Loading-unloading Rate Research Articles

Evolution of the damage precursor based on the felicity effect in shale

Damage precursors during hydraulic fracturing in shale gas reservoirs may be better understood if the deformation, failure, and acoustic emission (AE) characteristics under cyclic loading are known. Therefore, the purpose of this paper is to investigate the quantitative damage based on the Felicity effect under constant stress lower limit uniaxial cyclic loading-unloading rates (0.5, 1.0, 1.5, 2.0, and 2.5 kN/s). Variations in the b-value and the spatiotemporal evolution of cumulative AE were also used to observe how shale fractures formed. The findings reveal that during the unloading stage, there are many cumulative AE events when the stress level is low (≤1.50 kN/s) but that this number drops significantly when the stress level increases above (>2.0 kN/s). The AE amplitude, AE counts, and cumulative AE energy of each cycle in a loading-unloading test show an increasing trend, but the rate increases in the last cycle. During the whole process of loading and unloading, the Kaiser effects were present in the 3rd cycle at stress levels (≤1.5 kN/s). Still, the Felicity effect appeared in the 2nd and 1st cycles during 2.0 and 2.5 kN/s cyclic loading. The Kaiser effect occurs in the linear elastic stage, while the Felicity effect occurs in the crack initiation and crack damage stage. Furthermore, the Felicity ratio (FR) variations during shale deformation and failure can be divided into four phases: (Phase I = 1.01 ≥ FR > 0.89), (Phase II = 0.89 ≥ FR > 0.48), (Phase III = 0.48 ≥ FR > 0.23), and (Phase IV = FR ≤ 0.23). The b-value is relatively higher under the loading rate below (≤1.50 kN/s), indicating an increase in the number of small AE events. In contrast, the fact that the b-value is relatively smaller under the loading rate above (>2.0 kN/s) indicates that, the number of large AE events increases the number of cracks and fractures. These findings provide important design references for damaged precursors during hydraulic fracturing in shale gas reservoirs.

Characterization of rabbit corneal biomechanical properties after corneal refractive surgery based on rapid loading-unloading uniaxial tensile test

In order to understand how the biomechanical properties of rabbit cornea change over time after corneal ablation, 21 healthy adult rabbits were used in this study, with the left eye as experimental side and the right eye as the control side. Firstly, a lamellar knife was used to remove a portion of the anterior corneal surface tissue (30%~50% of the original corneal thickness) from the left eye of each rabbit, as an animal model simulating corneal refractive surgery. Secondly, postoperative experimental rabbits were kept for one, three, or six months until being euthanized. Strip specimens were produced using their corneas in vitro to perform a uniaxial tensile test with an average loading-unloading rate of approximately 0.16 mm/s. Finally, the visco-hyperelastic material constitutive model was used to fit the data. The results showed that there was a significant difference in the viscoelastic parameters of the corneas between the experimental and the control eyes at the first and third postoperative months. There was a difference in tangential modulus between the experimental and the control eyes at strain levels of 0.02 and 0.05 at the third postoperative month. There was no significant difference in biomechanical parameters between the experimental and the control eyes at the sixth postoperative month. These results indicate that compared with the control eyes, the biomechanical properties of the experimental eyes vary over postoperative time. At the third postoperative month, the ratio of corneal tangential modulus between the experimental and the control eyes significantly increased, and then decreased. This work lays a preliminary foundation for understanding the biomechanical properties of the cornea after corneal refractive surgery based on rapid testing data obtained clinically.

Bulk moduli of sandstones subjected to isotropic stress: Simultaneous static and dynamic experimental study

We designed an experiment to simultaneously measure the dynamic and static elastic moduli of the reservoir rocks. The static moduli experiments were conducted by using strain gauges while the dynamic moduli were calculated from the measurement of ultrasonic P- and S-wave velocities at a central dominant frequency of 1 MHz by P- and S-wave transducers housed inside the pressure cell. To increase the accuracy of our dynamic measurements we directly measured S-wave velocity and no estimation has been used to predict S velocity from its recorded P- velocity, which is customary in past studies. Our experimental design had a fixed loading-unloading stress rate at 1 MPa/min. We observed that for sandstones with porosity ranging from 8% to 24%, the dynamic bulk moduli can be up to 44% higher than the static moduli. The results are in agreement with some, but not all of the existing empirical equations in the literature. We confirmed that by using P-wave velocity -a non-destructive method- the UCS (Unconfined Compressive Strength) value for sandstones could also be estimated. Dynamic bulk's modulus ranged from 4-13GPa while the static bulk modulus was simultaneously measured and ranged from 2-11GPa for the same samples. This paper extended to measure dynamic Young's modulus and Poisson's ratio for four time periods of the study to investigate the effect of stress and time relaxation on the properties of the sandstones. We measured the elastic properties of non-loaded samples before applying the stress, right after the unloading, 20 days and 60 days after the experiment. The pattern for all the samples showed an increase of Young's modulus right after the stress application and then gradual decrease of this value over time as a result of relaxation; however, most of the samples could not reach the original values of the moduli due to irreversible deformation at micro-level. Dynamic moduli show great sensitivity to detection of irreversible deformations as compared to static moduli. Finally, we checked the compatibility of empirical equations on predicting UCS values based on the P-wave velocity for sandstones. The predicted UCS by the nominated equation is quite accurate, which shows the great potential of dynamic studies as a non-destructive experiment to estimate this value for the sandstones.

Experimental Investigation on Deformation and Strength Behavior of Marble with the Complex Loading-Unloading Stress Path

The excavation of deep tunnel in rock mass undergoes complex loading and unloading stress paths, resulting in rib spalling, flaking, and even severe rockburst disasters. Based on the variation law of the stress path of the surrounding rock, laboratory tests of rock mechanics are designed, and the deformation and strength behavior of marble with different initial confining pressure and unloading rates are systematically studied. By introducing strain increment, the characteristic stress, and the dilatancy index, the rock’s dilatancy and brittleness under different unloading conditions are quantitatively analyzed. During unloading, the energy transformation mechanism of rock is described, and the law of deformation and failure is discussed based on characteristic energy. The rock failure strength fitting formula is given by applying the Mogi–Coulomb criterion and elastic strain energy criterion. The advantages of the elastic strain energy criterion are theoretically explained. This study shows that comprehensive consideration of the complex stress paths, confining pressure levels, and the loading-unloading rates of surrounding rock is an effective way to accurately study unloading rock characteristics. The results can provide theoretical basis for stability analysis of high-stress underground engineering.

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

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

Acoustic Emission Simulation on Coal Specimen Subjected to Cyclic Loading

The damage and failure state of the loaded coal and rock masses is indirectly reflected by its acoustic emission (AE) characteristics. Therefore, it is of great significance to study the AE evolution of loaded coal and rock masses for the evaluation of damage degree and prediction of collapse. The paper mainly represents a numerical simulation investigation of the AE characteristics of coal specimen subjected to cyclic loading under three confining pressures, loading‐unloading rates, and valley stresses. From the numerical simulation tests, the following conclusions can be drawn: (1) The final cycle number of coal specimen subjected to cyclic loading is significantly influenced by the confining pressure, followed the valley stress. With the increase in confining pressure or valley stress, the cycle number tends to increase. However, the loading‐unloading rate has a little influence on it. (2) The AE counts of coal specimen subjected to cyclic loading are greatly influenced by the confining pressure and the valley stress. With the increase in the confining pressure, the cumulative AE counts at the 1st cycle tend to increase but decrease at a cycle before failure; with the decrease in the valley stress, the cumulative AE counts per cycle increase in the relatively quiet phase. However, the loading‐unloading rate has a little influence on it. (3) The failure mode of coal specimen subjected to cyclic loading is significantly influenced by the confining pressure. Under the uniaxial stress state, there is an inclined main fractured plane in the coal specimen, under the confining pressures of 5 and 10 MPa, the coal specimen represents dispersion failure. The loading‐unloading rate and valley stress have little influence on it. (4) The AE ratio is proposed, and its evolution can better reflect the different stages of coal specimen failure under cyclic loading. (5) The influence of confining pressure on the broken degree of coal specimen subjected to cyclic loading is analyzed, and the higher the confining pressure, the more broken the failed coal specimen.

A new hyper-viscoelastic model for investigating rate dependent mechanical behavior of dual cross link self-healing hydrogel

Self-healing hydrogels have been considered as an appropriate material for the biomechanical applications. Time-dependency and hyperelasticity are the significant mechanical behavior of these materials. In this research, a new hyperelastic strain energy function based on the polynomial-logarithmic terms was generalized to hyper-viscoelastic model for investigating the mechanical behavior of the dual cross self-healing hydrogel. The model parameters were determined by fitting with the experimental results of Long et al. and the material stability of the model in the pure shear and balance biaxial modes were investigated. It was observed the minimum strain rate for considering the rate dependent behavior is 0.003/s and below of this threshold the rate-dependent behavior could be neglected. The relaxation behavior of the hydrogel was simulated and results represented a good agreement with the experimental results. By ensuring the material stability, the cyclic loading was simulated and it was observed after three cycles the preconditioned state could be reached. Moreover, it was observed the energy dissipation depends on the loading-unloading rates. The hyper-viscoelastic model was used to simulate the healing process in the ABAQUS software using the VUMAT user subroutine. It was seen at least 300 s should be considered between the load/unload cycles to observe the healing phenomenon.

“Pop-in” and “pop-out” effect in monocrystalline silicon. A statistical investigation

AbstractPop-in and pop-out effects in silicon (Si) have long been known. They were evidenced in the indentation loading-unloading curves as a sudden displacement discontinuity. They consist in a sudden contraction (pop-in) or a sudden expansion (pop-out) of the material underneath the indenter in a short period of time and are attributed to Si phase transformations that take place during the nanoindentation procedure. In this paper, first we provide a statistic analysis of such pop-in/pop-out events depending on the maximum indentation load and second we examine the dependence of their appearance on the indentation loading-unloading rate.

Optimization of Raw Materials for Preparation of Transparent Soil Based on Analytic Hierarchy Process

The application of man-made transparent soil has greatly contributed to the development of the visual research in physical model test. Comparing to the traditional model test, the transparent soil has advantages with respect to transparency, visualization, lower cost and utility et al. However, the transparency of material itself seriously restricted the effect of the results during the model text. This paper took the transparency as the evaluation standard, based on the Analytic Hierarchy Process (AHP) to make clear the factors on transparency of transparent soil which are: Purity and transparency of materials, matching degree of refractive index, size distribution of aggregate, air content and loading-unloading rate while consolidation and taking the commonly used combinations of raw materials as the example, the optimal combination was obtained. The work described in this study can provide a certain theoretical guidance for selection of raw materials and to improve the transparency during the preparation of transparent soil.

Nanoscale variation in energy dissipation in austenitic shape memory alloys in ultimate loading cycles

Wavy behaviours of hysteresis energy variation in nanoscale bulk of thermomechanical austenitic NiTi shape memory alloy are reported in ultimate nanoindentation loading cycles. One sharp and two spherical tips were used while two loading–unloading rates were applied. For comparison, another austenitic copper-based shape memory alloy, CuAlNi shape memory alloy, and a metal with no phase transition, elastoplastic Cu, were investigated. In shape memory alloys, the hysteresis energy variation ultimately undergoes a linear decrease with internal wavy fluctuations and no stabilisation was observed. The internal energy fluctuation in these alloys was found dissimilar depending on the loading–unloading rate and the indentation tip geometry. In contrast, there was an absence of both overall and internal variations in hysteresis energy for Cu after the second loading cycle. The underlying physics of these variations is discussed and found to be attributed to both the created dislocations and ratcheting thermal–mechanical behaviour of the phase-transformed volume in shape memory alloys.

Combinational rate effects on the performance of nano-grained pseudoelastic Nitinols

Combinational loading-unloading rate effects were studied on the behavior of NiTi shape memory alloys (SMAs) under nanoindentation loads. While combinational loading rates showed negligible effects on the performance of NiTi SMAs, the combinational unloading rates did show significant effects on hysteresis energy. The heating-cooling phenomenon during the loading stage and the sole cooling during the unloading stage explain the effects. This study elucidates the nature of thermomechanical SMAs' behaviors during complex compressive loadings with the presence of solid-state phase transition.

Influence of loading holding time under quasistatic indentation on electrical properties and phase transformations of silicon

The quasistatic Vickers indentation of Si (100) were applied to investigate the influence of loading holding time on the changes of electrical resistance and phase transformation in the indentation zone. For all used loading regimes with different holding times (2 s, 10 s, 1 h and 10 h) in combination with constant loading-unloading rate (250 mN/s) the electrical resistance in the region of residual indentations was found to be lower than before indentation. It was shown that this is connected with the formation of semimetallic Si-III phase and amorphous Si of higher pressure induced by creep process developed under long lasting pressure. The longer the holding time, the greater lowering of electrical resistance in the indentation region was observed, with the exception of the holding time above 1 h, this being explained by a decelerating creep rate of Si for this interval of time leading to a halt of further extending of amorphous and Si-III regions of lower electrical resistance.

Effect of Load Waveform on Creep-Fatigue Crack Propagation in Lead-Free Solder

Crack propagation tests of lead-free solder were conducted using center-notched plates under cyclic tension-compression of three waveforms : pp waveform having fast loading and unloading rates, cp-h waveform having a hold time under tension, and cc-h waveform having a hold time under tension and compression. In fatigue loading at fast loading-unloading rates, i.e. pp waveform, the path of crack propagation was macroscopically straight, perpendicular to the maximum principal stress direction. The introduction of creep components by tension and compression holds in cc-h waveform promoted shear-mode crack propagation even under tension-compression loading. For fatigue loading of pp waveform, the crack propagation rate was expressed as a power function of the fatigue J-integral and the relation was identical for load-controlled and displacement-controlled conditions. The creep component due to the hold time greatly accelerates the crack propagation rate when compared at the same values of the fatigue J integral or the total J integral (the sum of fatigue J and creep J integrals). The creep crack propagation rate was expressed as a power function of the creep J integral for each case of cp-h and cc-h waveforms. The crack propagation rate for cp-h waveform is higher than that for cc-h waveform. The predominant feature of fracture surfaces was striations for pp waveform and grain boundary fracture for cp-h waveform. Grain fragmentation was evident on the fracture surface made by cc-h waveform.

Simultaneous determination of mechanical properties and physiologic parameters in living rat brain

Mechanical properties were determined in living adult rat brain. Reconstructed magnetic resonance images of the rat brain before and after 2 mm compression with a 4.06 mm diameter vinyl screw showed the total volumetric strain was maximal at the site of indentation. The pressure response to stepwise brain compression showed a linear relationship to the point of respiratory compromise. Instrumented indentation was performed on live brain with intact dura using a 4-mm-diameter flat punch indenter to a maximum depth 1.2 mm at loading-unloading rates not exceeding 0.34 N/min and 1.2 mm/min. The calculated elastic modulus showed no consistent change after death. Creep deformation over 15 s was 7.86+/-1.6% in live brain and 27.0+/-0.24% after death. In constant multicycle indentation, displacement from 1st to 10th cycle increased 8.0+/-1.7% in life and 12.9+/-2.8% after death. The results suggest that elastic properties of rat intracranial contents do not change immediately after death, while changes in the viscous properties are substantial. The process of measuring these properties can alter physiological parameters.

Effect of Ca2+ Ions on the Adhesion and Mechanical Properties of Adsorbed Layers of Human Osteopontin

Using an atomic force microscope and a surface force apparatus, we measured the surface coverage, adhesion, and mechanical properties of layers of osteopontin (OPN), a phosphoprotein of the human bones, adsorbed on mica. OPN is believed to connect mineralized collagen fibrils of the bone in a matrix that dissipates energy, reducing the risk of fractures. Atomic force microscopy normal force measurements showed large adhesion and energy dissipation upon retraction of the tip, which were due to the breaking of the many OPN-OPN and OPN-mica bonds formed during tip-sample contact. The dissipated energy increased in the presence of Ca2+ ions due to the formation of additional OPN-OPN and OPN-mica salt bridges between negative charges. The forces measured by surface force apparatus between two macroscopic mica surfaces were mainly repulsive and became hysteretic only in the presence of Ca2+: adsorbed layers underwent an irreversible compaction during compression due to the formation of long-lived calcium salt bridges. This provides an energy storage mechanism, which is complementary to energy dissipation and may be equally relevant to bone recovery after yield. The prevalence of one mechanism or the other appears to depend on the confinement geometry, adsorption protocol, and loading-unloading rates.

Numerical and Experimental Evaluation of the Damping Properties of Shape-Memory Alloys

This paper presents and compares two different uniaxial constitutive models for superelastic shape-memory alloys (SMAs), suitable to study the dependence of the stress-strain relationship on the loading-unloading rate. The first model is based on the inclusion of a direct viscous term in the evolutionary equation for the martensite fraction and it shows how the material response is bounded between two distinct rate-independent models. The second model is based on a rate-independent evolutionary equation for the martensite fraction coupled with a thermal balance equation. Hence, it considers mechanical dissipation as well as latent heat and includes the temperature as a primary independent variable, which is responsible of the dynamic effects. The ability of both models to reproduce the observed reduction of damping properties through the modification of the hysteresis size is discussed by means of several numerical simulations. Finally, the capacity of the constitutive equations to simulate experimental data from uniaxial tests performed on SMA wires and bars of different size and chemical composition is shown.

10410 SUS304ステンレス鋼の高温低サイクル疲労における雰囲気効果について : ひずみ速度の影響(材料(2))

For these twenty years, we have continued low-cycle fatigue tests of SUS304 stainless-steel at 650C in air and in high vacuum to investigate the effect of tensile strain hold time at several loading-unloading strain rates. In vacuum, much more hold time effect was found than in air. Concept of linear damage rule is found to be applicable to life prediction of these fatigue results.

Post-yield compressed semicrystalline poly(butylene terephthalate): energy storage and release

Post yield deformation of semicrystalline poly(butylene terephthalate) (PBT) is studied by differential scanning calorimetry (DSC) measurements on compressed specimens after unloading. In particular, the effects of strain level, loading-unloading rate, and deformation temperature are analyzed. DSC traces indicate that a remarkable fraction of the mechanical work of deformation (in the range from 25 up to 62%) is stored in the material after unloading. Final strain dependence of stored energy values for specimens deformed up to 40% follows the general S-shaped trend observed for many amorphous and semicrystalline polymers. The ratio of the stored energy to the mechanical work of deformation (Δ U ST/ W) is decreasing as the final deformation level increases. For a given final strain level, the amount of energy stored in specimens deformed under T g increases as either loading or unloading rates increase: in particular, both Δ U ST and Δ U ST/ W values are linearly increasing with the logarithm of loading rate. On the other hand, energy storage for specimens deformed at T g results to be practically independent from the loading rate. Moreover, as the deformation temperature increases from 25 to 100 °C, Δ U ST values markedly decrease, while the ratio Δ U ST/ W is almost constant around an average value of about 51%.

Temperature and Time Effects on the “Adhesion Dynamics” of Poly(butyl methacrylate) (PBMA) Surfaces

The authors present a surface force apparatus (SFA) study of the effects of time and loading-unloading rates on the adhesion of solid polymeric surfaces of poly(butylmethacrylate). They used the equilibrium JKR theory of adhesion or contact mechanics as a framework for analyzing the adhesion dynamics of two surfaces during nonequilibrium (viscoelastic, plastic) adhesion and separation. PBMA films of thickness {approximately}2 {micro}m were prepared on curved mica surfaces by casting from a solution of methyl ethyl ketone. Pull-off forces from adhesive contact were measured at different temperatures around the glass-rubber transition temperature (T{sub g} {approx} 25 C) at different loads and contact times, and hysteretic loading-unloading cycles were measured at different rates. On entering the rubber regime, the effective surface energies deduced from the pull-off forces increase dramatically, by up to 3 orders of magnitude above the equilibrium value, with increasing contact time and load. Strong entanglements across the interface, probably through reptation, increase the effective area of contact with time, giving rise to the high pull-off forces observed. Bulk viscoelastic deformations of the surface profiles accompany the time-dependent adhesion processes. The existence of at least two different relaxation (energy dissipating) processes, one at the molecular level and the other atmore » the microscopic to macroscopic level, can be inferred from these experiments. The implications of the results for understanding the adhesion, fracture strength, and crack-propagation of elastic versus viscoelastic materials are discussed.« less

Relationship between adhesion and friction forces

The Surface Forces Apparatus technique was used to measure the normal (perpendicular) and lateral forces between variously prepared surfaces under both dry and lubricated conditions. 'Normal' forces include the force vs distance functions, F(D), for surfaces separated by thin liquid films as well as the adhesion forces and energies, γ, for two surfaces in adhesional contact. 'Lateral' forces include the static and kinetic friction forces F of the surfaces as they slide past each other at a given separation, D. The results show that very thin liquid films confined between two solid surfaces can sustain both normal and shear forces or stresses. The results further indicate that the normal force, F(D) or γ, may be directly related to the static friction force, Fs, and simple equations are proposed that relate these forces (by 'static' friction force is meant the lateral force that must be applied to initiate motion, but not necessarily to maintain this motion). In contrast, the kinetic friction force, Fk, which is the force that must be continually applied to maintain motion at a given velocity, was found to be related, not to the equilibrium or reversible interaction but to the dissipative or irreversible part of the adhesion or interaction energy during a loading-unloading cycle. There is a high degree of correlation in the way that normal forces and friction forces are affected by changes in applied load or pressure, sliding velocity, loading-unloading rates and temperature. These systematic correlations can be conveniently represented by non-equilibrium 'adhesion' and 'friction' phase diagrams.