Critical Stress Ratio Research Articles

Constitutive Damage Model for Rubber Fiber-Reinforced Expansive Soil under Freeze-Thaw Cycles.

To elucidate the degradation mechanism of expansive soil-rubber fiber (ESR) under freeze-thaw cycles, freeze-thaw cycle tests and consolidated undrained tests were conducted on the saturated ESR. The study quantified the elastic modulus and damage variables of ESR under different numbers of freeze-thaw cycles and confining pressure, and proposed a damage constitutive model for ESR. The primary findings indicate that: (1) The effective stress paths of ESR exhibit similarity across different numbers of freeze-thaw cycles, the critical stress ratio slightly decreased by 8.8%, while the normalized elastic modulus experienced a significant reduction, dropping to 42.1%. (2) When considering the damage threshold, the shear process of ESR can be divided into three stages: weak damage, damage development, and failure. As strain increases, the microdefects of ESR gradually develop, penetrating macroscopic cracks and converging to form the main rupture surface. Eventually, the damage value reaches 1. (3) Due to the effect of freeze-thaw cycles, initial damage exists for ESR, which is positively correlated with the number of freeze-thaw cycles. The rubber fibers act as tensile elements, and the ESR damage evolution curves intersect one after another, showing obvious plastic characteristics in the late stage of shear. (4) Confining pressure plays a role in limiting the development of ESR microcracks. The damage deterioration of ESR decreases with an increase in confining pressure, leading to an increase in ESR strength. (5) Through a comparison of the test curve and the theoretical curve, this study validates the rationality of the damage constitutive model of ESR under established freeze-thaw cycles. Furthermore, it accurately describes the nonlinear impact of freeze-thaw cycles and confining pressure on the ESR total damage.

Effect of grain size on tensile behavior and the underlying deformation modes in a Mg-5Y sheet

This work aims to further understand the grain size effects on individual slip/twining activities at grain scale and their correlation with the tensile behavior, for a Mg-5Y sheet with mean grain size range of 3–130 μm, based on slip trace/electron backscatter diffraction (EBSD) analysis. The correlation between tensile yield strength and the corresponding grain size fitted well with the Hall-Petch relationship, i.e., the k value was 191 MPa·μm1/2, with an R2 of 0.96. According to the identified 1004 sets of slip traces in 2477 grains, basal <a> slip was always dominant and tended to increase (from 47.2% to 71.5%) with grain size increased from 3 to 85 μm. Meanwhile, the percentage of pyramidal II <c+a> slip exhibited a marked decline from 34.5% to 8.9%, while that of prismatic <a> and pyramidal I <c+a> slip changed slightly. The decreased pyramidal II <c+a> slip activity was consistent with the decreased tensile yield strength as grain size increased. The twinning activity was limited and insensitive to grain size. In addition, the geometrically necessary dislocation (GND) density was increased with increasing grain size. Based on the slip activity statistics, the critical resolved shear stress (CRSS) ratios were estimated, which exhibited a significant grain size effect. Specifically, CRSSpris/CRSSbas showed negative grain size dependence, while the opposite was true for CRSSpyrIICA/CRSSbas. This study provides valuable grain-scale experimental evidence for the grain size effect on individual slip activity and CRSS ratios, which contributes to a better understanding of the Hall-Petch relationship in Mg-Y alloy.

Microstructure and dynamic behaviours of polyurethane-cured sea sand under traffic–load–induced stress path

Employing sea sand as fill material for roadbeds presents significant challenges due to its naturally high dispersibility and low bearing capacity, which contribute to substantial settlement deformations under traffic load impacts. In this investigation, a two-component polyurethane was applied to enhance mechanical properties of sea sand. Alterations in the microstructure and dynamic behaviours of the polyurethane-cured sea sand were observed via Scanning Electron Microscopy (SEM) and hollow cylindrical torsional shear testing. It was found that polyurethane is incorporated into the sea sand as adhesives between particles, attachments on the particles and floating adhesives. With an increase in polyurethane content, a transition from a granular to a solid state in the sand was noted, accompanied by a progressive improvement in structural integrity. This resulted in an enhanced bonding effect at interparticle contacts with diminishing relative particle movements during shearing, leading to an increase in the critical dynamic stress ratio and a decrease in the maximum damping ratio, with both ratios being higher in cured sea sand with lower polyurethane content compared to that with higher content. Additionally, high polyurethane content induced strain hardening in the cured sea sand, resulting in a higher maximum dynamic shear modulus in low-content cured sea sand compared to high-content. Furthermore, the dynamic shear modulus ratio in sea sand with high polyurethane content was found to increase with the number of vibrations.

The Significance of the Critical Stress Ratio in the Formulation of Nonlinear Constant Life Diagrams for CFRP Laminate Life Prediction

The Significance of the Critical Stress Ratio in the Formulation of Nonlinear Constant Life Diagrams for CFRP Laminate Life Prediction

Strength behaviour of stacked phosphogypsum incorporating dissolution–recrystallisation equilibrium

Large phosphogypsum (PG) stacks risk dam failure, with an insufficient consensus on the shear strength parameters for stability analysis. To this end, a combination of scanning electron microscopy (SEM) and triaxial tests was undertaken to investigate the underlying mechanism between crystal structure and shear strength of in situ and remoulded PG samples. The shear strength and deformation of PG were significantly affected by dissolution and recrystallisation. Dissolution weakened the cementation between particles, leading to a stabilisation of approximate 11 kPa under different confining pressures in the initial shear stage. The hardening phenomenon was related to the formation of cluster crystals under saturated conditions. An increase from 1.57 to 1.73 in the critical state stress ratio on remoulded samples occurred as the K0 consolidation time increased from 4 to 28 days. The compressive deformation of PG is accompanied by chemical consolidation, which is mainly impacted by the consolidation conditions (saturation) rather than the consolidation time. In the engineering design of the PG stacks, φ’ could be taken to a higher value at saturation and c’ could be higher when the dry density is higher than 1.2.

Critical state behaviour of an unsaturated kaolin mixture

In this paper, a series of suction-controlled triaxial tests were conducted to investigate the hydromechanical behaviour of an unsaturated kaolin mixture. The studied variables included the mean net stress, suction, and initial dry density. The suction was controlled over a wide range – in the span of 0–390 MPa using the axis translation method and the vapour equilibrium technique, aiming to holistically study the mechanical response of unsaturated soils. The discussion focused on the critical state behaviour and dilatancy characteristics of the tested soil. The experimental results indicate that the ductility of the soil decreases and shifts towards brittleness with increasing suctions. The critical state stress ratio (Ma) of the soil exhibits a significant increase with suction, and this increase becomes more pronounced with higher initial dry density. Conversely, the impact of suction on the critical state line in the specific volume-mean net stress plane (v-lnpnet plane) diminishes with higher initial dry density. Furthermore, suction notably influences the stress-dilatancy relationship of kaolin mixtures, while the effect of confining pressure appears to be marginal. The influence of suction on the stress-dilatancy relationship primarily stems from its impact on the critical stress ratio (Ma), which can be normalized by dividing the stress ratio by the critical state stress ratio. Lastly, the stress-dilatancy equation of the modified Cam-clay model is extended to capture the effect of suction on the dilatancy characteristics of unsaturated soils.

Calculation of the CRSS ratios of Ti80 alloy and its application in prediction of texture in Pilger cold rolling

The accurate critical resolved shear stress (CRSS) ratios of different slip systems and deformation history are vital for the texture simulation and controlling for Ti80 alloy pipe during Pilger cold rolling process. This study proposed a comprehensive framework for determining these parameters. A method to calculate the CRSS ratio based on the statistics of activated slip systems was proposed, which could effectively eliminate the error of activated slip systems proportion caused by microtexture. No twinning was observed in the deformation of Ti80 alloy, and the activated slip systems of {0002}<11 2‾ 0>, {101‾ 0}<112‾ 0>, {101‾ 1}<112‾ 0> and {112‾ 2}<112‾ 3> were observed through uniaxial in-situ tensile test combined with EBSD at room temperature. And the CRSS ratio of Ti80 alloy has been calculated approximately as τBasal<a>: τPrism<a>: τPyram<a>: τPyram<a> = 1:0.8:3.5:6. Based on visco-plastic self-consistent (VPSC) model and the calculated CRSS, the texture with shear strain and without shear strain was simulated respectively in the Pilger cold rolling process. Meanwhile, the mechanism of texture formation was analyzed. The texture component was [0001] ‖ TD, and [11-20]‖ AD when the traditional velocity gradient neglecting shear strain was adopted in simulation. However, the shear strain in ZR direction would cause the texture to rotate 30° around the [0001] axis. Compared with that only considering the velocity gradient in the normal strain direction, the rolling texture can be more accurately predicted when considering the history of velocity gradient in all directions.

A shear‐transformation‐zone model for time‐dependent behaviours of clay

AbstractA shear‐transformation‐zone (STZ) model is proposed for time‐dependent behaviours of clay, in which the viscoplastic deformation is described by the evolution of a temperature‐like state variable. The model is featured by rate‐dependent dilatancy and a unique critical state stress ratio. In its present form, it has nine parameters, most of which can be handily calibrated, and can predict the rate‐dependent undrained shear strength, primary, and secondary creep, as well as stress relaxation for normally consolidated clay under complex stress paths using a single set of parameters. The capabilities of the model have been verified by available experimental results on five different clays.

Exploring the micro-to-macro response of granular soils with real particle shapes by way of μCT-aided DEM analyses

This contribution provides high-fidelity images of real granular materials with the aid of X-ray micro-computed tomography (μCT), and employs a multi-sphere representation to reconstruct non-spherical particles. Through discrete-element method (DEM) simulations of granular samples composed of these non-spherical clumps, the effect of particle shape on the macroscopic mechanical response and microscopic soil fabric evolution is examined for soil assemblies under triaxial compression. Simulation results indicate that materials with more irregular particles tend to show higher shear resistance in both peak and critical states, while exhibiting higher void ratio under isotropic loading conditions and in the critical state. The proposed critical state parameters for describing the sensitivity of the mean coordination number to confining pressures are larger as particles become more irregular. At a microscopic level of observation, directional and scalar parameters of particle contacts are sensitive to predefined particle shapes. More irregular materials appear to exhibit higher fabric anisotropy with respect to particle orientation in the critical state, while the branch vector is affected by both contact modes and particle shape. The critical stress ratio from the simulation results is validated by comparing with experimental results, and further found to be linearly linked to the shape-weighted fabric anisotropy indices.

Undrained permanent deformation characteristics of Yellow River silt under one-way cyclic loads

As a new type of engineering construction filler, it is particularly important to know the shakedown and permanent deformation characteristics of the Yellow River silt under cyclic load. In this study, a series of undrained cyclic triaxial tests for Yellow River silt are carried out by using GDS triaxial apparatus, the effects of relative density, loading frequency, confining pressure and cyclic stress ratio on the development curve of permanent strain are explored. Based on the shakedown theory and combined with the data of permanent strain development curve of Yellow River silt at different stress levels, a calculation model for its critical dynamic stress and limit cyclic stress ratio under shakedown state is determined. Further analysis is conducted on the development law of the permanent strain curve of Yellow River silt under shakedown state, and a prediction model for permanent strain of Yellow River silt considering different parameters was established. Then the accuracy of the model is verified. Combining with splitting summation method, the settlement of foundation can be calculated.

Microstructure and enhanced strength and ductility of Ti-Zr-O alloys prepared by a laser powder bed fusion process

Non-toxic and biocompatible Ti-Zr-O alloys with excellent comprehensive properties of strength and ductility were prepared from Ti-ZrO2 powder mixtures by a laser powder bed fusion (LPBF) process. The substitutional Zr atoms and interstitial O atoms, formed by decomposition of ZrO2 during laser irradiation, were dissolved into crystal lattice of Ti, resulting in significant increases in lattice constant c and axial ratio c/a. The Ti-Zr-O alloys were characterized by fine needle-like microstructure with weakened texture compared to pure Ti. The needle-like microstructure may be generated through the growth of α-nuclei according to the Burgers orientation relationship during β→α phase transformation, and the reduction of crystallographic anisotropy in the Ti-Zr-O alloys is due to the formation of α grains with multiple variants. The LPBFed Ti-Zr-O alloys exhibited significantly enhanced strength and maintained good ductility, overcoming the strength-ductility trade-off dilemma. For example, the yield strength and ultimate tensile strength (UTS) of the Ti-1.48Zr-0.66 O alloy reached 1014 MPa and 1073 MPa, respectively, and its elongation at fracture remained at 17 %. The strength enhancement is due to the solid solution strengthening of O and Zr and grain refinement strengthening, of which the solid solution strengthening of interstitial O atoms is the most dominant contributor to the improvement in strength of the LPBFed Ti-Zr-O alloys. The good ductility is mainly attributed to the activation of pyramidal slips due to reduced critical resolved shear stress (CRSS) ratios between pyramidal and prismatic planes, especially dislocation slips along <c + a> directions on the pyramidal planes due to the fine-grained microstructure. The activation of multiple slip systems, including prismatic and pyramidal slips, contributes to the improved ductility of the LPBFed Ti-Zr-O alloys.

Compressive residual strength of the pultruded glass-fiber composite after tension-compression fatigue

We experimentally determined the decrease of residual compressive strength of the pultruded glass-fiber laminate after tension-compression cyclic loading. The adapted Arcan rig was used for tension-compression fatigue tests. The cyclic load was applied with the critical stress ratio R=−0.87. The residual compressive strength was determined after applying the predefined number of loading cycles with the stress amplitudes of 242 MPa and 173 MPa. The results indicated that the residual compressive strength was reduced about 20% at 77% of fatigue life under the stress amplitude of 242 MPa and at 83% of fatigue life under the stress amplitude of 173 MPa. The microstructural analysis showed that the crack growth path and failure mode depend on the stress amplitude.

Deformation and Strength of Unsaturated Loess—Hydraulic Coupling Effects under Loads

The volumetric change in unsaturated loess during loading causes serious damage to the foundation and structure, accompanied by changes in hydraulic conditions. Therefore, quantifying the change in the load effect of loess under hydraulic coupling is of great significance for revealing the mechanism of hydraulic interaction. This study conducts isotropic compression and undrained shear tests on unsaturated compacted loess, simultaneously introducing the strength parameter η to enhance the Glasgow coupled model (GCM). The objective is to elucidate the hydraulic and mechanical coupling mechanism, where saturation increases under mechanical effects lead to strength degradation. The results show that saturation increases under mechanical effects improve the compressibility of the sample, and saturation has a direct impact on the stress–strain relationship. The increase in water content and confining pressure increases the trend of the critical state stress ratio M decreasing, and the strain softening trend increases. The compression of volume during shear tests increases the saturation, changes the hydraulic characteristics of loess, and affects the deformation and strength of loess. The modified GCM improves the applicability and prediction accuracy of unsaturated loess under the same initial state. The research results are of great significance for revealing the hydraulic and mechanical behavior of loess.

Glass Beads Test with True Triaxial Stress Path Achieved by Conventional Triaxial Apparatus

The impact of fabric anisotropy, fractal dimension, and breakage on the strength and deformation of granular materials were diminished by uniform-size spherical glass beads. Triaxial drained and undrained tests were performed on glass beads based on a novel method to substitute true triaxial stress paths with conventional triaxial apparatus equivalents with varying intermediate principal stress coefficients (b-values). The result indicates that all specimens manifested a noticeable strain-softening phenomenon. The peak strength decreased with increasing b-value, and the specimens showed more pronounced dilatancy. This pattern is similar to the results of the true triaxial test in current research. Compared to the undrained test, the peak friction angle in the drained test displayed a greater variation with varying b-values, which indicated that the mechanical response of glass beads is sensitive to water. This difference provides experimental evidence for comprehending effective stress in granular materials with constant friction coefficients. The experiments reflect the effect of b-value changes on the p-q stress path, as well as on the peak stress ratio, the state transition stress ratio, and the critical state stress ratio. The specimens exhibited a distinct shear band at different b-values ranging from 0.2 to 0.6, which is different from observations in conventional triaxial tests for granular materials.

Use of Linear Extrapolation to Estimate Critical State Void Ratio from Drained Triaxial Shear Tests on Dense Cohesionless Soil

Within the strain level attainable in drained triaxial tests, it is not uncommon for dense cohesionless soil to be sheared insufficiently to reach the critical state. Linear fitting of the correlative data from the maximum stress ratio or minimum dilatancy to the end of the test, and then extrapolating these fitted lines to the critical stress ratio or zero dilatancy has been frequently used to estimate the critical state void ratio. However, the linear extrapolation method is empirical and involves different choices of correlative test data, which leads to different estimates. Therefore, a series of simulations of drained tests on dense Toyoura sand are performed using a state-dependent model. Multiple data sets are generated, including void ratio e, volumetric strain εv, stress ratio η, and dilatancy D. The linear extrapolation accuracy of the e–η, e–D, and εv–D data sets is examined. It turns out that the e–η data set is best suited. The goodness of the e–η data set is examined against 18 sets of experimental data on dense sand. In addition, the selection of the start point for extrapolation is shown to influence the estimates. The latter 50% of the post-peak data is found to be reliable.

Natural state parameter for sand

Based on the frictional state concept, the natural state parameter for sands is defined as an extension of the state parameter defined by Been and Jefferies. The proposed definition of the natural state parameter is the sum of the distance between the normalised difference of the current stress ratio and the critical frictional stress ratio and the difference between the current and critical frictional state void ratio for the same mean principal stress. Therefore, it combines the difference between the current and critical frictional state in the q ‒ p’ and e ‒ p’ planes and can be treated as an extension of Been and Jefferies’ definition of the state parameter in the e ‒ p’ plane. The results of drained triaxial compression tests for Toyoura sand and Dog’s Bay sand, presented in the literature, are analysed. The values of the natural state parameter at failure for these sands are equal to zero. Therefore, the critical state in the q ‒ p’ and e ‒ p’ planes can be determined by analysing the conditions at failure. At failure, the deformations of the samples are almost homogeneous, and the stresses and deformations (void ratios) can be correctly determined. Additionally, the critical frictional state and critical state are very similar for these sands. The relationship between the dilatancy and the state parameter at failure, similar to that given by Been and Jefferies, was obtained directly by using the frictional state concept and the proposed definition of the natural state parameter. The natural state parameter, like the state parameter, can be used for modelling of sands in the future.

On the friction dependency of the stress Lode angle

AbstractThe shape of the failure locus of a material is significant for its strength predictions. Even when constitutive models include the same critical stress surface, different critical stress ratios can be predicted for an identical applied isochoric strain path. In this article, we investigate critical stress predictions of different constitutive models, which include the surface according to Matsuoka–Nakai (MN). We perform analytical investigations, true triaxial test simulations with hypoplasticity and barodesy, and discrete element modelling (DEM) simulations to investigate the friction dependency of the stress Lode angle. Our results demonstrate that in hypoplasticity, the direction of the deviatoric stress state at critical state depends solely on the direction of the applied deviatoric strain path. In contrast, in barodesy, the predictions are also dependent on the friction angle of the material. In addition, we compare these results with those obtained with a standard elastoplastic MN model. To validate this friction dependency on the stress Lode angle, we conduct DEM simulations. The DEM results qualitatively support the predictions of barodesy and suggest that a higher friction results in a higher Lode angle at critical stress state.

Creep and stress relaxation experiments of 1960-grade high-strength steel wire at elevated temperatures

With the increasing spacing of large-span structures, the application of ultra-high-strength steel wire with a strength approaching or exceeding 2000 MPa is rapidly expanding. However, the related research on its creep and stress relaxation behaviour is still limited. In this paper, a total of 30 high-temperature creep tests and 31 high-temperature stress relaxation tests were conducted on 1960-grade high-strength steel wire (1960-HSSW) with a diameter of 5.0 mm. The full process creep strain curves were obtained by reinserting and resetting the high-temperature extensometer. The maximum creep strain measured was 50.67 %. The creep and stress relaxation curves of different high-strength steel wires (steel strands) were compared, revealing significant variations in mechanical properties among different steel wires. The steady-state creep rate and high-temperature creep rupture critical stress ratio of the 1960-HSSW were given. Especially, the critical stress ratio became lower than the yield strength reduction coefficient at temperatures exceeding 400 °C and it indicated that the 1960-HSSW could undergo creep rupture before yield. The stress relaxation coefficient was introduced to consider the stress relaxation of 1960-HSSW. Stress relaxation curves for the 1960-HSSW were provided at temperatures ranging from 100 to 550 °C. Moreover, based on the microstructure observed under transmission electron microscopy, it was found that damage occurred in the 1960-HSSW after exposure to 300 °C. Therefore, a critical temperature of 300 °C was recommended for the fire protection of 1960-HSSW, which could be the theoretical support for its fire protection design. Additionally, a high-temperature creep prediction model, which includes expressions for the termination time, was established for the 1960-HSSW. As a result, a conservative prediction of the high-temperature creep for the 1960-HSSW was provided. Moreover, A stress relaxation coefficient model was also provided. The predicted results of the aforementioned models were in good agreement with experimental results.

In-situ investigation of tensile anisotropy mechanism in an advanced Ti2AlNb-based alloy associated with CRSS ratio and damage model

Combined with in-situ tensile test and electron backscatter diffraction technology, the critical resolved shear stress (CRSS) ratio of O phase and the damage model of grain boundaries were proposed to reveal the tensile anisotropy mechanism of Ti–22Al–25Nb alloy isothermally forged in B2 phase region. In-situ observation suggests that the single slip mode of lamellar O phase is the major deformation behavior, and its preferential slip dominates the yield of the material. Based on the types, number, Schmid factor (SF) and orientation of slip activation, the CRSS ratio of basal <a>, prism <a>, first-order and second-order pyramidal <c+a> slips for O phase is estimated to be 1.19: 1: 1.37: 1.39. Meanwhile, basal and prism <a> slips mainly appear the radial and axial directions (RD and AD) samples with [012] and [100] texture, while the [001], [010] and [212] texture of OD (45° to RD) sample shows an increase in pyramidal <c+a> slips. Thus, the slip activation of O phase depends on the grain orientation and CRSS, resulting in significant strength anisotropy. Furthermore, the microcracks and secondary cracks at grain boundaries are significantly affected by the slip accumulation of lamellar O phase at the O/O and O/B2 interfaces. Considering the stress state of the grain boundary, a damage model about crack nucleation and propagation is proposed to explain the ductility anisotropy. From this, the RD sample has a higher crack nucleation and propagation resistance than the AD and OD samples due to the flattened morphology of B2 grains.

Impact of particle elongation on the behavior of round and angular granular media: Consequences of particle rotation and force chain development

We developed a 2D discrete element model to simulate shearing response of elongated round and angular particles. Model was calibrated and validated by comparing numerical results with corresponding biaxial shearing tests on circular (round) and hexagonal (angular) rods at microscopic and macroscopic scales. Then, the systematic effect of particles aspect ratio was investigated on quasi-static shearing response of round and angular granular materials. Macroscopically, we observed a nonlinear tendency wherein as the aspect ratio decreased from 1, the critical state stress ratio initially increased, reaching a maximum, followed by a decreasing trend. This effect was more prominent in round samples. Microscopically, decreasing the aspect ratio from 1 reduced particle rotations and increased the mean coordination number. Elongated particles exhibited significant contact anisotropy, forming irregular force chains, facilitating interparticle sliding, and reducing overall strength. Additionally, we explored the impact of the interparticle friction coefficient. A high value of interparticle friction coefficient led to a monotonically increasing strength with elongation, underscoring the importance of accurately calibrating microscopic friction coefficients.