How hydrogen enhances dislocation mobility and dislocation generation rate (Solid solution softening and hardening) Reiner Kirchheim Institut für Materialphysik Georg-August-Universität Göttingen www.uni-goettingen.de I2CNER Kyushu-University, Japan Outline: 1. Introduction 2. Dualism of solute/defect-interaction, the defactant concept 3. Hydrogen embrittlement (during fatigue) 4. Direct evidence for softening by hydrogen (nanoindentation and internal friction) 5. Solid solution softening and hardening by mobile defactants Present and future activities in the area of hydrogen in metals 1,4x10 -6 1,2x10 -6 release rate ([H]/[Fe]/s) heat rate 1. Analysing electrochemical permeation techniques and thermal desorption spectroscopy 2. Interaction of hydrogen with dislocations in iron and nickel (with MPIE) sample 3. Developing a hydrogen probe and using it for friction and wear (with KircTec) a) 1x10 b) 3x10 1,0x10 -6 8,0x10 -7 6,0x10 -7 4,0x10 -7 2,0x10 -7 c) 1x10 -3 -3 d) 3x10 e) 1x10 f) 3x10 -2 -4 -4 -5 g) 1x10 -5 0,0 0 100 200 300 400 500 600 700 temperature (K) 4. Modeleling hydrogen embrittlement (with I2CNER, Brian Somerday) 6 H-Probe 4 3 2 1 5 YUKITAKA MURAKAMI, TOSHIHIKO KANEZAKI, and YOJI MINE METALLURGICAL AND MATERIALS TRANSACTIONS A, 41A (2010) 2548 Fatigue of stainless steel softening hardening no H 23 wppm 70 wppm 89 wppm “Can hydrogen both soften and strengthen a material in the same test? This apparently is so and is proposed to be a consequence of the dual nature of softening associated with smaller activation energies and hardening associated with the nature of localized slip.“ New results and methods since 1980 1. 2. 3. 4. H-H interaction und increasing excess affects dislocation motion First principle calculations Defactant concept Nanoindentation The defactant concept R. Kirchheim, Acta Materialia 55 (2007) 5129 hydogen, boron, carbon, oxygen, scandium,... solute A ↔ defect surface, grain bond., stack. fault, disloc., vacancies (attractive interaction gain energy by segregation) Who is gaining this energy? gain information about solute binding energy gain information about changing defect energy Dualism of solute defect interaction! H-interacting with defects and lowering its own energy material structure potential trace energy distribution energy distribution n(E)dE= E single crystal (E E o ) Eo n(E) single crystal + vacancy o E E t E (1 ct ) ( E E o ) ct ( E Et ) n(E) E single crystal + dislocation K2 Eo E single crystal + grain boundary (1 ct ) ( E E o ) 2 Eo Et n(E) E amorphous state 2 Eo c ( E Et ) 2 exp 2 ct (E E o )2 exp 2 1 n(E) Apply Fermi-Dirca-Statistics to evaluate µ(c) or use measured µ(c) to evaluate n(E) ( E E o )3 n(E) n( E )dE 1 exp[( E ) / kT ] 1 2 cf/c D/Do rH/ rH o 0.8 1.6 r2 (nm2) ratio of quantities (deformed/anneald various techniques to measure H/dislocation-interaction in Pd 0.6 0.4 SANS 1.2 0.8 0.4 0.2 0 -7 -6 -5 -4 ln(H/Pd) 0 102 103 10 concentration atppm H/Pd 1 rH rH 0 D D 0 cf c Only free hydrogen atoms contribute to resistance and diffusivity 104 cH, H Interaction of hydrogen with dislocations, Site energy distribution & Fermi-Dirac Statistics q r const. Fermi-Dirac & T=0 approximation r (c) K c chemical potential, kJ/Mol R -60 core interaction H in Pd -40 strain field interaction disloc. density r -20 H-H interaction 0 with H-H interaction 0 2 4 6 8 reciprocal square root of concentration, 102 (H/Pd)-0.5 ( c ) Wc loc K r c What is the binding energy of hydrogen to dislocations? What about iron? 10 Modelling kinetics of hydrogen embrittlement no traps with traps internal H (same H) external H (same H) same diffusible H same diffusible H same permeation cdDd same permeation cdDd fast supply, internal sources low supply, internal sinks same diffusible H same permeation cd D d same diffusible H same permeation cdDd low supply, no sources fast supply, no sinks Modelling mechanisms of hydrogen embrittlement 1. Hydrogen enhanced decohesion 2. Increasing dislocation generation rate and/or mobility with hydrogen no hydrogen Formation energy of dislocation is decreased! contributes to HELP (Birnbaum, Robertson, Sofronis) but also to AIDE (Lynch) 3. Ease of void generation no hydrogen with hydrogen Surface energy of newly formed voids is decreased ductile fracture Voids may be formed more easily in the presence of vacancies, Nagumo et al. The defactant concept R. Kirchheim, Acta Materialia 55 (2007) 5129 hydogen, boron, carbon, oxygen, scandium,... solute A ↔ defect surface, grain bond., stack. fault, disloc., vacancies (attractive interaction gain energy by segregation) Who is gaining this energy? gain information about solute binding energy gain information about changing defect energy Dualism of solute defect interaction! Surface energy reduction: generation of interfaces Germany has a long lasting tradition in reducing the liquid/air interfacial energy by natural solutes (surfactants) Grease = oil/water emulsion A competitor for segregation of surfactant molecules is the oil/liquid interface annihilation of interfaces Gibbs Adsorption Equation d Γ Ad A Γ A RTd ln cA GA=0 GA= Gsat dA=0 D/kT Can we use the Gibbs equation for other discontinuities (vacancies, dislocations, ….) of matter as well? Hydrogen interacting with defects and changing their formation energy dΦ d ( F nH H ) 2 r H H SdT PdV Vdr M dnM nH d H New! definition of measurable GA: i.e. dislocations: ΓA nh r T ,V , nM , H Pd V ,T , nM , H applicable to all defects (stacking faults, dislocations, kinks, vacancies etc.): d Γ H d h = defect formation energy GH = solute excess (number of A-atoms per area, length or number) alloying addition stabilizing a defects = Defactant (defect acting agent) nH r H2 T ,V , nM , M How does hydrogen effect plasticity of metals? 1. Hydrogen is a defactant regarding dislocations Hydrogen reduces the line energy increases the rate of disln. generation decreases the rate of disln. annihilation higher dislocation densities Cold rolling Pd-H sheets (reducing thickness by 50%) 0.0 H/Pd 1.0 at.-% H/Pd 0.5 at.-% H/Pd 3 µm 3 µm 3 µm 1.2 140 Vickers hardness relative dislocation density Increasing dislocation density in the presence of defactant hydrogen 1.0 0.8 0.6 0.4 0.2 0 0 130 120 110 100 90 0.2 0.4 0.6 0.8 H-concentration (at.-%) 0 0.2 0.4 0.6 H-concentration (at.-%) 0.8 Carbon and nitrogen as defactants for grain boundaries in iron N C aΓ C N gC 3 Γ C c c gP V V V d 0 w%C 0.2 w%C C-atoms in grains C-atoms in gb 8 0.4 w%C carbon (this work, Fe+graphite) nitrogen (Mittemeijer, Fe+Fe3N) cgP 1 c d 3ΓC 3ΓC 8 2x10 5 8 10 1x10 20 0 0 5000 10000 0.8 w%C 3 carbon (Takaki, Fe-C) 8 3x10 15000 3 solute concentration (mole/m ) grain size (nm) inverse grain size, 1/d (1/m) 4x10 METALS AND MATERIALS International 10 (2004) 533~539 Setsuo Takaki, Toshihiro Tsuchiyama, Koichi Nakashima, Hideyuki Hidaka, Kenji Kawasaki, and Yuichi Futamura Consequences: dislocation formation t 100 mV Increasing chemical potential of hydrogen Barnoush & Vehoff (Al, Ni, FeAl) Nibur et al. & Yokogawa et al. (steel) P -900 mV -1100 mV Defect generation by solutes (hydrogen) dislocation generation in V-H Nanoindentation (Berkovich Indents) d Γ H dH Uniaxial compression tests (UCT) 0 H/V 0.03 H/V Pd-H 2 m 0 H/V 0.03H/V BI: Pop-in load goes down → Dislocation energy (DE) is lower UCT: Lower DE → higher r → less localized shear slip → barrel shape 1 m “pop-ins in the load displacement curves“ 0,40 cH = 0 cH = 0.01 H/V Pop-in Load, P (mN) 0,35 Load (nm) 0,30 0,25 0,20 0,15 0,10 0,05 0,00 0 10 20 30 40 50 60 0,34 0,32 0,30 0,28 0,26 0,24 0,22 0,20 0,18 0,16 0,14 0,12 0,10 0,08 0,06 0,04 0,02 0,00 RTip = 250 3x(RTip = 77 1/ 3 t max 0,00 0,01 0,02 0,03 0,04 0,05 6 Er2 0.31 3 2 P R 0,06 Hydrogen Concentration, cH (H/V) Displacement (nm) 0,65 9 line energy (nJ/m) Maximum Shear Stress, tmax (GPa) 10 8 7 6 o 3-4 H-atoms/b 0,60 0,55 0,50 d Γ Ad A 0,45 5 0,00 0,01 0,02 0,03 0,04 0,05 Hydrogen Concentration, cH (H/V) disl exp( 3) rcorebt max 8 0,06 0,40 -10 0 -9 -8 + -7 -6 -5 - ln(H/V)=D/RT -4 A -3 -2 speed of tip = 10 m/s = 10 nm/ns time to first pop-in ≈ 0.1 ns a2 Hydrogen jump time: t 6D H-Diff.-Coeff. D=5.10-10 cm2/s Jump distance: a = 0,25 nm t = 2.10-7 s = 200 ns How do dislocations move after their generation? Studying dislocation motion by measuring internal friction edge dislocation b dl b f dl f dl f b= Burgers vector dl = line element f= Peach-Koehler force srew dislocation b b f dl f f dl How does hydrogen effect plasticity of metals? 1. Hydrogen is a defactant regarding dislocations Hydrogen reduces the line energy increases the rate of disln. generation decreases the rate of disln. annihilation higher dislocation densities 2. Hydrogen is a defactant regarding kinks Hydrogen reduces the kink formation energy increases the rate of double kink generation higher dislocation mobility, if controlled by kink formation Kink generation studied b internal friction (bcc metals Nb, Ta, Mo, Fe) Example: Niobium (+ Hydrogen) G. Funk, PhD thesis, University of Stuttgart, 1985 720 K S-K(O) -peak: double kink generation on 71o dislocations -peak: double kink generation on screw dislocations S-K-peak (Snoek-Köster- or coldwork-peak) : double kink generation and movement of kinks on dislocations in the presence of solute atoms Example: Iron (+ Hydrogen) I.G. Ritchie et al., phys. stat. sol. (a) 52 (1979) 331 (suggested first in the 50‘s that the activation energy of the - and -relaxations are equal to the formation energies of kink pairs) Alfred Seeger Relaxation time for the S-K-peak: H HM t SK 2H K H KM H HM T cd exp RT 2 2 H K double kink formation energy, H KM kink migration energy hydrogen (solute) migration energy, cd H concentrat ion at dislocatio n H dB cd cb exp RT H dB hydrogen binding energy cb bulk concentrat ion H SK 2 H K H KM H HM H dB for cd 1 M M 2 H H H for cd 1 K K H Conclusions: S-K peaks appear at higher temperatures compared to the peak of the naked dislocation, because 2 H K H KM H HM 2 H K H KM Thus in iron and niobium the S-K peak arises from 71o dislocations. Already Alfred Seeger realized the peculiar behavior of hydrogen: “The kink-pair formation enthalpy in 71o dislocations in -Fe has been determined by Kronmüller et al.  as 0.048 eV. The activation enthalpy of about 0.21 eV observed in some experiments [22, 23, 64] may be associated with the above process. The difference between the two activation enthalpies is larger than the range of possible migration enthalpies of H in -Fe . This is an indication that in the case of hydrogen the theory needs further refinement.” “We suggest also that H adsorption to the core of screw dislocations makes double-kink nucleation easier and shifts the peak from ~300 K to 120 to 200 K. Only a few hydrogen atoms on a typical segment length would be required to enhance the double-kink nucleation, …“ John Hirth The defactant-concept provides the proof for Hirth‘s hypothesis! What are the consequences on the macroscopic scale? Softening and hardening by solutes (hydrogen) Orowan equation modified by Argon: without solutes: d brv bra t g t m dt t g characteri stic time of kink formation t m characteri stic time of kink motion increasing solute concentration: t g decreases because of the defactant concept t m increases because of solute drag d 1 brv brat g t m bra / t m 1 bra / t g t g t m t g t m dt d bra t g t m dt 1 t g t m bra / t g and t g (solute softening) t m t g bra / t m and t m (solute hardening) tg tm 1) srew dislocation t g1 t m1 time constant for kink pair generation b dl time constant for kink motion tg tm d bra bra dt t g t m t g b f f f dl 2) low solute content t g 2 t g1 and t m2 t m1 but t g 2 t m2 solute softening tg tm d bra bra dt t g t m t m solute hardening 3) high solute content t g 3 t g 2 and t m3 t m2 but t g 3 t m3 ? ? ? ? Missing reliable evaluation procedures for trapping measurements in steel! Promote the defactant concept as a tool for microstructural engineering! R. Kirchheim, In Solid State Physics, eds. H. Ehrenreich and F. Spaepen, Elsevier, Amsterdam (2004), Vol. 59, 203-305 R. Kirchheim, Acta Materialia 55 (2007) 5129 R. Kirchheim, Int. J. of Materials Research 100 (2009) 483-487 Financial support: DFG and State of Lower Saxonia Thank you for your attention!
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