Type of fracture in metal The concept of material trength and fracture ha long been tudied to overcome failure. The introduction of malleable iron during the revolution of material contruction led to the perception of brittle and ductile fracture a well a fatigue failure in metal. Failure in metallic material can be divided into two main categorie: Ductile failure : Ductile fracture involve a large amount of platic deformation and can be detected beforehand. Brittle failure: Brittle fracture i more catatrophic and ha been intenively tudied.
Claification: Ductile v Brittle Failure Fracture behavior: Very Ductile Moderately Ductile Brittle Adapted from Fig. 8.1, Calliter 7e. Ductile fracture i uually deirable! %AR or %EL Large Ductile: warning before fracture Moderate Small Brittle: No warning
Example: Failure of a Pipe Ductile failure: --one piece --large deformation Brittle failure: --many piece --mall deformation Figure from V.J. Colangelo and F.A. Heier, Analyi of Metallurgical Failure (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Son, Inc., 1987. Ued with permiion.
Factor affecting mode of fracture Metallurgical apect Temperature State of tree (notch effect) Strain rate Loading condition
Ductile v. Brittle Failure cup-and-cone fracture brittle fracture
Failure mode High energy i aborbed by microvoid coalecence during ductile failure (high energy fracture mode) Le catatrophic Low energy i aborbed during trangranular cleavage fracture (low energy fracture mode) More catatrophic
Evolution to failure: necking Moderately Ductile Failure void nucleation void growth and linkage hearing at urface fracture Reulting fracture urface (teel) particle erve a void nucleation ite. 50 50 mm From V.J. Colangelo and F.A. Heier, Analyi of Metallurgical Failure (2nd ed.), Fig. 11.28, p. 294, John Wiley and Son, Inc., 1987. (Orig. ource: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.) 100 mm Fracture urface of tire cord wire loaded in tenion. Courtey of F. Roehrig, CC Technologie, Dublin, OH. Ued with permiion.
Microvoid hape Microvoid hape i trongly influenced by the type of loading. Uniaxial tenile loading Equiaxed dimple. Shear loading Elongated and parabolic dimple pointing in the oppoite direction on matching fracture urface. Tenile tearing Elongated dimple pointing in the ame direction on matching fracture urface.
Theoretical coheive trength of metal In the mot baic term, trength i due to the coheive force between atom. The attractive and repulive force acting on the two atom lead to coheive force between two atom which varie in relation to the eparation between thee atom. The theoretical coheive trength σ max can be obtained in relation to the ine curve and become. theoretical Eg a o Coheive force a a function of the eparation between atom. where g i the urface energy (J/m 2 ) a o i the untrained interatomic pacing Note: Convenient etimate of σ max ~ E/10.
Example: Determine the coheive trength of a ilica fibre, if E = 95 GPa, g = 1 J. m -2, and a o = 0.16 nm. Thi theoretical coheive trength i exceptionally higher than the fracture trength of engineering material. Thi difference between coheive and fracture trength i due to inherent flaw or defect in the material which lower the fracture trength in engineering material. Griffith explained the dicrepancy between the fracture trength and theoretical coheive trength uing the concept of energy balance.
Fractographic obervation The proce of cleavage fracture conit of three tep: 1) Platic deformation to produce dilocation pile-up. 2) Crack initiation. 3) Crack propagation to failure. Ditinct characteritic of brittle fracture urface: in brittle fracture 1) The abence of gro platic deformation. 2) Grainy or Faceted texture. 3) River marking or tre line (chevron nothce). Brittle fracture indicating the origin of the crack and crack propagation path
Brittle Failure Arrow indicate point at which failure originated
Ideal v Real Material Stre-train behavior (Room T): E/10 perfect mat l-no flaw carefully produced gla fiber TS engineering material << TS perfect material E/100 typical ceramic 0.1 typical trengthened metal typical polymer DaVinci (500 yr ago!) oberved... -- the longer the wire, the maller the load for failure. Reaon: -- flaw caue premature failure. -- Larger ample contain more flaw! e Reprinted w/ permiion from R.W. Hertzberg, "Deformation and Fracture Mechanic of Engineering Material", (4th ed.) Fig. 7.4. John Wiley and Son, Inc., 1996.
Stre Concentration for A Circular Hole y =0 x =- y a q x r y =3 x =0 Tenile tree reach 3 time of the applied tre at tre concentration point.
Flaw are Stre Concentrator! m 2 o a t 1/ 2 K t o t where t = radiu of curvature o = applied tre m = tre at crack tip K t = tre concentration factor Adapted from Fig. 8.8(a), Calliter 7e.
Concentration of Stre at Crack Tip Adapted from Fig. 8.8(b), Calliter 7e.
Engineering Fracture Deign Avoid harp corner! o Stre Conc. Factor, K t r, fillet radiu w max h Adapted from Fig. 8.2W(c), Calliter 6e. (Fig. 8.2W(c) i from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.) 2.5 2.0 1.5 increaing w/h 1.0 0 0.5 1.0 harper fillet radiu = max o r/h
Stre concentration for different geometrical hape
Stre Concentration at A Dicontinuity
Crack Propagation Crack propagate due to harpne of crack tip A platic material deform at the tip, blunting the crack. brittle Energy balance on the crack Elatic train energy- platic deformed region energy tored in material a it i elatically deformed thi energy i releaed when the crack propagate creation of new urface require energy
Theorie of brittle fracture Griffith theory of brittle fracture The firt analyi on cleavage fracture wa initiated by Griffith uing the concept of energy balance in order to explain dicrepancy between the theoretical coheive trength and oberved fracture trength of ideally brittle material (gla). Irwin and Orowan modified the Griffith theory to include platic deformation at the crack tip.
Griffith Fracture Theory t Elatic energy releaed by crack formation: 2a 2 a 2 t E Energy to create new urface 2atg 4atg 2 Potaniyel Enerji (U) 4atg U U U 2 2 t 0 a E 4atg a cr 2 a 2 t E U Çatlak boyu (a) U a 4tg cr 2Eg a 2 2 at E 0
When Doe a Crack Propagate? Crack propagate if the applied tre i above critical tre where i.e., m > c E = modulu of elaticity g = pecific urface energy a = one half length of internal crack 2Eg a For ductile => replace g by g + g p where g p i platic deformation energy c 1/ 2
Griffith theory of brittle fracture Oberved fracture trength i alway lower than theoretical coheive trength Griffith explained that the dicrepancy i due to the inherent defect in brittle material leading to tre concentration lower the fracture trength Conider a through thickne crack of length 2a, ubjected to a uniform tenile tre σ, at infinity. Crack propagation occur when the releaed elatic train energy i at leat equal to the energy required to generate new crack urface. The tre required to create the new crack urface i In plane train condition, it i given by:
Modified Griffith equation The Griffith equation i trongly dependent on the crack ize a, and atifie only ideally brittle material like gla. Irwin and Orowan uggeted Griffith equation can be applied to brittle material undergone platic deformation before fracture by including the platic work, g p, into the total elatic urface energy required to extend the crack wall, giving the modified Griffith equation a follow
Criterion of Failure g and g p are material propertie. G c = 2(g + g p ) (J / m 2 ) G c i called critical energy releae rate, and it i a material property. Applied energy releae rate i G= 2 a/e Failure occur if G > G c In many cae we would like to know the deign tre. For a given crack length, a, Failure occur if > cr G c E a Alo, if the i given we can find the critical crack length for failure.
Linear Elatic Fracture Mechanic It can be hown that the tre field,, at the tip of a crack i a function of the tre intenity factor, K. Notice: infinity a r 0 K i a function of the applied tre, the crack length, and the geometry. K= f(,a) r q Uually K = Y a ( MPa m ) Critical K that a material can tand: K c the fracture toughne. Failure occur if K > K c
P K Y a K Y a P Y 1 Y 1.12 K P / t a (c)
G or K, which approach i correct From Griffith, GE a K GE From LEFM, K / a If we write in term of material propertie G c Kc E 2
KIc(MPa m 0.5 ) 100 70 60 50 40 30 20 10 7 6 5 4 3 2 1 0.7 0.6 0.5 Fracture Toughne Metal/ Alloy Steel Ti alloy Al alloy Mg alloy Graphite/ Ceramic/ Semicond Diamond Si carbide Al oxide Si nitride <100> Si crytal <111> Gla -oda Concrete Polymer PET PP PC PS PVC Polyeter Compoite/ fiber C-C( fiber) 1 Al/Al oxide(f) 2 Y 2 O 3 /ZrO 2 (p) 4 C/C( fiber) 1 Al oxid/sic(w) 3 Si nitr/sic(w) 5 Al oxid/zro 2 (p) 4 Gla/SiC(w) 6 Gla 6 Baed on data in Table B5, Calliter 7e. Compoite reinforcement geometry i: f = fiber; f = hort fiber; w = whiker; p = particle. Addition data a noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook, Vol. 21, ASM Int., Material Park, OH (2001) p. 606. 2. (55 vol%) Courtey J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanic of Ceramic, Vol. 7, Plenum Pre (1986). pp. 61-73. 4. Courtey CoorTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Compoite for Application in Technology for Advanced Engine Program", ORNL/Sub/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp. 978-82.
Toughne veru Strength
Deign Againt Crack Growth Crack growth condition: K K c = Y a Larget, mot treed crack grow firt! --Reult 1: Max. flaw ize dictate deign tre. deign Y K c a max --Reult 2: Deign tre dictate max. flaw ize. a max a max 1 K Y c deign 2 fracture fracture no fracture a max no fracture
Deign Example: Aircraft Wing Material ha K c = 26 MPa-m 0.5 Two deign to conider... Deign A --larget flaw i 9 mm --failure tre = 112 MPa Ue... c Y K max Deign B --ue ame material --larget flaw i 4 mm --failure tre =? Key point: Y and K c are the ame in both deign. --Reult: c a 112 MPa 9 mm 4 mm c a max c a max A B Reducing flaw ize pay off! Anwer: ( c ) B 168 MPa
Deign againt fracture a c decreae dramatically with decreaing toughne, epically if the deign tre i to be increaed.
Loading Rate Increaed loading rate... -- increae y and TS -- decreae %EL y TS e larger TS Why? An increaed rate give le time for dilocation to move pat obtacle. e maller y e
Impact loading: -- evere teting cae -- make material more brittle -- decreae toughne Impact Teting (Charpy) Adapted from Fig. 8.12(b), Calliter 7e. (Fig. 8.12(b) i adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Propertie of Material, Vol. III, Mechanical Behavior, John Wiley and Son, Inc. (1965) p. 13.) final height initial height
Impact Energy Increaing temperature... --increae %EL and K c Temperature Ductile-to-Brittle Tranition Temperature (DBTT)... FCC metal (e.g., Cu, Ni) BCC metal (e.g., iron at T < 914 C) polymer Brittle More Ductile High trength material ( y > E/150) Ductile-to-brittle tranition temperature Temperature Adapted from Fig. 8.15, Calliter 7e.
Temperature v. Charpy
Deign Strategy: Stay Above The DBTT! Pre-WWII: The Titanic An oil tanker that fractured in a brittle manner by crack propagation around it girth. Reprinted w/ permiion from R.W. Hertzberg, "Deformation and Fracture Mechanic of Engineering Material", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Son, Inc., 1996. (Orig. ource: Dr. Robert D. Ballard, The Dicovery of the Titanic.) WWII: Liberty hip Problem: Ued a type of teel with a DBTT ~ Room temp.