Stress Hysteresis Loops Research Articles

A one‐dimensional phenomenological constitutive model of shape memory alloys considering the cyclic degradation of two‐way memory effect

AbstractThis study introduces a one‐dimensional phenomenological constitutive model designed to describe two‐way shape memory effect (TWSME) and its associated cyclic degradation. The model utilizes the logistic function to formulate the phase transformation equation, incorporates the expansion of key parameters into their respective fatigue functions to characterize the fatigue phenomenon, and integrates a phase transformation rate regulation function into the differential form of the phase transformation equation. This integration facilitates the control over the entire phase transformation process and the simulation of incomplete transformations. The model is distinguished by its comprehensive functionality, simple form, ease of calculation, and the clear and direct influence of key parameters. Furthermore, it offers a degree of flexibility because each function within the framework is replaceable. The simulation of the TWSME strain and recovery stress hysteresis loop deformation has been successfully conducted, enabling the description of internal hysteresis loops caused by incomplete transformation. The validity of the model is corroborated by comparing it with existing experimental results.

Cross-Scale Characteristics of Damage Evolution in Granite under High-Confining Pressure Cyclic Loading

The rock properties under periodic load are important to the stability of engineering works. It needs to analyze the mechanical properties and damage of deeply buried rock under periodic load. Taking granite in a mine as the research object, designed the experiment involving different cycles under different confining pressures and constant periodic upper and lower limit loads, carried out corresponding high-confining pressure cyclic loading experiment. The results show that a closed stress hysteresis loop is formed during loading and unloading cycles under different confining pressures. The hysteresis loop area of axial deformation decreases gradually with an increase of cycles. With the confining pressure increasing, the deformation modulus decreases gradually. However, under the same confining pressure, the deformation modulus remains almost unchanged as the number of loading–unloading cycles increase. As the number of cycles increase, the residual displacement shows an increasing trend whereas the axial and circumferential strains decrease. This can be explained by primary cracks gradually becoming compacted with the increase of cycles so that the proportion of axial elastic strain increases, the proportion of circumferential elastic strain increases. Fractal analysis of the T2 spectrum shows that the sample has fractal characteristics before and after cyclic loading.

Dynamic Shear Failure of Freeze-Thawed Tibet Hornfels Subjected to Multilevel Cyclic Shear (MLCS) Loads: Insights into Structural Dependent Failure Characteristics

Abstract Shear instability behavior is typical failure mode of rock mass in civil and mining engineering. Many attempts have been performed for rock joints or nonpersistent rock bridge under static shear conditions, yet the shear failure of rock mass subjected to cyclic or fatigue shear conditions is not well understood. Multilevel cyclic shear (MLCS) loading experiments were carried out on freeze-thawed hornfels to reveal the fracture and energy evolution characteristics using a self-special designed rock dynamic shear testing apparatus. The effect of the preexisting natural fracture on rock shear strength, deformation, energy dissipation, and shear failure pattern were experimentally investigated. The testing results show that aperture of open-mode fractures increases quickly, and this kind of natural fracture contributed a lot to rock failure. The evolution of stress hysteresis loop and its pattern are impacted by natural fracture, and it determines the damage accumulation. In addition, a damage evolution model was proposed to describe the damage evolution defined by the dissipated energy; the model can well describe the two-stage damage propagation for each cyclic stage and the entire cyclic loading process. Good agreement was found among the irreversible strain, energy dissipation, and failure morphology that are influenced by the preexisting natural fractures. It is suggested that the rock dynamic shear failure behaviors are rock structural dependent; the disturbed stress alters the energy dissipation and release characteristics.

Influence of stress amplitude on the dynamic characteristics of phyllite samples under triaxial multi-stage cyclic loading

The generation of a rockslide in an earthquake event is strongly dependent on the dynamic characteristics of the rock materials constituting the rock slope. In this study, phyllite samples were extracted from the Donghekou landslide area of Qingchuan County. The landslide occurred during the 2008 Wenchuan earthquake and the samples were made to undergo multi-stage cyclic loading and unloading tests under triaxial compression conditions. The confining pressure during the tests was 10 MPa, the loading frequency was 2 Hz, the loading waveform was sine wave, and 60 loading cycles were carried out at each level of stress. From the dynamic axial stress–strain curves, the effect of stress amplitude on the hysteresis loop area, the dynamic elastic modulus, the dynamic damping ratio, and the damping coefficient of the phyllite samples was analyzed. The results are as follows. (1) The strain–stress hysteresis loop area experienced a rapid increase as the stress amplitude exceeded a certain value, indicating that the rock samples have entered an accelerating crack propagation stage under high levels of cyclic loading. (2) As the stress amplitude increases, the dynamic elastic modulus, the dynamic damping ratio, and the damping coefficient of the rock sample followed a similar two-phase evolution law. There was a rapid reduction in the three parameters relative to the initial value in Phase I. Moreover, there was a minor change in Phase II. (3) The effect of the number of loading cycles number on dynamic elastic modulus and damping parameters was much more obvious under the lower levels of cyclic loading than under the higher levels.

Two-Phase Solutions for One-Dimensional Non-convex Elastodynamics

We explore the local existence and properties of classical weak solutions to the initial-boundary value problem for a class of quasilinear equations of elastodynamics in one space dimension with a non-convex stored-energy function, a model of phase transitions in elastic bars proposed by Ericksen (J Elast 5(3–4):191–201,1975). The instantaneous phase separation and formation of microstructures of such solutions are observed for all smooth initial data with initial strain having its range that overlaps with the phase transition zone of the Piola–Kirchhoff stress. Moreover, we can select those solutions in a way that their phase gauges are close to a certain number inherited from a modified hyperbolic problem and thus give rise to an internal strain–stress hysteresis loop. As a byproduct, we prove the existence of a measure-valued solution to the problem that is generated by a sequence of weak solutions but not a weak solution itself. It is also shown that the problem admits a local weak solution for all smooth initial data and local weak solutions that are smooth for a short period of time and exhibit microstructures thereafter for certain smooth initial data.

A time-domain modeling of systems containing viscoelastic materials and shape memory alloys as applied to the problem of vibration attenuation

It is widely known that traditional damping materials such as elastomers present a number of interesting characteristics when applied for vibration mitigation, such as inherent stability and good damping performance in relatively broad frequency bands, besides cost effectiveness. However, the behavior of those materials is highly dependent upon environmental and operational parameters such as excitation frequency and temperature. Another typical drawback is the added weight entailed by viscoelastic treatments. Especially regarding environmental influences, uncontrolled temperature variations and moisture can jeopardize the damping capacity and endurance of viscoelastic dampers. On the other hand, shape memory alloys present potential advantages in vibration damping due to their large pseudoelastic hysteresis loop in stress–strain relationship and can be used both as a damping material and structural elements in various engineering applications. Thus, it becomes apparent the convenience of combining both types of materials in such a way to explore the advantageous features of each of them. In this paper, a time-domain modeling procedure of structures containing both viscoelastic materials and shape memory alloys is addressed. The main goal is the development of a finite-element-based methodology intended to perform the analysis of engineering structures treated by passive constraining layer damping and pseudoelastic shape memory alloy wires for vibration mitigation. The viscoelastic behavior is modeled by using a four parameter fractional derivative model. To model the hysteresis response of the shape memory alloy, a phenomenological simplified model suitable for performing the parametric study of such dynamic system is used. After the discussion of various theoretical aspects, the time-domain responses are calculated for a three-layer sandwich beam containing viscoelastic materials and shape memory alloy wires and the main features of the modeling methodology are highlighted.

Atomistic characterization of pseudoelasticity and shape memory in NiTi nanopillars

Molecular dynamics simulations are performed to study the atomistic mechanisms governing the pseudoelasticity and shape memory in nickel–titanium (NiTi) nanostructures. For a 〈110〉 – oriented nanopillar subjected to compressive loading–unloading, we observe either a pseudoelastic or shape memory response, depending on the applied strain and temperature that control the reversibility of phase transformation and deformation twinning. We show that irreversible twinning arises owing to the dislocation pinning of twin boundaries, while hierarchically twinned microstructures facilitate the reversible twinning. The nanoscale size effects are manifested as the load serration, stress plateau and large hysteresis loop in stress–strain curves that result from the high stresses required to drive the nucleation-controlled phase transformation and deformation twinning in nanosized volumes. Our results underscore the importance of atomistically resolved modeling for understanding the phase and deformation reversibilities that dictate the pseudoelasticity and shape memory behavior in nanostructured shape memory alloys.

Experimental characterizations of bending fatigue of a four-step 3-D braided rectangular composite under different stress levels

This article reports the bending fatigue behavior of a four-step 3-D rectangular braided composite at different stress levels. The S–N curve and the stress vs. deflection history were recorded to investigate the bending fatigue behaviors of the braided composite. Specifically, the area of the stress hysteresis loop in each loading cycle and the accumulated area of the whole loading cycles were calculated from the stress vs. deflection history curves. All the integral areas were compared at different stress levels for analyzing the energy absorption. Then, the energy absorptions during the bending fatigue were compared to analyze the energy dissipation mechanisms taking place during the fatigue process. The stiffness degradation was also calculated to show the fatigue damage. The damage morphologies of the 3-D braided composite specimens were photographed to compare the failure modes under different stress levels.

Shear thinning and antithixotropic behavior of a heated cross‐linked waxy maize starch dispersion

Cross‐linked waxy maize (CWM) starch dispersions (2.6%, w/w) were heated in the range 60°C to 80°C and in a retort at 120°C. All the heated dispersions exhibited shear‐thinning behavior except for that heated for 15 min at 60°C which showed slight shear‐thickening. The consistency index (K) increased with heating time and was exponentially correlated to the granule size and the notional volume fraction. CWM starch dispersions heated for 8, 15 and 30 min at 120°C exhibited counterclockwise (antithixotropic) shear rate‐shear stress hysteresis loops. Similar behavior was observed when dispersions were sheared in three continuous cycles and they became more viscous with each shear cycle. Clusters of granules were found in sheared retorted dispersions that may have been shear induced. Gelatinized granules viewed with SEM appeared to have folds and crevices which may have aided in cluster formation.

Different Effects of Whole Egg and Egg-Yolk on Emulsion Preparation from a Fish Meat Product.

The yolk-added emulsified product prepared from sardine meat had a more viscoeiasdic strucdure than the 'whole egg'-added product because it deveioped large G', G values and large shear stress. However, the yolk-added product showed a smaller value of yield stress and a markedly smaller value was shown at asoybean oil to sardine meat ratio of 1.1. The consistency and flow behavior indexes of increasing shear rate determination were larger in the yolk-added product than in the 'whole egg'-added product. In the yolk-added product, the oil droplets were smaller, more uniform and larger in number. Therefore, the sum of the interactions between the oil droplets was larger. This microstrucdure is reiaded to the above rheological results. A drastic change in shear response was found between a soybean oil ratio of 1.1 and 1.7 in both the'whole egg'-added and the yolk-added products but was more pronounced in the yolk-added product. When the shear rate vs. shear stress hysteresis loop of the yolk-added product was considered in comparison with that of the 'whole egg'-added product, at a low oil ratio the strucdure breakdown was not induced by the shear, and at a high oil ratio a great structure breakdown was induced. This result means that the three dimensional structure developed with the high oil ratio was broken down by the shear. In the products with higher oil radios of 1.7 and 2.5, the relative amount of emulsifier do oil was very small. Therefore, the emulsifying layer around an oil droplet was thin, and the oil droplets tended to coalesce without the shear. If shear was applied, the emulsion was easily broken down due to the further progress of coalescence. From microscopic observation, it was found that many large oil droplets were present in the products with higher oil radios of 1.7 and 2.5.

Attenuation Stress Hysteresis Loops and Low‐Frequency Internal Friction Associated with Thermomechanical Breakaway of Dislocations

AbstractMeasurements of ultrasonic attenuation and velocity changes are performed on 5N aluminium during the application of a low frequency bias stress. The characteristics of the attenuation‐stress Δα = f(σ) loops are studied as a function of the repetition of loading, amplitude σm of loading stress, temperature, and pretreatment of the sample (prestrain, ageing time, or temperature). The results show that at least two kinds of dislocation‐point defect breakaway mechanisms are involved in the experiments. Then a model is developed in order to calculate from the attenuation‐stress hysteretic loop a low frequency internal friction decrement δα: peak events versus amplitude (δα = f(σm)) are thus observed, in good accordance with classical models of internal friction associated with breakaway of dislocations; the activation energy for depinning and the space between pinning points are deduced from these peaks and their evolutions are followed as a function of the pretreatment of the sample. In addition, although the internal friction decrements δα and δ, obtained directly from torsion pendulum, have some similar characteristics, a noticeable difference appears in the decrement levels which is especially explained by the characters of the solicitation in bias stress and torsion pendulum experiments, respectively, one sided and alternative; their effects are discussed in terms of dislocation mechanisms.

Viscoelastic Hysteresis. Part II. Numerical and Experimental Examples

Several types of viscoelastic shear stress hysteresis loops were obtained for three forms of time-dependent shear rate inputs and four different polymer solutions. A correlation plot based on two dimensionless groups from the Bird-Carreau nonliner viscoelastic model demonstrates the experimental conditions required to obtain the various types of loops. The data were used to evaluate the predictive capabilities of the Bird-Carreau model and a “slowly varying flow” approximation to the same model. The “slow flow” model predicted the hysteresis response for experiments where the time of the experiment was larger than a characteristic time of the fluid. The model was qualitatively correct for a much wider range of experimental conditions. Five types of primary normal stress difference hysteresis loops are reported along with a demonstration of a method to calculate the “zero shear rate” limiting value of the primary normal stress material function θ0.

Viscoelastic Hysteresis. Part I. Model Predictions

Hysteresis loops on a shear stress versus shear rate plot have been reported by numerous investigators studying polymeric fluids. Both clockwise and counterclockwise loops have been observed. Currently available nonlinear viscoelastic models can be used to derive expressions for these hysteresis loops as well as for the corresponding normal stress hysteresis loops. It is suggested that the hysteresis loop experiment may be particularly useful for the testing of nonlinear viscoelastic models.