Efficient Matrix Product State Method for periodic boundary conditions

We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ 100 - 1000 in typical cases. We test the method on the S=1/2 and S=1 Heisenberg chains. It is also applicable to non-translationally invariant cases. The new method makes ground state calculations with periodic boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.Comment: Final published versio

SPD deformation of pearlitic, bainitic and martensitic steels

The deformation behavior of nearly fully pearlitic, bainitic and martensitic steels during severe plastic deformation is summarized in this paper. Despite their significantly different yield stresses and their microstructures, their hardening behavior during SPD is similar. Due to the enormous hardening capacity the SPD deformation is limited by the strength of the tool materials. The microstructure at the obtainable limit of strain are quite similar, which is a nanocrystalline structure in the order of 10 nm, dependent on the obtainable strain. The nanograins are partially supersaturated with carbon and the grain boundaries are stabilized by carbon. Another characteristic feature is the anisotropy in grain shape which results in an anisotropy of strength, ductility and fracture toughness. The results are important for the development of ultra-strong materials and essential for this type of steels which are frequently used for application where the behavior under rolling contact and sliding contact is important

Thermal stabilization of metal matrix nanocomposites by nanocarbon reinforcements

Metal matrix composites reinforced by nanocarbon materials, such as carbon nanotubes or nanodiamonds, are very promising materials for a large number of functional and structural applications. Carbon nanotubes and nanodiamonds-reinforced metal matrix nanocomposites with different concentrations of the carbon phase were processed by high-pressure torsion deformation and the evolving nanostructures were thoroughly analyzed by electron microscopy. Particular emphasis is placed on the thermal stability of the nanocarbon reinforced metal matrix composites, which is less influenced by the amount of added nanocarbon reinforcements than by the nanocarbon reinforcement type and its distribution in the metal matrix

How the interface type manipulates the thermomechanical response of nanostructured metals : A case study on nickel

The presence of interfaces with nanoscale spacing significantly enhances the strength of materials, but also the rate controlling processes of plastic flow are subject to change. Due to the confined grain volumes, intragranular dislocation-dislocation interactions, the predominant processes at the micrometer scale, are replaced by emission of dislocations from and their subsequent accommodation at the interfaces. Both processes not only depend on the interfacial spacing, but also on the atomistic structure of the interface. Hence, a thorough understanding how these processes are affected by the interface structure is required to predict and improve the behavior of nanomaterials. The present study attempts to rationalize this effect by investigating the thermomechanical behavior of samples consisting of three different interfaces. Pure nickel samples with predominant fractions of low- and high-angle as well as twin boundaries with a similar average spacing around 150 nm are investigated using high temperature nanoindentation strain rate jump tests. Depending on the interface structure, hardness, strain rate sensitivity and apparent activation volumes evolve distinctively different with testing temperature. While in case of high-angle boundaries for all quantities a pronounced thermal dependence is found, the other two interface types behave almost athermal in the same temperature range. These differences can be rationalized based on the different interfacial diffusivity, affecting the predominant process of interfacial stress relaxation

Nanostructure and properties of a Cu-Cr composite processed by severe plastic deformation

A Cu-Cr composite was processed by severe plastic deformation to investigate the role of interphase boundaries on the grain size reduction mechanisms. The as-deformed material exhibits a grain size of only 20nm. This gives rise to a dramatic increase of the hardness. Some deformation induced Cu super saturated solid solutions were clearly exhibited and it is shown that they decrease the hardness. The formation of such supersaturated solid solution and their influence on the mechanical properties are discussed

Effects of microstructure and crystallography on crack path and intrinsic resistance to shear-mode fatigue crack growth

The paper focuses on the effective resistance and the near-threshold growth mechanisms in theferritic-pearlitic and the pure pearlitic steel. The influence of microstructure on the shear-mode fatigue crackgrowth is divided here into two factors: the crystal lattice type and the presence of different phases.Experiments were done on ferritic-pearlitic steel and pearlitic steel using three different specimens, for whichthe effective mode II and mode III threshold values were measured and fracture surfaces were reconstructed inthree dimensions using stereophotogrammetry in scanning electron microscope. The ferritic-pearlitic andpearlitic steels showed a much different behaviour of modes II and III cracks than that of the ARMCO iron.Both the deflection angle and the mode II threshold were much higher and comparable to the austenitic steel.Mechanism of shear-mode crack behaviour in the ARMCO iron, titanium and nickel were described by themodel of emission of dislocations from the crack tip under a dominant mode II loading. In other testedmaterials the cracks propagated under a dominance of the local mode I. In the ferritic-pearlitic and pearliticsteels, the reason for such behaviour was the presence of the secondary-phase particles (cementite lamellas),unlike in the previously austenitic steel, where the fcc structure and the low stacking fault energy were the mainfactors. A criterion for mode I deflection from the mode II crack-tip loading, which uses values of the effectivemode I and mode II thresholds, was in agreement with fractographical observations

Real Hydrostatic Pressure in High-Pressure Torsion Measured by Bismuth Phase Transformations and FEM Simulations

Hydrostatic pressure is a significant parameter influencing the evolution of microstructure and phase transformations in the high-pressure torsion (HPT) process. Currently, there are significant arguments relating to the magnitude of the real hydrostatic pressure during the process. In this study, phase transformations in bismuth, copper and titanium combined with the finite element method (FEM) were employed to determine the real pressure in processing disc samples by HPT. Any break in the variation of steady-state hardness (monitored experimentally by in-situ torque and temperature rise measurements) versus pressure was considered as a phase transition. FEM simulations show that the hydrostatic pressure is reasonably isotropic but decreases with increasing distance from the disc center and remains unchanged across the disc thickness. Both experiments and simulations indicate that the mean hydrostatic pressure during HPT processing closely corresponds to the compressive load over the disc area plus the contact area between the anvils.1166Ysciescopu