Ivano Benedetti

Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material micro-structures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to two-dimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.

A boundary element model for structural health monitoring using piezoelectric transducers

In this paper, for the first time, the boundary element method (BEM) is used for modelling smart structures instrumented with piezoelectric actuators and sensors. The host structure and its cracks are formulated with the 3D dual boundary element method (DBEM), and the modelling of the piezoelectric transducers implements a 3D semi-analytical finite element approach. The elastodynamic analysis of the structure is performed in the Laplace domain and the time history is obtained by inverse Laplace transform. The sensor signals obtained from BEM simulations show excellent agreement with those from finite element modelling simulations and experiments. This work provides an alternative methodology for modelling smart structures in structural health monitoring applications.

A micro-mechanical model for grain-boundary cavitation in polycrystalline materials

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.

A Microstructural Model for Micro-Cracking in Piezoceramics

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.

A Model for High-Cycle Fatigue in Polycrystals

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).

A Computational Study on Crack Propagation in Bio-Inspired Lattices

A computational preliminary study on the fracture behaviour of two kinds of finite-size bio-inspired lattice configurations is presented. The study draws inspiration from recent investigations aimed at increasing the fracture energy of some materials through small modifications of their microstructure. Nature provides several examples of strategies used to delay or arrest damage initiation and crack propagation. Striking examples are provided by the micro-architecture of several kinds of wood. In this study, the effects on crack propagations induced by architectural alterations inspired by the microstructure of wood are computationally investigated. In an age in which tight control of the micro-architecture can be achieved, e.g. through high-resolution 3D printing, it is of interest to investigate whether, starting from a baseline cellular architecture, it is possible to achieve superior material performance by simple but smart topological modifications.

A Thermodynamically Consistent CZM for Low-Cycle Fatigue Analysis

A cohesive zone model for low-cycle fatigue analysis is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variable. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the damage activation condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behavior without any fatigue degradation for low levels loading conditions.

A Novel Micro-Mechanical Model for Polycrystalline Inter-Granular and Trans-Granular Fracture

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.

Dual Boundary Element Model of 3D Piezoelectric Smart Structures

In this paper, the application of the dual boundary element method (DBEM) in the field of structural health monitoring (SHM) is explored. The model involves a 3D host structure, which is formulated by the DBEM in the Laplace domain, and 3D piezoelectric transducers, whose finite element model is derived from the electro-mechanical behaviour of piezoelectricity. The piezoelectric transducers and the host structure are coupled together via BEM variables. The practicability of this method in active sensing applications is demonstrated through comparisons with established FEM and parametric studies.

A Grain-Scale Model of Inter-Granular Stress Corrosion Cracking in Polycrystals

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.