Geometry of plastic deformation in metals as piecewise isometric transformations.

Deformation mechanisms of crystalline solids has been the subject of research for more than two centuries. The theory of dislocations dominates modern views but still has significant gaps demanding the introduction of additional concepts for the coherent quantitative description of physical phenomena. In this work, we propose a coherent geometric description of motion and deformation in crystalline solids as piecewise isometric transformations (PWIT). The latter only includes operations that, similar to interatomic spacing in crystalline lattice, do not alter distances between reference points, i.e. translations, rotations and mirror reflections. The difference between solid-body translations and plastic deformations is that the isometric transformations have discontinuities that in real-life materials realise through dislocations (termination of shifts), disclinations (termination of rotations), and twins (mirror reflections). The conceptual description of plastic deformations as PWIT can be useful for the better description of physical phenomena, proposing new hypothesis, and for developing predictive analytical models. In this paper, the use of this conceptual description enables proposing new hypothesis about the nature of such interesting phenomena in severe plastic deformation as (i) stationary 'solid state turbulence' stage in high pressure torsion, and (ii) rate of mass transfer (mechanically assisted diffusion) in simple-shear deformation.

Mechanical Properties of Thermoplastic Polyurethane-Based Three-Dimensional-Printed Lattice Structures: Role of Build Orientation, Loading Direction, and Filler.

This study addresses the influence of build orientation and loading direction on the static and dynamic mechanical properties of three-dimensional-printed thermoplastic polyurethane-based lattice structures (with different cell shape). Specimens were printed in horizontal, 45° angle, and vertical orientations. Three-point bending tests showed that the investigated specimens are characterized by a strong anisotropy of the mechanical properties, which depends on the loading direction. In this regard, the influence of the loading direction is much stronger for the specimens printed vertically or at an angle of 45°, whereas the properties of the lattice structures printed horizontally are almost isotropic. The best set of mechanical properties (regardless of the loading direction) is shown by the samples of lattice materials, with square cells obtained by horizontal orientation of the polymer layers. The possibility of significant (one order of magnitude) increase in strength properties with satisfactory ductility is shown by using an epoxy polymer as a filler. A mathematical model of the bending of a mesostructured beam was established, which made it possible to describe qualitatively the various mechanisms of its destruction, such as: the breaking of the bonds between the polymer layers due to their mutual sliding and flaking, and the rapture of the layers themselves. The findings presented here provide new insights into the development of lattice structures with unique mechanical properties for a wide range of applications.

Gripping Prospective of Non-Shear Flows under High-Pressure Torsion.

The article presents a theoretical study of the regimes of high-pressure torsion (HPT) for which slippage of the deforming material on the interfaces with anvils is possible. The approach taken is a generalisation of the currently accepted view of the HPT process. It enables a rational explanation of its salient features and the effects observed experimentally. These include a lag in the rotation angle of the specimen behind that of the anvils, an outflow of the material from the deformation zone, enhancement in gripping the specimen with anvils with increasing axial pressure, etc. A generalised condition for gripping the specimen with anvils, providing a basis for an analytical investigation of the HPT deformation at a qualitative level, is established. The results of the analytical modelling are supported by finite-element calculations. It is shown that for friction stress below the shear stress of the specimen material (i.e., for the friction factor m < 1), plastic deformation is furnished by non-shear flows, which expands the range of possible process regimes. The potential of these flow modes is impressive, which is reflected in the second meaning of the word "gripping" in the title of the article. Non-shear flows manifest themselves in the spreading of the material over the anvil surfaces whose cessation signifies the end of deformation and the beginning of slippage of the specimen as a whole. The model shows that for m < 1 such a finale is inevitable at any axial pressure. It predicts, however, that the highest achievable strain is increased when the axial pressure is raised in the course of the HPT process. Unlimited deformation of the specimen is only possible for m = 1, when slippage of the deforming material relative to the anvils is suppressed.

Mechanical Properties of Flexible TPU-Based 3D Printed Lattice Structures: Role of Lattice Cut Direction and Architecture.

This study addresses the mechanical behavior of lattice materials based on flexible thermoplastic polyurethane (TPU) with honeycomb and gyroid architecture fabricated by 3D printing. Tensile, compression, and three-point bending tests were chosen as mechanical testing methods. The honeycomb architecture was found to provide higher values of rigidity (by 30%), strength (by 25%), plasticity (by 18%), and energy absorption (by 42%) of the flexible TPU lattice compared to the gyroid architecture. The strain recovery is better in the case of gyroid architecture (residual strain of 46% vs. 31%). TPUs with honeycomb architecture are characterized by anisotropy of mechanical properties in tensile and three-point bending tests. The obtained results are explained by the peculiarities of the lattice structure at meso- and macroscopic level and by the role of the pore space.

Microstructure, Texture and Mechanical Properties in Aluminum Produced by Friction-Assisted Lateral Extrusion.

The Friction-Assisted Lateral Extrusion Process (FALEP) is a severe plastic deformation (SPD) technique for producing metal sheets from bulk metal or powder in one single deformation step at room temperature. In the present work, aluminum Al-1050 was deformed by FALEP. Then, its microstructure was examined by EBSD; the crystallographic texture by X-ray; material strength, ductility, and the Lankford parameter by tensile testing; the latter also by polycrystal plasticity simulations. It is shown that the microstructure was highly refined, with the grain size reduced more than 160 times down to 600 nm under the imposed shear strain of 20. The obtained texture was a characteristic simple shear texture with a shear plane nearly parallel to the plane of the sheet. The yield and ultimate strengths increased by about 10 times and three times, respectively. The Lankford parameter was 1.28, which is very high for aluminum, and due to the specific shear texture, unusual in a sheet. All these exceptional characteristics of Al-1050 were obtained thanks to the efficiency of the FALEP SPD process, which is a promising candidate for industrial applications.

The Earth's Lithosphere Inspires Materials Design.

Structural patterns found in living organisms have long been inspiring biomimetic materials design. Here, it is suggested that a rich palette of patterns occurring in inanimate Nature, and especially in the Earth's lithosphere, could be not less inspirational for design of novel architectured materials. This materials design paradigm is referred to as lithomimetics and it is demonstrated that some of the patterns found in the lithosphere can be emulated by established processes of severe plastic deformation. This opens up interesting avenues for materials design in which potentially promising structural patterns are borrowed from the lithosphere's repository. The key aim here is to promulgate the "lithomimetics" paradigm as a promising approach to developing novel architectured materials.

Mechanical Modelling of the Plastic Flow Machining Process.

A new severe plastic deformation process, plastic flow machining (PFM), was introduced recently to produce sheet materials with ultrafine and gradient structures from bulk samples in one single deformation step. During the PFM process, a part of a rectangular sample is transformed into a thin sheet or fin under high hydrostatic pressure. The obtained fin is heavily deformed and presents a strain gradient across its thickness. The present paper aims to provide better understanding about this new process via analytical modelling accompanied by finite element simulations. PFM experiments were carried out on square commercially pure aluminum (CP Al) billets. Under pressing, the material flowed from the horizontal channel into a narrow 90° oriented lateral channel to form a fin sheet product, and the remaining part of the sample continued to move along the horizontal channel. At the opposite end of the bulk sample, a back-pressure was applied to increase the hydrostatic pressure in the material. The experiments were set at different width sizes of the lateral channel under two conditions; with or without applying back-pressure. A factor called the lateral extrusion ratio was defined as the ratio between the volume of the produced fin and the incoming volume. This ratio characterizes the efficiency of the PFM process. The experimental results showed that this ratio was greater when back-pressure was applied and further, it increased with the rise of the lateral channel width size. Finite element simulations were conducted in the same boundary conditions as the experiments using DEFORM-2D/3D software, V11.0. Two analytical models were also established. The first one used the variational principle to predict the lateral extrusion ratio belonging to the minimum total plastic power. The second one employed an upper-bound approach on a kinematically admissible velocity field to describe the deformation gradient in the fin. The numerical simulations and the analytical modelling successfully predicted the experimental tendencies, including the deformation gradient across the fin thickness.

The self-similarity theory of high pressure torsion.

By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to ß q , with ß being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval ß, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of ß. The results obtained have important practical implications for the proper design and analysis of HPT experiments.