Global Stress Field Research Articles

Neo-Alpine uplift and subsidence zones in the Western Carpathians: Product of kinematic activity on Cenozoic AnD3 (NW-SE and NE-SW) and AnD4 (E-W – subequatorial and N-S – submeridian) regional faults

Article presents the role of disjunctive (brittle and brittle-ductile) regional faults of two Cenozoic Neo-Alpine orogenic phases in the Western Carpathians: The AnD3 phase, producing conjugate systems of NW-SE (dominantly dextral shearing) as well as NE-SW (dominantly sinistral shearing), and younger AnD4 phase manifested with regional faults of subequatorial (E-W) and submeridian (N-S) courses (with dominantly uplift and subsidence kinematics). The disintegration of upper crust by kinematic activity on both (AnD3 and AnD4) fault systems produces the origin of block-shaped setting with lateral offsets, eventual rotation (in AnD3), as well as mutual uplifts or subsidences (in AnD4) of individual blocks. This tectonic setting represents the most striking morphological feature at the end of Cenozoic Neo-Alpine orogenic cycle, frequently overprinting or re-activating older tectonic structures. Article provides an interpretation that parallel with the applied global stress field, the AnD4 subequatorial (E-W) and submeridian (N-S) coursing faults can originate also by merging of individual segments of synthetic (oriented N-S) and antithetic (oriented E-W) megashears between parallel AnD3 shear faults of both systems (NW-SE or NE-SW). Merging of individual segments of antithetic shears arranged naturally in one line creates a predisposition for the origin of equatorial (E-W) trending faults, while merging of synthetic segments produces meridian (N-S) trending faults, both being principal in later AnD4 phase.

The Upper Mantle Geoid for Lithospheric Structure and Dynamics

AbstractGeoid anomalies offer crucial information on the internal density structure of the Earth, and thus, on its constitution and dynamic state. In order to interpret geoid undulations in terms of depth, magnitude and lateral extension of density anomalies in the lithosphere and upper mantle, the effects of lower mantle density anomalies need to be removed from the full geoid (thus obtaining the residual “upper mantle geoid”). However, how to achieve this seemingly simple filtering exercise has eluded consensus for decades in the solid Earth community. While there is wide agreement regarding the causative masses of degrees >10 in spherical harmonic expansions of the upper mantle geoid, those contributing to degrees <7–8 remain ambiguous. Here we use spherical harmonic analysis and recent tomography and density models from joint seismic‐geodynamic inversions to derive a representative upper mantle geoid, including the contributions from low harmonic degrees. We show that the upper mantle geoid contains important contributions from degrees 5 and 6 and interpret the causative masses as arising from the coupling between the long‐wavelength lithospheric structure and the sublithospheric upper mantle convection pattern. Importantly, the contributions from degrees 3 < l < 8 do not show a simple power‐law behavior (e.g., Kaula's rule), which precludes the use of standard filtering techniques in the spectral domain. Our upper mantle geoid model will be useful in studies of (a) lithospheric structure, (b) dynamic topography and mantle viscosity, (c) lithosphere‐asthenosphere interactions and (d) the global stress field within the lithosphere and its associated hazards.

Establishment and experimental verification of a three-dimensional finite element model for residual stress in surface processing of Inconel 718 alloy by laser cladding

The local load and residual stress changes of conventional forged Inconel 718 alloy can be simulated in a two-dimensional (2D) cutting simulation model, but the type and distribution of global residual stress field of the alloy cannot be predicted during laser cladding layer cutting. To address the shortcomings of conventional 2D cutting simulation models for forging Inconel 718 alloy, this paper proposed a 3D closed-loop finite element model, and taking the dry-side milling process of Inconel 718 alloy laser cladding layer as an example, the generation mechanism and distribution of residual stress are predicted during the machining process. Further testing of surface, near-surface, and subsurface residual stresses was conducted to analyze the specific distribution of residual stresses in the workpiece. The results indicated that the uneven distribution of cutting stress and temperature on the workpiece had a significant non-stationary thermal-mechanical effect on the surface of the machined workpiece; the distribution of surface residual stress was uneven, with the significant tensile residual stress at the workpiece boundary. As the depth increases, the influence of mechanical effects dominated, and the compressive residual stress was generated on the subsurface of the workpiece. Residual stress testing was conducted on the surface/near-surface, and the experimental results were consistent with the simulation results of the closed-loop simulation model. In the subsurface, residual stress showed a similar trend of change. This study compensated for the shortcomings of conventional finite element simulation and provided the reference value for the application of three-dimensional finite element simulation in laser cladding materials.

Long-term life stress mapping algorithm of the deep-sea pressurized spherical shell based on digital-twin technology

Aiming at the difficulty of the global stress field monitoring of the deep-sea pressurized spherical shell in real time, this paper proposes a long-term life stress field reverse mapping algorithm based on digital-twin technology. Specifically, a high-fidelity FEM model is established based on the titanium alloy data, structure construction data and model test data. The Elastic modulus E and Poisson's ratio υ are selected as the structure characteristic parameters based on the preliminary small sample test results. The sensitivity analysis is carried out. And then, stress monitoring location selection results is proposed considering the factors such as mutual independence, installation conditions, and economic costs. The Long-Short Term Memory network (LSTM) together with the FEM results is tailored and employed to build the reverse mapping model. The mapping error is below 1% and compared to the FEM model, the efficiency of the proposed model is improved by more than 60 times.

Investigation of Plasticity Effects on Growing Fatigue Cracks Using the CJP Model of Crack Tip Fields.

A growing fatigue crack gives rise to a plastic enclave that envelops the crack and can exert a shielding effect on the crack from the global elastic stress field driving fatigue propagation. This work presents the potential of the CJP model of crack tip fields to investigate the plasticity-induced shielding effects on growing fatigue cracks as well as its ability to characterise the size and shape of the plastic zone generated at the tip of a growing fatigue crack. The model was specifically developed to consider the influence of the plastic enclave generated around a fatigue crack on the surrounding elastic material. Different aspects related to fracture mechanics and its implications for fatigue crack growth have been investigated, namely plasticity-induced crack shielding, the retardation effect induced on fatigue crack growth due to the application of an overload and the estimate of the size and shape of the crack tip plastic zone. The model has been successfully applied by analysing displacement fields experimentally measured by DIC in different CT specimens made of 2024-T3 aluminium alloy and commercially pure titanium. Results presented in this work intend to contribute to a better understanding of the shielding effects during fatigue crack growth.

Effect of a gap on the open hole tension strength of carbon fiber reinforced plastic laminates

Tensile tests of quasi-isotropic laminates with a circular open hole, which include a gap in the hole area, were conducted to demonstrate the effect of the gap on the strength. The test showed that the reduction in the open-hole strength owing to the gap was less significant than that in the no-hole tensile strength. A two-dimensional mechanical model of quasi-isotropic laminates with an arbitrary inclined gap was proposed and analytically solved to obtain a closed-form expression for the stress concentration. An approximate expression was provided as the sum of the global uniform stress field and the local stress field near the open hole, which was solved based on a complex variable method. The present analytical solution agrees well with the corresponding two-dimensional finite element solutions. The solution indicated that the stress increase owing to the gap is limited at the stress concentration area. The analytical results were consistent with the experimental results.

Study on the global stress field of the rock mass under compression and shear considering three kinds of crack parameters

AbstractThe mechanical behavior of the cracked rock mass is controlled by the crack initiation and propagation under compression and shear. The key to predicting the wing crack initiation angle is to correctly describe the distribution of the stress field at the crack tip. First, the previous studies are reviewed, and their inadequacies are discussed in detail. Next, according to the experimental results, three kinds of crack parameters (i.e., geometry, strength, and deformation) are introduced, and a stress transfer model on the crack face under compression and shear considering crack parameters is proposed. Then, the relevant formulae of stress intensity factors (KI and KII) and non‐singular term (T‐stress) at the crack tip are obtained. Finally, the proposed model is verified by other researchers' test results, and the effects of three kinds of crack parameters and the rock property on the distribution of tangential stress at the crack tip are discussed.

Timing and Origin of Compressional Tectonism in Mare Tranquillitatis

AbstractThe lithosphere of the Moon has been deformed by tectonic processes for at least 4 billion years, resulting in a variety of tectonic surface features. Extensional large lunar graben formed during an early phase of net thermal expansion before 3.6 Ga. With the emplacement of mare basalts at ∼3.9–4.0 Ga, faulting and folding of the mare basalts initiated, and wrinkle ridges formed. Lunar wrinkle ridges exclusively occur within the lunar Maria and are thought to be the result of superisostatic loading by dense mare basalts. Since 3.6 Ga, the Moon is in a thermal state of net contraction, which led to the global formation of small lobate thrust faults called lobate scarps. Hence, lunar tectonism recorded changes in the global and regional stress fields and is therefore an important archive for the thermal evolution of the Moon. Here, we mapped tectonic features in the non‐mascon basin Mare Tranquillitatis and classified these features according to their respective erosional states. This classification aims to provide new insights into the timing of lunar tectonism and the associated stress fields. We found a wide time range of tectonic activity, ranging from ancient to recent (3.8 Ga to <50 Ma). Early wrinkle ridge formation seems to be closely related to subsidence and flexure. For the recent and ongoing growth of wrinkle ridges and lobate scarps, global contraction with a combination of recession stresses and diurnal tidal stresses, as well as with a combination of South Pole‐Aitken ejecta loading and true polar wander are likely.

Crack propagation mechanism of rock-like specimens containing non-parallel flaws subjected to internal hydraulic pressure and shear loading

The rock masses with existing discontinuous joints are more prone to failure under the combination of fissure water and shear loading. Therefore, combining laboratory experiments with discrete element simulation, the mechanism of crack initiation, propagation, and coalescence in rock-like specimens (a type of high brittle cement mortar material) with non-parallel flaws under shear loading and internal water pressure is investigated. The results reveal that for specimens with various flaw dip angles the propagation direction of all newly generated cracks is basically parallel to the shearing loading. When the flaw inclination angle reaches −30°, the cracks initiated near pre-existing flaw tips are the result of the combined effects of fluid pressure and compressive stress fields. Compared with the hydraulic fracturing curve, both plateau period and water pressure fluctuations appear in the selected domain near the crack propagation paths, which can demonstrate that the evolution of water pressure is extremely complex due to the constant crack healing and opening. With the increase of water pressure, the global stress field becomes more uniform, and the stress concentration near pre-existing flaw tips is weakened, indicating that water pressure can lead to local stress redistribution. Ultimately, the work is expected to provide guidance to the safe construction of tunnel excavation under complex geological conditions.

Experimental and Numerical Investigation on the Dynamic Failure Envelope and Cracking Mechanism of Precompressed Rock under Compression-Shear Loads

The complex response of underground geomaterials subjected to dynamic disturbance arises from the microstructure redistribution under high in- situ stress and the resulting fracture behaviors at multiaxial stress states. Inclined specimens were employed in an axially constrained split Hopkinson pressure bar (SHPB) system to achieve a combination of compression-shear stress states and static-dynamic loads. The loading rate under investigation ranged from 500 to 4,000 GPa/s, along with the axial prestress of 7, 21, 35, 49, and 63 MPa on specimens with an inclination of 0°, 3°, 5°, and 7°. The modified SHPB experimentation and discrete-element method modeling were implemented to unravel the combined effects of the loading rate, preload, and stress path on the failure mechanism of sandstone specimens involving the failure strength and envelope, fracturing pattern, fragmentation, and microcracking process. The positive rate dependence of the failure strength and Drucker–Prager envelope was observed. The preload showed double effects on the failure strength, indicated by an upper bound of the failure envelope as it expanded with the increasing preload. The microdamage accumulated during preloading and the global stress field collectively influenced the failure pattern of the inclined specimen, altering from a shear fracturing mode under dynamic loading or high-preload static-dynamic loading to an axial splitting mode near the specimen surface under low-preload static-dynamic loading.

Study on the maximum tangential strain criterion for the initiation of the wing-crack under uniaxial compression

The global stress field function of an infinite plate with a closed inclined crack under uniaxial compression is presented, then the stress field at the crack tip is obtained, namely the formulae of KI, KII and T-stress are obtained. A new maximum tangential strain (MTSN) criterion is proposed to predict the initiation of the crack under compression by considering singular and non-singular terms based on the classical MTSN criterion. The influence factors on KII are analyzed and the effects of T-stress on the tangential strain at the crack tip under different critical plastic zones (rc), dip angel of crack (β), friction coefficients of crack surface (f) and Poisson’s ratio (ν) are studied. The comparison of the wing-crack initiation angle measured from the experimental results and predicted by the proposed criterion and other researchers’ models are made. The following findings are obtained. First of all, the proposed global stress field function satisfies the far-field and crack surface stress boundary conditions. The singular term of KII and non-singular term of T-stress vary with the effective shear stress along the crack surface. When the effective shear stress is zero, there is still singularity at the crack tip, which is completely opposite to the classical theory, and there are two components of T-stress (i.e. Tx and Ty, which is parallel and perpendicular to the crack surface respectively). While there is a third component of T-stress (i.e. Txy, which along the xy direction) when the effective shear stress is greater than zero. Next, the comparison of the wing-crack initiation angle measured from the experimental results and predicted by the proposed criterion and other researchers’ models are made. The results of the proposed method are consistent with the experiments very well, especially when the effective shear stress decreases to zero with the increase of friction coefficient (f). Finally, the tangential strain field at the crack tip are effected significantly by the critical plastic zones (rc), dip angel of crack (β), friction coefficients of crack surface (f) and Poisson’s ratio (ν).

Effect of gap on strengths of automated fiber placement manufactured laminates

Tensile and compressive tests of automated fiber placement (AFP) manufactured quasi-isotropic laminates with repeating embedded gaps or overlaps are conducted and reveal significantly lower tensile and compressive strengths compared to those of normal laminates in spite that the gaps and overlaps cut no fiber. The reduction in tensile strength is greater than that of the compressive strength. A two-dimensional mechanical model of the quasi-isotropic laminates with an arbitrary inclined gap is proposed and analytically solved using a super-position technique as the sum of a global uniform stress field that satisfies equilibrium and compatibility conditions by applying a virtual force at both ends of the gap and a local stress field caused by the virtual force. The local problem is approximately solved using a Green function technique. The stress and strain fields under a unidirectional load are obtained in a closed-form expression in which the effect of the tapered portions typically observed at both sides of the gap is incorporated. The present analytical solution agrees with the finite element solution. The derived expression shows that significant stress concentration occurs at the end portion of the gap.

Experimental and computational modeling of bulk residual stress for aeronautical components with distinct geometries

To predict and minimize machining distortion in the manufacturing process, bulk residual stresses in aeronautical components with distinct geometries were investigated via experimental mechanics and numerical simulation. The residual stress state was appropriately simplified according to geometric/processing feathers and deformation patterns of the investigated parts. In each case study, an optimal experimental method was selected to reconstruct the concerned stress tensor. Thereafter, qualitative comparison and validation were performed using cross-method verification and/or numerical simulation. Additionally, the spatial resolution and distribution characteristics of the residual stress were analyzed and discussed in detail. The results revealed that thermal and mechanical nonuniformity caused by material processing is the main source of bulk residual stress in the investigated components. Furthermore, the effectiveness of the contour method on the measurement of different geometric components was verified by numerical simulation. Combining the accurate measurement of the characteristic plane and the appropriate numerical simulation of the global stress field, an engineering-oriented approach for full-field stress evaluation was proposed. This research can provide valuable engineering guidance and suggestions for stress evaluation and distortion analysis prior to manufacturing of integral structures.

Pattern of Global Crustal Stresses of the Earth

The results of tectonophysical inversion of the global tectonic stress field are considered from the position of explaining the active forces that cause the lithospheric plate movements. The analysis of regularities of the stress state of the main structural elements of Earth’s lithosphere—ocean spreading, transformations, active continental margins, and intracontinental orogeny—is performed. It is shown that the stresses in most of the ocean lithosphere, including subduction zones, correspond to active traction forces from the submerged and weighted part of the lithosphere. A low level of deviatoric stresses in subduction zones and the presence of dynamo pair with sharply different mode of stress state were found. Horizontal compression is observed in the crust of the continental slope, and horizontal tension is observed in the ocean lithosphere, so the boundaries of lithospheric plates should not be considered as a source of increased horizontal compressive stress in the crust of continents. The formation of a horizontal compression regime in the crust of intracontinental orogens, as well as in the crust of active continental margins orogens, is associated with residual stresses of rocks that have been exhumed from the depths of the crust. A generalizing scheme for the formation of the global crustal stress field of the Earth is proposed, which corresponds to modern data on the movements of lithospheric plates and the deep structure of the upper mantle.

Multiscale investigation of micro-scale stresses at composite laminate free edge

The free edge effect is well understood at the laminate and lamina scale. The influence of the microstructure on micro-scale stresses and free edge cracking, however, is less known. This work aims at a better understanding of the effect of microscopic features on micro-scale stresses and the tendency of initial micro-cracking at the laminate free edge. To this end, a two-scale finite element (FE) modelling approach is developed. It consists of a meso-scale model to capture the laminate stacking sequence and the global stress field under a given loading condition, and a micro-scale model to predict the local constituent level stresses at the free edge. The two models were coupled one-way through a strain localization rule. A procedure to determine the boundary conditions for micro-scale FE models containing a free edge was proposed. The model was used to examine the 90/90 interface in [25N/−25N/90N]S IM7/8552 carbon/epoxy composite laminates. The effects of thermal and tensile loading were investigated independently to understand the influence of the interlaminar microstructure on micro-scale stresses at free edges during manufacture and under mechanical loading. The results agreed with the trend of free edge pre-cracks and progressive damage observed in experiments.

Numerical and experimental analysis of a composite rear spar subjected to random fatigue loading conditions

The work presents a numerical and experimental analysis of a full-scale fatigue test on a CFRP rear spar of an aircraft solicited by a load history representative of variable load levels during the flight conditions. The structural element is essentially a double-T section with a hole and presents a repair by scarfing and hot bond process. The global stress field of the component was determined by a numerical model realized with a commercial FEM code. The numerical model is realized to reproduce the component geometry and stacking sequence, the representative constraints and service loads. The real component has been subjected to cyclic random fatigue stresses and subsequently a static bending load to evaluate the residual strength. Finally, the experimental results obtained, illustrated and discussed, were compared with the numerical ones.

Fatigue crack growth in a compressor stage of a turbofan engine by FEM-DBEM approach

In this work, the fatigue crack-growth process in a rotating disk of an aircraft gas turbine engine has been simulated. The considered crack nucleated in the attachment between a blade and the disk of a compressor stage, both made of a two-phase titanium alloy.The fatigue crack-growth process of such crack has been simulated by means of two codes, ABAQUS and BEASY, based on Finite Element Method (FEM) and Dual Boundary Element Method (DBEM) respectively. In particular, a variant of the submodelling technique, based on the superposition principle, has been used for coupling the two codes in order to exploit simultaneously their peculiar strength points. The FEM code has been used to compute the global stress field whereas the DBEM code has been used to calculate the fracture parameters, useful to predict the crack-growth evolution. The J-integral method and the Minimum Strain Energy Density Criterion (MSED) have been used for calculating K values and predicting crack kinking respectively.In this work, the FEM-DBEM crack path is compared with both the path obtained by a full-scale experimental test and the path predicted via a full FEM approach: having in an initial stage considered the only centrifugal load, with no allowance e.g. for the fluid pressure on the blades and for the blade dynamic behaviour, some discrepancies are found between numerical and experimental results.The computational advantages of the proposed submodelling approach are highlighted, in addition to a preliminary fatigue assessment provided for the considered compressor disk (further analyses are under development).

Global mapping and analysis of lunar wrinkle ridges

Lunar wrinkle ridges were globally mapped, and the morphological parameters, including length, width, elevation offset, and orientation, were also calculated. The results include the identification of 2839 segments with a total length of 25,560.69km, and the mean width, height, elevation offset, and orientation of all the wrinkle ridges are 3.70km, 0.31km, 46.37m, and -1.99 degrees, respectively, after weighted by the length. Based on their morphologies and distribution, lunar wrinkle ridges were classified into three categories: concentric, parallel, and isolated ridges, and most of the wrinkle ridges are distributed over basalts, although a few extend to nearby highlands. The relations between the morphological parameters were further quantitatively analyzed, and a similar linear correlation between the width and height was found in each class of lunar ridges, implying that small and large ridges were formed as a continuum and that the three classes of ridges were probably formed by some common processes. Finally, the relations between the lunar wrinkle ridges and other geomorphic phenomena were analyzed, indicating that purely volcanic origin or buried premare structures are difficult to reconcile with the investigation. In addition, the consistency between the occurrence of the lunar wrinkle ridges and the some thickness of lunar maria indicates that the formation of lunar wrinkle ridges is closely related to the lunar maria; however, the statistical NW or NE orientation of each class of lunar wrinkle ridges also suggests a suitable global stress field involved in their formation process.

A rock-mechanical assessment of Mercury's global tectonic fabric

Mercury's global tectonic history is thought to have been dominated by two major processes: tidal despinning and global contraction. Each process is expected to have produced a distinctive global stress field and resultant fault pattern. Thousands of thrust-fault-related landforms documented on Mercury can be attributed to global contraction, but no global signature of tidal despinning has been conclusively documented. Because global contraction operated throughout an extended portion of Mercury's geologic history, any tidal despinning pattern either would have formed together with global contraction, or would have been modified by global contraction after despinning was complete. Here, we reassess global fracture patterns predicted to result from tidal despinning and from a combination of tidal despinning and global contraction. We specifically make use of rock strength and deformability parameters appropriate for Mercury's fractured lithosphere. Results indicate that a tidal despinning pattern would consist only of a global set of opening-mode fractures (joints) in the upper part of the lithosphere, whereas the combination of tidal despinning and global contraction would have produced a global population of thrust faults, with no preferred orientations in the polar regions but with an increasing preference for north–south orientations toward the equator. If an equatorial bulge from an early state of rapid spin was supported by Mercury's lithosphere, two end-member scenarios for the timing and duration of these two processes may be considered. In one, tidal despinning predated global contraction; in the other, tidal despinning and global contraction overlapped in time. We test the predictions of both scenarios against the distribution and orientations of Mercury's tectonic landforms. The global pattern of thrust faults is generally consistent with predictions for the scenario under which tidal despinning and global contraction temporally overlapped.

A statistical meso-damage mechanical method for modeling trans-scale progressive failure process of rock

Starting from the concept of Representative Volume Element (RVE) at the mesoscopic scale, a statistical meso-damage mechanical method (SMDMM) is developed to model the trans-scale progressive failure process of rock, based on the statistical and continuum damage mechanics theory and the finite element method (FEM). The proposed mesoscopic constitutive law of RVE is established within the framework of elastic–brittle-damage theory in which the double damage functions correspond to a tensile and compressive damage surface. A statistical approach is employed to describe the mesoscopic heterogeneity of rock material. The damage evolution and accumulation of mesoscopic RVEs is used to reflect the macroscopic failure characteristics of rock. The global stress and strain fields are solved by the FEM. An element represents a RVE, the initiation and propagation of meso-macroscopic trans-scale cracks and their interaction are manifested by removing the failed elements. Numerical analyses are carried out on a few groups of laboratory-scale rock specimens and the effects of RVE size, material homogeneity and quasi-static loading step length are investigated. Finally, a full-scale Atomic Energy of Canada Limited (AECL) Mine-by test tunnel is simulated. The proposed SMDMM is calibrated and validated for its trans-scale modeling capability to reproduce the shape and size of excavation damage zone profile around the tunnel. Accordingly, the simulation results are compared with experimental observations and numerical results predicted by other models. It is shown that the SMDMM has good performance for modeling the rock failure process from meso- to engineering/field-scale.