Deformation of materials

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In the field of mechanics of materials, stress is a measure of the internal forces within a material that result from external loads. It is defined as the force per unit area and expresses the intensity of the internal forces exerted by the particles of a material on each other. When an object is subjected to stress, it may experience deformation or failure, depending on the magnitude of the stress and the properties of the material. The measure of this deformation is called strain.

Most materials that are used are generally polycrystalline, consisting of millions of single crystals called grains. These grains have different orientations of the atomic lattice and are separated from neighboring grains by interfaces known as grain boundaries (GB). It is well established that the irreversible (or plastic) deformation of a sample primarily results from the nucleation and propagation of micrometric (or even nanometric) linear defects in the regular crystal lattice, known as dislocations. These dislocations move through the grain and interact with each other or with GBs, which can act as sinks, traps, or sources of dislocations.

Today, we have a good understanding of how a single dislocation interacts with a single model grain boundary (GB), but understanding the response of multiple real GBs (contained in a real bulk polycrystalline sample) to numerous dislocations is still a major scientific challenge. This complexity is further compounded by the fact that there are more than hundreds of billions of dislocations per cm³ of sample interacting with billions of GBs. Additionally, factors such as the distribution of GBs, other types of interfaces, grain shape, grain orientation and defects in the bulk sample (i.e. its microstructure) also need to be considered. Due to this inherent complexity, we must link two extreme scales: the sample (or macro) scale and the dislocation (or micro) scale. It is clear that these two worlds interact with each other, but the connections between them remain extremely difficult to understand due to the need for extrapolation.

The response of a single grain of interest in a polycrystalline sample cannot be understood individually without taking into account its relationship to its neighboring grains. Surprisingly, there is a lack of literature on this crucial point. For example, it is commonly assumed that the stress experienced by one grain is the same as that experienced by the entire specimen, i.e. the stress field inside one grain (σ) is assumed to be the same as the macroscopic stress field applied (Σ) on the sample during the deformation test. As a result, the influence of the surrounding microstructure and crystalline anisotropy are often considered to be negligible. Despite intense research, this question remains partially unexplored to date, largely due to numerous technological issues.

Solving this mystery by nature requires a breakthrough in existing approaches. Micromechanical modeling coupled with experiments can provide important insights. Such computational schemes require constitutive equations that are “fed” with experimental criteria and parameters, capturing the important operative mechanisms. However, such valuable experiments are still limited and all suffer from numerous constraints, making interpretations unreliable.