Step Loading Conditions Research Articles

Numerical Simulation of Physical Properties of Coal Sample Under Step Loading Conditions

Numerical Simulation of Physical Properties of Coal Sample Under Step Loading Conditions

Experimental study of anchor bolt stress evaluation with hybrid optical fiber monitoring

The evaluation of mechanical properties of bolts is crucial for ensuring the long-term stability and continuous maintenance of underground engineering. Current research prioritizes the development of highly adaptable bolt mechanical behavior monitoring methods. By utilizing bolts with embedded sensors, the working status and surrounding environment can be monitored without affecting the original support structure, enabling effective disaster prevention monitoring. In this study, we introduce an innovative hybrid monitoring system based on strain gauges, Fiber Bragg Gratings (FBG), and Brillouin Optical Time Domain Analysis (BOTDA). A specialized dynamometer with temperature compensation is employed to collect axial force data under step loading conditions. We compare the sensing characteristics of various methods and derive the strain transmission coefficients of fiber sensors at different distances. The results demonstrate that the FBG and BOTDA accurately reflect the magnitude and change patterns of the monitored parameters, highlighting the potential application of this novel system for bolt monitoring. This work proposes a unique fiber optic temperature compensator and strain transmission coefficient analysis method to promote the evaluation quality of anchor bolt stress behaviors, which would provide realistic significance to enhance the accuracy and reliability of bolt mechanical property evaluation in underground engineering.

Creep damage model of rock with varying-parameter under the step loading and unloading conditions

The creep characteristics of rock under step loading and unloading conditions were investigated in this study. Based on the generalized Burgers model, the total strain of rock was decomposed into elastic, viscoelastic, varying-parameter viscoelastic, and viscoplastic strains considering the damage. The four strains were connected in series to establish a new varying-parameter creep damage model that can characterize the creep characteristics of rock under step loading and unloading conditions as well as identify and verify the model parameters. The study results showed that the varying-parameter creep damage model could better describe the creep characteristics of rock under step loading and unloading conditions, significantly the non-linear both the strain and time of attenuation creep and accelerated creep. The model fitting curve was highly consistent with the experimental data, and the correlation coefficient R2 was greater than 0.98, which thoroughly verified the accuracy and rationality of the model. These findings can provide theoretical support for analyzing the deformation and long-term stability of rock and soil.

Research on viscoelastic behavior of semi‐crystalline polymers using instrumented indentation

AbstractIn this study, the viscoelastic behavior of a polyamide 12 (PA12) polymer was evaluated using instrumented indentation technology based on a rheological model. The creep compliance and retardation spectra were obtained to analyze the viscoelastic response during the holding stage according to the rheological model under different preloading conditions. The results showed that the viscoelastic responses were independent of the indentation depth or load under step loading conditions. However, the creep compliance increases, and the peak intensity of the retardation spectrum decreases with a decrease in the preloading rate owing to the structural relaxation observed during the preloading stage under ramp loading conditions. Furthermore, softening dispersion can be completed during the loading stage under continuous stiffness measurement (CSM) conditions. As the preloading strain rate changes, the peak of the retardation spectrum gradually decreases until it disappears completely. Moreover, studies on indentation creep using the CSM method are challenging because of the complicated viscoelastic response observed during the preloading stage.

Evaluation of crack opening phenomenon using subset-optimized digital image correlation

This paper presents crack opening phenomenon evaluation using digital image correlation (DIC) with a statistically optimized subset size. In conventional DIC analysis, the subset sizes varying from several pixels to more than hundred pixels have been often selected by experts' subjective judgement based on conventional subset size determination algorithms. Since these conventional subset size determination algorithms, however, calculate speckle pattern features at a certain location of a single target image, it is difficult to consider not only all speckle pattern features within region of interest (ROI) but also the random measurement noises during the digital image acquisition process. To overcome the technical limitation, a statistical optimization algorithm of the subset size, which calculates the optimal subset size by the 3-loop iteration of normalized cross correlation within the entire ROI, is newly proposed. In addition, the optimal subset-based DIC analysis is applied to crack opening phenomenon evaluation in a mock-up concrete specimen under step loading conditions. The validation test results show 3.6 μm maximum error compared with the ground truth which is obtained by direct measurement, while a conventional subset size determination algorithm-based DIC analysis produces the maximum error of 62.7 μm.

Robust ceramic based self-lubricating coating on Al–Si alloys prepared via PEO and spin-coating methods

Ceramic based self-lubricating coating was successfully fabricated on Al-based plasma electrolytic oxidation (PEO) ceramic coating in this work. The coating was reinforced with thermosetting polyimide (PI) containing tungsten disulfide (WS2) fillers. The morphology, chemical composition and phase structure of the PEO, PEO/PI and PEO/PI/WS2 coatings were observed by SEM, EDS and XRD, respectively. Tribological properties of the coatings were comparatively investigated using a reciprocating pin-on-block tribotester under different conditions. Under dry sliding conditions, the friction coefficient of PEO/PI/WS2 coating was about 0.4, which was 50% lower than that of PEO coating. Meanwhile, the wear rate of counter pin cooperated with PEO/PI/WS2 coating was only 0.04 mg min−1, which was 90.9% lower than that of PEO coating. Under step loading conditions, the load was ultimately increased to 70 N and the total duration time was about 35 min, while the corresponding values of PEO coating were 30 N and 13 min, respectively. These are owed to the hard ceramic coating and the soft self-lubricating coating, which can improve the load capacity and decrease the friction, of the ceramic based self-lubricating coating.

Considerations about the choice of layerwise and through-thickness global functions of 3-D physically-based zig-zag theories

A generalization of physically-based fixed degrees of freedom 3-D zig-zag theories is developed, which allows for any arbitrary choice of layerwise and representation functions. Thereby users can choose arbitrarily the representation case-by-case. This paper aims to prove that the choice of global and layerwise functions is immaterial whenever coefficients are recalculated exactly (via symbolic calculus) by the enforcement of interfacial stress continuity, boundary conditions and equilibrium in point form, as prescribed by the elasticity theory. Vice versa, accuracy of theories partially fulfilling constraints will prove to largely depend on the assumptions made and to be inadequate when strong layerwise effects rise, under distributed/localized step loading and boundary conditions other than simply supported edges (tests carried out in closed-form). The present and previous authors’ theories are tested with the aim to understand in which cases an adequate level of accuracy is still achieved by lower-order theories that are derived as particularizations.

Local ratcheting assessment of steel samples undergoing various step and block loading conditions

Ratcheting response of notched SS316 samples was examined under various loading steps and blocks. Asymmetric stress cycles following various loading blocks of Low-High-High (LHH) and High-Low-Low (HLL) sequences were applied on steel plates with notch sizes of 5, 9 and 12 mm. Local strains were measured through strain gauges mounted at the vicinity of circular notch roots. Nominal ratcheting was found to gradually progress up to a saturation limit at which ratcheting magnitude and rate stayed unchanged. Over applied cyclic loads from the first block to the 100th, local ratcheting data have shown highest rate of progress between blocks 1 and 5. Local ratcheting data at the last step of blocks 1–5 have shown an overlap reflecting a constraint induced due to evolution of plastic zone at the vicinity of notch root. The Ahmadzadeh-Varvani (A-V) kinematic hardening rule was coupled with the Neuber’s rule to assess ratcheting at the notch root of steel samples. This framework enabled to predict local ratcheting over loading steps and blocks as asymmetric stress cycles were nominally applied. Local ratcheting curves predicted by the coupled framework were compared with those simulated through finite element method (FEM) through use of ABAQUS software and on the basis of Chaboche kinematic hardening model. The coupled framework showed a closer agreement with experimental data over loading steps and blocks than those simulated through FEM. Computed ratcheting curves were yet to address imbricating ratcheting curves over last steps of loading blocks in a manner similar to those of measured data.

Uniaxial Ratcheting Assessment of 304 Stainless Steel Samples Undergoing Step-Loading Conditions at Room and Elevated Temperatures

AbstractThe present study evaluates ratcheting response of 304 stainless steel samples subjected to various step-loading conditions at room and elevated temperatures using the kinematic hardening rules of Ohno–Wang (O–W), AbdelKarim–Ohno (AK–O), and Ahmadzadeh–Varvani (A–V). The hardening rules were employed along with the visco-plastic flow rule to account for the time-dependent response of 304 stainless steel samples. Ratcheting over low–high–low loading sequences consistently showed a small drop in ratcheting strain over the third loading step. This is mainly due to plastic strain accumulation over the first two loading steps preventing ratcheting strain to drop significantly with a drop in the mean stress. Moreover, dynamic recovery terms in these models were further modified through the inclusion of an exponential function developed by Kang to address the dynamic strain aging phenomenon. Low ratcheting rate and shakedown shortly after a few stress cycles within loading steps as operating temperatures varied between 400 and 600 °C were attributed to dynamic strain aging phenomenon in SS304 steel alloy. Progressive ratcheting response and their stress–strain hysteresis loops were highly influenced at various operating temperatures, stress levels, and stress rates. Coefficients in the dynamic recovery term of the A–V model controlled ratcheting progress and hysteresis loops agreeable with those of experimental data over consecutive loading steps. Choices of material constants and the number of segments defined from stress–strain curve based on the O–W and AK–O models noticeably influenced the ratcheting response of steel samples. Predicted ratcheting values by means of the A–V, O–W, and AK–O models were discussed and compared with those of the experimental data.

Viscoplastic Ratcheting Response of Materials under Step-Loading Conditions at Various Cyclic Stress Levels

The present study intends to assess ratcheting response of rate-dependent SS316L, SS316L(N), and 63Sn37Pb alloys under various step-loading conditions at room temperature through use of the Ahmadzadeh-Varvani (A-V) model developed based on a viscoplastic flow rule. The choice of viscoplastic description enabled the model to control plastic strain increments over loading progress at various stress rates. Predicted ratcheting over asymmetric loading cycles and multi-step cycles was influenced by cyclic stress levels, stress rates, and sequence of loading steps. Predicted ratcheting in steel samples SS316L and SS316L(N) over the second loading step in Low-High and High-Low loading sequences was primarily influenced with the stress amplitude in the second step. Multi-step-loading sequences High-Low-High and Low-High-Low in solder samples revealed how noticeable the impact of mean stress on ratcheting is. Predicted ratcheting values by means of the A-V model closely agreed with experimental data of alloys examined in this study.

Elastostatic assessment of several mixed/displacement-based laminated plate theories, differently accounting for transverse normal deformability

Several multilayered physically-based plate theories are derived under different limiting assumptions on displacement, strain and stress fields, either in displacement-based or mixed Hu-Washizu and Helinger-Reissner form, and assuming different layerwise functions. Their features are reminiscent to those of theories published in the literature, or are entirely new. The present study aims to evaluate how different forms of description of the transverse normal deformation and stress affect accuracy. At the same time, the purpose is also to see if a much broader degree of generalization of what characterizing currently available physically-based zig-zag theories can be achieved through a redefinition of coefficients obtained by imposing the fulfillment of physical constraints, namely interfacial stress compatibility and local equilibrium equations across the thickness through use of symbolic calculus tool. Besides calculating exactly quantities, this tool enables users to choose representation form and zig-zag functions as desired, keeping fixed the d.o.f. to five. Challenging benchmarks with strong layerwise effects are considered, for which an accurate description of the transverse normal deformation effect is important. They include distributed/localized step loading and different boundary conditions. Effects of constraint stresses at supports are accounted for. Numerical results show that whenever the whole set of physical constraints is enforced across the thickness to redefine coefficients, the choice of the representation form and of zig-zag functions is immaterial and more importantly, accurate results are obtained with few variables and a low expansion order of solutions. Otherwise results are sensitive to the choices made.

Experimental study on dynamic voltage uniformity of a 2-kW air-cooled PEMFC

The existing kW-class air-cooled proton exchange membrane fuel cells (PEMFC) usually control the exhaust valve and fan according to the manufacturer’s recommendations of the purge interval and the optimum temperature, respectively. However, the single-cell voltage and its uniformity under dynamic working conditions are not considered. Nonetheless, single-cell voltage and its uniformity are important factors that reflect and affect the performance and lifetime of the stack. Therefore, it is necessary to investigate the dynamic uniformity of the single-cell voltages under conventional control mode. Based on a self-built 2-kW air-cooled PEMFC test platform, this paper investigated the voltage responses and the single cell dynamic voltage uniformity for PEMFC under dynamic working conditions. For the step loading and unloading conditions, it was observed that the larger the step amplitude, the greater the voltage overshoot or undershoot, the greater the volatility of the single-cell voltage, and the longer the time to restore stability. In particular, large step loading at small currents and large step unloading at high currents can seriously damage single-cell voltages and their uniformity. In addition, large step unloading at high currents has a greater negative impact on the cell voltage than large step loading. For a continuous loading or unloading situation with a constant slope, dynamic variable loading experiments with different frequencies and amplitudes were designed to reach a specified current from different initial currents. It was observed that with an increase in the loading and unloading amplitude and frequency, the uniformity of single-cell voltage becomes worse. However, the effect of ramp loading is greater than that of ramp unloading. Finally, based on these experimental results, dynamic variable loading suggestions involving the voltage uniformity were proposed, which have certain guiding significance and reference value for the practical applications of kW-class air-cooled PEMFC.

Characterizing the Viscoelastic Properties of Hydrogel Thin Films by Bulge Test

In this work, we carried out bulge test for quantifying the viscoelastic properties of poly (vinyl alcohol) (PVA) thin films with custom-developed apparatus. A viscoelastic bulge deformation (VBD) model based on the elasticity–viscoelasticity correspondence principle and spherical cap equation is established to describe the bulge deformation of polymeric thin films. The VBD model can be used to determine the time-dependent modulus by bulge test for polymeric films. Uniaxial compressive relaxation test and PRONY series fitting method are used to define the constitutive parameters of the VBD equations. We presented two types of VBD models in frequency domain under linear loading and step loading conditions. Through inverse Laplace transformation, the proposed VBD model can effectively predict the bulge deformation of PVA hydrogel thin film. Numerical simulations are also conducted to validate the VBD model under step loading conditions. This work provides a methodology to characterize the viscoelastic properties of polymeric films by bulge test.

Ratcheting of 304 stainless steel under multiaxial step-loading conditions

The present study predicts ratcheting response of 304 tubular stainless steel samples undergoing multiaxial step-loading histories by means of nonlinear kinematic hardening rules of Ohno–Wang (O–W), Chen–Jiao–Kim (C–J–K) and the modified rule on the basis of Ahmadzadeh–Varvani (A–V) model. The plastic strain increment, dε¯p, and the backstress unity vector a¯/|a¯| as components in the MaCaulay brackets enabled the modified rule to track different ratcheting directions over multiaxial loading. Term (2−n¯⋅a¯/|a¯|) further regulated coefficient γ2 to account the effect of non-proportionality. The modified rule held term to prevent the model experiencing plastic shakedown.Predicted ratcheting results by means of O–W model showed deviation from experimental data. Chen–Jiao–Kim modified the O–W model and possessed lower ratcheting results as compared with those of predicted by the O–W. The hardening rules enabled to assess ratcheting in different directions as loading steps possessed high–low sequence in the second and third steps. The choice of hardening rule to assess ratcheting of steel samples was found very much dependent on complexities involved with ratcheting algorithms, their constitutive equations and framework, coefficients, and Central Processing Unit (CPU) time required to run ratcheting programs over loading steps.

Study of the effects of damage accumulation on wear

Numerous wear equations based on distinct models to predict the wear, are available in the literature. However, most of these models require properties that usually are not easy to obtain, and simple models derived from the Archard equation remain the main base to use in practical situations, by engineers and designers, to predict product life. This equation predicts that wear is a linear function of sliding distance and load, which agrees with several real cases. One important aspect that is neglected in laboratory, in the evaluation of wear rates, is that the tests performed under conditions of uniform contact do not reflect what very often happens with equipments that have operating regimes that can vary from periodic or random and change those contact conditions. Because the additivity is a property of linear functions, this work aims to discuss the application of the additivity property to the Archard equation. A pin-on-disc technique was used to test a hard steel 100Cr6 sphere against a gray cast iron disc. These materials were selected to minimize the adhesion wear component. Different contact conditions, namely normal loads and sliding distances, were investigated to establish a linear basic equation to test as a model to take into account the accumulation of damage resulting from the step loading conditions studied, applying successive different blocks of load. Friction was measured along the experiments and an energetic model was discussed as an alternative way to model the wear. At the end of the tests SEM observations were used to evaluate the wear mechanisms based on the wear scar morphologies.

Structural behaviour and deformation patterns in loaded plain concrete ground‐supported slabs

AbstractThe work presented in this paper is considered to be an attempt to contribute towards a better understanding of the structural behaviour of plain concrete slabs under step loading conditions. The Concrete Society Technical Report TR34 “Concrete Industrial Ground Floors” is in its 3rd edition (2003) and is currently under review. TR34 covers the design of concrete ground‐supported slabs containing fibres, both steel and synthetic, as an alternative to mesh reinforcement. This work reports on tests carried out at different critical loading locations, including the centre, edges and corners of a 6.0 × 6.0 × 0.15 m deep plain concrete slab. The test results are compared with theoretical values derived using available design codes and other information sources. The results show a notable difference between the test results and the theoretical values.

Models for dynamic evaluation of mudstone/shale cap rocks and their applications in the Lower Paleozoic sequences, Sichuan Basin, SW China

The estimation of the sealing capability of cap rocks dynamically is one of the fundamental geological problems that must be resolved in petroleum exploration. In this paper, a porosity–capillary pressure (ϕ–Pc) method was used to estimate the sealing capacity during cap rock burial and a permeability–capillary pressure (K–Pc) plus over-consolidation ratio (OCR) method to estimate the sealing capacity during uplift. Based on 120 capillary pressure–porosity measurements, a ϕ–Pc mathematical model has been established for the burial phase. By analyzing the permeability data measured from 12 mudstone/shale samples from different stratigraphic intervals under step loading conditions, a permeability–confining pressure (K–P) mathematical model has been constructed. Moreover, capillary pressure–permeability data measured from 141 mudstone or shale cap rocks have been used to establish a K–Pc mathematical model for seal capacity evaluation during uplift. Additionally, the OCR of mudstone or shale was calculated from the results of reconstructed burial and uplift histories. These mathematical models were used in case studies in the Sichuan Basin, South China. The results indicate that capillary pressure (Pc) is inadequate in evaluating sealing capacity of cap rocks but the combination of parameters Pc and OCR works well. The agreement between calculated and measured values shows the effectiveness and reliability of the models for dynamic estimation of the sealing capacity of mudstone/shale cap rocks established in this study.

Ratcheting assessment of steel alloys under step-loading conditions

The present study examines the capability of a recently modified hardening rule to characterize ratcheting response of materials subjected to multi-step uniaxial stress cycles. The modified hardening rule was developed based on Armstrong–Frederick (A–F) hardening rule through implementing new ratcheting rate dependent coefficients γ2 and δ. These coefficients were estimated by means of calibrated curves for any given stress levels defined from the uniaxial single-step ratcheting response at various cyclic stress levels. At a constant mean stress, ratcheting strain progressively increased as stress amplitude over steps of loading history increased. Similar response was also evident for step-loading with constant stress amplitude while the values of mean stress increased. For high–low histories, the trend of predicted ratcheting strain from higher to lower magnitudes found agreeable with that of experimental data. The discrepancy of the predicted and experimentally ratcheting strain values in the high–low step loading however was due to constancy in the shape and size of translating yield surface in the modified kinematic hardening rule. The modified hardening rule was employed to assess ratcheting response of SS316L, SA333, SS316L(N) and 1070 steel alloys under various step-loading conditions. Predicted ratcheting data at various stress level were found in good agreements as compared with the experimental ratcheting strains.

Mechanical behaviour of a steel fibre reinforced concrete ground slab

Concrete ground slabs are essential components of modern buildings and structures. This common structural element has been used in great numbers in buildings and structures of various forms and sizes throughout the world for decades. The utilisation of fibre reinforced concrete for ground slab purposes has gained significant momentum in recent years. The third edition of report TR34, published by the UK Concrete Society in 2003, has paid attention to the design of concrete ground slabs with significant emphasis on the use of steel and synthetic fibres as an alternative to fabric reinforcement. TR34 is currently under review and this paper attempts to contribute towards a better understanding of the mechanical behaviour of steel fibre reinforced concrete slabs under step loading conditions. This work reports on tests carried out at different locations (centre, edges and corners) of a 6·0 × 6·0 × 0·15 m steel fibre reinforced concrete slab. A significant difference was found between the test results and theoretical values derived using available design codes.

Poroviscoelastic Two-Dimensional Anisotropic Solution with Application to Articular Cartilage Testing

The transverse anisotropic poromechanics solution for the two-dimensional Mandel-type problem geometry is extended in this paper to account for the orthotropic nature of the porous media, thus mimicking the response of articular cartilage samples when subjected to load perturbation. The anisotropic solution presented takes into account the viscoelastic and anisotropic nature of the fluid-saturated cartilage specimen sandwiched between two impermeable rigid plates and subjected to quasi-static step loading conditions; thus simulating the unconfined compressive test responses of cartilage samples in biomechanics laboratory setups. The solution addresses the stress, fluid pressure, and displacement results due to load application through exact modeling of the intrinsic nature of the orthotropic viscoelastic matrix structure as well as the compressible interstitial fluid flow responses. Poromechanical parameter characterization and modeling of biological tissues, such as cartilage, will find this analytical solution to the two-dimensional anisotropic poroviscoelastic geometry very useful. This problem will not only serve as a benchmark for validating numerical schemes and simulations but also assist in calibrating laboratory results on biological tissues, including cyclic loadings.