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,*,*,*,*,*,*,1,2024/10/7,The strength theory which have crack in body,2,2024/10/7,GOAL,:,recount conventional strength theory of nonindividual body.,Fundamental assumption of elastic and plastic theory.,Basic approach and equation to solve the stress .,Description and analysis of one points stress state,.,APPLY,：,strength design,Calculate external force,；,Count one points stress state,（,theory of elasticity and plasticity,）；,Verdict a points stress is critical state(yield or destroy) or not according to the strength condition.,ATTENTION,：,Generally used for checking.,Brief summary of first four chapters,3,2024/10/7,Uncertainties during stress analysis,Indeterminacy of external load.,Indeterminacy during stress analysis.,Indeterminacy of material characteristics.,Practical application:,Security coefficient which bigger than one.,Designs basic idea,nonindividual body,never damage,Problems and solves during,strength design,4,2024/10/7,Reality of engineering damage,5,2024/10/7,Who is responsible for the air crash?,In1979,there was a largest disaster event in American history, more than 270 people died.,Reason: Connection which connect engines and wings had fractured.,Review of the history,Railway,：,England,，,wheel,、,track,、,orbital fracture,Bridge,：,Belgium,，,14 accidents in 4 years,Steamship,：,World War Two,，,American freighter,、,tanker,，,weld,Airplane,：,British,“,comet,”,Missile,：,American,“,Polaris,”,Pressure vessel,：,Aerospace plane,、,In the 1950s,American,“,Polaris,”,solid fuel engine was fractured when launch. The material was high-strength steel, yield strength,s,=1400MPa,，,working stress,900MPa,。,Accident case,6,2024/10/7,When it damage, working stress is much less than materials yield limit,；,The primary cause of damage is that there are all kinds of defects or cracks 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 accidents,Where do cracks come from,？,Material defect,；,Fatigue initiation,；,Damages in machining,、,manufacture,、,assemble and so on.,7,2024/10/7,After 1950s, Crack-containing body strength theory was been researched and developed,：,Fracture Mechanics,How to solve it ?,Fissure can cause rupture failure,，,how to analyse and control?,If you dont know how to analyse,，,constructional element will have fissures, and then useless.,8,2024/10/7,5.1 Introduction,5.2 The crack-tips stress-strain field,5.3 Stress intensity factor and its solution,5.4 Brittle ruptures K-factors,5.5 The popularization of linear elastic fracture mechanics in small scale yielding,5.6 Elastic-plastic fracture mechanics,5.7 Fatigue crack growth rate,5.,Crack-containing body strength theory,9,2024/10/7,5.1.1 Development process of fracture mechanics,5.1.2 Research contents of fracture mechanics,5.1.3 Several basic conception of fracture mechanics,Brittle rupture and ductile fracture,Trans-granular fracture and inter-granular fracture,The division of length and break related disciplines,5.1.4 Fracture analysis,Macro-fracture analysis,Micro-fracture analysis,5.1,Introduction,10,2024/10/7,15 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 problem.(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 Development process of fracture mechanics,11,2024/10/7,In,1958 ，Irwin, with amendments to broaden the scope of application of linear elastic fracture mechanics；Wells,propose,COD ;,In,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 growth rate,;,Study on quantitative analysis of dynamic fracture,is in the ascendant,5.1.1 Development process of fracture mechanics,12,2024/10/7,Research the power and resistance of material or structures crack growth(initiation).,Fracture criterion and its scope of application and applicable conditions.,Apply to the analysis of multiple structure,：,Process of crack from initiation, extending to unstability .,Estimation the life of structure with cracks,：,Fatigue problems.,The goal of fracture mechanics is quantificationally research on the conditions of fracture which caused by he reason that the main crack in the supporting body extend (including static load and the expansion under fatigue load) .,5.1.2 Research contents of fracture mechanics,13,2024/10/7,5.1.2 Research contents of fracture mechanics,Engineering application,Under 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 it need to expand to the critical crack length (or number of load cycles)?,-Remaining life,What function relations between residual strengths of structure and crack lengths?,14,2024/10/7,Issues relate to material select,What 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?,5.1.2 Research contents of fracture mechanics,15,2024/10/7,Fracture mechanics involve many problems of mechanics, materials science and engineering application, it can be used to process,：,When structure has been set, cracking is know, how about this structures bearing capacity(residual intensity)?,When structure has been set, external load is know, how much is the allowing maximum crack(Damage tolerance)?,Knowing of damage tolerance and external load of structure, how to make each component of structure meet dimensional requirement(damage tolerance design)?,Life time calculation.,（,Fatigue crack growths life,）,Selecting material.,5.1.2 Research contents of fracture mechanics,16,2024/10/7,Brittle fracture and ductile fracture,Toughness,：,Ability of materials absorb energy during the elastic-plastic deformation which before material break.,5.1.3 Several basic conception of fracture mechanics,17,2024/10/7,Brittle fracture and ductile fracture,When breaking, there is not obvious plastic 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 pattern.,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 fracture,Notice,：,The relativity of concept,（,Influence by temperature, stress,and environment,）,5.1.3 Several basic conception of fracture mechanics,18,2024/10/7,Trans-granular fracture and inter-granular fracture,Cleavage forms,(Simple abruption of atomic binding),Brittle fracture,Slip and empty aggregation,Ductile fracture,Fracture arouse by temper brittleness or,crystal boundary has brittle phase, hydrogen,embrittlement and any other reasons,it always belongs to the brittle fracture.,5.1.3 Several basic conception of fracture mechanics,19,2024/10/7,The division of length dimension and break related discipline (Subject),5.1.3 Several basic conception of fracture mechanics,20,2024/10/7,The division of length dimension and break related discipline,(,Fissure,),Static cracking(Stress analysis),Subcritical crack growth (fracture criterion),Unstable extensions,Crack arrest,5.1.3 Several basic conception of fracture mechanics,21,2024/10/7,5.1.4 Fracture analysis (concept),Metal fracture: After metal components break ,the general terms of damaged parts outward appearance. Recording the process of cracks generation, propagation and fracture.,Fracture analysis,：,Using methods of macroscope and microscope to analyse and research to fracture morphology.,Purpose,：,Analyze the material organization 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 cause of accident.,Method: Macro-fracture analysis , micro-fracture ananlysis.,22,2024/10/7,5.1.4 Fracture analysis(Macroscopic),Macro-fracture analysis,Through macroscopic fracture 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；,C,an judge the quality of the material,.,Distinguish between the static load fracture and fatigue fracture,23,2024/10/7,5.1.4 Fracture analysis(Macroscopic),S,tatic load fracture,：three elements,Fiber area,Radiation,area,Shear lip area,Non-gap tensile specimen and impact test sample fracture chart,24,2024/10/7,5.1.4 Fracture analysis(Macroscopic),Radiation area shape,Counter directional,crack source,25,2024/10/7,5.1.4 Fracture analysis(Macroscopic),T,hree regions of the fracture surface,exist or not, size, location, scale and shape,etc. will have great change along with the difference of material intensity levels, stress conditions, size dimensions, geometric forms, inside and outside flaws and positions, temperature, external environment and so on.,The toughness of material is good, the area that textile fiber area occupies is big, even has not,r,adiation,area,is full of fiber area and s,hear lip,.,Material with big brittleness, the radiation area increases, fiber area reduces, even will not have fiber area and s,hear lip, and the pattern of emission area is very tiny, becomes less obvious and presents other characteristics.,26,2024/10/7,5.1.4 Fracture analysis(Macroscopic),Fatigue fracture,27,2024/10/7,5.1.4 Fracture analysis(Macroscopic),Macroscopic fracture analysis method,Observing whether there have radiation pattern or herringbone pattern on fracture surface, we can find the crack source position according to the trace; Meanwhile, according to the relative scale of r,adiation,area,and fiber area we can roughly estimated fracture properties. The bigger the proportion that the radiation area accounts is, then the brittleness is bigger.,Observing whether there is shell pattern on the fracture surface, if it is, it indicates that the component is fatigue fracture, and we can find the fatigue initiation according to the trace.,Observing to the rough degree, gloss and color of fracture. The fracture is rougher, the color is gloomier, indicated that in the fracture growth process the plastic deformation is bigger, the degree of ductile fracture is bigger; Otherwise, fracture is thin and flat, multi-gloss, it means that the proportion of brittle fracture is significant.,28,2024/10/7,5.1.4 Fracture analysis(Microscopic),M,icro,-,fracture analysis,In addition to being able to understand the cause of the fracture, but,can,also,study mechanisms of fracture occurred.,Method,：transmission electron microscope（,TEM,）,and,scanning electron microscope,M,icro fracture morphology：,C,leavage fracture,T,oughness nest,fracture,Fatigue fracture,29,2024/10/7,5.1.4 Fracture analysis(Microscopic),Cleavage fracture is a kind of transgranular fracture,on a specific crystal surface, occur due to the simple breakdown of atomic key fracture.,Within a grain, c,leavage crack has relatively flat,. It must change direction at the grain boundary, so cleavage fracture is composed of many small smooth planes which orientation is slightly different, each group of small plane represents a grain;,The most,important,character of cleavage fracture is rivers pattern,。,C,leavage fracture,: A kind of the crispest fracture form,which occurs in the crystallization material.,30,2024/10/7,5.1.4 Fracture analysis(Microscopic),T,oughness nest,fracture,：,T,oughness nest,fracture is a main type of ductile fracture, it also belongs to transgranular fracture;,The chief feature of the fracture surface of t,oughness nest,fracture is to have dimple;,According to the different force, it will form different shapes of dimple, there are isometric toughness nest, parabolic toughness nest and elongation toughness nest and so on.,Fracture surface presents rough and irregular shape.,31,2024/10/7,5.1.4,Fracture analysis (Microscopic),Isometric toughness nest,Parabolic toughness nest,Elongation toughness nest,32,2024/10/7,5.1.4,Fracture analysis (Microscopic),Fatigue fracture,The chief feature of fatigue fracture is there is shell pattern(or names beach pattern, tree-ring pattern) in the fatigue zones(fracture growth area). Sometimes it is unclear with the observation of macroscopic method, and presents clear with the micro approach. Shell patterns stripes are basic parallel, but slightly curved, present wave-shaped; Stripe line is perpendicular to the crack dehiscence direction; Each stripe represents a load process, stripe total number is the number of varying load; The trace of top and bottom fracture correspond completely.,33,2024/10/7,5.2 The crack-tips stress and displacement field,Crack,Basic types of crack,The stress field and displacement field nearby crack-tip,34,2024/10/7,5.2 The crack-tips stress and displacement field,Crack,The 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 and fatigue crack produce when structure are used in different environment.,35,2024/10/7,5.2.1,Basic types of crack,According to the location of crack,：,Through-wall crack,Surface crack,Hidden crack,According to crack stress situation,：,opening mode(I),Sliding mode(),Tearing mode(,),5.2.1,Basic types of crack,Mode I (opening mode): Bear with crack surface vertical normal stress, crack surface displacement along the Y direction, crack opening.,，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.,Mode III(tearing mode): Bear with shearing strength,of plane YZ, , crack surface displacement along the Z direction, and crack surface tears in Z direction.,37,2024/10/7,5.2.2 The stress field and displacement field nearby crack-tip,Analytical method:,According to elastic theory;,Analysing the boundary conditions;,Solve the stress field and displacement field,38,2024/10/7,Stress 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.,To make crack growth, must,0.,Namely only the tensile stress can cause cracks open extensions,Discussing to the situation that a infinite plate which have a 2a-long penetrating crack, and its two ends subject to tensile stress,that is perpendicular to the crack.,39,2024/10/7,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,),。,s,s,x,y,2,a,dx,dy,r,q,s,y,s,x,t,x,y,s,s,q,y,a,r,=,+,2,2,1,cos,q,q,2,3,2,sin,sin,t,s,q,q,q,xy,a,r,=,2,2,2,3,2,sin,cos,cos,s,s,q,x,a,r,=,-,2,2,1,cos,q,q,2,3,2,sin,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,d,x,、,dy,；,Using methods of elastic mechanics, we can obtain any points (r,) normal stress,x,y,and shear stress,xy,nearby the crack-tip, that is:,5.2.2 The stress field and displacement field nearby crack-tip,(5-1),40,2024/10/7,What fracture mechanics care for is the stress field nearby crack-tip.,The above equation is the dominant term of crack-tips stress field, also have r,0,step term etc.,0, stress,ij,tend to be infinity at r,-1/2,step, existing singularity; And then r,0,step become subordinate, it can be ignored.,(5-1)the above equation may write as,：,s,p,f,q,ij,ij,K,r,=,1,2,(,),K,a,1,=,s,p,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 r,0,step as the dominant term.,s,s,x,y,2,a,dx,dy,r,q,s,y,s,x,t,x,y,5.2.2 The stress field and displacement field nearby crack-tip,41,2024/10/7,K reflect the strength of crack-tip stress field; The subscript 1 means it is mold 1.,If,ij,is bigger, then,K is bigger; Crack size a is bigger, then K is bigger.,The K dimension is ,stress,lengh,1/2,，,in common use MPa,m,Crack-tips stress intensity factor,K,1,：,f(a,W,.),is geometric correction function, it can be checked through handbook.,Particularly, when aw or a/w,0, i.e.,For the infinite width,center cracked plate which bearing stretch,，,f=1,；,For the infinite width unilateral crack plate, f=1.12.,5.2.2 The stress field and displacement field nearby crack-tip,Formula (5-1) is the solution of center through crack infinite plane.,Fracture mechanics research indicate that K1 can more generally write as:,K,a,f,a,W,1,=,s,p,(,.,.,.,),42,2024/10/7,5.2.2 The stress field and displacement field nearby crack-tip,The stress and displacement near the crack-tip of sliding mode crack.,43,2024/10/7,5.2.2 The stress field and displacement field nearby crack-tip,The stress and displacement near the crack-tip of tearing mode crack,44,2024/10/7,5.3 Stress intensity factor and its solution,The general formula of crack-tips stress field and displacement field:,Analysis of stress field,：,The stress 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;,Conclusion: The stress is not suitable as establishing the physical parameter of strength condition.,45,2024/10/7,5.3 Stress intensity factor and its solution,The character of SIF,：,The SIF is measurement 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.,Conclusion: Establishes failure condition to be suitable by using the SIF.,46,2024/10/7,5.3 Stress intensity factor and its solution,General formula of SIF,Calculation method of SIF,Method of calculation,Method of look-up table,Method of superposition,47,2024/10/7,5.3 Stress intensity factor and its solution,The superposition principle of sought of SIF,The decomposition and superposition of stress,Structure and force decomposition and superposition at the same time,In view of different kinds of crack, considering complex criteria.,48,2024/10/7,5.3 Stress intensity factor and its solution,The,superposition of SIF,49,2024/10/7,5.4 The K
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