Exercice 6

1. 1 Exercice 6

2. 2 1.1 Interactions between dislocations Consider two parallel screw dislocations. Let us just consider the stress fields due to dislocations (no applied load). The force acting on (2) due to the stress field of dislocation (1) is given by the Peah-Koehler force. We can demonstrate that it is equal to .. The dislocations tend to repel each other if they have the same sign. F is attractive when dislocations have opposite signs. Note that no forces act between a pair of parallel dislocations consisting of a pure edge and a pure screw, as expected from the lack of mixing of their stress fields.Consider two parallel screw dislocations. Let us just consider the stress fields due to dislocations (no applied load). The force acting on (2) due to the stress field of dislocation (1) is given by the Peah-Koehler force. We can demonstrate that it is equal to .. The dislocations tend to repel each other if they have the same sign. F is attractive when dislocations have opposite signs. Note that no forces act between a pair of parallel dislocations consisting of a pure edge and a pure screw, as expected from the lack of mixing of their stress fields.

3. 3 1.1 Interactions between dislocations Consider two parallel screw dislocations. Let us just consider the stress fields due to dislocations (no applied load). The force acting on (2) due to the stress field of dislocation (1) is given by the Peah-Koehler force. We can demonstrate that it is equal to .. The dislocations tend to repel each other if they have the same sign. F is attractive when dislocations have opposite signs. Note that no forces act between a pair of parallel dislocations consisting of a pure edge and a pure screw, as expected from the lack of mixing of their stress fields.Consider two parallel screw dislocations. Let us just consider the stress fields due to dislocations (no applied load). The force acting on (2) due to the stress field of dislocation (1) is given by the Peah-Koehler force. We can demonstrate that it is equal to .. The dislocations tend to repel each other if they have the same sign. F is attractive when dislocations have opposite signs. Note that no forces act between a pair of parallel dislocations consisting of a pure edge and a pure screw, as expected from the lack of mixing of their stress fields.

4. 4 1.2 Interactions between dislocations and solute atoms If the material is subjected to a pressure P, the strain energy is changed by the presence of the point defect by pdeltaV. For a screw dislocation EI=0 If the material is subjected to a pressure P, the strain energy is changed by the presence of the point defect by pdeltaV. For a screw dislocation EI=0

5. 5 1.2 Interactions between dislocations and solute atoms Point defects (vacancies, self-intertitials, substutitional and intertitial impurities, interact with dislocations. The most important contribution to the interaction between a point defect and a dislocation is usually that due to rhe distortion the point defect produces in the surrounding crystal. The distortion may interact with the stress field of the dislocation to raise or lower the elastic strain energy of the crystal. This change is the interaction energy EI. The simplest model of a point defect is an elastic sphere of natural radius A, which is inserted into a spherical hole of radius Ra. The sphere and matrix are isotropic with the same shear modulus G and Poisson’s ratio nu (not right in reality, but the modulus effect is neglected because it is much smaller then the distortion effect). The difference between the defect and the hole volumes is the misfit volume Vmis=Vs-Vh. The mosfit paramter delta is positive for oversized defects and negative for undersized ones. On inserting the sphere in the hole, Vh changes. The total volume change experienced by an infinite matrix is DVh (for the strain in the matrix is pure shear with no dilatational part. In a finite body, however, the requirement that the outer surface be stress-free results in a total volume change given by (see equation).Point defects (vacancies, self-intertitials, substutitional and intertitial impurities, interact with dislocations. The most important contribution to the interaction between a point defect and a dislocation is usually that due to rhe distortion the point defect produces in the surrounding crystal. The distortion may interact with the stress field of the dislocation to raise or lower the elastic strain energy of the crystal. This change is the interaction energy EI. The simplest model of a point defect is an elastic sphere of natural radius A, which is inserted into a spherical hole of radius Ra. The sphere and matrix are isotropic with the same shear modulus G and Poisson’s ratio nu (not right in reality, but the modulus effect is neglected because it is much smaller then the distortion effect). The difference between the defect and the hole volumes is the misfit volume Vmis=Vs-Vh. The mosfit paramter delta is positive for oversized defects and negative for undersized ones. On inserting the sphere in the hole, Vh changes. The total volume change experienced by an infinite matrix is DVh (for the strain in the matrix is pure shear with no dilatational part. In a finite body, however, the requirement that the outer surface be stress-free results in a total volume change given by (see equation).

6. 6 If the material is subjected to a pressure P, the strain energy is changed by the presence of the point defect by pdeltaV. For a screw dislocation EI=0 If the material is subjected to a pressure P, the strain energy is changed by the presence of the point defect by pdeltaV. For a screw dislocation EI=0

7. 7 1.2 Interactions between dislocations and solute atoms For an edge dislocation … For an oversized defect (delta and epsilon >0), EI is positive for sites above the slip plane and negative below.This is because the edge dislocation produces compression in the region of the extra half-plane and tension below. The position of attraction and repulsion are reversed for an undersized defect. We find the results already discussed on vacancy diffusion. Defects tend to congregate in core regions where EI is large and negative and dense atmospheres of solute atoms can form : Cottrell atmospheres. It requires diffusion and so temperature For an edge dislocation … For an oversized defect (delta and epsilon >0), EI is positive for sites above the slip plane and negative below.This is because the edge dislocation produces compression in the region of the extra half-plane and tension below. The position of attraction and repulsion are reversed for an undersized defect. We find the results already discussed on vacancy diffusion. Defects tend to congregate in core regions where EI is large and negative and dense atmospheres of solute atoms can form : Cottrell atmospheres. It requires diffusion and so temperature

8. 8 1.2 Interactions between dislocations and solute atoms For an edge dislocation … For an oversized defect (delta and epsilon >0), EI is positive for sites above the slip plane and negative below.This is because the edge dislocation produces compression in the region of the extra half-plane and tension below. The position of attraction and repulsion are reversed for an undersized defect. We find the results already discussed on vacancy diffusion. Defects tend to congregate in core regions where EI is large and negative and dense atmospheres of solute atoms can form : Cottrell atmospheres. It requires diffusion and so temperature For an edge dislocation … For an oversized defect (delta and epsilon >0), EI is positive for sites above the slip plane and negative below.This is because the edge dislocation produces compression in the region of the extra half-plane and tension below. The position of attraction and repulsion are reversed for an undersized defect. We find the results already discussed on vacancy diffusion. Defects tend to congregate in core regions where EI is large and negative and dense atmospheres of solute atoms can form : Cottrell atmospheres. It requires diffusion and so temperature

9. 9 2. Strain hardening mechanismsSingle crystal stress-strain curve Décrire ce que l’on observe par les differents microscopes et dire multislup – forest dislocationsDécrire ce que l’on observe par les differents microscopes et dire multislup – forest dislocations

10. 10 2. Strain hardening mechanismsSingle crystal rotation Dire qu’en plus, il y a rotation du réseau cristallin , ce qui favorise le glissement multiple.Dire qu’en plus, il y a rotation du réseau cristallin , ce qui favorise le glissement multiple.

11. 11 2. Strain hardening mechanisms Prendre une approche purement mecanique – necessité d’identifier les parametres et si on change un peu le materiau, par exemple sa taille de grain, il faut recommencer l’identificationPrendre une approche purement mecanique – necessité d’identifier les parametres et si on change un peu le materiau, par exemple sa taille de grain, il faut recommencer l’identification

12. 12 2. Strain hardening mechanisms Prendre une approche physicienne. On sait que le mecanisme est le durcissement par la foret. On derive l’expression. Il faut maintenant connaitre l’evolution de ro avec gama. Nous n’avons pas encore montre la loi d’Orowan, penses tu le faire au prochain cours puisque c’est de la cinematique ? Ici on suppose que le libre parcours moyen est constant, or c’est faux dans la realite. En combinant toutes les equations, on obtient l’expression de teta. Ici, tout est connu ou mesurable puisqu’en gros le lpm correspond à la taille de grain.Prendre une approche physicienne. On sait que le mecanisme est le durcissement par la foret. On derive l’expression. Il faut maintenant connaitre l’evolution de ro avec gama. Nous n’avons pas encore montre la loi d’Orowan, penses tu le faire au prochain cours puisque c’est de la cinematique ? Ici on suppose que le libre parcours moyen est constant, or c’est faux dans la realite. En combinant toutes les equations, on obtient l’expression de teta. Ici, tout est connu ou mesurable puisqu’en gros le lpm correspond à la taille de grain.

13. 13 2. Strain hardening mechanisms Dans l’approche précédente, on a oublie que l’on avait plusieurs systemes glissements qui ne durcissent pas de la meme manière (cela depend s(ils ont glisse). On donne l’expression generale et de meme pour l’evolution de ro avec cette fois ro qui integre un LPM qui decroit avec la deformation : egale à la taille de grain au debut puis a la taille des cellules. Enfin, l’ecrouissage etant parabolique, il faut que le modele sature aussi, ce qui n’est pas pour l’instant. On rajoute un terme d’annihilation.Dans l’approche précédente, on a oublie que l’on avait plusieurs systemes glissements qui ne durcissent pas de la meme manière (cela depend s(ils ont glisse). On donne l’expression generale et de meme pour l’evolution de ro avec cette fois ro qui integre un LPM qui decroit avec la deformation : egale à la taille de grain au debut puis a la taille des cellules. Enfin, l’ecrouissage etant parabolique, il faut que le modele sature aussi, ce qui n’est pas pour l’instant. On rajoute un terme d’annihilation.

14. 14 2. Strain hardening mechanisms Décrire ce que l’on observe par les differents microscopes et dire multislup – forest dislocationsDécrire ce que l’on observe par les differents microscopes et dire multislup – forest dislocations