Fracture of materials
Fracture of materials Classification of fractureⅠ ① Amount of plastic deformation Vertical fracture Cup and cone Type fracture Brittle fracture Small plastic deformation Shear fracture （Separation of slip plane） Chisel point fracture Ductile fracture Large plastic deformation Fracture surface geometry Classification of fractureⅡ ② Transgranular and intergranular fracture Intergranular Brittle fracture fracture Fracture occurs along grain boundary Transgranular fracture Ductile fractur Fracture occurs in the grain Intergranular and transgranular fracture Classification of fracture III ③ Atomic level σ Relation between slip and cleavage plane Cleavage plane σ （a） Cleavage fracture fcc bcc hcp Slip plane ｛111｝ ｛110｝ ｛112｝ ｛123｝ ｛0001｝ ｛1010｝ ｛1011｝ Cleavage plane Non ｛100｝ ｛0001｝ τ Slip plane Materials τ （b） Shear fracture Al、Cu、Ni Cr、Mo、V W、β-Ti Ag、Au Zn、Mg Be、Sn γsteel α-Ti Mild steel Fractography Fractography? Method of observation and analysis of fracture surface which records progress of fracture. Fracture surface Process of fracture 例． Initiation of crack Crack growth Final fracture Fracture shows peculiar appearance Macro-fractography Naked Angle/color Loupe Appearance Micro-fractography Optical River pattern Electon Microscopic appearance Characteristics of ductile fracture surfaceⅠ Geometry of fracture surface depends on stress state. Tensile fracture Plain strain Perpendicular fracture surface Plain stress Shear fracture Slant type (shear) fracture surface Example Cup and cone type Macroscopic ～ Difference between tensile and shear Color of fracture surface ： Gray Microscopic ～ Dimple formation Shear fracture Chisel point fracture Characteristics: mentioned later Characteristics of brittle fracture surfaceⅡ Geometry Cleavage Color ： Metal gray Fracture pattern Perpendicular fracture surface Roughness Chevron pattern Starter notch Fatigue crack Chevron pattern Brittle fracture surface Shear lip Characteristics of fatigue fracture surfaceⅢ Ductile materials ・Low cyclic stress and thick plate Perpendicular; fracture surface ・High cyclic stress and thin plate Slant fracture surface Brittle materials Beach mark Initiation point ◎ Color ： Gray Fatigue Perpendicular fracture surface For random cyclic stress Beach mark Final fracture （Ductile） （Brittle fatigue fracture ⇒ Metal luster Microscopic characteristicsⅠ（Ductile①） Microscopic characteristics of ductile fracture Dimple … Many dips are formed Ripple Wavy pattern 25μm (a) 25μm (b) 25μm (c) 25μm (d) Tensile ductile fracture in stainless steel（28% Cr－9% Ni steel ） （Ductility）； (a) ＜ (b) ＜ (c) ＜ (d)） Characteristics of ductile fracture surfaceⅡ σ1 σ1 σ1 （a） Equaxed dimple ττ σ2 σ2 ττ σ1 （b） Elongated dimple （Shear load） M M （c） Elongated dimple （Tear load） Characteristics of brittle fracture surfaceⅣ Characteristics of brittle fracture ① River pattern When crack propagates on cleavage plane in which dislocation exists, River pattern is formed. ◎ Crack initiation is in grain boundary ◎ Flow of river pattern ＝ Propagation direction of crack growth 20μm River pattern for mild steel at low temperature impact load Characteristics of fatigue fracture surface Ⅵ Characteristics of fatigue fracture surface Striation Microscopic Depending on loading、 point of fracture surface 2μm Fracture mechanism changes each stage of growth Striation （25% Cr－5% Ni steel） Microscopic pattern depends on each stage of crack growth Always don’t observe Ductile fractureⅠ Ductile fracture Theoretical shear strength Macro ～ Cup and cone etc. Micro ～ Dimple Perfect crystal without defect X Elastic line in X＝O τ τ a Slip plane τ ⎛ 2πX ⎞ τ=τmax sin ⎜ ⎟ ⎝ b ⎠ O X b Theoretical shear strength （τmax ： Shear stress between atoms ） Next Ductile fractureⅡ Elastic line at X＝O τ ◎ Whiskerー Material without dislocation O X ◎ Normal materilas 1/10 ～ 1/100 （ τ at X＝0 ） …（ 4.1） 2πX ⎛ 2πX ⎞ sin ⎜ τ = τmax ≒ τ ⎟ max b b ⎝ ⎠ （ For small θ ⎛X⎞ τ = Gγ = G ⎜ ⎟ ⎝a⎠ ⇒ sin θ≒θ） …（ 4.2） τmax G ⎛ 1 ⎞⎛ b ⎞ = ⎜ ⎟⎜ ⎟G ≒ 10 ⎝ 2π⎠⎝ a ⎠ …（ 4.3） Ductile fractureⅢ Initiation and growth of void Void : Initiates at inclusion and delaminate from matrix Maximum shear at 45 degree （a） （b） （c） Cup and cone type tensile fracture process （d） Brittle fractureⅠ σ X Theoretical cleavage fracture strength Brittle fracture surface a0 Cleavage plane Macro ～ Chevron pattern Micro ～ River pattern、Tonge σ Elastic line at X=0 Brittle fracture Absorbed energy : Small Stored energy in material is consumed to grow crack Stress σ a0 σmax λ／2 Displacement X Rapidly crack growth ⇒ Instant fracture Balance position Brittle fractureⅡ Elastic line at X=0 Stress σ a0 σmax a0 ：Distance between atoms ◎ Whisker Without dislocation ⇒ Near value ◎ High strength steel etc. λ／2 Displacement X Balance position （Sine fuction） Difference of one order more …（ 4.4） 2πX ⎛ 2πX ⎞ σ = σmax sin ⎜ ≒ σ ⎟ max λ λ ⎝ ⎠ （For small θ ⇒ sin θ≒θ） （Stress-strain relation at X＝0） ⎛X⎞ σ = Eε = E ⎜⎜ ⎟⎟ ⎝ a0 ⎠ …（ 4.5） σmax ⎛ λ ⎞⎛⎜ E ⎞⎟ = ⎜ ⎟⎜ ⎟ ⎝ 2π⎠⎝ a 0 ⎠ …（ 4.6） Brittle fractureⅢ Elastic line at X=0 Stress σ a0 Work used delamination of atoms σmax Energy consumes formation of new free surface λ／2 Displacement X γ： Surface energy per unit area Balance position σmax ⎛ λ ⎞⎛⎜ E ⎞⎟ = ⎜ ⎟⎜ ⎟ ⎝ 2π⎠⎝ a 0 ⎠ …（4.6） λ 2 0 ∫ λσmax ⎛ 2πX ⎞ σmax sin ⎜ = 2γ ⎟ dX = π ⎝ λ ⎠ …（4.7） Two new free surfaces σmax ⎛ Eγ⎞ 12 E ⎟⎟ ≒ = ⎜⎜ 10 ⎝ a0 ⎠ …（4.8、4.9） Brittle fracture Ⅳ （Griffith’s theory①） Fracture strength of perfect brittle material with crack σ UE ： Strain energy stored in plate Free plane σ2 UE = ×πc 2 2E πc 2σ2 UE = E ρ : Rigid solution 2c US ： Energy to form crack plane U s = 2 × 2γc = 4γc σ Two planes Next Rate of energy Brittle fractureⅤ （ Griffith’s theory ②） dU E 2πcσ2 = dc E dU S = 4γ dc Criterion of fracture dU E dU S = dc dc …（4.12） 2πcσ2 = 4γ E Griffith’s equation Crack length c Variation of energy rate With increasing crack length ⎛ 2 Eγ ⎞ σ= ⎜ ⎟ ⎝ πc ⎠ 1 2 …（4.13） （Plane stress state） Fig. An oil barge that fractured in a brittle manner by crack propagation around its girth （The New York Times） Classification of fractureⅣ ④ Loading and environment Impact failure Static, Environmental Corrosion 3% σ Static fracture 13% Delay fracture、 Stress corrosion cracking 5% 11% Themal fatigue Corrosion fatigue Fretting fatigue Fatigue 60% 8% Fatigue t Loading and fracture Low cycle fatigue Classification of fracture About 80% of fracture was caused by fatigue Microscopic fracture surfaceⅢ（Ductile fracture③） Microvoid along grain boundary Crack growth inside Grain boundary Elongated dimple 2μm (a) Shallow dimple 25μm Shallow (b) 組織 図．Two phase stainless steel （25% Cr-5% Ni steel） Microscopic fracture surfaceⅤ（Brittle fracture②） Brittle fracture surface ② Tongue appearance … Twin deformation related τ τ 20μm Twin Bound. Bound. 図．High Cr ferrite steel（475℃ageing Fracture analysisⅠ ① Wire Rope failure to catch shark Macroscopic Wire Rope ⇒ Microscopic Large Necking Dimple Ductile fracture 5μm 10μm (a) Equiaxed dimple (b) Elongated dimple 図．Microscopic appearance of wire-rope Fracture anaysisⅡ ② Rail fracture surface Beach mark (a) … Fatigue (b) … Brittle fracture (a) Chevron pattern (b) 10μm （a） Striation 15μm （b） River pattern Fracture anaysisⅢ ③ Bolt fracture surface for ship Striation Beach mark 10μm 図．Bolt（SUS304）microscopic appearance Under cyclic loading Fatigue facture Measurement of striation space Fatigue crack growth rate Ductile fractureⅣ ◎ Microstructure effect ・Content Void formation ⇒ Inclusion ・Size, Geometry ・Distribution ● Globular martensite Sample geometry、Stress condition ○ Ferriteト‐globular perrite Ductility △ Ferrite‐layer perrite Sulfide Inclusion(2 phase) Vol.% Ductile fracture model （McClintock） Brittle fractureⅥ ①） ［Ⅰ］ Mechanical factor ① ・ Low temperature ・ Loading rate ・ Notch ・ Thickness Locally stress increases Constrain of plastic deformation Brittle Toughness evaluation Hammer Sharpy impact test Measure Potential energy of Hammer ＝ h1 α Remained Energy after impact ＋ Absorbed energy of material （Toughness） β h2 Notched specimen Sharpy impact tester Brittle fractureⅦ 80 Rate of reduction of area 160 Tensile test 60 120 40 80 Impact test Absorption energy 20 40 0 0 -200 -150 -100 -50 0 50 100 150 Ductile Absorption energy J Reduction of area ％ ［Ⅰ］ Mechanical factors ② （Ductile-Brittle Transition Behavior） Ductile-Brittle Transition Temperature Temperature ℃ Brittle Ductile-Brittle Transition Brittle fractureⅧ Absorption energy J ［Ⅰ］ Mechanical factors ③ （Question） Which is the best steel for tanker? Each steel is the same strength. Oil Natural Gas Gas ⇒ Liquid Temperature decreases （a） （b） （c） Ductile Brittle High risk of brittle fracrure Under low temperature Material must keep ductile Temperature ℃ D.-B. transition temp. must be low （Ex. ： Titanic sinked in 1912.4.14） ・ Notch effect Notch induces Stress concentration and high three axis stress condition ・ Plate thickness Thickness increases, Three axis stress condition becomes high. Brittle fractureⅨ ［Ⅱ］ Microstructure effect ① （Crystal structure, Chemical composition） bcc crystal （Mild steel） σ Low temperature brittle Cleavage plane fcc crystal （Cu、Al、Ni、18%Cr-8%Ni stainless steel） Difficult brittle σ LiquidO2 orLiquidN2 vessel P, C, O, H etc. Low toughness Transition temp. Brittle C、P Increase Urge Ni、Mn Decrease Restraint Brittle fractureⅩ ［Ⅱ］ Microstructure ② （Carbon steel） C content of carbon steel High Transition temperature Low absorption energy Brittleness General High strength Charpy impact energy J High carbon Brittle Temperature ℃ Fine grain High strength ＋ Improvement of toughness Creep fractureⅠ（Creep phenomenon） Creep? Under a stress and temperature Plastic deformation is induced. Failure Strain ε （Ex. Accelerated creep Steady creep Heating W Transient creep High temperature Deformation ～ Stress and Time Work hardening Cancellation Softening） Deformation depends on time and loading Work hardening Softening Time t Creep fractureⅡ（Creep strength） Creep rate at steady creep stage Strain ε Failure Small creep rate Creep rate Time to tolerance strain =long using period Creep strength （例） A constant stress of 100MPa Steady creep Strain=0.01% 103 Hours Creep strength =100MPa at 0.01% ／ 103 h Time t Creep fractureⅢ Stress increase Strain Temperature increase Steady creep rate ％／hr ［Ⅰ］ Effects of temperature and stress ［Ⅱ］ Microstructure effect Time Time ℃ Temperature and stress increases Steady creep is dominant Creep rate increases Creep strength decreases Fcc crystal Large Activated energy High creep strength Creep fractureⅣ ［Ⅲ］ Grain size Normal temperature=Low Strengthening Refinement strength High temperature Grain size refinement Creep strength decreases Under high temperature Grain boundary slip ・ Substitutional element Interaction between dislocation or vacancy is restrained And then creep strength increases. ・ Stacking fault energy decreases, creep strength increases Creep fractureⅤ Void A A ⇒ B B C C Cavity A A ⇒ B C C A B C Grain boundary B A ⇒ Cavity Particle B W type cracking C r type cracking Two type intergranural cracking at high temperature creep 脆性破壊ⅩⅠ（脆性破壊に及ぼす諸因子の影響⑥） ［Ⅱ］ 材料学的因子の影響 ③ （熱処理） ・ ４７５℃脆化 熱処理で性質が変化 （教科書 P126 図4.32） ・ 高温焼戻し脆化 Cr Mn 添加 高温焼戻し 粒界偏析 脆化 ・ 青熱脆化 軟鋼を200~350℃で負荷 ひずみ時効 （転位の固着作用の促進） 20μm 20μm 時効材 未時効材 脆性破面 延性破面 図．35% Cr-5% Niフェライト鋼の ４７５℃時効の引張破面形態に及ぼす影響 脆化 ・ σ相脆化 高Crを持つαステンレス鋼など 700~900℃ σ相 （脆性な第２相析出） 加熱 著しい脆化 巨視的破面の特徴Ⅳ（疲労破面②） （教科書 P100, 図4.6） 疲労破壊 微視組織の影響 大 結晶粒ごとに き裂の進展方向が変化 組織の痕跡が破面上に残る １mm ※ 脆性破面も巨視的には類似 微視的な特徴（破壊機構）が異なる 破面の色彩 図．粗大結晶粒をもつ二相ステンレス鋼 （25% Cr－5% Ni鋼） 破壊事故破面解析事例Ⅳ ④ その他 （破壊の実例） ◎ ジェット戦闘機 「F‐111」の破壊事故 （1969年） ⇒ 主翼の金具に疲労き裂が発生し、 このき裂のわずかな進展により早期運転中に破壊 ◎ 日航ジャンボ機墜落事故 （1985年） ⇒ 機体後部圧力隔壁が金属疲労により破壊し、機体もろとも御巣鷹山に墜落 ◎ 高速増殖炉「もんじゅ」のナトリウム漏洩事故 （1995年） ⇒ 温度計さやの金属疲労が原因で、大量のナトリウムが漏洩 ◎ 京福電鉄事故、ブレーキ制御棒の破断 （2000年） ⇒ ブレーキ制御棒の金属疲労が進み破断に至った ◎ 中華航空機墜落事故 （2002年） ⇒ 金属疲労による機体の空中分解による墜落。
© Copyright 2024