Skip to main content
SpringerLink
Log in

Brittle Fracture

  • Chapter
  • First Online:
Mechanical Behaviour of Materials

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 191))

  • 7033 Accesses

Abstract

This chapter deals with brittle fracture especially by cleavage and embrittlement by segregation of impurities at grain boundaries or by irradiation.

Cleavage follows specific crystallographic planes in metals. A criterion gives the tendency for cleavage versus intergranular fracture. The conditions for crack tip blunting allow writing another criterion indicating the tendency for intrinsic brittleness. Owing to the very high value of the theoretical fracture stress, local stress raisers are needed to explain cleavage initiation: they are various defects in ceramics, dislocation pile-ups and inclusions in metals. Other obstacles, such as grain boundaries must be overcome for cleavage crack propagation. The Beremin model based on the analysis of Weibull accounts for the statistical nature of cleavage. The theory of Batdorf introduces the effect of the crack orientations. Care is needed to insure the validity of the models. They are extended to fracture toughness, in small scale yielding as well as in large scale yielding. The way to obtain the parameters of the models is described. In applications to steels, the presence of multiple barriers needs to be introduced in the modelling. It is necessary to take account of dynamic and of stress triaxiality effects. The Beremin model was applied to bainitic steels, and adapted to include plasticity. The fracture toughness of steels is statistically distributed and shows size effects. Loading rate and prestraining effects, warm prestraining effect, effect of inhomogeneities, especially in welds, are described and modelling discussed. Description of cleavage in other BCC metals as well as in HCP zinc and magnesium are given.

Temper embrittlement of steels results from the segregation of impurities to the grain boundaries. The thermodynamics and kinetics models of this segregation are discussed. The embrittlement is explained by the modifications of the boundary and surface energies due to this segregation. It influences also the conditions for intrinsic brittleness as opposed to crack blunting. Examples of temper embrittlement of steels are given. Overheating of steels is another phenomenon producing intergranular fracture.

Irradiation hardens metals and produces a shift of the DBT temperature. Impurities play a major role in this phenomenon. It is possible to model this shift.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Fracture toughness, which is introduced here simply to show the existence of a threshold, is discussed later.

  2. 2.

    The far-field stresses are written in uppercase letters in order to distinguish them from local stresses.

  3. 3.

    Here Σ designates a type of coincidence site lattice and not a macroscopic stress. For the definition of Σ in bicrystals see e.g.; Priester (2006). Σ is an odd integer number in cubic crystallographic structures. Similarly here θ is the tilt angle between two neighbouring grains.

  4. 4.

    Irving Langmuir (1881–1957) was an American chemist and physicist. He was awarded the 1932 Nobel Prize in chemistry for his work in surface chemistry. He was the first industrial (General Electric) chemist to become a Nobel laureate.

  5. 5.

    This temperature T ’0 should not be confused with the temperature θ 0 of the Master Curve approach introduced in Sect. 3.4.4.1 and in Eq. 3.47.

  6. 6.

    Several relationships were proposed to relate the irradiation damage expressed in terms of fluence (n/cm2) to the number of displacements per atom (dpa) (see e.g. Guionnet et al. 1982).

References

  • Agnew SR, Yoo MH, Tomé CN (2001) Application of texture simulation to understanding mechanical behavior of Mg and solid solution alloys containing Li or Y. Acta Mater 49:4277–4289

    Google Scholar 

  • Agnew SR, Horton JA, Yoo MH (2002) Transmission electron microscopy investigation of <c + a> dislocations in Mg and α – solid solution Mg – Li alloys. Metall Mater Trans A 33A:851–858

    Google Scholar 

  • Akamatsu M, van Duysen J-C, Pareiga P, Auger P (1995) Experimental evidence of several contributions to the radiation damage in ferritic alloys. J Nucl Mater 225:192–195

    Google Scholar 

  • Al Mundheri M, Soulat P, Pineau A (1989) Irradiation embrittlement of a low alloy steel interpreted in terms of a local approach to cleavage fracture. Fatigue Fract Eng Mater Struct 12:19–30

    Google Scholar 

  • Alexander DJ, Bernstein IM (1989) Cleavage fracture in pearlitic eutectoïd steel. Metall Trans A 20A:2321–2335

    Google Scholar 

  • Anderson PM, Wang JS, Rice JR (1990) Thermodynamic and mechanical models of interfacial embrittlement. In: Olson GB, Azrin M, Wright ES (eds) Innovations in ultrahigh-strength steel technology. Sagamore army research conference proceedings, vol 34, pp 619–649

    Google Scholar 

  • Andrieu A, Pineau A (2012) Prediction of crack path and fracture toughness of heterogeneous materials: application to welds. Eng Fract Mech (Private communication)

    Google Scholar 

  • Andrieu A, Pineau A, Besson J, Ryckelynck D, Bouaziz O (2012a) Beremin model: methodology and application to the prediction of the Euro toughness data set. Eng Frat Mech (to appear)

    Google Scholar 

  • Andrieu E, Pineau A, Besson J, Bouaziz O, Ryckelynck D (2012b) Bimodal Beremin-type model for brittle fracture of inhomogeneous ferritic steels: theory and application. Eng Fract Mech (to appear)

    Google Scholar 

  • Aoki K, Izumi O (1979) Improvement in room temperature ductility of L1/2 type intermetallic compound Ni3Al by boron addition (in Japanese). J Jpn Inst Metal 43:1190–1196

    Google Scholar 

  • ASTM E 1921-02 (2002) Standard test method for determination of reference temperature T0 for ferritic steels in the transition range

    Google Scholar 

  • Auger P, Pareiga P, Akamatsu M, Blavette D (1995) APFIM investigation of clustering in neutron-irradiated Fe-Cu alloys and pressure vessel steels. J Nucl Mater 225:225–230

    Google Scholar 

  • Bakker A, Koers RWI (1991) Prediction of cleavage fracture events in the brittle-ductile transition region of a ferritic steel. In: Blauel JG, Schwalbe K-H (eds) Defect assessment in components – fundamentals and applications. ESIS/EG 9. Mechanical Engineering Publications, London pp 613–632

    Google Scholar 

  • Batdorf SB, Crose JG (1974) A statistical theory for the fracture of brittle structures subjected to non-uniform polyaxial stresses. J Appl Mech 41:459–464

    MATH  Google Scholar 

  • Becker TL, Cannon RM, Ritchie RO (2002) Statistical fracture modelling: crack path and fracture criteria with application to homogeneous and functionally graded materials. Eng Fract Mech 69:1521–1555

    Google Scholar 

  • Beremin FM (1981) Cavity formation from inclusions in ductile fracture of A508 steel. Metall Trans A 12:723–731

    Google Scholar 

  • Beremin FM (1983) A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall Trans A 14A:2277–2287

    Google Scholar 

  • Bernauer G, Brocks W, Schmitt W (1999) Modifications of the Beremin model for cleavage fracture in the transition region of a ferritic steel. Eng Fract Mech 64:305–325

    Google Scholar 

  • Besson J (2004) Local approach to fracture, collective book. Presses de l’Ecole Nationale Supérieure des Mines de Paris

    Google Scholar 

  • Bezensek B, Banerjee A (2010) A local approach model for cleavage fracture and crack extension direction of functionally graded materials. Eng Fract Mech 77:3394–3407

    Google Scholar 

  • Bezensek B, Hancock JW (2007) The toughness of laser welded joints in the ductile-brittle transition. Eng Fract Mech 74:2395–2419

    Google Scholar 

  • Bordet SR, Karstensen AD, Knowles DM, Wiesner CS (2005a) A new statistical local criterion for cleavage fracture in steel – Part I: Model presentation. Eng Fract Mech 72:435–452

    Google Scholar 

  • Bordet SR, Karstensen AD, Knowles DM, Wiesner CS (2005b) A new statistical local criterion for cleavage fracture in steel – Part II: Application to an offshore structural steel. Eng Fract Mech 72:453–474

    Google Scholar 

  • Bordet SR, Tanguy B, Besson J, Bugat S, Moinereau D, Pineau A (2006) Cleavage fracture of RPV steel following warm pre-stressing: micromechanical analysis and interpretation through a new model. Fatigue Fract Eng Mater Struct 29:799–816

    Google Scholar 

  • Bouyne E (1999) Propagation et arrêt de fissures de clivage dans l’acier 2 1/4 Cr-1Mo. Ph.D. thesis, Ecole des Mines de Paris

    Google Scholar 

  • Bouyne EH, Flower M, Lindley TC, Pineau A (1998) Use of EBSD technique to examine microstructure and cracking in a bainitic steel. Scrip Mater 39:295–300

    Google Scholar 

  • Bouyne E, Joly P, Houssin B, Wiesner C, Pineau A (2001) Mechanical and microstructural investigations into the crack arrest behavior of a modern 2 ¼ Cr – 1 Mo pressure vessel steel. Fatigue Fract Eng Mater Struct 24:105–116

    Google Scholar 

  • Briggs TL, Campbell JD (1972) The effect of strain rate and temperature on the yield and flow of polycrystalline Niobium and Molybdenum. Acta Mater 20:711–724

    Google Scholar 

  • Brillaud C, Hedin F (1992) In-service evaluation of French pressurized water reactor vessel steel. In: Stoller R, Kumar A, Gelles D (eds) Effects of radiation on materials: 15th international symposium. ASTM STP 1125. ASTM, Philadelphia pp 23–49

    Google Scholar 

  • Buswell JT, Phythian WJ, McElroy RJ, Dumbell S, Ray PHN, Mace J, Sinclair RN (1995) Irradiation-induced microstructural changes and hardening mechanisms in model PNR reactor pressure vessel steels. J Nucl Mater 225:196–214

    Google Scholar 

  • Byun T, Farrell K (2004) Irradiation hardening behavior of polycrystalline metals after low temperature irradiation. J Nucl Mater 326:86–96

    Google Scholar 

  • Carassou S, Renevey S, Marini B, Pineau A (1998) Modelling of the ductile to brittle transition of a low alloy steel. In: Brown MW, de los Rios ER, Miller Sheffield KJ (eds) Fracture from defects ECF 12. EMAS Publishing, Cradley Heath, UK pp 691–696

    Google Scholar 

  • Carr FL, Goldman M, Jaffe LD, Buffum DC (1953) Isothermal temper embrittlement of SAE 3140 steel. Trans AIME 197:998

    Google Scholar 

  • Chen SP, Voter AF, Boring AM, Albers RC, Hay PJ (1990) Investigation of the effects of boron on Ni3Al grain boundaries by atomistic simulations. J Mater Res 5:955–970

    Google Scholar 

  • Chu C, Needleman A (1980) Void nucleation effects in bi-axially stretched sheets. J Eng Mater Technol 102:249–256

    Google Scholar 

  • Cottrell AH (1958) Theory of brittle fracture in steel and similar metals. Trans AIME 212:192–203

    Google Scholar 

  • Cottrell AH (1989) Strengths of grain boundaries in pure metals. Mater Sci Technol 5:1165–1167

    Google Scholar 

  • Cottrell AH (1990a) Strengthening of grain boundaries by segregated interstitials in iron. Mater Sci Technol 6:121–123

    Google Scholar 

  • Cottrell AH (1990b) Strength of grain boundaries in impure metals. Mater Sci Technol 6:325–329

    Google Scholar 

  • Cox B (1990) Environmentally-induced cracking of zirconium alloys – a review. J Nucl Mat 170:1–23

    Google Scholar 

  • Crocker AG, Flewitt PEJ, Smith GE (2005) Computational modelling of fracture in polycrystalline materials. Int Mater Rev 50:99–124

    Google Scholar 

  • Curry DA, Knott JF (1979) Effect of microstructure on cleavage fracture toughness of quenched and tempered steels. Metal Sci 13:341–345

    Google Scholar 

  • Davis CL, King JE (1994) Cleavage initiation in the intercritically reheated coarse-grained heat affected zone – Part I: Fractographic evidence. Metall Mater Trans A 25A:563–573

    Google Scholar 

  • Davis CL, King JE (1996) Cleavage initiation in the intercritically reheated coarse-grained heat affected zone – Part II: Failure criteria and statistical effects. Metall Mater Trans A 27A:3019–3029

    Google Scholar 

  • Deruyttere A, Greenough GB (1956) The criterion for the cleavage fracture of zinc single crystals. J Inst Metals 84:337

    Google Scholar 

  • Deyber S, Alexandre F, Vaissaud J, Pineau A (2005) Probabilistic life of DA 718 for aircraft engine disks. In Loria EA (Ed) Superalloys 718, 625, 706 and derivatives; TMS pp 97–110

    Google Scholar 

  • Di Fant M, Le Coq V, Cleizergues O, Carollo G, Mudry F, Bauvineau L, Burlet H, Pineau A, Marini B, Koundy M, Sainte Catherine C, Eripret C (1996a) Mise en place d’une méthodologie simplifiée pour utiliser les critères locaux de rupture. Final report. Convention MRES 92:A.0334, IRSID RE 96.03. IRSID, Maizières-les-Metz

    Google Scholar 

  • Di Fant M, Le Coq V, Cleizergues O, Carollo G, Mudry F, Bauvineau L, Burlet H, Pineau A, Marini B, Koundy M, Sainte Catherine C, Eripret C (1996b) Development of a simplified approach for using the local approach to fracture. Euromech-Mecamat. Journal de Physique IV, Colloque C6 6:C6-503–C6-512

    Google Scholar 

  • Dodds RH, Anderson TL, Kirk MT (1991) A framework to correlate a/w ratio effects on elastic-plastic fracture toughness (Jc). Int J Fract 48:1–22

    Google Scholar 

  • Dumoulin P, Guttmann M, Foucault M, Palmer M, Wayman M, Biscondi M (1980) Role of molybdenum in phosphorus-induced temper embrittlements. Metal Sci 14:1–15

    Google Scholar 

  • Echeverria A, Rodriguez-Ibabe JM (1999) Brittle fracture micromechanisms in bainitic and martensitic microstructures in a C-Mn-B steel. Scrip Mater 41:131–136

    Google Scholar 

  • Erhart H, Grabke HJ (1981) Equilibrium segregation of phosphorus at grain boundaries of Fe-P-, Fe-C-P, Fe-Cr-P and Fe-Cr-C-P alloys. Metal Sci 15:401–408

    Google Scholar 

  • Evans AG (1983) Statistical aspects of cleavage fracture in steel. Metall Trans A 14A:1349–1355

    Google Scholar 

  • Fairchild DP, Howden DG, Clark WAT (2000a) The mechanism of brittle fracture in a micro-alloyed steel: Part I: Inclusion-induced cleavage. Metall Mater Trans A 31A:641–652

    Google Scholar 

  • Fairchild DP, Howden DG, Clark WAT (2000b) The mechanism of brittle fracture in a microalloyed steel: Part II: Mechanistic modelling. Metall Mater Trans A 31A:653–667

    Google Scholar 

  • Faulkner RG (1996) Segregation to boundaries and interfaces in solids. Int Mater Rev 41:198–208

    Google Scholar 

  • Fraczkiewicz A, Biscondi M (1985) Intergranular segregation of bismuth in copper bicrystals. J Phys C4:497–503

    Google Scholar 

  • Fraczkiewicz A, Wolski K, Delafosse D (2011) Ségrégation intergranulaire et rupture des matériaux cristallins. In: Priester L (ed) Joints de grains et plasticité cristalline. Hermès-Lavoisier, Paris, pp 289–332

    Google Scholar 

  • François D, Pineau A (2001) Fracture of metals – Part II: Ductile fracture. In: Bouchaud E, Jeulin D, Prioul C, Roux S (eds) Physical aspects of fracture. Kluwer, Dordrecht, pp 125–146

    Google Scholar 

  • François D, Pineau A, Zaoui A (1998) Mechanical behaviour of materials. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Friedel J (1964) Dislocations. Pergamon Press, Oxford

    MATH  Google Scholar 

  • Gale WF, Totemeier TC (eds) (2004) Smithells metals reference book, 8th ed. Elsevier Butterworth-Hainemann, London

    Google Scholar 

  • Gao X, Dodds RH (2000) Constraint effects on the ductile-to-brittle transition temperature of ferritic steels: A Weibull stress model. Int J Fract 102:43–69

    Google Scholar 

  • Gao X, Faleskog J, Shih CF (1998a) Cell model for nonlinear fracture analysis – II. Fracture-process calibration and verification. Int J Fract 89:374–386

    Google Scholar 

  • Gao X, Ruggieri C, Dodds RH (1998b) Calibration of Weibull stress parameters using fracture toughness data. Int J Fract 92:175–200

    Google Scholar 

  • Gao X, Faleskog J, Shih CF (1999) Analysis of ductile to cleavage transition in part-through crack using a cell model incorporating statistics. Fatigue Fract Eng Mater Struct 22:239–250

    Google Scholar 

  • Gas P, Guttmann M, Bernardini J (1982) Interactive co-segregation of Sb and Ni at the grain boundaries of ultra-high purity Fe-based alloys. Acta Metall 30:1309–1316

    Google Scholar 

  • Gell M, Smith E (1967) The propagation of cracks through grain boundaries in polycrystalline 3% silicon-iron. Acta Metall 15:253–258

    Google Scholar 

  • Gilman JJ (1954) Mechanism of ortho kink-band formation in compressed zinc monocrystals. J Metals 6:621–629

    Google Scholar 

  • Gilman JJ (1958) Fracture of zinc-mono-crystals and bi-crystals. Trans AIME 212:783–791

    Google Scholar 

  • Gourgues A-F, Flower HM, Lindley TC (2000) Electron backscattering diffraction study of acicular ferrite, bainite and martensite steel microstructures. Mater Sci Technol 16:26–40

    Google Scholar 

  • Griffiths JR, Owen DRJ (1971) An elastic-plastic stress analysis for a notched bar in plane strain bending. J Mech Phys Solids 19:419–431

    Google Scholar 

  • Groom JDG, Knott JF (1975) Cleavage fracture in prestrained mild steel. Metal Sci 9:390–400

    Google Scholar 

  • Guionnet C, Houssin B, Brasseur D, Lefort A, Gros D, Perdreau R (1982) Radiation embrittlement of PWR reactor vessel weld metals: nickel and copper synergism effects. ASTM STP782, Effect of radiation of materials, Eleventh conference. ASTM, Philadelphia, pp 392–411

    Google Scholar 

  • Gurland J (1972) Observations on the fracture of cementite particles in a spheroidized 1.05% C steel deformed at room temperature. Acta Metall 20:735–741

    Google Scholar 

  • Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: Part I: Yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99:2–15

    Google Scholar 

  • Guttmann M (1975) Equilibrium segregation in a ternary solution: a model for temper embrittlement. Surf Sci 53:213–227

    Google Scholar 

  • Guttmann M (1996) Grain boundary segregation and embrittlement in multicomponent systems: recent literature revisited. In: Hondros ED, Mc Lean M (eds) The Donald Mc lean symposium – structural materials engineering application through scientific insight. The Institute of Materials University Press, Cambridge, pp 59–81

    Google Scholar 

  • Guttmann M, Mc Lean D (1979) In: Johnson WC, Blakely JM (eds) Interfacial segregation. ASM, Metals Park, pp 251–348

    Google Scholar 

  • Guttmann M, Dumoulin P, Wayman M (1982) The thermodynamics of interactive co-segregation of phosphorus and alloying elements in iron and temper-brittle steels. Metal Trans 13A:1693–1711

    Google Scholar 

  • Haggag FM (1993) Effects of irradiation temperature on embrittlement of nuclear pressure vessel steels. In: Kluwer A, Gelles DS, Nanstad RK, Little EA (eds) Effects of radiation on materials 16th international symposium. ASTM STP1175. American Society for Testing and Materials, Philadelphia, pp 172–185

    Google Scholar 

  • Hahn GT (1984) The influence of microstructure on brittle fracture toughness. Metall Trans A 15A:947–959

    Google Scholar 

  • Hall EO (1951) The deformation and ageing of mild steel. II: Characteristics of the Lüders deformation. Proc R Soc Lond B64:742–747

    Google Scholar 

  • Hauser FE, Landon PR, Dorn JE (1956) The strength of concentrated Mg-Zn solid solutions. Trans ASM 48:986–1002

    Google Scholar 

  • Heerens J, Hellmann D (2002) Development of the Euro fracture toughness dataset. Eng Fract Mech 69:424–449

    Google Scholar 

  • Henry M, Marandet B, Mudry F, Pineau A (1986) Effets de la température et de la vitesse de chargement sur la ténacité à rupture d’un acier faiblement allié – Interprétation par des critères locaux. J de Mécanique Théorique et Appliquée 4:741–768

    Google Scholar 

  • Hippsley CA, Druce SG (1983) The influence of phosphorous segregation to particle/matrix interfaces on ductile fracture in a high strength steel. Acta Metall 31:1861–1872

    Google Scholar 

  • Hiranuma N, Soneda N, Dohi K, Ishino S, Dohi N, Ohata H (2004) Mechanistic modelling of transition temperature shift of Japanese RPV materials. In: 30th MPA seminar, Stuttgart, 6–7 October, pp 3.1–3.19

    Google Scholar 

  • Hirth JP, Rice JR (1980) On the thermodynamics of adsorption at interfaces as it influences decohesion. Metall Trans 11A:1501–1511

    Google Scholar 

  • Hofmann S, Lejček P (1996) Solute segregation at grain boundaries. Interface Sci 3:241–267

    Google Scholar 

  • Hughes GM, Smith G, Crocker AG, Flewitt PEJ (2005) An examination of the linkage of cleavage cracks at grain boundaries. Mater Sci Eng 21:1268–1274

    Google Scholar 

  • Hutchinson JW (1968) Plastic stress and strain fields at a crack tip. J Mech Phys Solids 16:337–347

    Google Scholar 

  • Kaechele LE, Tetelman AS (1969) A statistical investigation of microcrack formation. Acta Metall 17:463–475

    Google Scholar 

  • Kameda J, Mc Mahon CJ (1980) Solute segregation and brittle fracture in an alloy steel. Metall Trans A11:91–101

    Google Scholar 

  • Kantidis E, Marini B, Pineau A (1994) A criterion for intergranular brittle fracture of a low alloy steel. Fatigue Fract Eng Mater Struct 17:619–633

    Google Scholar 

  • Kenney KL, Reuter WG, Reemsnyder HS, Matlock DK (1997) Fracture initiation by local brittle zones in weldments of quenched and tempered structural alloy steel plate. In: Underwood JH, Mac Donald BD, Mitchell MR (eds) Fatigue and fracture mechanics, vol 28. ASTM STP 1321. American Society for Testing and Materials, Philadelphia, pp 427–449

    Google Scholar 

  • Kim YJ, Schwalbe KH (2001a) Mismatch effect on plastic yield loads in idealised weldments. I: Weld center cracks. Eng Fract Mech 68:163–182

    Google Scholar 

  • Kim YJ, Schwalbe KH (2001b) Mismatch effect on plastic yield loads in idealised weldments. II: Heat affected zone cracks. Eng Fract Mech 68:183–199

    Google Scholar 

  • Kirk M, Santos C, Eason E, Wright J, Odette GR (2003) Updated embrittlement trend curve for reactor pressure vessels steels. In: Trans of the 17th international conference on structural mechanics in reactor technology (SMIRT 17), Prague, 17–22 August, G01–G05

    Google Scholar 

  • Knott JF (1966) Some effects of hydrostatic tension on the fracture behaviour of mild steel. J Iron Steel Inst 204:104–111

    Google Scholar 

  • Knott JF (1967) Effects of strain on notch brittleness in mild steel. J Iron Steel Inst 205:966–969

    Google Scholar 

  • Knott JF (1973) Fundamentals of fracture mechanics. Butterworths, London

    Google Scholar 

  • Koval AY, Vasilev AD, Firstov SA (1997) Fracture toughness of molybdenum sheet under brittle-ductile transition. Int J Refract Metal Hard Mater 15:223–226

    Google Scholar 

  • Krasko GL (1997) Effect of impurities on the electronic structure of grain boundaries and intergranular cohesion in iron and tungsten. Mater Sci Eng A234–236:1071–1074

    Google Scholar 

  • Kroon M, Faleskog J (2005) Micromechanisms of cleavage fracture initiation in ferritic steels by carbide cracking. J Mech Phys Solids 53:171–196

    MATH  Google Scholar 

  • Kubo T, Wakashima Y, Amano K, Nagai N (1985) Effects of crystallographic orientation on plastic deformation and SCC initiation of zirconium alloys. J Nucl Mater 132:1–9

    Google Scholar 

  • Lambert-Perlade A (2001) Rupture par clivage de microstructures d’aciers bainitiques obtenues en conditions de soudage. Ph.D. thesis, École des Mines de Paris

    Google Scholar 

  • Lambert-Perlade A, Gourgues A-F, Besson J, Sturel T, Pineau A (2004) Mechanisms and modeling of cleavage fracture in simulated heat-affected zone microstructure of a high-strength low alloy steel. Metall Mater Trans A 35A:1039–1053

    Google Scholar 

  • Lee S, Kim S, Hwang B, Lee BS, Lee CG (2002) Effect of carbide distribution on the fracture toughness in the transition temperature region of an A 508 steel. Acta Mater 50:4755–4762

    Google Scholar 

  • Lei Y, O’Dowd NP, Busso EP, Webster GA (1998) Weibull stress solutions for 2-D cracks in elastic and elastic-plastic materials. Int J Fract 89:245–268

    Google Scholar 

  • Lejček P (2010) Grain boundary segregation in metals. Springer series in materials science. Springer, Heidelberg Dordrecht London New York

    Google Scholar 

  • Lemant F, Pineau A (1981) Mixed mode fracture of a brittle orthotropic material – example of strongly textured zinc sheets. Eng Fract Mech 14:91–105

    Google Scholar 

  • Lewandovsky JJ, Wang WH, Greer AL (2005) Intrinsic plasticity or brittleness of metallic glasses. Philos Mag Lett 85:77–87

    Google Scholar 

  • Lindley TC, Oates G, Richards CE (1970) A critical appraisal of carbide cracking mechanisms in ferrite/carbide aggregates. Acta Metall 18:1128–1136

    Google Scholar 

  • Liu CT, George EP (1990) Environmental embrittlement in boron-free and boron-doped FeAl (40 at %Al) alloys. Scrip Metall Mater 24:1285–1290

    Google Scholar 

  • Machida S, Miyata T, Hagiwara Y, Yoshinari H, Suzuki T (1991) A statistical study of the effect of local brittle zones (LBZ) on the fracture toughness (CTOD) of weldments. In: Blauel JG, Schwalbe K-H (eds) Defect assessment in components – fundamentals and applications. ESIS/EGF9. Mechanical Engineering Publications, London, pp 633–658

    Google Scholar 

  • Margolin BZ, Gulenko AG, Shvetsova VA (1998) Improved probabilistic model for fracture toughness prediction for nuclear pressure vessel steels. Int J Pres Ves Pip 75:843–855

    Google Scholar 

  • Martin-Meizoso A, Ocana-Arizcorreta I, Gil-Sevillano J, Fuentes-Pérez M (1994) Modeling cleavage fracture of bainitic steels. Acta Metall Mater 42:2057–2068

    Google Scholar 

  • Mc Lean D (1957) Grain boundaries in metals. Clarendon, Oxford

    Google Scholar 

  • Mc Mahon CJ, Cohen M (1965) Initiation of cleavage in polycrystalline iron. Acta Metall 13:591–604

    Google Scholar 

  • Militzer M, Wieting J (1986) Theory of segregation kinetics in ternary systems. Acta Metall 34:1229–1236

    Google Scholar 

  • Militzer M, Wieting J (1987) Interfacial two-dimensional phase transitions and impurity segregation. Acta Metall 35:2765–2777

    Google Scholar 

  • Militzer M, Wieting J (1989) Segregation mechanisms of temper embrittlement. Acta Metall 37:2585–2593

    Google Scholar 

  • Miller MK, Namstad RK, Sokolov MA, Russel KF (2006) The effects of irradiation, annealing and re-irradiation on RPV steels. J Nucl Mater 351:216–222

    Google Scholar 

  • Minami F, Arimochi K (2001) Evaluation of prestraining and dynamic loading effects on the fracture toughness of structural steels by the local approach. J Press Ves Technol 123:362–372

    Google Scholar 

  • Minami F, Iida M, Takahara W, Konda N, Arimochi K (2002) Fracture mechanics analysis of Charpy test results based on the Weibull stress criterion. In: François D, Pineau A (eds) From Charpy to present impact testing. Elsevier/ESIS, London, pp 411–418

    Google Scholar 

  • Moskovic R (2002) Modelling of fracture toughness data in the ductile-to-brittle transition temperature region by statistical analysis. Eng Fract Mech 69:511–530

    Google Scholar 

  • Mudry F (1988) A local approach to cleavage fracture. Nucl Eng Des 105:65–76

    Google Scholar 

  • Naudin C (1999) Modélisation de la ténacité de l’acier de cuve REP en presence de zones de segregation. Ph.D. thesis, Ecole des Mines de Paris

    Google Scholar 

  • Naudin C, Frund J-M, Pineau A (1999) Intergranular fracture stress and phosphorus grain boundary segregation of a Mn-Ni-Mo steel. Scrip Mater 40:1013–1019

    Google Scholar 

  • Neville DJ, Knott JF (1986) Statistical distributions of toughness and fracture stress for homogeneous and inhomogeneous materials. J Mech Phys Solids 34:243–291

    Google Scholar 

  • Nikolaev YA, Nikolaeva AV, Shtrombakh YI (2002) Radiation embrittlement of low-alloy steels. Int J Pres Ves Pip 79:619–636

    Google Scholar 

  • Odette GR, Lucas GE (2001) Embrittlement of nuclear reactor pressure vessels. JOM 53:18–22

    Google Scholar 

  • Odette GR, Yamamoto T, Rathbun H, He M, Hribernik M, Rensman J (2003) Cleavage fracture and irradiation embrittlement of fusion reactor alloys: mechanisms, multiscale models, toughness measurements and implications to structural integrity assessment. J Nucl Mater 323:313–340

    Google Scholar 

  • O’Dowd NP, Lei Y, Busso EP (2000) Prediction of cleavage failure probabilities using the Weibull stress. Eng Fract Mech 67:87–100

    Google Scholar 

  • Ohata M, Minami F, Toyoda M (1996) Local approach to strength mis-match effect on cleavage fracture of notched material. Euromech-Mecamat. J Phys IV 6:C6-269–C6-278

    Google Scholar 

  • Pahdi D, Lewandowski JJ (2004) Resistance curve behavior of polycrystalline niobium failing via cleavage. Mater Sci Eng A366:56–65

    Google Scholar 

  • Parisot R, Forest S, Pineau A, Grillon F, Demonet X, Mataigne JM (2004a) Deformation and damage mechanisms of zinc coatings on hot-dip galvanized steel sheets – Part I: Deformation modes. Metall Mater Trans A 35A:797–811

    Google Scholar 

  • Parisot R, Forest S, Pineau A, Nguyen F, Demonet X, Mataigne J-M (2004b) Deformation and damage mechanisms of zinc coatings on hot-dip galvanized steel – Part II: Damage modes. Metall Mater Trans A 35A:813–823

    Google Scholar 

  • Petch NJ (1953) The cleavage strength of polycrystals. J Iron Steel Inst 174:25–28

    Google Scholar 

  • Petti JP, Dodds RH (2005a) Calibration of the Weibull stress scale parameter, σ u using the master curve. Eng Fract Mech 72:91–120

    Google Scholar 

  • Petti JP, Dodds RH (2005b) Ductile tearing and discrete void effects on cleavage fracture under small-scale yielding conditions. Int J Solids Struct 42:3655–3676

    MATH  Google Scholar 

  • Pineau A (1981) Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. In: François D et al (eds) Advanced in fracture research, International conference on fracture, vol 5 (ICF 5). Pergamon press, Oxford 2, pp 553–577

    Google Scholar 

  • Pineau A (1992) Global and local approaches of fracture – transferability of laboratory test results to components. In: Argon AS (ed) Topics in fatigue and fracture. Springer, New York, pp197–234

    Google Scholar 

  • Pineau A (2003) Practical application of local approach methods. In: Milne I, Ritchie R, Karihaloo BL (eds) Comprehensive structural integrity, vol 7. Elsevier, Amsterdam, pp 177–225

    Google Scholar 

  • Pineau A (2006) Development of the local approach to fracture over the past 25 years: theory and applications. ICF 11 conference, Turin Italy. Int J Fract 138:139–166

    Google Scholar 

  • Pineau A, Joly P (1991) Local versus global approaches to elastic-plastic fracture mechanics. Application to ferritic steels and a cast duplex stainless steel. In: Blauel JG, Schwalbe KH (eds) Defect assessment in components-fundamentals and applications. ESIS/ECF 9. Mechanical Engineering Publications, London pp 381–414

    Google Scholar 

  • Pineau A, Pardoen T (2007) Failure of metals. In: Milne I, Ritchie R, Karihaloo BL (eds) Comprehensive structural integrity, vol 2. Elsevier, Amsterdam, pp 684–797

    Google Scholar 

  • Priester L (2006) Les joints de grains. De la théorie à l’ingénierie. EDP Sciences, Les Ulis

    Google Scholar 

  • Qiao Y, Argon AS (2003a) Cleavage crack-growth resistance of grain boundaries in polycrystalline Fe-2% Si alloy: experiments and modeling. Mech Mater 35:129–154

    Google Scholar 

  • Qiao Y, Argon AS (2003b) Cleavage cracking resistance of high angle grain boundaries in Fe-3% Si alloy. Mech Mater 35:313–331

    Google Scholar 

  • Qiao Y, Kong X (2004) An energy analysis of the grain boundary behavior in cleavage cracking in Fe-3 wt %Si alloy. Mater Lett 58:3156–3160

    Google Scholar 

  • Raoul S (1999) Rupture intergranulaire fragile d’un acier faiblement allié induite par la ségrégation d’impuretés aux joints de grains: influence de la microstructure. Ph.D. thesis, Université Paris Sud, France

    Google Scholar 

  • Raoul S, Marini B, Pineau A (1999) Rupture intergranulaire fragile d’un acier faiblement allié induite par segregation d’impuretés aux joints des grains. J Phys IV-9:179–184

    Google Scholar 

  • Rathbun HJ, Odette GR, Yamamoto T, Lucas GE (2006) Influence of statistical and constraint loss size effects on cleavage fracture toughness in the transition – a single variable experiment and database. Eng Fract Mech 73:134–158

    Google Scholar 

  • Raynor GV (1960) Magnesium and its alloys. Wiley, New York

    Google Scholar 

  • Rice JR (1976) Hydrogen and interfacial cohesion. In: Thompson AW, Bernstein IM (eds) Effect of hydrogen on behaviour of materials. Metallurgical Society of AIME, New York, pp 455–466

    Google Scholar 

  • Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids 16:1–12

    MATH  Google Scholar 

  • Rice JR, Thomson R (1974) Ductile versus brittle behavior of crystals. Philos Mag 29:73–97

    Google Scholar 

  • Rice JR, Wang JS (1989) Embrittlement of interfaces by solute segregation. Mater Sci Eng A107:23–40

    Google Scholar 

  • Rice JR, Beltz GE, Sun Y (1992) Peierls framework for dislocation nucleation from a crack tip. In: Argon AS (ed) Topics in fracture and fatigue. Springer, New York, pp 1–58

    Google Scholar 

  • Ritchie RO, Knott JF, Rice JR (1973) On the relationship between critical tensile stress and fracture toughness in mild steel. J Mech Phys Solids 21:395–410

    Google Scholar 

  • Rodriguez-Ibabe JM (1998) The role of microstructure in toughness behaviour of microalloyed steels. Mater Sci Forum Microalloy Steels 284–286:51–62

    Google Scholar 

  • Roos E, Alsmann U, Elsässer K, Eisele W, Seidenfuss M (1998) Experiments on warm prestress effect and their numerical simulation based on local approach. In: Brown MW, de los Rios ER, Miller KJ II (eds) ECF12 fracture from defect, EMAS Publishing Cradley Heath, UK, pp 939–944

    Google Scholar 

  • Ruggieri C, Gao X, Dodds RH (2000) Transferability of elastic-plastic fracture toughness using the Weibull stress approach: significance of parameter calibration. Eng Fract Mech 67:101–117

    Google Scholar 

  • Saito N, Mabuchi M, Nakanishi N, Kubota K, Higashi K (1997) The aging behavior and the mechanical properties of the Mg-Li-Al-Cu alloy. Scrip Mater 36:551–555

    Google Scholar 

  • Samant AV, Lewandowski JJ (1997a) Effects of test temperature, grain size and alloy addition on the cleavage fracture stress of polycrystalline niobium. Metall Mater Trans A 28A:389–399

    Google Scholar 

  • Samant AV, Lewandowski JJ (1997b) Effects of test temperature, grain size and alloy additions on the low-temperature fracture toughness of polycrystalline niobium. Metall Mater Trans A 28A:2297–2307

    Google Scholar 

  • Schuster I, Lemaignan C (1989a) Characterization of zircaloy corrosion fatigue phenomena in an iodine environment – Part I: Crack growth. J Nucl Mater 166:348–356

    Google Scholar 

  • Schuster I, Lemaignan C (1989b) Characterization of zircaloy corrosion fatigue phenomena in an iodine environment – Part II: Fatigue life. J Nucl Mater 166:357–363

    Google Scholar 

  • Seah MP (1977) Grain boundary segregation and the T-t dependence of temper brittleness Acta Metall 25:345–357

    Google Scholar 

  • Seah MP (1980) Absorption-induced interface decohesion. Acta Metall 28:955–962

    Google Scholar 

  • Seah MP, Hondros E (1973) Grain boundary segregation. Proc R Soc Lond A30:191–211

    Google Scholar 

  • Sherry AH, Lidbury DPG, Connors DC, Dowling AR (2001) Modelling of size effects on fracture in the brittle-to ductile transition regime. In: International conference on fracture, 10 (ICF 10), Hawaii

    Google Scholar 

  • Smith E (1966) The nucleation and growth of cleavage microcracks in mild steel. In: Proceedings of the conference on physical basis of yield and fracture. Inst Phys & Phys Soc, Oxford, pp36–46

    Google Scholar 

  • Sokolov M, Nanstad R, Miller M (2004) Effect of radiation on fracture toughness and microstructure of a high-Cu RPV weld. J ASTM Int 1(9):123–137

    Google Scholar 

  • Stöckl H, Böschen R, Schmitt W, Varfolomeyev I, Chen JH (2000) Quantification of the warm prestressing effect in a shape welded 10 Mn Mo Ni 5-5 material. Eng Fract Mech 67:119–137

    Google Scholar 

  • Stroh AN (1954) The formation of cracks as a result of plastic flow. Proc R Soc Lond A 223:404–414

    MathSciNet  MATH  Google Scholar 

  • Sumpter JDG (1993) An experimental investigation of the T stress approach. In: Hackett EM, Schwalbe K-H, Dodds RH (eds) Constraint effects in fracture. ASTM STP 1171, pp 492–502

    Google Scholar 

  • Tagawa T, Miyata T, Aihara S, Okamoto K (1993) Influence of martensitic islands on cleavage fracture toughness of weld heat-affected zone in low carbon steels. International symposium on low carbon steels for the 1990s, Pittsburgh, Pennsylvania, USA. Minerals. Met Mat Soc, Warrendale, pp 493–500

    Google Scholar 

  • Tanguy B, Besson J, Pineau A (2003) Comment on: “Effect of carbide distribution on the fracture toughness in the transition temperature region of an A508 steel.”. Scrip Mater 49:191–197

    Google Scholar 

  • Tanguy B, Besson J, Piques R, Pineau A (2005a) Ductile-to-brittle transition of an A508 steel characterized by Charpy impact test – Part I: Experimental results. Eng Fract Mech 72:49–72

    Google Scholar 

  • Tanguy B, Besson J, Piques R, Pineau A (2005b) Ductile-to-brittle transition of an A 508 steel characterized by Charpy impact test – Part II: Modelling of the charpy transition curve. Eng Fract Mech 72:413–434

    Google Scholar 

  • Tanguy B, Bouchet C, Bugat S, Besson J (2006) Local approach to fracture based prediction of the ΔT56J and ΔTKIC100 shifts due to irradiation for an A508 pressure vessel steel. Eng Fract Mech 73:191–206

    Google Scholar 

  • Tavassoli A, Bougault A, Bisson A (1983) The effect of residual impurities on the temper embrittlement susceptibility of large A508, class 3, vessel forgings. In: Proceedings of the international conference on the effects of residual impurity and micro-alloying elements on weldability and weld properties, Welding Institute, pp 43.1–43.9

    Google Scholar 

  • Tavassoli A, Soulat P, Pineau A (1989) Temper embrittlement susceptibility and toughness of A508 class 3 steel. Residual and unspecified elements in steels. ASTM STP1042. American Society for Testing and Materials, Philadelphia, pp 100–113

    Google Scholar 

  • Tigges D, Piques R, Frund J-M, Pineau A (1994) Shallow crack effect on fracture toughness in a low alloy steel. In: Schwalbe K-H, Berger C (eds) Structural integrity, experiments-models-applications. Proceedings of the 10th biennial European conference on fracture, ECF10. EMAS, Warley, pp 637–646

    Google Scholar 

  • Toyoda M (1988) Fracture toughness evaluation of steel welds. Review part II. University of Osaka, Osaka

    Google Scholar 

  • Tracey DM (1976) Finite element solutions for crack-tip behavior in small-scale yielding. J Eng Mater Technol 98:146–151

    Google Scholar 

  • Trouvain C (1989) Approches globale et locale de la rupture fragile d’un acier faiblement allié; Influence des segregations et de l’irradiation, Technical report. CEA, Saclay

    Google Scholar 

  • Tweed JH, Knott F (1987) Micromechanisms of failure in C-Mn weld metals. Acta Metall 35:1401–1414

    Google Scholar 

  • Wagenhofer M, Gunawardane HP, Natishan ME (2001) Yield and toughness transition prediction for irradiated steels based on dislocation mechanics. In: Rosinski ST, Grossbeek ML, Allen TR, Kumar (eds) Effect of radiation on materials: 20th international symposium. ASTM STP 1045. ASTM, Philadelphia, pp 97–108

    Google Scholar 

  • Wallin K (1989) The effect of ductile tearing on cleavage fracture probability in fracture toughness testing. Eng Fract Mech 32:523–531

    Google Scholar 

  • Wallin K (1991a) Fracture toughness transition curve shape for ferritic structural steels. In: Theoh SH, Lee KH (eds) Proceedings of the joint FEFG. ICF international conference on fracture of engineering materials and structures. Elsevier, London, pp 83–88

    Google Scholar 

  • Wallin K (1991b) Statistical modelling of fracture in the ductile-to-brittle transition region. In: Blauel JG, Schwalbe K-H (eds) Defect assessment in components – fundamentals and applications. ESIS/ECF 9. Mechanical Engineering Publications, London, pp 415–445

    Google Scholar 

  • Wallin K (1993) Statistical aspects of constraint with emphasis on testing and analysis of laboratory specimens in the transition region. In: Hackett EM, Schwalbe K-H, Dodds RH (eds) Constraint effects in fracture. ASTM STP 1171. American Society for Testing and Materials, Philadelphia, pp 264–288

    Google Scholar 

  • Wallin K, Saario T, Torronen K (1984) Statistical model for carbide induced brittle fracture in steel. Metal Sci 18:13–16

    Google Scholar 

  • Wang JS (2002) Internal hydrogen-induced embrittlement in iron single crystals. In: Chang T-J, Rudnicki JW (eds) Multiscale deformation and fracture in materials and structures. The James R. Rice 60th anniversary volume. Kluwer Academic Press, Dordrecht, pp 31–85

    Google Scholar 

  • Wang LG, Wang CY (1998) Effect of boron and sulfur on the electronic structure of grain boundaries in Ni. Comput Mater Sci 11:261–276

    Google Scholar 

  • Was GS (2007) Fundamentals of radiation materials science. Springer, Berlin/Heidelberg

    Google Scholar 

  • Westbrook JH, Aust KT (1963) Solute hardening at interfaces in high-purity lead-I: grain and twin boundaries. Acta Metall 11:1151–1176

    Google Scholar 

  • Wu SJ, Knott JF (2004) On the statistical analysis of local fracture stress in notched bars. J Mech Phys Solids 52:907–924

    Google Scholar 

  • Xia L, Cheng L (1997) Transition from ductile tearing to cleavage fracture: a cell-model approach. Int J Fract 87:289–306

    Google Scholar 

  • Xia L, Shih FC (1996) Ductile crack growth – III. Transition to cleavage fracture incorporating statistics. J Mech Phys Solids 44:603–639

    Google Scholar 

  • Yahya OML, Borit F, Piques R, Pineau A (1998) Statistical modeling of intergranular brittle fracture in a low alloy steel. Fatigue Fract Eng Mater Struct 21:1485–1502

    Google Scholar 

  • Yu SR, Yan ZG, Cao R, Chen JH (2006) On the change of fracture mechanism with test temperature. Eng Fract Mech 73:331–347

    Google Scholar 

  • Zener C (1949) Micromechanism of fracture. In: Fracturing of metals, ASM Cleveland Ohio, pp 3–31

    Google Scholar 

  • Zhou ZL, Liu SH (1998) Influence of local brittle zones on the fracture toughness of high strength low-alloyed multipass weld metals. Acta Metall Sin (Engl Lett) 11:87–92

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. École Centrale de Paris, Paris, France

    Prof. Dr. Dominique François

  2. École des Mines de Paris Paris Tech Centre des Matériaux UMR CNRS, Évry Cedex, France

    André Pineau

  3. Academy of Engineering, Paris, France

    André Pineau & Prof. André Zaoui

  4. French Académie des Sciences, Paris, France

    Prof. André Zaoui

Authors
  1. Prof. Dr. Dominique François
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. André Pineau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Prof. André Zaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

François, D., Pineau, A., Zaoui, A. (2013). Brittle Fracture. In: Mechanical Behaviour of Materials. Solid Mechanics and Its Applications, vol 191. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4930-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-4930-6_3

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4929-0

  • Online ISBN: 978-94-007-4930-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation