Unloading Modulus Research Articles

Acoustic emission-based sound velocity characteristics of ceramic matrix composites

Based on the Christoffel equation, using the relationship between the composite stiffness matrix and the elastic constant, the orthotropic model was applied to the acoustic properties of 2D-C/SiC composites, and the expression of the material sound velocity was obtained. Through the cyclic loading and unloading test, the sound velocity changes at different stress levels during the entire tensile process were measured. The damage characterization of the sound velocity on the 2D-C/SiC composite was studied. The results show that as the stress level continues to increase, the sound velocity gradually decreases, and the material The degree of damage has a greater impact on the propagation speed of sound waves in the 2D-C/SiC composite; the unloading modulus and reloading modulus are introduced to replace the sound velocity theory to calculate the tangent modulus. It is found that the theoretical results are in good agreement with the test results, and the error increases with the increase of load; The sound wave velocity decreases with the damage of the 2D-C/SiC composite, and based on this attenuation relationship, the damage characterization based on the sound velocity was established.

Experimental study of the mechanical behavior of calcareous sand under repeated loading-unloading

Understanding the mechanical behavior of calcareous sand under repeated loading-unloading is important to engineering design for island-reef underground caverns and pile foundation projects. In this study, we conducted conventional consolidated-drained triaxial shear tests on calcareous sand collected from the South China Sea under different effective confining pressures, and then, we performed multiple sets of triaxial repeated loading-unloading tests on calcareous sands with equivalent physical properties under different deviatoric stress levels and effective confining pressures. Based on the results, we conducted an in-depth investigation of the effects of the loading mode and effective confining pressure on the strain softening behavior and shear strength angle of calcareous sand. We studied the variation in the unloading rebound modulus as the effective confining pressure and deviatoric stress level changed, verified the applicability of the Dunkan-Chang model’s estimation equation for the unloading rebound modulus to calcareous sand, and established the relationship among the volume contraction during unloading, the effective confining pressure, and the deviatoric stress level. The results of this study provide an important basis for selecting appropriate parameters for island-reef construction engineering.

Experimental investigation on the effects of fabric architectures on mechanical and damage behaviors of carbon/epoxy woven composites

The mechanical behaviors and damage evolutions of carbon/epoxy woven fabric composites with three different geometries, i.e., one plain weave and two twill weave patterns with different areal densities, are studied under tensile loading. The effects of weave patterns on mechanical properties are investigated by monotonic and cyclic tension tests. Remarkable variations in stress–strain curve, Poisson’s ratio, residual strain and strain map exist in the three composites. Crimp ratio is found to be a critical factor to govern the mechanical properties. With smaller crimp ratio, a quasi-linear stress–strain curve with higher elastic modulus and strength is observed. The stress–strain curves of composites with higher crimp ratio contain transition stages with significant tangent modulus degradation. Elastic modulus, strength and damage initiation are all correlated with the crimp ratio linearly regardless of the fabric pattern. Dramatic nonlinear evolution in Poisson’s ratio occurs in the composite with higher crimp ratio. Cyclic tension results indicate that the residual strain is a more appropriate damage indicator than the unloading elastic modulus. Microstructure examination shows that damage developments are essentially related to the fabric geometry, and result in various mechanical behaviors. This study provides important insights into the geometry-deformation mechanism-mechanical property relationship of the woven composites.

Springback behavior and a new chord modulus model of copper alloy during severe plastic compressive deformation

Abstract The copper alloy in the unloading process after severe plastic compressive deformation (SPCD) exhibits obvious nonlinear stress-strain relationship and hysteresis behavior, and generates severe springback deformation. The severe strain hardening and softening effects occurring in the SPCD and the anisotropy of the material will affect the springback behavior of the material. In this paper, the samples obtained along the different directions (rolling direction, short-thickness direction, transverse direction, and 45° direction) of copper alloy hot-rolled plates were used to perform the quasi-static single pass compression tests with different deformation ratios (0.25 %–90 %). The springback behavior of the copper alloy under the SPCD was investigated. The effects of the strain hardening, strain softening and anisotropy on the springback behavior of the material were revealed. The variation relationships of the instantaneous tangent modulus and the chord modulus in unloading with stress and strain at different deformation stages (elastic stage, yield stage, strain hardening stage, and strain softening stage) were analyzed. A new chord modulus in a power exponential form was proposed. According to the unloading characteristic of the SPCD, the Yoshida-Uemori chord modulus model and the QPE model were modified. The applicability and accuracy of the unloading chord modulus models for the SPCD were evaluated and compared by using the power exponential chord modulus model, the modified QPE chord modulus model, the modified Yoshida-Uemori chord modulus model, and the Yoshida-Uemori chord modulus model, respectively. Besides, based on the proposed chord modulus model in a power exponential form, a 1-D E T model in a power exponential form was also proposed to describe the nonlinear unloading process and the variation of the slope of the unloading curves after the SPCD. The results indicated that the springback behavior of SPCD is obviously different from those of small plastic compressive deformation and elastic compressive deformation. The proposed chord modulus model in a power exponential form can accurately predict the chord modulus and springback strain in the unloading after the SPCD.

Mechanical properties of soft soils experiencing lateral unloading under initial excess pore water pressure

The mechanical properties of soft soils were investigated through triaxial lateral unloading tests under different initial excess pore water pressures and confining pressures. The lateral unloading stress–strain, strength parameters, and initial unloading moduli of soft soils are presented and discussed in this study. The results show that soft soils abruptly undergo unloading failure. The lower confining pressure and the higher initial excess pore water pressure can result in intensive unloading failure behavior. The unloading strength of soft soils linearly decreases as the initial excess pore water pressure increases. The stress–strain curve is characterized as strain hardening. The cohesion and initial unloading moduli of soft soils drastically reduce when the initial excess pore water pressure exceeds 20 kPa. The conclusions obtained in this study can provide a theoretical reference for the design and numerical analysis of underground spaces in soft soils.

Determination of the Unloading Modulus of Deformation in Dispersive Soils and Its Accounting in Designing

The aspects of determining the moduli of unloading and reloading of dispersed soils were considered. Sample tests involving triaxial compression devices showed that these parameters depend on the stress-strain state. The ratios between the primary loading and reloading moduli accepted in design practice were significantly underestimated, which led to errors in determining the settlement of structures. In accordance with the results of the study, a methodology for determining the moduli of unloading and reloading was proposed.

Dependency of the Young's modulus to plastic strain in DP steels: A consequence of heterogeneity?

The accurate springback prediction of dual phase (DP) steels has been reported as a major challenge. It was demonstrated that this was due to the lack of understanding of their nonlinear unloading behavior and especially the dependency of their unloading moduli on the plastic prestrain. An improved compartmentalized finite element model was developed. In this model, each element was assigned a unique linear elastic J2 plastic behavior without hardening. The model's novelty lied in the fact that:(i)a statistical distribution was discretized in a deterministic way and used to assign yield stresses to structures called compartments,(ii)those compartments were randomly associated with the elements through a random compartment element mapping (CEM).Multiple CEM were simulated in parallel to investigate the intrinsic randomness of the model. The model was confronted with experimental data extracted from the literature and it was demonstrated that the model was able to reproduce the dependence of the apparent moduli on the tensile prestrain. It was also observed that the evolution of the apparent moduli was predicted even if it was not an explicit input of the experimental dataset used to identify the input parameters of the model. It was then deduced that the shape of the hardening and the dependency of moduli on the prestrain were two manifestations of a single cause: the heterogeneous yield stress in DP steels.

Experimental study on influence of excess pore water pressure and unloading ratio on unloading mechanical properties of marine sedimentary soft soils

The paper discussed the effects of pore water pressure and unloading ratio on the mechanical properties of soft soils. The Shenzhen marine sedimentary soft soils were selected in this study. The results revealed that the excess pore water pressures had significant weakening effects on the unloading strength of soft soils. Comparing with the unloading strength without excess pore water pressure, the reduction rate of unloading strengths at excess pore water pressure ranging from 20 to 60 kPa were found to be 3.4%–21.4% and 1.3%–19.2% for unloading ratio 0.0 and 0.5 respectively. Meanwhile, the excess pore water pressures had greater impact to cohesion than to internal friction angle. The unloading failure modes of soft soils are sudden and concealed, and the lower confining pressures and higher excess pore water pressures can make the unloading failure more destructive. Moreover, the initial unloading modulus is linearly proportional to the confining pressure but linearly inversely proportional to the excess pore water pressure.

Cyclic response of spherical cell porous aluminum alloy-polyurethane composites

This work presents the experimental characterization of open-cell spherical cell porous aluminum alloy-polyurethane composites (SCPAA/PU composites) under a single full unloading/reloading cycle and seven complete repeated cycles, respectively. Three batches of SCPAA/PU composites are prepared for each loading pattern. The present paper mainly focuses on the three characteristic parameters, including unloading modulus, plastic strain and stress degradation ratio. The test results show that cyclic stress-strain curves of the composites under the two loading patterns exhibit the post-peak strain softening. Moreover, unloading modulus of the composites increases firstly and then reduces rapidly. The effect of the repeated cycles on the unloading modulus is closely associated with the applied strain. Initially, plastic strain ascends linearly with the increment of the applied strain, whereas, after a threshold strain, the growth rate slows down gradually. And the plastic strain is independent of the repeated cycles. Stress degradation ratio remains almost stable within a threshold strain and then reduces swiftly. The effect of the repeated cycles on the stress degradation ratio is also observed to be related to the applied strain.

Effect of microstructure and mechanical properties on tensile loading-unloading characteristics of cold-rolled DP780 steels

Tensile loading-unloading characteristic of three cold-rolled DP780 steels was studied. Similar hardening behaviour was showed by these steels even with different chemical composition and microstructures. Tensile loading-unloading tests with prestrain between 0.5% and 8% were carried out on Instron tensile testing machine. Sample microstructures were analysed by EBSD and SEM. Hardness of ferrite and martensite were measured by nanohardness instrument. Total unloading recovery strain, which is related to unloading chord modulus (Echord), can be divided into elastic strain and microplastic strain. The results showed that there was no correlation between unloading microplastic strain (εmp) and phase fraction or phase size within the scope of this study. However, with the increase of flow strength increment, εmp increases while Echord reduction becomes larger. Furthermore, εmp depends on the phase yield strength ratio between martensite phase and ferrite phase (σm/σf), emp increases as the σm/σf increase for a given flow strength increment. The results showed that the springback of DP780 steels can be improved by reducing the yield strength difference between martenstie and ferrite.

Effects of Hardening Model and Variation of Elastic Modulus on Springback Prediction in Roll Forming

In this paper, the uniaxial loading–unloading–reloading (LUR) tensile test was conducted to determine the elastic modulus depending on the plastic pre-strain. To obtain the material parameters and parameter of Yoshida-Uemori’s kinematic hardening models, tension–compression experiments were carried out. The experimental results of the cyclic loading tests together with the numerically predicted response of the plastic behavior were utilized to determine the parameters using the Ls-opt optimization tool. The springback phenomenon is a critical issue in industrial sheet metal forming processes, which could affect the quality of the product. Therefore, it is necessary to represent a method to predict the springback. To achieve this aim, the calibrated plasticity models based on appropriate tests (cyclic loading) were implemented in commercial finite element (FE) code Ls-dyna to predict the springback in the roll forming process. Moreover, appropriate experimental tests were performed to validate the numerical results, which were obtained by the proposed model. The results showed that the hardening models and the variation of elastic modulus have significant impact on springback accuracy. The Yoshida-Uemori’s hardening represents more accurate prediction of the springback during the roll forming process when compared to isotropic hardening. Using the chord modulus to determine the reduction in elastic modulus gave more accurate results to predict springback when compared with the unloading and loading modulus to both hardening models.

Mechanical behavior of intact completely decomposed granite soils along multi-stage loading–unloading path

Completely decomposed granite (CDG) soils in Shenzhen, China are usually subjected to loading-unloading due to the demolition/reconstruction of buildings and excavation/backfilling of foundation pits during the rapid development of the city. To investigate the mechanical behavior including the failure mode of the CDG soils under loading-unloading, consolidated drained triaxial tests along multi-stage loading-unloading paths were carried out in this study. Four types of loading sequences with one, two, three, and four loading-unloading cycles, respectively, were applied to investigate the mechanical properties of the CDG soil. Test results show that, as the number of the loading-unloading cycles increased from one to four, the effective cohesion (c') increased from 45.4 to 63.6 kPa; however, the effective friction angle (φ') first increased from 22.0° to 27.1° and then decreased to 19.0°. These results are mainly related to the strain-hardening property of the CDG soil after compressed by a relatively low deviator stress in the first two cycles and the structural damage of the specimens caused by a higher deviator stress in the last two cycles. In addition, the secant modulus also increased in the first two cycles, but decreased in the last two cycles due to the aggravation of soil structural damage. However, the unloading modulus (Eur) decreased all the way from 162.9 to 22.7 MPa is attributed to the number of loading-unloading cycles and the different confining stresses applied in the tests. The unloading modulus was not only affected by the confining pressure and, more importantly, also affected by the accumulated structural damage of soils.

High-pressure compressibility and shear strength data for soils

Soil behaviour is often an important consideration in the design of protective systems for blast and impact threats, as the properties of a soil can greatly affect the impulse generated from buried explosive devices, or the ability of a soil-filled structure to resist ballistic threats. Numerical modelling of these events often relies on extrapolation from low-pressure experiments. To develop soil models that remain accurate at very high pressures there is a need for data on soil behaviour under these extreme conditions. This paper demonstrates the use of a high-pressure multi-axial test apparatus to provide compressibility and shear strength data for four dry sandy soils. One-dimensional compression experiments were performed to axial stresses of 800 MPa, where the effects of particle-size distribution were observed with respect to compressibility and bulk unloading modulus. Each soil followed a bilinear normal compression line (NCL): more uniform soils initially had higher compression indices, but all four NCLs began to converge at void ratios below e ≈ 0.3. The failure surface of a sand was characterized to mean effective stress [Formula: see text] > 400 MPa using reduced triaxial compression experiments, removing the need to rely on extrapolation from low-pressure data.

Study of Elastic Behavior of Alloyed Steel upon Cyclic Loading

To study the mechanical properties and elastic behaviour of Q&P steel, which is a type of advanced high strength steel, uniaxial tension and cyclic loading tests have been conducted. Scanning electron microscope (SEM), transmission electron microscope (TEM), and X-ray diffraction (XRD) tests have been conducted on deformed samples with different degrees of deformation to analyse the microscopic mechanisms of their change in elastic modulus. The results have been shown a significant growth in the elastic modulus of alloyed steel after the initial unloading, followed by a decrease in the elastic modulus with the increase in the degree of unloading. The unloading and reloading paths showed a clear nonlinearity and formed a closed loop. The unloading chord modulus also decreased gradually with the increase in a pre-strain. The results of SEM, TEM, and XRD have been shown that the phase transformation variation is the strongest during the early stage of plastic deformation, and then gradually decreases. Cyclic loading has promoted the transformation from austenite to martensite. Interactions of the residual stress, phase transformation, and dislocation movement affecting the change in elastic modulus are determined through this research.

Pile Side Resistance in Sands for the Unloading Effect and Modulus Degradation

A total of 36 groups of sand-concrete interface loading and unloading direct shear tests were used to analyze the mechanical properties of the pile side-soil interface. The test results show that the interface residual shear stress for the same applied normal stress tends to be constant for the rough sand-concrete interface. The initial shear modulus and peak shear stress of the interface both decrease with the degree of unloading and increase with the interface roughness. The maximum amount of interface shear dilatancy increases with the degree of unloading, and the maximum amount of interface shear shrinkage decreases with unloading for the same interface roughness. A pile side resistance-displacement model is established using the shear displacement method. The proposed function considers both the radial unloading effect and modulus degradation of soil around the pile. The effect of radial unloading and interface roughness on the degradation of the equivalent shear modulus is analyzed using a single fitting parameter b. Good agreement of the proposed model is confirmed by applying the direct shear tests of the 36 groups.

Mechanical characteristics of well cement under cyclic loading and its influence on the integrity of shale gas wellbores

This paper focuses on the effect of repeated loading and unloading conditions on cement sheaths during staged fracturing. Triaxial compression and cyclic loading/unloading tests were designed for cement at room temperature and elevated temperatures of 95 °C and 130 °C. Based on the mechanical characteristics of cyclic loading and unloading, in the staged fracturing simulation process, numerical simulation of the cement sheath in both shallow and deep formations was performed. The following observations were made. (1) The elastic modulus of the cement was high at room temperature but lower under 95 °C and 130 °C. However, the deformation performance was greatly improved at higher temperatures, showing significant mechanical properties of an elastoplastic material. (2) In the cyclic loading test, the residual strain of the cement increased as the number of cycles at room temperature increased, and the unloading secant modulus was larger than that of the initial loading segment. The cement cumulative residual strain was larger under a higher temperature, and there was a significant “rebound hysteresis” in the unloading curve; the unloading secant modulus value also increased. The numerical simulation of staged fracturing produced the following conclusions. (1) The cement sheath in the shallow formation undergoing fracturing was at risk of circumferential tensile failure, and the severity of tensile failure increased with an increasing number of fracturing stages. (2) The cement sheath in the deep formation was at risk of plastic failure under compression, and the cement sheath gradually entered the plastic yield state as the number of fracturing stages increased.

Cutting-induced end surface effect on compressive behaviour of aluminium foams

Three cutting methods, i.e. electrical discharge machining (EDM), band saw (BS) and water jet (WJ), were used to prepare cuboid samples of closed-cell aluminium Alporas foam. On the end surfaces of the prepared samples, local roughness of mesoscopic structural components (i.e. cell wall, node and facet) and global roughness for the entire cut surface were measured using confocal microscopy. Furthermore, quasi-static uniaxial compression tests were performed with intermittent unloading-reloading. In the initial stage of compression, the measured loading stiffness and unloading elastic modulus are highest, intermediate and lowest for the EDM-cut, BS-cut and WJ-cut samples, respectively. This difference in measured compressive properties has been correlated with the difference in end-surface roughness associated with different cutting methods. However, the peak and plateau of compressive stress and the unloading elastic modulus in the plateau stage are insensitive to cutting method. An analytical model has been developed to elucidate the observed compressive behaviour and shed light on the responsible mechanisms.

A Springback Prediction of 1.5 GPa Grade Steel in Roll Forming Process for Automotive Sill-Side Inner Component

Roll forming has been widely used to produce steel sheet with low formability such as Ultra High Strength Steel (UHSS). It allows the steel sheet to be formed through successive bending process into a desired shape which even cannot be formed by press brake forming. Although the process effectively improves the formability of UHSS, there still the remains accuracy issue such as springback, flair, bow and so on. Especially, springback of UHSS is one of the major challenges in roll forming process as much as press forming process. In this paper, the springback of 1.5 GPa grade steel in roll forming process was numerically investigated for automotive sill-side inner component. The material behavior was described by using the selected hardening models: isotropic hardening (Piecewise linear model), linear kinematic hardening (Prager model [6]), nonlinear kinematic hardening model (Yoshida-Uemori model [7]). A commercial software LS-DYNA was utilized for the analysis. Eighteen successive roll stages were modelled for the simulation. From the results, it was found that the springback prediction during roll forming process could be successfully achieved when the complicated material behaviors including Bauschinger effect, nonlinear transient hardening, and changeable unloading modulus are taken into account for the Finite Element (FE) simulation.

Anelasticity Influence of Wire Rope on the Calculation of Freight Ropeway Bearing Cable

The force-displacement data during loading and unloading process is obtained by wire rope stretch experiment, which includes 7 different diameters ropes. Based on the data, deformation curves of elastic extension are established. It is shown that the loading and unloading curves compose of the elastic hysteresis loop because the wire rope during unloading shows obvious anelasticity. Analysing the elastic deformation curve characteristics, the values of loading and unloading curve parameters are provided by fitting the experimental data. The loading elastic modulus is constant independent of initial load, and the unloading elastic modulus is non-linear which is related with the maximum load. The elastic modulus is applied to the calculation of freight ropeway bearing cable. Compared the result with the actual project data, it shows that the method considering the wire rope anelasticity can improve the precision of bearing cable calculation.

Contact line friction and surface tension effects on seismic attenuation and effective bulk moduli in rock with a partially saturated crack

ABSTRACTThe effect of surface phenomena occurring at the interfaces between immiscible fluids and a solid on the seismic attributes of partially saturated rocks has not yet been fully studied. Meanwhile, over the past two decades considerable progress has been made in the physics of wetting to understand effects such as contact line friction, contact line pinning, contact angle hysteresis, and equilibrium contact angle. In this paper, we developed a new rock physics model considering the aforementioned effects on seismic properties of the rock with a partially saturated plane‐strain crack. We demonstrated that for small wave‐induced stress perturbations, the contact line of the interface meniscus will remain pinned, while the meniscus will bulge and change its shape through the change of the contact angles. When the stress perturbation is larger than a critical value, the contact line will move with advancing or receding contact angle depending on the direction of contact line motion. A critical stress perturbation predicted by our model can be in the range of ∼102−104 Pa, that is typical for linear seismic waves. Our model predicts strong seismic attenuation in the case when the contact line is moving. When the contact line is pinned, the attenuation is negligibly small. Seismic attenuation is associated with the hysteresis of loading and unloading bulk moduli, predicted by our model. The hysteresis is large when the contact line is moving and negligibly small when the contact line is pinned. Furthermore, we demonstrate that the bulk modulus of the rock with a partially saturated crack depends also on the surface tension and on the contact angle hysteresis. These parameters are typically neglected during calculation of the effecting fluid moduli by applying different averaging techniques. We demonstrate that contact line friction may be a dominant seismic attenuation mechanism in the low frequency limit (<∼10 Hz) when capillary forces dominate over viscous forces during wave‐induced two‐phase fluid flow.