Constant External Load Research Articles

Damage indicators evolution during cyclic loading of composite plate with hole

Novel experimental method, which provides quantitative description of damage indicators evolution caused by fatigue loading of composite specimens with stress concentrators, was developed. Damage parameters are derived as deformation response to artificial notch inserting. This notch is extended from the edge of central through hole in plane rectangular specimen under constant external load. Current values of damage indicators are obtained at different stages of fatigue loading. These data reveal dependencies of required parameters on loading cycle number. The damage accumulation function for involved cycle range is quantitatively constructed on this base. It is found that this function is related to the first stage of the process investigated. The results obtained represent the essential link in the design of further experiments.

A novel method for investigating ice-substrate interfacial rheology and long-term adfreeze strength through loading-unloading creep test

Ice cementation and ice-substrate adfreeze force are the primary contributors to the high bearing capacity of pile foundations in cold regions and the stability of frozen walls in areas subjected to artificial freezing. Given the significant temperature sensitivity of ice’s shear rheology, engineering structures in ice or ice-rich soils continue to deform even under constant external loads. A thorough understanding of shear creep and the long-term adfreeze force at the ice-substrate interface is essential for predicting the continuous deformation of these structures. However, research into the shear creep behavior at frozen interfaces has historically been constrained by the precision of temperature control in experimental settings and the complexity of load paths in shear testing devices. In this study, a temperature- and stress-control device for interface shear creep is assembled firstly, and multilevel loading-unloading creep tests on steel pipes embedded in layered frozen ice were conducted. Through the decoupling of deformation progression, the viscoelastic and viscoplastic shear behaviors at the steel-ice interface under various temperatures and shear stresses were characterized, the principle of sustainable interfacial shear creep along with its underlying physical mechanism were proposed. Subsequently, with the aid of a modified nonlinear Burger model, various interfacial shear creep parameters were derived. Results reveal that the interfacial generalized shear modulus continuously improves but with a gradually weakening degree until a point of accelerating creep is reached. Additionally, the long-term adfreeze force is found to be less than half of the short-term strength, which significantly decreases as the temperature approaches the water phase transition zone. Interestingly, the stress exponent associated with the interfacial steady creep rate is considerably smaller than that predicted by Glen’s law. This research provides a theoretical basis instrumental in the engineering design in cold regions and those structures employing artificial freezing techniques.

Effect of Wear on Symmetric Hole-Entry Hybrid Journal Bearing Compensated by Orifice Restrictor Under Turbulent Regime

This study examines the impact of wear and turbulent flow on symmetric hole-entry hybrid journal bearings with orifice restrictors. Dufranes’s abrasive model for wear effect and Constantinescu’s lubrication model for turbulent flow have been used. A modification has been made to the Reynolds equationand utilized the finite element method to solvealong withflow equation of an orifice restrictor. For selected wear depth parameter values and Reynolds numbers,computed results have been acquired. The minimum fluid film thickness increases for worn bearings when operating under a turbulent regime rather than a laminar regime. Further, the stiffness coefficient decreases for constant external load when worn/unworn bearings function in a turbulent regime.

STABILITY OF RODS WITH INITIAL IMPERFECTIONS IN THE FORM OF ECCENTRICITY OF LOAD APPLICATION UNDER LINEAR AND NON-LINEAR CREEP CONDITIONS

Stability of a compressed rod having initial imperfections in the form of eccentricity of applied load under conditions of linear and nonlinear creep is considered. It is noted that all real elements have some initial imperfections in the form of technological deflections, eccentricities of applied loads, etc., so they begin to bulge from the very beginning of loading. Another important factor in stability theory is the consideration of material creep. In this regard, the loading process is divided into two phases: the instantaneous loading process and the creep phase under constant external load. Moreover, creep can be time-limited or unrestricted. In the paper formulas for determination of critical forces of stability loss of the rod having initial imperfections, under short-term and long-term action of load are obtained. The equation allowing to determine time of the first crack appearance is derived. Derived are equations the roots of which are loads at action of which the first cracks appear at initial moment of time and at arbitrarily long period of load action. Analysis of acting force determining the character of rod deformation is executed. From the constructed stability equation it is possible to determine the critical force corresponding to the critical length of the section with cracks. For similar problems in nonlinear formulation formulas for determining critical force and critical displacement corresponding to maximum load are obtained. For the case of long duration load the equation which establishes relationship between load and displacement is obtained. Equation for determination of critical force under prolonged action of load has been derived. It has been established that critical displacement is the same under short- and continuous action of load. It is shown that at any intermediate moment critical displacement can be achieved under load lying in certain interval. Keywords: stability, rod, initial imperfection, eccentricity, linear creep, non-linear creep, critical force, crack, critical displacement.

Responses of a Strongly Forced Mathieu Equation—Part 2: Constant Loading

AbstractThe present study deals with the response of a damped Mathieu equation with hard constant external loading. A second-order perturbation analysis using the method of multiple scales (MMS) unfolds resonances and stability. Non-resonant and low-frequency quasi-static responses are examined. Under constant loading, primary resonances are captured with a first-order analysis, but are accurately described with the second-order analysis. The response magnitude is of order ϵ0, where ϵ is the small bookkeeping parameter, but can become arbitrarily large due to a small denominator as the Mathieu system approaches the primary instability wedge. A superharmonic resonance of order two is unfolded with the second-order MMS. The magnitude of this response is of order ϵ and grows with the strength of parametric excitation squared. An nth-order multiple scales analysis under hard constant loading will indicate conditions of superharmonic resonances of order n. Subharmonic resonances do not produce a non-zero steady-state harmonic, but have the instability property known to the regular Mathieu equation. Analytical expressions for predicting the magnitude of responses are presented and compared with numerical results for a specific set of system parameters. In all cases, the second-order analysis accommodates slow time-scale effects, which enable responses of order ϵ or ϵ0. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric amplifiers.

Approximate coefficient of restitution for nonlinear viscoelastic contact with external load

We derive an approximate coefficient of restitution (CoR) for a single bead impacting the ground when a constant external load acts upon the colliding body. Some of the main applications concern classical nonlinear viscoelastic models such as the Kuwabara-Kono model, Simon-Hunt-Crossley model, and Hertzian stiffness with linear damping, however the proposed approach applies to a wide class of nonlinear viscoelastic contact models. It is shown that suitable expansions allow to derive a computable expression of the CoR which provides accurate predictions for a valuable range of external loads, viscosity coefficients and impact velocities.

A new approach for the prediction of fatigue life in rolling bearings based on damage accumulation theory considering residual stresses

Today, the service life calculation of rolling bearings is standardized in ISO 281, based on the theory of Lundberg and Palmgren. In the standard calculation method, material properties such as fatigue limit stress were taken into account by introducing the fatigue limit stress proposed by Ioannides and Harris. This standard calculation method provides a reasonable range of fatigue life in good agreement with experimental results under ideal test conditions such as constant external load. However, complex operating conditions of bearings such as varying loads and oscillating motion are not considered. Therefore, there is a need for a new analytical calculation model that can predict the fatigue life of rolling bearings operating under these complex conditions. This makes it possible to advance the application of rolling bearings and optimize their use in machines such as wind turbines. In the proposed approach, the fatigue life is determined based on the Palmgren-Miner linear damage rule, evaluating the subsurface stresses below the rolling contact using the S-N curve according to the fatigue criterion proposed by Lundberg and Palmgren. All rolling contacts that occur in an internal stress cycle due to the internal dynamic behavior during rotating operations are evaluated individually and referred to as partial damage risks. The partial damage risks are accumulated linearly according to the Palmgren-Miner theory to obtain the load cycle to failure. At this time, the loaded volume is assessed along the depth from the contact area to the core of the bearing ring, which makes it possible to indicate the depth position of fatigue occurrence in terms of crack initiation. The material properties such as the fatigue limit stress and the probability of failure are taken from the S-N curve itself. To consider the residual stress, a simple link concept is suggested by using the ratio of the maximum contact pressure to the yield criteria. The proposed approach can be extended to calculate oscillating fatigue life regarding the number of rolling contacts at a given oscillation amplitude. In this study, it can be confirmed that the analytically determined fatigue lifetime according to ISO 281 is still close to the bearing life test result. In addition, it shows that the results obtained using the proposed approach agree well with the calculation results obtained using ISO 281.

Generating Human Arm Kinematics Using Reinforcement Learning to Train Active Muscle Behavior in Automotive Research.

Computational human body models (HBMs) are important tools for predicting human biomechanical responses under automotive crash environments. In many scenarios, the prediction of the occupant response will be improved by incorporating active muscle control into the HBMs to generate biofidelic kinematics during different vehicle maneuvers. In this study, we have proposed an approach to develop an active muscle controller based on reinforcement learning (RL). The RL muscle activation control (RL-MAC) approach is a shift from using traditional closed-loop feedback controllers, which can mimic accurate active muscle behavior under a limited range of loading conditions for which the controller has been tuned. Conversely, the RL-MAC uses an iterative training approach to generate active muscle forces for desired joint motion and is analogous to how a child develops gross motor skills. In this study, the ability of a deep deterministic policy gradient (DDPG) RL controller to generate accurate human kinematics is demonstrated using a multibody model of the human arm. The arm model was trained to perform goal-directed elbow rotation by activating the responsible muscles and investigated using two recruitment schemes: as independent muscles or as antagonistic muscle groups. Simulations with the trained controller show that the arm can move to the target position in the presence or absence of externally applied loads. The RL-MAC trained under constant external loads was able to maintain the desired elbow joint angle under a simplified automotive impact scenario, implying the robustness of the motor control approach.

Mixed-lubrication analysis of misaligned journal bearing considering turbulence and cavitation

By integrating the average flow equation and Ng–Pan turbulence model using the boundary condition of mass conserving [Jakobsson-Floberg-Olsson (JFO)], a mixed lubrication model for misaligned bearing was established considering the effects of turbulence and cavitation. The numerical solution was obtained using a finite difference scheme. The results indicate that the frictional force and moment calculated using the JFO boundary condition are greater than those calculated using the Reynolds boundary condition under the constant external load. In high speed conditions, the turbulence begins to play a role, which makes the maximum oil film pressure and moment decrease and the minimum oil film thickness, cavitation zone, and friction coefficient increase. The boundary condition and turbulence have important effects on the equilibrium position of the axis. The misalignment leads to an obvious increase in the friction of the mixed lubrication area and a slight decrease in that of the hydrodynamic lubrication area.

Low-cycle fatigue damage accumulation near the cold-expanded hole by crack compliance data

Novel destructive method is implemented for quantitative assessment of fatigue damage accumulation in the stress concentration zone near the cold-expanded hole, which is characterized by residual stress influence. Damage accumulation is reached by preliminary push–pull loading of plane specimens with cold-expanded holes. Artificially introduced narrow notches, emanating from the hole edge at different stages of low-cycle fatigue, serve to manifest a damage level. Deformation response to local material removing is measured by electronic speckle pattern interferometry (ESPI) in terms of in-plane displacement components. Notches are inserted under constant external load to increase the measurement accuracy by reaching optimal fringe density. Normalized values of the notch mouth open displacement (NMOD), in-plane displacement component acting in the notch direction (U), the stress intensity factor (SIF), the T-stress and the biaxiality ratio are used as current damage indicator. Numerical integration of curves, describing an evolution of each fracture mechanics parameter, produces the damage accumulation function in an explicit form. It is established that all five fracture mechanics parameters give very close results. Developed approach is the essential link in predictable joints design to reach maximal beneficial effect of cold hole expansion on the fatigue life improvement of advanced aerospace structures.

Features of Thermomechanical Stability of Anionic-Cation Exchange Matrix "Polikon AC" on Viscose Non-Woven Materials.

The thermomechanical stability of the anion–cation exchange matrix “Polikon AC” on viscose nonwoven materials is investigated. In this work, a molecular model of a solvation environment for experimentally obtained “Polikon AC” mosaic membranes is refined. Mosaic membranes on a viscose fiber base were fabricated by the method of polycondensation filling. The temperature dependence of deformation was investigated for dry and wet anion and cation exchange membrane components at a constant tensile load of 1.5 N and a heating rate of 8 °C/min. The effect of moisture content on the deformation of anionite and cationite fragments under a constant external tensile load of 1.5 and 3 N in a temperature range up to 100 °C was studied.

Micromechanical modelling of the anisotropic creep behaviour of granular medium as a fourth-order fabric tensor

The main objective of the present work is to develop a micromechanics approach to predict the macroscopic anisotropic creep behaviour of granular media. To this end, the linear viscoelastic behaviour of the inter-particle interaction at contact is adopted, and the contact distribution is characterized by a fourth-order fabric tensor in the local scale. Then, fourth-order tensor fabric-based micromechanical approaches based on Voigt and Reuss localization assumptions are applied to granular media in the Laplace–Carson space. With help of the inverse Laplace–Carson transformation of these obtained models, the macroscopic anisotropic creep behaviour of granular media submitted to a constant external loading is examined. Finally, the obtained results by specializing the Burgers model into the obtained models are compared with the numerical simulations in the particle flow code (PFC2D) to illustrate the validation and the accuracy of the analytical models for the macroscopic anisotropic creep behaviour of granular media.

Crossover of Failure Time Distributions in a Model of Time-Dependent Fracture

An important question in the theory of fracture is what kind of lifetime distributions may exist for materials under load. Here, this is studied in the context of a one-dimensional fracture model with local load sharing under a constant external load, “creep.” Simulations of the system with Weibull distributed initial lifetimes for the elements show that the limiting distribution follows from extreme statistics and takes the Gumbel form eventually, with longer and longer crossovers in the system size from a Weibull-like distribution, depending on the initial Weibull exponent.

Evolution of fracture mechanics parameters relevant to narrow notch increment as a measure of fatigue damage accumulation

An unconventional destructive method for quantitative assessment of fatigue damage accumulation in the stress concentration zone is proposed and verified. Damage accumulation in strain gradient area is reached by preliminary push–pull loading of plane specimens with open holes. Narrow notches, emanating from the hole edge at different stages of low-cycle fatigue, serve to manifest a damage degree. These notches are inserted under constant external load. Deformation response to local material removing is measured by electronic speckle pattern interferometry (ESPI) in terms of in-plane displacement components. It is shown that normalized values of the notch mouth open displacement (NMOD), the stress intensity factor (SIF) and the T-stress can reliably be used as current damage parameter. Numerical integration of curves, describing an evolution of fracture mechanics parameters, produces the damage accumulation function in an explicit form. It is established that all three fracture mechanics parameters give close results.

Influence of stress ratio on residual stress evolution near cold-expanded hole due to low-cycle fatigue by crack compliance data

Modified version of the crack compliance method is used for determination of stress intensity factor (SIF) related to narrow notches emanating from cold-expanded holes. These notches are inserted at different stages of low-cycle fatigue under constant external load. It is shown how residual SIF values, generated by residual stress field influence, can be separated from total experimental SIF values. Residual SIF values, obtained at different stage of low-cycle fatigue with the same stress range Δσ = 350 MPa but different stress R = –0.4 and R = –1.0, provide quantitative description of residual stress evolution near cold-expanded hole. It shown that maximal residual stress relaxation of order 20 per cent occurs at 95 lifetime per cent for both loading programs.

Evolution of the fracture mechanics parameters in the vicinity of the hole in conditions of low-cycle fatigue according to the data of modeling a crack with narrow notches

We propose a new method for studying the effect of low-cycle fatigue on the evolution of the fracture mechanics parameters in conditions of loading plane specimens with stress concentrators. Three programs of loading with a constant value of the stress range and different values of the stress ratio, as well as two programs with a constant value of the stress ratio but different stress ranges are considered. One program is common for both cases. All the programs include uniaxial tension-compression. Each program was implemented by testing a batch of the same specimens from seven to nine in each. One specimen from each batch was assigned to assess the durability. The other specimens were brought to various stages of low-cycle fatigue in each program. Experimental data were obtained for cracks of different length which were modeled by a sequence of three narrow notches launched from a through hole in a rectangular specimen. Each notch was exposed to constant external load of the same level. The deformation response to a small increment in the notch length at a constant external load was measured at different stages of low-cycle fatigue using electronic speckle pattern interferometry. The interference fringe patterns used as initial experimental data provided determination of the tangential components of in-plane displacements directly on the notch sides and the values of notch opening were thus determined from the results of direct measurements. The transition from measured displacement components to the values of the stress intensity factor and T-stress was performed using the relationships of a modified version of the crack compliance method based on Williams formulation. Distributions of the fracture mechanics parameters along the notches were obtained at various stages of cyclic loading. The dependences of the crack mouth opening displacement, the stress intensity factor and the T -stress on the number of loading cycles are constructed for the notches of a fixed length at different stages of low-cycle fatigue. It is shown that experimental distributions of the stress intensity factor values over the life time practically coincide for all four combinations of the loading cycle parameters.

Shape Memory Polymer Foam with Programmable Apertures

In this work, a novel type of polyester urethane urea (PEUU) foam is introduced. The foam was produced by reactive foaming using a mixture of poly(1,10–decamethylene adipate) diol and poly(1,4–butylene adipate) diol, 4,4′-diphenylmethane diisocyanate, 1,4–butanediol, diethanolamine and water as blowing agent. As determined by differential scanning calorimetry, the melting of the ester-based phases occurred at temperatures in between 25 °C and 61 °C, while the crystallization transition spread from 48 °C to 20 °C. The mechanical properties of the foam were simulated with the hyperplastic models Neo-Hookean and Ogden, whereby the latter showed a better agreement with the experimental data as evidenced by a Pearson correlation coefficient R² above 0.99. Once thermomechanically treated, the foam exhibited a maximum actuation of 13.7% in heating-cooling cycles under a constant external load. In turn, thermal cycling under load-free conditions resulted in an actuation of more than 10%. Good thermal insulation properties were demonstrated by thermal conductivities of 0.039 W·(m·K)−1 in the pristine state and 0.052 W·(m·K)−1 in a state after compression by 50%, respectively. Finally, three demonstrators were developed, which closed an aperture or opened it again simply by changing the temperature. The self-sufficient material behavior is particularly promising in the construction industry, where programmable air slots offer the prospect of a dynamic insulation system for an adaptive building envelope.

A phenomenological constitutive model for semicrystalline two-way shape memory polymers

Recently, two-way shape memory effect (2W-SME) has been demonstrated in several types of shape memory polymers (SMPs). Unlike classical one-way shape memory effect (1W-SME), these polymers can switch back and forth repeatedly between two different shapes without subsequent programming procedure. The reversible actuation can be realized either under a constant external tensile load, which is referred to as quasi 2W-SME, or under zero load, which is referred to as true 2W-SME. Most recently, actuation under an external compressive load, which is referred to as advanced 2W-SME, has also been discovered. Test results have shown that semicrystalline 2W-SMPs exhibit 2W-SME in two distinct regions due to two different mechanisms: one is due to entropic elasticity above the crystallization temperature, and the other is due to melt/crystallization transition below the crystallization temperature. While several constitutive models have been developed over the years for semicrystalline 2W-SMPs, there is currently a lack of effort towards modeling the true and advanced 2W-SME within the two-mechanism framework. In this study, we developed a thermomechanical constitutive model which captured both the entropic elasticity and melt/crystallization events. The modeling results and test results show reasonable agreement. It is found that the model captured the three types of 2W-SMEs: quasi 2W-SME, true 2W-SME, and advanced 2W-SME. It is also found that proper tensile programming before the first thermomechanical cycle can make a semicrystalline SMP exhibit all the three types of 2W-SMEs. This study may serve as a design tool to enhance applications of semicrystalline 2W-SMPs in engineering structures and devices.

Performance of concrete-filled stainless steel tubular (CFSST) columns after exposure to fire

Abstract The post-fire performance of concrete-filled stainless steel tubular (CFSST) columns subjected to an entire loading–fire history, including four characteristic phases: (i) ambient temperature loading, (ii) heating, (iii) cooling with constant external loads, and (iv) post-fire loading, is investigated in this paper. Sequentially coupled thermal-stress analyses are performed using ABAQUS to establish the temperature field and structural response of CFSST columns. To improve the precision of the finite element analysis (FEA) models, the influence of moisture on the thermal conductivity and specific heat of the concrete in the heating and cooling phases is considered by using subroutines. Existing fire and post-fire test data on CFSST columns are used to validate the FEA modelling. Comparisons between FEA and test results indicate that the accuracy of the model is acceptable; the FEA model is then extended to simulate CFSST columns subjected to the four characteristic phases. The behaviour of the CFSST columns during the four characteristic phases is explained by analysis of the temperature distribution, load versus axial deformation relations, failure modes and internal force redistribution. The excellent post-fire performance of CFSST columns is examined in comparison with traditional concrete-filled carbon steel tubular (CFST) columns with the same total cross-sectional area. The residual strength index is studied with respect to a series of parametric analyses. It is found that the residual strength of CFSST columns is higher than that of CFST columns after the same fire exposure, and that the diameter of the stainless steel tube, slenderness, heating time ratio and load ratio have a significant influence on the residual strength index.

Creep behavior due to interface diffusion in unidirectional fiber-reinforced metal matrix composites under general loading conditions: a micromechanics analysis

In this paper, the creep behavior due to interface diffusion in unidirectional fiber-reinforced metal matrix composites under general transverse loading conditions is studied. A micromechanics model is adopted to estimate the average stresses in fibers, which is demonstrated to be of reasonable accuracy by comparing with finite element analysis. The creep deformation due to interface diffusion is characterized by a tensor-form creep strain rate, which is related to the components of average stress in fibers and possesses incompressibility. The derived creep strain tensor is then introduced into fibers as eigenstrain to estimate the effect of creep strain on stress redistribution in composites. Eventually, the macroscopic creep strain of composites under constant external loads and the stress relaxation at fixed displacements due to interface diffusion are calculated by the incremental creep analysis procedures based on the average field theory. The effects of loading conditions on the overall creep behavior are examined in detail. Results of this study show that under the fixed strain condition, the initial biaxial stress ratio actually varies rather than remains unchanged during the stress relaxation process. In both constant stress and constant strain conditions, stresses in fibers have a propensity to approach hydrostatic stress state, thus suppressing the interface diffusion. These findings were not reported in previous researches and may bring new understanding on diffusion-induced creep deformation in metal matrix composite materials.