We report here on recent work aimed at clarifying the definition of various atomic-level stress measures and the relationships between them. We also offer a definition for the local elastic constants. Finally, we examine the convergence of volume-averaged versions of these quantities to their continuum counterparts as the length scale, the radius of the averaging volume in the present case, approaches the continuum scale.

Multiscale plastic deformation in the heat affected zone (HAZ) of a Ni-based single crystal superalloy has been characterized using white microbeam synchrotron diffraction measurements together with OIM imaging, electron and optical microscopy. Characteristic length scales on the macro, meso and nano scale are determined. Dissolution of the γ' – phase particles during heating and secondary precipitation of γ' – phase during cooling is found, as well as formation and multiplication of dislocations. This process is more intense as one approaches the fusion line (FL). In the regions immediately neighboring the FL, γ' - phase particles dissolve completely and reprecipitate from the solid solution in the form of very small (50-70nm) particles. In the immediate vicinity of the FL, the temperature gradient and the rate of it's change reaches maximal values and causes the formation of large amounts of dislocations. Dislocations are concentrated in the ã matrix of the single crystal superalloy. X-ray Laue diffraction (both conventional and microbeam) and electron microscopy show that alternating dislocations slip systems dominate in the HAZ with typical Burgers vector b=[110]. Local lattice rotations in different zones of the weld joint are linking with the microslip events in different zones of the weld.

Simulating radiation damage production and evolution in materials is a problem spanning many orders of magnitude in both time and length scales. Therefore, any one simulation method will be inadequate for studying radiation damage. We apply several modeling techniques to study radiation damage in oxides, specically MgO, Al-doped MgO and MgAl2O4 spinel. We use molecular dynamics to simulate damage production in collision cascades, where energies between 400 eV and 5 keV were investigated. The kinetic behavior of the resulting defects was probed on long time scales using temperature accelerated dynamics. Molecular statics was used to calculate fundamental properties of these defects, and density functional theory calculations support the basic results of the empirical potential studies. Finally, a chemical rate theory model is developed to understand the impact of the atomic scale behavior on dislocation loop size.

With models being developed at different levels of observation, length scales become an issue. In particular for simulation models that have to line-up and be compatible, this issue requires due attention. Different approaches can be adopted to bridge these length scales, each with their own pros and cons. In this contribution, two different approaches to deal with the scale differences in models for hardening concrete structures will be presented. Based on the parameters involved in the stress calculation of hardening concrete (macro)structures, the approaches are clarified. The first approach is based on the “bridging” concept whereas the second approach follows the Ribbon concept. Both concepts are discussed in terms of length scale bridging and its consequences for the modelling results. The paper ends with a discussion about the parameter variations related to the different length scales by means of a probabilistic approach.

A Kraton® poly (styrene-ethylene/butylene-styrene) (SEBS) Triblock copolymer, with hexagonally packed PS cylinders embedded within the Poly (ethylene/butylene) (E/B) matrix, has been studied using simultaneous small- and wide-angle X-ray diffraction (SAXD/WAXD) as a function of mechanical deformation. SAXD studies on unstrained samples not only show a series of concentric diffraction rings, that index as the successive orders of a two-dimensional hexagonal lattice of side a ≈ 30 nm, but also indicate the presence of a broader, more diffuse, diffraction ring of a different character centered at a spacing of 7.8 nm. At 65% strain, a four-point X-cross pattern develops and emerges from the {1010} diffraction ring for the unstrained sample. The fundamental spacing of the hexagonal lattice increases, and in addition the first evidence of discrete layer lines appears, orthogonal to the strain direction (SD). At higher strains, both the layer line spacing and the angle of the X-cross, relative to the SD, increase. These changes in layer line spacing as a function of strain provide additional insight into the extent of deformation imposed on the flexible matrix with shearing of PS cylinders layers relative to each other. Also, with increasing strain, the diffuse 7.8 nm diffraction signal transforms into a streak, parallel to the SD and centered on a reciprocal plane orthogonal to the SD. In the simultaneously recorded WAXD (4 nm-0.2 nm) patterns, an initial single diffraction ring observed at no strain, steadily transforms with strain into a symmetric pair of concentrated arcs centered on the equator. These X-ray diffraction results enable a delineation to be made between rotation and relative shear of layers of PS rods and the simultaneous strain-induced crystallization of the flexible matrix.

Even though semi-crystalline polymers are closer to composite, even nano-composite material, little work has been done to predict their properties as in the case of composite or filled polymer. In their work Halpin and Kardos [1] proposed to determine the elastic modulus of semi-crystalline polymers. The lamellae are supposed to be like fibers. An adjustable parameter in this model was linked to the crystallite shape ratio. However, this model is well adapted for low volume fraction, which is not the case of semi-crystalline materials like Polypropylene (PP) and Polyethylene (PE). Other authors were interested in the evolution of the microstructure and large deformation of the semi-crystalline polymer using a new developed model [2]. The main ideas of the model were adapted by other authors to predict the elasto-visco-plastic behavior [3,4]. The predicted initial modulus variation of PE versus the crystalline fraction does not fit the experimental values. The aim of our work is to establish a relationship between the microstructure and elastic properties of the semicrystalline polymer. To fulfill this goal, experimental investigations of two kinds of polymers, Polypropylene and Polyethylene, are done. Micro-mechanical models are tested in order to choose which model is better adapted for these materials. A comparison of modeling and experiments will be presented.

Cryomilling is a method of producing nanostructured morphologies from a range of starting metals and alloys. This process substantially increases the strength of lightweight alloys. In this work, we characterize the microstructure of Al alloy 5083 following cryomilling, hot isostatic pressing (HIP), and extrusion. The yield strength of the cryomilled 5083 Al is approximately twice that of conventional wrought 5083 Al and the room temperature microhardness essentially is unchanged following annealing at temperatures that approach 0.8 Tm. Using complementary transmission electron microscopy (TEM) techniques such as energy filtered (EFTEM) and weak beam imaging we investigate the mechanisms responsible for the mechanical properties. A survey of the microstructure identifies several sources of strengthening. These include: submicron grain sizes in the as-extruded material, precipitates, and metal-oxide phases. Also, the Mg in the alloy is expected to contribute some solid solution strengthening. TEM images show that lattice dislocations frequently are pinned at the precipitate interfaces. Continued precipitation and grain boundary pinning by oxide particles at elevated temperatures may account for the persistence of hardness following annealing.

This paper presents a computationally intensive, multiscale constitutive model for 3D-woven composites exhibiting progressive damage. The model is based on analysis of a representative volume element (RVE), which is derived from the actual woven architecture. The link between the local phenomena and the overall response is described by a transformation field analysis (TFA) in terms of stress concentration factors and influence function, which reflect the microgeometry and properties of the constituents. In this way, the local geometric and physical effects are represented in the model with substantial details so that the local stress and strain fields and the overall response could be accurately computed. It seems to be a reliable approach to capture the effects of the material heterogeneity and damage on wave dispersion and attenuation in shockwave problems. The RVE/TFA-based constitutive model was implemented into the DYNA finite element code, and simulations of shock and impact problems were performed to describe the various damage mechanisms. The TFA model is computationally intensive and requires massively parallel computing. This paper examines the effects of the local field representation, and the in situ damage phenomena on the overall response.

A mesoscopic simulation methodology has been used to investigate the effect of the initial grain size distribution and grain boundary (GB) mobilities on the development of abnormal grain growth in a single-phase polycrystalline material. Our studies show that regardless of the initial grain size distribution, in the absence of variability in GB properties, the system evolves by normal grain growth characterized by a uniform self-similar grain-size distribution, i.e. the presence of a few large grains in the initial microstructure does not promote abnormal grain growth. On the contrary, the presence of a limited set of grains having GBs with higher mobilities may lead to abnormal grain growth provided the biased GB mobility values are larger than certain threshold values. Kinetic and topological aspects of normal to abnormal grain growth transition are investigated.

The self-affine character of the fracture surfaces of metals, polymers and ceramics has been well documented over the past two decades. It has been established that these surfaces are selfaffine objects characterized by so called ‘universal’ roughness exponents independent of the microstructure and the loading conditions. Here we show that the self-affine correlation length is closely associated with the microstructure heterogeneities. We also explore the possibility of the existence of attractor values that govern the fracture process, as opposed to universal exponents. The possible origin of this behavior is also briefly discussed.

First-principles generalized pseudopotential theory (GPT) provides a fundamental basis for transferable multi-ion interatomic potentials in transition metals and alloys within density-functional quantum mechanics. In central bcc transition metals, where multi-ion angular forces are important to structural properties, simplified model GPT or MGPT potentials have been developed based on canonical d bands to allow analytic forms and large-scale atomistic simulations. Robust, advanced-generation MGPT potentials have now been obtained for Ta and Mo and successfully applied to a wide range of structural, thermodynamic, defect and mechanical properties at both ambient and extreme conditions. Selected applications to multiscale modeling discussed here include dislocation core structure and mobility, atomistically informed dislocation dynamics simulations of plasticity, and thermoelasticity and high-pressure strength modeling. Recent algorithm improvements have provided a more general matrix representation of MGPT beyond canonical bands, allowing improved accuracy and extension to f-electron actinide metals, an order of magnitude increase in computational speed for dynamic simulations, and the still-in-progress development of temperature-dependent potentials.

Evidence of both solute drag as well as differences in migration mechanisms of certain boundary types has been found for an Al-Zr alloy. In-situ Transmission Electron Microscopy (TEM) annealing experiments coupled with Scanning Transmission Electron Microscopy (STEM) showed a stark contrast between Zr segregation at small and large scales. Specifically, Zr was found to segregate to, as well as precipitate at boundaries of grains smaller than 2 microns, whereas less segregation and no precipitation was found at large grains sizes, or long annealing times. Motivated by these results and those previously obtained by Orientation Imaging Microscopy (OIM), Local Electrode Atom Probe Microscopy with an Imago™ LEAP® microscope, was used to determine the concentrations of Zr and Al ions at grain boundaries; the results confirmed those from the STEM.

Underdamped dislocation motion through local pinning obstacles is studied computationally using a stochastic dislocation dynamics scheme. The global dislocation velocity is observed to be non-linearly stress dependent. Strongly non-Arrhenius dynamics are found at a higher stress range. The statistical analysis indicates that the correlation of the local dislocation kinetic energy is extended and exceeds the average obstacle spacing as temperature decreases, which can lead to the inertial dislocation bypass of the obstacles.

In this paper we present model calculations of the deformation of a glassy polymer film supported by a plastically deforming metal substrate. The focus is on the resulting roughening of the free polymer surface. In the calculations a mixed-mode rate independent cohesive zone has been employed as the interface between the metal and the polymer. The mechanical behavior of the polymer is characterized by an elastic regime, a softening regime and finally a hardening regime. Above the yield point of the polymer shear bands occur that transfer the evolving roughness of the deforming metal through the polymer coating. It turns out that in this regime the resulting rms roughness at the free polymer surface may be higher than that of the underlying metal substrate. For this to occur the thickness of the coating must be higher than the correlation length of the rough metal substrate.

Advances in the development of multiscale failure models are dependent on the development of techniques for accurately characterizing the nature of spatial heterogeneity. Nth-nearest neighbor statistics offer a means of quantitatively and qualitatively characterizing deviation from complete spatial randomness (CSR). This investigation has determined the mean distances to the Nthnearest neighbor for CSR dispersions of monodisperse spheres in 2D and 3D for N up to 200. To evaluate data obtained from micrographs, mean Nth-nearest neighbor distances have also been collected for planar slices through 3D arrays of monodisperse spheres. Results are presented for a volume fraction of 0.20 in the form of an “Inhibition Ratio”, which compares the results collected for finite disks and spheres with the values expected for 2D and 3D point processes.

Shock-induced twinning and martensitic transformation in BCC-based polycrystalline metals (Ta and U-6wt%Nb) have been observed and studied using transmission electron microscopy (TEM). The length-scale of domain thickness for both twin lamella and martensite phase is found to be smaller than 100 nm. While deformation twinning of {112}<111>-type is found in Ta when shock-deformed at 15 GPa, both twinning and martensitic transformation are found in Ta when shock-deformed at 45 GPa. Similar phenomena of nanoscale twinning and martensitic transformation are also found in U6Nb shock-deformed at 30 GPa. Since both deformation twinning and martensitic transformation occurred along the {211}b planes associated with high resolved shear stresses, it is suggested that both can be regarded as alternative paths for shear transformations to occur in shock-deformed BCC metals. Heterogeneous nucleation mechanisms for shock-induced twinning and martensitic transformation are proposed and discussed.

The annihilations of screw dislocation dipoles via cross-slip in Cu were simulated using constant-temperature constant-stress molecular dynamics. The cross-slip mechanism and annihilation process of flexible dislocations in a large dipole configuration was identified as a dynamic variant of the Friedel-Escaig mechanism. The cross-slip rate was found to exhibit exponential dependence on the temperature, from which the activation enthalpy for the cross-slip process was calculated by the Arrhenius relation.

The objective of this investigation is to formulate a model to predict the theoretical strength for styrene-diene thermoplastic elastomers (TPEs) that takes into account the failure processes occurring at the molecular level. Styrenic TPEs may fail via either chain pull-out, in which the polystyrene (PS) end-blocks are pulled out of the glassy PS domains, or chain scission, in which the C-C bonds in the elastomer mid-blocks are ruptured. By relating the microscopic deformation of an individual chain to the macroscopic strain rate, the maximum force a chain can sustain is obtained. The theoretical strength of the material is then computed by determining the force sustained by the PS domains and matrix chain sections intersecting a planar unit area at the onset of failure. The model has been used to investigate the effect of PS molecular weight, PS content, and strain rate on the ultimate strength.

In the study the effect of scaling the material structure on the fracture behaviour of concrete is investigated. Next to this the size effect of concrete fracture strength and fracture energy is studied. The fracture mechanism of concrete made with different size aggregates are tested numerically. A lattice type fracture model is adopted to simulate the fracture mechanisms in concrete. The heterogeneity of the concrete is implemented using a regular pattern of circular particles on top of the lattice of beams. The results obtained show that with the model a structural size effect is obtained, which his however partly an artefact of the model. Furthermore a dependency of strength, fracture energy and brittleness of the aggregate size is found.