冲击与动态断裂

动态裂纹传播—实验及数值模拟冲击动力学专题爆炸与冲击载荷下材料和结构的破坏•裂纹导致破坏——断裂•应力波导致拉伸破坏——层裂•多点破坏——碎裂•韧性材料的热力学耦合破坏——绝热剪切断裂—主要内容•断裂和动态断裂•裂纹传播动力学–脆性材料的传播韧性；–裂纹的传播行为；•实验及现象观察；•分析及数值模拟；•总结断裂事例断裂力学历史•Griffith'senergyrelation;•Irwin'smodificationofGriffith'srelation–UsingofStressratherthanEnergy:SIF;•Elastic-plasticfracturemechanics–Rice’sJ-Integral;–HRRSolution(Huchinson,RiceandRosengren)–DugdaleandBarrenblatSolution;•Fullyplasticfracture•Engineeringapplications•Others:–Dynamicfracture,crackdynamics,interfacecrack,etc.(WorkofFreund,Needleman,etc)AlanGriffith固体力学中被应用最多的16篇文献•ESHELBYJD,Thedeterminationoftheelasticfieldofanellipsoidalinclusion,andrelatedproblems.PROCEEDINGSOFTHEROYALSOCIETYOFLONDONSERIESA-MATHEMATICALANDPHYSICALSCIENCES241(1226):376-396,1957•WILLIAMSML,Mechanicalpropertiesofsubstancesofhighmolecularweight.19.Thetemperaturedependenceofrelaxationmechanisminamorphouspolymersandotherglass-formingliquids.JOURNALOFTHEAMERICANCHEMICALSOCIETY,77(14),3701-3707,1955•GRIFFITHAA,Thephenomenaofruptureandflowinsolids.PhilosophicalTransactionsoftheRoyalSocietyofLondon,SereisA,221:163-198,1921•MATTHEWSJWandBLAKESLEEAE,Defectsandepitaxialmultilayers:1.Misfitdislocations.JOURNALOFCRYSTALGROWTH27(DEC):118-125,1974•RICEJR,Apathindependentintegralandapproximateanalysisofstrainconcentrationbynotchesandcracks,JOURNALOFAPPLIEDMECHANICS35(2):379-386,1968•TaylorGI,Plasticstraininmetals.JOURNALOFTHEINSTITUTEOFMETALS62:307-324,1938.TimesCited:1817•DUGDALEDS,Yieldingofsteelsheetscontainingslits.JOURNALOFTHEMECHANICSANDPHYSICSOFSOLIDS8(2):100-104,1960•BIOTMA,Theoryofpropagationofelasticwavesinafluid-saturatedporoussolid.1.Low-frequencyrange.JOURNALOFTHEACOUSTICALSOCIETYOFAMERICA28(2):168-178,1956•MINDLINRD,Influenceofrotatoryinertiaandshearonflexuralmotionsofisotropicelasticplates.JOURNALOFAPPLIEDMECHANICS-TRANSACTIONSOFTHEASME18(1):31-38,195•BiotMA,Generaltheoryofthree-dimensionalconsolidation.Source:JOURNALOFAPPLIEDPHYSICS12(2):155-164,FEB1941.TimesCited:1447•ESHELBYJD,Thecontinuumtheoryoflatticedefects.SOLIDSTATEPHYSICS-ADVANCESINRESEARCHANDAPPLICATIONS3:79-144,1956•RICEJR,ROSENGREGF,Planestraindeformationnearacracktipinapower-lawhardeningmaterial.JOURNALOFTHEMECHANICSANDPHYSICSOFSOLIDS16(1):1-12,1968•HUTCHINSONJW,Singularbehavioratendofatensilecrackinahardeningmaterial.JOURNALOFTHEMECHANICSANDPHYSICSOFSOLIDS16(1):13-31,1968•MORIT,TANAKAK,Averagestressinmatrxandaverageelasticenergyofmaterialswithmisfittinginclusions.ACTAMETALLURGICA21(5):571-574,1973•BROOKSAN,HUGHESTJR,StreamlineupwindPetrov-GalerkinformulationsforconvectiondominatedflowswithparticularemphasisontheincompressibleNavier-Stokesequations.COMPUTERMETHODSINAPPLIEDMECHANICSANDENGINEERING32(1-3):199-259,1982•GURSONAL,Continuumtheoryofductilerupturebyvoidnucleationandgrowth,1.Yieldcriteriaandflowrulesforporousductilemedia.JOURNALOFENGINEERINGMATERIALSANDTECHNOLOGY-TRANSACTIONSOFTHEASME99(1):2-15,1977断裂力学和动态断裂力学断裂力学-FailureMechanicsofaStructureContainingaCrackABranchinSolidMechanicsAnalyticalAspect:CalculatetheDrivingForceonaCrackExperimentalAspect:CharacterizetheMaterial'sResistancetoFractureK=?KC=?KKC?动态断裂力学的一般课题•静止裂纹承受动态载荷作用——动态起裂韧性;•快速传播裂纹——传播韧性;•快速传播裂纹的止裂——止裂韧性;•其他：层裂、碎裂、动态损伤、绝热剪切等等;应力波作用下的静止裂纹动态断裂能（韧性）的加载速率相关性DuctileFractureCriticalStrainBrittleFractureCriticalStressstacdyncGGstacdyncGGConstantGcGcincw.strainrateGcdecw.temp快速传播裂纹诱发应力波Freund’s关于运动裂纹尖端应力场的解快速裂纹传播现象涉及物理现象•ACrackpropagatesunderstatic/dynamicloading;•Dynamicenergyreleaserate;•Limitingvelocity;•Velocitytoughening;•Cracktipprocessandtougheningmechanisms•Stressesincrack-tipzone;•Crackpathinstability;动态应力强度因子的实验测量运动裂纹尖端焦散线（Ravi-Chandar）CausticsatBranchedCrackTips突加载荷作用下的裂纹传播过程CrackPropagatesStationaryCrackKIC-VelocityRelationshipFracturetoughnessincreaseswithincreasingcrackvelocity(velocity-toughening)脆性PMMA板材中的裂纹的高速传播问题•背景•实验方法•试验结果•数值模拟和讨论动态脆性裂纹传播•脆性裂纹的动态传播是一个古老而始终激发思考的固体力学问题。研究的重要性与其说在于问题的实际工程价值不如说在于问题丰富的物理数学内涵以及趣味性：–裂纹的传播速度：•理论极限速度•低极限速度•超音速/跨音速裂纹；–裂纹传播的稳定性•路径稳定性：弯曲、分叉；•速度稳定性：加速、减速、震荡；–断裂的材料学特征：断面形貌，断裂机制；–动态裂纹传播的力学机制•主-微裂纹相互作用；•惯性和应力波影响，边界效应，材料非线性–动态裂纹传播研究的科学手段：实验技术、动态加载和测试技术，微观诊断技术，数学分析方法，数值模拟手段。脆性裂纹在一个无限长带板中的传播问题•尽可能地排除其他干扰因数，通过对一个最简单的裂纹传播问题进行研究获得有价值信息。CrackVelocityMeasurement“Instabilityinthepropagationoffastcracks”Finebergetal.Phy.Rev.B45(1)1992Fineberg等的测试结果实验—试样制备实验材料：PMMA板材；D=3mm材料参数：E=3000MPa；n=0.35；r=1.23/gcm试样尺寸：A（320×240mm）；B（320×200mm）；C（320×160mm）；D（240×240mm）；E（240×200mm）布置导线：银粉导电漆，丝网印刷技术，间距d1=2.5mm；线宽d2=0.6mm带有断裂线的试样示意图采用印刷方式制备导线的试样实物试验装置及方法实验中的PMMA试样加载时PMMA试样和夹具示意图裂纹传播位置到达时间测定逻辑电路试验方法用MTS万能试验机对试样PMMA准静态轴向加载到特定的载荷水平，这时试样内储存了一定的弹性能，片刻用锋钢刀片在试样拉伸的中央垂直方向刻一个微小裂纹，因为PMMA材料很脆，微小裂纹沿着试样中间传播，依次割断试样上的银漆导电线（A1-A2-A3------），连接数字逻辑电路在信号输出端O输出一系列的信号（0-1-0-1------），每次跳跃时间就是裂纹传播到特定银漆导电线位置。新实验结果—典型信号记录vdLdtLt裂纹传播速度确定：裂纹在实践中的传播速度0501001502002503000100200300400500600700800900CrackVelocity(m/s)CrackLength(mm)A01A02A03A04A05A06A07A08A09A10A11Specimen320*240050100150200250300100200300400500600700800900CrackVelocity(m/s)CrackLength(mm)C01C02C03C04C05C06C07C08Specimen320*1600501001502002500100200300400500600700800CrackVelocity(m/