An adaptive multi-level model for multi-scale ductile fracture analysis in heterogeneous aluminum alloys

This paper addresses the multi-scale modeling of ductile fracture in microstructures characterized by a dispersion of hard and brittle heterogeneities in a softer ductile matrix. An adaptive multi-level model is developed with different inter-scale transfer operators and interfaces. Micro-mechanical analysis in regions of dominant damage is performed to capture the important micro-mechanical damage modes that are responsible for deterring the overall failure properties of these alloys. Regions of macroscopic homogeneity are otherwise modeled with constitutive relations derived from homogenization of evolving variables in representative volume elements. These two length scales of analysis, in conjunction with an intermediate swing level, form a three-level coupled multi-scale model to capture ductile crack propagation. The capabilities of the proposed model are demonstrated for a cast aluminum alloy

Reliability analysis and micromechanics: A coupled approach for composite failure prediction

This work aims at associating two classical approaches for the design of composite materials: first, reliability methods that allow to account for the various uncertainties involved in the composite materials behaviour and lead to a rational estimation of their reliability level; on the other hand, micromechanics that derive macroscopic constitutive laws from micromechanical features. Such approach relies on the introduction of variabilities defined at the microscale and on the investigation of their consequences on the material macroscopic response through an homogenization scheme. Precisely, we propose here a systematic treatment of variability which involves a strong link between micro- and macroscales and provides a more exhaustive analysis of the influence of uncertainties. The paper intends to explain the main steps of such coupling and demonstrate its interests for material engineering, especially for constitutive modelling and composite materials optimization. An application case is developed throughout on the failure of unidirectional carbon fibre-reinforced composites with a comparative analysis between experimental data and simulation results

Multi-scale reliability analysis of composite structures – Application to the Laroin footbridge

This work aims at developing a new methodology for the reliability assessment of composite structures and their design optimization. It relies on the coupling of well established methods: homogenization scheme for the mechanical modelling of composite materials and reliability methods to account for their inherent variability. Moreover, such approach is based on an accurate treatment of inherent uncertainties of these mechanical systems at various scales, including microscopic and macroscopic levels, that provides newperspectives for structural design. As an illustration, we propose to apply the multi-scale reliability analysis on the case of the Laroin footbridge (France) with carbon–epoxy stay cables. Since the reliability assessment of such structure is evaluated through the fibre failure, numerical simulations require the coupling of reliability methods, finite element modelling to derive macroscopic loading within cables and micromechanics to estimate the effective elastic properties of composite and local responses within constituents. Results demonstrate the feasibility of the coupled approach at a structure scale and its main interests for the optimization phase of materials and engineering structures

Voronoi cell finite element modelling of the intergranular fracture mechanism in polycrystalline alumina

The mechanisms of fracture in polycrystalline alumina were investigated at the grain level using both the micromechanical tests and finite element (FE) model. First, the bending experiments were performed on the alumina microcantilever beams with a controlled displacement rate of 10 nm s–1 at the free end; it was observed that the intergranular fracture dominates the failure process. The full scale 3D Voronoi cell FE model of the microcantilever bending tests was then developed and experimentally validated to provide the insight into the cracking mechanisms in the intergranular fracture. It was found that the crystalline morphology and orientation of grains have a significant impact on the localised stress in polycrystalline alumina. The interaction of adjacent grains as well as their different orientations determines the localised tensile and shear stress state in grain boundaries. In the intergranular fracture process, the crack formation and propagation are predominantly governed by tensile opening (mode I) and shear sliding (mode II) along grain boundaries. Additionally, the parametric FE predictions reveal that the bulk failure load of the alumina microcantilever increases with the cohesive strength and total fracture energy of grain boundaries

Microstructural topology effects on the onset of ductile failure in multi-phase materials - a systematic computational approach

Multi-phase materials are key for modern engineering applications. They are generally characterized by a high strength and ductility. Many of these materials fail by ductile fracture of the, generally softer, matrix phase. In this work we systematically study the influence of the arrangement of the phases by correlating the microstructure of a two-phase material to the onset of ductile failure. A single topological feature is identified in which critical levels of damage are consistently indicated. It consists of a small region of the matrix phase with particles of the hard phase on both sides in a direction that depends on the applied deformation. Due to this configuration, a large tensile hydrostatic stress and plastic strain is observed inside the matrix, indicating high damage. This topological feature has, to some extent, been recognized before for certain multi-phase materials. This study however provides insight in the mechanics involved, including the influence of the loading conditions and the arrangement of the phases in the material surrounding the feature. Furthermore, a parameter study is performed to explore the influence of volume fraction and hardness of the inclusion phase. For the same macroscopic hardening response, the ductility is predicted to increase if the volume fraction of the hard phase increases while at the same time its hardness decreases

Microstructure Control and Performance Evolution of Aluminum Alloy 7075 by Nano-Treating.

Nano-treating is a novel concept wherein a low percentage of nanoparticles is used for microstructural control and property tuning in metals and alloys. The nano-treating of AA7075 was investigated to control its microstructure and improve its structural stability for high performance. After treatment with TiC nanoparticles, the grains were significantly refined from coarse dendrites of hundreds of micrometers to fine equiaxial ones smaller than 20 μm. After T6 heat treatment, the grains, with an average size of 18.5 μm, remained almost unchanged, demonstrating an excellent thermal stability. It was found that besides of growth restriction factor by pinning behavior on grain boundries, TiC nanoparticles served as both an effective nucleation agent for primary grains and an effective secondary phase modifier in AA7075. Furthermore, the mechanical properties of nano-treated AA7075 were improved over those of the pure alloy. Thus, nano-treating provides a new method to enhance the performance of aluminum alloys for numerous applications

Multiscale computational homogenization: review and proposal of a new enhanced-first-order method

This is a copy of the author 's final draft version of an article published in the Archives of computational methods in engineering. The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-016-9205-0The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several fields of knowledge. In solid mechanics, the multiscale approaches which consider the macro-scale deformation gradient to obtain the homogenized material behaviour from the micro-scale are called first-order computational homogenization. Following this idea, the second-order FE2 methods incorporate high-order gradients to improve the simulation accuracy. However, to capture the full advantages of these high-order framework the classical boundary value problem (BVP) at the macro-scale must be upgraded to high-order level, which complicates their numerical solution. With the purpose of obtaining the best of both methods i.e. first-order and second-order, in this work an enhanced-first-order computational homogenization is presented. The proposed approach preserves a classical BVP at the macro-scale level but taking into account the high-order gradient of the macro-scale in the micro-scale solution. The developed numerical examples show how the proposed method obtains the expected stress distribution at the micro-scale for states of structural bending loads. Nevertheless, the macro-scale results achieved are the same than the ones obtained with a first-order framework because both approaches share the same macro-scale BVP.Peer ReviewedPostprint (author's final draft

Fracture initiation in multi-phase materials: a systematic three-dimensional approach using a FFT-based solver

This paper studies a two-phase material with a microstructure composed of a hard brittle reinforcement phase embedded in a soft ductile matrix. It addresses the full three-dimensional nature of the microstructure and macroscopic deformation. A large ensemble of periodic microstructures is used, whereby the individual grains of the two phases are modeled using equi-sized cubes. A particular solution strategy relying on the Fast Fourier Transform is adopted, which has a high computational efficiency both in terms of speed and memory footprint, thus enabling a statistically meaningful analysis. This solution method naturally accompanies the regular microstructural model, as the Fast Fourier Transform relies on a regular grid. Using the many considered microstructures as an ensemble, the average arrangement of phases around fracture initiation sites is objectively identified by the correlation between microstructure and fracture initiation -- in three dimensions. The results show that fracture initiates where regions of the hard phase are interrupted by bands of the soft phase that are aligned with the direction of maximum shear. In such regions, the hard phase is arranged such that the area of the phase boundary perpendicular to the principal strain direction is maximum, leading to high hydrostatic tensile stresses, while not interrupting the shear bands that form in the soft phase. The local incompatibility that is present around the shear bands is responsible for a high plastic strain. By comparing the response to a two-dimensional microstructure it is observed that the response is qualitatively similar (both macroscopically and microscopically). One important difference is that the local strain partitioning between the two phases is over-predicted by the two-dimensional microstructure, leading to an overestimation of damage