Reconstruction Of Stress Fields Research Articles

An iterative technique for the reconstruction of residual stress fields in a butt-welded plate from experimental measurement, and comparison with welding process simulation

Residual stress is a factor which potentially affects the integrity of welded components. We have developed a methodology of assessment to establish the state of residual stress in a butt-welded plate by using a limited set of experimental measurements obtained using neutron diffraction. The unique longitudinal and transverse residual stress components, as a result of the welding process, are measured across the weld in three depths through the thickness. The measured residual stresses are then used to estimate a stress distribution for each stress component. The estimated stress distribution is then mapped to a finite element model of the weld plate, before adopting an iterative solution to reconstruct the residual stress fields. In addition, a traditional welding simulation is performed using the same weld plate details to predict and compare the residual stress distributions. It is shown that accurate residual stress field reconstruction is possible in and around the area of measurement using the limited measurement data from the neutron diffraction technique. In the estimated stress profiles, an upper-bound distribution is implemented in the weld and Heat Affected Zone (HAZ). This increases the efficiency and reduces the complexity of modelling. In the meantime, conservatism in the estimated stress is secured.

Reconstruction of the paleostress field of the Kokdjot Block, Malyi Karatau ridge (South Kazakhstan)

Reconstruction of the paleostress field of the Kokdjot Block, Malyi Karatau ridge (South Kazakhstan) was done as a result of the detailed structural study. Kink-bands and fold-axes were used for indicate stress field reconstruction. Study areas of the Kokdjot Block are located from the northwest to the southeast of the Kokdjot plateau and are characterized as both clastic sedimentary rocks of greenschist and phyllite facies of metamorphism and clastic and carbonates sedimentary rocks. Two stress fields have been identified as corresponding to Caledonian (Late Ordovician) and Hercynian deformations. The earlier tectonic event is characterized by horizontal compression of the northeastern trend and later tectonic event is characterized by the shear stress field at the west-north-west trend of the compression axis.

ТОМОГРАФИЯ, ОСНОВАННАЯ НА ПРЕДСТАВЛЕНИИ МОДЕЛИ ПОЛИНОМАМИ ЧЕБЫШЕВА: ПРИМЕРЫ ИСПОЛЬЗОВАНИЯ

The paper deals with the three-dimensional travel-time tomography of the first arrivals. The model is represented by Chebyshev polynomials. This allows one to use a priori information about the model effectively and reduce the number of recoverable parameters to the required minimum. Also, such a model representation makes it possible to obtain a very efficient algorithm for solving the two-point ray-tracing problem for three-dimensional media, which is necessary for tomography. Examples of solving the three-dimensional cross-well tomography, as well as examples using tomography for the reconstruction of stress fields in the coal-rock mass are presented.

Local Stress-Field Reconstruction Around Holes in a Plate Using Strain Monitoring Data and Stress Function

This study reconstructs a two-dimensional stress field from measured strain data. The advantage of using stress functions is that the stress equilibrium and strain compatibility are automatically satisfied. We use the complex stress functions given by the finite series of polynomials. Then, we find the proper set of coefficients required to make the best fit to the measured strain data. Numerical examples represent the stress concentration problems around a hole(s) in a plate. It is demonstrated that the present method reconstructs the stress field around the hole(s), and the estimated stress agrees with the finite element (FE) analysis result.

К вопросу о реконструкции остаточных напряжений и деформаций пластины после дробеструйной обработки

Предметом исследования является математическое описание формы и напряженно-деформированного состояния стальной пластины, подвергнутой односторонней дробеструйной обработке, его экспериментальное подтверждение и применение результатов для верификации методов реконструкции полей остаточных напряжений и деформаций по экспериментальным данным. Подобная пластина используются на производстве в качестве калибровочного образца для определения времени пневмодробеструйной обработки, необходимого для формирования в поверхностном слое обрабатываемого изделия сжимающих тангенциальных остаточных напряжений заданной величины, а сам метод калибровки оказывается удобным и довольно широко распространенным для различных способов поверхностно упрочняющей обработки. Источником остаточных напряжений в данном случае является пограничный слой пластических деформаций, наводимый рассматриваемым технологическим процессом. Для постановки задачи задается структура поля тензора пластических деформаций. Форма и напряженно-деформированное состояние упругой пластины с пограничным слоем пластических деформаций были рассчитаны численно, в результате чего были выявлены качественные особенности данных полей, ослаблены граничные условия задачи и сформулированы гипотезы о структуре решения соответствующей пространственной задачи теории упругости, которое далее было найдено аналитически. Показано, что в рамках приближения плоского напряженного состояния в поперечных направлениях результат точно соответствует формуле Давиденкова - Биргера, связывающей зависимость тангенциальной компоненты остаточных напряжений от координаты по толщине пластины с функцией прогибов. Получена явная формула для зависимости остаточной (пластической) деформации от координаты по толщине. Проанализированы источники погрешностей полученных выражений и способы их коррекции. Проведен эксперимент по односторонней дробеструйной обработке калибровочной пластины, изготовленной из закаленной стали 65Г, для которой выполнено травление обработанной поверхности с измерением изменения стрелы прогиба (метод Н. Н. Давиденкова). С помощью полученных экспериментальных данных были численно реконструированы профили остаточных напряжений и деформаций с разумной точностью. Результат применим к широкому классу задач для упругих тел с упрочняющими покрытиями, а также имеет определенную методическую ценность для усовершенствования основ экспериментального исследования таких задач, позволяет формулировать и подтверждать экспериментом гипотезы о структуре решения, изучать связь рассматриваемых полей в предельных случаях, верифицировать применение различных способов учета остаточных напряжений и деформаций в численных расчетах. Найденное решение может быть использовано для верификации полей напряжений и перемещений при выборе различных вариантов предварительно напряженных или деформированных поверхностных оболочечных конечных элементов в рамках пакетов прикладных программ для расчета усталостной долговечности деталей машин с поверхностными упрочняющими покрытиями и также представляется опорным для исследования поверхностно упрочненных тел с криволинейной свободной границей, к которым сводится большинство практически важных задач.

Seismic Velocity Changes in the Backarc Continental Crust After the 2011 Mw 9.0 Tohoku‐Oki Megathrust Earthquake

AbstractThe 2011 Mw 9.0 Tohoku‐Oki megathrust earthquake accompanied coseismic and postseismic displacements around the eastern Eurasian continental plate. Noise cross correlations produced transient seismic waveforms along interstation paths in the Korean Peninsula. We measured the traveltime changes of the fundamental mode Rayleigh waves over the range of 0.03–0.08 Hz after the megathrust earthquake. The temporal seismic velocity changes in the lower crust were assessed from the traveltime changes. The traveltimes increased instantly after the megathrust earthquake and were gradually recovered over several hundreds to thousands of days. The instant shear wave velocity decreases ranged between 0.731 (±0.057)% and 4.068 (±0.173)%. The temporal medium perturbation might be caused by the transient uniaxial tensional stress due to the coseismic and postseismic displacements. The medium properties may be recovered by progressive stress field reconstruction.

Teсtonophysical conditions of main fault activation in the Lower Amur region in the Cenozoic: Origination and evolution of conjugate basins

The reconstruction of stress fields in the Lower Amur region allowed us to subdivide them into four groups. Two groups are related to the fields of the strike-slip fault type and others to the reverse and normal fault types. As a result of structural analysis, it has been established that the stress fields differ in age and correspond to different stages of deformation. It has been shown that origin and evolution of the Cenozoic basins in the Lower Amur region were related to the paleogeodynamics of the faults, which served as a northeastern continuation of the Tan-Lu Fault System, as well as of the NW-striking faults at the lower reaches of the Amur River. Based on the data obtained, a new model of the origin, formation, and evolution of basins in the Lower Amur region is proposed.

Etiology of ankle osteoarthritis in an Asian population

The paper presents a seismic data interpretation approach to reconstruction of stress fields in rocks at any stage of coal mining. The approach involves: thee-axial compression testing of coal in order to find an empirical relation between elastic wave velocity and stresses; coal bed tomography using standard monitoring systems and taking signals generated by dynamic events (with the energy higher than the background level) as the probing signals; formulation and solving of a boundary inverse problem within a geomechanical model of an object under analysis where the input data is the velocity field reconstructed in the illuminated area of coal bed by tomography. The laboratory data of the coal specimens tested by the von Karman scheme have been approximated to plot analytical relationships between P-waves velocity, axial stress and confining pressure. The numerical experiments performed for a typical underground layout at coal producer “Vorkutaugol” have shown that given the accepted array of seismic pickups, the single-valued solution of the inverse problem requires good illumination of coal bed areas with the spatial stress gradient.

Stress field reconstruction in an active mudslide

Meso-scale structures from gravitational slope deformation observed in landslides and deep-seated gravitational slope failures are very similar to those of endogenous ones. Therefore we applied palaeostress analysis of fault-slip data for reconstructing the stress field of an active mudslide in Pechgraben, Austria. This complex compound landslide has developed in clayey colluvium and shale and was activated after a certain period of dormancy in June 2013. During the active motion on June 12, 2013, 73 fault-slip traces at 9 locations were measured within the landslide body. The heterogeneous fault-slip data were processed in term of palaeostresses, the reconstructed palaeostress tensor being characterized by the orientations of the three principal stress axes and the stress ratio (which provides the shape of the stress ellipsoid). The results of the palaeostress analysis were compared to airborne laser scan digital terrain models that revealed dynamics and superficial displacements of the moving mass prior and after our survey. The results were generally in good agreement with the observed landslide displacement pattern and with the anticipated stress regime according to Mohr-Coulomb failure criteria and Anderson's theory. The compressional regime was mostly registered at the toe in areas, where a compressional stress field is expected during previous mass-movement stages, or at margins loaded by subsequent landslide bodies from above. On the other hand, extension regimes were identified at the head scarps of secondary slides, subsequently on bulged ridges at the toe and in the zone of horst-and-graben structures in the lower central part of the main landslide body, where the basal slip surface probably had locally convex character. Strike-slip regimes, as well as oblique normal or oblique reverse regimes were observed at the lateral margins of the landslide bodies. The directions of principal stresses could be used as markers of landslide movement directions. Although the multiphase strain indicators were, in general, relatively poorly preserved, the palaeostress analysis revealed several different deformation phases at some landslide parts related to different evolution episodes of the complex landslide. Palaeostress analysis based on the multiple inversion method is an affordable approach for reconstructing stress fields within landslides in soft material. This method is an inexpensive and objective tool for stress field reconstruction even in heterogeneous stress field conditions where the distinction of different faults generations may be impossible.

Tectonic stress field analysis of the northern part of the Kuril–Okhotsk region before the May 24, 2013 deep-focus earthquake

This paper presents the results of reconstruction of the modern tectonic stress field of the northern part of the Kuril–Okhotsk region prior to the May 24, 2013 deep-focus earthquake. This earthquake is the strongest deep-focus earthquake not only in the Okhotsk region but also in the world over the entire period of seismic observations. The tectonic stress field is reconstructed using the method of cataclastic analysis (MCA) of the earthquake source mechanism data. New data on the depth variations of regional tectonic stress field are obtained.

Use of Tomography in Stress–Strain Analysis of Coal–Rock Mass by Solving Boundary Inverse Problems

The paper presents a seismic data interpretation approach to reconstruction of stress fields in rocks at any stage of coal mining. The approach involves: thee-axial compression testing of coal in order to find an empirical relation between elastic wave velocity and stresses; coal bed tomography using standard monitoring systems and taking signals generated by dynamic events (with the energy higher than the background level) as the probing signals; formulation and solving of a boundary inverse problem within a geomechanical model of an object under analysis where the input data is the velocity field reconstructed in the illuminated area of coal bed by tomography. The laboratory data of the coal specimens tested by the von Karman scheme have been approximated to plot analytical relationships between P-waves velocity, axial stress and confining pressure. The numerical experiments performed for a typical underground layout at coal producer “Vorkutaugol” have shown that given the accepted array of seismic pickups, the single-valued solution of the inverse problem requires good illumination of coal bed areas with the spatial stress gradient.

Formation and destruction mechanism as well as major controlling factors of the Silurian shale gas overpressure in the Sichuan Basin, China

Taking the Well JY1 and Well PY1 in the Eastern Sichuan Basin as examples, the formation mechanism of shale gas overpressure was studied by using the cross plot of acoustic versus density logging data. During the processes of hydrocarbon generation and the uplifting, the pressure evolution of fluids in shale gas layers was reconstructed by fluid inclusions and PVTSIM software. The major factors controlling the evolution of shale gas overpressure were established according to the study of fracture, the timing of the uplifting, and episodes of tectonic deformation. Our results showed that the main mechanism of overpressure in the Silurian shale gas reservoirs in the Sichuan Basin was the fluid expansion, which was caused by hydrocarbon generation. Since the Yanshanian, the strata were uplifted and fluid pressure generally showed a decreasing trend. However, due to the low compression rebound ratio of shale gas reservoir rocks, poor connectivity of reservoir rocks, and low content of formation water and so on, such factors made fluid pressure decrease, but these would not be enough to make up the effects of strata erosion resulting in a further increase in fluid pressure in shale gas reservoirs during the whole uplifting processes. Since the Yanshanian, the Well PY1 zone had been reconstructed by at least three episodes of tectonic movement. The initial timing of the uplifting is 130 Ma. Compared to the former, the Well JY1 zone was firstly uplifted at 90 Ma, which was weakly reconstructed. As a result, low-angle fractures and few high resistance fractures developed in the Well JY1, while high-angle fractures and many high resistance fractures developed in the Well PY1. In totality, the factors controlling the overpressure preservation in shale gas reservoirs during the late periods include timing of late uplifting, superposition and reconstruction of stress fields, and development of high-angle fractures.

Reconstruction of 3D stress field in coal–rock mass by solving inverse problem using tomography data

The theoretically evaluated multi-disciplinary approach enables determination of stress state of a coal–rock mass in the area of coal cutting using a package of geomechanical and geophysical information. The approach is based on successive solutions of two inverse problems in the framework of a geomechanical model: coal-bed tomography and assessment of horizontal components of external stress field. The numerical experiments demonstrate resolvability of the inverse problems given appropriate monitoring system ensures sufficient seismic coverage of a coal-bed in the domain of steep spatial gradients of elastic waves and the presence of regular composition in the frequency range of the order of hundreds of hertz in the sounding signal generated by a cutter–loader and/or other coal-face work machinery.

On the application of genetic algorithms and gradient methods for problem of initial stress field reconstruction in poroelastic inhomogeneous column

On the application of genetic algorithms and gradient methods for problem of initial stress field reconstruction in poroelastic inhomogeneous column

Предварительные результаты полевых тектонофизических исследований в районе западного побережья Антарктического полуострова

The purpose of the paper is to describe and analyze deformations of the mesolevel (joints, slickensides, folds and etc.) in the West Antarctica rock complexes of different age, to reconstruct the conformity stress fields and to identify deformation stages. We used the conventional structural geology techniques and methods of tectonophysics: structural- paragenetic (reconstruction of stress field by system of conjugated fractures) and kinematic (by slicken-sides). Totally 3246 joints, 23 slicken-sides, 126 dykes and 53 quartz veins were measured and other deformation structures were described at 105 observation points. For each observation point or group of points the stress tensor has been reconstructed, and for Argentine Islands areal distribution of the stress tensor orientations has been plotted. The regional stress field with horizontal NE-SW compressional axis and the horizontal NW-SE extensional axis has been identified. The orientation of the extensional axis across the strike of main rift structures allows us to relate their origination with extensional deformation stage. The conditions for extension of continental lithosphere could appear in the Early Cenozoic as a result of slab isolation during plate subduction. The compressional deformations are less and associated mainly with gabbros. The compressional stage preceded by extensional one and, probably, coincided in time with crystallization of gabbro massifs in Late Cretaceous. The anomalies in orientation of regional stress field have been revealed. They are associated with rotation of conjugate fracture in horizontal plane in the shear zones and can serve as their indicators. A lot of measurement on Galindez Island allowed to us reconstructed the local stress fields and the associated vertical movements. Inherited character of the fractures is revealed. It is shown that dikes and quartz veins use older system of discontinuities, whereas modem fractures are implemented on the existing dikes and contacts of various rock complexes.

Inverse determination of the regularized residual stress and eigenstrain fields due to surface peening

A modified stress function approach is developed for reconstruction of residual stress and eigenstrain fields from limited experimental measurements. The modified approach is successfully applied to three experimental case studies where residual stresses are introduced by surface peening. The smooth reconstructed residual fields not only minimize the deviation of measurements from its approximation but also satisfy all continuum mechanics requirements. Furthermore, a comprehensive discussion is performed on regularity of the solution in Tikhonov scheme and the regularization parameter is then determined utilizing Morozov discrepancy principle. Newton iterative method is also shown to have an excellent fast convergence to the regularization parameter while effectively reduces the computational cost.

Numerical Reconstruction of Residual Stress Fields from Limited Measurements

By finding stress states which are consistent both with any existing experimental measurements and with elasticity theory, residual stress fields can often be reconstructed from incomplete measurement data. We discuss such methods of residual stress reconstruction, their implementation using finite element analysis, and the measurement strategies which enable them. In general, reconstruction of residual stress fields must be formulated as an inverse problem, which can usually be solved using stress basis functions. However, prior knowledge of the form of the residual stress field and/or underlying eigenstrain distribution often allows the problem to be reduced such that inverse methods become unnecessary, greatly simplifying the analysis. Two examples of when residual stress field reconstruction can be simplified in this way are given.

A method for reconstruction of residual stress fields from measurements made in an incompatible region

A method is introduced by which the complete state of residual stress in an elastic body may be inferred from a limited set of experimental measurements. Two techniques for carrying out this reconstruction using finite element analysis are compared and it is shown that for exact reconstruction of the stress field via this method, the stress field must be measured over all eigenstrain-containing regions of the object. The effects of error and incompleteness in the measured part of the stress field on the subsequent analysis are investigated in a series of numerical experiments using synthetic measurement data based on the NeT TG1 round-robin weld specimen. It is hence shown that accurate residual stress field reconstruction is possible using measurement data of a quality achievable using current experimental techniques.

Influence of Errors of Determination of Stresses Near a Crack Tip on the Accuracy of Computation of the Coefficients of the Williams Series Under Mode II Loading

We model and analyze the influence of errors of the determination of stress fields on the accuracy of computation of the coefficients of the Williams expansion and reconstruction of stress fields under mode ІІ loading.

Plastic stress field reconstruction based on stress orientations data

This paper presents an investigation of the applicability of the stress trajectories concept and the stress trajectories – slip lines alternations method to geomechanical problems. We extend our approach introduced for the stress analysis of two-dimensional plastic bodies to the problem of the stress reconstruction in plastic regions of the lithosphere. The method is developed for the Cauchy boundary value problem and utilizes the data on principal directions as one of the boundary conditions. For this purpose the first order stress indicators of the World stress map (WSM) project database (release 2008) are utilized in computations. The set of considered boundary conditions is supplemented by the normal derivatives of the stress orientations. Complete formulation of the problem involves a yield condition. Although the general approach is not limited to a specific yield criterion, present calculations are performed for the Mohr-Coulomb criterion. Applications of the method include the stress reconstructions in three regions of the Earth’s crust (Swiss Alps, Tibetan plateau and Eastern Anatolia). The continuous boundary conditions are derived by an averaging method applied to the discrete data in immediate vicinity of the starting boundary. Thereafter, for the chosen strength parameters of the Mohr-Coulomb theory (friction angle and cohesion), the unique grids of stress trajectories and slip lines are determined. These fields are further compared against the WSM data available inside the regions. The computations are made for different strength parameters in order to provide the best fit to the data. The results of the analysis are presented as two plane fields: the map of normalized mean stresses and the grid of corresponding trajectories of principal directions. The normalization parameter is unknown (it represents an initial value of the mean stress in a single node of the boundary), which is a consequence of non-uniqueness of the stress reconstruction problem based on the data on stress orientations alone. The reconstructed stress orientations are compared with the observations from the WSM database.