Materials Theory最新文献

Crystal plasticity primarily arises from the motion and interactions of dislocations. Consequently, one may expect a continuum theory of plasticity to emerge as a statistical continuum theory of interacting ‘particles’ – where these particles are, in fact, dislocations, i.e., extended and flexible moving curves. Due to the long range elastic interactions between dislocations, pair correlations play an important role for the emerging plastic characteristics of crystals. For these systems correlations arise not only from the relative positions of different dislocations (pair correlations) but also from non-trivial self correlations that reflect the geometry of individual dislocations as connected lines. The self correlations reflect interactions between segments of the same dislocation, which, for example, yield a tendency for dislocations to be straight. These self correlations need to be understood because they usually dominate numerically obtained correlation data from dislocation distributions.

In this paper, we derive analytical expressions for self correlations in various hypothetical dislocation configurations which can serve as approximations for more general dislocation systems. The most general configurations we analyse are uncorrelated dislocations that form circular loops with a given distribution of radii. Additionally, we also derive pair correlations in various dipole-like configurations of dislocation pairs.

Furthermore, we examine the radius distribution obtained from discrete dislocation dynamics simulations and show that these match radius distributions obtained from a maximum information entropy ansatz considering dislocation curvature. Our results suggest that to obtain a physically meaningful radius distribution within this maximum information entropy framework, an additional curvature-related variable must be introduced – one that has not yet been considered in continuum dislocation dynamics.

Existing phase field (diffuse interface) models for void evolution in solids are not quantitative, in the sense that they do not capture the physics of the sharp interface counterpart. In this work, we introduce a thermodynamically consistent, quantitative phase field model for void evolution in crystalline solids under irradiation. This model considers both vacancies and self-interstitials in the description of void evolution. Unique to this model is fixing the evolution of the non-conserved order parameter describing void surface dynamics by two contributions associated with the interactions of vacancies and interstitials with the void surface by incorporating two mobility parameters in the corresponding Allen–Cahn equation. Asymptotic matching of the phase field model with the sharp-interface theory fixed the two Allen–Cahn mobility parameters in terms of the kinetics of the point defect-surface reactions. The Landau and the gradient coefficients in the free energy construction of the system in its diffuse-interface description are fixed using thermodynamic arguments in terms of the interfacial energy and diffuse interface width. With all the parameters in the phase model clearly expressed in terms of the sharp interface counterparts, we have a novel, quantitative phase field formalism for void evolution in the presence of point defects. To validate this new formalism, several simple test cases were carried out showing the void evolution under simple defect supersaturation scenarios.

The mean nearest-neighbor distance is an important clustering/ordering metric in quantitative spatial analysis of microstructures; especially for materials containing particles or voids. Nearest-neighbor distance (d_NN) distributions in three-dimensional (3D), random-sequential-addition, uniform, hard-sphere, computer-generated patterns have been studied for volume fractions from 0.0001 to 0.35. Normal distributions can well fit these d_NN distributions and they provide insight into the study of nearest-neighbor (NN) metrics such as means, medians, and modes. Furthermore, we report on the development of an estimator for the 3D mean d_NN (μ_NN) based upon stochastic tiling. Stochastic tiling models involve random rotations of polyhedral space-filling tiles which allows the calculation of the probabilities for d_NN distributions. Solutions are presented for volume fractions ≈0.10 to the cubic theoretical maximum of ≈0.52. Extrapolating solutions to lower volume fractions also provides reasonable estimates. There is good agreement between the μ_NN estimates compared to the computer-generated random patterns. In the volume fraction region where deviations from these estimates exist, there is an apparent transition in the relationship between the fitted normal distribution means and the NN distance means at a volume fraction ≈0.25. Suggestions for areas of future research are highlighted.

Graphical Abstract

A personal, but quite general viewpoint on current morphogenic plasticity developments is given by elaborating on dislocation patterning and deformation bands with an eye on Nasr Ghoniem’s pioneering contributions to material instabilities. It is based on the gradient approach advocated by the author in the early 1980s and subsequently pursued by him and his co-workers, as well as other leading scientists, including Ghoniem himself. Since the physical origin of plastic flow in metals is due to the existence of dislocations, a brief discussion on the removal of classical elasticity singularities for this type of line defects is provided based on a gradient modification of Hooke’s law and its extension to also include fractional and fractal effects. The article will thus first briefly revisit early efforts on pattern-forming instabilities in plasticity and then discuss the need for combined gradient-stochastic models to capture plastic heterogeneity phenomena at small scales. It will continue with listing easy-to-use fractional/fractal dislocation solutions for potential implementation to respective dislocation-based computer simulations and conclude with a few remarks on possible extensions of the Laplacian-based gradient approach described herein to other multiscale/multiphysics phenomena. The last topic is an open issue that has not been pursued as yet in the material physics and mechanics community. Even though some of our new unpublished results are preliminary and sporadically shared with the community in conference presentations available at the internet, it is hoped that they can still inspire a much-needed collective collaboration and more elaborate interdisciplinary studies in the near future.

The investigation of strain hardening in metals is complex, with the outcome depending on experimental conditions, that may involve microstructural history, temperature and loading rate. Hardening is commonly measured, after mechanical processing, through controlled mechanical testing, in ways that either distinguish elastic (stress) from total deformation measurements, or by identifying plastic slip contributions. In this paper, we conjecture that hardening effects can be unraveled through statistical analysis of total strain fluctuations during the evolution sequence of profiles, measured in-situ, through digital image correlation. In particular, we hypothesize that the work hardening exponent is related, through a power-law relationship, to a particular exponent arising from principal component analysis. We demonstrate a scaling analysis for synthetic data produced by widely applicable crystal plasticity models for polycrystalline solids.

Graphical Abstract

Precipitation hardening, a cornerstone of alloy strengthening, finds widespread application in engineering materials. Comprehending the underlying mechanisms and formulating models bear crucial significance for engineering applications. While classical macroscopic theoretical models based on the line tension model have historically guided research efforts, their reliance on simplifications, assumptions, and parameter adjustments limits their predictability and expansibility. Moreover, the challenge of understanding the intricate coupling effects among various hardening mechanisms persists. One fundamental question to achieve the transition of material design paradigms from empirical trial-and-error methods to predictive-and-design approaches is to develop more physics-based multiscale modelling methods. This review aims to elucidate the physical mechanisms governing precipitation hardening and establish a tailored bottom-up multiscale modelling framework to steer the design of new alloys. The physical scenarios of precipitation hardening are firstly summarized, including particle shearing, Orowan bypass, and dislocation cross-slip and climb. Afterwards, an in-depth discussion is given regarding the application of macroscopic models and their correlation with the mechanisms and precipitation characteristics. As for the multiscale modelling methods, we categorize them into three main types: slip resistance based approaches, misfit stress field based approaches, and energy based approaches. By integrating multiscale modelling with the physical scenarios, we systematically addressed the key idea of the multiscale coupling framework, and their scale transfer procedure, applicability, advantages, and limitations. Some examples of coupling different types of multiscale methods and considering precipitates with complicated shapes are also presented. This study not only furnishes insightful comprehension of precipitation hardening, but also guides the development of multiscale modelling methodologies for other types of hardening effects in alloys.

The mechanical behavior of most metals in engineering applications is dominated by the grain size. Physics-based models of the interaction between dislocations and the grain boundary are important to correctly predict the plastic deformation behavior of polycrystalline materials. Dislocation-grain boundary interaction is complex and a challenge to model. We present a model for simulating the physical transmission of dislocations through grain boundaries within Discrete Dislocation Dynamics tools. The properties (glide plane, Burgers vector, initial length) of the transmitted dislocation are chosen based on geometric criteria as well as a maximization of the resolved shear stress of the transmitted dislocation. Additionally, stress and displacement transparency as well as the discontinuity are ensured via a grain boundary dislocation – a butterfly-like geometry in the general case – whose properties are selected to minimize the residual Burgers vector at the interface. This additional ‘grain boundary dislocation’ allows a direct comparison as well as a calibration of the model with experiments on the macroscale particularly for neighboring grains with a high dislocation density contrast. Two basic examples illustrate the model and an application to a 40-grain polycrystal demonstrates the scalability of the approach.

During plastic flow in metals, dislocations from slip systems with different glide planes collide to form junctions. After being in-residence within the dislocation network for some period of time, these junctions then break, thereby liberating the attached dislocation lines. In this work we use random forest discrete dislocation dynamics simulations to quantify the junction formation rate and junction residence time as a function of stress for all junction types in face-centered cubic metals. We then relate these quantities to the dislocation link-length distribution, which is found to exhibit an exponential form. This enables us to quantify the mean junction strength and also the slip system interaction coefficients. Finally, using the link-length model we obtain a flow rule for our systems which is physics-based with all parameters determined from DDD simulations. The insights here provide a path forward for a dislocation network theory of plastic flow based on the link-length distribution.

The increase in the yield stress due to the presence of obstacles to dislocation motion such as precipitates is a multiscale phenomenon. The details on the nanoscale when an individual dislocation runs into a precipitate play an important role in determining plasticity on a macroscopic scale. The classical analysis of this phenomenon is due to Bacon, Kocks and Scattergood (BKS) from early 1970’s and has been followed by a large body of work both developing the theory and applying it to real experiments and their understanding. Beyond the microscopic details the next level of complexity is met in the micrometer scale when the physics of the yielding and the yield stress depend on two mechanisms: the dislocation-precipitate interaction, and the collective dynamics of the whole ensemble of dislocations in the volume. In this review we discuss the BKS relation and collective dislocation dynamics in precipitation-hardened crystals in the light of recent research, including large-scale discrete dislocation dynamics simulations, statistical physics ideas, and machine learning developments.

Stress-driven segregation at dislocations can lead to structural transitions between different linear complexion states. In this work, we examine how platelet array linear complexions affect dislocation motion and quantify the associated strengthening effect in Al-Cu alloys using atomistic simulations. The presence of platelet complexions leads to the faceting of the dislocations, with nanoscale segments climbing upwards along the platelet growth direction, resulting in a complex configuration that restricts subsequent dislocation motion. Upon deformation, the leading partial dislocation must climb down from the platelet complexions first, followed by a similar sequence at the trailing partial dislocation, in order to overcome the precipitates and commence plastic slip. The dislocation depinning mechanism of linear complexions is strikingly different from traditional precipitation-strengthened alloys, where dislocations overcome obstacles by either shearing through or looping around obstacles. The critical shear stress required to unpin dislocations from platelet complexions is found to be inversely proportional to precipitate spacing, which includes not just the open space (as observed in Orowan bowing) but also the region along the platelet particle where climb occurs. Thus, linear complexions provide a new way to modify dislocation structure directly and improve the mechanical properties of metal alloys.