Softening Stage Research Articles

Study on Characteristic and Energy of Argillaceous Weakly Cemented Rock under Dynamic Loading by Hopkinson Bar Experiment

To study the mechanical properties of argillaceous weakly cemented rock under dynamic loading, a sample reconstituted and graded loading scheme is firstly designed, and then the reorganization rock sample is used as the research object. Using a Hopkinson pressure bar test, the responses of an argillaceous weakly cemented rock mass under different reorganization loads and different impact velocities is studied, and changes in specimen shape after impact are also analyzed. The study found that with increased of the recombination load, the amplitude of the transmitted wave increases. With increasing impact velocity, the rate of the increase in the incident wave amplitude is much larger than that of the transmission wave amplitude. The dynamic stress–strain curve can be divided into a compaction stage, an approximate linear elastic stage, a microcrack growth stage and a strain softening stage. The larger the reorganization load is, the less obvious the compression stage of the stress–strain curve is, and the greater the elastic modulus is. The peak strength and elastic modulus increase with increasing strain rate before 500 s−1. When the reorganization load is increased, the deformation decreases, and its impact resistance increases. With increasing impact velocity, the deformation of the specimen increases.

Shear strength of landfill liner interface in the case of varying normal stress

Landfills are sequentially filled by solid waste lifts, thus normal stress on the liner interface changes in different shear stages, which may affect selection of interface strength in landfill slope stability analysis. Shear tests were conducted at the liner interfaces of geomembrane/geotextile (GM/GT) and geomembrane/geocomposite/sand (GM/GC/Sand), and the normal stress changed in different shear stages. Values of friction angles on both the GM/GT and GM/GC/Sand interfaces obtained by direct and simple shear tests under increasing normal stress in the hardening, softening, and large-displacement stages were lower than those obtained by the traditional direct shear test. The reduction was greater for peak friction angles. Since the peak liner interface strength obtained by staged loading is lower than the peak interface strength by using the traditional shear test method, using the peak shear strength obtained from the traditional direct shear test for the base floor liner to conduct slope stability analysis may cause an un-conservative result. It is necessary to consider the effects of normal stress changes on the liner interface strength in landfill slope stability analysis.

Assessment effects of post-harvest softening on the quality of safou (Dacryodes edulis) produced in Agboville (South-East, Côte d´Ivoire)

The objective of this study was to assess the impact of post-harvest softening on parameters (nutritional and anti-nutritional) of saffron pulp (Dacryodes edulis). Thus, the safou fruits were picked at physiological maturity and stored at room temperature (27±1.2 °C) for 12 days during which five stages of softening (S0, S1, S2, S3 and S4) were defined. The softening index of D. edulis fruits varied from 0.86±0.06 mm to 3.53±0.03 mm (edulis) and from 0.85±0.05 mm to 2.86±0. 04 mm (parvicarpa). This study reveals that the softening index is significantly different (p

A modified HJC model for improved dynamic response of brittle materials under blasting loads

Abstract The original Holmquist-Johnson-Cook (HJC) model, which can only capture the compressive behaviour but not the tensile behaviour of brittle materials, is modified in this study. First, the Lode-angle function is introduced to the yield strength surface to consider the changes in the substantial shear strength between the tensile and compressive meridians. A hyperbolic function is used to describe the strain rate effect under dynamic tensile loading. An exponential model is introduced to express the tensile softening stage of brittle material and define the tensile damage variable. Then the modified HJC model is implemented in LS-DYNA via user subroutine UMAT. Further the modifications are validated by single element tests and rock mechanical laboratory experiments. The verification results show that the modified HJC model can effectively describe the tensile responses of brittle material under static and dynamic loading. Last, a comparison between a blasting-crater field test and the corresponding numerical prediction by the modified HJC model is carried out. The comparison results demonstrate that the shape and size of the crater predicted by the modified HJC model show a good agreement with the field test data. Therefore, the modified HJC model has the capacity to capture the tensile and compressive behaviours and damage evolution of brittle material.

Cohesive Zone Modeling of Crack Propagation in FCC Single Crystals via Atomistic Simulations

This paper presents a cohesive zone model of fracture in Cu and Ni single crystals under tension, based on an atomistic analysis. The molecular-statics approach based on the conjugate-gradient method was used to investigate the crack-growth behavior at the atomic level. The fracture toughness was evaluated on the basis of energy considerations, and the cohesive traction was calculated using the J integral and the atomic-scale separation in the cohesive zone. The cohesive traction and separation curves obtained using computational data from atomistic simulations were compared with the exponential form of continuum mechanics. The results showed that the exponential form satisfactorily represented the cohesive zone properties of Cu. However, the cohesive traction and separation curves for Ni were found to deviate from the exponential form in the softening stage, owing to small-scale nonlinear features near the cohesive zone.

A variable-order fractional model of tensile and shear behaviors for sintered nano-silver paste used in high power electronics

Next generation power electronics demand not only miniaturization and integration, but also higher power and harsher operation conditions. However, the conventional lead-free solders can't meet these requirements. Sintering of nano-silver paste has already become one of popular substitutes, as it can achieve low temperature packaging and high temperature operation. The mechanical performance of sintered nano-silver paste is of great importance for its applications in high power electronics. In this study, a variable-order fractional constitutive model is adopted to characterize tensile behaviors of sintered nano-silver paste at different strain rates and ambient temperatures. A comparative study with the well-known Anand model is conducted to present the advantages of the proposed model with simpler formulation, higher accuracy and fewer parameters. The fractional order is also found to well indicate the evolution of mechanical properties along with varying strain rates or temperatures. Furthermore, the model is firstly extended to describe shear experimental data at different temperatures, especially those with strain softening stages. All simulation results reveal that the variable-order fractional model is an effective tool in characterizing both tensile and shear behaviors and demonstrating the evolution of mechanical properties.

Nonlinear fracture of two-dimensional transition metal carbides (MXenes)

As a newly discovered two-dimensional (2D) material group, MXene has exceptional thermal- electronic properties. However, its mechanical behavior, especially fracture, remains unexplored. In-situ SEM tensile experiments show that the fracture of MXene is quite nonlinear with a much-prolonged softening stage in comparison with other 2D materials, which is suspected to be caused by the anisotropy and relatively thick monolayer of MXenes. In this work, molecular dynamic (MD) modeling is conducted to investigate the anisotropic fracture behavior of two types of MXenes (Ti2C and Ti3C2) with different monolayer thickness. Both pristine and defected MXenes are investigated. Results show that: (1) MXene tends to fracture along zigzag direction, (2) atomic vacancies at the crack tip have limited effects on the overall fracture behavior, (3) a thicker monolayer can produce a larger cohesive zone due to the ‘thinning’ process, (4) complex fracture paths are to be expected for mixed-mode fractures.

Shear Band Characterization of Clayey Soils with Particle Image Velocimetry

Identifying the spatial distribution of deformation and shear band characteristics is important for accurately modeling soil behavior and ensuring the safety of nearby geotechnical structures. However, most research on the shear behavior of soils has focused on granular soil and clay-rich rocks, with little focus on clayey soil, and the entire shearing process from the initial state to failure has not been observed. This study evaluated the spatial distribution and evolution of deformation in clayey soils from the initial state to the post-failure state and the shear band characteristics. Plane strain tests were performed on normally consolidated and over-consolidated clay specimens, and digital images were captured through a transparent side wall for particle image velocimetry (PIV) analysis. PIV was performed to evaluate the displacement and deformation of soil particles. The results show that the shear-strain behaviors of two clays during the shearing process could be divided into four stages: initial, peak, softening, and steady state. Shear bands were observed to form in the softening stage, and the shear band slopes were compared to values in the literature. These results can be used to characterize shear bands in clay as well as predict failure behavior and guide reinforcement at actual sites with soft ground.

A new analytical model of wellbore collapse pressure based on stability theory

In theory, the wellbore collapse for the petroleum drilling belongs to the limit point instability, and should be treated as the stability problem, but instead of the strength problem. For this purpose, a new analytical model was established to determine the collapse pressure based on the stability theory. Using the elastoplastic mechanics, the stress and displacement around the wellbore were solved, and the equilibrium path (i.e., the relation between the inner pressure and the radial displacement) was proposed. According to the equilibrium path, it can be found that the wellbore collapse occurs at the end of the plastic softening stage and the beginning of the residual stage. Additionally, a comprehensive numerical validation was performed based on the numerical methods, to examine the proposed analytical model. The stress and displacement around the wellbore by the proposed method agree well with those from the numerical method, with a deviation of less than 8.9%. Finally, the parametric analysis was performed to investigate the effects of the plastic hardening modulus, the plastic softening modulus, the yielding stress, the strength limit and the residual strength on the equilibrium path. The results show that the collapse pressure decreases as the plastic hardening modulus, the plastic softening modulus, the yield limit and the residual strength increasing. On the contrary, an increasing of the strength limit can increase the wellbore collapse pressure, which is different to the common understanding.

Application of fast multipole boundary element method for two-dimensional nonlinear interface debonding of particulate composites

A fast multipole boundary element method (BEM) is used herein to simulate the two-dimensional interfacial debonding of particulate composites. The behavior of the interface between the inclusion and the matrix is modeled using a nonlinear constitutive relationship. Interface debonding is implemented by decoupling the node pair. In the proposed method, the degree of freedom (DOF) of the interfacial traction changes to that of displacement of the free surface; thus, the number of DOFs of each node pair prior to and after decoupling is the same, which facilitates the simulation better than the finite element method. In simulating the softening stage of the nonlinear interfacial deformation, the stress in the node pair is assumed to be unloaded to zero and then reloaded to a new equilibrium state. A fast multipole expansion technique is applied within the developed BEM to solve the large-scale problem of debonding particulate composites whereby millions of DOFs can be calculated via a step-wise calculation method that provides high precision interface stress results. A comparison of these results with the analytical solution for a single inclusion case demonstrates the high stress accuracy and effectiveness of the developed fast multipole BEM to solve large-scale nonlinear interface problems.

Study on the Internal Force of Geomembrane of Landfill in Heavy Metal Contaminated Area

In order to analyze the tension stress of Geomembrane in the seepage control system of landfill in heavy metal contaminated area under the action of the overlying landfill weight, the internal force of Geomembrane in landfill is studied in this paper. Firstly, according to the internal force analysis of Geomembrane model, the basic equation of Geomembrane is obtained, and the equation is analyzed by finite difference numerical solution, so as to analyze the internal force of Geomembrane in landfill. The method can analyze three stress states of Geomembrane-clay interface at different positions: elastic state, softening state and residual state, which makes the stress analysis of Geomembrane on landfill slope more reasonable. Parametric analysis shows that when the strength loss and the difference between residual displacement and peak displacement are small in the softening stage, the peak strength of Geomembrane-clay interface has little influence on the maximum tensile stress of Geomembrane, and its residual strength is the main controlling factor; and when the softening characteristics of Geomembrane-clay interface are obvious, the influence of peak strength and residual displacement is more obvious.

Test and simulation of circular steel tube confined concrete (STCC) columns made of plain UHPC

This study presents experimental and numerical investigations on circular steel tube confined ultra high performance concrete (UHPC) columns under axial compression. The plain UHPC without fibers was designed to achieve a compressive strength ranged between 150 MPa and 200 MPa. Test results revealed that loading on only the UHPC core can generate a significant confinement effect for the UHPC core, thus leading to an increase in both strength and ductility of columns, and restricting the inherent brittleness of unconfined UHPC. All tested columns failed by shear plane failure of the UHPC core, this causes a softening stage in the axial load versus axial strain curves. In addition, an increase in the steel tube thickness or the confinement index was found to increase the strength and ductility enhancement and to reduce the magnitude of the loss of load capacity. Besides, steel tube with higher yield strength can improve the post-peak behavior. Based on the test results, the load contribution of the steel tube and the concrete core to the total load was examined. It was found that no significant confinement effect can be developed before the peak load, while the ductility of post-peak stage is mainly affected by the degree of the confinement effect. A finite element model (FEM) was also constructed in ABAQUS software to validate the test results. The effect of bond strength between the steel tube and the UHPC core was also investigated through the change of friction coefficient in FEM. Furthermore, the mechanism of circular steel tube confined UHPC columns was examined using the established FEM. Based on the results of FEM, the confining pressures along the height of each modeled column were shown. Furthermore, the interaction between the steel tube and the UHPC core was displayed through the slip length and shear stresses between two surfaces of two materials.

Analysis of the Elastic‐Plastic Theoretical Model of the Pull‐Out Interface between Geosynthetics and Tailings

Aiming at the strain‐hardening and strain‐softening phenomena between geosynthetics and tailings during pull‐out tests, bilinear and trilinear shear stress‐displacement softening models were proposed. The pull‐out process of the hardening reinforcement was divided into the elastic stage, elastic‐hardening transition stage, and pure hardening stage. The pull‐out process of the softened reinforcement was divided into the elastic stage, elastic‐softening transition stage, pure softening stage, softening‐residual transition stage, and pure residual stage. The expressions of the interface tension, shear stress, and displacement at the different stages under a pull‐out load were derived through the interface basic control equation. At the same time, the evolution law of the interface shear stress at different pull‐out stages was analysed, and the predicted results of the two elastic‐plastic models were compared with the experimental results. The results show that the predicted results are in good agreement with the experimental data, which verifies the validity of the proposed two elastic‐plastic models for the progressive failure analysis of reinforcement at the pull‐out interface. During the process of pull‐out, the transition stage is not obvious. When the reinforcement is in the elastic stage, the nonlinearity and maximum value of the interface shear stress increase with an increase in the elastic shear stiffness, while the tensile stiffness shows the opposite trend. When the reinforcement is in the hardening or softening stage, the larger the hardening (softening) shear stiffness is, the larger the change range of shear stress is and the more obvious the hardening (softening) characteristics of the reinforcement are. The results comprehensively reflect the progressive failure of reinforcement‐tailing interfaces with different strain types and provide theoretical support for the study of the interface characteristics of geosynthetic‐reinforced tailings.

Study on failure mechanical characteristics and damage constitutive model of sandstone with different numbers of holes

Abstract The existence of holes in rock is one of the key factors for the instability of underground rock mass engineering. Combined with acoustic emission equipment, uniaxial compression tests of rock specimens with different numbers of holes in the rock were carried out. The results show that with the number of holes increases, the value of peak strength and elastic modulus of the rock decrease. The acoustic emission (AE) counts gone through stable, slow increase, a sudden increase and towards zero four stages and there are corresponding to the initial compaction stage, elastic stages, strain hardening stage and post-peak strain softening stage of the stress-strain curves approximately. Based on the AE events, damage variables of rocks were obtained. The damage evolution process of rock can also be divided into three parts, including stable damage stage, slowly increasing damage stage and sharply increasing damage stage. According to Duncan model, the damage variable is introduced to obtain the rock damage constitutive model. No matter it is the pre-peak initial compaction stage, the linear elasticity stage, the strain hardening stage or the post-peak strain softening stage, the fitting curves are in good agreement with the test curves. It also illustrates the rationality of the damage constitutive model.

An experimental investigation on the tensile stiffness in layered rock interface using the digital image correlation technique

Tensile stiffness of interfacial layered rock is the basis of studying the law of interlaminar propagation of hydraulic cracks. We used similar materials to make simulated specimens of sand-mud layered rock with prefabricated cracks, and used the digital image correlation (DIC) technique together with the three-point bending (TPB) test to obtain the strain field near the prefabricated crack tip in tensile state. Combined with the tensile stress in the corresponding area calculated by the load of the tester, the tensile stress-displacement curve at the interface of layered rock is obtained, and the tensile stiffness and interfacial fracture law at the interface of layered rock is calculated by the curve. The results show that in the process of tensile failure, before reaching its peak value, the interfacial tension stress of layered rock has a linear elastic deformation stage followed by a short hardening stage. Upon reaching the peak value, it is accompanied by interfacial failure and macro-cracks, and then the load decreases and enters the softening stage, which results in the complete destruction of the interface. The tensile stiffness values of layered rock with different sizes vary greatly, which indicates that the interfacial tensile stiffness values are sensitive to the specimen size and have a size effect. The results are of great significance to the study of the law of hydraulic fracture propagation in the interface of layered rock.

Особенности деформации стекло- и углепластиков с матрицей Т-107 при растяжении

The article presents the results of a study on the mechanical properties of glass (T-10-14 filler) and carbon-fiber (Formosa TC-35 12K) reinforced plastics in an epoxy matrix T-107. It was found that the mechanical properties of carbon fiber were superior to fiberglass. Regardless of the composition of the composite, there are two distinct stages on the deformation curves of experimental samples based both on carbon and glass fibers, which correspond to elastic deformation and softening stages associated with the failure of composite fibers. Taking account for the significant difference between the elastic moduli and tensile strength of carbon and glass fibers, on the one hand, and the polymer matrix, on the other, it was suggested that the observed effect of softening of the composites is associated with the process of sequential breaking of the fibers as the applied load increases. Basing on the proposed idea, a model of deformation of a polymer composite material based on the sequential fracture of the filler fiber with increasing the applied load has been developed. According to this model, the observed increase in the applied load at the stage of strain hardening is associated with the presence of dispersion of the fibers of the samples by the values of strength, i. e. there is a distribution of the strength characteristics of the fiber along the length. With an increase in the length of a fiber in the sample, and, consequently, the length of the sample itself, the probability of appearance of thread sections with an even lower level of strength increases. Thus, in general, the tensile strength of the composite measured in the experiment should decrease. This dependence of the strength characteristics of the composite on the geometrical parameters of the product is determined by the fiber strength distribution function along its length, which can be determined from the experimental curves of tensile specimens of composites. Taking into account the proposed model, the obtained experimental results are used to estimate the distribution function g(f) of the probability of detection of its strength value per unit length of fiber.

Water Softening Mechanism and Strength Model for Saturated Carbonaceous Mudstone in Panzhihua Airport, China

To identify the water softening mechanisms that caused landslides in Panzhihua Airport, China, property and saturation tests of the mudstones extracted from a representative landslide were proposed. In this paper, water saturation tests were carried out on samples of carbonaceous mudstone collected from the east side of the No. 12 landslide at the airport. A number of different analytical techniques and mechanical tests were used to determine changes in chemical composition, mineral assemblages, and mudstone structural characteristics, including shear strength, after the mudstone had been softened. Three kinds of changes caused by water and three mudstone softening stages are proposed. The results show that the water has a significant influence on the properties of the mudstone, so the stability of the mudstone in the watery period is a big threat to the upper structure. A model for water immersion mudstone strength softening is developed. The model incorporates a permeability coefficient, the hydraulic gradient, and time; the model can be used to determine the mudstone’s shear strength and internal friction angle. This study provides a reference for the study of rock softened by water immersion.

Modeling micro-cracking and failure in short fiber-reinforced composites

Composites made of reinforcing short fibers embedded into brittle matrices, like, e.g., fiber-reinforced concretes, exhibit enhanced strength and ductility properties. Their failure process induced by tensile loadings involves hardening and softening stages as a result of matrix multiple micro-cracking, due to stress bridging of fibers across matrix micro-cracks, and strain localization phenomena.In the present paper, a variational model is proposed for the description of the intriguing failure mechanisms observed in short fibre-reinforced composites subjected to tensile loadings. The key modeling idea is to schematize the composite as a mixture of two phases, a brittle phase, representative of the matrix, and a ductile phase, accounting for the fibers reinforcement, which are coupled by elastic bonds.Different modeling levels of increasing complexity are proposed, ranging from a simplified one-dimensional analytical model to a three-dimensional variational model. Within the variational formulation, specific damage and plastic energies are assigned to the two phases, incorporating non-local gradient terms, and governing equations and evolution laws for the internal variables, as yield inequalities, consistency conditions and normality rules, are deduced from minimum principles. Parameters calibration is discussed as well as the importance of three internal lengths incorporated into the model. Moreover, the variational structure of the problem allow for a straightforward finite element implementation based on an incremental energy minimization algorithm and several aspects of the response are highlighted by means of numerical examples.

Cyclic deformation and cracking behavior of 316LN stainless steel under thermomechanical and isothermal fatigue loadings

Isothermal fatigue (IF) tests at 250 °C, 350 °C and 450 °C, and thermomechanical fatigue (TMF) tests of 316LN stainless steel within the temperature range of 250–450 °C under in-phase (IP) and out-of-phase (OP) mechanical strain-temperature phase angles were carried out. Comparison of the cyclic deformation behavior, microcrack nucleation mechanisms, crack growth and failure behavior were performed between the IF test at 450 °C (IF-450 °C) and TMF tests. Results showed that the cyclic deformation behavior was governed by the combination of thermally activated recovery process, dynamic strain aging (DSA) and nitride precipitations for IF-450 °C and TMF tests. The occurrence of DSA and nitride precipitations including Z-phase and MX phase were found to promote the planar slip of dislocations and enhance the cyclic stress response. The occurrence of recovery process, however, offset the strengthening effects caused by DSA and precipitations, accelerating the softening stage. The intergranular cracking was attributed to the strong impingement of slip bands on severely oxidized grain boundaries, which can be found only on the specimen surface or near-surface regions. The transgranular cracking, resulting from the cyclic slip localization which was characterized by the formation of persistent slip markings (PSMs) in the form of surface intrusions and extrusions was enhanced by the presence of brittle oxide. The ultimate failure was still dominated by the transgranular propagation.

Strain rate effect on the acoustic emission characteristics of concrete under uniaxial tension

Abstract Concrete is an important engineering material whose tensile property plays an important role in structural safety. Thus, the effect of strain rate on crack evolution in concrete during tension cracking cannot be neglected. Within a strain rate range of 10−6 to 10−4 s−1, an acoustic emission monitoring test for the whole process of concrete under uniaxial tension including the post-peak softening stage was conducted. Moreover, damage evolution, along with the cracking mechanism of concrete at various strain rates was discussed with respect to the effect of strain rate on acoustic emission. The results show that the acoustic emission activity of concrete is delayed due to an increase in strain rate. This indicates that the hysteresis of deformation and cracking can be observed in a uniaxial tension test of concrete. During the whole loading process, as the strain rate increased, the average level of the acoustic emission hit rate increased significantly, indicating that an increase in strain rate accelerates crack initiation and propagation in concrete. Average acoustic emission values, duration and energy also show an increasing trend, and the scatter distribution range between them and the acoustic emission amplitude changes significantly, a fact that can be used to identify the damage degree of concrete under different strain rates. A peak frequency and cd4 band wavelet energy spectrum coefficient tends to decrease, while the ca8 band wavelet energy spectrum coefficient increases. In other words, the proportion of low frequency acoustic emission signals increases, indicating that an increase in strain rate increases the proportion of macroscopic cracks in concrete. At various strain rates, the average level of acoustic emission characteristic parameters and the proportion of high frequency signals at the post-peak stage in concrete are higher than those at the pre-peak stage, indicating that the development of microcracks in concrete mainly concentrates during the post-peak softening stage.