Hydrogen and Stress Induced Delayed Fracture
V. P. Larionov
V. V. Lepov
V. E. Mikhailov
The Institute of Physical and Technical Problems of the North
SB RAS
Russian Academy of Science
1, Oktyabrskaya Street
Yakutsk, 677891, Russia;
email: fteh@yacc.yakutia.su
The experimental investigations of the crack growth dynamics due to hydrogen embrittlement have shown that precracked zone has cyclic evolution from rising diffusion of hydrogen and localization of plastic deformation to ultimate (or critical) level damage accumulation, crack forming and crack growth by leap [1]. Dynamics of crack propagation may be presented in the labile coordinates of the crack tip as step-by-step change over the stages of: 1) the precritical defect evolution, when hydrogen is accumulated and deformation has been located in accordance with equilibrium solution, 2) the due attainment of the next critical state, and 3) the act of immediate fracture, corresponding to the crack propagation (see fig.1, à.).
It is difficult to define the plastic deformation and hydrogen content in precracked zone during delayed fracture (DF) by usual techniques due to strong localization, complexity and coupling of the processes proceeds. So the analytical-numerical imitation and specific nondestructive X-ray experimental techniques application of DF phenomenon studies assumes especial meaning.
With reference to concept of hydrogen diffusion in embrittlement area there is the large number of models of the coupled diffusion, including as phenomenological and half-empirical, and numerical-analytical approaches [2-8]. Given approaches based on the rising diffusion equation (Gorsky' effect) in form, offered by Cottrell C.L.M [9]:
(1)
where C - concentration, D - diffusivity, M - molar part, ms and m0 - chemical potentials of dissolved hydrogen in metal with and without hydrostatic pressure s h accordingly, VH.- molar volume. The purely numerical decisions of a problem coupled diffusion as by FEA [10], and with use of nonequilibrum thermodynamics principles [11-14] are known.
However, in view of the fact that above mentioned problem was not studied well, there is no model which could describe all phenomenon attributes observed, particularly different features of the hydrogen effect on deformation characteristics of material.
The reason it that the experiment
shows qualitative differences of processes at embrittlement depending
on conditions, at which there is the stress and hydrogen induced
fracture. It is the various initial conditions, hence, define
qualitatively other embrittlement process kinetics. It is essential
also, that in given works hydrogen back influence to material
not take into account.
It is a necessary to explore mechanical properties of material as a function of hydrogen contents for really coupled solution. In this case, crack growth at the crack tip may be present as step-by-step local ultimate material characteristics' changes (fig.1, b)..
Last investigations in the field of deformation theory and fracture mechanics of metallic materials shown, that the plastic flow already comes before crack surface forming, independently of fracture nature [15]. Translation sliding in this case accompanied rotational modes, and microdeformation (dislocations' motion) simultaneously goes with macroplastic flow, that covered 3-D structure elements. This is support more efficiently energy dissipation of deformed metal and comply with the second law of thermodynamics at microscopic level introduced by I.Prigogine for irreversible remote from equilibrium complex system [16].
Figure
2There is a theoretical structural model, offered for the description of hydrogen effect on the deformation properties of metallic materials [17]. It's shown on fig.2.
The energy dissipation patterns at plastic deformation are setting by hydrogen presence in material, that exert an effect on crack growth dynamics. Hydrogen increases the mobility of dislocations and its reproduction rate, so to cause premature failure plastic flow strongly confined at the crack tip [18-20].
The activation mechanism of hydrogen effect on a lattice has been proposed. So for the estimation of the hydrogen effect to plastic flow initiation stress on the mesial level the logistic dependence engaged. The so-called mesial level may consider here as a boundary between the levels of intensity turbulization and macro raptures (cracks) forming, according to the physical mesomechanics of inhomogeneous structures' approach [15]. Thus, the hydrogen embrittlment problem may resolve in frames of mechanics of continua and fracture mechanics. Real order of material near the crack tip controlled by not only the strain field, but hydrogen assisted reversibles and non-reversibles changes too.
Every moment the attainment of
an ultimate state in the developed model characterized by the
critical value of certain measure of material damage. In common
case it is a vector: 
, where 
- loading vector, t - time. Times of the ultimate state
attainment defined by the two-parametrical criterion of resource
estimate. Fracture time defined by the critical crack length criterion.
In framework of the given approach mathematical model of coupled diffusion-plasticity developed and numerically actualised at crack tip taking into account the hydrogen effect to material physical-mechanical properties. The control volume technique and exponential differential scheme [21] used for modelling on mesial level by final differences method. Equation (1) and conditions
,
(2)
where 
- boundary of analysis area and 
- initial
and boundary hydrogen concentration,
defined a typical boundary problem.
The definitive finite difference analog obtained given below:
(3.1)
(3.2)
where VH - molar hydrogen volume, sh - hydrostatic stress, Pe - diffusion Pekle' criterion analogous, H - single Heaviside function. Yield stress dependence against hydrogen concentration expressed by the activation law, and it oversimplified dependence given below:
(4)
where 
- yield stress, j - iteration's number, 
- critical hydrogen concentration, defined empirically or from
thermodynamics approach. Stress and strain distribution assumed
according HRR (Hatchinson-Rice-Rosengren) solution for elastic-plastic
materials. In this task formulation obtained that hydrogen speedly
achived it's citical value on two crack tip opening distance.
On fig.1, a) presented the hydrostatic stress distribution, on
b) stress gradient, and on c) hydrogen concentration near crack
tip distribution.
Formal representation [22] and Galerkin's method applied for the macro-modelling (at real geometry) by the final element method (FEM). The equation (1) used in follow boundary problem:
(3.1)
where J - surface hydrogen flow, CT - trapped hydrogen concentration, and QT - fraction of hydrogen traps against lattice vacancies. Simplifity numerical analyses show hydrogen induced stress and strain localisation near notch.
The main difficulty of the numerical solution connected with the necessary of solution stability maintenance at each time step, including repeat optimize sampling, due the material characteristics' variation. This procedure is similar to the approach used in so-called h- and p-versions of FEM, or geometry-element analysis and geometry-element modelling accordingly, which a necessary of elements strongly reduced, sampling and modelling of the examined region simplified.
As well known X-ray diffractometry may take some information about ordering of material structure, in area analysed. So X-ray local "in situ" diffraction experiment are conducted, including shooting of small (0.1 mm diameter) area near crack tip at plastic flow for only hydrogen saturated (1), only stressed (2) and hydrogen saturated and stressed specimens (fig.4).
Low-alloy steel specimens saturated by hydrogen in special high-pressure and high-temperature camera at different conditions (approximately for 4 and 6 sm3/100g hydrogen mean contents, that mean 0.5 and 1 hour at 100 ata and 4500C). Loading in experiment was a 3-point bendind. After two steps it became statical and not changed during 14 days. Two specimens has been cracked, other (seven) has non-reversible plasic deformation.
X-ray diffractometry has shown,
that widening of a line and parameter of a lattice in stress relaxation
process undergo a maximum. The hydrogen influences on the relaxation
kinetics near the notch (crack) tip. The localization of plastic
stress in relaxation process results in moving of a distortion
maximum and leads to change of the local parameters of X-ray diffraction.
The results of experiments explained by structural model as change of an ordering structure. This is a result of interaction the stress and hydrogen fields (in other words, between fields of sliding and distortions' abilities of a material). Here hydrogen acts as irreversible material damage catalyst.
The initial and boundary conditions at computer analysis corresponded to the conditions of an experiment. Results show the strong localisation of stress and strain fields under the action of hydrogen. That is agreed with data of experiment.
Authors thanks Alymov V.T., Head of Laboratory, IMASH, Moscow, for experiment's help.
This work are proceed with partial
support of Russian Science Foundation (grant ¹ 96-01-01370).
1. Strength rising of welding constructions of the North. /O.I.Sleptzov, V.Ye. Mikhailov, V.G.Petushkov, et all.- Novosibirsk: Nauka, 1989.- 223 p.
2. Cherepanov G.P. //Corrosion.- 1973.- V.29.- N.8.- P.305-309.
3. Liu. //Theoretical and Applied Analysis.- Ser.D.- 1972.- V.92.- N.2.- P.767-772.
4. Alymov V.T. //Phys.and Chem. Mechanisc.- 1975.- N.6.- P.12-15.
5. Gerberich W.W., Chen Y.T. // Met.Trans.- 1975.- V.A6.- N.2.- P.271-278.
6. V.Leeuven, Platean H.P. //Corrosion.- 1975.- V.31.- N.2.- P.42-50.
7. Johnson H.H., Morlett J.G., Troiano A.R. Hydrogen, Crack Initiation and Delayed Failure in Steel. //Trans.Met.Soc.AIME.- 1958.- V.212.- P.528-538.
8. Andreikiv A.E., Panasiuk V.V., Kharin V.S. //Phys.and Chem.Mechanics. - N.3.- 1978.- P.3-23.
9. Cottrell C.L.M. //Weld.Journal.- 1953.- V.32.- P.257s-264s.
10.Sofronis P., McMeeking R.M. //J.Mech.Phys.Solids.- 1989. V.37.- No.3.- P.317-350.
11. Michel B., Michael D.//Cryst.Res.Tech.- 1983.- V.18.- P.615-631
12. Michael D., Hussack I., Michel B. //FMC.- 1985.- 14.- P.173-183.
13. Aifantis E.C. //Acta Mech.- 1980.- N.37.- P.265-278.
14. Novacki W. //Arch.Mech.- 1971.- V.23.- P.731-749.
15. Panin V.Ye., Likhachev V.A., Grinyaev Yu.V., Structural levels of deformation of solids, Novosibirsk, Nauka, 1989.- 223 p.
16. Prigogine I., From Being to Becoming: Time and Complexity in physical sciences, San Fracnisco, W.H.Freeman and Company, 1980.- 320 p.
17. Lepov V.V. Sinergetic Approach to Estimation of Weld Element Resistance against the Induced Hudrogen Delayed Fracture. Abtract of dissertation to awarding of the degree of Kandidat of Technical Science.- Yakutsk, YaRC SB RAS, 1994.- 24 p.
18. Lunarska E., Novak V., et all.: Scripta Metal.- 1983.- V.17.- P.705-710.
19. Ladna, B., Birnbaum, H.K.: Acta Metal..- 1987.- V.35.- pp. 1775-1788.
20. Zhang T., Chu W., Hsiao C.: Scient. Sinica A.- 1986.- XXIX.- N.11.- P.1157-171.
21. Patankar, S., Numerical heat transfer and fluid flow, Hemisphere Publishing Corp., New York, 1980.- 150 p.