Strain Gradient Plasticity Modelling of Precipitation Strengthening

University dissertation from KTH Royal Institute of Technology

Abstract: The introduction of particles and precipitates into a matrix material results in strengthening effects. The two main mechanisms involved in this matter are referred to as Orowan and shearing. To numerically study this phenomenon is the motivation to the research done, which is presented here in this thesis. The heterogeneous microscale state of deformation in such materials brings in size scale effects into the picture. A strain gradient plasticity (SGP) theory is used to include effects of small scale plasticity. In addition, a new interface formulation is proposed which accounts for the particle-matrix interactions. By changing a key parameter, this interface model can mimic the level of coherency of particles, and hence is useful in studying different material systems.The governing equations and formulations are then implemented into an in-house SGP FEM program. The program is equipped with axi-symmetric and three-dimensional modelling capabilities. Different distributions of particles are considered, from which proper representative volume elements (RVEs) are constructed. These RVEs are then analyzed under different loadings, and homogenization methods are utilized to evaluate macroscopic response of the material. A quantity of interest is the increase in yield stress of material due to presence of particles and precipitates. Comprehensive parametric studies are carried out to study the effects of different parameters on the strengthening. A closed formsolution is obtained, which suggests the strengthening increases by increasing the surface area of particles per unit volume of material.The work done is presented in four appended papers. Paper A uses an axi-symmetric model to set the theoretical basis for the rest of the papers. Effects of different key parameters on the strengthening are studied and presented in this paper. Since the axisymmetric model is numerically cheap, an extensive amount of analyses are carried out. Paper B is about the expansion of the theory introduced in the first paper into 3D space. The micromechanical model is composed of a cuboid RVE with eight different particles, one at each corner. The inclusion of more than one particle is a key parameter in studying the effects of size distribution.The idea of having the most general micromechanical model is the theme of Paper C. Here, a completely random distribution of particles in 3D space is taken into account. In addition, the results of all carried out analyses are tested against experimental results from different material systems. Last paper, Paper D, summarizes a successful effort to include Shearing mechanism in the micromechanical model. The RVE is equipped withan embedded slip plane, and yet has the features introduced in previous papers. Hence, it has the ability to cover both strengthening mechanisms observed in precipitated materials.