Stress Superposition Research Articles

Mechanical interactions between neighbouring roots during pullout tests

The quantification of root reinforcement function is important for landscape managers and engineers. The estimation of root mechanical reinforcement is often based on models that do not consider the potential interaction between neighbouring roots. Root-soil mechanical interactions related to the root spacing and bundle geometry remain unclear including potential effects on the reliability of the current models. The objective of this study is to quantify the mechanical interactions among neighbouring roots or roots networks using modelling approaches and pullout laboratory experiments. Based on simple geometrical characterization of individual root geometry, we calculated dissipation patterns of frictional root-soil interfacial stresses in radial and longitudinal directions. Considering simple superposition of shear stresses within the soil matrix, we quantified characteristic root densities at which the radial mechanical interactions influence global pullout behaviour of the root bundle both for branched and unbranched roots. Laboratory pullout tests on root bundles were carried out at root spacings of 15, 35 and 105 mm. In addition, we tested effects of non-parallel (crossing) root bundle geometry. We found no significant statistical differences in root pullout force for the different root spacing in parallel alignment of roots. Branches increase pullout force by 1.5 times. Moreover, the mean displacement at the pullout peak-force was 7.2 % of length for unbranched roots and about 4.1 % of length for branched roots. The model shows its potential comparing it with empirical results concerning the holes leaved by roots, according with the branch pattern. The study quantifies the influence of root spacing and arrangement geometry within a root bundle on its mechanical behaviour. The assumption of “non-interacting” neighbouring roots in root reinforcement methods is no longer valid for root spacing less than 15 mm and root reinforcement methods. Moreover crossing roots shown a statistical difference. This information is important for improved understanding root reinforcement mechanisms in steep hill slope and the interplay between anchoring /failure and root bundle pullout vs root breakage.

Application of time–temperature–stress superposition on creep of wood–plastic composites

Time–temperature–stress superposition principle (TTSSP) was widely applied in studies of viscoelastic properties of materials. It involves shifting curves at various conditions to construct master curves. To extend the application of this principle, a temperature–stress hybrid shift factor and a modified Williams–Landel–Ferry (WLF) equation that incorporated variables of stress and temperature for the shift factor fitting were studied. A wood–plastic composite (WPC) was selected as the test subject to conduct a series of short-term creep tests. The results indicate that the WPC were rheologically simple materials and merely a horizontal shift was needed for the time–temperature superposition, whereas vertical shifting would be needed for time–stress superposition. The shift factor was independent of the stress for horizontal shifts in time–temperature superposition. In addition, the temperature- and stress-shift factors used to construct master curves were well fitted with the WLF equation. Furthermore, the parameters of the modified WLF equation were also successfully calibrated. The application of this method and equation can be extended to curve shifting that involves the effects of both temperature and stress simultaneously.

A nonlinear dynamic finite element approach for simulating muscular hydrostats

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney–Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton–Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

A ductile–brittle fracture model for material ductile damage in plastic deformation based on microvoid growth

The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. In this paper, a ductile–brittle fracture criterion derived from a microvoid mechanical model is proposed for microdamage and fracture of metallic material under large elastic–plastic deformation and has been proved to be effective in the analysis of metal forming process. Using this criterion, the analyses of microdamage and ductile–brittle fracture for tensile specimens in complex stress-states have been carried out. The results from these analyses on damage development and fracture are in good agreement with the experimental ones, and from microview point are reasonable for cracked specimens.

Accuracy of AISC Methods in Predicting Flexural Strength of Concrete-Encased Members

This paper investigated the accuracy of the AISC analysis methods in determining flexural strength of concrete-encased members. Analytical results from analyses performed using the AISC methods and a proposed method were compared with test data for 32 specimens. Results from this study showed that the method of superposition of elastic stresses and method of plastic stress distribution on the steel section alone overly underestimated flexural strength of the concrete encased composite members studied herein. On the other hand, the method of plasticstressdistributiononthecompositesection,themethodofstraincompatibility,andtheproposedmethodwellpredicted flexuralstrength of the encased composite members including members without shear anchors, suggesting that composite action can be developed in encased composite members without shear anchors when sufficient confinement is provided by transverse reinforcement. In addition, studies of effects oflongitudinalandtransversereinforcementon flexuralbehaviorofencasedcompositememberswereconductedtoidentifycrucialparameters. Theparametersexaminedhereinincludedreinforcementratio,steel flangearea,steelshapedepth,andtransversereinforcementspacing.Impli- cationsandrecommendationsdrawnfromthestudiesarediscussed.DOI:10.1061/(ASCE)ST.1943-541X.0000640.©2013American Society of Civil Engineers. CE Database subject headings: Flexural strength; Structural members; Stress distribution; Strain; Concrete. Author keywords: Flexural strength; Encased composite members; SRC; Plastic stress distribution; Strain compatibility.

Investigations on the material property changes of ultrasonic-vibration assisted aluminum alloy upsetting

Numerous studies have shown the benefit of ultrasonic-vibration assisted metal forming. This benefit include a reduction in forming forces, which might be attributed to the superposition of stress, increased temperatures, the effects of interface friction, and energy absorption of dislocation. This study conducts a series of experiments and analyses to investigate the main mechanisms of a reduction in forming forces during ultrasonic-vibration assisted A6061-T6 aluminum alloy upsetting.The findings of this research confirm that, under frictionless conditions, ultrasonic vibration still reduced forming forces, and ultrasonic vibration can increase the temperature of specimens and soften specimen surface during upsetting. From metallographic analyses and micro-hardness tests, the results reveal that energy absorption of dislocation was occurred during upsetting, which also contribute to the reduction of forming force.This research concludes that the mechanisms of increased temperatures and energy absorption of dislocation can affect the material property and make a reduction in forming forces; however, the interface friction effect has nothing to do with a reduction in forming forces.

Neutron diffraction investigations on residual stresses contributing to the fatigue crack growth in ferritic steel tubular bridges

Fatigue crack growth observed in tubular K-joint specimens, typical of tubular bridge structures, always initiates at the chord crown toe locations whether the applied stress range is tensile or compressive. Even though other locations around the weld have highest hot-spot stresses, chord crown toe locations are still the most critical. This raises the question about the relevant tensile residual stress level at that location. The results of residual stress investigations, obtained using neutron diffraction measurements highlight that the direction and location of the maximum tensile residual stresses in K-joints is substantially different from those in the more usual tubular butt joints. Indeed, it is shown that the highest tensile residual stresses are oriented perpendicular to the weld direction, which is also the main orientation of the loading stresses applied in K-joints. This paper demonstrates that it is the complex geometry of the K-joint that causes the superposition of critical stresses, making these joints susceptible to fatigue cracking. Therefore, transverse residual stresses play a crucial part in the fatigue crack growth behaviour that applied stresses alone cannot explain.

Internal Force Calculation Method of the Double-Curved Arch Bridge Reinforcement Based on Stress Superposition

Increasing the section method is the commonest method in double-curved arch bridge reinforcement. In order to research on the force condition of main arch ring in double-curved arch bridge reinforcement, we use internal force superposition method and stress superposition method to deduce the stress distribution of arch ring, and make contrastive analysis on each construction stage in bridge reinforcement. Internal force superposition method is unsafe; the stress superposition meets the actual situation.

The development of design guidelines for the application of formed-in-place gaskets

This technical feature discusses the dimensioning and design of formed-in-place gaskets – both anaerobic gaskets and silicone sealants. The differences between these two groups are highlighted using data from strength tests done to quantify the influence of different environmental factors. The effect of these factors, including temperature, layer thickness, superposition of assembly stress, and surface cleanliness and the material of the assembly parts, is also demonstrated. Finally, the resulting difference in flange design requirements for anaerobic gaskets and sealants is described.

Field Experiment Study on the Bearing Characteristics of Squeezed Branch Pile in Loess Area

The load-transferring mechanism under the action of vertical load and the role of bearing load by bearing disks in loess area were analyzed based on results of field static loading test of the squeezed branch piles. The results indicate that load transfer law of squeezed branch pile is transferred from top to bottom, and load of bearing disks is about 60 percent of the top load of the pile, stress superposition efficiency existed between bearing disks, and the minimum critical spacing of disks is 2D (D is the diameter of the bearing disk), the estimated bearing capacity of the squeezed branch pile is higher than the measured value.

On the prediction of initiation life for fatigue crack emanating from small cold expanded holes

The cold expansion method is an effective method widely used for retarding the initiation of the fatigue crack. In the present work, the finite element analysis is performed to determine the residual stress distribution around the cold expanded hole and the ɛ−N method is implemented to predict the fatigue crack initiation lives. The superposition of the mean stress is used to analyze the fatigue crack initiation. It is found that the effect of Kf, which decreases the Kt effect, must be taken into account for the small stop-hole. Estimates of the fatigue life quantities correlate well with the experimental results.

Delayed yielding in creep, time–stress superposition and effective time theory for a soft glass

In this work we investigate creep flow of aqueous suspension of Laponite, a model soft glassy material, at different aging times and stresses. We observe that this system shows time - aging time - stress superposition over a range of aging times and stresses when real time scale is transformed into effective time scale. Existence of superposition in an effective time domain facilitates prediction of long and very short time rheological behavior. Analysis of the observed behavior from effective time approach suggests that superposition is possible only when the shape of a relaxation time spectrum is preserved at various aging times and stresses. We also observe that creep curves at low aging times and greater stresses demonstrate delayed but sudden yielding. The critical time, at which material yields, increases with increase in aging time and decrease in stress. We argue that local rejuvenation of part of the glassy material causes variation in the rate of evolution of relaxation modes. The resulting interplay between aging and rejuvenating modes lead to delayed yielding as observed experimentally.

Optimum Arrangement of Prestressed Cables in Rock Anchorage

Prestressed cables in anchorage are usually arranged with equal length, and the rock's stability is weakened by tensile stress concentrating in the front end of the grouted portion. Besides, the construction of the prestressed cables is always difficult because of too small cable spacing. Based on the anchorage design used in the construction of the West River Bridge of New Nanning-Guangzhou Railway, the prestressed cable group were improved to be quincunx arrangement which is long cables alternating with short ones, so as to decrease the superposition of tensile stress. When anchorages bear the prestressed force and bridge construction loads, the change of rock slope's displacement and anchoring force were studied comparatively by three dimensional numerical simulation, which were carried on in two conditions, one is the prestressed cable group arranged with equal length while the other is quincunx. The research shows that, compared with the equal length arrangement, prestressed cable group adopting quincunx arrangement can further reduce the displacement of the rock slope, increase the short cable's anchoring force and save engineering costs while keep the rock anchorage system safely when bearing bridge construction loads.

Experimental Study of High-Frequency Vibration Assisted Micro/Mesoscale Forming of Metallic Materials

Micro/mesoscale forming is a promising technology for mass production of miniature metallic parts. However, fabrication of micro/mesoscale features leads to challenges due to the friction increase at the interface and tool wear from highly localized stress. In this study, the use of high-frequency vibration for potential application in micro/mesoscale forming has been investigated. A versatile experimental setup based on a magnetostrictive (Terfenol-D) actuator was built. Vibration assisted micro/mesoscale upsetting, pin extrusion and cup extrusion were conducted to understand the effects of workpiece size, excitation frequency, and the contact condition. Results showed a change in load reduction behavior that was dependent on the excitation frequency and the contact condition. The load reduction exhibited in this study can be explained by a combination of stress superposition and friction reduction. It was found that a higher excitation frequency and a less complicated die-specimen interface were more likely to result in a friction reduction by high-frequency vibration.

Prediction of the long-term behaviour of high modulus fibres using the stepped isostress method (SSM)

A new accelerated technique, called the stepped isostress method (SSM), is presented that allows accelerated testing of materials to determine their creep response, and in particular, their creep-rupture behaviour. The approach in SSM testing is similar to the more familiar stepped isothermal method (SIM) but the acceleration is now obtained by increasing the stress in steps rather than stepping the temperature. Additional stress provides energy to the system in an analogue of the effect of heat in SIM. This method relies on the time–stress superposition concept. Various theories, assumptions and the different steps of the method are described in detail. This method is advantageous when compared with SIM because there is no need to use elevated temperatures, which may affect the chemical properties of the tested materials. The applicability of this method is investigated. The paper presents testing on Kevlar 49 yarns using SSM. The resulting creep curves and rupture times are compared with those obtained from SIM and conventional creep testing carried out in the past. The results show good correlation between the three test methods. The ability to carry out reliable creep tests in a reasonable time at low stress levels allows a designer to have much more confidence in the data for creep-rupture behaviour for fibres and allows confident prediction of structural lifetimes.

Generation and growth of nanocracks near blunt cracks in nanocrystalline solids

Abstract A theoretical model is suggested which describes generation and growth of nanoscale cracks (nanocracks) near tips of blunt cracks in nanocrystalline solids. Within the model, stress concentration near pre-existent/growing blunt cracks induces grain boundary sliding which leads to formation of dislocations at triple junctions of grain boundaries. The superposition of the external stress concentrated near tips of blunt cracks and stresses created by these dislocations is capable of initiating generation and growth of nanocracks. The characteristics of the nanocrack generation and growth in nanocrystalline Al and α-Fe are calculated, and the effects of these processes on toughness/ductility of nanocrystalline solids are discussed.

Influence of Surface Treatments on Fretting Fatigue Life Prediction in TA15

The objective of this work was to evaluate life prediction methodologies involving fretting fatigue of TA15 materials with advanced surface treatments. Fretting fatigue tests were performed on TA15 specimens with and without advanced surface treatments. Laser shock processing and low plasticity burnishing have been shown to produce deep compressive residual stresses with relatively little cold work. Testing showed these advanced surface treatments improved fretting fatigue strength by approximately 50 %. This work presents a mechanics based lifing analysis of these tests that takes into account the local plasticity and the redistribution of residual stresses due to the contact loading. The use of superposition of the residual stresses into the contact stress analysis results in unconservative crack growth life predictions. Finite element analyses were conducted to predict the redistribution of residual stresses due to the contact loading. The redistributed residual stresses were used to make improved crack growth life predictions when possible. The results showed very little redistribution of residual stresses for the advanced surface treatments.

Stiffness and strength aspects in the design of automotive coil springs for McPherson front suspensions: a case study

The current paper deals with the elastic and stress analysis of a side-load spring, which is employed in cars belonging to the medium segment of the European automotive market. In the design of this kind of spring both the elastic characteristics and the fatigue strength have to be considered as significant aspects. Side-load springs, indeed, have a thrust axis which results in skew with respect to the damper axis; for this reason they are widely employed in front McPherson automotive suspensions in order to minimize the side force acting on the strut damper, which is responsible for the undesired damper-sticking phenomenon. In addition to this particular elastic property, as a consequence of the research effort in reducing the mass of components typical of the automotive industry, these springs have to face very high working stresses. The structural reliability of the spring must therefore be ensured by high residual stresses, which are induced by presetting and shot peening treatment at the end of the manufacturing process. The evolution of the thrust axis during suspension travel was analysed by a finite element (FE) model of the spring–seats assembly, built starting from a three-dimensional (3D) scan of the spring. In addition an experimental campaign was planned in order to measure the residual stresses at several points along the spring by X-ray diffraction. The actual stresses were then obtained as the superposition of those produced by the external loads, computed by means of the FE model, and the measured residual stresses. The beneficial effect of residual stresses on the structural reliability is discussed with a theoretical fatigue analysis on the basis of different multiaxial criteria. A mechanism of residual stress generation, based on the superposition of stresses coming from presetting and shot peening, is also suggested with the aid of FE simulations.

An analysis of the measurement principle of smart brackets for 3D force and moment monitoring in orthodontics

Measuring the three-dimensional (3D) force–moment ( F/ M) systems applied for correcting tooth malposition is highly desirable for accurate spatial control of tooth movement and for reducing traumatic side effects such as irreversible root resorption. To date, suitable tools for monitoring the applied F/ M system during therapy are lacking. We have previously introduced a true-scale orthodontic bracket with an integrated microelectronic stress sensor system for 3D F/ M measurements on individual teeth with a perspective for clinical application. The underlying theoretical concept assumes a linear correlation between externally applied F/ M systems and mechanical stresses induced within the smart bracket. However, in combined applications of F/ M components the actual wire-bracket contacts may differ from those caused by separate applications of corresponding individual F/ M components, thus violating the principle of linear superposition of mechanical stresses. This study systematically evaluates this aspect using finite element (FE) simulations and measurements with a real smart bracket. The FE analysis indicated that variability in the wire-bracket contacts is a major source for measurement errors. By taking the critical F/ M combinations into account in the calibration of the real smart bracket, we were able to reduce the mean measurement error in five of the six F/ M components to values <0.12 N and <0.04 N cm. Bucco-lingually directed forces still showed mean errors up to 0.21 N. Improving the force measurement accuracy and integrating components for telemetric energy and data transfer are the next steps towards clinical application of intelligent orthodontic appliances based on smart brackets.

The theoretical strength of fcc crystals under multiaxial loading

Atomistic modeling of a special triaxial loading of six perfect fcc crystals is performed by means of pseudopotential density functional method. The triaxial stress state is simulated as a superposition of axial pressure and transverse biaxial stresses. The transverse stresses are treated as adjustable parameters and their influence on the theoretical compressive strength is evaluated for the 〈100〉 and the 〈111〉 crystallographic orientations of the loading axis. The obtained results revealed that the compressive strengths are increasing linear functions of the transverse compressive stresses. On the other hand, the tensile transverse stresses lower the compressive strength. This implies that the compressive strengths of individual crystals approach a zero value when some critical (characteristic) levels of tensile biaxial stresses are reached. These stresses are then considered to be the theoretical tensile biaxial strengths.