Papers by Keyword: Micromechanics

Abstract: One of the most important features of a material to know before using it is the maximum limit of the load at which it fails. This paper presents a micromechanical strength theory to estimate the tensile strength of the unidirectional fiber reinforced composite. The fibers used can be considered transversely isotropic and elastic till failure, but the matrix material is considered to be Elastic-plastic. The mathematical formulation used is the Variational-Asymptotic Method (VAM), which is used to construct the asymptotically-correct a reduced-dimensional model that is free of a priori assumption regarding the kinematics. The 3-D strain generated in each constituent material is explicitly expressed in 1-D strains and initial curvatures. The advantage of using VAM is that the stress state correlation of constituent materials is taken care of while applying warping constraints. Prandtl-Reuss plasticity theory has been implemented for the plastic region constitutive relationship. The other advantage of this work is that the load-bearing capacity of the composite beyond the elastic region has been considered. Good agreement has been found between experimental data and VAM analysis.

Abstract: A new numerical method for homogenization of elastic properties of dispersedly-reinforced composites was presented. The method takes into account special model of adhesive contact. Homogenization of properties was performed by averaging the solutions of boundary value problems on representative volume cell (RVC) using the finite element method (FEM). A new approach of calculation of components of effective tensor of elastic moduli was proposed. A heterogeneous finite element model with elements of two types was built: three-dimensional tetrahedron elements for every phases and spring element with zero-length for adhesion layer with zero-thickness. The results of homogenization of elastic properties of dispersedly-reinforced composites with variable stiffness of the adhesive layer between phases were obtained and analyzed. The homogenization results were compared with the available experimental data.

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: Actuation response of NiTiHf high temperature SMAs can be enhanced by means of suitable heat treatment on the material through precipitation hardening. Heat treatments can be chosen carefully to improve the performance of the NiTiHf SMAs in order to meet the requirements of targeted applications to design more robust and efficient high temperature solid-state actuator systems. The present work aims to develop a novel approach to model and predict the behavior of heat-treated NiTiHf SMAs. The predictions of the thermomechanical response of NiTiHf SMAs are based on Representative Volume Elements (RVEs). The precipitated NiTiHf SMA is modeled as a composite consist of of thermo-elastic non-transforming precipitates and a polycrystalline SMA matrix. The structural effect of precipitates and the effect of Hf-concentration gradient resulted from Hf depletion during precipitation are included. The composition distribution resulting from the elemental depletion and the transformation temperature distributions in the SMA matrix are related. In the present work, these relations are developed from experimental measurements on several NiTiHf compositions. Thermo-mechanical responses of Ni_50.3Ti_29.7Hf₂₀ heat-treated at 500°C for 48h at different loading conditions are predicted and the correlations with experimental results demonstrate the validity of the proposed framework.

Abstract: Ultra-high molecular weight polyethylene (UHMWPE) is a tough semi-crystalline polymer employed widely as a bearing material in total joint replacements. The micromechanical model has been presented that predicts stiffness of UHMWPE as an aggregate of crystalline inclusions (lamellae) embedded in a rubbery matrix of amorphous polymer chains. The differential scheme was chosen for its ability to represent the interaction between an inclusion and the matrix. Numerical simulations show that increasing lamellar thickness results in less stiffness, less shear stress imposed on the lamellae, indicates that thick lamellae are desirable for UHMWPE materials utilized in total joint replacement bearings.

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: A predictive microscale-informed model that takes into account the precipitate–shape memory performance relations and allows for the evaluation of the effective thermomechanical response of precipitated Ni-rich NiTi shape memory alloys on the basis of composition and heat treatment is presented. The model considers the structural effect of the precipitates (coherency stresses due to the lattice mismatch between the precipitates and the matrix material and precipitate volume fraction), as well as the effect of the Ni-concentration gradient in the matrix, resulting from Ni-depletion during precipitate growth. The predictive capability of the model is tested against experimental data obtained fromNi₅₀.₇Ti (at. %) that has been heat treated under different conditions and good agreement is shown.