Notch effects in tensile behavior of AM60 magnesium alloys

The deformation and failure behavior of an AM60 magnesium alloy was investigated using tensile test on circumferentially notched specimens with different notch radii. The strain and stress triaxiality corresponding to the failure point were evaluated using both analytical and finite element analyses. Combining with systematical observations of the fracture surfaces, it is concluded that deformation and failure of AM60 magnesium alloy are notch (constraint) sensitive. The failure mechanisms change from ductile tearing to quasi cleavage with the increase of constraint

Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials

In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave propagation through a phononic structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is here used to investigate the forced wave propagation through locally resonant metamaterials. The perturbation approach reveals that energy exchange may occur between propagative and evanescent waves induced by quadratic nonlinear local interaction

On Micromechanical Parameter Identification With Integrated DIC and the Role of Accuracy in Kinematic Boundary Conditions

Integrated Digital Image Correlation (IDIC) is nowadays a well established full-field experimental procedure for reliable and accurate identification of material parameters. It is based on the correlation of a series of images captured during a mechanical experiment, that are matched by displacement fields derived from an underlying mechanical model. In recent studies, it has been shown that when the applied boundary conditions lie outside the employed field of view, IDIC suffers from inaccuracies. A typical example is a micromechanical parameter identification inside a Microstructural Volume Element (MVE), whereby images are usually obtained by electron microscopy or other microscopy techniques but the loads are applied at a much larger scale. For any IDIC model, MVE boundary conditions still need to be specified, and any deviation or fluctuation in these boundary conditions may significantly influence the quality of identification. Prescribing proper boundary conditions is generally a challenging task, because the MVE has no free boundary, and the boundary displacements are typically highly heterogeneous due to the underlying microstructure. The aim of this paper is therefore first to quantify the effects of errors in the prescribed boundary conditions on the accuracy of the identification in a systematic way. To this end, three kinds of mechanical tests, each for various levels of material contrast ratios and levels of image noise, are carried out by means of virtual experiments. For simplicity, an elastic compressible Neo-Hookean constitutive model under plane strain assumption is adopted. It is shown that a high level of detail is required in the applied boundary conditions. This motivates an improved boundary condition application approach, which considers constitutive material parameters as well as kinematic variables at the boundary of the entire MVE as degrees of freedom in...Comment: 37 pages, 25 figures, 2 tables, 2 algorithm

Microscopically derived free energy of dislocations

The dynamics of large amounts of dislocations is the governing mechanism in metal plasticity. The free energy of a continuous dislocation density profile plays a crucial role in the description of the dynamics of dislocations, as free energy derivatives act as the driving forces of dislocation dynamics. In this contribution, an explicit expression for the free energy of straight and parallel dislocations with different Burgers vectors is derived. The free energy is determined using systematic coarse-graining techniques from statistical mechanics. The starting point of the derivation is the grand-canonical partition function derived in an earlier work, in which we accounted for the finite system size, discrete glide planes and multiple slip systems. In this paper, the explicit free energy functional of the dislocation density is calculated and has, to the best of our knowledge, not been derived before in the present form. The free energy consists of a mean-field elastic contribution and a local defect energy, that can be split into a statistical and a many-body contribution. These depend on the density of positive and negative dislocations on each slip system separately, instead of GND-based quantities only. Consequently, a crystal plasticity model based on the here obtained free energy, should account for both statistically stored and geometrically necessary dislocations

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

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