Local Stress Field Research Articles

Locally exact asymptotic homogenization of periodic materials under anti-plane shear loading

A new implementation of the asymptotic homogenization theory for anti-plane shear loading is constructed based on locally exact elasticity solutions of unit cell problems at different orders in the asymptotic field expansion. The approach is a generalization of the previously developed locally exact homogenization theory for the determination of homogenized elastic moduli under uniform stress fields. The new theory has been developed for periodic materials in the presence of stress gradients and non-vanishing microstructural scale relative to the structural dimensions. The local interior unit cell problems are solved exactly up to the third order using Fourier series representations of the microfluctuation functions. The exterior unit cell periodic boundary value problems at different orders are tackled by an asymptotic extension of the previously introduced balanced variational principle for periodic materials. The effectiveness of the theory is verified by solving a structural problem with varying number of inclusions directly, and comparing the local fields with those reconstructed by the locally exact asymptotic homogenization approach. The theory is also employed to assess the accuracy of an uncoupled homogenization-localization approach in the reconstruction of local stress fields in periodic materials with different levels of microstructural refinement in the presence of stress gradients. The present contribution provides the foundation for further extension of the new locally exact asymptotic homogenization theory to in-plane loading problems of unidirectionally reinforced periodic materials.

Hydrogenation-induced lattice expansion and its effects on hydrogen diffusion and damage in Ti–6Al–4V

Hydrogen uptake in titanium alloys leads to the formation of hydride phases, which in-turn cause severe embrittlement upon further deformation. The embrittlement micro-mechanisms are complicated by the distinct hydrogen diffusion and solution characteristics of the α and β phases, which arise from their different crystal structures. To improve the fundamental understanding of the room temperature interplay among hydrogen, the present phases and the hydride that is formed at their interface, we investigated the hydride formation process in Ti–6Al–4V alloy by in situ scanning electron microscopy and electron backscatter diffraction analyses during hydrogen charging, and post-mortem synchrotron diffraction tests. These investigations reveal that the lattice expansion of the hydrogenated β phase introduces a localized stress field near the phase boundary, which, in turn, induces hydrogen confinement therein, eventually facilitating the hydride growth along the boundary. The volumetric expansion of the α-to-hydride transformation extends the local stress field, influencing the work-hardening and damage evolution in the alloy. We discuss these findings and the overall damage initiation and propagation taking place in the hydrogenated alloy, based on the interplay among the present phases and hydrogen.

Local microstructure and micromechanical stress evolution during deformation twinning in hexagonal polycrystals

Abstract

Rib loading effects on weld root fatigue failure modes at rib‐to‐deck welded joint

AbstractThe service life of orthotropic steel decks is dependent on the fatigue resistance of rib‐to‐deck welded joints, which is often tested using two kinds of experimental models in terms of the rib loading condition. Different weld root fatigue failure modes have been observed in the different models, but the role of rib loading remains unclear. This paper aims to clarify the effect of rib loadings on the weld root fatigue failure modes at rib‐to‐deck welded joints. The loadings are decomposed into the deck loadings and rib loadings according to the principle of superposition. Formulae of the weld root notch stress intensity factors and T‐stress under rib loadings are developed by multiparameter regression analysis and subsequently used for the local stress analysis. The fatigue failure modes determined from the local stress field agree well with the experimental results. The results reveal that the weld root failure modes depend on the rib loadings but are independent of the weld geometries. The averaged strain energy density (SED) that can capture both weld geometry and loading condition effects is used to correlate the fatigue test data of different weld root failure modes. The SED is capable of evaluating the fatigue strength of the rib‐to‐deck welded joint failed by different weld root failure modes with a narrow scatter band.

Critical role of cationic local stresses on the stabilization of entropy‐stabilized transition metal oxides

AbstractEntropy‐stabilized transition metal oxides ([MgNiCoCuZn]O) (ESO) in recent years have received considerable attention owing to their unique functional properties. Solution combustion and solid state syntheses resulted in crystallites varying from 5‐15 nm to 3‐5 μm respectively. Phase stability studies showed that all the systems containing Cu2+ions in the ESO lattice segregated upon slow cooling in the furnace. It was only when ESO was quenched in air from 1000°C the lattice stabilized to a single phase. Experiments concomitant with molecular dynamics (MD) simulations demonstrated that the local stress fields around the cations played a critical role in stabilizing the single phase. The local stress fields are a result of Jahn‐Teller distortion induced by the Cu2+ions in the lattice. It is clearly established that in the absence of the minimization of the local stress fields around the Cu2+ions, segregation leading to the formation of a multi‐phase material is imminent for this particular composition.

Geometric confinement governs toughness and strength in defective diamond nanowires

Using classical molecular dynamics simulations and the virial description of atomic stress, this paper reveals that effective toughness and strength in defective diamond nanowires (NWs) are governed by the geometric confinement of atoms at the critical sites of the NWs. Results suggest existence of five characteristic regimes in defective NWs under applied deformation. They include the defective regime, the surface regime, the core regime, the surface-core intersection regime, and the defect-core intersection regime. The defective regime and the surface regime soften the NW and carry the maximum angular deformation at the expense of breaking local symmetry of atomic structure. On the other hand, the intersecting regimes tend to preserve the symmetry, carry the most aggressive linear deformation, and act as the critical sites for localization of atomic stress. In the defect-core intersecting regime, the differential response of its neighboring regimes to linear and angular deformations as well as the elastic fields emanating from its critical sites impose an intricate effect comprising geometric confinement and propensity to retain local symmetry. Consequently, the highest localization of elastic energy and atomic stress takes place at the critical sites of the defect-core regime and it controls the effective toughness and strength behavior of the defective nanowires. Although size-dependent variation in strength and toughness is controlled primarily by surface softening, defect-induced alteration of strength and toughness is governed by the geometric confinement. Furthermore, an atomistic analysis reveals that the localized stress fields grow radially outward from the defective regime for defective NWs, whereas in defect-free NWs they evolve inward from the surface.

Mechanical control on patterns of overburden deformation induced by dyke-fed sandstone intrusions: Insights from numerical experiments

Conical sandstone intrusions, as a distinct type of hydrocarbon reservoir, remain poorly understood regarding their emplacement mechanics. Here, we report a numerical modelling study of conical sandstone intrusions using the two-dimensional discrete element method. We built numerical models that contain bonded elastic particles with predefined mechanical properties in an open box as the overburden. A thin tube filled with unbonded particles, and connected to the upper box, was used to model the feeder dyke. The dynamic behavior of the assembly was enabled by the displacement of a driving wall that defines the lower boundary of the feeder dyke. The results show that the model composed of soft materials produced a pair of conical, opening-mode fractures in the host sediments as the result of tensile stress concentrations in the fracture tip zones. The overburden deformation was largely localised within the sediments adjacent to the sandbody, and without the formation of a forced fold and significant uplift of the surface. In contrast, the model composed of stiffer materials produced conical fractures that have closed lower segments and opening upper segments with a reverse sense of shear. The intrusion also caused a forced fold in the overburden, with a vertical opening-mode fracture generated in the fold hinge. The modelling results demonstrate that dyke-fed sand intrusions can significantly distort the local stress field and the overburden can be subjected to fracturing and/or folding due to differential compaction during gradual inflation of the intrusive sandbody. Importantly, deformation patterns of the overburden in response to sandstone intrusion largely depend on mechanical properties of the host sediments.

Quantifying the dynamics of dislocation kinks in iron and tungsten through atomistic simulations

When high-Peierls-barrier materials such as iron (Fe) and tungsten (W) are deformed, dislocation kinks can be easily activated. The subsequent kink dynamics may dictate the dislocation mobility and the material's overall performance under certain conditions. In this work, taking the thermal-induced kink diffusion along ½<111> screw dislocation lines as an example, the kink dynamics in b.c.c. iron and tungsten are quantified through atomistic simulations. Results show that in both Fe and W, the kink dynamics, including its diffusion coefficient (Dkink) and dissipation parameter (γkink), are sensitive to the dimension (noted as L) of a simulation cell size along the dislocation line direction: the larger L, the higher Dkink, and the smaller γkink. A scaling law for describing the three-stage L-dependent kink dynamics is extracted from a series of computational analysis of the kink diffusion along dislocations with L ranging from tens to hundreds of nanometers. It is found that, if a converged Dkink is desired from atomistic simulations, the minimum L needs to be at least hundreds of nanometers. This is beyond the reach of an atomic-level model using a modest computational resource. To explain the L-dependent kink dynamics, we calculate the kink-induced local stress fields using two different atomistic stress formula, i.e., a widely-used Virial and a recently developed mechanical stress formula. Results suggest: (i) the L-dependent kink dynamics is caused by the long-range elastic interaction between the kink and its periodic images; and (ii) the Virial stress formula underestimates such interactions. This work lays the continuum description of kink-controlled dislocation dynamics on an atomistic foundation. It will also support the development of multiscale methods for addressing the coupled dynamics between the motion of a μm-long dislocation line and the atomic-level kink diffusion along the line itself in b.c.c. metals or other high-Peierls-barrier materials under deformation.

Multiaxial fatigue assessment of tube-tube steel joints with weld ends using the peak stress method

In the context of fatigue design of welded structures, the peak stress method (PSM) is a rapid numerical technique in engineering that applies an approach based on notch stress intensity factors (NSIFs). To estimate NSIFs, the PSM requires only a single stress value calculated using either 2D or 3D finite element (FE) models discretised using coarse meshes, with the adoptable element size being some orders of magnitude larger than required to calculate the NSIFs based on local stress fields. In this study, the PSM was applied to the fatigue assessment of tube-tube steel joints with weld ends subjected to combined loadings: pure axial, pure torsion, in-phase and out-of-phase axial-torsion loadings, all with two load ratios, i.e., R = 0 and R = −1. Experimental fatigue results generated in a previous study by some of the authors have been reanalysed in this study through the application of PSM to 3D FE models, including an idealised weld end geometry. The experimental fatigue crack initiation location was properly estimated using PSM, and there is good agreement between the experimental results and the relevant PSM based design curve.

Structural rearrangement at medium-range and its effects on the magnetic properties and crystallization behaviors of a Fe-based amorphous alloy

The structure-property relationships in amorphous alloys are far from being fully understood. Here we show an unusual structural rearrangement occurring over medium-range length scale prior to crystallization for a (Fe0.5Co0.5)72Si4B20Nb4 amorphous alloy ribbon upon heating by in-situ synchrotron diffraction, whereas the short-range structure shows no anomaly. During the above process, local stress field generates and results in the enlargement of coercivity. This can be further supported by the magnetic force microscopy images showing an enhancement of magnetic phase contrast after annealing the sample at a temperature where the unusual structural change occurs. Moreover, the average grain size derived from the transmission electron microscopy images of the crystallized (Fe0.5Co0.5)72Si4B20Nb4 ribbon is much smaller than that of (Fe0.5Co0.5)76Si4B16Nb4, suggesting the slow crystallization kinetics caused by the local stress field. This work highlights the role of medium-range order in determining the properties of amorphous alloys.

Residual stress effect governing electromigration-based free-standing metallic micro/nanowire growth behavior

In this study, the effect of residual stress in a film on the growth behavior of a free-standing metallic micro/nanowire due to electromigration (EM) is examined. The growth of a wire is accompanied by atomic diffusion, accumulation of atoms, and release of compressive EM-induced localized hydrostatic stress due to the accumulation of atoms. Hence, the growth of the wire dominantly depends on the EM-induced localized stress caused by the accumulation of atoms. Because rigid passivation generates a strong localized stress field in the metallic interconnect, with greater accumulation of atoms, the EM-induced localized stress state for wire growth is influenced by passivation conditions, including the thickness and residual stress associated with passivation. Two samples with different passivation thicknesses, resulting in different levels of residual stress, were used to elucidate the influence of passivation conditions on the growth performance of Al microwires. The growth rate was experimentally measured. An x-ray diffraction system was used to obtain the value of residual stress in passivation, demonstrating that a higher absolute value of compressive residual stress results in a lower growth rate. In contrast, a lower absolute value increases the growth rate of the wire and can decrease the delamination risk of the topmost passivation, deposited by sputtering. Contrarily, a passivation that is too thin, resulting in a lower absolute value of compressive stress, increases the risk of passivation crack due to the accumulation of atoms by EM. A suitable passivation thickness for a desired wire growth must be determined based on this finding.

Effect of excavation stress condition on hydraulic fracture behaviour

The fracture behaviour of single- and multi-stage hydraulic fracturing (HF) under varying excavation stress conditions was studied using a flow-coupled discrete element method (DEM). Conventional HF theories and analytical solutions for excavation stress redistribution are used to verify the numerical model. The numerical simulation results indicated that for the single-stage HF, both the in situ stresses and injection location have major influences on the HF propagation path, caused by the redistributions of the local maximum and minimum principal stresses under excavation conditions. Fractures generally propagate perpendicular to the local minimum principal stress (σmin) and also propagate preferentially towards the area with lower σmin. Hydraulic fractures propagation is dominated by tensile failure, and the generation of fracture branches is disfavored because of the high local compressive stress field induced by the HF process itself. As for multi-stage HF, different excavation stress conditions may cause different fracture development performances because of alterations of the preferred fracture orientation, blunting of propagating fractures, or creating a more complex fracture geometry in the affected zone. Therefore, when using high-pressure HF for preconditioning the rock mass to assist mechanical excavation in hard rock mining, performance can be enhanced by understanding the impact of stress changes and careful selection of appropriate HF methods depending on the in situ stress.

Nanoscale evolution of stress concentrations and crack morphology in multilayered CrN coating during indentation: Experiment and simulation

The layered architecture approach allows designing mechanical and fracture properties of hard coatings. The current study investigates the performance of a multilayered CrN coating, consisted of 5 μm CrN sublayers of very similar mechanical properties and microstructure but different residual stress states, during in-situ wedge indentation. A finite element model of the indentation was developed and validated against measurements of the local multiaxial stress fields during indentation, characterized by means of X-ray nanodiffraction analysis with a spatial resolution of 500 nm. By means of numerical fracture mechanics the effect of the multilayered structure on the formation and morphology of mode II cracks is analyzed. The configurational force concept was applied to investigate the crack driving forces and crack extension angles of static cracks in different geometrical arrangements. The simulation results agree well with the experimental findings and reveal a shielding effect preventing an interface-near crack from entering the CrN layer with the higher compressive residual stresses. Furthermore, the possibility to match the numerical results with the locally resolved experiments allowed determining validated material parameters for the deformation and fracture behavior. The work revealed e.g. that a KIIC of around 1 MPa∙m1/2 is an appropriate choice for the investigated CrN coating.

Insight into Perovskite Antiferroelectric Phases: Landau Theory and Phase Field Study

The appearance of commensurate and incommensurate modulations in perovskite antiferroelectrics (AFEs) is not understood. And the dielectric and elastic properties of the AFE domain boundaries are lack of investigation. In this work, a novel Landau theory is proposed to understand the transformation of AFE commensurate and incommensurate phases, by considering the coupling between the oxygen octahedral tilt mode and the polar mode. The relationship between the modulation periodicity and temperature is obtained. Using the phase field study, we show that the suppressed polarization at the AFE domain boundaries can lead to a remnant polarization and local elastic stress field.

Uniaxial Experimental Study of the Deformation Behavior and Energy Evolution of Conjugate Jointed Rock Based on AE and DIC Methods

Conjugate joint is one of the most common joint forms in natural rock mass, which is produced by different tectonic movements. To better understand the preexisting flaws, it is necessary to investigate joint development and its effect on the deformation and strength of the rock. In this study, uniaxial compression tests of granite specimens with different conjugate joints distribution were performed using the GAW‐2000 compression‐testing machine system. The PCI‐2 acoustic emission (AE) testing system was used to monitor the acoustic signal characteristics of the jointed specimens during the entire loading process. At the same time, a 3D digital image correlation (DIC) technique was used to study the evolution of stress field before the peak strength at different loading times. Based on the experimental results, the deformation and strength characteristics, AE parameters, damage evolution processes, and energy accumulation and dissipation properties of the conjugate jointed specimens were analyzed. It is considered that these changes were closely related to the angle between the primary and secondary joints. The results show that the AE counts can be used to characterize the damage and failure of the specimen during uniaxial compression. The local stress field evolution process obtained by the DIC can be used to analyze the crack initiation and propagation in the specimen. As the included angle increases from 0° to 90°, the elastic modulus first decreases and then increases, and the accumulative AE counts of the peak first increase and then decrease, while the peak strength does not change distinctly. The cumulative AE counts of the specimen with an included angle of 45° rise in a ladder‐like manner, and the granite retains a certain degree of brittle failure characteristics under the axial loading. The total energy, elastic energy, and dissipation energy of the jointed specimens under uniaxial compression failure were significantly reduced. These findings can be regarded as a reference for future studies on the failure mechanism of granite with conjugate joints.

Crustal seismic anisotropy of the Northeastern Tibetan Plateau and the adjacent areas from shear-wave splitting measurements

SUMMARYThe Northeastern Tibetan Plateau has thickened crust and is still undergoing strong active crustal shortening and deformation. Crustal anisotropy can provide clues to how the crust is currently deforming and evolving. We use an automatic method to analyse the upper-crustal anisotropy of the NE Tibetan Plateau and the adjacent region using local earthquakes recorded at 39 permanent seismic stations during the period 2009–2018. The majority of the dominant fast directions are consistent with the maximum horizontal stress orientation, suggesting that the upper-crustal anisotropy is mainly controlled by the regional or local stress field. Several fault-parallel measurements are observed for stations on or near to the main faults. These fault-parallel fast directions indicate that the main mechanism of upper-crustal anisotropy is associated with shear fabric caused by deformation. Fast directions neither fault-parallel nor stress-parallel are observed at stations lying several kilometres away from fault zones, likely reflecting the combined influence of stress-aligned microcracks and active faults. A comparison between our upper-crustal anisotropy parameters and those inferred from previous anisotropy studies that used receiver function and teleseismic shear wave splitting measurements suggests that the crust has the same deformation mechanisms as mantle anisotropy in the southern part of the Western Qinling Fault, whereas the upper-crustal anisotropic mechanism is different from those of lower crust and mantle anisotropy in the northern part of the Western Qinling Fault. These observations imply that the Western Qinling Fault may be an important boundary fault.

Calculation of the work of adhesion of polyisoprene on graphite by molecular dynamics simulations

ABSTRACT Elastomeric compounds are reinforced with fillers such as carbon-black and silica to improve mechanical, dynamical, and tribological properties. The stability and physical properties of these materials are dominated by the intermolecular interactions occurring at the polymer/particles interface that determine the magnitude of the polymer/particles adhesion. Using molecular dynamics simulations, in this work, we evaluate the solid–liquid interfacial tension and the corresponding work of adhesion for a system composed of graphite/Polyisoprene 100% cis-1,4 within a range of molar masses and temperatures. We employ a simulation strategy for estimating the surface tension of fluid/vacuum and fluid/solid interfaces that use directly the local stress fields in the Irving–Kirkwood formalism. Using such procedure, we decompose the stress field into the individual components of the stress tensor and correlate them with the values of the work of adhesion in the different systems analyzed. Abbreviation: PI (100% 1,4); MD: molecular dynamics; PT lateral component of the stress; PN normal component of the stress.

Estimation of near-surface attenuation in the tectonically complex contact area of the northwestern External Dinarides and the Adriatic foreland

Abstract. Seismically induced ground motion at a site is generally influenced by the seismic source, the propagation path and the local site conditions. Over the last several decades, researchers have consistently asserted that for near-site attenuation, the spectral parameter κ is subject primarily to the site conditions. In this research, we estimated the parameter κ based on the acceleration amplitude spectrum of shear waves from local earthquakes recorded by seismological stations situated in the western part of Croatia from the slope of the high-frequency part. The spatial distribution of κ values is comparable with seismological, geophysical and geological features, with the published coda-Q values for each station as well as with the isoseismal maps for selected stronger earthquakes in the study area. The complex pattern of longitudinal and transversal major late-orogenic fault zones dissecting early-orogenic thin-skinned tectonic cover in the Kvarner area and the shallow depth to the Moho (Mohorovičić discontinuity) in the Adriatic foreland (southern Istria) are probably responsible for a significant part of wave attenuation and for the anisotropy of attenuation. Regional near-surface attenuation distribution and modelled macroseismic fields point to the conclusion that attenuation properties of rocks in the northwestern External Dinarides are far from isotropic, and the most likely anisotropy sources are the preferential orientations of cracks and fractures under the local tectonic stress field, trapping of waves along major faults (waveguides), and/or attenuation within the fault zones. These results are important for gaining further insight into the attenuation of near-surface crust layers in the northwestern External Dinarides and the associated Adriatic foreland as well as in similar geotectonic settings.

Deciphering the Stress State of Seismogenic Faults in Oklahoma and Southern Kansas Based on an Improved Stress Map

AbstractFault location and geometry are critical considerations in the reactivation of preexisting faults. Here, we combine relocated earthquake catalogs and focal mechanisms to delineate seismogenic faults in Oklahoma and southern Kansas and analyze their stress state. We first identify and map seismogenic faults based on earthquake clustering. We then obtain an improved stress map using 2,047 high‐quality focal mechanisms. The regional stress map shows a gradual transition from oblique normal faulting in western Oklahoma to strike‐slip faulting in central and eastern Oklahoma. Stress amplitude ratio shows a strong correlation with pore pressure from hydrogeologic models, suggesting that pore pressure exhibits a measurable influence on stress patterns. Finally, we assess fault stress state via 3‐D Mohr circles; a parameter understress is used to quantify the level of fault criticality (with 0 meaning critically stressed faults and 1 meaning faults with no applied shear stress). Our results indicate that most active faults have near vertical planes (planarity &gt;0.8 and dip &gt;70°), and there is a strong correlation between fault length and maximum magnitude on each fault. The fault trends show prominent conjugate sets that strike [55–75°] and [105–125°]. A comparison with mapped sedimentary faults and basement fractures reveals common tectonic control. Based on 3‐D Mohr circles, we find that 78% of the faults are critically stressed (understress ≤0.2), while several seismogenic faults are misoriented with high understress (&gt;0.4). Fault geometry and local stress fields may be used to evaluate potential seismic hazard, as the largest earthquakes tend to occur on long, critically stressed faults.

Influence of the stress state on the cross-slip free energy barrier in Al: An atomistic investigation

The influence of the stress state on the cross-slip rate in Al was analyzed by means of molecular dynamics simulations and transition state theory. The activation energy barrier in the absence of thermal energy was determined through the nudged elastic band method while the cross-slip rates were determined using molecular dynamics simulations for different magnitudes of the Schmid stress on the cross-slip plane, and of the Escaig stresses on the cross-slip and glide planes. The enthalpy barrier and the effective attempt frequency were determined from the average rates of cross-slip obtained from the molecular dynamics simulations. It was found that the different stress states influence the cross-slip rate assuming harmonic transition state theory. Moreover, the theoretical contributions to the enthalpy barrier (configurational and due to the interaction of the applied stress with the local stress field created by the defect) were identified from the atomistic simulations while the entropic contribution to the activation energy could be estimated by the Meyer-Neldel rule. Based on these results, an analytical expression of the activation enthalpy for cross-slip in Al as a function of the different combinations of Schmid and Escaig stress states was developed and validated. This expression can be easily used in dislocation dynamics simulations to evaluate the probability of cross-slip of screw dislocation segments.