Heterogeneous Stress State Research Articles

Modeling Features of Both the Rupture Process and the Local Tsunami Wave Field from the 2011 Tohoku Earthquake

This paper presents the numerical simulation of the displacement distribution in the source of the 2011 Tohoku earthquake, based on the following assumptions on the geometry and mechanics of the source, and features of the subduction zone structure: displacement in the source is determined by specifying a reduced friction coefficient on the plate interface, considering heterogeneous initial stress state of the medium; source is considered in the framework of the Lay–Kanamori model as two consecutive subsources with deep and shallow location; a nonlinear elasto-plastic model of behavior of the medium under the Mohr–Coulomb yield criterion is applied. For the numerical modeling, a program code FLAC 3D implementing an explicit finite-difference scheme solution is used. The resulting lithosphere displacement distribution was used for computation of the tsunami source for given earthquake. The numerical simulation of the corresponding tsunami wave field was performed.

Simulation and prediction of the development of dynamic recrystallization during the deformation of low-alloy low-carbon steel blanks

The results of physical modeling of plastic forming using a torsional plastometer are used to analyze the effect of the temperature–deformation parameters on the development of dynamic recrystallization in a low-alloy low-carbon steel. A technique is proposed to predict the structure formation in zones with a heterogeneous state of stress, and it is based on the results of numerical simulation and physical modeling. This technique can be applied to optimize the process of plastic forming and the subsequent finishing treatment of complex-shape parts.

Resolving Fine-Scale Heterogeneity of Co-seismic Slip and the Relation to Fault Structure.

Fault slip distributions provide important insight into the earthquake process. We analyze high-resolution along-strike co-seismic slip profiles of the 1992 Mw = 7.3 Landers and 1999 Mw = 7.1 Hector Mine earthquakes, finding a spatial correlation between fluctuations of the slip distribution and geometrical fault structure. Using a spectral analysis, we demonstrate that the observed variation of co-seismic slip is neither random nor artificial, but self-affine fractal and rougher for Landers. We show that the wavelength and amplitude of slip variability correlates to the spatial distribution of fault geometrical complexity, explaining why Hector Mine has a smoother slip distribution as it occurred on a geometrically simpler fault system. We propose as a physical explanation that fault complexity induces a heterogeneous stress state that in turn controls co-seismic slip. Our observations detail the fundamental relationship between fault structure and earthquake rupture behavior, allowing for modeling of realistic slip profiles for use in seismic hazard assessment and paleoseismology studies.

Heterogeneous stress state of island arc crust in northeastern Japan affected by hot mantle fingers

AbstractBy considering a thermal structure based on dense geothermal observations, we model the stress state of the crust beneath the northeastern Japan island arc under a compressional tectonic regime using a finite element method with viscoelasticity and elastoplasticity. We consider a three‐layer structure (upper crust, lower crust, and uppermost mantle) to define flow properties. Numerical results show that the brittle‐viscous transition becomes shallower beneath the Ou Backbone Range compared with areas near the margins of the Pacific Ocean and the Japan Sea. Moreover, several elongate regions with a shallow brittle‐viscous transition are oriented transverse to the arc, and these regions correspond to hot fingers (i.e., high‐temperature regions in the mantle wedge). The stress level is low in these regions due to viscous deformation. Areas of seismicity roughly correspond to zones of stress accumulation where many intraplate earthquakes occur. Our model produces regions with high uplift rates that largely coincide with regions of high elevation (e.g., the Ou Backbone Range). The stress state, fault development, and uplift around the Ou Backbone Range can all be explained by our model. The results also suggest the existence of low‐viscosity regions corresponding to hot fingers in the island arc crust. These low‐viscosity regions have possibly affected viscous relaxation processes following the 2011 Tohoku‐oki earthquake.

Microstructure based fatigue life prediction framework for polycrystalline nickel-base superalloys with emphasis on the role played by twin boundaries in crack initiation

Fatigue crack initiation in polycrystalline materials is dependent on the local microstructure and the deformation mechanism, and can be attributed to various mechanistic and microstructural features acting in concert like the elastic stress anisotropy, plastic strain accumulation, slip-system length, and grain boundary character. In nickel-base superalloys, fatigue cracks tend to initiate near twin boundaries. The factors causing fatigue crack initiation depend on the material's microstructure, the variability of which results in the scatter observed in the fatigue life. In this work, a robust microstructure based fatigue framework is developed, which takes into account i) the statistical variability of the material's microstructure, ii) the continuum scale complex heterogeneous 3D stress and strain states within the microstructure, and iii) the atomistic mechanisms such as slip-grain boundary (GB) interactions, extrusion formations, and shearing of the matrix and precipitates due to slip. The quantitative information from crystal plasticity simulations and molecular dynamics is applied to define the energy of persistent slip bands (PSB). The energy of a critical PSB and its associated stability with respect to the dislocation motion is used as the failure criterion for crack initiation. This unified framework provides us with insights on why twin boundaries act as preferred sites for crack initiation. In addition to that, the computational framework links scatter observed in fatigue life to variability in material's microstructure.

Numerical investigation of fatigue strength of grain size gradient materials under heterogeneous stress states in a notched specimen

A possible consequence of forging in common steels is the apparition of a grain size gradient in the width of the component. For railway axles in service, this microstructure gradient is superimposed to the stress gradient introduced by the external load of rotatory bending imposed on the axle. To investigate the combined effects of these gradients on the fatigue lifetime of a forged railway axle, a numerical investigation of the effects of microstructure gradients inserted in a notched specimen is proposed, with respect to different fatigue indicators. In particular, the predictions of an approach based on the theory of critical distances seem to be very promising in this case.

ANALYSIS OF RUBBER FORMING PROCESS OF FIRE BARRIER FROM TITANIUM CP2 ALLOY FOR AW 139 HELICOPTER

This paper presents conditions of forming products from titanium sheets by means of rubber stamping method. After introducing the issues connected with these elements manufacturing for aviation industry, considering standards and legal regulations, technological problems occurring during forming deep stiffening ribs. The results in the characteristic curvatures and distortion in the final products were generated in the process heterogeneous internal stress state. The Authors aimed at explaining and presenting of solutions limiting occurrence of chosen shape faults, which disqualify these products application in aviation industry. The proposed solutions significantly reduced the incidence of these unfavorable phenomena. The modified method of rub ber stamping of firewall from titanium alloy CP-2 sheet was successfully implement ed in manufacturing conditions of PZL Swidnik.

Fully coupled thermal–electric-sintering simulation of electric field assisted sintering of net-shape compacts

A fully coupled thermal–electric-sintering finite element model was developed and implemented to predict heterogeneous densification in net-shape compacts using electric field assisted sintering techniques (FAST). FAST is a single-step processing operation for producing bulk materials from powders, in which the powder is heated by the application of electric current under pressure. Previous modeling efforts on FAST have mostly considered the thermal–electric aspect of the problem and have largely neglected the sintering aspect of the problem. A new model was developed by integrating a phenomenological sintering model into a previously established thermal–electric finite element framework to predict the densification kinetics of the sample. The model was used to quantify the effect of specimen geometry on the evolution of thermoelectric gradients and resulting heterogeneous sintering kinetics during FAST processing of a conductive powder. It is shown that the new model which considers sintering kinetics and density-dependent properties provides a substantial increase in accuracy compared to thermal–electric only models. It is also shown that small changes in local resistance due to densification can greatly impact the distribution of thermoelectric gradients during the process, which are exacerbated by heterogeneous stress states induced by sample geometry. Experimental characterization of sintered specimens is used to provide qualitative validation of the model predictions.

Thermomechanical Effects in PVTα Measurements

Knowledge of the different properties of thermoset composite materials is of great importance for the manufacturing of high quality composite parts. The resin bulk modulus is one of them and is essential to define the composite parts compressive behaviour under uniform compression. The evolution of this property with temperature and conversion degree of reaction is a challenging task and has been tentatively measured with a home-made apparatus, named PVTα, on which temperature, volume change and degree of cure are simultaneously recorded. But as the sample is contained in a non-reactive and deformable capsule, which mechanical behaviour may interfere with the measurement, a validation is required. The aim of this work is to develop a finite element model of the problem in order to simulate the thermal mechanical behaviour of the sample and the capsule, and so to validate the measurement process. The multiphysical numerical model accounts for phase change kinetics and non-linear thermal properties as well as thermo-dependent elastic properties, all problems being solved through a strong iterative coupling scheme. Mechanical contact problems between the capsule and the resin sample are handled through a penalization method contact algorithm which enables to capture the effects of chemical and thermal shrinkage in the sample and the capsule. The heterogeneous stress state generated by the material transformation is assumed to induce heterogeneous strain states which may lead to misinterpretations of macroscopic measurements. This model is a first approach and will be improved using a more sophisticated rheological model. Nevertheless, results show that the usual experimental analysis method can be used as long as the gel point is not reached. After a certain conversion degree, the measured bulk modulus is different from the effective one so corrections have to be brought.

Determination of Anisotropic Plastic Constitutive Parameters Using the Virtual Fields Method

The aim of the present study is to retrieve all the anisotropic plastic constitutive parameters from uniaxial loading. A complex geometry which can provide very heterogeneous stress states in a uniaxial tensile test was chosen for steel sheet specimens. A digital image correlation technique was used for the full-field heterogeneous strain measurement. The orthotropic Hill1948 yield criterion with Swift isotropic hardening was adopted as an elasto-plastic constitutive model. The virtual fields method (VFM) was employed as an inverse analytical tool to determine the constitutive parameters. All the parameters were successfully identified using the VFM by combining two tensile test results obtained in rolling and transverse directions.

The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

We investigate the evolution of heterogeneous stress states along frictional interfaces. Using finite-element simulations, we model the occurrence of precursory slip sequences on a deformable-deformable as well as a deformable–rigid interface between two solids. Every interface rupture creates a stress concentration at its arrest position and erases the stress concentrations produced by previous slip events. While the interface is sticking perfectly between two slip events, erased stress concentrations reappear and survive several cycles of ruptures. Such reestablished stress concentrations are smaller than they were before the rupture. We show that the decrease rate of these stress concentrations is exponential with respect to the number of subsequent events and that the bulk viscoelasticity is at the origin of this history effect. During a slip event, the friction tractions at the interface change almost instantaneously, which leads, between two ruptures, to a relaxation-resembling viscous effect that restores the stress concentration. We describe the decrease rate analytically and highlight that it is proportional to the ratio of the viscous over the instantaneous Young’s moduli, and illustrate it by varying the material properties in our simulations.

Survival of Heterogeneous Stress Distributions Created by Precursory Slip at Frictional Interfaces

We study the dynamics of successive slip events at a frictional interface with finite-element simulations. Because of the viscous properties of the material, the stress concentrations created by the arrest of precursory slip are not erased by the propagation of the following rupture but reappear with the relaxation of the material. We show that the amplitude of the stress concentrations follows an exponential decay, which is controlled by the bulk material properties. These results highlight the importance of viscosity in the heterogeneous stress state of a frictional interface and reveal the "memory effect" that affects successive ruptures.

A quantitative analysis of room temperature recrystallization kinetics in electroplated copper films using high resolution x-ray diffraction

Time-resolved in situ x-ray diffraction measurements were used to study the room-temperature recrystallization kinetics of electroplated copper thin films with thicknesses between 400 and 1000 nm. The thinnest films exhibited limited recrystallization and subsequent growth of grains, while recrystallized grains in the thicker films grew until all as-plated microstructure was consumed. For all films, recrystallized grains that belonged to the majority texture component, ⟨111⟩, started growing after the shortest incubation time. These grains exhibited volumetric growth until they achieved the film thickness. After this point the growth mode became planar, with the ⟨111⟩-type grains growing in the plane of the film. Grains with the ⟨100⟩ direction normal to the film surface started growing after the ⟨111⟩-type grains switched to planar growth. However, the planar growth of this texture component finished at the same time as the growth of the ⟨111⟩ grains. Profile fitting of the 111 peak permitted the separation of the diffraction signals from recrystallized and as-plated grain populations. The average strains in these two populations, calculated from the peak position of the corresponding {111} reflections, were different, indicating a heterogeneous stress state within this texture component. The increasing volume fraction of recrystallized ⟨111⟩ grains with time was monitored via the variation in the diffracted intensity. This variation could be represented by the Johnson–Mehl–Avrami–Kolmogorov model.

An earthquake model with interacting asperities

SUMMARY A model is presented that treats an earthquake as the failure of asperities in a manner consistent with modern concepts of sliding friction. The mathematical description of the model includes results for elliptical and circular asperities, oblique tectonic slip, static and dynamic solutions for slip on the fault, stress intensity factors, strain energy and second-order moment tensor. The equations that control interaction of asperities are derived and solved both in a quasi-static tectonic mode when none of the asperities are in the process of failing and a dynamic failure mode when asperities are failing and sending out slip pulses that can trigger failure of additional asperities. The model produces moment rate functions for each asperity failure so that, given an appropriate Green function, the radiation of elastic waves is a straightforward calculation. The model explains an observed scaling relationship between repeat time and seismic moment for repeating seismic events and is consistent with the properties of pseudo-tachylites treated as fossil asperities. Properties of the model are explored with simulations of seismic activity that results when a section of the fault containing a spatial distribution of asperities is subjected to tectonic slip. The simulations show that the failure of a group of strongly interacting asperities satisfies the same scaling relationship as the failure of individual asperities, and that realistic distributions of asperities on a fault plane lead to seismic activity consistent with probability estimates for the interaction of asperities and predicted values of the Gutenberg–Richter a and b values. General features of the model are the exterior crack solution as a theoretical foundation, a heterogeneous state of stress and strength on the fault, dynamic effects controlled by propagating slip pulses and radiated elastic waves with a broad frequency band.

Hydrogen-induced delayed cracking in the AISI 301 unstable austenitic steel sheet

This work aims to study the hydrogen-induced delayed cracking related to the martensitic transformation in the AISI 301 unstable austenitic stainless steel. It happens because the metastable austenite is substantially transformed into α ′ -martensite due to the deformation occurring during the clamp-forming operation. To understand this phenomenon, morphological and chemical analyses have been made. The martensite fraction in the inside bend radius was measured by X-ray Diffraction (XRD) and the breaking patterns were observed using a Scanning Electron Microscope (SEM). The clamps breaking patterns observed after delayed cracking show a brittle intergranular fracture in the bend radius. Under laboratory conditions and after hydrogen-charged clamps, delayed cracking occurred. The main fractographic feature observed in cracked clamps is the intergranular Hydrogen Embrittlement (HE). This brittle behavior is intensified by the high heterogeneous stress state in the material and the high content of martensite.

Anisotropic elastocreep in glacial ice: A mechanism for intergranular melt and recrystallization

[1] Bonded ice crystals under pressure are in a heterogeneous stress state because of the mechanical anisotropy of constituent grains. This condition plays a role in intergranular melt and recrystallization, which in turn influence properties such as permeability and biologic habitability. To examine this, we develop an anisotropic elastocreep model simulating subgrain-scale stresses in polycrystalline ice, choosing in particular the thermal and deformational regime of the Lake Vostok accretion ice. A critical assumption with regard to localized melting is the macroscopic deviatoric stress. Our calculations indicate that for a macroscopic deviatoric stress of 50 kPa, ice at 0.04°C below the bulk melting temperature would contain regions, at scales ∼1% the grain size, where the liquid phase is thermodynamically favored. This translates to scales of ∼5 mm in the lower few meters of the Vostok accretion under a deviatoric stress that is plausible near the lake perimeter. Less internal melting is indicated in analyses of ice relatively far from the lake margins due to the assumed presence of lower macroscopic deviatoric stress. Simulated strain energy jumps of 1–2% across grain boundaries of accretion ice near the lake boundaries are large relative to free surface energy, indicating the importance of the former in boundary migration recrystallization. Collectively, these findings are consistent with measured dislocation densities (>107–1010 m−2) and irregular grain morphologies found in core samples. The calculated melting point depressions associated with anisotropy fall short of experimental values by a factor of ∼2, while the calculated strain rates deviate by ∼20%.

Coupling of eruptions and earthquakes at Mt. Etna (Sicily, Italy): A case study from the 1981 and 2001 events

Changes in Coulomb failure stress (ΔCFS) induced by dike propagation during two flank eruptions on Mt. Etna (1981 and 2001) are calculated for the most seismically active faults on the east slope of the volcano (the right‐lateral Timpe fault system, oriented NNW‐SSE, and the left‐lateral Pernicana fault, oriented E‐W). Calculations performed using Coulomb 2.5 software indicate that intrusion of a NNW dike on the NW side of the volcano (1981 eruption) rises ΔCFS on both the Timpe and Pernicana faults. In contrast, intrusion of a N‐S dike at high elevation on the south flank (2001 eruption) rises ΔCFS only on Timpe fault System. These results are compatible with the observed pattern of seismicity, but emphasize an extremely heterogeneous state of stress on the east flank of the volcano.

Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for face-centered cubic crystals

The fracture toughness of ductile materials depends upon the ability of the material to resist the growth of microscale voids near a crack tip. Mechanics analyses of the elastic–plastic deformation state around such voids typically assume the surrounding material to be isotropic. However, the voids exist predominantly within a single grain of a polycrystalline material, so it is necessary to account for the anisotropic nature of the surrounding material. In the present work, anisotropic slip line theory is employed to derive the stress and deformation state around a cylindrical void in a single crystal oriented so that plane strain conditions are admitted from three effective in-plane slip systems. The deformation state takes the form of angular sectors around the circumference of the void. Only one of the three effective slip systems is active within each sector. Each slip sector is further subdivided into smaller sectors inside of which it is possible to derive the stress state. Thus the theory predicts a highly heterogeneous stress and deformation state. In addition, it is shown that the in-plane pressure necessary to activate plastic deformation around a cylindrical void in an anisotropic material is significantly higher than that necessary for an isotropic material. Experiments and single crystal plasticity finite element simulations of cylindrical voids in single crystals, both of which exhibit a close correspondence to the analytical theory, are discussed in a companion paper.

Le bassin de Tizi n'Test (Haut Atlas, Maroc) : exemple d'évolution d'un segment oblique au rift de l'Atlantique central au Trias

Detailed mapping completed by a microtectonic study of the Tizi n'Test Triassic basin, located along the Tizi n'Test fault zone in the Moroccan High Atlas, has allowed us to improve the knowledge on the geometry of the structures and the activity of faults during the Triassic extensional events related to the rifting of the central Atlantic. The latter are reflected by the development of a rift, at present inverted and deformed by the collision of Africa and Europe, comprising kilometric-scale grabens and half-grabens bounded by major faults trending ENE–WSW, with a dip towards the NNW, and a dip-slip syndepositional motion. Inverse analysis of fault slickenside populations shows a heterogeneous Triassic state of stress. However, in the most significant measurement sites, the maximum horizontal stress σ1 is vertical, while the minimum stress σ3 is horizontal with a NW–SE trend. The strike-slip component appears to be very small during the Triassic, a noticeable fact because of the obliquity of the basin with respect to the Atlantic rift.

Earthquakes as a coupled shear stress‐high pore pressure dynamical system

The migration, coalescence and localization of slip, seismicity, and zones of high pore pressure are modeled using a porosity reduction mechanism to drive pore pressure within a fault zone in excess of hydrostatic. Increased pore pressure in discrete cells creates zones of low effective stress, which induces slip that may propagate to surrounding cells depending on the local state of stress. At slip, stress is transferred using the solution for a rectangular dislocation in an elastic half‐space, and pore pressures are redistributed by conserving fluid mass. Using simple assumptions about fault rheology and permeability, it is shown that the interaction between shear stress and effective stress evolves to a state of earthquake clustering with repeated events, locked zones, and large variations in fault strength. The model evolves from a uniform shear stress state on a strong fault, to a heterogeneous shear stress state on a weak fault.