Strain Percolation Research Articles

The Strain Rate Sensitivity of Heterogeneous Thin Film Metallic Glasses: Interplay Between Nanoscale Heterogeneity and Dynamic Plasticity

The dynamic mechanical properties of metallic glasses (MGs) are crucial to capturing the deformation signatures as well as for structural and functional applications. In this work, we investigate the influence of nanoscale structural heterogeneity of MGs on dynamic plasticity, focusing on the variation in strain rate sensitivity and the transition of deformation mechanisms, using a combined experimental and simulation approach. The Cu50Zr50 thin-film MGs with different nanoscale heterogeneities are synthesized using magnetron sputtering and further characterized using dynamic force microscopy and nanoindentation. All the films exhibit a strain rate hardening effect, but a transition in strain rate sensitivity as the indentation rate increases has been found in the MG with a higher heterogeneity. To understand the underlying mechanisms, mesoscale shear transformation zone dynamics simulations are performed on model Cu50Zr50 MGs. The simulation results are able to capture the experimental trend. Notably, the transition in strain rate sensitivity for a heterogenous MG stems from a change in deformation mechanisms: from structure-dictated strain localization at a lower strain rate to stress-dictated strain percolation into a shear band at a higher strain rate. The observed strain rate sensitivity and the corresponding mechanisms are summarized in a deformation mechanism map where nanoscale structural heterogeneity and strain rate are varied. We envision our study not only providing insights into the structure and property relationship of MGs on the nanoscale but also will facilitate the design of heterogeneous MGs for dynamic applications.

In-plane and out-of-plane deformation at the sub-grain scale in polycrystalline materials assessed by confocal microscopy

High-resolution digital image correlation (HR-DIC) techniques have become essential in material mechanics to assess strain measurements at the scale of the elementary mechanisms responsible of the deformation in polycrystalline materials. The purpose of this study is to demonstrate the use of laser scanning confocal microscopy (LSCM) coupled with DIC techniques to deepen knowledge on the deformation process of a polycrystalline nickel-based superalloy at room temperature. The LSCM technique is capable of detecting both in-plane and out-of-plane strain localization within slip bands at the sub-grain level. The LSCM observations are consistent with previous in-situ scanning electron microscopy (SEM) studies: The onset of crystal plasticity occurs primarily near Σ3 twin boundaries with macroscopic loading in the elastic domain (macroscopic stress as low as 80% of the 0.2% offset yield strength (Y.S.0.2%)). This intense irreversible strain localization occurs with either a high Schmid factor (μ > 0.43) or a significant elastic modulus difference between the pair of twins (ΔΕ > 100 GPa). In the plastic deformation domain, transgranular slip activity following slip systems with the highest Schmid factor is mostly responsible for the deformation at the grain level, thus leading to strain percolation. The simultaneous in-plane and out-of-plane deformation assessment via the HR-LSCM-DIC technique was found to be essential for the identification of active slip systems. Finally, the HR-LSCM-DIC technique enabled the quantification of the glide amplitude involved in the three-dimensional shearing process at the grain level that solely in-plane measurements cannot provide.

Spatial correlation of elastic heterogeneity tunes the deformation behavior of metallic glasses

Metallic glasses (MGs) possess remarkably high strength but often display only minimal tensile ductility due to the formation of catastrophic shear bands. Purposely enhancing the inherent heterogeneity to promote distributed flow offers new possibilities in improving the ductility of monolithic MGs. Here, we report the effect of the spatial heterogeneity of elasticity, resulting from the inherently inhomogeneous amorphous structures, on the deformation behavior of MGs, specifically focusing on the ductility using multiscale modeling methods. A highly heterogeneous, Gaussian-type shear modulus distribution at the nanoscale is revealed by atomistic simulations in Cu64Zr36 MGs, in which the soft population of the distribution exhibits a marked propensity to undergo the inelastic shear transformation. By employing a mesoscale shear transformation zone dynamics model, we find that the organization of such nanometer-scale shear transformation events into shear-band patterns is dependent on the spatial heterogeneity of the local shear moduli. A critical spatial correlation length of elastic heterogeneity is identified for the simulated MGs to achieve the best tensile ductility, which is associated with a transition of shear-band formation mechanisms, from stress-dictated nucleation and growth to structure-dictated strain percolation, as well as a saturation of elastically soft sites participating in the plastic flow. This discovery is important for the fundamental understanding of the role of spatial heterogeneity in influencing the deformation behavior of MGs. We believe that this can facilitate the design and development of new ductile monolithic MGs by a process of tuning the inherent heterogeneity to achieve enhanced ductility in these high-strength metallic alloys.

Diffraction-amalgamated grain boundary tracking for mapping 3D crystallographic orientation and strain fields during plastic deformation

By amalgamating the X-ray diffraction technique with the grain boundary tracking technique, a novel method, diffraction-amalgamated grain boundary tracking (DAGT), has been developed. DAGT is a non-destructive in-situ analysis technique for characterising bulk materials, which can be applied up to near the point of fracture. It provides information about local crystal orientations and detailed grain morphologies in three dimensions, together with high-density strain mapping inside grains. As it obtains the grain morphologies by utilising X-ray imaging instead of X-ray diffraction, which latter is typically vulnerable to plastic deformation, DAGT is a fairly robust technique for analysing plastically deforming materials. Texture evolution and localised deformation behaviours have here been successfully characterised in Al–Cu alloys, during tensile deformation of 27% in applied strain. The characteristic rotation behaviours of grains were identified, and attributed to the effects of interaction with adjacent grains on the basis of the 3D local orientation and plastic strain distributions. It has also been revealed that 3D strain distribution in grains is highly heterogeneous, which is not explained by known mechanisms such as simple incompatibility with adjacent grains or strain percolation through soft grains. It has been clarified that groups consisting of a few adjacent grains may deform coordinately, especially in shear and lateral deformation, and the characteristic deformation pattern is thereby formed on a mesoscopic scale.

Microstructural model for the time‐dependent thermomechanical analysis of cast irons

AbstractIn this paper, a multiscale modelling approach is followed for the modelling of time and temperature dependent behaviour of compacted graphite cast iron (CGI) material. Cast irons are often used in heavy duty machinery parts subjected to elevated temperatures for prolonged periods of time. This, in combination with its complex heterogeneous microstructure, plays the crucial role in determining the life time of the material. In this work a 2D microstructural model of CGI is developed. The geometry is based on the micrographs of the material. The pearlitic matrix is modelled with the temperature dependent elasto‐visco‐plastic model calibrated on the pearlitic steel experiments. The graphite particles are modelled as anisotropic elastic. The results of the simulations of tensile and stress relaxation tests at different temperatures between 20 °C and 500 °C show that the macroscopic mechanical behaviour of the ma‐terial deteriorates rapidly above 350 °C. At the microstructural scale, the anisotropic graphite particles act as stress concentrators promoting the formation of strain percolation paths, that become more critical at higher temperatures. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Enabling microstructure-based damage and localization analyses and upscaling

This paper presents a framework that enables microstructural modelling of complex microstructures involving damage, localization and fracture. Classical computational homogenization schemes hinge on the separation of scales and the existence of representative volume elements. Due to the accumulation of micro-damage, the microstructural volume elements gradually loose their representative character and evolve towards a unique volume with a developing strain localization band, rendering classical homogenization approaches inapplicable.The assumption that the representative nature of the microstructure along the strain localization band is preserved enables the definition of advance scale transition relations for both imposing the overall macroscale load and coarse graining the cohesive behaviour of the strain localization band. Newly developed strain percolation path aligned boundary conditions have been used for this purpose. It is shown that this enables the development and progressive evolution of a strain localization band with minimal interference of the imposed boundary conditions. In addition to classical homogenization of the stress–strain response, a coarse graining scheme for the effective cohesive behaviour of the strain localization band is proposed. This enables the assessment of the microstructural evolution within the strain localization band and simultaneously provides the effective cohesive response useful for macroscale failure models.

Chemical self-organization length scales in non- and nano-crystalline thin films

This paper identifies different length scales λ s for strain-reducing chemical bonding self-organizations (CBSO) in non-crystalline and nano-crystalline thin films. CBSOs are differentiated spectroscopically, and explained by semi-empirical bond-constraint theory (SE-BCT). Non-crystalline thin film CBSOs are characterized by molecular scale, strain-reducing chemical ordering with λ s > 0.6 nm, and extending to at most 1 nm. The non-random bonding results in reduced defect densities that are enabling for device applications. Nano-crystalline transition metal oxide thin films display qualitatively different properties in two distinct nano-scale regimes in which the length scale metric is defined by π-bond coupling between atoms in strings of neighboring primitive unit cells (PUCs): (i) type I with nano-grain dimensions and λ s ∼ 2 nm (or <4 PUCs), and (ii) type 2 with nano-grain sizes and λ s > 3–4 nm (>6 PUCs). There are also diphasic nano-crystalline/non-crystalline technologically important thin films in which strain percolation is also minimized by CBSOs that combine molecular and PUC scales of order. Representative non-crystalline, nano-crystalline and diphasic nano-crystalline/non-crystalline thin film materials with qualitatively different behaviors and degrees of phase stability/metastability are addressed.

Critical behavior of a strain percolation model for metals with unstable locks

Using a strain percolation model proposed for the transport of mobile dislocations through a dislocation cell structure in a deforming metal, we have further explored the critical behavior of the model when there are some unstable locks present in the system that may be broken by the stress field of incident dislocations. The presence of such locks changes dramatically some of the characteristic features of the system. One such change is a fractal distribution of broken locks within a strained cluster leading to a model parameter-dependent critical point. In the critical regime, growth of a strained cluster as well as the distribution of broken locks within the cluster exhibits universal power-law behavior well explained by ordinary two-dimensional percolation theory. This random aspect of the model at large scales appears to arise from a self-organizing critical behavior of cells that evolve into a state of a minimum stable strain.

Critical behavior of a strain percolation model for metals.

Extensive simulations of a strain percolation model for a deforming metal have been performed to examine its strain behavior. We find that the total strain exhibits critical power-law behavior that is well explained by two-dimensional percolation theory. Near the critical point, most of the strained cells organize themselves around a state having the minimum or at least marginally stable strain regardless of the initial conditions. A strain much greater than the minimum stable strain generally decays to a lower value when transmitted to an unstrained cell. The universal behavior of the total strain in the system is a consequence of the self-organizing character of the strain in the critical cluster. Although the probability distributions for the total strain and cluster size appear to exhibit nonuniversal behavior, this may merely represent a transient response before crossover to a true asymptotic, universal behavior occurs. Other critical aspects of the model are also discussed.

Self-organized critical behavior in a deforming metal

It has been shown that the transport of mobile dislocations through blocking dislocation walls in a deforming metal can be treated by a simple percolation theory. Two different mechanisms for strain propagation are proposed in the strain percolation model. In the first case, the strain propagates between adjacent dislocation cells by activation of sources within the walls. In the second case, as an additional mechanism, unstable locks can be unzipped by a nearby dislocation pileup which can lead to a large localized strain. Previous simulations have shown that both cases belong to the same universality class as standard percolation. Further extensive simulations of the model have been performed to understand how the geometrical aspects of a strained percolating cluster are related to the strain itself. In our case, the strain is an additional variable not present in standard percolation theory. We find that the total strain and the mean strain per strained cell show power-law behavior in the critical regime, and obtain a scaling function which explains its critical behavior. Other percolation and critical aspects of the model are also discussed in terms of the initial strain, correlation length (which is a characteristic length scale), and model parameters.

Strain percolation: physical considerations

In previous papers, we have introduced a percolation model for the transport of strain through a deforming metal. In this paper, we review the results from that model, and discuss how the model can be applied to the deformation problem. We summarize the principal observational features of deformation and propose that the discrete percolation events correspond to slip line formation in a deforming metal. It is shown that the deforming solid is a self-organizing system. It is recognized that deformation is localized in space and time, that deformation is fundamentally rate-dependent, that hardening depends on relaxation processes associated with discrete percolating events, and that secondary slip is an essential part of band growth and relaxation processes.

Theory of strain percolation in metals: mean field and strong boundary universality class

For the percolation model of strain in a deforming metal proposed earlier, we develop sum rule and mean field approximations which predict a critical point. The numerical work is restricted to the simpler of two cases proposed in the earlier work, in which the cell walls are “strong”, and unzipping of the dislocation entities which lock the walls into the lattice is not permitted. For this case, we find that strain percolation is a new form of correlated percolation, but that it is in the same universality class as standard percolation.

Theory of Strain Percolation in Metals

We demonstrate that a deforming metal is a self-organizing critical system, and that the stress-strain law can be expressed as an integration of certain derivatives of internal variables along the critical line of the system.

Geophysical Variables and Behavior: LXXVI. Seasonal Hydrological Load and Regional Luminous Phenomena (UFO Reports) within River Systems, the Mississippi Valley Test

We hypothesized that an equilibrium in seasonal variations between water load and both seismicity and reports of odd, spherical, luminous phenomena within the river basin should result in systematic but phase-lagged relationships between these variables. Within 320 km of the confluence of the Mississippi System, the monthly variation of a specific and major class of UFO reports (which appear to represent luminous phenomena that are generated by tectonic strain) peaked 3 to 4 months ( r = 0.87) after the river crested. The phase lag between these luminous phenomena and seismic activity within the same region was about 6 months. The results support the model that river load-induced strain and fluid percolation into and diffusion within the earth's crust promote the production of natural luminous phenomena.