Investigation of the Shear Mechanical Behavior of Sandstone with Unloading Normal Stress after Freezing–Thawing Cycles

Freezing–thawing action has a great impact on the physical and mechanical deterioration processes of rock materials in cold areas where environmental changes are very complicated. The direct shear test under unloading normal stress was adopted to investigate the shear mechanical behavior of sandstone samples after a freezing–thawing cycle in this paper. The failure shear displacement (Dsf), the failure normal displacement (Dnf), the shear displacement of unloading (Dsu), and the normal displacement of unloading (Dnu) were analyzed to describe the evolution of shear and normal deformation during the test. The results indicated that the shear displacement increased as the freezing–thawing cycle duration increased in a direct shear test under unloading normal stress. The unloading rate and the number of freezing–thawing cycles affected the failure pattern of the rock sample significantly in both the direct shear test under unloading normal stress and the direct shear test. The three-dimensional inclination angle, the distortion coefficient, and the roughness correlation coefficient of the fracture surface are dependent on the number of freezing–thawing cycles and the unloading rate. The surface average gradient mode of the fracture surface decreased as the freezing–thawing cycle times and unloading rate rose.

Experimental Study on Mechanical Properties and Seepage Laws of Raw Coal under Variable Loading and Unloading Rates

This manuscript studied the effects of variable axial pressure loading rate and variable confining pressure unloading rate on the deformation behavior and seepage characteristics of raw coal under alternate loading and unloading of axial pressure and confining pressure. It believed that as axial stress increases, axial strain ε 1 decreases, radial strain ε 3 increases, and permeability k decreases, and ε 1 ′ , ε 3 ′ , and k ′ increase when confining pressure is decreases. With the loading of axial stress and the unloading of confining pressure, the variation amplitudes of ε 1 ′ , ε 3 ′ , and k ′ values reduce gradually. During axial stress loading, the rise in the amplitude of ε 1 is larger than that of ε 3 and the reduction in the amplitude of k , indicating that ε 1 is more sensitive to axial stress than ε 3 and k . During unloading of confining pressure, the increase rate of ε 3 is larger than that of ε 1 and k ; also, ε 3 showed a high sensitivity to confining pressure. In the stage of axial stress loading and confining pressure unloading, the evolution law of deformation and permeability parameters is basically consistent with the change in loading and unloading rate.

An Experimental Research on Surrounding Rock Unloading during Solid Coal Roadway Excavation

In order to further explore the deformation and failure essence of the deep coal body, based on the characteristics of surrounding rock stress adjustment before and after solid coal roadway excavation, an experiment of unloading confining pressure and loading axial pressure of the coal body was designed and conducted in this study. Based on test results, the failure mechanics and energy characteristics of the coal body were analyzed through experiments. Rapid unloading is considered a key factor contributing to lateral deformation and expansion failure, which exacerbates the deterioration of coal body and reduces the deformation energy storage capacity of coal. On the other hand, the larger loading rate tends to shorten the accumulation time of microcracks and cause damage to the coal body, resulting in strengthening the coal body and improving energy storage. Under the circumstance that the coal body is destroyed, the conversion rates of the internal deformation energy and dissipated energy are more significantly affected by unloading rate. The increasing unloading rate and rapid decreases in the conversion rate of deformation energy make the coal body more vulnerable to damage. Under the same stress conditions, the excavation unloading is more likely to deform, destroy, or even throw the coal than the experiment unloading. In order to reduce or avoid the occurrence of deep roadway excavation accidents, the understanding of the excavation unloading including possible influencing factors and the monitoring of the surrounding rock stress and energy during the excavation disturbance should be strengthened. It can be used as the basis for studying the mechanism of deformation and failure of coal and rock and dynamic disasters in deep mines, as well as the prediction, early warning, prevention, and control of related dynamic disasters.

An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of $$0.01~{\rm {s}}^{-1}$$ 0.01 s - 1 and for different unloading rates, i.e. $$0.01$$ 0.01 , $$0.1$$ 0.1 and $$1.0~{\rm {s}}^{-1}$$ 1.0 s - 1 . The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. $$0.5$$ 0.5 -$$18~{\rm {Hz}}$$ 18 Hz which corresponds to unloading rates $$0.46$$ 0.46 -$$16.41~{\rm {s}}^{-1}$$ 16.41 s - 1 , using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. $${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$ λ ˙ U < 1.0 s - 1 ), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate $$125.2~{\rm {s}}^{-1}$$ 125.2 s - 1 , the viscous dissipation is significant such that the amount of dissipated energy increases approximately by $$125.4\%$$ 125.4 % from the lowest unloading rate. The critical tearing energy is obtained to be $$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$ 7.04 kJ / m 2 using classical method and $$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$ 5.12 kJ / m 2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately $$37.5\%$$ 37.5 % .

Effect of Co-Addition of Ag and Cu on Mechanical Properties of Sn–5Sb Lead-Free Solder

Sn–Sb lead-free solders are considered to substitute the tin–lead solders due to their great mechanical properties. At room temperature, the mechanical properties of Ni/Au/Sn–5Sb/Au/Ni and Ni/Au/Sn–5Sb–0.3Ag–0.05Cu/Au/Ni linear solder joints were investigated by nanoindentation experiments at different loads. The results showed that the Sn–Sb intermetallic compound (IMC) was distributed in the β-Sn matrix in Ni/Au/Sn–5Sb/Au/Ni solder joints. Co-addition of Cu and Ag resulted in the formation of the rod-shaped Cu6Sn5 and the fine granular Ag3Sn IMCs. At the same load and loading/unloading rate, the indentation depth and residual indentation morphologies of Ni/Au/Sn–5Sb–0.3Ag–0.05Cu/Au/Ni solder joints were smaller than those of Ni/Au/Sn–5Sb/Au/Ni solder joints. The hardness of the two kinds of solder joints decreased with the increase in load, while the Young’s modulus was independent of load. In addition, compared to the Ni/Au/Sn–5Sb/Au/Ni solder joints, the hardness, Young’s modulus and stress exponents of Ni/Au/Sn–5Sb–0.3Ag–0.05Cu/Au/Ni solder joints achieved an improvement due to the co-addition of Ag and Cu.

Influence of Confining Pressure Unloading Rate on the Strength Characteristics and Fracture Process of Granite Using Lab Tests

In order to study the mechanical behaviors and fracture process properties of granite under confining pressure unloading with constant axial pressure, RMT-150B rock mechanics test system and acoustic emission detector were used to study the mechanical properties and fracture process characteristics of deeply buried granite specimens under different combinations of initial confining pressures and unloading rates. The results show that when the unloading rate is small, the deviatoric stress-strain curve of granite specimens will yield an unloading platform, and the specimens show significant characteristics of ductility; when the unloading rate is large, the specimens show characteristics of brittleness. Besides, the axial strain rate increases with the increase of initial confining pressure and unloading rate, and the axial strain rate fluctuates. The ratio of axial strain increment to confining pressure increment of granite specimens decreases with the increase of the unloading rate, and a faster unloading rate and a higher initial confining pressure will restrain the axial deformation of granite sample. The normalized confining pressure decreased parameter of granite specimen increases with the increase of initial confining pressure. When the unloading rate is relatively high, it plays a dominant role in the compressive strength of granite specimens. The Mohr–Coulomb strength criterion can better reflect the strength characteristics of specimens under confining pressure unloading. The cohesion of granite specimens decreases with the increase of unloading rate, and the internal friction angle increases with the increase of unloading rate. Notably, the unloading rate presents a weakening effect on the cohesion of the specimen and a strengthening effect on the internal friction angle of the specimen, and the former effect is stronger than the latter one. When the unloading rate is small, the acoustic emission ringing count increases more evenly, and the deformation and damage of the specimen develop slowly; when the unloading rate is high, the acoustic emission ringing count increases to the maximum instantaneously at the initial stage of confining pressure unloading, and the specimen is damaged rapidly, showing the characteristic of sudden fracture. The fracture mode of granite specimens is affected by the unloading rate and initial confining pressure. At the same unloading rate, the specimens with high initial confining pressure show typical tensile fracture characteristics, while the specimens with low initial confining pressure mainly suffer from shear fracture or shear-tension composite fracture. With the increase of unloading rate, the fracture characteristics of specimens show a transition from shear or shear-tension composite fracture to tensile fracture.

Experimental Study on Triaxial Unloading Failure of Deep Composite Coal-Rock

With the deep mining of coal, the phenomenon of high ground stress is more likely to cause dynamic disaster. In view of the above problems, this paper takes the unloading process of coal mining as the background to study the effects of mining rates under different conditions on the mechanical properties and triaxial failure criterion of composite coal-rock, so as to provide a theoretical basis for the prevention and control of dynamic disasters in coal mines. The composite coal-rock models with a composite ratio of 1 : 1 : 1 were tested under different unloading rates or confining pressures. The results show that the triaxial unloading process of coal-rock can be divided into five stages: compaction, single elasticity, elastic-plastic unloading, partial fracture, and complete fracture. In this paper, the failure criterion of composite coal-rock triaxial unloading is derived. The unloading rate has an exponential relationship with the triaxial compressive strength, and the relationship between initial confining pressure and compressive strength is linear. The triaxial compressive strength is determined by both. The peak strains ε of all samples under different unloading conditions were around 0.01. And initial confining pressure had an influence on the strain variation trend during the unloading of composite coal-rock. The higher the initial confining pressure, the greater the elastic modulus. In addition, an increase of initial confining pressure led to the increase of the total energy converted into dissipated part in the process of fracture and caused the obvious increase of the rebound characteristics of the curve. However, the unloading rate had no influence on the strain trend.

Mechanical Characteristics of Frozen Sandstone under Lateral Unloading: An Experimental Study

The lateral unloading strength and deformation of surrounding frozen rock are the key parameters for safety evaluation of frozen shaft construction. A low-temperature and high-pressure rock triaxial test system was used to simulate freezing construction, and a constant axial pressure unloading confining pressure test was carried out on frozen sandstone. The effects of freezing temperature, initial confining pressure, and unloading rate on the strength, deformation, and failure modes of frozen sandstone are studied. The main results of the study are as follows: (1) under the initial confining pressure of 20 MPa, the temperature of the sandstone decreases from 20°C to –5°C, and the peak stress and elastic modulus of triaxial compression increase by approximately 3 times. Under lateral unloading conditions, the peak stress of frozen sandstone is about 2∼3 times that of 20°C sandstone, and the peak strain of 20°C sandstone is smaller than that of frozen sandstone. The temperature of frozen sandstone decreases and the rate of increase in the peak stress of triaxial compression is slightly less than the rate of increase in the peak stress of lateral unloading. (2) The initial confining pressure of frozen sandstone increases, the growth rate of axial and radial strain increases, the radial strain dominates the failure process, and the lateral unloading strength decreases significantly. (3) The lateral unloading rate of frozen sandstone increases, the peak strength increases, and the axial and radial strain decrease. At a low unloading rate, partial creep deformation occurs. (4) The frozen rock sample undergoes tensile splitting failure under lateral unloading. According to the stress-strain curve of the frozen rock sample, the relationship between changes in the deformation modulus and changes in the confining pressure unloading amount during the unloading process of the rock sample is obtained.