Grain boundary sliding

Grain boundary sliding (GBS) is a material deformation mechanism where grains slide against each other. This occurs in polycrystalline material under external stress at high homologous temperature (above ~0.4) and low strain rate and is intertwined with creep. Homologous temperature describes the operating temperature relative to the melting temperature of the material. There are mainly two types of grain boundary sliding: Rachinger sliding, and Lifshitz sliding. Grain boundary sliding usually occurs as a combination of both types of sliding. Boundary shape often determines the rate and extent of grain boundary sliding.

Grain boundary sliding is a motion to prevent intergranular cracks from forming. Keep in mind that at high temperatures, many processes are underway, and grain boundary sliding is only one of the processes happening. Therefore it is not surprising that Nabarro Herring and Coble creep is dependent on grain boundary sliding. During high temperature creep, wavy grain boundaries are often observed. We can simulate this type of boundary with a sinusoidal curve, with amplitude h and wavelength λ. Steady-state creep rate increases with rising λ/h ratios. At high λ and high homologous temperatures, grain boundary sliding is controlled by lattice diffusion (Nabarro-Herring mechanism). On the other hand, it will be controlled by grain boundary diffusion (Coble Creep). Additionally, when λ/h ratios are high, it may impede diffusional flow, therefore diffusional voids may form, which leads to fracture in creep. Many people have developed estimations for the contribution of grain boundary sliding to the total strain experienced by various groups of materials, such as metals, ceramics, and geological materials. Grain boundary sliding contributes a significant amount of strain, especially for fine grain materials and high temperatures. It has been shown that Lifshitz grain boundary sliding contributes about 50-60% of strain in Nabarro–Herring diffusion creep. This mechanism is the primary cause of ceramic failure at high temperatures due to the formation of glassy phases at their grain boundaries.

Rachinger sliding Rachinger sliding is purely elastic; the grains retain most of their original shape. The internal stress will build up as grains slide until the stress balances out with the external applied stress. For example, when a uniaxial tensile stress is applied on a sample, grains move to accommodate the elongation and the number of grains along the direction of applied stress increases.

Lifshitz sliding Lifshitz sliding only occurs with Nabarro–Herring and Coble creep. The sliding motion is accommodated by the diffusion of vacancies from induced stresses and the grain shape changes during the process. For example, when a uniaxial tensile stress is applied, diffusion will occur within grains and the grain will elongate in the same direction as the applied stress. There will not be an increase in number of grains along the direction of applied stress.

Accommodation mechanisms When polycrystalline grains slide relative to each other, there must be simultaneous mechanisms that allow for this sliding to occur without the overlapping of grains (which would be physically impossible). Various accommodation mechanisms have been proposed to account for this issue.

Dislocation movement: Dislocations can move through the material by processes such as climb and glide to allow for compatibility Elastic distortion: When the sliding distance is small, the grains can deform elastically (and sometimes recoverably) to allow for compatibility Diffusional accommodation: Using diffusional creep mechanisms, the material can diffuse along grain boundaries or through grains to allow for compatibility Grain boundary sliding accommodated by diffusional flow: Grain boundary sliding accommodated by diffusional flow takes place by grain-switching while preserving grain shape. This type of mechanism is synonymous to Nabarro Herring and Coble creep but describes the grain at superplastic conditions. This concept was originally proposed by Ashby and Verral. During grain switching, we can describe the process through three steps: a) Initial state b) Intermediate stage c) Final state. During the intermediate stage, there must first be an applied stress exceeding the “threshold” stress so that there is an increase in grain boundary area which is provided by the diffusional flow that occurs once the threshold stress is achieved. Under the assumption that the applied stress is much greater than the threshold stress, the strain rate is greater than conventional diffusional creep. The reason for this is that for grain switching diffusion, the distance is about 1/7 the distance of diffusional creep and there are two more paths to grain switching in comparison with diffusional creep. Thus, this will lead to about an order magnitude higher strain rate than diffusional creep. Grain boundary sliding accommodated by dislocation flow: At superplastic temperature, strain rate and stress conditions, dislocations are rarely observed because they are quickly emitted and absorbed at grain boundaries. However, careful studies have been conducted to verify that dislocations are indeed emitted during superplastic deformation. During dislocation flow, the shape of the grain must be ensured to not change. Based on models of super plasticity, transitioning from dislocation creep to super plasticity occurs when the sub grain size is less than the grain size. The sub grain size: often denoted as d’ can be described in the equation below:

d ′ b = 10 G τ {\displaystyle {d' \over b}={10G \over \tau }} , Where it has an inverse relationship with shear stress.

Deformation rate from grain boundary sliding Generally speaking, the minimum creep rate for diffusion can be expressed as:

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