W.A. Curtin

Atomistic/continuum coupling in computational materials science

Important advances in multi-scale computer simulation techniques for computational materials science have been made in the last decade as scientists and engineers strive to imbue continuum-based models with more-realistic details at quantum and atomistic scales. One major class of multi-scale models directly couples a region described with full atomistic detail to a surrounding region modelled using continuum concepts and finite element methods. Here, the development of such coupled atomistic/continuum models is reviewed within a single coherent framework with the aim of providing both non-specialists and specialists with insight into the key ideas, features, differences and advantages of prevailing models. Some applications and very recent advances are noted, and important challenges for extending these models to their fullest potential are discussed.

CNT-reinforced ceramics and metals

Recent research on the incorporation of carbon nanotubes (CNTs) into ceramic and metal matrices to form composite structures is briefly reviewed, with an emphasis on processing methods, mechanical performance, and prospects for successful applications.

Atomic mechanism and prediction of hydrogen embrittlement in iron

Hydrogen embrittlement in metals has posed a serious obstacle to designing strong and reliable structural materials for many decades, and predictive physical mechanisms still do not exist. Here, a new H embrittlement mechanism operating at the atomic scale in α-iron is demonstrated. Direct molecular dynamics simulations reveal a ductile-to-brittle transition caused by the suppression of dislocation emission at the crack tip due to aggregation of H, which then permits brittle-cleavage failure followed by slow crack growth. The atomistic embrittlement mechanism is then connected to material states and loading conditions through a kinetic model for H delivery to the crack-tip region. Parameter-free predictions of embrittlement thresholds in Fe-based steels over a range of H concentrations, mechanical loading rates and H diffusion rates are found to be in excellent agreement with experiments. This work provides a mechanistic, predictive framework for interpreting experiments, designing structural components and guiding the design of embrittlement-resistant materials.

A coupled atomistic/continuum model of defects in solids

Abstract A method is introduced for reducing the degrees of freedom in simulations of mechanical behavior of materials without sacrificing important physics. The method essentially combines the quasicontinuum (QC) method with continuum defect models such as the discrete dislocation (DD) method. The QC formulation is used to couple a fully atomistic region to a defect-free elastic continuum. Defects existing in the elastic continuum region of the full problem of interest are treated by the DD-like methods with special boundary conditions. The full coupled problem is then solved by an Eshelby-like procedure involving superposition of the QC and DD problems, and is appropriate in both 2d and 3d. Special attention is given to dealing with dislocation defects. A procedure for the “passing” of dislocation defects from the atomistic to the continuum description in 2d problems is also presented. The overall 2d method with dislocation defects is validated by comparing the predictions of the coupled model to “exact” fully atomistic models for several equilibrium dislocation geometries and a nanoindentation problem in aluminum, and excellent agreement is obtained. The method proposed here should find application to a broad host of problems associated with the multiscale modeling of atomistic, nano- and micromechanical behavior of crystalline solids under mechanical loads.

Stochastic Damage Evolution and Failure in Fiber-Reinforced Composites

Publisher Summary This chapter describes the stochastic damage evolution and failure in fiber-reinforced composites. The accomplishments in the area of modeling of the mechanical properties of fiber-reinforced composites are reviewed with an emphasis on accurately predicting ultimate tensile strength, stress–strain behavior, and reliability. The model composite studies consists of a volume fraction of continuous cylindrical fibers embedded in a matrix material in a unidirectional arrangement. The reinforcing fibers are generally brittle materials and so are linearly elastic up to the point of failure. The point of failure in any individual length of fiber is determined by the largest flaw or crack in that particular fiber. The interface between the fibers and matrix occupies a vanishing fraction of the total composite volume but plays a critical role in determining many composite properties related to damage and strength. In polymer and metal matrices, the interface becomes important when fibers break. In ceramic matrices, the interface is critical first when the matrix cracks and then again when the fibers break. It is found that increasing stress causes flaws to fail, slip/exclusion zones to form or increase in length, and exclusion zones to increasingly overlap until the entire fiber is subsumed within the exclusion zones and the test saturates. The in situ fiber strength and fracture mirrors are also elaborated.

Basal and prism dislocation cores in magnesium: comparison of first-principles and embedded-atom-potential methods predictions

A binary embedded-atom method (EAM) potential is optimized for Cu on Ag(111) by fitting to ab initio data. The fitting database consists of DFT calculations of Cu monomers and dimers on Ag(111), specifically their relative energies, adatom heights, and dimer separations. We start from the Mishin Cu-Ag EAM potential and first modify the Cu-Ag pair potential to match the FCC/HCP site energy difference then include Cu-Cu pair potential optimization for the entire database. The optimized EAM potential reproduce DFT monomer and dimer relative energies and geometries correctly. In trimer calculations, the potential produces the DFT relative energy between FCC and HCP trimers, though a different ground state is predicted. We use the optimized potential to calculate diffusion barriers for Cu monomers, dimers, and trimers. The predicted monomer barrier is the same as DFT, while experimental barriers for monomers and dimers are both lower than predicted here. We attribute the difference with experiment to the overestimation of surface adsorption energies by DFT and a simple correction is presented. Our results show that the optimized Cu-Ag EAM can be applied in the study of larger Cu islands on Ag(111).The core structures of screw and edge dislocations on the basal and prism planes in Mg, and the associated gamma surfaces, were studied using an ab initio method and the embedded-atom-method interatomic potentials developed by Sun et al and Liu et al. The ab initio calculations predict that the basal plane dislocations dissociate into partials split by 16.7 angstrom (edge) and 6.3 angstrom (screw), as compared with 14.3 angstrom and 12.7 angstrom (Sun and Liu edge), and 6.3 angstrom and 1.4 angstrom (Sun and Liu screw), with the Liu screw dislocation being metastable. In the prism plane, the screw and edge cores are compact and the edge core structures are all similar, while ab initio does not predict a stable prismatic screw in stress-free conditions. These results are qualitatively understood through an examination of the gamma surfaces for interplanar sliding on the basal and prism planes. The Peierls stresses at T = 0K for basal slip are a few megapascals for the Sun potential, in agreement with experiments, but are ten times larger for the Liu potential. The Peierls stresses for prism slip are 10-40MPa for both potentials. Overall, the dislocation core structures from ab initio are well represented by the Sun potential in all cases while the Liu potential shows some notable differences. These results suggest that the Sun potential is preferable for studying other dislocations in Mg, particularly the textless c + a textgreater dislocations, for which the core structures are much larger and not accessible by ab initio methods.

Failure of fiber composites : a lattice green function model

A new powerful numerical technique for investigating the failure of fiber reinforced composites is presented. The technique utilizes 3D lattice Greens functions to calculate load transfer from broken to unbroken fibers, and also includes the important effects of fiber/matrix sliding. The inherent flexibility of the technique in adjusting the spatial extent of load transfer allows for the study of many aspects of real composite failure processes which have been unobtainable to date. Using this technique, composite reliability, the influence of manufacturing defects on performance, and the overall optimization of composite performance can all be investigated in detail. Initial results using this approach show that load transfer and the existence of spatially-staggered fiber breaks play an important role in determining strength and toughness of composites. Furthermore, the critical configurations of fiber breaks that initiate catastrophic failure are complicated 3D objects and any single spatial plane is composed mainly of sliding fibers rather than broken fibers, with a few strong fibers intact within the critical defect.

The origins of high hardening and low ductility in magnesium

Magnesium is a lightweight structural metal but it exhibits low ductility—connected with unusual, mechanistically unexplained, dislocation and plasticity phenomena—which makes it difficult to form and use in energy-saving lightweight structures. We employ long-time molecular dynamics simulations utilizing a density-functional-theory-validated interatomic potential, and reveal the fundamental origins of the previously unexplained phenomena. Here we show that the key 〈c + a〉 dislocation (where 〈c + a〉 indicates the magnitude and direction of slip) is metastable on easy-glide pyramidal II planes; we find that it undergoes a thermally activated, stress-dependent transition to one of three lower-energy, basal-dissociated immobile dislocation structures, which cannot contribute to plastic straining and that serve as strong obstacles to the motion of all other dislocations. This transition is intrinsic to magnesium, driven by reduction in dislocation energy and predicted to occur at very high frequency at room temperature, thus eliminating all major dislocation slip systems able to contribute to c-axis strain and leading to the high hardening and low ductility of magnesium. Enhanced ductility can thus be achieved by increasing the time and temperature at which the transition from the easy-glide metastable dislocation to the immobile basal-dissociated structures occurs. Our results provide the underlying insights needed to guide the design of ductile magnesium alloys.

A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites

Abstract A new numerical model is proposed for simulating the mechanical behavior of unidirectional composites which is based on a three-dimensional (3D) shear-lag model. The 3D shear-lag model considers the micro-damage phenomena of interfacial debonding and interfacial yielding. In order to confirm the validity of the model, the calculated stress concentration is compared with the HVD model (Hedgepeth JM, Dyke P. Local stress concentrations in imperfect filamentary composite materials. J Comp Mater 1967;1:294–309) in the appropriate limit. Monte Carlo simulations with the present shear-lag model were then conducted to obtain the ultimate tensile strength (UTS) as a function of fiber strength and interfacial properties. The damage progression and formation of clusters versus the type of interfacial damage, and the size-scaling of the tensile strengths, are carefully examined. Coupled with a size-scaling analysis, model predictions for tensile strength show good agreement with experiment.

Quantitative prediction of solute strengthening in aluminium alloys

Despite significant advances in computational materials science, a quantitative, parameter-free prediction of the mechanical properties of alloys has been difficult to achieve from first principles. Here, we present a new analytic theory that, with input from first-principles calculations, is able to predict the strengthening of aluminium by substitutional solute atoms. Solute-dislocation interaction energies in and around the dislocation core are first calculated using density functional theory and a flexible-boundary-condition method. An analytic model for the strength, or stress to move a dislocation, owing to the random field of solutes, is then presented. The theory, which has no adjustable parameters and is extendable to other metallic alloys, predicts both the energy barriers to dislocation motion and the zero-temperature flow stress, allowing for predictions of finite-temperature flow stresses. Quantitative comparisons with experimental flow stresses at temperature T=78 K are made for Al-X alloys (X=Mg, Si, Cu, Cr) and good agreement is obtained.