Marisol Koslowski

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic ‘butterfly’ curves; and others.

A multi-phase field model of planar dislocation networks

In this paper we extend the phase-field model of crystallographic slip of Ortiz (1999 J. Appl. Mech. ASME 66 289–98) and Koslowski et al (2001 J. Mech. Phys. Solids 50 2957–635) to slip processes that require the activation of multiple slip systems, and we apply the resulting model to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane is described by means of multiple integer-valued phase fields. We show how all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field. The model is used to ascertain stable dislocation structures arising in an array of finite twist boundaries. These structures are found to consist of regular square or hexagonal dislocation networks separated by complex dislocation pile-ups over the intervening transition layers.

Mesoscale modeling of dislocations in molecular crystals

Understanding the inelastic deformation of molecular crystals is of fundamental importance to the modeling of the processing of drugs in the pharmaceutical industry as well as to the initiation of detonation in high energy density materials. In this work, we present dislocation dynamics simulations of the deformation of two molecular crystals of interest in the pharmaceutical industry, sucrose and paracetamol. The simulations calculate the yield stress of sucrose and paracetamol in good agreement with experimental observation and predict the anisotropy in the mechanical response observed in these materials. Our results show that dislocation dynamics is an effective tool to study plastic deformation in molecular crystals.

Scaling laws in plastic deformation

In crystalline materials, plastic deformation is driven by the non-local long-range interaction of dislocations. This interaction is responsible for a series of features that obey scaling laws, such as the formation of fractal cellular structures, the intermittent plastic flow with scale-free avalanches following a power law and the Hall–Petch relation in which the yield stress depends on the sample size following a power law. A phase-field model of dislocations is described. The present theory is able to reproduce the jerky character of dislocation motion as well as size dependence in small-scale plasticity.

Large-Scale 3D Phase Field Dislocation Dynamics Simulations On High-Performance Architectures

In this paper we present the development and performance of a three-dimensional phase field dislocation dynamics (3D PFDD) model for large-scale dislocation-mediated plastic deformation on high-performance architectures. Through the parallelization of this algorithm, efficient run times can be achieved for large-scale simulations. The algorithm’s performance is analyzed over several computing platforms including Infiniband, GigE, and proprietary (SiCortex) interconnects. Scalability is considered on data sets up to 2,0483, along with the efficiency on up to 2,048 processors. Results show that scalability improves as the size of the data set increases and that the overall performance is best on the Infiniband interconnect. In addition, a performance model has been developed to predict run times and efficiency on large sets of data running on multiple processors. This performance analysis shows that this parallel code is capable of harnessing the greater computer power available from petascale systems.

An Experimental and Theoretical Investigation of Creep in Ultrafine Crystalline Nickel RF-MEMS Devices

The creep behavior of ultrafine crystalline RF microelectromechanical systems (RF-MEMS) devices is investigated in this paper. The RF-MEMS devices are characterized through a highly accurate capacitance-sensing setup, under a special bi-state bias condition. In particular, the devices are kept continuously biased (on-state) for up to 1400 h, but the bias voltage is momentarily removed for 1 min every hour in order to record the off-state capacitance. Measurements at two bias voltages of 20 and 40 V are reported. The capacitance measurement uncertainty is less than 200 aF and the long-term stability is better than 4 fF throughout the measurement period. Furthermore, we report the creep behavior under the same bi-state bias condition through independent direct optical measurements conducted with a confocal microscope-based setup. The measurement uncertainty for the vertical displacement reported in these measurements is less than 50 nm. These measurements show for the first time the entire profile evolution of the deflected beams and membranes for up to 168 h. Both the capacitance and optical measurements reveal the same trends for the creep behavior of the devices. A physics-based creep model for the ultrafine crystalline nickel devices is also included in this paper. The required model parameters are obtained by fitting the simulation results to the measured creep curve under a bias voltage of 20 V. Using the same material parameters and geometry, this model correctly captures the rate of deformation during the steady-state creep stage at 40 V. The model reveals that the observed steady-state creep deformation at both 20 and 40 V is dominated by Coble creep.

Dynamics of surface-coupled microcantilevers in force modulation atomic force microscopy – magnetic vs. dither piezo excitation

Force modulation atomic force microscopy is widely used for mapping the nanoscale mechanical properties of heterogeneous or composite materials using low frequency excitation of a microcantilever scanning the surface. Here we show that the excitation mode – magnetic or dither piezo, has a major influence on the surface-coupled microcantilever dynamics. Not only is the observed material property contrast inverted between these excitation modes but also the frequency response of the surface-coupled cantilever in the magnetic mode is near-ideal with a clear resonance peak and little phase distortion thus enabling quantitative mapping of the local mechanical properties.

Engineering curvature in graphene ribbons using ultrathin polymer films.

We propose a method to induce curvature in graphene nanoribbons in a controlled manner using an ultrathin thermoset polymer in a bimaterial strip setup and test it via molecular dynamics (MD) simulations. Continuum mechanics shows that curvature develops to release the residual stress caused by the chemical and thermal shrinkage of the polymer during processing and that this curvature increases with decreasing film thickness; however, significant deformation is only achieved for ultrathin polymer films. Quite surprisingly, explicit MD simulations of the curing and annealing processes show that the predicted trend not just continues down to film thicknesses of 1-2 nm but that the curvature development is enhanced significantly in such ultrathin films due to surface tension effects. This combination of effects leads to very large curvatures of over 0.14 nm(-1) that can be tuned via film thickness. This provides a new avenue to engineer curvature and, thus, electromagnetic properties of graphene.

Phase-field modeling of defect nucleation and propagation in domains with material inhomogeneities

We present a phase-field approach that couples the representation of material heterogeneities with discontinuities in the displacement field to describe defects and damage evolution. This method in contrast to discrete models does not require topological changes in the mesh representation reducing the complexity in the implementation of the numerical simulation. Both defects and material inhomogeneities are described in terms of phase fields and their evolution and interaction follows from a set of analogous equations delivering a unified theory that couples the response of heterogeneous materials with displacement discontinuities seamlessly. We show the effectiveness of the model by predicting dislocation structures in a 3D periodic array of voids in nickel single crystal and the nucleation and evolution of crazes in polymethyl methacrylate.

PUQ: A code for non-intrusive uncertainty propagation in computer simulations

Abstract We present a software package for the non-intrusive propagation of uncertainties in input parameters through computer simulation codes or mathematical models and associated analysis; we demonstrate its use to drive micromechanical simulations using a phase field approach to dislocation dynamics. The PRISM uncertainty quantification framework (PUQ) offers several methods to sample the distribution of input variables and to obtain surrogate models (or response functions) that relate the uncertain inputs with the quantities of interest (QoIs); the surrogate models are ultimately used to propagate uncertainties. PUQ requires minimal changes in the simulation code, just those required to annotate the QoI(s) for its analysis. Collocation methods include Monte Carlo, Latin Hypercube and Smolyak sparse grids and surrogate models can be obtained in terms of radial basis functions and via generalized polynomial chaos. PUQ uses the method of elementary effects for sensitivity analysis in Smolyak runs. The code is available for download and also available for cloud computing in nanoHUB. PUQ orchestrates runs of the nanoPLASTICITY tool at nanoHUB where users can propagate uncertainties in dislocation dynamics simulations using simply a web browser, without downloading or installing any software. Program summary Program title: PUQ Catalogue identifier: AEWP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEWP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: MIT license No. of lines in distributed program, including test data, etc.: 45075 No. of bytes in distributed program, including test data, etc.: 3318862 Distribution format: tar.gz Programming language: Python, C. Computer: Workstations. Operating system: Linux, Mac OSX. Classification: 4.11, 4.12, 4.13. External routines: SciPy, Matplotlib, h5py Nature of problem: Uncertainty propagation and creation of response surfaces. Solution method: Generalized Polynomial Chaos (gPC) using Smolyak sparse grids. Running time: PUQ performs uncertainty quantification and sensitivity analysis by running a simulation multiple times using different values for input parameters. Its run time will be the product of the run time of the chosen simulation code and the number of runs required to achieve the desired accuracy.