Fixed Loading Rate Research Articles

Dynamic Tensile Failure Characteristics and Energy Dissipation of Red Sandstone under Dry–Wet Cycles

Studying the dynamic properties of rocks in complex environments is of great significance to the sustainable development of deep-sea metal mineral resource extraction. To investigate the influence of dry–wet cycles on the dynamic tensile properties and energy dissipation of red sandstone, a series of dynamic Brazilian disc tests was carried out through the split Hopkinson pressure bar (SHPB) apparatus. The dynamic tensile behaviors and energy dissipation distribution of the red sandstone specimens after different dry–wet cycles (0, 10, 20, 30 and 40 cycles) were analyzed in this study. The degree of dynamic tensile fragmentation and energy dissipation of red sandstone is significantly affected by the loading rate. Specifically, when the number of dry–wet cycles remains constant, an increase in loading rate results in a significant reduction in the average fragment size, while the energy consumption density exhibits an approximately linear increase. At a fixed loading rate, the energy consumption density decreases approximately linearly with the increase in dry–wet cycles, and the higher the loading rate, the more sensitive the energy consumption density is to the dry–wet cycle. Under a fixed number of dry–wet cycles, the dynamic tensile strength has an exponential relation with the increase in energy consumption density.

Effects of pre-static loads on the dynamic pure mode I and mixed mode I–II fracture characteristics of rocks

Rocks in deep underground engineering are prone to encounter pre-static loads and dynamic disturbances simultaneously. Meanwhile, pure mode I and mixed mode I–II fractures are common in brittle materials including rocks. Understanding the mode I and mixed mode I–II fracture mechanisms of rocks subjected to coupled static-dynamic loads is thus imperative and beneficial to the stability of underground rock engineering structures. In this study, using the improved split-Hopkinson pressure bar (SHPB) loading system, coupled static-dynamic mode I and mixed mode I–II fracture tests are conducted on notched semi-circular bend (NSCB) granite specimens. With the aid of high-speed digital image correlation (HS-DIC), 3D scanning technology and scanning electron microscope (SEM), the effects of pre-static loads on dynamic fracture characteristics of granite are comprehensively investigated. Experimental results show that both the dynamic and total fracture toughness reveal evident rate dependence. At a fixed loading rate, the dynamic fracture toughness decreases with increasing pre-static loads, while the total fracture toughness barely changes, indicating that the enhanced rate sensitivity compensates for the weakening effect induced by the pre-static load. The progressive fracture progress shows that with the increase of pre-static loads, the crack initiation time of the specimen is shortened and the crack propagation velocity increases. 3D scanning results show that the fractal dimension of the fracture surface continues to rise as the pre-static load increases, illustrating the fracture surface becomes rougher. In addition, the connection between macroscopic fracture characteristics and microscopic fracture mechanism of granite subjected to static-dynamic loading is discussed by SEM. The quantity and size of the micro-defects inside the internal structure of rocks increase with increasing pre-static load, revealing that the pre-static load degrades rock structure and leads to a negative response to dynamic fracture toughness.

Influence of loading rate on the infrared radiation of PMMA

Infrared thermography has widely been used in observing and recording failure processes. The loading rate is a critical parameter that influences the infrared radiation (IR) in the mechanical experiment. However, little work has been done regarding its influence on infrared radiation. In order to conduct an in-depth study on the influence of loading rates on IR, a series of three-point bending experiments were conducted on PMMA samples for the IR test. Then, the influence was explained through a physical model derived from the first law of thermodynamics. The experimental results showed that under a fixed loading rate, the change rate of the IR emission was constant, and the relationship between the IR emission and loading time exhibited a linear trend. The variation between the change rate of IR emission and the loading rate can be expressed by the exponential function. The insights gained from this study will be of assistance to obverse the loading processes by infrared thermography.

Experimental study on influence of wetting-drying cycle on dynamic fracture and energy dissipation of red-sandstone

To study the influence of the wetting-drying cycles and loading rate on dynamic fracture toughness and energy dissipation of rocks under the dynamic loads, the split Hopkinson pressure bar (SHPB) system was used to perform the dynamic impact tests on NSCB specimens of red sandstone after different wetting-drying cycles. The loading rate response characteristics of fracture toughness of specimens after different wetting-drying cycles were analyzed, and the energy dissipation law of dynamic fracture under the impact loads was obtained. The results show that under a given number of wetting-drying cycles, with the increase of loading rate, the dynamic fracture toughness shows an overall trend of increasing. When the critical loading rate K˙IC is exceeded, the dynamic fracture toughness no longer increases. At the fixed loading rate, the dynamic fracture toughness of red sandstone decreases linearly with the increase of wetting-drying cycles, and the higher the loading rate, the more sensitive the fracture toughness to the wetting-drying cycle. With the increase of the loading rate, the dynamic fracture energy increases exponentially and becomes more sensitive to the loading rate. Under the fixed wetting-drying cycles, the dynamic fracture toughness of red sandstone has a logarithmic relationship with the increase of fracture energy.

On the Effect of Shear Loading Rate on Contact Area Shrinking in Adhesive Soft Contacts

Adhesion and, its interplay with friction, is central in several engineering applications involving soft contacts. Recently, there has been an incredible push towards a better understanding on how the apparent contact area evolves when a shear load is applied to an adhesive soft contact, both experimentally and theoretically. Although soft materials are well-known to exhibit rate-dependent properties, there is still a lack of understanding in how the loading rate could affect the contact area shrinking. Indeed, most of the experiments involving a sphere-flat contact have been conducted at a fixed loading rate, and, so far, analytical models have assumed a constant work of adhesion, independent on the peeling velocity. Here, by using linear elastic fracture mechanics, an analytical model is derived for the contact of a rigid sphere on a soft adhesive substrate, which is aimed at elucidating the effect that a rate-dependent work of adhesion has on the contact area shrinking. The model results show that contact area reduction is very sensitive to the loading rate, with slower loading rates promoting a stronger shrinking, which seems in agreement with Literature results. Furthermore it is shown that rate effects enhance the apparent interfacial toughness, i.e. more energy is needed to drive the system from full stick up to gross sliding.

Unified approach to characterize the strength of cement stabilized macadam subjected to different loading modes

Cement stabilized macadam base is the primary stress diffusion and bearing layer of semi-rigid asphalt pavement, therefore its mechanical behavior directly affects pavement performance. The indirect tensile strength, unconfined compressive strength, and bending strength are the essential parameters for evaluating the bearing capacity of cement stabilized macadam. In the design of a pavement structure, the conventional mixing strength values of a test sample are analyzed and calculated at a fixed loading rate. By using this procedure, the influence of the mixing method and the different loading rates on the strength values are ignored. Besides, the strength obtained by using the fixed loading rate with different loading modes has significant differences. As a result, the artificial randomness of the strength parameter in the design of a semi-rigid asphalt pavement structure increases. In an attempt, to improve the effectiveness and completeness of the strength parameters of cement stabilized macadam under different loading modes, mechanical tests were conducted on samples prepared with both vibration mixing and conventional mixing methods. This procedure included, indirect tensile strength test, unconfined compressive strength test, and four-point bending strength test under different loading rates. The results of these strength tests each group of samples (vibration and conventional mixing method) were compared. Besides, all samples were subjected to 6 different loading rates when conducting each loading mode. These experimental values were analyzed. The loading rate and the strength value have a power function relationship and the correlation of strength rates was revealed. The results demonstrated that the vibration mixing method increases the indirect tensile strength, unconfined compressive strength, and four-point bending strength by 13%, 14%, and 10%, respectively. A unified strength model (S/S0 = 0.9841 + 0.16856ln (0.01019 + v/v0) under two mixing methods and various loading modes were established by using the variation between loading rate ratio and strength ratio. In the unified model, the strength under vibration mixing and conventional mixing methods, and the strength among different loading rates can be converted, which improved the test efficiency. The established unified model solves the problem of uncertainty and uniqueness of strength parameters under different loading modes. The accuracy of the semi-rigid asphalt pavement structure resistance design was effectively improved, thereby providing theoretical guidance for the construction of semi-rigid base asphalt pavement engineering.

Understanding the response of aluminosilicate and aluminoborate glasses to sharp contact loading using molecular dynamics simulation

Experimental studies have shown that glass systems with high boron content exhibit superior crack resistance under sharp contact loading. However, the underlying mechanism is still not fully understood. In this context, we carried out classical molecular dynamics simulations on sodium aluminosilicate and sodium aluminoborate systems to investigate the effect of boron on the response of glass to nanoindentation. A rigid V-shaped indenter is used to indent the glass sample with a fixed loading rate, during which the indenter interacts with the glass via a repulsive force field. The indenter angle and tip radius are varied to study the effect of indenter sharpness, as what has been done in experiments. These simulated nanoindentation tests reveal how the stress/strain field and the glass structure evolve with deformation underneath the indenter. It was found that a large number of boron atoms in the plastic zone change from three- to fourfold coordination during the loading process, and most of them revert back to the threefold coordination state during the unloading process. Our study shows that this “reversible” boron coordination change plays a critical role in increasing the damage resistance of glass.

Effect of Thermal Treatment on the Dynamic Behaviors at a Fixed Loading Rate of Limestone in Quasi-vacuum and Air-filled Environments

Abstract Thermal damage in rock engineering occurs in the air-filled and quasi-vacuum environments of rock mass located near or far from the free surface. Meanwhile, dynamic loads are encountered frequently in engineering practice. In this study, 39 limestone samples are prepared, and a series of laboratory tests, including split Hopkinson pressure bar (SHPB), nuclear magnetic resonance (NMR) and optical microscopy analyses, are conducted to investigate the effects of temperature and the environment on the dynamic mechanical properties of limestone. The results show that the macro-physical and dynamic mechanical properties of limestone after thermal treatment can be divided into two stages by a critical temperature of 450°C, at which the thermal damage factor is 0.71 and 0.75 in the quasi-vacuum and air-filled environments, respectively. In the first stage, with temperatures varying from 25°C to 450°C, the thermal damage due to expansion and fracturing slightly influences the related parameters, except the P-wave velocity. However, in the second stage, with temperatures ranging from 450°C to 900°C, the thermal damage caused by mineral decomposition and hydration leads to a remarkable decrease in the dynamic bearing and anti-deformation capacities. The environment plays a negligible role in the first stage but an important role in the second stage, and the dynamic compressive strength and modulus of samples after thermal treatment in the air-filled environment are much lower than those in the quasi-vacuum environment. Both the temperature and environment of thermal treatment should be considered in engineering practice, especially when the temperature exceeds 450°C.

Fatigue Equation of Cement-Treated Aggregate Base Materials under a True Stress Ratio

The objective of this article is to establish a fatigue equation based on the true stress ratio for cement-treated aggregate base materials. The true stress ratio herein means the ratio of the stress and the true strength of the cement-treated aggregate base materials related to loading rates and curing times. The unconfined compressive strength tests and compressive resilience modulus tests were carried out under various loading rates and curing times of 3, 7, 14, 28, 60, 90 days, respectively. According to the test results, the relationship between the unconfined compressive strength (a mix design parameter in China) and the compressive resilience modulus (a structural design parameter and the construction quality control parameter in China) of the cement-treated aggregate base material with different curing times was established. However, it was found that the strengths varied with the loading rates, which is not reflected in the existing fatigue equations. Therefore, it is questionable to obtain the stress ratio of fatigue tests with a fixed strength value obtained from the standard strength test where the loading rate is fixed (in China, the fixed loading rate is 1 mm/min for cement-treated aggregate base materials). Thus, in this paper, the four-point bending strength (i.e., flexural strength) test was carried out at different loading rates to resolve such deficiencies. Based on the strength test results at different loading rates, the true stress ratio of the fatigue test corresponding to the fatigue loading rate can be calculated. Then the four-point bending fatigue test was conducted to establish an improved fatigue equation characterized by the true stress ratio. The results show that the patterns of variation for unconfined compressive strength increasing with the curing time were similar to that of the compressive resilience modulus. The fatigue equation curve based on the true stress ratio can be extended to the strength failure point of (1, 1), where both the true stress ratio and the fatigue life value are one. The internal relationship between the strength failure and the fatigue failure was unified. This article provides a theoretical method and basis for unifying the mix design parameters and the construction quality control parameters.

An Experimental Study on the Edgewise Compressive Failure of Paper Honeycomb Sandwich Panels with Respect to Various Aspect Ratios

The present work investigates the edgewise compression failure for honeycomb paperboards. Various panels are tested under a fixed loading rate with varying aspect ratios. The influence of the varying properties aspect ratio on yield strength is recorded. The experimental results indicate that the honeycomb paperboards are subject a decrease in yield strength with an increase in aspect ratio towards more slender bodies. Buckling was not observed in any of the tested specimens. All experiments are conducted under the general framework of ASTM C364/C364M -16 with a few noted changes.

Numeral modeling of fracture failure of recycled aggregate concrete beams under high loading rates

Fracture tests of recycled aggregate concrete (RAC) beams of different sizes were conducted under high loading rates. In order to characterize the effect of high loading rate on the behavior of RAC beams, two new material models were used together with the commercial finite element software \(\hbox {ABAQUS}^{\mathrm{R}}\). One model is a viscoelastic model that can predict the increase of stiffness (modulus of elasticity) of RAC with increasing loading rate, and the other model is a multiphase composite model that can determine the effective stiffness of RAC taking into account the special internal structure of recycled aggregate. Two different cases were considered in the numerical simulation. Case 1 is for fixed beam size under different loading rates, and Case 2 is for fixed loading rate with different beam sizes. For Case 1, the simulation results of the maximum loads under three different strain rates agreed with test data quite well. The Force-CMOD curves of the numerical simulation and test data showed similar trends. The higher the strain rates, the wider the high stresses spread in the crack propagation zone. The good agreements with the test data indicated that the two new material models can characterize the effect of high loading rate on RAC beams very well. For Case 2, three beam sizes and one loading rate was studied. The post-peak Force versus CMOD curves from the simulation follow the same trend of the test data. The stress distributions in the beams of different sizes are similar. On the other hand, the maximum loads predicted by the numerical model did not agree very well with test data. This is due to the fact that the maximum forces of RAC notched beams exhibited size effect, which was not considered in the fracture criteria adopted in \(\hbox {ABAQUS}^{\mathrm{R}}\) and not in the two new material models. This will be a topic for future research.

Effects of anionic surfactant on n-hexane removal in biofilters

The biodegradability of three anion surfactants by biofilm microorganisms and the toxicity of the most readily biodegradable surfactant to biofilm microorganisms were examined using batch experiments, and the optimal concentration of SDS for enhanced removal of hexane was investigated using two biotrickling filters (BTFs) for comparison. Results showed that SDS could be biodegraded by microorganisms, and its toxicity to microorganisms within the experimental range was negligible. The best concentration of SDS in biofiltration of n-hexane was 0.1 CMC and the elimination capacity (EC) of 50.4 g m−3 h−1 was achieved at a fixed loading rate (LR) of 72 g m−3 h−1. When an inlet concentration of n-hexane increased from 600 to 850 mg m−3, the removal efficiency (RE) decreased from 67% to 41% by BTF2 (with SDS) and from 52% to 42% by BTF1 (without SDS). SDS could enhance hexane removal from 43% (BTF1) to 60% (BTF2) at gas empty-bed residence time (EBRT) of 7.5 s and an inlet concentration of 200 mg m−3.

Bronchoscopist-directed Continuous Propofol Infusion for Targeting Moderate Sedation During Endobronchial Ultrasound Bronchoscopy

Propofol use for sedation during routine flexible bronchoscopy is expanding. However, there are concerns over propofol's reliability in targeting moderate sedation during more complex and lengthy procedures, such as endobronchial ultrasound (EBUS) bronchoscopy. Its delivery by continuous infusion, which provides a steady sedation effect, may be a practical model for achieving reliable outcomes in this setting. We tested a continuous propofol infusion protocol targeting moderate sedation for EBUS bronchoscopy. A fixed loading rate of 125 mcg/kg/min and initial maintenance rate of 75 mcg/kg/min were used. Sedation assessments were performed every 2.5 minutes. The infusion was adjusted by a nurse under the direction of the bronchoscopist to maintain moderate sedation, normal vital signs, and patient comfort. Prospectively collected data from the first 31 patients using the protocol were analyzed. A mix of EBUS types was performed in a fellowship training environment. Median procedure duration was 51 minutes (interquartile range, 41 to 75 min). Ninety-four percent of total bronchoscopy time was spent in moderate sedation, whereas only 1.9% was occupied by agitation-related delays. Average propofol dose per case was 0.07 mg/kg/min (±0.020), and infusion adjustments were required once every 8 minutes. Sampling goals were met in all patients, and diagnostic and nodal staging accuracies were 90% and 91%, respectively. All tumor specimens sent for genetics were sufficient for analysis. There were no major procedure-related complications. Bronchoscopist-directed continuous propofol infusion is effective and practical for reliably and safely targeting moderate sedation during EBUS bronchoscopy, without sacrificing the breadth and accuracy of the procedure.

Relaxation and relief in stressed solids in terms of superellipse equation: concrete

There is a large group of monotonic exo-processes, such as relaxation, shrinkage and maturity, which is realised over finite time and whose first derivative is infinite at the beginning of the process and zero at the end. The differential equation of exo-processes is given in this paper. Its analytical solution represents the left-hand upper quadrant of a superellipse and contains the time-operator, which links the exo-process with time. It is shown that relaxation can be successfully described by an exo-equation without recourse to viscosity, plasticity, rheological models or regression equations. The analytical expression for the operator of relaxation comprises three material parameters – the duration of total relaxation, the actual potential of relaxation and the exponent of the superellipse. The half-realisation factor, which reflects the rate of relaxation, is defined. The operator of relaxation is independent of the stressing, being a transparent function of time. It correctly represents the stress drop even for a fraction of a second, a fact of the highest importance in the context of fatigue. The superellipse equation describes relaxation in a wide range of solids besides concrete, giving clear evidence that it is a distinct process with its own physics and rules. The operator of instant relaxation, called relief (usually taken as a decrease in the apparent elastic modulus) is obtained from the equation of relaxation, where the time under load is represented by the reciprocal of the rate of loading. The operator of relief is independent of the stresses and is constant for a fixed loading rate. For structural concrete under a normative rate of loading, relief can account for 18% of the decline in the static versus dynamic modulus of elasticity.

Forced Unbinding of Individual Urea–Aminotriazine Supramolecular Polymers by Atomic Force Microscopy: A Closer Look at the Potential Energy Landscape and Binding Lengths at Fixed Loading Rates

Atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS) was used to study the forced unbinding of quadruple self-complementary hydrogen-bonded urea-aminotriazine (UAT) complexes in hexadecane (HD). To elucidate the bond strength of individual linkages the unbinding forces of UAT supramolecular polymers were investigated for the first time. The bond rupture was probed at three different, fixed piezo retraction rates in far from equilibrium conditions. The number of supramolecular bonds (N) between AFM tip and the surface was determined by independent knowledge of the linker length. The observed rupture force of urea-aminotriazine (UAT)-based supramolecular polymer chains was found to decrease with increasing rupture length. The dependence of the most probable rupture force on N was in quantitative agreement with the theory of uncooperative bond rupture for supramolecular linkages switched in series. Experiments with three different, fixed loading rates provided identical values (within the experimental error) for the characteristic bond length x(β) and the off-rate constant in the absence of force k(off)(f = 0). The value of x(β) was found to agree with literature data on the hydrogen-bond distance obtained via crystallographic data of the hydrogen-bonded dimer. This work broadens the scope of our previous report showing that relevant parameters of the bond energy landscape can be derived from a single data set of rupture events at a fixed loading rate for supramolecular linkages switched in series.

Optimization of enzymatic hydrolysis for ethanol production by simultaneous saccharification and fermentation of wastepaper

The present study investigated the development of high sugar production by optimization of an enzymatic hydrolysis process using both conventional and statistical methods, as well as the production of ethanol by the selected wastepaper source. Among four sources of pretreated wastepaper including office paper, newspaper, handbills and cardboard, office paper gave the highest values of cellulose (87.12%) and holocelluloses (89.07%). The effects of the amount of wastepaper, the pretreatment method and the type of enzyme on reducing sugar production from office paper were studied using conventional methods. The highest reducing sugar production (1851.28 µg L(-1); 37.03% conversion of glucose) was obtained from the optimal condition containing 40 mg of office paper, pretreated with stream explosion and hydrolysed with the combination of cellulase from Aspergillus niger and Trichoderma viride at the fixed loading rate of 20 FPU g(-1) sample. The effects of interaction of wastepaper amount and enzyme concentration as well as incubation time were studied by a statistical method using central composite design. The optimal medium composition consisted of 43.97 µg L(-1), 28.14 FPU g(-1) sample and 53.73 h of wastepaper, enzyme concentration and incubation time, respectively, and gave the highest amount of sugar production (2184.22 µg L(-1)) and percentage conversion of glucose (43.68%). The ethanol production from pretreated office paper using Saccharomyces cerevisiae in a simultaneous saccharification and fermentation process was 21.02 g L(-1) after 36 h of cultivation, corresponding to an ethanol volumetric production rate of 0.58 g ethanol L(-1) h(-1).

Experiments on granular rheology: Effects of particle size and fluid viscosity

We report the results of shear experiments of a thick layer of dry and liquid‐saturated glass beads, a simplified model of fault gouge, in order to clarify and to compare how the particle size and fluid viscosity affect the granular rheology. We sheared sorted glass beads and measured the temporal variation of stress that fluctuates owing to stick‐slip behavior. We found that the stress drop and slip recurrence intervals increase with the particle size because of larger static bulk friction. The forms of stress‐time series data for different particle size are not self‐similar; the form changes toward a sawtooth‐like temporal variation as the particle size increases, which can be characterized using two newly defined dimensionless numbers. In addition, we show that there is a continuous transition from constant slip velocity toward constant stress drop time as the particle size increases. We also determined the shear band width using the time‐lapsed images of the sheared glass beads and found that the number of particles comprising the shear band decreases with the particle size. When the glass beads are saturated with viscous liquid, lubrication causes the rheology to change from frictional to viscous and to increase the slip recurrence interval, and these properties can be used to distinguish from the particle size effects. Under a fixed loading rate, there is a viscosity that minimizes the stress needed for shearing, at which we can separate the frictional and viscous regimes.

Shear-induced pressure changes and seepage phenomena in a deforming porous layer - II

We present the results of an analytical investigation into the deformation behaviour of a three-layer permeable material that provides solutions of the stress equilibrium equations and the equation of continuity coupled with Darcy's law. Two distinct regimes are investigated. The first is the one in which the externally applied fluid pressures are significant, the second is the limit in which these pressure increases are insignificant. The typical time constant τ for the process is derived. In the latter case the long-term behaviour of the fluid pressure in the three layers is entirely determined by the applied shear stress rate and a stable steady state appears. When there is an external fluid pressure increase no steady state settles and the leading term in the long-time expansion is proportional to the time t. The instability that is created in this way needs examination as the hydraulic failure that is associated with it will take place at the position where the pressure increase is greatest. Note that the flow that follows from the pressure gradient is greatest in the vicinity of the top layer, which is presumed to be more permeable: k1/k2≈ 103. All this holds for slow processes where the time constant is long compared to the consolidation time. The stress state in the material in the vicinity of the granular layer becomes therefore more anisotropic, which may cause the surrounding material to fail. The problem of melt extraction in a flattening and deforming plume head at the base of the lithosphere was investigated. For a fixed loading rate of 10−15 s−1, excess pressures and flow rates are of the order 107 to 109 Pa, and ca. 10−13 m s−1 respectively, increasing with increasing rate of shear. Evaluation of the ratio of hydrostatic pressure to isotropic stress points to hydraulic fracturing as a potentially important aspect of the long-term deformation behaviour.

The temperature dependence of the strength of adhesion between steels and epoxy-rubber glues and polyamides in a rubberlike state

We have studied the temperature dependence of the strength of adhesion between steel 45 and epoxy-rubber glues and polyamide coatings in a rubberlike (high elasticity) state, measured at a fixed loading rate. An empirical relationship is established between the adhesion strength σ and the temperature above the glass transition point.

The temperature dependence of the strength of adhesion between epoxy-rubber glues and steels

We have studied the temperature dependence of the strength of adhesion between epoxy-rubber glues and steel 45 measured at a fixed loading rate. It is established that the adhesion strength σ exhibits a linear decrease with increasing temperature, predicted by the kinetic theory of fracture, only in the temperature interval between the characteristic values T t and T b. Below T t, the adhesion strength is independent of the temperature, while at T>T b, the slope of the σ(T) curve decreases with increasing temperature. Deviations from the kinetic theory predictions are explained by a change in the fracture mechanism (with tunneling transitions being involved in the fracture at low temperatures) and by variation of the parameter γ (at elevated temperatures). The values of the activation energy and activation volume of the fracture are determined.