Local Strain State Research Articles

The mechanistic origins of heterogeneous void growth during ductile failure

In 1969, Rice and Tracey proposed that the rate of void growth during ductile failure is a strong function of the hydrostatic stress state. Numerous in-situ x-ray computed tomography (XCT) studies demonstrated that the average rate of void growth is well-predicted by modified versions of the Rice-Tracey equation. However, recent in-situ XCT studies of void growth demonstrated that individual voids grow in highly heterogeneous manners in a way that is not predicted by Rice-Tracey or similar models. Model-based studies using crystal plasticity finite element (CP-FE) suggest that local effects of grain orientation play a strong role during void growth, but we lack experimental data to test this hypothesis. The present study leverages recent advances in laboratory-based diffraction contrast tomography (Lab-DCT) and in-situ XCT to systematically examine the effects of grain orientation on void growth experimentally in an Al-2219 alloy. CP-FE modeling was used to assess the local stress states associated with voids and their influence on void growth rates. These data indicate that void growth is not simply controlled by the local hydrostatic stress or stress triaxiality. Additionally, no clear relationship between void growth rates and grain orientation were observed. Instead, void growth rates were highly stochastic in ways that could not be directly linked to the local stress or strain states. The combination of experimental and modeling data suggests that our current assumptions regarding the mechanisms of void growth are flawed and that additional factors, which may include the local dislocation density, affect the rate of void growth.

Strain Solitons in an Epitaxially Strained van der Waals-like Material.

Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch. Novel electronic properties of strain solitons were predicted and observed. To date, strain solitons have been observed only in exfoliated crystals or mechanically strained crystals. The lack of a scalable approach toward the generation of strain solitons poses a significant challenge in the study of and use of their properties. Here, we report the formation of strain solitons with epitaxial growth of bismuth on InSb(111)B by molecular beam epitaxy. The morphology of the strain solitons for films of varying thickness is characterized with scanning tunneling microscopy, and the local strain state is determined from atomic resolution images. Bending in the solitons is attributed to interactions with the interface, and large angle bending is associated with edge dislocations. Our results enable the scalable generation of strain solitons.

Structural Performance of Additively Manufactured Composite Lattice Structures: Strain Rate, Cell Geometry, and Weight Ratio Effects

The proliferation of ordered cellular structures in industrial and technological applications is justified by their superior mechanical performance, including tunable energy absorption strategies and potential multifunctionality. This research evaluates the mechanical response of composite lattice structures fabricated using vat photopolymerization additive manufacturing process and printable particulate composite materials. Several generations of modified printable resins are prepared by hybridizing flexible resin with varying glass microballoons reinforcement weight percentages. Multifaceted characterization regiments highlight the process–property–performance interrelationship by submitting printed composite structures to quasi‐static and impact‐loading scenarios combined with digital stills and high‐speed photography, respectively. Image analyses of optical and scanning electron micrographs quantify the dimensional accuracy of the composite lattice structures with cylindrical and hexagonal cellular geometries. The mechanical characterization uncovers the effect of cell geometry and reinforcement on the global structural behavior, eliciting differences in load‐bearing capacity, local strain developments, and structural densification. Exploratory digital image correlation supports the global structural deformations, revealing their relationship with the developed local strain state within the unit cells. The outcomes of this research elucidate the effect of strain rate, unit cell geometry, and reinforcing ratios on the structural performance of composite lattice structures at the macro‐ and microstructure levels.

High strain rate constitutive and fracture characterization of AA7075-T6 sheet under various stress states

The stress state and strain rate dependent fracture behavior of high strength aluminum sheet, AA7075-T6, is characterized experimentally and numerically. Experiments were performed using shear, hole tension, notch tension, and groove tension specimen geometries at strain rates in the regime 10−2 – 500 s−1. The temperature change on the specimen surface was measured utilizing high speed thermal imaging, while strains were acquired using DIC-based optical measurements. Mild positive rate sensitivity was observed in the flow response for equivalent strains up to approximately 20%, while the flow stress decreased at higher (500 s−1) strain rates as the strain levels increased. An increase in temperature was observed within the gauge region of the specimens during elevated strain rate (500 s−1) tests leading to thermal softening. Positive strain rate sensitivity was observed in the measured axial force response for the hole tension and notch tension specimens. The fracture limits of the AA7075-T6 in the shear, hole tension, and notch specimens decreased between strain rates of 0.01 and 10 s−1, then increased at strain rates between 10 and 500 s−1. A strain rate and temperature dependent Hockett–Sherby (HS-SRT) constitutive model was proposed to capture the dependency of the flow stress on the equivalent plastic strain, strain rate, and temperature. The generalized Drucker-Prager (GDP) fracture model was extended to capture the effect of strain rate on fracture initiation. Numerical simulations of the coupon experiments were then performed to extract the local stress and strain states to calibrate the GDP fracture model across the range of strains considered.

Investigations on the compression-shear coupled stress waves propagating in heterogeneous rock

In order to investigate the heterogeneous responses in complex rocks, a compression-shear coupled constitutive relationship with four coupled parameters is established and a generalized wave equation is obtained. Based on the generalized self-consistent theory, the approach to determine the four coupling parameters related to local stress and strain state in the heterogeneous rock with multiphase components is proposed. A meso finite element model (meso-FEM) is employed to calibrate the calculation process according to four load paths. Based on the generalized wave equation, three characteristic wave velocities of 3-D plane waves are derived to describe the compression-shear coupled effect on wave propagation. These wave velocities (e.g. the primary wave and secondary wave) are different from those of the conventional compression wave and shear wave due to the coupled effects. As an example, the theoretical method is further employed to investigate wave velocities in the heterogeneous granular medium due to particle rotation. It indicates that wave velocities in the looser medium are related to local rotation and local strain. Particle rotation has significant effects on the wave velocities, which causes severe heterogeneity and compression-shear coupling effect in particle material. Both the heterogeneous distribution of internal materials and particle rotation affect wave velocities. The results provide a profound theoretical explanation for the heterogeneity of rock and are expected to provide a comprehensive understanding of the physical mechanism of the effect of heterogeneity on wave velocity.

Relevant Choices Affecting the Fatigue Analysis of Ni-Ti Endovascular Devices.

Ni-Ti alloys are widely used for biomedical applications due to their superelastic properties, which are especially convenient for endovascular devices that require minimally invasive insertion and durable effects, such as peripheral/carotid stents and valve frames. After crimping and deployment, stents undergo millions of cyclic loads imposed by heart/neck/leg movements, causing fatigue failure and device fracture that can lead to possibly severe consequences for the patient. Standard regulations require experimental testing for the preclinical assessment of such devices, which can be coupled with numerical modeling to reduce the time and costs of such campaigns and to obtain more information regarding the local state of stress and strain in the device. In this frame, this review aimed to enlighten the relevant choices that can affect the outcome of the fatigue analysis of Ni-Ti devices, both from experimental and numerical perspectives.

Controlling and visualizing fracture of 2D crystals by wrinkling

Shaping two-dimensional (2D) crystals with well-defined edges along specific directions remains technically challenging due to the intrinsic lattice discreteness and anisotropy in their fracture toughness. The patterns of crystal cleavage are determined by the fracture resistance and loading conditions, and usually display kinking features. We show that the fracture of single-crystalline 2D films (MoS2, MoTe2, graphene) can be controlled by mechanically-induced wrinkles, and the distortion of their profiles can visualize the distorted local strain state near the crack tip. In thin samples with stretch-induced wrinkles, the elastic driving force with effective anisotropy steers crack propagation, resulting in straight edges following the corrugation profile. In contrast, thick samples remain flat under stretch for their elevated bending resistance, and the cracks advance with sawtooth patterns following the zigzag motif. The experimental findings are explained by wrinkling-induced elastic anisotropy, which dominates over fracture anisotropy. The control of fracture in 2D crystals can be applied to fabricate micro- and nanostructures for their applications in electromechanical and optoelectronic devices.

Life-cycles of a lava lake: Ambrym volcano, Vanuatu

Eighteen years of heat flux data collected by the Moderate Resolution Imaging Spectroradiometer (MODIS) are used to investigate cycles of lava lake activity at Ambrym volcano in Vanuatu. Lava lakes are dynamic manifestations of open-vent volcanic behaviour and time-series analysis of this behaviour reveals the timing and magnitude of magmatic processes. Pulsatory fluctuations in heat flux of > 50 MW over periods of 30 to >100 days during lava lake activity are interpreted to represent episodes of magma replenishment. These are periodically interrupted by rapid falls in heat flux (50–100 MW over <5 days) or variations in the relative heat flux from lava lakes in different vents of the volcano, which are interpreted to represent changes to the shallow plumbing system feeding lava lake activity. Sudden lava lake drainage and flank eruptions can interrupt or terminate lava lake cycles. Heat flux patterns preceding such events do not show an obvious consistent pattern, suggesting that different magmatic processes may initiate these potentially hazardous surges in eruption intensity. Comparison with the dynamics of other lava lakes reveals similarities in long-term behaviour, despite differences in lava lake size, surface motion or degassing. Collectively this suggests fundamental similarities in the processes that sustain open-vent behaviour, including, the stability of magma supply, conduit-plumbing/geometry and local strain-state.

Visualization and control of oxygen dopant ordering in a cuprate superconductor

A proper amount of excess oxygen plays a significant role in hole-doped cuprate high-Tc superconductivity. Here, we directly resolve the interstitial oxygen atoms are located in the spacer La2O2+δ layers of La2CuO4+δ superconductors via integrated differential phase contrast (iDPC) technique. The distribution of dopant oxygen in La2CuO4+δ is observed to be related with local strain states. Induced large in-plane stress in the La2CuO4+δ film forms periodic alternating tensile and compressive strain in the La–O layers. The mobile interstitial oxygen dopants get self-organized, instead of randomly distributed, to form oxygen-depleted stripes separated by ordered oxygen interstitials. The influence of dopant oxygen on the local atomic lattice and electronic structure was further examined by density functional theory (DFT) calculations. The interplay between the interstitial oxygen dopants and the CuO6 octahedra not only accommodates the distortions of the local atomic arrangement but also alters the electronic states by transferring charge from the LaO planes to the CuO2 planes. Our results may also be applicable to other oxygen-doped cuprates with high-Tc superconductivity.

Superior strength-ductility synergy of layered aluminum under uniaxial tensile loading: The roles of local stress state and local strain state

A typical layered Al composed of alternating fine-grained layers (FLs) and coarse-grained layers (CLs), fabricated by hot pressing and hot rolling, exhibits a superior strength-ductility synergy under uniaxial tensile loading compared with monolithic Al. The mechanism behind the excellent mechanical properties was elucidated from the perspective of local stress state and local strain state. We found that the operative slip systems of CLs cannot be predicted by the classical Schmid factor, indicating a complex local stress state differing from global uniaxial tension. The so-called local multiaxial stress state, probably caused by the deformation incompatibility between constituent layers, was then proposed, and proved feasible for predicting the slip systems in CLs. On the other hand, the digital image correlation revealed that the strong strain partitioning leads to the transformation of local strain state on CLs from uniaxial to biaxial stretch despite under uniaxial tensile loading. Such the local strain state was incorporated into the Taylor ambiguity method, which can derive magnitudes of operative slip systems in the CLs grains with different orientations. The Taylor ambiguity results agreed well with the multiple microbands formation revealed by the quasi in-situ electron backscatter diffraction coupled with a novel misorientation mapping approach. The characteristic slip system activation and dislocation microbands governed by the local stress state and local strain state imply more latent hardening, hence enhancing the strain hardening capability of layered Al. Our work provides a new direction to achieve a superior strength-ductility synergy by designing local stress/strain and tailoring corresponding deformation mechanisms.

Application of different imaging techniques for the characterization of damage in fiber reinforced polymer

The heterogeneous and anisotropic nature of fiber reinforced polymers induces the initiation of various damage mechanisms at different scales. Even though full-field surface measurements may successfully track damage development, such approaches do not provide insights into the material bulk. The present work aims at comparing surface and bulk full-field measurements (via Digital Image/Volume Correlation) for a comprehensive analysis of polymer composite damage. Bulk measurements revealed that damage initiated at the microscale, thus contributing to surface localization phenomena. Full-field surface measurements could not capture the local strain states that the constituents were subjected to, which led to final fracture.

Study of the ITER TF CICC Mechanical Behavior Under Cool-Down and Repetitive EM Loadings

High-current and high-field superconducting magnets sustain huge electromagnetic loads. On top of that, the high field constraint pushes towards the use of high-performing superconducting Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strands, which are strain sensitive. In recent fusion magnets, the loads reach few hundreds of kN/m in static and sometimes cyclic regimes. These loads modify the strands local strain state and the overall mechanical properties of the cable. In this article, the finite element mechanical code MULTIFIL is applied to model an ITER Cable-In-Conduit Conductor (CICC) petal for the Toroidal Field (TF) coil under operating loadings. The local strain maps and the macroscopic mechanical behavior of the cable are analyzed for both thermal and electromagnetic loadings. A possible explanation for the initial drop of the current sharing temperature observed in some of the TF CICCs tested in the SULTAN facility (PSI, Villigen) is proposed. The impact of important model parameters, such as the void fraction and the friction coefficient between strands, on the mechanical behavior of the conductor is investigated.

Finite Element Modelling of a Parabolic Trough Collector for Concentrated Solar Power

Nowadays the design of large-scale structures can be effectively improved by the adoption of numerical models. Even if experimental tests still play a fundamental role, a methodological approach that combines experimental testing and modelling technique can significantly improve the understanding of the matter. This, in fact, would result in a more reliable optimization process, drastically reducing efforts and uncertainties towards the implementation of the final product. The present work deals with the development of a finite element model for the analysis of a full-scale prototype of an innovative parabolic trough collector. The collector is analysed under several load conditions in order to evaluate its structural behaviour. Each load configuration is also numerically reproduced. Moreover, it is demonstrated that the model is capable of reproducing both the global (stiffness) and local (strain state) behaviour of the structure. Specifically, the comparison between experimental data and numerical results show a good agreement for the global parameter torsional stiffness. Local strain values are also well reproduced in high-stressed zone. Thus, the model can be used as a reliable “virtual tool” for designers to evaluate the suitability of layout modifications, thereby replacing and reducing the amount of commonly needed experimental tests and, consequently, reducing time and costs. Finally, an example of the potentiality of the finite element model adopted for a computer-aided engineering approach is shown to determine the most promising solution for increasing the torsional stiffness of the trough, while simultaneously limiting the required experimental tests.

A new continuum model for viscoplasticity in metallic glasses based on thermodynamics and its application to creep tests

In this study, we developed a new continuum model for the time-dependent plasticity of metallic glasses based on the laws of thermodynamics. In this model, the free energy of a material point is formulated as not only the local strain state but also the local atomic concentration (or the free volume). Atomic kinetics, controlled by the gradient of the chemical potential, is linked directly with the plastic deformation by a new plastic flow rule. Finite element implementation of our model is validated through the classical uniaxial tension and simple shear tests in which the shear band instability and shear-dilatation phenomena are reproduced. Applied to the creep of Cu-Zr metallic glass, our model captures the transition of two distinct power laws for the creep strain rate vs. applied stress relations around a critical stress. These two power laws, below and above the critical stress, correspond to two different diffusion mechanisms activated by the thermal energy gradient and strain energy gradient, respectively. At last, we carry out a linear perturbation analysis to explain the origin of the critical stress as well as its dependence on the sample size.

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyses in solid mechanics.The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which allows mimicking the internal variables required to account for history-dependent behaviors since the RNN is self-equipped with hidden variables that have the ability of tracking loading history. On the other hand, in order to achieve accuracy under multi-dimensional non-proportional loading conditions, training of the RNN is achieved using sequential data. In particular the sequential training data are collected from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The random loading paths are generated in a way similar to a random walking in stochastic process and allow generating data for a wide range of strain-stress states and state evolution.The accuracy and efficiency of the RNN-based surrogate model is tested on the structural analysis of an open-hole sample subjected to several loading/unloading cycles. It is shown that a similar accuracy as with a FE2 multi-scale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.

Flexoelectricity-induced retention failure in ferroelectric films

Retention failure is deleterious on ferroelectric domain stability, resulting in data loss in ferroelectric memories. However, the understanding of the origin of retention failure remains a challenge for the lack of a direct experimental evidence. Here, using a combination of piezoelectric force microscopy, atomic-scale scanning transmission electron microscopy and reciprocal space mapping, we report that the polarization retention failure is caused by a strain gradient induced flexoelectric field in tetragonal ferroelectric films. Atomic imaging reveals that the strain gradient is introduced by tensile strains, which is resultant from the vertically distributed Pb-rich anti-phase domains. This strain gradient couples with polarizations and results in flexoelectric fields in the films, leading to the retention failure in the films. Our study directly underlines the atomic mechanisms behind the strain gradient induced macroscopic retention failure behavior and clarifies the effect of local strain state on domain relaxation processes, thus can shed light on further understanding and improving the retention properties of oxide ferroelectrics.

Ferroelectric photovoltaic and flexo‐photovoltaic effects in (1 − x)(Bi0.5Na0.5)TiO3‐xBiFeO3 systems under visible light

AbstractThe anomalous photovoltaic (APV) effect has witnessed great progress from classical ferroelectric photovoltaics to flexo‐photovoltaics. Both call for an extension of the spectral response range. Here, we present a comprehensive study on the ferroelectric, photoelectric, and photovoltaic properties of pure (Bi0.5Na0.5)TiO3 (BNT) and 0.3(Bi0.5Na0.5)TiO3–0.7BiFeO3 (0.3BNT‐0.7BFO) ceramics. The data show that pure BNT with typical ferroelectricity exhibits intriguing photovoltaic effect even when illuminated by 550 nm visible light, while the 0.3BNT‐0.7BFO solid solution with enhanced visible light absorption shows no ferroelectric photovoltaic due to the negligible ferroelectricity but striking strain‐induced flexo‐photovoltaic effect. Transmission electron microscopy analysis reveals distinctions in the domain structures and local strain states in pure BNT and 0.3BNT‐0.7BFO ceramics, which may account for their differences in photovoltaic behavior. These findings not only deepen the understanding of photovoltaic mechanisms induced by ferroelectric polarization and flexoelectric effect but also highlight a possible candidate for multifunctional photoelectric applications.

Evolution of β-phase precipitates in an aluminum-magnesium alloy at the nanoscale

Aluminum alloys in the 5xxx series are susceptible to sensitization due to the formation of β (Al3Mg2) at grain boundaries at moderate to low temperatures. Little is known about the mechanism of β phase formation, which is thought to be preceded by the metastable phases β’’ and β’. Using high-resolution transmission electron microscopy (HRTEM), energy dispersive x-ray spectroscopy (EDS), and precession electron diffraction (PED), we determine a parameter space for β phase precipitates at various sensitization temperatures and investigate their growth habits and local matrix strain states along grain boundaries. Our findings reveal that metastable β-related phases are present at low aging temperatures, while the equilibrium β phase is present at temperatures well above the previously described solvus of similar alloys. Furthermore, the phases were found to prefer particular grain boundary planes and contribute to the local grain boundary strain state differently. Overall, these findings present a unified view of β phase evolution and its contribution to lattice strain environments in aluminum magnesium alloys, which serves as a foundation for use in a range of temperatures and environments.

Numerical simulation and behavior insights of steel columns with SMA bolts towards earthquake resilience

Shape memory alloys (SMAs) are high-performance metallic materials that can experience large strain and still recover their initial shape through either temperature-induced effect (shape memory) or stress-induced effect (superelasticity). The superelasticity of SMAs is very attractive to the earthquake resilient design because of the inherent material feature with excellent self-centering (SC) and energy dissipation capabilities. This paper presents a comprehensive numerical simulation of the steel columns with SMA bolts. A finite element model was validated by tests of two SC steel columns in terms of global hysteresis loops and local strain states. Subsequently, special attention to the effects of prestrain in the SMA bolts, bidirectional loading, and multi-earthquake loading was paid to offer insights into the cyclic responses of the SC steel column. Results showed that the steel columns equipped with SMA bolts could exhibit satisfactory and stable flag-shaped hysteresis loops with excellent SC and energy dissipation capabilities under different loading conditions. In addition, SC column exhibited nearly equivalent seismic performance under multi-earthquake loading. Therefore, the SC steel columns can achieve earthquake resilient design that requires no (or minimal) repair even after strong earthquakes and remains highly functional for immediate aftershocks or future earthquakes.

Effect of grain orientation and local strains on void growth and coalescence in titanium

Ductile fracture has been extensively studied in metals with weak mechanical anisotropy such as copper and aluminum. The fracture of more anisotropic metals, especially those with a hexagonal crystal structure (e.g. titanium), remains far less understood. This paper investigates the ductile fracture process in commercially pure titanium (CP-Ti) with particular emphasis on the influence of grain orientation and local state of strain on void growth. An experimental approach was developed to directly relate the growth of a void in three dimensions to its underlying grain orientation. Grain orientation was obtained by electron back scattered diffraction on void-containing CP-Ti sheets prior to their diffusion bonding. Changes in void dimensions were measured during in-situ straining within an x-ray tomography system. The strong influence of the embedded grain orientation and that of its neighbors on void growth rate and coalescence has been experimentally quantified. Finite element crystal plasticity simulations that take into account both grain orientation and the local strain state were found to predict the experimental void growth. Grains where basal slip dominates show the largest void growth rates because they are closer to a plane strain condition that favors void growth and coalescence.