The effect of material orientation on void growth

In this work, we have brought to light the effect of material orientation on void growth. For that purpose, we have performed finite element calculations using a cubic unit-cell model with a spherical void at its center and subjected to periodic boundary conditions. The behavior of the material is described with an elastic isotropic, plastic orthotropic constitutive model with yielding defined by Yld2004-18p criterion (Barlat et al., 2005). We have used the multi-point constraint subroutine developed by Dakshinamurthy et al. (2021) to enforce constant values of macroscopic stress triaxiality and Lode parameter in calculations that have been carried out for different stress states resulting from the combination of T=0.33, 1 and 2, with L=-1, 0 and 1 (axisymmetric tension, generalized shear and axisymmetric compression, respectively). Firstly, we have performed numerical simulations in which the loading directions are collinear with the orthotropy axes of the material, so that the principal directions of macroscopic stress and strain are parallel. Investigation of the cases for which the minor loading axis coincides either with the rolling, the transverse or the normal direction, has shown that the initially spherical void turns into an ellipsoid whose rate of growth and eccentricity depend on both stress state and material orientation. A key result is that for specific material orientations the anisotropy switches the effect of Lode parameter on void growth, reversing the trends obtained for isotropic von Mises materials. Secondly, we have carried out calculations using a novel strategy which consists of including angular misalignments within the range 0<\theta<90, so that one loading direction is parallel to one of the symmetry axes of the material, and \theta is the angle formed between the other two loading directions and the second and third orthotropy axes. In fact, to the authors’ knowledge, these are the first unit-cell calculations ever reported in which the material is modeled using a macroscopic anisotropic yield function with prescribed misalignment between loading and material axes and, at the same time, the macroscopic stress triaxiality and the Lode parameter are controlled to be constant during loading. The finite element calculations have shown that the misalignment between loading and material axes makes the void and the faces of the unit-cell to rotate and twist during loading. Moreover, the main contribution of this work is the identification of an intermediate value of the angle for which the growth rate of the void reaches an extreme value (minimum or maximum), so that the numerical results indicate that material orientation and angular misalignment can be strategically exploited to control void growth, and thus promote or delay localization and fracture of anisotropic metal products. The conclusions of this research have been shown to be valid for three different materials (aluminum alloys 2090-T3, 6111-T4 and 6013) and selected comparisons have also been performed using two additional yield criteria (CPB06ex2 and Yld2011-27p).

Macroscopic stress-strain response and strain localization behavior of biopolymer-treated soil

Enhancement of soil engineering properties with biopolymers has been shown recently as a viable and environmentally benign alternative to cement and chemical stabilization. Interest in biopolymer-treated soil is evident from the upsurge of related research activities in the last five years, most of which have been of experimental nature. However, biopolymers have not yet found their way into engineering practice. One of the reasons for this may be the absence of computational models that would allow engineers to incorporate biopolymer-treated soil into their designs. Therefore, the main goal of this study is to numerically capture a macroscopic stress-strain response and investigate the effect of biopolymers on the onset of strain localization. Several diagnostic strain localization analyses were conducted, thus providing strain and stress levels at the onset of strain localization, along with the orientations of the deformation band. Several unconfined compression and triaxial tests on the plain and biopolymer-treated soils were modeled. Results showed that biopolymers significantly improved the mechanical behavior of the soil and affected the onset of strain localization. The numerical results were confirmed by the digital image analysis of the unconfined compression tests. Digital image processing successfully captured high strain concentrations, which tend to occur close to the peak stress.

Stress minimization for lattice structures. Part I: Micro-structure design

Lattice structures are periodic porous bodies which are becoming popular since they are a good compromise between rigidity and weight and can be built by additive manufacturing techniques. Their optimization has recently attracted some attention, based on the homogenization method, mostly for compliance minimization. The goal of our two-part work is to extend lattice optimization to stress minimization problems two-dimensionally. The present first part is devoted to the choice of a parametrized periodicity cell that will be used for structural optimization in the second part of our work. In order to avoid stress concentration, we propose a square cell microstructure with a super-ellipsoidal hole instead of the standard rectangular hole often used for compliance minimization. This type of cell is parametrized two-dimensionally by one orientation angle, two semi-axis and a corner smoothing parameter. We first analyse their influence on the stress amplification factor by performing some numerical experiments. Second, we compute the optimal corner smoothing parameter for each possible microstructure and macroscopic stress. Then, we average (with specific weights) the optimal smoothing exponent with respect to the macroscopic stress. Finally, to validate the results, we compare our optimal super-ellipsoidal hole with the Vigdergauz microstructure which is known to be optimal for stress minimization in some special cases. This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization

This paper makes a rigorous case for considering the continuum derived by the homogenization of extensive quantities as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance of the macroscopic balance laws.

An in situ synchrotron study of the localized B2↔B19′ phase transformation in an Ni–Ti alloy subjected to uniaxial cyclic loading–unloading with incremental strains

High-resolution in situ synchrotron X-ray diffraction was applied to study a cold-drawn and solution-treated 56Ni–44Ti wt% alloy subjected to uniaxial cyclic loading–unloading with incremental strains. The micro-mechanical behaviour associated with the partial and repeated B2↔B19′ phase transformation at the centre of the sample gauge length was studied with respect to the macroscopic stress–strain response. The lattice strains of the (110)B2 and different B19′ grain families are affected by (i) the transformation strain, the load-bearing capacity of both phases and the strain continuity maintained at/near the B2–B19′ interfaces at the centre of the gauge length, and (ii) the extent of transformation along the gauge length. With cycling and incremental strains (i) the elastic lattice strain and plastic strain in the remnant (110)B2 grain family gradually saturate at early cycles, whereas the plastic strain in the B19′ phase continues to increase. This contributes to accumulation of residual strains (degradation in superelasticity), greater non-linearity and change in the shape of the macroscopic stress–strain curve from plateau type to curvilinear elastic. (ii) The initial 〈111〉B2 fibre texture transforms to [120]B19′, [130]B19′, [150]B19′ and [010]B19′ orientations. Further increase in the applied strain with cycling results in the development of [130]B19′, [102]B19′, [102]B19′, [100]B19′ and [100]B19′ orientations.

Twinning and Detwinning Mechanisms in Beta-Ti Alloys

We have investigated {332}<113> twinning and detwinning mechanisms in β-Ti alloys. Microstructure-twinning relations were evaluated in a β-Ti-15Mo (wt.%) alloy by statistical analysis of the evolving twin structure upon deformation by in-situ SEM testing and electron backscattering diffraction (EBSD). We find that most of the primary twins (~80%) correspond to the higher stressed variant and follow Schmid’s law with respect to the macroscopic stress. Detwinning mechanism was evaluated in a multilayered β-Ti-10Mo-xFe (x: 1-3 wt.%) by EBSD. We find that the detwinning process consists of two independent events that occur at two different microstructural regions, i.e. twin tips located at grain interiors and grain boundaries. Both detwinning modes can be explained from a thermodynamic standpoint where the boundary dissociation processes minimize the boundary free energy.