The Portevin–Le Chatelier (PLC) effect describes a serrated stress–strain curve or jerky flow, which some materials exhibit as they undergo plastic deformation, specifically inhomogeneous deformation. This effect has been long associated with dynamic strain aging or the competition between diffusing solutes pinning dislocations and dislocations breaking free of this stoppage.
The onset of the PLC effect occurs when the strain rate sensitivity becomes negative and inhomogeneous deformation starts. This effect also can appear on the specimen's surface and in bands of plastic deformation. This process starts at a so-called critical strain, which is the minimum strain needed for the onset of the serrations in the stress–strain curve. The critical strain is both temperature and strain rate dependent. The existence of a critical strain is attributed to better solute diffusivity due to the deformation created vacancies and increased mobile dislocation density. Both of these contribute to the instability in substitutional alloys, while interstitial alloys are only affected by the increase in mobile dislocation densities.
History
While the effect is named after Albert Portevin and François Le Chatelier, they were not the first to discover it. Félix Savart made the discovery when he observed non-homogeneous deformation during a tensile test of copper strips. He documented the physical serrations in his samples that are currently known as Portevin–Le Chatelier bands. A student of Savart, Antoine Masson, repeated the experiment while controlling for loading rate. Masson observed that under a constant loading rate, the samples would experience sudden large changes in elongation (as large as a few millimeters).
Underlying physics
Much of the underlying physics of the Portevin-Le Chatelier effect lies in a specific case of solute drag creep. Adding solute atoms to a pure crystal introduces a size misfit into the system. This size misfit leads to restriction of dislocation motion. At low temperature, these solute atoms are immobile within the lattice, but at high temperatures, the solute atoms become mobile and interact in a more complex manner with the dislocations. When solute atoms are mobile and the dislocation velocity is not too high, the solute atoms and dislocation can move together where the solute atom decreases the motion of the dislocation.
The Portevin-Le Chatelier effect occurs in the specific case where solute drag creep is occurring and there is an applied stress, with a material dependent range, on the sample. The applied stress causes the velocity of the dislocations to increase, allowing the dislocation to move away from the solute. This process is commonly referred to as “breakaway”. Once the dislocation has moved away from the solute, the stress on it decreases which causes its velocity to decrease. This allows the solute atoms to “catch up” with the dislocation. As soon as the solute atom catches up, the stress on the dislocation significantly increases, causing the process to repeat.
The cyclic changes described above produce serrations in the plastic region of the stress strain diagram of a tensile test that is undergoing the Portevin-Le Chatelier effect. The variation in stress also causes non-homogeneous deformation to occur throughout the sample which can be visible to the naked eye through observation of a rough finish.
Conditions that affect the PLC effect
Temperature
Temperature affects both the speed of band propagation through the material and the critical strain. The speed of band propagation is proportional to the temperature (lower temp lower speeds, higher temp higher speeds). Often the critical strain will first decrease due to temperature. The temperature effect on the PLC regime is caused by the increased ability of the solutes to diffuse to the dislocations with increasing temperature. Although the mechanism of diffusion is not entirely understood, it is believed that solute atoms diffuse by either volume (high temperature), by diffusion in stacking fault ribbons between partial dislocations (intermediate temperature) or pipe diffusion (low temperature).
Strain rate
While temperature is related to the rate of diffusion, strain rate determines the time the dislocations take to overcome these obstacles, and has a dramatic effect on the conditions of the PLC effect. So generally, the critical stress will decrease with imposed strain rate. Also the higher the stress rate, the lower the band speed.