Mechanical Behaviour of Materials Chapter 11 Hardening mechanics in metals

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1 Mechanical Behaviou of Mateials Chapte 11 Hadening mechanics in metals D.-Ing. 郭瑞昭

2 Intoduction to Alloy Stengthening Hadening by solute atoms -Solid solution stengthening (inteaction between solute atoms and dislocations) Hadening by second phases -Pecipitation-Hadening (inteaction between pecipitation phases and dislocations) -Dispesion-Hadening (inteaction between dispesion phases and dislocations)

3 Stengthening mechanism: 0 dimension defects

4 Point defect inteaction with dislocations- Cottell Pinning One of the simplest to undestand is the inteaction between the elastic stess fields of a dislocation and a point defect. Cottell was the fist to calculate the enegy involved in such an inteplay fields. The only stesses acting on edge dislocation ae y σxy σxx (-x,-y) θ σ ij defect x F l F def dis ( σdef bdis) def dis σxyb σxxb 0 dis

5 Solid Solution Stengthening: Elastic Inteactions Misfit volume: ΔV Distotion induced by point defects 0 (1+δ) 0 (1+ε) Hole adius: 0 Defect initial adius: Defect final adius: y 0 0 (1+δ) 0 (1+ε) ΔV Δ V e 4 π 3 4 π π π 3 ε ΔV e (1 + ε ) [ 3 (1 + ε ) 1] [ 1+ 3ε 1] Vmis Vs Ve 3 π 3 δ π 3 0 defect x ΔV ( ν ) ν V mis θ Total volume change

6 Solid Solution Stengthening: Elastic Inteactions E misfit ΔVσ p σ p 1+ ν 1 ν Gb 3π sin θ E misfit + ν 1 ν 1 3 Gb sinθ 3π 4π0 δ 4A 3 sinθ A ν ν Gbδ 3 0 F E misfit sin θ A 2

7 Solid Solution Stengthening: Elastic Inteactions F sin θ A 2 A ν ν Gbδ 3 0 F max Δτ c bl F aveage fee dislocation length dislocation density L / V l F Fmax Δτ c bl F Asinθ 2 bl ρ Fmax Asinθ Δτ C C c 2 bl bρ Solute concentation N / V Concentation of solute atoms F Fom M.A. Meyes and K.K. Chawla, mechanical behavio of mateials, Cambidge Univesity pess, 2009.

8 Solid solution stengthening Δτ ε ΔC c Δτ c C δ -0.1 to 0 fo vacancies to fo substitutional solute 0.1 to 1.0 fo intestitute atoms

9 Solid solution stengthening In addition to elastic misfit inteaction, thee ae othe souces of dislocation-solute inteactions: 1. Paelastic inteaction (lattice paamete effect) 2. Dielastic inteaction (shea modulus effect) 3. Chemical inteaction (Suzuki effect) Howeve, thei contibutions ae less impotant than the size effect.

10 Why is the diffeence of Solid Solution Stengthening between substitutional and intestitial solution?

11 Phenomenon of Solid Solution Stengthening Al2O3 When the dislocation mobility in a solid is esticted by the solute atoms, the esultant stengthening is called solid-solution-hadening. (a) Incease in stength, σ, of steel as a function of content of solute. The solid lines epesent substitutional solute additions, while the dashed line epesents intestitial solute additions. (Afte F. B. Pickeing and T. Gladman, ISI Special Repot 81, Ion and Steel Inst., (London: 1963), p. 10). (b) Incease in stength of sapphie (monocystalline alumina) with small additions of chomium at 1400 C (Adapted fom K. P. D. Lagelof, B. J. Pletka, T. E. Mitchell, and A. H. Heue, Radiation Effects, (.87 (1983) 74

12 Solid solution stengthening: substitutional solutions

13 Solid solution stengthening: substitutional solutes

14 Whee ae positions of Intestitial Atoms in the Cubic Lattice? (a) Positions of intestitial atoms in the cube. (b) Cabon atom shown as a poduce of a tetagonal distotion.

15 Question? a C 1.54 A a Fe 2.52 A R C /R Fe 0.61 Octahedal Tetahedal /R fcc 0.41 /R fcc 0.22 /R bcc 0.16 /R bcc 0.29

16 Bcc R C /R Fe 0.61 /R /R 0.291

17 Fcc D C 1.54 A D Fe 2.52 A A /R 0.41 /R 0.22 R C /R Fe 0.61

18 Stengthening mechanism: 3 dimension defects

19 Second Phases: Pecipitation and Dispesion Al-Cu alloy Two alloy systems using this stengthening technique ae aluminum alloys and nickelbased supealloys. Pecipitation: pecipitation of pecipitates out fom a homogenous, supesatuated solid solution. Dispesion: incopoated had, insoluble second phases in a soft metallic matix with a maximum volume faction of 3-4%. Al-Li alloy supealloy (a) θ pecipitates (at gain boundaies) and θ pecipitates (in gain inteio) in Al Cu alloy. (Coutesy of K. S. Vecchio.) (b) Al3Li pecipitates in Al Li alloy (TEM, dak field). (Coutesy of K. S. Vecchio.) (c) γ pecipitates and aged cabides in a

20 Yield Stength Supealloys and TD Nickel Pecipitation Compaison of yield stength of dispesionhadened thoia-dispesed (TD) nickel with two nickel-based supealloys stengthened by pecipitates (IN-792) and diectionally solidified (DS) MAR M 200. Dispesion

21 Dislocation-Pecipitate/Dispesion Inteaction Two of the impotant models can be explained the stengthening due to pecipitates: a. Dislocations cutting though the paticles in the slip plane b. Dislocations cicumnavigating aound the paticles in the slip plane

22 Bowing (passing though) mechanism d Gb d αgb α τ 2 2 1/ 2 2 π π f f V d d V : the paticle adius d: the aveage paticle spacing between two paticles Vf: the paticle volume faction V Gb f 2 1/ Δ α τ d

23 Cutting mechanism

24 Dislocation cut though The pesence of gain boundaies has an additional effect on the defomation behaviou of a mateial by seving as an effective baie to the movement of glide dislocations. F γ max max F bl F c τ f E E C b d d c / 2 3/ 2 3/ γ γ τ Effective inteface enegy f Δτ c F c l b γ τ 1/ 3 6 b C E l c d F τ V l C f F

25 Dislocation cut though and bow out

26 Pecipitation teatment

27 Pecipitation teatment Fom K. Bowman, mechanical behavio of mateials, John Wiley & Sons Inc, 2004.

28 Pecipitation teatment Fom K. Bowman, mechanical behavio of mateials, John Wiley & Sons Inc, 2004.

29 Al-Cu Pecipitation

30 Summay of Stengthening mechanisms Zeo dimensional defect: Solid Solution stengthening solute atoms dislocations inteaction Δτ sol ε Δc 1 dimensional defect: Cold woking stengthening dislocations dislocations inteaction Δτ dis αgb ρ 2 dimensional defect: Gain bounday stengthening gain bounday dislocations inteaction Δτ gb kd dimensional defect: Second phase stengthening Δτ c f Pecipitation/ Dispesion dislocations inteaction Δτ OR f

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