For the most computer simulation experiments, initial transient stage is very critical if one applies the load suddenly in order to establish steady state (or stationary state for nonlinear system) regime where the strain rate suppose to be constant. Sudden application of the load results jerky motion which is also known as Gibbs phenomena if one uses the Fourier representation to describe the dynamical behaviour of the system. Because of which for the large inertial systems one has to apply the loading using an exponential function as cofactor with a well define relaxation time obtain by try and error to reach the desired loading level asymptotically. ApplForce = [1- exp (-t/THO] DesiredForce.

The answer is yes. There is a lot of literature available in the field of dynamic material behaviour on this topic. See for instance the works of Marc Meyers et al.

I've been myself working on crystal plasticity modeling of Ti6Al4V using VPSC and have incorporated strain rate effects to explain the competition between the different slip and twinning systems.

However, be extremely careful with the concept of strain rate in the framework of crystal plasticity modeling: in many models, 'strain rate' is a mathematical concept being the amount of deformation in a given calculation step, which has nothing to do with the physical strain rate!

Yes, strain rate have effect on CRSS. It can be visualized by considering Orowan relation of strain rate=Rho*b*v, rho is dislocation density, b is magnitude of burger vector and v is dislocation velocity. Further v is related to effective shear stress (v vs tau_eff) and in turn CRSS. Hence making it strain rate dependent.

Thanks all for the valuable comments. I could understand it from HULL and BACON text book "Introduction to dislocations".

As rightly pointed out by Mr. Kulbir, the velocity depends on the thermal part of the CRSS and therefore to achieve higher strain rates (from orowan eqn) larger shear stresses are required.

My answer above is related to the dynamical testing where one observes the required force change for a given displacement under the given displacement rate. Than you may asked what happens to the response of the system (i.e., instantaneous value of the resolve shear stress versus strain) when one employs different rate of displacements? This procedure is extremely important for the observation of the response of nonlinear systems which have ineartial as well as the dissipative parts.

Orowan equation has nothing to the with the initial critical resolve shear which is defines as " The value of resolved shear stress reaches the critical value for the onset of dislocation motion. i.e., a stress just high enough to overcome the lattice resistance to dislocation motion". This value is the same for all slip systems in a crystal. RSS = Sigma cos theta cos Phi. where RSS=Sigma/2 for (101)[101) slip system. This result doesn't answer our question what so ever unless drag force coefficient B ( Stress = B Velocity) acting on the dislocation motion is constant (linear system). As long as system has inertial response initial resolve stress would be strain rate dependent, which causes the short duration transient regime beyond that one reaches steady state or stationary nonequilibrium state.

It is well known that the motion of dislocation is thermally activated. The velocity of the dislocation depends on the thermal part of the shear stress and further from the Orowan eqn, strain rate is proportional to the velocity of the dislocation. Hence, the strain rate relates to the shear stresses or simply flow stresses.

Dear Bharat one should be very careful in using thermodynamic or thermokinetics terminologies while discussion kinematik behaviour of dislocation with and without the externally applied force system. First of all " thermal part of shear stress" is meaningless terminology in mechanics as well as in thermodynamics. Without the presence of the applied forces on the system one talks about the spontaneous behaviour of dislocations, which are some how nonequilibrium configuration in regards to their mutual strain interaction energies at the given temperature and volume of the embedding matrix. Here you can't talk about the motion of a single dislocation but rather an ensemble of dislocations if you wish to use thermokinetic theory such as the activated state theory as applied to the recrystallization of cold worked metals and alloys.

I would recommend you to have a look at the theory of thermally activated deformation. The topic has been discussed in several books and one of the books I would recommend is by HULL and BACON " INTRODUCTION TO DISLOCATIONS".

The terminology I have used maybe specific.

Dear Bhabat according to your question above, you are interesting in the variation of CRSS with respect to the change in the strain rate under the constant temperature that means you are dealing with isothermal behaviour of gliding dislocations, which are moving with uniform velocity as Orowan connection reveals clearly in their respective slip planes. Steady state motion of gliding dislocation may be represented by

Force Acting on Dislocation Line =Mobility x Velocity. The force F in general may be given by Peach and Koehler vectorial equation as such F= t x (Sigma . b) where Sigma local stress dyadic action on the dislocation line segment, t is the unit tangent vector to the dislocation line and b is the Burgers vector which constant along the dislocation line but not the tangent vector for curved dislocations. The projection of F on the slip plane, which acts perpendicular to the dislocation segment is the driving force for glide , and the normal component of F to the glide plane F. n would be the driving force for the CLİMB motion (edge component only) . That is a nonconservative motion, which is the thermally activated that requires creation and/or annihilation of lattice points, which involves diffusion of vacancies and/or interstitials under the strain field of dislocations.

Dear Bhabat my young respectful colleague I don't need your advice today and not for those early nineteen sixties when I was a young MS&PhD student at Stanford !! while I was attending John Weertman' s lectures on the dislocation climb theory.

Theory of Dislocations By John Hirth and Jens Lothe is very good advance text.

Dislocations and Plastic Deformation by I. Kovacs and L. Zsoldos

Dislocations in Crystals by W.T Read is very good for those dealing with the historical development of theory.

Kontınuumstheorie der Versetzungen und Eigenspannungen by Ekkehart Kroner (Continuum Theory of Point Defects and Dislocations ) it is a very powerful mathematical treatment using vectorial algebra.

Dear Prof.,

I did not mean to give an advice. Kindly accept my apologies. It is good to know that you were fortunate enough to attend Prof. Weertman's lectures. The recommendation was made only for giving an idea on the terminology that I was using (i.e. thermal part of the shear stress).

You answer for dislocation motion is very informative which is now a standard in many text books.

I was mentioning that at a constant temperature, all strain rates cannot be achieved by single CRSS. This is because of the dependency of the velocity of the dislocation on the thermal part of the CRSS. The Peach-Koehler force (which you have clearly) stated is the mechanical part of the CRSS. Maybe at 0 K when thermal activation is absent, the strain rates doesn't affect the CRSS.

Dear Bharat,I thank you for your remarks. I have never satisfied with the existent theories dealing with the dislocations and kinks which are strongly interacting with the point defects to explain the mechanical behaviouır of crystalline solids exposed to static and dynamic loading (such as internal friction) since they are almost ad hoc in nature and they are lag of mathematical rigour to be used in computer simulations. I think I have done excellent work in collaboration with Professor Seeger to handle this problem in BCC metals, which are contaminated by light (H) as well as heavy interstitials (N, O, C). See our publication during the years of 1980-1990 since then I have switch to study interfaces and surfaces driven by electro and elastostatic forces using irreversible thermodynamic approach.

Best Regards.

Note: If one wises to make any contribution to this field he/she should be very very good in applied and computational mathematics, statistical and classical as well as quantum mechanics and plus some knowledge in thermodynamics (especially irreversible).

Generally, in crystal plasticity, the effect of rate comes in not through changing CRSS but through the definition of rate of slip shear deformation. It mimics the physics that you need higher stresses for higher strain rates. It is just a mathematical formulation which is common.