The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.

Influence of Hot Band Annealing on Cold-Rolled Microstructure and Recrystallization in AA 6016

The influence of an intermediate heat treatment at the end of hot rolling and before cold rolling on Cube texture formation during the final solution annealing of AA 6016 is investigated. Three hot bands with different initial grain sizes and textures are considered: the first one without annealing before cold rolling, while the other two hot bands are heat treated at 540 °C for 1 hour in air before being cold rolled. One of the heat-treated hot bands was left to cool down in air and the other inside the furnace. Electron-backscatter diffraction (EBSD) maps of the cold-rolled specimens and crystal plasticity simulations show no difference in the amount of Cube remaining in the microstructure at the end of cold rolling for all three specimens. The initial grain size of the hot band has no influence on the Cube texture fraction left in the microstructure at the end of cold rolling for thickness reductions higher than 65 pct. Nevertheless, the grain size of the hot band affects the shape and distribution of the Cube grains left in the microstructure and the kernel average misorientation in the cold-rolled specimens. Moreover, the heat treatment decreases the intensity of the beta fiber components (Brass, Copper, and S) in the hot band and promotes the formation of a cold-rolled microstructure with a low kernel average misorientation. Both these factors lower the probability of preferential Cube nucleation during solution annealing and keep the Cube volume fraction after recrystallization below 10 pct, while it reaches 25 pct without intermediate annealing

Depinning transition and thermal fluctuations in the random-field Ising model

We analyze the depinning transition of a driven interface in the 3d random-field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111]-direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3d-RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.Comment: 6 pages, including 9 figures, submitted for publicatio

2-loop Functional Renormalization Group Theory of the Depinning Transition

We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the non-analytic form of the dynamical action. This cures the inability of the 1-loop flow-equations to distinguish between statics and quasi-static depinning, and thus to account for the irreversibility of the latter. We prove two-loop renormalizability, obtain the 2-loop beta-function and show the generation of "irreversible" anomalous terms, originating from the non-analytic nature of the theory, which cause the statics and driven dynamics to differ at 2-loop order. We obtain the roughness exponent zeta and dynamical exponent z to order epsilon^2. This allows to test several previous conjectures made on the basis of the 1-loop result. First it demonstrates that random-field disorder does indeed attract all disorder of shorter range. It also shows that the conjecture zeta=epsilon/3 is incorrect, and allows to compute the violations, as zeta=epsilon/3 (1 + 0.14331 epsilon), epsilon=4-d. This solves a longstanding discrepancy with simulations. For long-range elasticity it yields zeta=epsilon/3 (1 + 0.39735 epsilon), epsilon=2-d (vs. the standard prediction zeta=1/3 for d=1), in reasonable agreement with the most recent simulations. The high value of zeta approximately 0.5 found in experiments both on the contact line depinning of liquid Helium and on slow crack fronts is discussed.Comment: 32 pages, 17 figures, revtex

Current Challenges and Opportunities in Microstructure-Related Properties of Advanced High-Strength Steels

This is a viewpoint paper on recent progress in the understanding of the microstructure–property relations of advanced high-strength steels (AHSS). These alloys constitute a class of high-strength, formable steels that are designed mainly as sheet products for the transportation sector. AHSS have often very complex and hierarchical microstructures consisting of ferrite, austenite, bainite, or martensite matrix or of duplex or even multiphase mixtures of these constituents, sometimes enriched with precipitates. This complexity makes it challenging to establish reliable and mechanism-based microstructure–property relationships. A number of excellent studies already exist about the different types of AHSS (such as dual-phase steels, complex phase steels, transformation-induced plasticity steels, twinning-induced plasticity steels, bainitic steels, quenching and partitioning steels, press hardening steels, etc.) and several overviews appeared in which their engineering features related to mechanical properties and forming were discussed. This article reviews recent progress in the understanding of microstructures and alloy design in this field, placing particular attention on the deformation and strain hardening mechanisms of Mn-containing steels that utilize complex dislocation substructures, nanoscale precipitation patterns, deformation-driven transformation, and twinning effects. Recent developments on microalloyed nanoprecipitation hardened and press hardening steels are also reviewed. Besides providing a critical discussion of their microstructures and properties, vital features such as their resistance to hydrogen embrittlement and damage formation are also evaluated. We also present latest progress in advanced characterization and modeling techniques applied to AHSS. Finally, emerging topics such as machine learning, through-process simulation, and additive manufacturing of AHSS are discussed. The aim of this viewpoint is to identify similarities in the deformation and damage mechanisms among these various types of advanced steels and to use these observations for their further development and maturation.</p

A multi-scale crystal plasticity model for cyclic plasticity and low-cycle fatigue in a precipitate-strengthened steel at elevated temperature

peer-reviewedIn this paper, a multi-scale crystal plasticity model is presented for cyclic plasticity and low-cycle fatigue in a tempered martensite ferritic steel at elevated temperature. The model explicitly represents the geometry of grains, sub-grains and precipitates in the material, with strain gradient effects and kinematic hardening included in the crystal plasticity formulation. With the multiscale model, the cyclic behaviour at the sub-grain level is predicted with the effect of lath and precipitate sizes examined. A crystallographic, accumulated slip (strain) parameter, modulated by triaxiality, is implemented at the micro scale, to predict crack initiation in precipitate-strengthened laths. The predicted numbers of cycles to crack initiation agree well with experimental data. A strong dependence on the precipitate size is demonstrated, indicating a detrimental effect of coarsening of precipitates on fatigue at elevated temperature. (C) 2016 Elsevier Ltd. All rights reserved.ACCEPTEDpeer-reviewe

Universal scaling behavior of non-equilibrium phase transitions

One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to a given universality class have the same critical exponents, and certain scaling functions become identical near the critical point. It is the aim of this work to demonstrate the usefulness of universal scaling functions for the analysis of non-equilibrium phase transitions. In order to limit the coverage of this article, we focus on a particular class of non-equilibrium critical phenomena, the so-called absorbing phase transitions. These phase transitions arise from a competition of opposing processes, usually creation and annihilation processes. The transition point separates an active phase and an absorbing phase in which the dynamics is frozen. A systematic analysis of universal scaling functions of absorbing phase transitions is presented, including static, dynamical, and finite-size scaling measurements. As a result a picture gallery of universal scaling functions is presented which allows to identify and to distinguish universality classes.Comment: review article, 160 pages, 60 figures include