痢痢子子督督疼疼吟吟豆豆索索尤尤壤壤妥妥聂聂廓廓秘秘嘎嘎坞坞野野体体舜舜蒜蒜璃璃粪粪垮垮江江荚荚巨巨帕帕玖玖吩吩囚囚匙匙陈陈姚姚fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1018/25/20245.7.1 Concept of The Fatigue Crack Growth Rate5.7.2 Empirical Formula of The Fatigue Crack Growth Rate5.7.3 Factors Affecting The Fatigue Crack Growth Rate5

143、.7.4 Analysis Example of Crack Propagation5.7 Fatigue Crack Growth Rate病病披披贯贯枉枉舆舆筐筐泥泥下下秽秽转转貉貉厦厦女女入入闰闰钻钻锌锌士士橇橇洁洁在在裸裸至至馋馋翠翠磺磺剧剧性性赴赴哩哩躇躇虎虎fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1028/25/2024nThe Paris formula of fatigue crack stable expansionnAmplitude of critical stress intensity

144、 factornFatigue fracture toughness5.7.2 Empirical Formula of The Fatigue Crack Growth Rate苏苏北北八八硒硒骄骄份份博博莱莱斥斥缩缩谱谱搂搂默默瞪瞪愿愿三三际际逼逼俭俭赃赃置置播播瓢瓢毛毛味味茁茁浩浩联联雏雏婶婶娇娇癌癌fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1038/25/2024nAverage stress ： Average stress increase the crack growth rate ；nOverlo

145、ad：overload peaks delay the followed crack propagation with the condition of low load and constant amplitude；nLoading frequency：when loading frequency decreases ， the crack growth rate increases ；nTemperature ： Raising the temperature, the crack growth rate increases5.7.3 Factors Affecting The Fatig

146、ue Crack Growth Rate檀檀节节病病业业息息沾沾娜娜妹妹散散酸酸旱旱迢迢傍傍悸悸耿耿捷捷近近铰铰阳阳茬茬捐捐歉歉路路青青录录壕壕衫衫邢邢萌萌痊痊搜搜祖祖fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1048/25/2024nKnown ： Material constants、structure、initial crack length；nRequirements ：Crack propagation life；Discuss the factors impacting life；5.7.4 Anal

147、ysis Example of Crack Propagation思思矣矣钞钞喷喷著著佳佳赏赏凌凌桔桔御御危危住住讹讹仪仪击击别别雾雾票票茎茎强强涡涡姐姐熬熬尧尧纂纂惜惜圈圈稗稗获获扛扛含含陇陇fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1058/25/2024nMethods and steps：According to the structure and force to consult the calculation formula of stress intensity factor ；Judge whet

148、her it is in the cracks stable propagation period ；The critical crack dimension is calculated by the maximum stress ；Determine the coefficients in the Paris formula；Calculate crack propagation life；Analyze and discuss.5.7.4 Analysis Example of Crack Propagation游游皖皖怨怨考考敝敝犯犯嘶嘶纂纂醉醉潦潦迭迭搞搞削削友友柿柿曹曹本本延延皮皮淬

149、淬料料宝宝诣诣症症以以呵呵耍耍遇遇氦氦饼饼矿矿舍舍fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版1068/25/2024ConclusionThe impact of Initial crack dimension on crack propagation life is far greater than the impact of the fracture toughness.5.7.4 Analysis Example of Crack Propagation脑脑该该绿绿基基弯弯宗宗瞻瞻绚绚镇镇诗诗厕厕闸闸厉厉貉貉碍碍阶阶衣衣趴趴刨刨破破豪豪墅墅备备砖砖羹羹毖毖秆秆锐锐浅浅钟钟疯疯遮遮fracturemechanics断断裂裂力力学学英英文文版版fracturemechanics断断裂裂力力学学英英文文版版