Dislocation climb is non-conservative motion of edge dislocations and is by emission or absorption of point defects, i.e., vacancies/interstitials. Dislocation creep occurs by climb controlled process for pure metals and class M (or II ) alloys. But for class A (or class I alloys), it is glide controlled and is generally observed that this shows an inverse primary creep. In the intermediate temperature/stress regime, for pure metals and class II alloys, it is well known that the normal primary creep behavior is observed and the steady-state creep rate shows the power-law type stress dependence (PL Creep) with the power-law exponent nearly equal to 5. It is also called as HT creep (M.F. Ashby and H.J. Frost, Deformation Mechanism Maps Book). This climb controlled dislocation creep is in line with the model proposed by Weertman that predicts power-law stress exponent, n = 4.5.

Whereas, for glide controlled creep as observed in class I (or class A) alloys, the power-law exponent is nearly equal to 3. In this case glide is slower (due to solute atmosphere forms and due to solute drag) than the climb and dislocation glide is rate controlling (since the processes are assumed to be sequential, glide is slower than the climb). 

On the other hand, the model for creep proposed by Barrett and Nix deals with the jogs on screw dislocations (jogs are of edge character) and they move by climb (emission/absorption of point defects). But a steady-state can be obtained when the chemical force on the jogs is balanced by force on the dislocation (due to the applied stress).  This model obtains a hyperbolic-sine dependence of steady-state creep rate for stress. Please see :- "A model for steady state creep based on the motion of jogged screw dislocations", Acta Metallurgica, Volume 13, Issue 12, December 1965, Pages 1247–1258.

But your question is on "Dyson Model":This model questions the usual power-law description of creep as inadequate in describing the creep behavior of particle strengthened alloys. It deals with CDM approach of creep modelling. It is connected to  creep of particle strengthened alloys (for actual engineering situations), since particles do coarsen during service and it incorporates in the kinetic equation, the relevant microstructural parameters like inter-particle spacing, volume fraction of particles. The expression derived by Dyson is hyperbolic-sine type (instead of power-law creep rate equation). 

Dear Dr. Qihua XU,

I don't wan to be give you a trivial answer. Beacuse may be I did not catch just your point.

But if you question: why the dislocation behavior can influence on the grain boundary sliding and how? 

can be intrepreted as: how "dislocations in side the grains ...can affect the GB behaviour"

If I undertood well (that is to say if this is yor question) I can give an answer and some advices in literature.

The dislocations cited by the author can be those who "create" the GB itself.

In our Review regarding BG:

Present State of the Controversy about Grain Boundary Relaxation; Il Nuovo Cimento Vol 14 D N3 March 1992 (please tell me if you do not find it:

[email protected] 

we describe very clever models of GBs as a network of dislocations Ds (as for examople: G. M. Ashmarin et al X Conferencija Metaloznawcka PAN, Kracow, Poland, 1977

Then, the GBdislocations can glide, climb, generate kinks or jogs, etc.

Different mechanisms for the overall gluiede will rise to different laws.

Is is easy taht these Ds can give a contribute to the other phenomenon : Ds inside the grains. Because creep is a High T phenomenon and a t high T the GBs are active.

Dr. Bernardo Molinas, VeneziaTecnologie, Venice, Italy  

   Climb occurs by emission/absorption of vacancies/interstitials at dislocations. Each individual step is reversible. Hence hyperbolic sine.

   Glide of dislocations occur generally by intersection of obstacles. Afterwards the dislocation moves on until stopped by another obstacle. This step is not reversible. Hence generally power law.

   For glide of dislocations with jogs see

J. P. Hirth and J. Lothe, Theory of Dislocations, p.588,

          Wiley, New York (1982).

    Without knowing the geometrical details of modelling this combined glide/climb process in grain boundaries the question cannot be answered.

Gunther Schoeck

Dear Dr. Qihua Xu, it is very difficult to answer in brief every thing you have asked. It requires studying some of the papers I list down. 

1) Sequential and Parallel Processes: creep occurs by glide and climb: (a) if the processes are sequential (i.e., in series), then the slower one will be the rate controlling. Generally climb velocity is slower and is climb controlled dislocation creep (glide + climb but climb controlled). (b) If the processes are in parallel, then the faster one will be the rate controlling. 

2) Dyson Model: Dyson developed the model for "particle strengthened alloys" based on climb-glide mechanism and derived the kinetic creep equation where creep rate is hyperbolic-sine function of stress and interparticle spacing. It adds on further to the work of Kocks on jerky glide; this means that the model is applicable at stresses lower than that  required for particle shear or Orowan bowing. It is unlike the model by Ansell and Weertman which assumes that dislocation climb is rate controlling (glide and climb in series or sequential processes, slower one is rate determining).

3) Please see the paper by Dyson (in MST 2009: derivation of creep rate equation is given) and the following papers which explain the Dyson model for particle strengthened alloys. 

(i) "Microstructure based creep constitutive model for precipitation strengthened alloys: theory and application", B. F. Dyson, Materials Science and Technology 2009, VOL 25, page 213.

(ii) "Micromechanism-Quantification for Creep Constitutive Equations", B. F. Dyson, M. McLean, IUTAM Symposium on Creep in Structures Solid Mechanics and its Applications Volume 86, 2001, pp 3-16 .

(iii) "Creep and creep modelling of a multimodal nickel-base superalloy", James Coakley, David Dye, Hector Basoalto, Acta Materialia 59 (2011) 854–863. 

4) For 'Grain Boundary Sliding': please see: "A UNIFIED APPROACH TO GRAIN BOUNDARY SLIDING IN CREEP AND SUPERPLASTICITY",  T.G. LANGDON, Acta Metallurgica et  Materialia, Vol. 42, No. 7, pp. 2437-2443, 1994.

Good luck and best wishes.

Dislocation climb is non-conservative motion of edge dislocations and is by emission or absorption of point defects, i.e., vacancies/interstitials. Dislocation creep occurs by climb controlled process for pure metals and class M (or II ) alloys. But for class A (or class I alloys), it is glide controlled and is generally observed that this shows an inverse primary creep. In the intermediate temperature/stress regime, for pure metals and class II alloys, it is well known that the normal primary creep behavior is observed and the steady-state creep rate shows the power-law type stress dependence (PL Creep) with the power-law exponent nearly equal to 5. It is also called as HT creep (M.F. Ashby and H.J. Frost, Deformation Mechanism Maps Book). This climb controlled dislocation creep is in line with the model proposed by Weertman that predicts power-law stress exponent, n = 4.5.

Whereas, for glide controlled creep as observed in class I (or class A) alloys, the power-law exponent is nearly equal to 3. In this case glide is slower (due to solute atmosphere forms and due to solute drag) than the climb and dislocation glide is rate controlling (since the processes are assumed to be sequential, glide is slower than the climb). 

On the other hand, the model for creep proposed by Barrett and Nix deals with the jogs on screw dislocations (jogs are of edge character) and they move by climb (emission/absorption of point defects). But a steady-state can be obtained when the chemical force on the jogs is balanced by force on the dislocation (due to the applied stress).  This model obtains a hyperbolic-sine dependence of steady-state creep rate for stress. Please see :- "A model for steady state creep based on the motion of jogged screw dislocations", Acta Metallurgica, Volume 13, Issue 12, December 1965, Pages 1247–1258.

But your question is on "Dyson Model":This model questions the usual power-law description of creep as inadequate in describing the creep behavior of particle strengthened alloys. It deals with CDM approach of creep modelling. It is connected to  creep of particle strengthened alloys (for actual engineering situations), since particles do coarsen during service and it incorporates in the kinetic equation, the relevant microstructural parameters like inter-particle spacing, volume fraction of particles. The expression derived by Dyson is hyperbolic-sine type (instead of power-law creep rate equation). 

The hyperbolic sine relationship is not fundamentally based in theory, it is just a guesstimate transition  ("power law breakdown") from power-law creep to fully plastic yield as you get to higher stresses. I think it is described in Ashby & Frost's "Deformation Mechanism Maps" book.

I might have written something on this in The_Presentation_of_High_Strain-Rates_on_Deformation_Mechanism_Maps. Ah yes, eqn. 5 in that report.

Philip

Technical Report The Presentation of High Strain-Rates on Deformation Mechanism Maps

The hyperbolic-sine (Garofalo proposed it for creep) equation is used in hot working constitutive analysis. The empirical Garofalo hyperbolic-sine law is preferred as it becomes power-law at low stresses and exponential at higher stresses (Materials Science and Engineering A 528, 2011, 6066–6071). Hence it describes well the flow stress dependence of strain rate for the entire stress/strain rate regime in hot working applications.

But, the question by Dr. Qihua Xu is connected to Dyson model and is related to understanding the tertiary creep modelling of particle strengthened alloys based on continuum creep damage mechanics (CDM) approach. Dr. Qihua Xu, Please go through the paper:- "Microstructure based creep constitutive model for precipitation strengthened alloys: theory and application", B. F. Dyson, Materials Science and Technology 2009, VOL 25, page 213.

   Climb occurs by emission/absorption of vacancies/interstitials at dislocations. Each individual step is reversible. Hence hyperbolic sine.

   Glide of dislocations occur generally by intersection of obstacles. Afterwards the dislocation moves on until stopped by another obstacle. This step is not reversible. Hence generally power law.

   For glide of dislocations with jogs see

J. P. Hirth and J. Lothe, Theory of Dislocations, p.588,

          Wiley, New York (1982).

    Without knowing the geometrical details of modelling this combined glide/climb process in grain boundaries the question cannot be answered.

Gunther Schoeck

Dear and Respected Prof. Gunther Schoeck,

But I do like to know at intermediate stresses and temperatures (for pure metals and class II alloys), why power-law creep (climb controlled as generally agreed upon) is the favorite (as is generally observed) with observed n = 5. Further, for the glide controlled creep in class A (or class I) alloys, power-law is observed with n = 3. That means, the power-law is generally preferred and is shown to be obeyed in dislocation creep region. The hyperbolic-sine (Garofalo) equation describes the stress dependence of creep rate for the entire stress range as it boils down to power-law at low stresses and exponential at higher stresses. But still, the issues related to mechanistic aspects are not understood completely (at least, not yet completely clear to me). But what is generally agreed upon is that (1) creep is governed by diffusion assisted climb controlled process in power-law creep regime at intermediate T and stresses for pure metals and class M alloys, (2) whereas, it is glide controlled with power - law and n  =3 for class A alloys.

Dr. Qihua Xu, if you can get an opportunity to learn from the pioneer and the legend Prof. G. Schoeck, it will be great. I also like to learn from Prof. Gunther Schoeck.

In fact in one of DSA paper on Alloy D9 (S. Vekadesan, C. Phaniraj, P.V. Sivaprasad, P. Rodriguez, Acta Materialia 03/1992; 40(3):569-580), I have explained the 'High Tempearture-A' (HT-A) regime of serrated flow on the basis of Schoeck-Seeger locking. 

Best wishes.

Hi Qihua Xu. Let me add some small points to the previous answers. We have good experience with hyperbolic sine (or exponential) function of stress. It can be used for fitting minimum or steady-state creep rates for many materials in a certain stress and temperature ranges (see our papers). In many papers published by Dyson you may find the application to several steels, aluminum and titanium alloys.

Regarding the theoretical background: the exponential law was introduced by Prandtl in 1928, so it has a long tradition (in many textbooks the hyperbolic sine law is called Prandtl's creep law). Please have a look on the original paper of Prandtl

http://onlinelibrary.wiley.com/doi/10.1002/zamm.19280080202/abstract;jsessionid=F73C6AAF4C028036C6F2D37802EF93A3.f01t01

If you are really interested in climb-plus-glide mechanisms of inelastic deformation, please consult  recently published papers on dislocation dynamics simulations coupled with diffusion of vacancies. See for example this paper

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.265504 

During straining the dislocation move on the slip plane and this movement is known as dislocation glide. The strain is manifestation of dislocation glide. When dislocation meets an obstacle in the slip plan its glide stops and there is no further strain. In case of creep the dislocations acquire sufficient energy to overcome the obstacle by shifting its slip plane above or below the obstacle by adjusting/subsuming the vacancies. Once this happens the deformation under creep continues.