Triaxial Stress State Research Articles

Review of fatigue of bulk structural adhesives and thick adhesive joints

ABSTRACT Fatigue of structural adhesives has been investigated through joints and a little number of works investigate bulk adhesive behaviour itself. Aerospace and automotive engineering focuses more on joint configuration studies, which are correlated with practical applications. Previous works showed that for thin adhesive joints, material properties measured by bulk adhesive testing and joint testing are similar despite the triaxial stress states developing in the adhesive bondlines. However, with the introduction of structural adhesives in construction industry, thicker bondlines have emerged where the bulk adhesive material dominates the joint behaviour. This review work summarises works on the fatigue of bulk structural adhesives used mainly in the construction industry investigating structural adhesives fatigue behaviour either through experiment on joints or on bulk adhesive specimens. The work focuses on thick adhesive bondlines in joints, and discusses the controversy that is over whether adhesive properties from joints or from bulk material should be used.

Formability and densification behavior of two-layered structure powder metallurgical hot-pressed Al-Cu/Al composites during hot-upsetting

An experimental investigation has been performed on the hot formability and densification characteristics of Al-Cu/Al two-layered structure composites. The two-layered composites having different Cu compositions in the Al-Cu layer such as (Cu: 5wt. %, 10wt. %, and 15wt. %) were prepared using the powder metallurgy (P/M) route. The composites were hot-pressed as layer by layer in a steel cylindrical die at 550°C temperature with 0.9 initial relative density (IRD) and 0.1 s−1strain rate. The preforms were hot deformed between two flat dies with a capacity of 50-ton hydraulic press machine at a temperature range of 150°C – 450°C under triaxial stress state condition. The hot-upsetting behaviour of preforms was analyzed until the cracks begin on the cylindrical preform at the outer surface. The effect of different Cu composition and various deformation temperatures on two-layered preforms were discussed. Results revealed that the (10wt. %Cu) preform achieved good cooperative deformation behaviour between Al-Cu and Al layers at the interface region. The relationship between the process parameters was discussed such as the effect of axial stress ([Formula: see text]), relative density ( R) on axial strain ([Formula: see text]) and formability stress index ( β), different stress ratio parameters ([Formula: see text], [Formula: see text]) on relative density ( R).

Experimental Study on Influence of Intermediate Principal Stress on the Permeability of Sandstone

In engineering, it is considerably important to understand the evolution process of sandstone deformation and permeability under complex stress conditions. Although numerous scholars have reported on sandstone permeability, many of their studies are only based on uniaxial or conventional triaxial stress conditions. In practical engineering, in situ stress evidently indicates three-dimensional anisotropy. In recent years, many scholars have performed experimental studies on rock permeability under true triaxial stress. There are, however, few investigations related to the influence of intermediate principal stress and intermediate principal stress coefficient on sandstone permeability; moreover, the mechanism is unclear. In this study, the permeability of sandstone under true triaxial stress conditions is measured using a true triaxial apparatus. The results show that the intermediate principal stress has significant effects on permeability and deformation of sandstone sample. Under different principal stress conditions, the permeability is observed to decrease with the increase of the principal stress. With increasing intermediate principal stress coefficient b (from 0 to 1), the major principal strain and the minor principal strain always compressed and finally decreased by 27.31 and 36.96%, while the intermediate principal strain finally changes from expansion to compression (from − 0.045 to 0.255%). Also the normalized permeability loss increased from 9.57 to 16.59%. In addition, by fitting the experimental data with several permeability models, it was found that a true triaxial permeability model can well describe the changes in sandstone permeability. Based on the fitting parameters, the influence of intermediate principal stress and its coefficient on the stress sensitivity of sandstone was analyzed.

Effect of freeze-thaw cycles on the strength behaviour of recompacted loess in true triaxial tests

Freeze-thaw induced change in the strength behaviour of the underlying loess is an important cause of the instability of artificially excavated and natural loess slopes. The loess is mostly in a true triaxial stress state, which was rarely considered in previous strength tests. This study explored the effect of freeze-thaw cycles on the strength behaviour of recompacted loess under true triaxial stress and its relationship with the meso-structure by carrying out freeze-thaw tests, true triaxial tests and scanning electron microscope (SEM) tests. Freeze-thaw cycles exhibit little effect on the shape of the stress-strain curves of recompacted loess, while more significant changes were observed with different b-values. The shear strength first decreases with freeze-thaw cycles and then increases to a constant after five cycles, while it continues to decrease with the b-value. For strength parameters, the cohesion decreases after freeze-thaw and tends to stabilize after five cycles while the internal friction angle is less affected. As the b-value grows, the cohesion first grows and then declines, with the peak value at b = 0.5 while the internal friction angle varies within a narrow range (28.11° - 32.53°). The effect of freeze-thaw on the shape of the failure surface for recompacted loess on the π plane is negligible but pronounced on the size of the failure surface. SEM images and the specimen size imply that the structure of recompacted loess tends to be loose after freeze-thaw cycles, corresponding to a greater pore area ratio and the decrease in the cohesion. Moreover, both the orientation and circularity of soil particles show limited changes, which reveals the insignificant change in the internal friction angle with freeze-thaw

A simplified transient technique for porosity and permeability determination in tight formations: Numerical simulation and experimental validation

AbstractA simplified pulse decay method (PDM) with only a single downstream reservoir is proposed to replicate the in situ conditions for reservoir fluid flow, where the pore pressure at any location declines as production continues. The proposed PDM also allows determining the effective porosity and permeability for the core sample under replicated in situ conditions. A mathematical model is firstly established to closely represent the experimental design and verify the feasibility of the method. The analytical solutions of the model are derived to calculate the effective sample porosity and permeability. A series of experiments are then conducted under triaxial stress condition, and a detailed comparison is also made between the PDMs with a single upstream reservoir and a single downstream reservoir. The experimental results showed that accurate measurements on effective sample porosity and permeability can be achieved by the single downstream reservoir PDM due to its capability of better replicating the in situ fluid flow behavior, which extends the application of the transient technique. It is also found that the pore pressure along the sample changes linearly, and its gradient varies with time, indicating the applicability of the single‐reservoir PDMs in permeability determination. This method also lays a foundation for studying flow behavior when a second fluid phase evolves during pressure decline, which occurs in many reservoirs.

Assessment of Notch Effect Based on Finite Element Analysis and Digital Image Correlation Technique

Triaxial state of stress experienced by structural components due to complex geometry, discontinuities, or type of loading can be studied by tensile testing of notched specimens. Herein, assessment of tensile deformation of 316LN austenitic stainless under the uniaxial and triaxial stresses is presented based on finite element (FE) analysis and digital image correlation (DIC). To study their effects, notches of different root radii are incorporated in flat smooth specimens. The strength of the material increases in the presence of notch. Among the various constitutive expressions, the Swift equation provides a better representation of the tensile response for the smooth specimen. The analysis is further extended by incorporating Swift equation parameters as the deformation model in the FE analysis for notched specimens. The tensile response of the notched specimens is predicted well using the FE analysis. The in‐house algorithm is developed for DIC and used to estimate the strain in smooth and notched specimens by speckle‐pattern image analysis. The total displacement of smooth and notched specimens obtained from the FE analysis and DIC technique is comparable to the experimental results. Both the techniques complemented each other in understanding the deformation behavior of the steel.

Experimental study on the anisotropy of the effective stress coefficient of sandstone under true triaxial stress

The effective stress principle plays an important role in the study of the permeability evolution and mechanical behavior of coal and rocks. A key to evaluating the effective stress is determining the evolution of the effective stress coefficient α. However, conventional triaxial stress-path tests are not suitable for reproducing the actual stress state of coal and rocks and thus determining the effective stress coefficient. Therefore, this study was conducted to investigate the anisotropic characteristics of the effective stress coefficient for sandstone under different true triaxial stress and pore pressure conditions. The results show that the effective stress coefficient exhibits anisotropy due to the different principal strains in three directions and the anisotropy of pore structure, and it is closely linked with the pore pressure and principal stress. An increase in pore pressure causes sandstone particles that block the seepage channel to migrate, which reduces the sensitivity of permeability to principal stress, increasing the effective stress coefficient. When principal stress increases, pores and fractures are compressed, which reduces the sensitivity of permeability to pore pressure, resulting in a decrease in α. However, as principal stress continues to increase, effective stress coefficients can increase in the directions of major and intermediate principal stresses, while an α3 beyond unity appears in the direction of minor principal stress. This is related to the pore fluid flowing through highly compressible clay aggregates, in which the pore area is large, and the sensitivity of permeability to pore pressure is enhanced. The effective stress coefficient increases with an increase in permeability due to the effect of porosity. A new formula for calculating the volumetric strain of a linear elastic isotropic porous medium is established based on the anisotropy of the effective stress coefficient, which can be applied to experimental results.

Three-dimensional visualization of the evolution of pores and fractures in reservoir rocks under triaxial stress

To study the evolution of pores and fractures in reservoir rocks under triaxial stress conditions at the mesoscale, three-dimensional (3D) visualization of coal and shale was performed using computed tomography (CT) scanning and real-time acoustic emission (AE) signal monitoring. The experiment verified that the pores and fractures of the reservoir rocks increased, and the AE signals increased accordingly with the increase in stress. The pore and fracture evolution processes in coal and shale under triaxial stress conditions can be divided into three stages: initial, expansion, and penetration. Compared with coal, the pores and fractures in shale have a shorter penetration stage, indicating that the shale failure process is more rapid. Based on the Rickman formula, modified brittleness index calculation formulas for the tested shale were established. The results of the modified calculations and the CT scan results of pores and fractures can be mutually verified.

Effect of B4C on strength coefficient, cold deformation and work hardening exponent characteristics of Mg composites

The emphasis of this exploration was to examine the workability and work hardening performance of Mg (Magnesium) specimen and Mg-B4C composites created via the powder metallurgy technique. The pure Mg and Mg-B4C composites are made with distinct weight percentages (Mg-5% B4C, Mg-10% B4C, and Mg-15% B4C) at the unit aspect ratio. The powders and composites characterization are executed by SEM (Scanning Electron Microscope), EDS (Energy Dispersive Spectrum) with an elemental map, and XRD (X-ray Diffraction) examination. It displays that, the B4C particles were dispersed consistently with the Mg matrix. The workability and work hardening examination was conducted in triaxial stress conditions using the cold deformation process. The consequence of workability stress exponent factor (βσ), distinct stress proportion factors (σm/σeff and σθ/σeff), instantaneous work hardening exponent (ni), work hardening exponent (n), coefficient of strength (k) and instantaneous coefficient of strength (ki) are recognized. The outcome displays that Mg-15% B4C specimen has greater workability and work hardening parameter, initial relative density, and triaxial stresses compared with the Mg specimen and Mg-(5–10%) B4C composites.

Alternative method to determine the uniaxial-strain compressibility of cohesive sandstone

Compaction and subsidence risk related to hydrocarbon production are frequently assessed using Geertsma models. The underlying theory assumes linear poroelastic reservoir rock to compress by pore pressure depletion under uniaxial-strain conditions. Adequate mechanical testing techniques have been developed to measure the uniaxial-strain compressibility, although the execution of these methods is technically difficult and requires a significant level of experience. In this paper, a simplified technique is proposed to approximate the compressibility from triaxial strain data, which is different from earlier hydrostatic stress/uniaxial-strain conversion approaches. The method is applied to Berea outcrop sandstone and Groningen reservoir material, employing pore pressure depletion protocols under triaxial stress and uniaxial-strain boundary conditions. By interpolation of triaxial stress–strain data and adopting linear poroelastic theory, the uniaxial-strain compressibility required for the application of the Geertsma model is yielded. This does not require a priori information of elastic constants. Moreover, the interpolation technique allows for an independent check of the technical performance of the radial strain control system. The method holds for rocks that are close to linear poroelastic, subjected to stress conditions below the critical state line.

Study on triaxial creep behavior and the damage constitutive model of red sandstone containing a single ice-filled flaw

The freezing method is widely used in the construction of vertical shafts in water-rich strata. The formed frozen rock wall is often involved in the creep process, and in particular, the creep behavior of frozen fissured rock mass poses a great threat to construction safety. To better understand the creep instability law of ice-filled, fractured red sandstone under freezing and triaxial stress conditions, a series of triaxial creep tests on frozen red sandstone specimens containing a single, pre-existing flaw at −10°C and under a confining pressure of 4 MPa were carried out with a self-developed DRTS-500 subzero rock triaxial testing system. The multistage loading creep curves were obtained, and the evolution laws of deformation and damage for the frozen specimens in the primary (instantaneous), secondary (steady-state) and tertiary (accelerating) phases were analyzed. The nonlinear visco-elastoplastic constitutive model of red sandstone with a single ice-filled flaw was established according to the fractional calculus theory and the Kachanov damage theory. The results show that the initial creep property, unstable creep property and creep failure mode of frozen single-flaw red sandstone are significantly affected by the flaw dip angle. The proposed creep damage model can accurately describe the complete creep curves of frozen red sandstone with a single ice-filled flaw, especially in the unstable creep stage. The influences of the stress level and flaw dip angle on the creep parameters were analyzed, and sensitivity analyses of the characteristic creep parameters were carried out to verify the reliability and rationality of our creep model. This research can be applied to the assessment of collapse, cracking and other long-term failures and hence can be used as a theoretical basis of design in the freezing engineering of coal mine shafts.

GTN Model-Based Material Parameters of AZ31 Magnesium Sheet at Various Temperatures by Means of SEM In-Situ Testing

Magnesium alloys are primarily associated with complex forming mechanisms, which yield ductility at high temperatures. In sheet metal forming, high triaxiality stress states that favor the ductile damage mechanisms of void formation and growth are known to malleable metals. The formulation of coupled damage models has so far failed, due to the incomplete experimental determination of damage parameters for magnesium AZ31 thin sheet. A quantitative investigation was conducted to determine the ductile damage behavior of twin-roll cast, hot rolled, and annealed AZ31 thin sheet. Results on the mechanisms of void nucleation-, coalescence- and growth-rate were established at temperatures ranging from room temperature to 350 °C. In-situ tensile tests were carried out in a scanning electron microscope with three different specimen types: Simple tension specimens, notched specimens for high triaxiality stress state testing, and shear specimens. Through a comparative analysis of local strains measured by digital image correlation and local void volume fractions determined through post-mortem analysis of specimen cross-sections, GTN (Gurson–Tvergaard–Needleman) model-based material parameters were determined by experiment, representing a novel departure in the magnesium research landscape. The procedure developed in this context should also be transferable to other metals in the form of thin sheets.

Three-dimensional stress formula in fiber direction and its application under internal and external pressure

A three-dimensional (3D) fiber stress formula was developed to reduce the deviation of the two-dimensional (2D) fiber stress formula in calculating the 3D stress. The on-axis and off-axis stress–strain relationship was first presented. The 3D fiber stress formula was then derived analytically. Finite element method (FEM) of filament-wound (FW) thick-walled cylinders with symmetrical/balanced-layers was built, and numeric results were calculated and analyzed. Good agreement of the fiber stresses in the fiber direction and the strength ratios were achieved. It was found that the 3D fiber stress formula yields more accurate stress and lower strength ratio than the 2D formula in the triaxial stress state.

Hysteretic Behavior of Geopolymer Concrete with Active Confinement Subjected to Monotonic and Cyclic Axial Compression: An Experimental Study.

This paper investigated the performance of actively confined geopolymer concrete (GPC) through experiments. The mechanical properties of GPC under triaxial stress states were analyzed and discussed from the prospects of failure modes, axial peak stress and strain, monotonic and cyclic constitutive relationships. The experimental results demonstrated that the loading modes (monotonic loading and cyclic loading) had little effect on the failure mode and axial peak stress and strain. The improvement of the strength and ductility of GPC with the increase in confinement level was consistent with that of the conventional cement concrete while the strain enhancement of confined GPC was lower than that of confined conventional cement concrete at the same confinement level. The curves of the monotonic stress–strain and the envelop of cyclic compression were predicted through Mander’s model with good accuracy. The unloading/reloading models proposed by Lokuge were modified and the predicted cyclic hysteresis curves for actively confined GPC were in good agreement with the cyclic compression results. Findings from this study provide references for the application of geopolymer concrete.

Investigations on the influence of the triaxial state of stress on the failure of polyurethane rigid foams

This paper investigates the failure strain as a dependence of the stress triaxiality and the Lode angle parameter for polyurethane rigid foams (PUR) of two densities (100 and $$300\,\hbox {kg/m}^{3})$$ . Tests were carried out in tension for various configurations, resulting in different states of stress triaxiality at various Lode angles in the critical areas. The failure strain was determined for each setup using finite element analysis, as the tests were replicated with numerical models. The displacement at failure recorded in the experiments was imposed for the models, determining the failure strain as a function of stress triaxiality and the Lode angle parameter. The results were validated through the analysis of the failure of sandwich structures with aluminium faces and PUR cores.

Permeability-enhanced rate model for coal permeability evolution and its application under various triaxial stress conditions

Knowledge on permeability enhancement is of great significance for the exploitation of coalbed methane, shale gas, and tight gas. In this study, the volumetric strain of rocks is considered to be one of the most important permeability change factors. A new model based on the concept of the permeability-enhanced rate (PER), which is referred to as the permeability ratio variation of per volumetric strain, is derived based on Darcy’s law, the tablet flow model, and the theories of flow through porous media and capillary flow. To validate the PER model using coal samples under triaxial stress conditions, loading tests at different gas pressures and loading-unloading tests at different loading-unloading rates are conducted. In the loading tests, the PER evolution is quite different for the different gas pressures. The PER value at a gas pressure of 1 MPa reached 108.40, which was 1.69, 1.41, and 1.57 times as high as the PER value at 0.5 MPa, 3 MPa, and 5 MPa, respectively. In the loading-unloading tests, the PER value was calculated based on the initial porosity and the relative increment in the volumetric strain during the whole loading-unloading process. A lower loading-unloading rate implied a more connected failure surface, and the PER value was greatly enhanced in the post-peak phase. The results show that a good relation between the deformation and seepage characteristics is developed in the PER model. The PER can not only capture the failure process and describe the pore-fracture connectivity improvement induced under loading conditions but can also quantitatively evaluate the permeability evolution, which provides an easy and fundamental method to describe the relative degree of permeability change in the recovery of unconventional gas.

Fractional-order creep model for soft clay under true triaxial stress conditions

To investigate the creep characteristics of soft clay under true triaxial stress conditions, multistage loading creep tests using TSW-40 true triaxial apparatus were performed. The creep deformation characteristics, creep rate, and long-term strength of soft clay under a true triaxial stress path were studied. The results showed that the creep deformation and creep rate of soft clay increase with increasing major principal stress; the axial deformation is larger than the lateral deformation. The long-term strength and the equation for predicting the starting point of accelerated creep were obtained using the generalized shear stress. A four-element fractional-order creep (FFC) model based on the fractional Burgers creep model was established for soft clay and then extended to three dimensions. The model calculation results based on the parameters obtained using MATLAB’s Curve Fitting Toolbox were in good agreement with the experimental results. The comparison results showed that the 3D FFC model was more accurate at describing the entire creep curve of soft clay than the fractional Burgers model and the Burgers model, particularly regarding the accelerated creep characteristics. In conclusion, the results presented herein are expected to provide the scientific basis for determining soft clay creep instability under true triaxial stress conditions.

Analyzing the deformation and failure of geosynthetic-encased granular soil in the triaxial stress condition

The equivalent strength and stiffness of geosynthetic-encased soil are two important parameters for analysis of cellular geosynthetic-reinforced foundations and earth structures. However, limited analytical approaches exist for the estimation of these parameters, and this limitation hinders their applications in geotechnical engineering practice. In this study, an analytical method is proposed for the prediction of the stress-strain response of geosynthetic-encased soil by employing the soil response in the triaxial stress condition and the theory of thin cylinders. This method has the advantages of theoretical rigorousness and convenience for use and can consider soil nonlinearity, soil dilatancy, soil plasticity and soil-geosynthetic interaction. Different types of yield criteria for soils can be readily incorporated into the proposed method. The proposed method is validated against the results of triaxial compression tests on geosynthetic-encapsulated sand. The good agreement between the predicted stress-strain curves and the measured curves demonstrates the effectiveness of the method. In addition, design tables and parametric studies are provided by employing the formulated analytical method for application purposes.

Effects of loading rate on the compound dynamic disaster in deep underground coal mine under true triaxial stress

The compound dynamic disaster is an abrupt and violent energy-releasing process under the combined action of gas and geological tectonic stress in deep underground coal mines. To investigate the occurrence mechanism of compound dynamic disasters, a novel experimental approach was designed and the one free-face true triaxial tests with different loading rates were conducted. Results shown that the compound dynamic disaster can be classified into several stages: initial quiet period, local particles and fragments ejecting, mid-term quiet period, external coal plate bending accompanied by gas-emitting, dynamic disaster occurring process, and the final re-stabilized period. The presence of the gas can significantly facilitate the development of cracks and enhance the kinetic energy, thus increasing the probability of the compound dynamic disasters. Under the one free-face true triaxial engineering stress conditions, the mechanical properties (e.g. deformation and strength) of coal samples are obviously rate-dependent, and the peak stress exhibits an approximate logarithmically increase trend with increasing loading rate. After failure, several tensile-shear fractures approximately parallel to the intermediate principal stress direction and perpendicular to the free face are generated. And an arc-shaped coal-burst pit on the free face of coal sample is observed, and the pit volume increases with the increase of the loading rate. Moreover, the particle ejection kinetic energy increases gradually as the loading rate increased, suggesting a higher loading rate can enhance the intensity of the disaster. The findings may provide guidance for the prevention and control of the compound dynamic disasters in deep underground coal mines.

Fractal characteristics of acoustic emission of gas-bearing coal subjected to true triaxial loading

As coal mining proceeds deeper, coal and rock are subjected to growing stresses and gas pressures. Consequently, coal and rock gas dynamic disasters pose more and more considerable threats and hazards which should be warned in advance. Coal and rock in the field is actually in the true triaxial stress state. Study on deformation characteristics and precursory information of coal and rock under this state is meaningful for disaster warning. In this paper, experiments on the deformation, failure and acoustic emission (AE) characteristics of gas-bearing coal under true triaxial loading conditions were carried out. Besides, the variation law and fractal characteristics of AE under different gas pressures and confining stresses were analyzed. Furthermore, the effects of gas pressure and confining stress on the deformation, failure and fractal characteristics of coal were discussed. The results show that the process of AE variation under true triaxial loading conditions can be divided into two stages, namely the slow growth stage and the accelerated growth stage. A higher gas pressure corresponds to a shorter duration of slow growth stage, while a higher confining stress corresponds to a longer duration of slow growth stage. AE time series has fractal characteristics, and the correlation dimension can characterize the damage degree of a loaded coal sample. The dynamic changes, i.e., fluctuation-increase-decrease, in correlation dimension can accurately reflect the damage evolution process of a coal sample. In addition, the gradual reduction of correlation dimension can be used as the precursor information of coal sample instability and damage. The research results boast instructive significance for preventing the occurrence of coal and rock gas dynamic disasters and for reducing casualties and property loss in coal mines.