text: Oxide dispersion strengthening is based on incoherency of the oxide particles within the lattice of the material. Coherent particles have a continuous lattice plane from the matrix to the particles whereas incoherent particles do not have this continuity and therefore both lattice planes end at the interface. This mismatch in interfaces results in a high interfacial energy, which impedes dislocation. The oxide particles instead are stable in the matrix, which helps prevent creep. Particle stability implies little dimensional change, embrittlement, effects on properties, stable particle spacing, and general resistance to change at high temperatures. 
  Since the oxide particles are incoherent, dislocations can only overcome the particles by climb. If instead the particles are semi-coherent or coherent with the lattice, dislocations can simply cut the particles by a more favourable process that requires less energy called dislocation glide or by Orowan bowing between particles, both of which are athermal mechanisms. Dislocation climb is a diffusional process, which is less energetically favourable, and mostly occurs at higher temperatures that provide enough energy to advance via the addition and removal of atoms. Because the particles are incoherent, glide mechanisms alone are not enough and the more energetically exhausting climb process is dominant, meaning that dislocations are stopped more effectively. Climb can occur either at the particle-dislocation interface (local climb) or by overcoming multiple particles at once (general climb). In local climb, the part of the dislocation that is between two particles stays in the glide plane while the rest of the dislocation is climbing along the surface of the particle. For general climb, the dislocations all come out the glide plane. General climb requires less energy because the mechanism decreases the dislocation line length which reduces the elastic strain energy and therefore is the common climb mechanism. For γ’ volume fractions of 0.4 to 0.6 in nickel-based alloys, the threshold stress for local climb is only about 1.25 to 1.40 times higher than general climb. 
  Dislocations are not limited to either all local or all general climb as the path that requires less energy is taken. Cooperative climb is an example of a more nuanced mechanism where a dislocation travels around a group of particles rather than climbing past each particle individually. McLean stated that the dislocation is most relaxed when climbing over multiple particles because of the skipping of some of the abrupt interfaces between segments in the glide plane to segments that travel along the particle surface.
  The presence of incoherent particles introduces a threshold stress (σ), since an additional stress will have to be applied for the dislocations to move past the oxides by climb. After overcoming a particle by climb, dislocations can remain pinned at the particle-matrix interface with an attractive phenomenon called interfacial pinning, which requires additional threshold stress to free a dislocation out of this pinning, which must be overcome for plastic deformation to occur. This detachment phenomenon is a result of the interaction between the particle and the dislocation where total elastic strain energy is reduced. Schroder and Arzt explain that the additional stress required is due to the relaxation caused by the reduction in the stress field as the dislocation climbs and accommodates the shear traction. The following equations represent the strain rate and stress as a result of oxide introduction.
  Strain Rate:
  Threshold Shear Stress: