M.F. Horstemeyer

LENGTH SCALE AND TIME SCALE EFFECTS ON THE PLASTIC FLOW OF FCC METALS

We examine size scale and strain rate effects on single-crystal face-centered cubic (fcc) metals. To study yield and work hardening, we perform simple shear molecular dynamics simulations using the embedded atom method (EAM) on single-crystal nickel ranging from 100 atoms to 100 million atoms and at strain rates ranging from 107 to 1012 s−1. We compare our atomistic simulation results with experimental data obtained from interfacial force microscopy (IFM), nano-indentation, micro-indentation and small-scale torsion. The data are found to scale with a geometric length scale parameter defined by the ratio of volume to surface area of the samples. The atomistic simulations reveal that dislocations nucleating at free surfaces are critical to causing micro-yield and macro-yield in pristine material. The increase of flow stress at increasing strain rates results from phonon drag, and a simple model is developed to demonstrate this effect. Another important aspect of this study reveals that plasticity as reflected by the global averaged stress–strain behavior is characterized by four different length scales: (1) below 104 atoms, (2) between 104 and 106 atoms (2 μm), (3) between 2 μm and 300 μm, and (4) above 300 μm.

Microstructure-based fatigue modeling of cast A356-T6 alloy

Abstract High cycle fatigue (HCF) life in cast Al–Mg–Si alloys is particularly sensitive to the combination of microstructural inclusions and stress concentrations. Inclusions can range from large-scale shrinkage porosity with a tortuous surface profile to entrapped oxides introduced during the pour. When shrinkage porosity is controlled, the relevant microstructural initiation sites are often the larger Si particles within eutectic regions. In this paper, a HCF model is introduced which recognizes multiple inclusion severity scales for crack formation. The model addresses the role of constrained microplasticity around debonded particles or shrinkage pores in forming and growing microstructurally small fatigue cracks and is based on the cyclic crack tip displacement rather than linear elastic fracture mechanics stress intensity factor. Conditions for transitioning to long crack fatigue crack growth behavior are introduced. The model is applied to a cast A356-T6 Al alloy over a range of inclusion severities.

Interpretations of Indentation Size Effects

For very shallow indentations in W, Al, Au, and Fe-3wt%Si single crystals, hardness decreased with increasing depth irrespective of increasing or decreasing strain gradients. As such, strain gradient theory appears insufficient to explain the indentation size effect (ISE) at depths less than several hundred nanometers. Present research links the ISE to a ratio between the energy of newly created surface and plastic strain energy dissipation. Also, the contact surface to plastic volume ratio was nearly constant for a range of shallow depths. Based on the above, an analytical model of hardness versus depth provides a satisfactory fit to the experimental data and correlates well with embedded atom simulations. @DOI: 10.1115/1.1469004#

Modeling stress state dependent damage evolution in a cast Al–Si–Mg aluminum alloy

Abstract Internal state variable rate equations are cast in a continuum framework to model void nucleation, growth, and coalescence in a cast Al–Si–Mg aluminum alloy. The kinematics and constitutive relations for damage resulting from void nucleation, growth, and coalescence are discussed. Because damage evolution is intimately coupled with the stress state, internal state variable hardening rate equations are developed to distinguish between compression, tension, and torsion straining conditions. The scalar isotropic hardening equation and second rank tensorial kinematic hardening equation from the Bammann–Chiesa–Johnson (BCJ) Plasticity model are modified to account for hardening rate differences under tension, compression, and torsion. A method for determining the material constants for the plasticity and damage equations is presented. Parameter determination for the proposed phenomenological nucleation rate equation, motivated from fracture mechanics and microscale physical observations, involves counting nucleation sites as a function of strain from optical micrographs. Although different void growth models can be included, the McClintock void growth model is used in this study. A coalescence model is also introduced. The damage framework is then evaluated with respect to experimental tensile data of notched Al–Si–Mg cast aluminum alloy specimens. Finite element results employing the damage framework are shown to illustrate its usefulness.

A void–crack nucleation model for ductile metals

Abstract A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.

Atomistic simulations on the tensile debonding of an aluminum–silicon interface

Abstract In this paper we present Modified Embedded Atom Method (MEAM) simulations of the deformation and fracture characteristics of an incoherent interface between pure FCC aluminum and diamond cubic silicon. As a first approximation, the study only considers the normal tensile separation of a [100] interface with the principal crystallographic axis of the aluminum and the silicon aligned. The MEAM results show that the relaxed interface possesses a rippled structure, instead of a planar atomic interface, and such ripples act as local stress concentrators and initiation sites for interfacial failure. The stress–strain (traction–displacement) response of aluminum and silicon blocks attached at an interface depends on the distance from the interface that the boundary conditions are applied, i.e. the size of the atomic blocks, and the location of the measured opening displacement. Point vacancy defects near the interface are found to decrease the maximum normal tensile stress that the interface can support at a rate almost linearly proportional to the number fraction of the dispersed defects. A crack-like vacancy defect in the bulk aluminum or silicon must reach an area fraction (projected to the surface normal to the tensile axis) of about 50 or 30%, respectively, in order to shift the failure from the interface to the bulk materials. It is further demonstrated that the present results are consistent with continuum-based traction separation laws, provided that the opening displacement is measured near the physical boundary of the deforming cohesive zone (±10 A from the boundary of the Al–Si interface). As the opening displacements are measured farther from the interface, the traction–displacement response approaches that of classical linear elastic fracture mechanics.

Global response approximation with radial basis functions

In this article, a study is performed on the accuracy of radial basis functions (RBFs) in creating global metamodels for both low- and high-order nonlinear responses. The response surface methodology (RSM), which typically uses linear or quadratic polynomials, is inappropriate for creating global models for highly nonlinear responses. The RBF, on the other hand, has been shown to be accurate for highly nonlinear responses when the sample size is large. However, for most complex engineering applications only limited numbers of samples can be afforded; it is desirable to know whether the RBF is appropriate in this situation, especially when the augmented RBF has to be used. Because the types of true responses are typically unknown a priori, it is essential for high-fidelity metamodeling to have an RBF or RBFs that are appropriate for linear, quadratic, and higher-order responses. To this end, this study compares a variety of existing basis functions in both non-augmented and augmented forms with various types of responses and limited numbers of samples. This article shows that the augmented RBF models created by Wu’s compactly supported functions are the most accurate for the various test functions used in this study.

Atomistic finite deformation simulations: A discussion on length scale effects in relation to mechanical stresses

In this study, atomistic finite deformation calculations employing the Embedded Atom Method show three items of interest related to continuum field theory. First, a spatial size scale effect on the yield stress is found. In these calculations, mechanical yield point occurred from dislocation initiation at the edge of the numerical specimens. The spatial size scale continued to affect the plastic response up to strains of 30 percent in simple shear for nickel oriented at . The second point is related to the continuum mechanics observation about oscillating global shear stress under simple shear conditions is shown to dampen as the spatial size scale increases. As the spatial length scale increases, the continuum rotational effect coupled with the increase in dislocation population reduces the oscillatory behavior. This confirms the notion proposed by Bammann and Aifantis (1987) in that when more dislocations are initiated with different orientations of the Burgers vectors then the oscillations decrease. Finally, a length scale bridging idea is proposed by relating a continuum single degree offreedom loss coefficient, which relates the plastic energy to the total strain energy, to varying sizes of blocks of atoms. This study illustrates the usefulness of employing the Embedded Atom Method to study mechanisms related to continuum mechanics quantities.

Modified embedded atom method potential for Al, Si, Mg, Cu, and Fe alloys

A set of modified embedded atom method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element’s MEAM potential in order to study metal alloying. Previously published MEAM parameters of single elements have been improved for better agreement to the generalized stacking fault energy (GSFE) curves when compared with ab initio generated GSFE curves. The MEAM parameters for element pairs were constructed based on the structural and elastic properties of element pairs in the NaCl reference structure garnered from ab initio calculations, with adjustment to reproduce the ab initio heat of formation of the most stable binary compounds. The new MEAM potentials were validated by comparing the formation energies of defects, equilibrium volumes, elastic moduli, and heat of formation for several binary compounds with ab initio simulations and experiments. Single elements in their ground state crystal structure were subjected to heating to test the potentials at elevated temperatures. An Al potential was modified to avoid formation of an unphysical solid structure at high temperatures. The thermal expansion coefficient of a compound with the composition of AA 6061 alloy was evaluated and compared with experimental values. MEAM potential tests performed in this work, utilizing the universal atomistic simulation environment (ASE), are distributed to facilitate reproducibility of the results.

Computational nanoscale plasticity simulations using embedded atom potentials

Abstract In determining structure–property relations for plasticity at different size scales, it is desired to bridge concepts from the continuum to the atom. This raises many questions related to volume averaging, appropriate length scales of focus for an analysis, and postulates in continuum mechanics. In a preliminary effort to evaluate bridging size scales and continuum concepts with descritized phenomena, simple shear molecular dynamics simulations using the Embedded Atom Method (EAM) potentials were performed on single crystals. In order to help evaluate the continuum quantities related to the kinematic and thermodynamic force variables, finite element simulations (with different material models) and macroscale experiments were also performed. In this scoping study, various parametric effects on the stress state and kinematics have been quantified. The parameters included the following: crystal orientation (single slip, double slip, quadruple slip, octal slip), temperature (300 and 500 K), applied strain rate (10 6 – 10 12 s −1 ), specimen size (10 atoms to 2 μm), specimen aspect ratio size (1:8–8:1), deformation path (compression, tension, simple shear, and torsion), and material (nickel, aluminum, and copper). Although many conclusions can be drawn from this work, which has provided fodder for more studies, several major conclusions can be drawn. • The yield stress is a function of a size scale parameter (volume-per-surface area) that was determined from atomistic simulations coupled with experiments. As the size decreases, the yield stress increases. • Although the thermodynamic force (stress) varies at different size scales, the kinematics of deformation appears to be very similar based on atomistic simulations, finite element simulations, and physical experiments. Atomistic simulations, that inherently include extreme strain rates and size scales, give results that agree with the phenomenological attributes of plasticity observed in macroscale experiments. These include strain rate dependence of the flow stress into a rate independent regime; approximate Schmid type behavior; size scale dependence on the flow stress, and kinematic behavior of large deformation plasticity.