Quasicontinuum Simulations Research Articles

Effects of tool rake angle and workpiece surface roughness on nanocutting of cu investigated using Multiscale simulation

ABSTRACT The effects of tool rake angle and workpiece surface roughness on the cutting mechanism and mechanics of Cu are studied using quasi-continuum simulations. These effects are investigated in terms of atomic trajectories, stress distribution, cutting force, resistance factor, and cutting ratio. The simulation results show that negative rake angles lead to a larger cutting force, lower resistance coefficient, and higher cutting ratio than those obtained with positive rake angles. For tools with an initial rake angle of 2° to 8°, the rake angle becomes negative during the cutting process due to the strong adhesion interaction between the tool rake face and chips. The resistance coefficient decreases with increasing tool rake angle for rake angles in the range of 2° to 8°. Tools with negative rake angles of −2° to −8° have similar cutting ratios. The cutting ratio decreases and cutting force increases with increasing surface roughness of the workpiece.

A refinement indicator for adaptive quasicontinuum approaches for structural lattices

AbstractThe quasicontinuum (QC) method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse‐grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria—that drive refining coarse‐grained regions and/or increasing fully‐resolved regions—are generally associated with quantities relevant to the atomistic scale. In this contribution, a new refinement indicator is presented, based on the energies of dedicated cells at coarse‐grained domain surfaces. This indicator is incorporated in an adaptive scheme of a generalization of the QC method able to consider periodic representative volume elements, like the ones employed in most computational homogenization approaches. However, this indicator can also be used for conventional QC frameworks. Illustrative numerical examples of elastic indentation and scratch of different lattices demonstrate the capabilities of the refinement indicator and its impact on adaptive QC simulations.

Effects of constituting material and interfacial crack on mechanical response of nanoscale metallic bilayers – a quasi-continuum study

ABSTRACT The effects of the constituting material and an interfacial crack on the deformation and mechanical response of metallic bilayer films under tension are studied using quasi-continuum simulations in terms of atomic trajectories, stress distribution and the stress–strain curve. The simulation results show that bilayer films with identical constituting monolayers have higher tensile strength than that of those with different monolayers. For bilayer films with different monolayers, the layer interface acts as a barrier that resists dislocation propagation. Dislocation emission at a crack tip blunts the tip. Necking originates at the layer interface and develops on monolayers with relatively low strength. A rectangular crack is less likely to develop than a V-shaped crack.

FRACTURE AND CRACK PROPAGATION OF METALLIC BILAYERS USING QUASI-CONTINUUM SIMULATIONS

The effects of the constituting material, initial crack length, and crystal orientation on the fracture and mechanics of bilayers with an interface crack under tension are studied using quasi-continuum simulations in terms of atomic trajectories, strain distribution, the stress-strain curve, and the crack growth-strain curve. The simulation results show that at the initial tension stage, the bilayers exhibit linear elasticity regardless of initial crack length and constituting material. With an increase in initial crack length at a layer interface, the yield stress, yield strain, and ultimate stress of the bilayers decrease. Bilayers with along er initial crack under tension have faster crack growth. Bilayers with a structural orientation of [020] versus [101̅] have lower mechanical strength compared to that of those with structural orientations of [100] versus [010] and [1̅10] versus [010]. The Ni/Ni bilayer has the highest yield stress and ultimate stress under tension.

Effects of mold pattern characteristics on nanoimprinted aluminum investigated using quasi-continuum simulations

The effects of mold pattern characteristics on the mechanical deformation and mechanics of nanoimprinted aluminum are studied using quasi-continuum simulations in terms of atomic trajectories, strain distribution, and the imprinting stress-mold displacement curve. The simulation results show that a mold whose pattern has a larger period (S value) produces a larger imprinting stress on the substrate for deformation. The effect of mold taper angle on imprinting stress depends on the S value. The required imprinting stress for substrate deformation decreases when mold wear occurs, resulting in the appearance of more non-local atoms in the substrate because of a nonuniform stress distribution. The nucleation and propagation of dislocations in the substrate are significantly confined when the S value is very small (e.g., 150 Å).

Quasicontinuum Simulation of the Effect of Lotus-Type Nanocavity on the Onset Plasticity of Single Crystal Al during Nanoindentation.

Stress concentration around nanosized defects such as cavities always leads to plastic deformation and failure of solids. We investigate the effects of depth, size, and shape of a lotus-type nanocavity on onset plasticity of single crystal Al during nanoindentation on a (001) surface using a quasicontinuum method. The results show that the presence of a nanocavity can greatly affect the contact stiffness (Sc) and yield stress (σy) of the matrix during nanoindentation. For a circular cavity, the Sc and σy gradually increase with the cavity depth. A critical depth can be identified, over which the Sc and σy are insensitive to the cavity depth and it is firstly observed that the nucleated dislocations extend into the matrix and form a y-shaped structure. Moreover, the critical depth varies approximately linearly with the indenter size, regarding the same cavity. The Sc almost linearly decreases with the cavity diameter, while the σy is slightly affected. For an ellipsoidal cavity, the Sc and σy increase with the aspect ratio (AR), while they are less affected when the AR is over 1. Our results shed light in the mechanical behavior of metals with cavities and could also be helpful in designing porous materials and structures.

Nanowelding of nickel and copper investigated using quasi-continuum simulations

The effects of contact interference, crystal orientation, and material type on the cold nanowelding mechanism and mechanics are studied using quasi-continuum simulations. These effects are investigated in terms of atomic trajectories, strain distribution, and the stress–strain curve. The simulation results show that welding using a contact interference of 0 nm leads to the formation of the fewest defects inside the material during cold welding, and that the number of defects increases with increasing contact interference. For the Ni–Ni welding pair, welding using a contact interference of 0 nm with the structural orientation [110] versus [001] has the largest ultimate strength and longest elongation during tensile testing due to the formation of fewer defects during welding. The welding quality obtained with the Ni–Ni welding pair is higher than that obtained with Ni–Cu and Cu–Cu welding pairs. During the tensile deformation process, dislocations nucleate from the free surface, propagate along the close-packed plane, and then terminate at the other free surface.

Quasi-continuum simulations of side-to-side nanowelding of metals

The effects of contact length, crystal orientation, and material type of welded pairs on side-to-side nanowelding are studied using quasi-continuum simulations. These effects are investigated in terms of atomic trajectories, strain distributions, and stress-strain curves. The simulation results show that the welding strength of welded pairs increases with decreasing contact length, regardless of their structural orientations. Welding with structural orientations of [Formula: see text] (for one nanowire) and [111] (for the other nanowire) results in a significant yield phenomenon during the separation process due to the migration of the deformation region from the root of tips to the interior of the top tip above the welding interface. Welding with structural orientations of [111] and [Formula: see text] results in relatively poor elasticity and ductility. For welding with one type of material, during the separation process, damage may occur at the top tip instead of at the welding interface. The welding strength of the Ni-Ni welded pair is higher than those of the Ni-Cu and Cu-Cu welded pairs.

ADAPTIVE QUASICONTINUUM SIMULATION OF ELASTIC-BRITTLE DISORDERED LATTICES

The quasicontinuum (QC) method is a computational technique that can efficiently handle atomistic lattices by combining continuum and atomistic approaches. In this work, the QC method is combined with an adaptive algorithm, to obtain correct predictions of crack trajectories in failure simulations. Numerical simulations of crack propagation in elastic-brittle disordered lattices are performed for a two-dimensional example. The obtained results are compared with the fully resolved particle model. It is shown that the adaptive QC simulation provides a significant reduction of the computational demand. At the same time, the macroscopic crack trajectories and the shape of the force-displacement diagram are very well captured.

Quasicontinuum simulations of geometric effect on onset plasticity of nano-scale patterned lines

Onset plasticity of metallic nano-lines or nano-beams is of considerable scientific and technological interest in micro-/nano- mechanics and interconnects of patterned lines in electronic devices, where capability of resistance to deformation is important. In this study, a multiscale quasicontinuum (QC) method was used to explore such an issue in a nano-scale copper (Cu) line protruding from a relatively large single crystal Cu substrate during compression. The results show that the yield stress of a rectangular beam on the substrate can be greatly reduced compared with that of a flat surface of the same area. For the rectangular line, the aspect ratio (width/height) affects dislocation morphology at the onset plasticity without much change of yield stress. However, for the trapezoidal line, the yield stress decreases with the base angle (α), especially when the α is over 54.7°. As the sidewall orientation changes from 〈100〉 at α = 0°, then to 〈111〉 at α = 54.7° and finally to 〈110〉 at α = 90°, a higher surface energy could enable easier dislocation formation and lower yield stress. Meanwhile, it is found that the interaction between the line and the support substrate also shows a great effect on yield stress. Moreover, although it is possible to open two extra dislocation slip planes inside from the two bottom corners of the Cu line with the α over 54.7°, dislocation nucleation derived from them is only observed at α = 90°.

A Hessian-free Newton–Raphson method for the configuration of physics systems featured by numerically asymmetric force field

Numerically asymmetric force field is examined in particle-oriented problems such as Quasicontinuum modeling and simulation. To configure the ground state of a large-scale physical system featured by numerically asymmetric force field, we propose a Hessian-free Newton–Raphson method where the Newton equation is solved using central-difference based BiCGstab algorithm (denoted as HFNR-BiCGstab-diff for simplicity). A detailed analytical and experimental investigation on the convergence performance of the HFNR-BiCGstab-diff algorithm is given in this paper. A pure HFNR-BiCGstab-diff algorithm may suffer from unreliable start-up, particularly in the case that the initial guess is far from the minimizer. As a remedy, a hybrid method that couples HFNR-BiCGstab-diff with preconditioned nonlinear conjugate gradient algorithm (PNCG) is developed to achieve optimal computational performance. The algorithms addressed in this paper have been implemented using POSIX-Thread C++. Their performance has been evaluated using three-dimensional Quasicontinuum simulation problems, which are featured by asymmetric force field and large dimensional sizes up to 122,808 degree-of-freedom, as benchmarks. The numerical experiment on IBM SP2 demonstrates that, compared to alternative unconstrained optimization methods such as preconditioned nonlinear conjugate gradient algorithm, the hybrid algorithm saves 20%–60% running time.

Quasicontinuum Simulation of Nanotextile Based on the Microplane Model

The quasicontinuum (QC) method is a relatively new computational technique, which combines fast continuum and exact atomistic approaches. The key idea of QC is to reduce the computational cost by reducing degrees of freedom of the fully atomistic approach. In this work, a material model based on the idea of microplanes is used to realize the QC simplification. A formulation convenient for numerical simulation of materials with the structure similar to nanotextile is proposed. The relations between microscopic and macroscopic parameters are derived. Numerical tests show that the proposed model can reach a significant reduction of computational cost for the price of an acceptable error.

Nanoindentation simulation of coated aluminum thin film using quasicontinuum method

Two-dimensional quasicontinuum simulations of nanoindentation processes are conducted on aluminum thin films with nickel, copper, and silver coatings of different thicknesses under various indenter widths using the embedded atom method (EAM) potentials. To study the effects of protective coating on the mechanical behavior of coated aluminum thin films, the nanoindentation process is performed to determine the hardness, the critical indentation load for first dislocation emission, the critical indentation depth and other associated physical phenomena, such as defect nucleation and evolution beneath the indenter. The obtained results reveal that surface coatings at nanoscale contacts may have a pronounced effect on the perceived hardness of the surface. Aluminum thin films with nickel and copper coatings can adopt the hardness and critical indentation load of the coating material, whereas silver coating cannot improve the aluminum hardness at nanoscale contacts. The critical indentation depth increases with the decrease of coating thickness, which indicates that a softening phenomenon happens in the coated aluminum thin film. The critical indentation depth and the critical indentation load increase with the increase of the indenter width, while the indentation hardness decreases as the indenter width increases. The results are shown to be in good agreement with limited available experimental data and the analytical Rice–Thomson and Peierls–Nabarro dislocation models.

Indenter size effect on the reversible incipient plasticity of Al (001) surface: Quasicontinuum study**Project supported by the National Natural Science Foundation of China (Grant No. 51172040), the National Basic Research Program of China (Grant No. 2011CB606403), and the General Project of Scientific Research from Liaoning Educational Committee, China (Grant No. L2014135).

Indenter size effect on the reversible incipient plasticity of Al (001) surface is studied by quasicontinuum simulations. Results show that the incipient plasticity under small indenter, the radius of which is less than ten nanometers, is dominated by a simple planar fault defect that can be fully removed after withdrawal of the indenter; otherwise, irreversible incipient plastic deformation driven by a complex dislocation activity is preferred, and the debris of deformation twins, dislocations, and stacking fault ribbons still remain beneath the surface when the indenter has been completely retracted. Based on stress distributions calculated at an atomic level, the reason why the dislocation burst instead of a simple fault ribbon is observed under a large indenter is the release of the intensely accumulated shear stress. Finally, the critical load analysis implies that there exists a reversible-irreversible transition of incipient plasticity induced by indenter size. Our findings provide a further insight into the incipient surface plasticity of face-centered-cubic metals in nano-sized contact issues.

Indenter Size Effect on the Reversible Incipient Plasticity of Al (001) Surface Studied via Quasicontinuum Simulations

Indenter size effect on the reversible incipient plasticity of Al (001) surface is studied by quasicontinuum simulations. Two cylindrical indenters with the radii 2.5nm and 17.5nm are used to penetrate the surface respectively, in displacement-control in steps of 0.02 nm. Results show that the plasticity under the small indenter is reversible, since it is dominated by the nucleation of a thin deformation twin, which can be fully removed after withdrawal of the indenter, due to the imaging force and stacking fault energy. Under the large indenter, multiple slip systems are activated simultaneously when incipient plasticity occurs, a few twin, dislocation and stacking fault ribbons still remain under the surface when the indenter has been completely retracted, thus the plasticity is irreversible.

Strain Fields around Dislocation Cores Studied by Analyzing Coordinates of Discrete Atoms

Dislocation core structures in Au and Cu crystals are investigated by means of quasicontinuum simulations combined with the embedded atom method potentials. A dislocation pair in a graphene sheet, which is observed by Warner et al. experimentally, is also analyzed in the present work. The strain fields around these dislocations in Au, Cu, and graphene crystals are calculated by analyzing the coordinates of discrete atoms, which is a strain tensor calculation method proposed by Zimmerman et al., and compared with theoretical predictions based on Foreman dislocation model. It is shown that the strain fields given by Zimmerman theory are completely suitable for describing the dislocation core structures of Au, Cu and graphene crystals. However, compared with the results of Au and Cu, the Zimmerman strain field in the vicinity of graphene dislocation core is a little less accurate, possibly due to the effect of lattice symmetry of graphene, which needs to be clarified in the future study.

Summation rules for a fully nonlocal energy-based quasicontinuum method

The quasicontinuum (QC) method coarse-grains crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. A crucial cornerstone of all QC techniques, summation or quadrature rules efficiently approximate the thermodynamic quantities of interest. Here, we investigate summation rules for a fully nonlocal, energy-based QC method to approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of all atoms in the crystal lattice. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. We review traditional summation rules and discuss their strengths and weaknesses with a focus on energy approximation errors and spurious force artifacts. Moreover, we introduce summation rules which produce no residual or spurious force artifacts in centrosymmetric crystals in the large-element limit under arbitrary affine deformations in two dimensions (and marginal force artifacts in three dimensions), while allowing us to seamlessly bridge to full atomistics. Through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions, we compare the accuracy of the new scheme to various previous ones. Our results confirm that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors. Our numerical benchmark examples include the calculation of elastic constants from completely random QC meshes and the inhomogeneous deformation of aggressively coarse-grained crystals containing nano-voids. In the elastic regime, we directly compare QC results to those of full atomistics to assess global and local errors in complex QC simulations. Going beyond elasticity, we illustrate the performance of the energy-based QC method with the new second-order summation rule by the help of nanoindentation examples with automatic mesh adaptation. Overall, our findings provide guidelines for the selection of summation rules for the fully nonlocal energy-based QC method.

Multiscale computational modeling of deformation mechanics and intergranular fracture in nanocrystalline copper

This study presents the development and validation of a two-scale numerical method aimed at predicting the mechanical behavior and the inter-granular fracture of nanocrystalline (NC) metals under deformation. The material description is based on two constitutive elements, the grains (or bulk crystals) and the grain-boundaries (GBs). Their behaviors are determined atomistically using the quasicontinuum (QC) method by simulating the plastic deformation of [11‾0] tilt crystalline interfaces undergoing simple shear, tension and nano-indentation. Unlike our previous work (Péron-Lührs et al., 2013) however, the GB thickness is here calibrated in the model, providing more accurate insight into the GB widths according to the interface misorientation angle. In this contribution, the new two-scale model is also validated against fully-atomistic NC simulation tests for two low-angle and high-angle textures and two grain sizes. A simplified strategy aimed at predicting the mechanical behavior of more general textures without the need to run more QC simulations is also proposed, demonstrating significant reductions in the computational cost compared to full atomistic simulations. Finally, by studying the response of dogbone samples made of NC copper, we show in this paper that such a two-scale model is able to quantitatively capture the differences in mechanical behavior of NC metals as a function of the texture and grain size, as well as to accurately predict the processes of inter-granular fracture for different GB character distributions. This two-scale method is found to be an effective alternative to other atomistic methods for the prediction of plasticity and fracture in NC materials with a substantial number of 2-D grains such as columnar-grained thin films for micro-scale electro-mechanical devices.

Entropically Stabilized Dislocations

Dislocations are line defects that play a key role in the plasticity of crystalline materials and affect their thermal, chemical, and electrical properties. Typically dislocations are treated as stable defects; e.g., the equilibrium core structure of a dislocation is obtained by minimizing the crystal potential energy with respect to atom positions. Here we show for the first time the possibility of "entropically stabilized dislocations" that exist due to entropic effects without a corresponding potential energy well. An entropically stabilized dislocation was discovered in an accelerated multiscale quasicontinuum simulation. Its entropic nature was verified with fully atomistic free energy calculations and explained by a simple continuum-based model. This result has important consequences for the study of dislocations as well as for temporal multiscale methods that use information from the potential energy surface to accelerate time in molecular simulations.

“Positive” and “negative” edge dislocations simultaneously interacting with Σ11 GB during nanoindentation

Quasicontinuum simulations of “positive” and “negative” dislocations simultaneously interacting with Σ11 symmetrical tilt grain boundary (GB) during nanoindentation reveal two distinctive dislocation/GB interactions depending on the indenter size h and demarcated by a potential independent critical indenter size h¯cr. When h is less than h¯cr, lattice dislocations are eliminated by a reflected dislocation from dislocation-GB interaction. Meanwhile, less grain boundary dislocations (GBDs) are emitted. However, when h is greater than h¯cr, the “positive” and “negative” dislocations nucleate separately and interact with GB dependently due to one interaction site absorbing GBDs nucleated from another interaction site. The resulted GB configuration shows a regularly-stepped shape. Studies of a free-standing dissociated dislocation dipole (DP) shows that, hcr, depending on potentials, is a critical distance between two extended dislocations of a DP, at which the DP transforms configuration between stacking fault overlapping and non-overlapping configuration. The full edge DP model based on continuum theory, which does not take the strong interactions between partial dislocations into account, fails to predict hcr.