Dear Dr.  Basheer,  Your question is not well defined!   However, we can make the following statements:

The dislocation multiplication  ( increase in dislocation density) occurs during the plastic deformation  through the activation of  the various dislocation sources such as Frank-Read Sources,  large precipitate (inclusions) particles having sufficiently big sizes that can't be  cut through by the moving dislocations but rather go around and leaving dislocation loops.  There is relationship between the dislocation density and the plastic shear strain, which is given by   d= do+  a x Gamapm, , where  do  is initial (grown in) dislocation density  [metals: about  108 cm/cm3,  and ionic and covalent crystals 103 cm/cm3 ]  a  is a constant ( f metals:  about equal to  108  cm/cm3), m is about  =1.

The applied tensile stress) required to induced plastic flow  [ which corresponds to about  0.2%  elongation for  the most FCC metals and alloys )    is known as  the elastic limit  or  yield stress. In the  elastic region  dislocation density variations  are almost negligible, one can only talk about their rearrangements if the temperature is sufficiently high enough to allow dislocations  to  climb and cross slip to form polygonization or low angle grain boundaries etc. Best regards. 

There are various annihilation mechanisms, which reduces the dislocation density in the elastic region such as two  edge dislocations having opposite Burgers vector sliding  in the same slip planes, or through the non- conservative  climb and  plus  the slide motion reaching the same slip plane and combine with opposite one. Surfaces and grain boundaries  also act as sinks for the dislocations.  The straight  screw dislocation can change its slip plane by gliding (cross slip), which   doesn't require any conservative motion since its  Burgers vector is parallel to the dislocation line. Therefore annihilation of screw dislocations of opposite sign is very effective mechanism.  

Best you follow the brilliant explanations of Günter Gottstein in " Physical Foundations of Materials Science",

download it as a pdf-file from an earlier discussion on RG:

https://www.researchgate.net/post/Can_you_suggest_some_of_the_good_books_about_material_science_and_electrochemistry

Dear Dr. Bashir

From a mechanical point of view, real processing involves multi-axial loading. Depending on the instantaneous nature of the stress tensor at a point (e.g. compressive, tensile) density of dislocation can increase or reduce. You need more details about the process and loading to interpret/understand the changes.

Dear Dr.  Khoddam,  the crystal dislocations  can only recognize the follow stress acting on their slip or glide planes.  The shear stress  acting on the dislocation line is given by   n . Sigma. b    where  n  is  the surface  normal vector associated with the slip  or glide plane , and b  is the unit vector along the Burgers vector  B of the dislocation line.  Force acting may be written as     F= n . Gigma. B,    B is the Burgers vector.  Gigma  is the local stress tensor.   This is a local stress tensor as the name implies  will change along dislocation line as well as   during the motion of the mobile dislocations. For the static loading it  only depends on the space variable.

In the case of non conservative motion (i.e., climb of edge dislocations)  which is thermally activated process involving vacancies and/or interstitials,  The stress normal to the slip plane  of an edge  dislocation line  F= n . Gigma. n  is also a driving force for the climb process, which also involves short range diffusion of vacancies or interstitials depending open the sign of edge dislocation. 

I agree with all your explanations. The only thing that I can add is: when a multi-axial loading at a point arises, the compressive and tensile stress components can be transformed into shear components along the dislocation plane using the Mohre Circle and therefore even positive or negative stress tensor components can contribute into how the dislocation density changes.

Dear  Dr. Khoddam,  What you are saying orally is perfectly alright. I put that into the mathematical format using the dyadic representation of the second order tensors,  precisely.  Sigma in my comment  is a stress tensor given in dyadic format.  What happens when you have a pure hydrostatic stress,   which is represented  by   p  [1],  which yields    n.p[1] =  n p, where  [1]  is unit tensor, and the result  is n p.  That tells us that there is no shear  stress  acting on the given slip plane ( actually there is no shear  in any plane) , where  n is  the unit surface normal vector .   p  can be negative or positive.

Similarly if we have a screw dislocation in  isotropic media then this only interacts with the deviatoric part of the local stress tensor not the dilatation part.. The main reason;  the strain field generated by the screw dislocation has zero trace (no diagonal parts).    On the hand Edge dislocation has dilatation as well as deviatoric parts, can interact with any type of stress system. But   F= n . p [1]. B, = 0,   it can't  sllp under the pure hydrostatic pressure since  n.B= 0.

Best regards

I can't agree with you more on the special cases you discussed, but my point is about a general case of multi-axial loading which typically results in development of shear components along the slip planes.

Dear Dr. Khoddam,  Your are definitely right  having  disagree with me  by putting the special cases on the table,  which screws up everything  that the general argument claims for. But I am as a  theoretician,  always interesting with the special cases, singularities etc., which are mostly overlooked , and are  too tough deal with analytically.  Best Regards 

It is really depend on the the type of deformation, strain content and the property of the material. Mainly the dislocation density increases by increase the amount of deformation. Nevertheless  in some cases, for example strain reversal is happened and the density is reduced.Also, in severe plastic deformation methods after a certain amount of strain the dislocation density is remain the same and reduced due to recovery . Please read one of my publications which is attached to this email.

Article Processing twining induced plasticity steel through simple s...

If the strain reversal takes place in the elastic range (not necessarily in the linear stress-strain connection range) the mobile dislocation density reduces if you assume dislocation mechanism of elastic deformation. Actually one has no hysteresis in the elastic strain  reversal for the infinitely slow loading and unloading. If the deformation invıolves point defect movements from one stable configuration to another one, like the case of the anelastic relaxation phenomena in BCC metals and alloys where interstitial  O, C  and  N  moves from one octahedral site to another octahedral site according to the change in direction of the applied stress field. Then the strain reversal shows hysteresis with a dissipation of energy. By the same way, the  dislocations pinned down by the point defects can show cyclic anelastic strain changes with the dissipation of energy driven by  the applied oscillator stress systems.  

dear`sir please share all the information as loading condition  etc., i guess your ques. might be : what  is effect on dislocation under XRD and without XRD.

Dear Jeenager

There are certainly other techniques for measuring such as TEM and AFM, but the important question what happen to the dislocation density of the metal alloy after exposure to an external load and get the plast deformation. I guss we can arrange a new question about how to measure the density of dislocation for metal alloy by using other techniques without XRD diffraction. Thank you very much for the posts value of my friends and thanks to you also.

Thank you sir