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Certain metals experience a substantial deterioration in mechanical properties when exposed to a hydrogen environment, an effect termed hydrogen embrittlement. To understand, predict, and counteract this hydrogen‐assisted material degradation, sufficiently accurate material models are needed. According to the current hypothesis, hydrogen diffusion is driven by gradients of concentration and hydrostatic stress. To capture this, a phase‐field model is formulated as a multi‐field problem coupling deformation, crack propagation, and diffusion to analyze hydrogen‐promoted fracture. Here, the displacements, a fracture‐related phase‐field, the hydrogen lattice occupancy, and the chemical potential are considered as primary field variables. Approaches proposed in the literature often use an extrapolation of the hydrostatic stress calculated at the material point level onto the nodes and later use the B‐matrix to compute the gradient of hydrostatic stress. In order to circumvent this potentially inaccurate extrapolation, the model is recast into a mixed rate‐type variational setting, where the chemical potential—whose gradient governs the hydrogen flux—is obtained from the numerical solution of a saddle point problem. A representative boundary value problem is presented to demonstrate the applicability of the developed numerical framework. [ABSTRACT FROM AUTHOR]

Since many years ago, ultrasonic velocity has been used to investigate the physical and mechanical behaviour of rocks, thereby playing an important role in reservoir characterization and seismic interpretation. In order to develop the knowledge of ultrasonic tools, we performed a noble analysis on the ultrasonic behaviour of rocks under confining stress and evaluated a distinctive property of porous media that is measured as the area under the stress–velocity curve (here defined as S*). We further investigated its relationship with elastic and mechanical behaviours of rock. To validate the theoretical framework developed in this work, 20 core plugs from various rock units with complex microstructures were subjected to triaxial compressional tests to calculate their area under the curve. Calculations were made for crack‐closing, elastic and post‐elastic stages (e.g. pore collapse) along the ultrasonic velocity–stress curve. Moreover, the selected samples had their microstructure investigated by thin‐section studies to quantify their porosity and pore type. The results were analysed to check for the effect of pore type on S* in different stages of the stress–velocity curve. Based on the outputs of the analysis of variance and Pearson's correlation coefficient analysis, the curve had its shape and underlying area closely related to the porosity and pore geometry. Indeed, the results showed that the shale and sandstone with micro cracks and carbonate with stiff pores correspond to smaller and larger areas under the curve in crack‐closing and inelastic stages, respectively. Cross‐correlating the results to compressibility (inverse of bulk modulus), it was figured out that the calculated area under curve was well consistent with the compressibility. In addition, S* represents both static and dynamic behaviours of the rock, and the results revealed that the shape and curvature of the stress–velocity curve give valuable information about the rock microstructure. Another finding was the fact that the type of fluid and wave velocity seemingly affect the S*. Our findings can help interpret wave velocity behaviour in reservoir rocks and other stressful porous media. [ABSTRACT FROM AUTHOR]

We apply Muskhelishvili's complex variable method to solve the plane strain problem associated with two circular incompressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to uniform remote in‐plane normal stresses. An analytical solution to the problem is derived primarily with the aid of conformal mapping and analytic continuation. To demonstrate our analytical solution, we present detailed numerical results characterizing the internal uniform hydrostatic stresses within the two liquid inclusions, the nonuniform hoop stresses along the two circular liquid‐solid interfaces on the matrix side and the nonuniform rigid body rotations within the two circular liquid inclusions. [ABSTRACT FROM AUTHOR]

The hydrogen solubility in ferritic and martensitic steels is affected by hydrostatic stress, pressure, and temperature. In general, compressive stresses decrease but tensile stresses increase the hydrogen solubility. This important aspect must be considered when qualifying materials for high‐pressure hydrogen applications (e.g., for pipelines or tanks) by using autoclave systems. In this work, a pressure equivalent for compensating the effect of compressive stresses on the hydrogen solubility inside of closed autoclaves is proposed to achieve solubilities that are equivalent to those in pipelines and tanks subjected to tensile stresses. Moreover, it is shown that the temperature effect becomes critical at low temperatures (e.g., under cryogenic conditions for storing liquid hydrogen). Trapping of hydrogen in the microstructure can increase the hydrogen solubility with decreasing temperature, having a solubility minimum at about room temperature. To demonstrate this effect, the generalized law of the hydrogen solubility is parameterized for different steels using measured contents of gaseous hydrogen. The constant parameter sets are verified and critically discussed with respect to the high‐pressure hydrogen experiments. [ABSTRACT FROM AUTHOR]

Hydrogen as an energy carrier is politically supported and essential for the planned energy turnaround, but requires infrastructure for transport and storage of hydrogen on a large scale, which in turn requires the development of steels resistant to hydrogen‐induced damage. Since the experimental characterization of local hydrogen concentration is nearly impossible, but microstructure level effects are significant for damage initiation, it becomes essential to further develop accompanying numerical evaluation methods. These have to be able to quantitatively describe the effect of nonmetallic inclusions on the local hydrogen concentration as the detrimental effect of nonmetallic inclusions governs the resistance against hydrogen‐induced cracking. To capture this influence, the modeling approaches available in the literature are extended and made usable for tetrahedral elements. Validation is performed using numerical studies with specimens of different stress states. Submodels are exposed to a virtual cooling and then to a hydrogen loading. Based on the resulting residual stress fields, the local hydrogen concentrations around nonmetallic inclusions with different chemical compositions and geometry are investigated and evaluated. Herein, it can be shown that especially the hydrostatic stress has a large influence on the development of the local hydrogen concentration and that the influence is particularly strong for Al2O3‐inclusions. [ABSTRACT FROM AUTHOR]

Gravity waves generated by mountains are multiscale and three‐dimensional. Current orographic gravity wave drag parametrisation schemes assume that the waves are two‐dimensional, varying only in the vertical and along one horizontal direction. These schemes, therefore, do not represent the process of partial critical‐level filtering, whereby a portion of the wave spectrum is saturated where the winds parallel to the wavevectors become small. This results in an unrealistic vertical distribution of the momentum flux and forcing of the waves on the mean flow. In this paper, a method of accounting for partial critical‐level filtering in an orographic gravity wave drag parametrisation using the full spectrum of realistic topography is presented. This is achieved through binning of the expression for linear hydrostatic surface stresses, computed using Fourier transforms of the subgrid orographic heights within model grid boxes, into wavevector directions. The parametrisation is compared with idealised nonlinear simulations of flow over complex topography and is shown to perform well as the number of wavevector direction bins is increased. Implementation of the scheme into the Met Office Unified Model is tested using short‐range 5‐day forecasts. As is found from idealised simulations, the binned scheme leads to less forcing in the troposphere and increased forcing in the stratosphere within the model. The binned scheme is shown to alleviate biases in the upper stratosphere, between 45 and 65 km, as well as having significant local effects in the troposphere. [ABSTRACT FROM AUTHOR]

Mineral compositions are used to infer pressures, temperatures, and timescales of geological processes. The thermodynamic techniques underlying these inferences assume a uniform, constant pressure. Nonetheless, convergent margins generate significant non‐hydrostatic (unequal) stresses, violating the uniform pressure assumption and creating uncertainty. Materials scientists F. Larché and J. Cahn derived an equation suitable for non‐hydrostatically stressed geologic environments that links stress and equilibrium composition in elastic, multi‐component crystals. However, previous works have shown that for binary solid solutions with ideal mixing behavior, hundreds of MPa to GPa‐level stresses are required to shift mineral compositions by a few hundredths of a mole fraction, limiting the equation's applicability. Here, we apply Larché and Cahn's equation to garnet, clinopyroxene, and plagioclase solid solutions, incorporating for the first time non‐ideal mixing behavior and more than two endmembers. We show that non‐ideal mixing increases predicted stress‐induced composition changes by up to an order of magnitude. Further, incorporating additional solid solution endmembers changes the predicted stress‐induced composition shifts of the other endmembers being considered. Finally, we demonstrate that Larché and Cahn's approach yields positive entropy production, a requirement for any real process to occur. Our findings reveal that stresses between tens and a few hundred MPa can shift mineral compositions by several hundredths of a mole fraction. Consequently, mineral compositions could plausibly be used to infer stress states. We suggest that stress‐composition effects could develop via intracrystalline diffusion in any high‐grade metamorphic setting, but are most likely in hot, dry, and strong rocks such as lower crustal granulites. Plain Language Summary: The chemical compositions of many minerals found in rocks are sensitive to the pressure and temperature conditions at which the minerals form. Thus, we can use mineral compositions to deduce the formation conditions of rocks, giving us insights into important geological processes such as the global carbon cycle and continent formation. The techniques we use to determine these conditions assume that pressure is equal in all directions. However, minerals sometimes form in settings where there is significantly more pressure, or stress, in one direction than another due to, for example, colliding tectonic plates. As a result, there is uncertainty as to how to interpret the compositions of such minerals. In this work, we apply a theory developed by materials scientists that provides a way to quantify the expected compositions of different types of minerals based on the directions and magnitudes of stresses. This approach will enable us to use mineral compositions to learn more about the pressure and stress conditions in important geological settings such as within subduction zones and mountain belts. Key Points: Non‐ideal mixing increases stress‐induced composition changes in minerals by up to an order of magnitude compared to ideal mixingAll pertinent solid solution endmembers should be considered to determine how stress changes affect the composition of each endmemberStress‐induced composition effects are likely to develop in hot, dry rocks comprising strong minerals such as lower crustal granulites [ABSTRACT FROM AUTHOR]

Investigations of biphasic monodisperse soft (rubber) and stiff (glass) particle mixtures under hydrostatic conditions show an interesting behavior with regard to the effective stiffness. P‐wave modulus measured by acoustic wave propagation at ultrasonic frequencies showed a significant decline while more soft particles are added, that is, higher rubber volume fractions, due to a change in the microstructure of the granular medium. However, for small volume fractions of soft particles, it could be observed that the P‐wave modulus is increasing. This result cannot be explained by classical mixture rules or effective medium theories. For the understanding of those effects, a detailed insight into the microstructure of the granular medium is necessary. To gain this information and link it later back to the measured effective mechanical properties, high‐resolution micro X‐ray computed tomography (μXRCT) imaging is a well‐established tool. With μXRCT imaging, the granular microstructure can be visualized in 3D and characterized subsequently. Combining classical effective characterization methods with μXRCT imaging can help to solve a variety of multi‐scale problems. Performing the characterization step in situ, meaning inside the laboratory‐based μXRCT scanner, has the advantage that exactly the same samples are mechanically characterized and visualized. To address the mentioned observation above, we designed a low X‐ray absorbing oedometer cell with integrated broadband piezoelectric P‐wave transducers which enables this kind of investigation inside a laboratory‐based μXRCT scanner. The focus of this contribution is on the general experimental methodology which can be transferred to other multi‐scale problems. It starts with a description of the image acquisition and ends with the post‐processing of the in situ acquired image data. To demonstrate this, cylindrical samples consisting of the same monodisperse rubber and glass particle mixtures that were studied before under hydrostatic stress conditions are considered. Selected results are presented to explain the single steps. [ABSTRACT FROM AUTHOR]

Gibbs free energy, the fundamental thermodynamic potential used to calculate equilibrium mineral assemblages in geological systems, does not apply to non‐hydrostatically stressed solids. Consequently, there is debate over the significance of non‐hydrostatic stress in petrological and geophysical processes. To help resolve this debate, we consider the effects of non‐hydrostatic stress on the polymorph pairs kyanite/sillimanite, graphite/diamond, calcite/aragonite, and quartz/coesite. While these polymorphs are most relevant to metamorphic processes, the concepts developed are applicable to any single‐component solid reaction. We quantitatively show how stress variations normal to an interface alter equilibrium temperatures of polymorph pairs by approximately two orders of magnitude more than stress variations parallel to an interface. Thus, normal stress controls polymorph stability to first order. High‐pressure polymorphs are expected to preferentially nucleate normal to and grow parallel to the maximum stress and low‐pressure polymorphs, the minimum stress. Nonetheless, stress variations parallel to an interface allow for the surprising possibility that a high‐pressure polymorph can become more stable relative to a low‐pressure polymorph as stress decreases. The effects of non‐hydrostatic stress on mineral equilibrium are unlikely to be observed in systems with interconnected, fluid‐filled porosity, as fluid‐mediated reactions yield mineral assemblages at approximately constant pressures. In dry systems, however, reactions can occur directly between elastic solids, facilitating the direct application of non‐hydrostatic thermodynamics. Non‐hydrostatic stress is likely to be important to the evolution of metamorphic systems, as preferential orientations of polymorphic reactions can generate seismicity and may influence fundamental rock properties such as porosity and seismic anisotropy. Plain Language Summary: Geoscientists are interested in determining at what temperatures and pressures different minerals are stable in the Earth. This is because the breakdown and formation of minerals are important for processes such as the generation of earthquakes and the geochemical cycling of elements such as hydrogen and carbon. However, a key problem is that the calculations we use to determine if minerals are stable assume that pressure is equal in all directions. But if this were true, there would be no mountains or earthquakes which are caused by unequal pressures deep within our planet. This leaves the question of how do we determine mineral stability when pressure is not equal in all directions? In our work, we show that the pressure on each side of a mineral determines whether each side is stable. This means, for example, if one squeezes graphite hard enough in one direction, the squeezed sides will start to form diamond while the other sides remain graphite. Consequently, when pressure is not equal in all directions, minerals will break down or form in certain directions. This could create cracks for earthquakes, or allow water to enter rocks more easily, influencing subsurface fluid flow and element cycling. Key Points: Normal stress determines chemical potential and consequent phase stability on a given interface to first orderInterface‐parallel stresses can influence phase stability for interfaces near a reaction boundaryNon‐hydrostatic thermodynamics are directly applicable to dry systems undergoing solid‐solid reactions [ABSTRACT FROM AUTHOR]

This study combines the microstructural and petrological analysis of garnet and its inclusions in quartzite‐hosted garnetite from the ultrahigh‐pressure Lago di Cignana metaophiolite (Western Alps). We present a comprehensive record of metamorphism, compaction, and the state of stress during interaction between oceanic metasediments and infiltrating fluids along a major open‐system fluid pathway. The arrangement of garnet into garnetite layers is attributed to concomitant compaction and dissolution that resulted in the formation of a garnet stylolite. The fluid pulses that were accommodated by this pathway subsequently resulted in several stages of garnet deformation, dissolution, local reprecipitation, and recrystallization. Abundant evidence for pressure solution in garnet, alongside near‐hydrostatic to hydrostatic conditions indicated by elastic strains of quartz inclusions in garnet obtained through Raman spectroscopy, support low differential stresses during fluid–rock interaction. The high degree of dissolution recorded by the garnetite showcases the strong potential for compaction by fluid‐assisted volume loss and mass transfer. Dehydration of subducting rocks with subsequent migration of resulting fluids through the slab provides a mechanism of mass transfer and has the potential to drive compaction and exert control on differential stress along fluid pathways. [ABSTRACT FROM AUTHOR]

Summary: Inherent heterogeneity of a rock strongly affects its mechanical behavior. We numerically study the mechanisms governing the initiation, propagation, and ultimate pattern of borehole breakouts in heterogeneous rocks. A two‐dimensional finite element model incorporating material heterogeneity is established to systematically examine the effects of several key factors on borehole failure, including borehole diameter, far‐field stress, and rock heterogeneity. The inherent heterogeneity of a rock is explicitly characterized by prescribing the rock mechanical properties of mesoscale elements statistically obeying the Weibull distribution. Elastic damage mechanics is used to represent the constitutive law of the mesoscale element. We find that borehole diameter reduction remarkably changes the crack failure from tensile to shear and elevates the critical hydrostatic pressure. Far‐field stress anisotropy strongly affects the shape of the borehole breakout. Rock heterogeneity dictates the location of the preferred crack under the hydrostatic stress, which leads to local stress concentration, and determines the types of breakouts around the borehole. Our findings facilitate in‐depth understanding of the classic borehole stability problems in heterogeneous rocks. [ABSTRACT FROM AUTHOR]

This study reports the type IV fracture process and the influence of multiaxial stress state in ASME T92 welded joints during creep. The type IV fracture occurs at the fine‐grained heat‐affected zone (ie, FGHAZ), involving void initiation, growth, and coalescence, microcrack occurrence, propagation and extension, and eventual macrocrack with consequent joint failure. The creep damage is not uniformly distributed along the thickness direction in the FGHAZ, and the central part of the welded joint is the most seriously damaged region. The equivalent creep strain is higher at the external surface, but the stress triaxiality is larger in the centre section. Large equivalent creep strain could promote creep void initiation, whereas high hydrostatic pressure and stress triaxiality factor accelerate void growth in the FGHAZ of T92 joints. Besides, reducing groove angle and HAZ width of the joints is recommended to delay the occurrence of type IV cracking because of lower equivalent creep strain and stress triaxiality factor. [ABSTRACT FROM AUTHOR]

Summary: A bounding surface model is formulated to simulate the behavior of clays that are subject to an anisotropic consolidation stress history. Conventional rotational hardening is revisited from the perspective of thermodynamics. As the free energy cannot be accumulated infinitely upon critical state failure, the deviatoric back stress must vanish. This requires the rotated yield surface to be turned back to eventually align on the hydrostatic axis in the stress plane. Noting that most of the previous propositions violate this restriction, an innovative rotational hardening rule is formulated that is thermodynamically admissible. The bounding surface framework that employs the modified yield surface is applied to simulate elastoplastic deformations for overconsolidated clays, with which the overprediction of strength on the "dry" side can be greatly improved with reasonable results. Other important features, including contractive or dilative response and hardening or softening behavior, can also be well‐captured. It has been shown that the model can simulate three types of reconstituted clays that are sheared with initial conditions over a wide range of anisotropic consolidation stress ratios and overconsolidation ratios under both triaxial undrained and drained conditions. Limitations and potential improvement of the model regarding the fabric anisotropy at critical state have been discussed. [ABSTRACT FROM AUTHOR]

The evolution of residual stresses found within a silicon carbide/silicon carbide (SiC/SiC) ceramic matrix composite through thermal treatments was investigated using Raman microspectroscopy. Constituent stress states were measured before, during, and after exposures ranging from 900 to 1300°C for varying times between 1 and 60 minutes. Silicon carbide particles in the as‐received condition exhibited average hydrostatic tensile stresses of approximately 300 MPa when measured at room temperature before and after heat treatment. The room temperature Raman profile of the silicon matrix was altered in both shape and location with heat treatment cycles due to increasing activation of boron within the silicon lattice as heat treatment temperatures increased. By accounting for boron activation in the silicon–boron system, little to no permanent change of any constituent stresses were observed, and the silicon matrix subsequently exhibited a complimentary average hydrostatic compressive stress of approximately 300 MPa at room temperature, measured before and after heat treatment. This result builds upon previous literature and offers increased insight into boron activation phenomena measured through Raman spectroscopy methods. [ABSTRACT FROM AUTHOR]

Tension‐compression, tension‐tension, torsional, and 90° out‐of‐phase axial‐torsional fatigue tests were performed on a quenched and tempered U2 steel. All tests were conducted under force/torque control because macroscopic plastic strains were insignificant in the life range of interest (from 104 to 2 × 106 loading cycles). Stress‐based versions of the Fatemi‐Socie critical plane parameter and of the Smith‐Watson‐Topper parameter with a critical plane interpretation were evaluated using the experimental data. The Smith‐Watson‐Topper parameter was not able to correlate the test data. The Fatemi‐Socie method correlated most of the test data within factor‐of‐three boundaries. A modified Crossland invariant‐based parameter made of two interaction rules between the shear stress amplitude and the maximum hydrostatic stress, and of a definition of shear stress amplitude based on the maximum prismatic hull method, yielded fatigue life estimates in reasonable agreement with the experimental observations. [ABSTRACT FROM AUTHOR]

Ultrasonic elastic‐wave velocities, as well as the stress‐strain behavior, were measured on dry dune sand from Saudi Arabia under hydrostatic loading from 0 to 50 MPa. The samples came from the dune's crest, limb, and base. The experiments included several loading and unloading cycles. All samples exhibited irreversible deformation and porosity reduction during the tests due to grain repacking in low‐stress regimes and grain breakage at higher stress. The loading behavior was plastic, while the unloading/reloading behavior was elastic. In spite of noticeable porosity variations during the experiments, the elastic‐wave velocities mainly depended on the stress rather than on porosity. Our velocity versus stress data is very close to earlier published results, although the provenance of the sand is very different, pointing at a universality of such behavior in loose sand. Our results were matched by the contact Hertz‐Mindlin theory with varying coordination number and shear‐stiffness adjustment. We also offer a new theoretical model for the static bulk modulus measured in these experiments. This model is based on the concept of stress heterogeneity (stress chains or patches) in a granular pack and uses elastic bound averaging of the respective moduli of stressed and unstressed parts of the pack. The same model is used to describe the velocity versus stress behavior. These results and theory constitute a new installment into the published sparse data of the mechanical properties of unconsolidated sand as well as theoretical analyses thereof and are the first ever such data generated in Saudi Arabia. Key Points: New dataset on dune sand, velocity and deformationNew theory for elastic‐wave velocityNew theory for static bulk modulus [ABSTRACT FROM AUTHOR]

Rock strength criterion is a basic subject in mining engineering and petroleum engineering. It has important guiding significances to the process of underground energy exploitation. Different rocks have different strength envelopes. Most strength criteria have only one type of envelope in π plan. Thus, these criteria cannot predict different rock strengths accurately. Most criteria consider only the hydrostatic stress and the Lode angle effects and neglect their interaction. However, based on the experimental results in this study, there is an evident interaction between the two effects. In this study, a new strength criterion is proposed considering the hydrostatic stress and Lode angle effects, as well as the effect of hydrostatic stress on the Lode angle effect. Applicable results of previous experimental data showed that the proposed strength criterion has good applicability for different rocks. Compared with other strength criteria, this criterion has the advantage of being able to adjust the strength of the Lode angle effect based on the hydrostatic stress. This advantage allows the strength criterion to show different types of strength envelopes in the π plan and to accommodate different rocks under different stress states. The effect of hydrostatic stress on the Lode angle effect of rock may be caused by the proportion of particles destroyed in the rock. [ABSTRACT FROM AUTHOR]

Summary: This paper presents analytical elastic‐plastic solutions for static stress loading analysis and quasi‐static expansion analysis of a cylindrical cavity in Tresca materials, considering biaxial far‐field stresses and shear stresses along the inner cavity wall. The two‐dimensional static stress solution is obtained by assuming that the plastic zone is statically determinate and using the complex variable theory in the elastic analysis. A rigorous conformal mapping function is constructed, which predicts that the elastic‐plastic boundary is in an elliptic shape under biaxial in situ stresses, and the range of the plastic zone extends with increasing internal shear stresses. The major axis of the elliptical elastic‐plastic boundary coincides with the direction of the maximum far‐field compression stress. Furthermore, considering the internal shear stresses, an analytical large‐strain displacement solution is derived for continuous cavity expansion analysis in a hydrostatic initial stress filed. Based on the derived analytical stress and displacement solutions, the influence of the internal shear stresses on the quasi‐static cavity expansion process is studied. It is shown that additional shear stresses could reduce the required normal expansion pressure to a certain degree, which partly explains the great reduction of the axial soil resistance due to rotations in rotating cone penetration tests. In addition, through additionally considering the potential influences of biaxial in situ stresses and shear stresses generated around the borehole during drillings, an improved cavity expansion approach for estimating the maximum allowable mud pressure of horizontal directional drillings (HDDs) in undrained clays is proposed and validated. [ABSTRACT FROM AUTHOR]

Abstract: Metamorphic geology has accumulated a huge body of observation on mineral assemblages that reveal strong patterns in occurrence, summarized, for example, in the idea of metamorphic facies. On the realization that such patterns needed a simple explanation, there has been considerable a posteriori success from adopting the idea that equilibrium thermodynamics can be used on mineral assemblages to make sense of the patterns in terms of, for example, the pressure and temperature of formation of mineral assemblages. In doing so, a particularly simple implicit assumption is made, that mineral assemblages operate essentially hydrostatically. Structural geologists have studied the same rocks for different ends, but, remarkably, the phenomena they are interested in depend on non‐hydrostatic stress. We look at the effect of such behaviour on mineral equilibria. With adoption of some plausible assumptions about how metamorphism in the crust works, the consequence of minerals being non‐hydrostatically stressed is commonly second order in equilibrium calculations. [ABSTRACT FROM AUTHOR]

This article presents a review of selected multiaxial high-cycle fatigue criteria with an emphasis on their ability to take into account the mean stress effect and the effect of a biaxial stress state. It is shown that the predictions of the various criteria are very different for the case of biaxial tensile loads. This is in contrast to the case of combined tension-torsion loads, where the predictions are very similar. The second part of the article investigates which mechanical parameter (eg, the hydrostatic stress or the normal stress) is the most appropriate to take into account these cyclic stress states. [ABSTRACT FROM AUTHOR]

We have developed an analytical method to determine the segregation levels on the same tilt boundaries (TBs) at the same nanoscopic location by a joint use of atom probe tomography and scanning transmission electron microscopy, and discussed the mechanism of oxygen segregation at TBs in silicon ingots in terms of bond distortions around the TBs. The three-dimensional distribution of oxygen atoms was determined at the typical small- and large-angle TBs by atom probe tomography with a low impurity detection limit (0.01 at.% on a TB plane) simultaneously with high spatial resolution (about 0.4 nm). The three-dimensional distribution was correlated with the atomic stress around the TBs; the stress at large-angle TBs was estimated by ab initio calculations based on atomic resolution scanning transmission electron microscopy data and that at small-angle TBs were calculated with the elastic theory based on dark-field transmission electron microscopy data. Oxygen atoms would segregate at bond-centred sites under tensile stress above about 2 GPa, so as to attain a more stable bonding network by reducing the local stress. The number of oxygen atoms segregating in a unit TB area NGB (in atoms nm−2) was determined to be proportional to both the number of the atomic sites under tensile stress in a unit TB area nbc and the average concentration of oxygen atoms around the TB [Oi] (in at.%) with NGB ∼ 50 nbc[Oi]. [ABSTRACT FROM AUTHOR]

The effective shear and bulk viscosity, as well as dynamic viscosity, describe the rheological properties of the ceramic body during the liquid phase sintering process. The rheological parameters depend on the physical and thermo-mechanical characteristics of the material such as relative density, temperature, grain size, diffusion coefficient, and activation energy. In this paper, the numerical-experimental method has been developed to study both viscous and rheological behavior of hard porcelain ceramic body during liquid phase sintering. The other aim is to acquire a complete understanding of the response of an incompressible viscose material during sintering such as stress-strain relations, sintering, and hydrostatic stress. Densification results confirmed that the bulk viscosity was well-defined with relative density. The stress analysis proved that the sintering stress is more than the hydrostatic stress during the entire sintering time so, the sintering process occurs completely. Deflection results showed that the shear viscosity was a fair estimation of real ones. Dilatometry, SEM, XRD investigations as well as bulk viscosity simulation results confirmed that the 'mullitisation plateau' was presented as a very little extraordinary expansion at the final sintering stage. [ABSTRACT FROM AUTHOR]

It has been well-established that the non-singular T-stress provides a first-order estimate of geometry and loading mode (e.g. tension versus bending) effects on elastic-plastic crack-front field under mode I loading conditions. The objective of this paper is to exam the T-stress effect on three-dimensional (3D) crack-front fields under mixed-mode (modes I and II) loading. To this end, detailed 3D small strain, elastic-plastic simulations are carried out using a 3D boundary layer (small-scale yielding) formulation. Characteristics of near crack-front fields are investigated for a wide range of T-stresses ( T/ σ0 = −0.8, −0.4, 0.0, 0.4, 0.8). The plastic zones and thickness and angular and radial variations of the stresses are studied, corresponding to two values of the remote elastic mixity parameters Me = 0.3 and 0.7, under both low and high levels of applied loads. It is found that different T-stresses have a significant effect on the plastic zones size and shapes, regardless of the mode mixity and load level. The thickness, angular and radial distributions of stresses are also affected markedly by T-stress. It is important to include these effects when investigating the mixed-mode ductile fracture failure process in thin-walled structural components. [ABSTRACT FROM AUTHOR]

We develop a new method to construct periodic inclusions with uniform internal hydrostatic stress in an elastic plane subjected to uniform remote in-plane loading. The method is based on two particular conformal mappings which lead to a system of nonlinear equations from which the inclusion shapes are determined. We illustrate our results with several examples. In particular, we show that the ratio of the inclusion size to the period of the inclusion-matrix system changes with the inclusion aspect ratio and, in the specific case of uniform remote shear loading, the orientation of the inclusions is also altered. Finally, we show that if the period of the inclusion-matrix system exceeds roughly six times the inclusion size, such periodic inclusions can be treated approximately as periodic elliptical inclusions with specific aspect ratio and orientation determined by the corresponding elastic constants and uniform remote loading. [ABSTRACT FROM AUTHOR]

The problem of a spherical shell made of an elastic-plastic second gradient model for plastic materials and subjected to hydrostatic tension is considered. The elastic-plastic second gradient model is a simplified version (porosity neglected) of a second gradient model for plastic porous metals developed, some years ago, by Gologanu, Leblond, Perrin and Devaux, so-called GLPD model. The expressions of the velocity field as well as the ordinary and double stress components are determined for the cases where the spherical shell is modeled by a purely elastic, purely plastic, and elastic-plastic GLPD models. As expected, the solution developed in each case (elastic, ideal-plastic, and elastic-plastic) reduces to that of the first gradient as a special case when the characteristic length scale the GLPD model involves is negligible. Our results allow comparisons between the newly developed solution and the classical elastic-plastic solution for the same model problem; they also provide insights into the influence of the characteristic length scale on the newly developed solution. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the influence of initial stress on the frequency equation of flexural waves in a transversely isotropic circular cylinder permeated by a magnetic field. The problem is represented by the equations of elasticity taking into account the effect of the magnetic field as given by Maxwell's equations in the quasi-static approximation. The free stress conditions on the inner and outer surfaces of the hollow circular cylinder were used to form a frequency equation in terms of the wavelength, the cylinder radii, the initial stress and the material constants. The frequency equations have been derived in the form of a determinant involving Bessel functions and its roots given the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots, which correspond to various modes, have been verified numerically and represented graphically in different values for the initial stress. It is recognized that the flexural elastic waves in a solid body propagated under the influence of initial stress can be differentiated in a clear manner from those propagated in the absence of an initial stress. We also observed the initial stress has a great effect on the propagation of magnetoelastic flexural waves. Therefore this research is theoretically useful to convey information on electromagnetic properties of the material: for example through a precise measurement of the surface current induced by the presence of the magnetic field. [ABSTRACT FROM AUTHOR]

White-beam X-ray Laue microdiffraction allows fast mapping of crystal orientation and strain fields in polycrystals, with a submicron spatial resolution in two dimensions. In the well crystallized parts of the grains, the analysis of Laue-spot positions provides the local deviatoric strain tensor. The hydrostatic part of the strain tensor may also be obtained, at the cost of a longer measuring time, by measuring the energy profiles of the Laue spots using a variable-energy monochromatic beam. A new `rainbow' method is presented, which allows measurement of the energy profiles of the Laue spots while remaining in the white-beam mode. It offers mostly the same information as the latter monochromatic method, but with two advantages: (i) the simultaneous measurement of the energy profiles and the Laue pattern; (ii) rapid access to energy profiles of a larger number of spots, for equivalent scans on the angle of the optical element. The method proceeds in the opposite way compared to a monochromator-based method, by simultaneously removing several sharp energy bands from the incident beam, instead of selecting a single one. It uses a diamond single crystal placed upstream of the sample. Each Laue diffraction by diamond lattice planes attenuates the corresponding energy in the incident spectrum. By rotating the crystal, the filtered-out energies can be varied in a controlled manner, allowing one to determine the extinction energies of several Laue spots of the studied sample. The energies filtered out by the diamond crystal are obtained by measuring its Laue pattern with another two-dimensional detector, at each rotation step. This article demonstrates the feasibility of the method and its validation through the measurement of a known lattice parameter. [ABSTRACT FROM AUTHOR]

Stress migration (SM) is a phenomenon whereby atoms diffuse from a region of lower stress towards a region of higher stress because of the hydrostatic stress gradient. In this study, the fabrication of Cu nanowires at predetermined positions by controlling the direction of the atomic flux caused by SM is analysed. Cu nanowires are fabricated by rearranging accumulated atoms into wire-like crystals. First, the sites at which Cu atoms accumulate are found from finite element (FE) analysis and from the results obtained from experiments. Next, a technique is proposed for accumulating atoms by SM at predetermined sites. Finally, the successful fabrication of Cu nanowires at these sites is demonstrated. [ABSTRACT FROM AUTHOR]

Sand and glass bead samples were monotonically loaded from 0 to 50 MPa and then monotonically unloaded, all under hydrostatic stress conditions. Sand deformed irreversibly and its porosity loss was permanent. In contrast, the glass bead deformation was almost fully reversible with the initial porosity recovered. During loading, the static bulk modulus in all sand samples increased from 0 to about 0.5 GPa between 0‐ and 15‐MPa stress and remained constant for the remainder of the loading. Such behavior, somewhat unexpected in a granular system, means that sand deforms as a linear elastic body during loading from 15 to 50 MPa. The unloading behavior was very different—the static bulk modulus almost linearly decreased from about 4 GPa at 50 MPa to zero as the stress was reduced. Once again, this behavior was very different from that observed in glass beads, where the static bulk modulus during loading was essentially the same as during unloading and appeared to be a unique function of stress, independent of the direction of its variation. Moreover, the static and dynamic bulk moduli in glass beads, the latter computed from Vp, Vs, and density measured during the loading/unloading cycle, were very close to each other. In contrast, the dynamic bulk modulus in dry sand exceeded the static modulus during unloading by a factor of 1.5 to 2.0. We used a quantitative theory based on contact mechanics and the concept of stress heterogeneity in particulates to analytically match the observed results. Key Points: Measurements of static moduli of granular materialsDeformation of sand and glass beadsTheoretical explanation of results [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including application numerical calculation of M integrals for analyzing interacting cracks, impact of hydrostatic stress on flexural waves' frequency equation and laterally graded materials.