Papers by Keyword: Polycrystalline Materials

Abstract: Focusing 3-axis diffractometer set-up equipped with bent perfect crystal (BPC) monochromator and analyzer offers the sensitivity in determination of strains Dd/d < 10^-4 in polycrystalline materials which is about one order of magnitude higher with respect to that of conventional 2-axis neutron scanners. It also offers possibility of line profile analysis for reasonable sample volumes and counting times. In this paper, the feasibility of using the 3-axis set-up even for measurements of rather large bulk polycrystalline samples with an acceptable resolution is presented. As the 3-axis set-up exploits focusing in real and momentum space, by a proper adjustment of the curvature of the analyzer, a high-resolution determination of the lattice changes can also be achieved even on large irradiated gauge volumes, though with a slightly relaxed resolution. It can be successfully exploited namely, in the strain/stress measurements on samples exposed to an external load, e.g. in tension/compression rig, in aging machine etc. In addition to the original performance where the analysis is carried out by rocking the BPC analyzer and the neutron signal registered by a point detector, a new alternative is offered which uses a fixed rocking angle position of the analyzer and the detector signal is registered by a one-dimensional position sensitive detector (PSD). This trick makes possible in some cases the elastic strain/stress measurements considerably faster and thus reduces the drawback of the time consuming step-by-step analysis.

Abstract: Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electro-mechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for the design of such systems. The most popular numerical method for the analysis of micro-mechanical multi-physics problems, still in a continuum mechanics setting, is the Finite Element Method (FEM). Here we propose an alternative integral formulation for the grain-scale analysis of degradation and failure in polycrystalline piezoceramics. The formulation is developed for 3D aggregates and inter-granular failure is modelled through generalised cohesive laws.

Abstract: A grain-scale formulation for high-cycle fatigue inter-granular degradation in polycrystalline aggregates is presented. The aggregate is represented through Voronoi tessellations and the mechanics of individual bulk grains is modelled using a boundary integral formulation. The inter-granular interfaces degrade under the action of cyclic tractions and they are represented using cohesive laws embodying a local irreversible damage parameter that evolves according to high-cycle continuum damage laws. The consistence between cyclic and static damage, which plays an important role in the redistribution of inter-granular tractions upon cyclic degradation, is assessed at each fatigue solution jump, so to capture the onset of macro-failure. Few polycrystalline aggregates are tested using the developed technique, which may find application in multiscale modelling of engineering components as well as in the design of micro-electro-mechanical devices (MEMS).

Abstract: In this Chapter, the finite element simulations of diffusion processes in homogeneous and polycrystalline materials are presented as well as some analytical solutions and implementations of basic diffusion relations. For the homogeneous materials the presented examples show the changes in time of the concentration of diffusing matter within the semi-infinite system and simulation of anisotropic nature of diffusion processes.The polycrystalline materials have been analysed for three cases, namely influence of average grain size and the homogeneity of grain size on the macroscopic diffusivity as well as simulation of the diffusion strains. The homogenisation technique has been used to estimate the diffusion property of grains aggregates.

Abstract: In this contribution, we propose a cohesive grain-boundary model for hydrogen-assisted inter-granular stress corrosion cracking at the grain-scale in 3D polycrystalline aggregates. The inter-granular strength is degraded by the presence of hydrogen and this is accounted for by employing traction-separation laws directly depending on hydrogen concentration, whose diffusion is represented at this stage through simplified phenomenological relationships. The main feature of the model is that all the relevant mechanical fields are represented in terms of grain-boundary variables only, which couples particularly well with the employment of traction-separation laws.

Abstract: In this work, a novel grain boundary formulation for inter-and trans-granular cracking of polycrystalline materials is presented. The formulation is based on the use of boundary integral equations for anisotropic solids and has the advantage of expressing the considered problem in terms of grain boundary variables only. Inter-granular cracking occurs at the grain boundaries whereas trans-granular cracking is assumed to take place along specific cleavage planes, whose orientation depends on the crystallographic orientation of the grains. The evolution of inter-and trans-granular cracks is then governed by suitably defined cohesive laws, whose parameters characterize the behavior of the two fracture mechanisms. The results show that the model is able to capture the competition between inter-and trans-granular cracking.

Abstract: Crystal plasticity plays a crucial role in the mechanics of polycrystalline materials and it is commonly modeled within the framework of the crystal plasticity finite element method (CPFEM). In this work, an alternative formulation for small strains crystal plasticity is presented. The method is based on a boundary integral formulation for polycrystalline problems and plasticity is addressed using an initial strains approach. Voronoi-type micro-morphologies are considered in the polycrystalline case. A general grain-boundary incremental/iterative algorithm, embedding the flow and hardening rules for crystal plasticity, is developed. The key feature of the method is the expression of the micro-mechanical problem in terms of inter-granular variables only, resulting in a reduction of the number of DoFs, which may be appealing in multi-scale applications. Some numerical results, showing the potential of the technique, are presented and discussed.

Abstract: In this work, the grain-boundary cavitation in polycrystalline aggregates is investigated by means of a grain-scale model. Polycrystalline aggregates are generated using Voronoi tessellations, which have been extensively shown to retain the statistical features of real microstructures. Nucleation, thickening and sliding of cavities at grain boundaries are represented by specific cohesive laws embodying the damage parameters, whose time evolution equations are coupled to the mechanical model. The formulation is presented within the framework of a grain-boundary formulation, which only requires the discretization of the grain surfaces. Some numerical tests are presented to demonstrate the feasibility of the method.

Abstract: A two-scale three-dimensional approach for degradation and failure in polycrystalline materials is presented. The method involves the component level and the grain scale. The damage-induced softening at the macroscale is modelled employing an initial stress boundary element approach. The microscopic degradation is explicitly modelled associating Representative Volume Elements (RVEs) to relevant points of the macro continuum and employing a cohesive-frictional 3D grain-boundary formulation to simulate intergranular degradation and failure in the Voronoi morphology. Macro-strains are downscaled as RVEs' periodic boundary conditions, while overall macro-stresses are obtained upscaling the micro-stress field via volume averages. The comparison between effective macro-stresses for the damaged and undamaged RVEs allows to define a macroscopic measure of local material degradation. Some attention is devoted to avoiding pathological damage localization at the macro-scale. The multiscale processing algorithm is described and some preliminary results are illustrated.

Abstract: Diffraction methods for lattice strain measurement provide useful information concerning the nature of grains behaviour during elastoplastic deformation. The main advantage of the diffraction methods is the possibility of studying mechanical properties of polycrystalline materials separately in each phase and in groups of grains with a specific orientation. In this work we present application of the neutron and X-ray diffraction to study “in situ” deformation of two phase stainless steels during tensile loading. The experimental results are compared with self-consistent model.