Local Stress State Research Articles

Verification of Puck's criterion for CFRP laminates under multiaxial loads at ambient and cryogenic temperatures

Objective of the present study is the verification of Puck's failure criterion for multiaxial mechanical loading situations in the ambient and cryogenic thermal regimes. The assessment is based on the material data and the failure envelope determined in a previous study on uniaxially loaded single-ply specimens study. Here, the pre-existing experimental data base is complemented by experiments on specimens made from angle ply laminates featuring holes, tapered sections and combinations thereof. The specimens were tested at ambient temperature and in a liquid Helium environment at 4.2 K. For determination of the local stress states in the individual plies at the stress concentrations induced by the holes and tapered sections, the experiments were simulated numerically by the finite element method. It is found that Puck's criterion in most cases provides conservative results. Unresolved additional safety margins may develop if a structural failure in an inter-fiber mode requires development of larger delaminations of adjacent plies to form a through crack.

Injection-induced fault slip assessment in Montney Formation in Western Canada

Hydraulic stimulation to enhance energy extraction from geothermal and unconventional resources is typically accompanied by seismicity because injection changes pore pressures and temperatures, facilitating slippage of fractures and faults. Induced seismicity carries potential risk if events are large enough to damage infrastructure. The uncertainty invariably associated with the state of stress measurements and subsurface geomechanics parameters affects the analysis of fault slip and seismicity induced resulting from hydraulic fracturing. In this study, a probabilistic approach is used to assess the slip tendency of known faults crossing the compartmentalized Montney Formation of western Alberta and northeastern British Columbia. We first divide the formation into four different stress areas based on pore pressure deviations from hydrostatic. In each stress area, geomechanics parameters are expressed as probability distributions using multivariable datasets from borehole petrophysical data to injection-induced focal mechanisms. Monte Carlo simulations are applied to assess the potential slip tendency of local faults. We display the cumulative distribution function of critical pore pressure to cause slip on each fault by using analyses of the parameters of the Mohr–Coulomb shear failure criterion and local tectonic stress state. The results provide useful input for seismic hazard assessment and risk mitigation for local faults affected by high-rate fluid injection.

Micromechanics-Based Low Cycle Fatigue Life Prediction Model of ECAPed Aluminum Alloy

Ultrafine-grained aluminum alloys (UFG AA) show great potential in the design of fatigue-resistant lightweight alloys, and the methodology to assess low-cycle fatigue (LCF) life remains to be studied. In this work, a micromechanics-based LCF life prediction model is presented by conducting crystal plasticity finite element simulation (CPFEM). The fatigue indicator parameter (FIP) of maximum accumulated equivalent plastic strain energy, modulated by triaxiality, is developed to assess the material damage in the microstructure. Particularly, a new multiaxial strain parameter is proposed by considering the combined influence of the mean strain and non-proportional cyclic additional hardening effect, and then directly embedding into the cyclic J-integral. Finally, the reformulated Manson-Coffin relationship is theoretically constructed by correlating the crack tip opening displacement to the crack propagation equation. The results show the scatter fatigue life of UFG AA6061 is not only related to the inhomogeneous evolution of plastic deformation but also to the local stress state. Since the proposed approach considers both the deformation mechanisms at the micro-scale and the corresponding macroscopic responses, it can predict the LCF life of UFG AA with reasonable accuracy.

Influence of stress states on cleavage fracture in X70 pipeline steels

Stress state is a primary factor controlling the ductile fracture behavior of steels, which is typically represented as the combination of the stress triaxiality and Lode angle parameter. The cleavage fracture properties of pipeline steels at low temperatures are usually assessed under plane strain conditions, such as using the fracture mechanics experiments. In this study, the cleavage fracture properties of a X70 steel at liquid nitrogen temperature (−196 °C) are characterized over a broad range of stress states. A comprehensive experimental program is carried out by performing tensile tests using various flat specimens of different geometries immersed in liquid nitrogen, including shear, central hole, notched dog bone, and side grooved plane strain. Pronounced plasticity occurs prior to the final fracture within the tested range of stress states at the very low temperature. Anisotropy effects are considered by conducting tensile tests of fracture specimens along the rolling, diagonal and transverse directions. Finite element simulations of corresponding experiments are performed using an evolving quadratic plasticity model to extract the local stress state variables to establish the fracture criteria, which are formulated based on the critical values of plastic strain and maximum principal stress. The fracture strain of the investigated material at liquid nitrogen temperature is affected by the stress triaxiality, Lode angle parameter and loading direction.

Influence of non-uniform feature of thermally grown oxide thickness on the local stress state and cracking behavior in TBC

The growth of thermally grown oxide (TGO) at high temperatures is the main reason for inducing the cracking near the YSZ/bond coat interface in the thermal barrier coating (TBC). The non-uniform thickening of TGO can change the local stress state and crack evolution. In this work, a TBC model including non-uniform TGO is established to explore the effect of non-uniform feature of TGO on the local cracking behavior. The continuous growth of TGO is simulated by applying a stress-free strain. The arbitrary path propagation of cracks in YSZ and TGO is realized by the XFEM method. The influences of TGO non-uniform degree and lateral growth rate on the stress variation and crack evolution are discussed. The results show that the non-uniform growth of TGO increases the local oxide film thickness and decreases the amplitude of TGO/bond coat interface, which leads to a greater crack driving force than TGO uniform growth. The increase of TGO non-uniform degree will induce longer TGO crack. The coating life predicted by the uniform TGO model is overestimated. The increase of TGO lateral growth strain leads to the improvement of YSZ crack driving force and TGO crack length, which is independent of TGO non-uniform degree. The results in this study indicate that obtaining uniform TGO with a low growth rate by process optimization will be an important option to improve the durability of TBC.

Cracking behavior and delamination mechanism of lamellar structured TBC with localized mixed oxides

Mixed oxide (MO) with localized growth feature and high growth rate remarkably affects the lifetime of thermal barrier coatings (TBCs), which indicates that clarifying the ceramic cracking mechanism induced by MO is critical for developing new coatings with high durability. Two kinds of TBC models involving spherical and layered mixed oxides are created to explore the influence of MO growth on the local stress state and crack evolution during thermal cycle. The growth of α-Al2O3 is also included in the model. The undulating interface between ceramic coat and bond coat is approximated using a cosine curve. Dynamic ceramic cracking is realized by a surface-based cohesive interaction. The ceramic delamination by simulation agrees with the experimental observation. The effects of MO coverage ratio and growth rate on the TBC failure are also discussed. The results show that the MO growth causes the local ceramic coat to bear the normal tensile stress. The failure mode of coating is turned from α-Al2O3 thickness control to MO growth control. Once the mixed oxide appears, local ceramic cracking is easy to occur. When multiple cracks connect, ceramic delamination happens. Suppressing MO formation or decreasing MO growth can evidently improve the coating durability. These results in this work can provide important theoretical guidance for the development of anti-cracking TBCs.

Flow reversal triggers discontinuous shear thickening response across an erodible granular bed in a Couette-Poiseuille-like flow

Granular rheology is experimentally investigated in a vertical Couette-Poiseuille-like channel flow of photoelastic disks, where an erodible bed is sheared intermittently by an upward-moving shear band and a gravity-induced reverse flow. The shear band conforms to the existing nonlocal Eyring-like rheology but the bed exhibits discontinuous shear thickening from the Bagnold inertial regime near the band-bed interface to the Herschel-Bulkley plastic regime near the static wall. This newly discovered bed rheology is rate dependent and is associated with the fragility of the contact networks indicated by the statistics of local stress states inferred from the material photoelastic responses.

Complex deformation history of the Keszthely Hills, Transdanubian Range, Hungary

Abstract We have investigated the deformation history of the Keszthely Hills (Transdanubian Range, W Hungary), which belongs to the uppermost slice of the Austroalpine nappe system. This Upper Triassic to Upper Miocene sedimentary rock sequence documented the deformation of the upper crust during repeated rifting and inversion events. We investigated the structural pattern and stress field evolution of this multistage deformation history by structural data collection and evaluation from surface outcrops. Regarding the Mesozoic deformations, we present additional arguments for pre-orogenic (Triassic and Jurassic) extension (D1 and D2 phases), which is mainly characterized by NE–SW extensional structures, such as syn-sedimentary faults, slump-folds, and pre-tilt conjugate normal fault pairs. NW–SE-striking map-scale normal faults were also connected to these phases. The inversion of these pre-orogenic structures took place during the middle part of the Cretaceous; however, minor contractional deformation possibly reoccurred until the Early Miocene (D3 to D5 phases). The related meso- and map-scale structures are gentle to open folds, thrusts and strike-slip faults. We measured various orientations, which were classified into three stress states or fields on the basis of structural criteria, such as tilt-test, and/or superimposed striae on the same fault planes. For this multi-directional shortening we presented three different scenarios. Our preferred suggestion would be the oblique inversion of pre-orogenic faults, which highly influenced the orientation of compressional structures, and resulted in an inhomogeneous stress field with local stress states in the vicinity of inherited older structures. The measured post-orogenic extensional structures are related to a new extensional event, the opening of the Pannonian Basin during the Miocene. We classified these structures into the following groups: immediate pre-rift phase with NE–SW extension (D6), syn-rift phase with E–W extension (D7a) and N–S transpression (D7b), and post-rift phase with NNW–SSE extension (D8).

Structural diagenesis of deep carbonate rocks controlled by intra‐cratonic strike‐slip faulting: An example in the Shunbei area of the Tarim Basin, NW China

AbstractThe Ordovician fracture‐cavity reservoirs in the Shunbei area of the Tarim Basin, China, afford an exceptional opportunity to use petrological and geochemical data to investigate structural diagenesis in deep low‐porosity (‘tight’) carbonate rocks. We obtained the relative timings for the development of fracture veins using petrological and cathodoluminescence analyses of minerals from representative samples. Textural observations combined with geochemical data determined the source and timing of the mineral‐forming fluid. The conceptual model of the overall temporal evolutions of structure and fluid flow developed herein indicates that fluid flow is a consequence of strike‐slip fault activity and the local stress state. Strike‐slip faults control the development of fractured–vuggy reservoir space and provide driving force for fluid flow along and across layers. Simultaneously, the direction of fluid migration can be influenced by local stress conditions, while compressive stress may restrict fluid flow. Results of this study suggest that open fractures develop as a result of structural diagenesis, rather than resulting from a single structural factor. The findings of this study can be used to inform the exploration and exploitation of deeply buried faulted carbonate reservoirs worldwide.

Rock Properties and Modelled Stress State Uncertainties: A Study of Variability and Dependence

The safety and sustainability of subsurface applications requires a profound knowledge of the local stress state which is frequently assessed using 3D geomechanical-numerical models. Various factors lead to generally large uncertainties in these models. The variabilities in the rock properties as one of the sources of uncertainties and their influence on the modelled stress state is addressed herein. A generic 3D geomechanical-numerical model is used to investigate the influence of different distributions of variability and their effect on different stress states. The variability in rock properties clearly affects the uncertainties in the stress state in a positive correlation with differences that depend on the affected component of the stress tensor. The basic observation is that largest uncertainties are observed in the normal components of the stress tensor where the variabilities apparently are most effective. The same rock property variabilities affect the shear components uncertainties to a significantly lesser extent. Variabilities in the Young’s modulus and the Poisson’s ratio chiefly affect the uncertainties in sigma _{xx} and sigma _{yy}. The density variability, however, leads to highest uncertainties in sigma _{zz}. In general, variabilities in the Young’s modulus are most effective, followed by the Density and then the Poisson’s ratio. Furthermore, an influence of the tectonic stress regime on how the variability in the rock properties affects the stress state is observed. At the same time only a small effect is observed for different stress magnitudes. The eventual uncertainties in a modelled stress state depend not only on the uncertainties in the rock properties but also whether the uncertainties are found mainly in the Young’s modulus, the Poisson’s ratio or the Density. These findings indicate the importance to regard variabilities in rock properties as a source for significant uncertainties in geomechanical-numerical models. It is proposed to use the derived relations for an inexpensive quantification of uncertainties by means of a post-computation assignment of uncertainties to a stress model.

Design of a simple shear test for large strains with sequential re-machining of the specimen edges

The simple shear test is a standard experiment used for the calibration of plasticity models. For thin sheets, the specimen can be as simple as a rectangular strip, or feature optimized geometries of the free edges. These enhancements are mainly motivated by the undesirable initiation of fracture from the free edges, which limit the usable strain range of the test. Previous studies have shown that fracture from the edges occurs due to a local stress state close to uniaxial tension in these areas. In an attempt to increase the maximum strain, a sequential simple shear test is proposed. The specimen is a sheet metal strip with two opposing cut-outs with rounded concave edges. The specimen is mounted in a shear testing device, composed of two jaws with a prismatic joint connection. The shear test protocol includes multiple two-steps sequences. First, an interrupted shear test is performed up to a given value of displacement. Second, the shear testing device, along with the clamped specimen, is positioned in a milling machine and the rounded free edges of the specimen are re-machined. The application of the proposed testing protocol is presented for three engineering materials. It is found that the valid range of this experiment (i.e. the maximum strains attained before specimen failure) can be substantially extended through repeated re-machining of the specimen boundaries.

Frequency-magnitude distribution of earthquakes at Etna volcano unravels critical stress changes along magma pathways

The high seismic productivity of volcanic areas provides the chance to investigate the local stress conditions with great resolution, by analysing the slope of the frequency-magnitude distribution of earthquakes, namely the b-value. Here we investigated the seismicity of Mt. Etna between 2005 and 2019, focusing on one of the largest known episodes of unrest in December 2018, when most of the intruding magma aborted, rather oddly, its ascent inside the volcano. We found a possible stress concentration zone along magma pathways, which may have inhibited the occurrence of a larger eruption. If the origin of such hypothetical loaded region is related to tectonic forces, one must consider the possibility that geodynamic processes can locally result in such rapid crustal strain as to perturb the release of magma. Strong b-value time-variations occurred a few days before the unrest event, suggesting new possibilities for investigating the volcano state and impending eruptions.

Numerical Study of the Influence of Residual Thermal Stresses on the Fracture of Metal Matrix Composites

A numerical study of the mechanical behavior of the «aluminum-boron carbide» composite material under different thermomechanical loading is performed. The complex structure of the composites is explicitly taken into account in the calculations. Isotropic elastoplastic and elastic-brittle constitutive models are used to describe the mechanical response of the aluminum matrix and ceramic particles, respectively. Huber type fracture criterion taking into account the local stress state: bulk tension, or compression, is chosen to study the origination and propagation of cracks in ceramic particles. The composite material microvolume with a single boron carbide particle embedded into the aluminum matrix is considered. The influence of the residual thermal stresses arising during cooling of the composite material from temperature close to the temperature of recrystallization of aluminum to the room temperature on the ceramic particle fracture is investigated. Dynamic boundary value problems are solved numerically by the finite element method in the ABAQUS / Explicit software package.

Effects of grain boundary diffusion process on magnetic properties enhancement and microstructure evolution of hot-deformed Nd-Fe-B magnets

Grain boundary diffusion (GBD) process is an important approach for producing Nd-Fe-B magnets with high coercivity and high thermal stability. The GBD for hot-deformed Nd-Fe-B magnets with nanocrystalline microstructure is more complicated compared to sintered magnets. Here, we investigated the effects of different GBD methods, i.e., intergranular addition (in-situ GBD 1#), in-situ GBD from magnet surface during hot pressing and hot deformation (in-situ GBD 2#), and conventional GBD, on the magnetic properties and microstructure of hot deformed magnets. After the treatment by these three GBD approaches using 2 wt% Pr40Tb30Cu30 diffusion source, the coercivity of the hot-deformed magnet increases from 1281 to 1567, 1412 and 2022 kA/m, respectively. The coercivity enhancement is attributed to the formation of local (Nd,Tb)2Fe14B phase with strong magnetic anisotropy. Reduced grain orientation is found in both in-situ GBD 1# and conventional GBD treated samples mainly due to the local stress state variation and the rotation of platelet grains. Interestingly, the in-situ GBD 2# processed sample has a high orientation at diffusion surface, which may be caused by the modified surface state of the magnet by the diffusion source. Compared with the in-situ GBD processes, the conventional GBD exhibits a higher utilization efficiency of Tb. Since the in-situ GBD is effective to treat thick hot-deformed magnets, further effort should be aimed at enhancing its diffusion efficiency.

Specific Features of the Fine Structure and Local Stress State of 13Kh11N2V2MF Steel under Cyclic Loading

Specific Features of the Fine Structure and Local Stress State of 13Kh11N2V2MF Steel under Cyclic Loading

In-situ diffraction based observations of slip near phase boundaries in titanium through micropillar compression

We investigate local deformation within a dual-phase Ti6242 alloy by considering the interaction between α orientation (i.e., slip system) and the presence of β phase (i.e., fraction and morphology), and the corresponding evolution of stored dislocations. In-situ micropillar compression combined with micro-Laue diffraction and high angular resolution electron backscatter diffraction (HR-EBSD) shows that the high rate of geometrically necessary dislocation (GND) accumulation was observed in basal-slip oriented pillar, while easy formation of glide step with minimal GND accumulation was found in prism-slip oriented pillar. The difference is explained due to the role of the phase boundary for these slip configurations, where local stress concentrations can arise even in pillar with easy slip orientation (i.e., prism slip) if the phase boundary acts as a barrier to slip and results in inhomogeneity of local deformation. This study reveals significance of β phase in potentially modulating the local dislocation based hardening and hence local stress states within Ti polycrystalline aggregate.

Superior strength-ductility synergy of layered aluminum under uniaxial tensile loading: The roles of local stress state and local strain state

A typical layered Al composed of alternating fine-grained layers (FLs) and coarse-grained layers (CLs), fabricated by hot pressing and hot rolling, exhibits a superior strength-ductility synergy under uniaxial tensile loading compared with monolithic Al. The mechanism behind the excellent mechanical properties was elucidated from the perspective of local stress state and local strain state. We found that the operative slip systems of CLs cannot be predicted by the classical Schmid factor, indicating a complex local stress state differing from global uniaxial tension. The so-called local multiaxial stress state, probably caused by the deformation incompatibility between constituent layers, was then proposed, and proved feasible for predicting the slip systems in CLs. On the other hand, the digital image correlation revealed that the strong strain partitioning leads to the transformation of local strain state on CLs from uniaxial to biaxial stretch despite under uniaxial tensile loading. Such the local strain state was incorporated into the Taylor ambiguity method, which can derive magnitudes of operative slip systems in the CLs grains with different orientations. The Taylor ambiguity results agreed well with the multiple microbands formation revealed by the quasi in-situ electron backscatter diffraction coupled with a novel misorientation mapping approach. The characteristic slip system activation and dislocation microbands governed by the local stress state and local strain state imply more latent hardening, hence enhancing the strain hardening capability of layered Al. Our work provides a new direction to achieve a superior strength-ductility synergy by designing local stress/strain and tailoring corresponding deformation mechanisms.

Study of boundary layer effects at ply interfaces of laminated composites using homogenization theory

A conventional analysis of unidirectional composite laminates is based on the use of average (or homogenized) properties, of the heterogeneous media, at the ply level. Plies with different orientations are stacked up to create the laminate. At free edges of the laminate, strong interfacial boundary layers are created, giving rise to large transverse normal and shear stresses. Away from free edges, and on other boundaries, these boundary layers are not present. In this work, possibly for the first time, the interface between the plies is studied in interior regions, away from the free edge. This is important because the effective media creates a fictitious interface, and true local stress states may be very different from that obtained from the conventional analysis, due to a breakdown of inherent asymptotic assumptions. This study proposes a new micromechanical approach to resolve inter-ply interfaces. Using this method, it is shown that interfacial boundary layer plays a significant role in the local stress state. This is demonstrated through the specific example of a cross-ply laminate.

Defect initiation and accumulation kinetics in hard-coated WC-Co hardmetal under multi-axial loads at elevated temperature in a novel ball-in-cone test setup

In the metalworking industry, hard-coated WC-Co hardmetal tools are often used in machining applications. Generally, tool life is limited by pre-existing defects in the hardmetal substrate and defects that form during tool application. The complex, multi-axial loading situations and the high temperatures present in the cutting-edge area of machining tools are among the main reasons for the formation and growth of defects in operation. At present, there is a lack in experimental setups that can replicate these conditions. In the current work a novel material testing method is presented, which uses a spherical indenter and inclined specimen surfaces to apply multi-axial loads at 700 °C. The local stress state in the specimen was calculated using finite element simulation implementing an experimentally parameterized material model considering ratchetting and creep of the substrate material. Stresses ranging from mainly compressive to tensile-compressive were predicted. Initiation and accumulation kinetics of defects in the nm- to μm size regime were studied quantitatively. The comparison of stress calculations and damage development shows that positions with tensile-compressive stresses exhibited significantly higher defect formation rates than those with mainly compressive stresses.

Tidal modulation of seismicity at the Coso geothermal field

Studying the seismicity triggering response of fault systems to periodic stress fluctuations can improve our understanding of earthquake nucleation, rupture failure processes, and local stress states. Geothermal fields are well known to be susceptible to triggering, as the injection and extraction activities change the local stress and fluid flow conditions. Here, we examine the modulation of earthquakes by Earth tides within California's Coso geothermal field (CGF) and its vicinity. To maximize our resolution to detect modulation of small earthquakes, we take advantage of the new Quake Template Matching catalog in southern California, which has nearly twice as many events in the Coso region as the standard catalog and is complete down to about magnitude 0.3. We observe strong tidal triggering of earthquakes within the CGF, even though the fluctuations of tidal stresses are small (∼2 kPa). The tidally-triggered earthquakes tend to occur near the time of maximum tensile tidal stress. The signal is strongest near the edges of the zone of new production wells, suggesting fluid pressure gradients encourages triggering at tidal periods.