Strain Limit Research Articles

Experimental study on influence of ultrasonic vibration on forming limit

Applying ultrasonic vibration in sheet metal forming can change its forming mechanism and improve its formability. The uniaxial tensile and bulging forming limit experimental setups were designed to study the ultrasonic vibration and forming limit relationship induced by ultrasonic excitation, and the results under different experimental conditions were analyzed. It was found that ultrasonic vibration has different effects on the left and right sides of forming limit diagram (FLD). Under the same ultrasonic vibration frequency, the maximum increment of left and right major limit strain is about 9.3% and 8.7%, respectively. The former is larger than the latter, and the strain increment increases with the increase of ultrasonic vibration frequency, but the basic shapes of FLD are unchanged.

Development of bending limit strain and stress curves of bendability prediction for assembling automotive body panels

Development of bending limit strain and stress curves of bendability prediction for assembling automotive body panels

Integrated Design of Structure and Material of Epoxy Asphalt Mixture Used in Steel Bridge Deck Pavement

To comprehensively investigate the integrated structural and material design of the epoxy asphalt mixture used in steel bridge deck pavement, the following works have been conducted: 1. The strain level of steel bridge deck pavement was calculated; 2. The ultimate strain level of fatigue endurance for epoxy asphalt concrete was measured; 3. The effect of water tightness of epoxy asphalt mixture on the bonding performance of steel plate interface was tested. 4. For better performance evaluation, quantitative analysis of the anti-skid performance of epoxy asphalt mixture was carried out by testing the structure depth using a laser texture tester. Results show the following findings: 1. The fatigue endurance limit strain level of epoxy asphalt mixture (600 με) was higher than that of the steel bridge deck pavement (<300 με), indicating that the use of epoxy asphalt concrete has better flexibility and can achieve a longer service life in theory; 2. The epoxy asphalt concrete has significant water tightness to protect the steel plate interface from corrosion and ensure good bonding performance; 3. The porosity of epoxy asphalt mixture used in steel bridge deck paving should be controlled within 3%; 4. In terms of anti-skid performance of bridge deck pavement, the FAC-10 graded epoxy asphalt mixture is recommended when compared with EA-10C.

Cryogenic formability of a solution-treated aluminum alloy sheet at low temperatures

• A newly-designed digital image correlation (DIC) testing device at cryogenic temperatures was developed. • The cryogenic FLDs and FLSDs of the solution-treated Al-Cu-Mn alloy sheet were experimentally obtained. • The cryogenic FLD and FLSD ductile fracture models were determined to predict the drawing limits of the Al-Cu-Mn alloy sheet. In this paper, the analysis of the necking and limit strains of a solution-treated aluminum alloy sheet at extreme low temperatures is performed using a newly-designed test apparatus equipped with the digital image correlation (DIC) device. The forming limit diagram (FLD) and forming limit stress diagram (FLSD) ductile fracture models were used to predict the drawing limit and fracture resistance capacity of an Al-Cu-Mn alloy sheet under complex stress at room temperature (RT) and -160 °C. It was found that the FLD 0 value at -196 °C increased to 0.32 as compared to 0.23 at RT. The Al-Cu-Mn alloy sheets at -160 °C and -196 °C were found to have significantly higher limit strains than those at RT. The drawing height and limit major strain at the round corner of the cryogenic deep-drawn cups were found to be increased by 21.3 % and 9.7 %, respectively, as compared to those at RT. Moreover, a larger necking amount and higher fracture resistance of the Al-Cu-Mn alloy sheet could be achieved during cryogenic deformations. The obtained cryogenic FLDs and FLSDs can be used to accurately predict the damage evolution and failure occurrence for the forming of complex-shaped aluminum alloy components at low temperatures.

Microwave-assisted hydrothermal synthesis of a high-voltage microcube LiMn1.5Ni0.5O4−δ spinel cathode material

• High-quality LiMn 1.5 Ni 0.5 O 4−δ was synthesized by microwave-assisted hydrothermal method. • Microwave-treated LiMn 1.5 Ni 0.5 O 4−δ offers higher battery performance than LiMn 2 O 4. • Microwave irradiation modulates content of Mn 3+ and O vacancy improving performance. • Material with longer irradiation shows higher discharge capacity but less stability. • Improving intrinsic stability is required before practical use in Li-ion batteries. Electric vehicles (EVs) require high operating voltages as well as high-capacity batteries. One candidate material that has received a great deal of attention is the nickel-substituted “high-voltage” spinel LiMn 1.5 Ni 0.5 O 4 , which offers the advantages of both higher capacity and higher operating voltage than spinel LiMn 2 O 4 . These features, along with the relatively benign constituent elements, have made this material a top choice for the next generation of high-power batteries. In this study, LiMn 1.5 Ni 0.5 O 4−δ materials were synthesized by a microwave-assisted hydrothermal method. Analyses show that microwave irradiation enables the tuning of the Mn 3+ concentration, which is related to the degree of disorder and enhances the electrochemical performance. However, with increasing synthesis time, the material limit of the elastic strain was exceeded, and the structure became morphologically unstable, which deteriorated the electrochemical performance. Thus, further efforts are necessary to improve its intrinsic stability. The LiMn 1.5 Ni 0.5 O 4−δ cathode active material may be suitable for the rapid charging of electric vehicle batteries.

Controllable rectification on the irreversible strain limit of 2G HTS coated conductors

The second generation high-temperature superconducting coated conductors (CCs) have excellent electrical and mechanical properties, and are extensively used in superconducting devices such as fault current limiters, magnets and motors. During the operation of these superconducting devices, superconducting CCs inevitably bear the combination of electromagnetic force and thermal mismatch stress, resulting in straining of YBa2Cu3O7− δ (YBCO) layer along the tape length. It is well known that the strains of superconducting CCs cause degradation of critical current (I c). Generally, the irreversible strain limit () is used to characterize the phenomenon that I c of superconducting CCs degrades with axial strain. When the axial strain of superconducting CCs is less than , I c can be reversibly recovered by over 99% after being unloaded. Therefore, is a key parameter for the design and application of superconducting CC devices. For this reason, to carry out a practical engineering method for improving of superconducting CCs has become a challenge and aroused interests among researchers. This study is based on the idea of precompression. A 316LN stainless steel tape was pretensioned at 77 K to improve its elastic strain limit. Then, two superconducting CCs were soldered onto both surfaces of pretensioned stainless steel tape respectively. As a result, of the superconducting CCs can be controlled manually with different precompressions. Taking YBCO CCs produced by SuperPower Inc. as an example, the measurement results show that the of the YBCO CCs increased from 0.39% to 0.73%. Meanwhile, the thickness of the sample did not increase more than once.

Modeling the anisotropic plasticity and damage of AA7075 alloy in hot forming

The theory of unified visco-plastic damage constitutive equations has been frequently used to model the thermal flow behavior and damage evolution of various materials. But the anisotropic properties of materials were generally neglected in the previous studies. In this paper, a novel damage correction formula was proposed, which was expressed as a function of loading path and loading direction and used as a multiplier of a continuum damage model. By integrating a set of unified visco-plastic damage constitutive equations, the Yld2004-18p criterion and the damage correction formula, an improved anisotropic damage constitutive model was established. Anisotropic plasticity and anisotropic damage of AA7075 alloy under hot forming conditions can be properly modeled by this model. Material constants included in the three integrated functions were determined respectively based on different experimental data. The calibrated model is capable to accurately predict the forming limit curves of AA7075 alloy for different forming temperatures, strain rates and loading directions. The model was then numerically implemented in hot Nakajima simulations. The simulation results were evaluated comprehensively from the aspects of limit strain point, punch force- displacement curve, major strain field and fracture position. For further verification of the established model, hot forming simulation of a B-pillar was conducted and compared with a real B-pillar of AA7075 alloy fabricated via an industrial hot stamping process. It is concluded the anisotropic damage constitutive model can be numerically applied to accurately predict the plastic deformation and damage-induced fracture of AA7075 alloy under hot forming conditions.

New experimental approach to accelerate the development of internal swelling reactions (ISR) in massive concrete structures

Internal Swellings Reactions (ISR) are pathologies that are likely to degrade concrete by causing swelling, cracking and major disorders in structures. Many laboratory studies of internal swelling reactions are realized on relatively small size samples. Those laboratory samples do not allow to replicate real conditions to which the real concrete is submitted in its environment, in terms of aging kinetics, ionic transport, early age thermal history and mechanical conditions especially in massive structures. Therefore, an experimental approach to accelerate internal swelling reactions of concrete at the structure scale is developed to allow better observation and understanding of swelling reactions at a massive structure scale. Two representative massive concrete structures (2.4 × 1.4 × 1 m3) were realized under controlled and optimized conditions for the development of alkali-silica reaction (ASR) and delayed ettringite formation (DEF). An instrumentation system is developed thus allowing to monitor evolutions of the pathologies in the massive structures both internally and externally. The respective deformations and cracking were tracked for over 3 years. Results show different swelling kinetics and amplitudes among the mock-ups and allow validating the proposed approach. Expansions in massive structures vary greatly from analogous laboratory samples. Boundary conditions and confinement effects could hinder swelling along certain directions thus compensated by a higher expansion along unstressed directions which leads to an anisotropic behavior in the material and impacts the cracking orientation. Residual swelling tests reveal the chemical potential of the internal swelling reactions and define an upper strain limit for the structure. They reveal as well a scale effect on the reactional kinetics and on the swelling amplitude.

Improvement of energy damage index bounds for circular reinforced concrete bridge piers under dynamic analysis

AbstractAn improvement of energy damage index bounds for circular reinforced concrete (RC) bridge piers under dynamic time history analysis is presented in this study. The energy‐based damage model has been defined as a ratio of hysteresis dissipation energy to input energy for performance evaluation of circular RC bridge pier systems. Based on the energy balance equation, the mentioned damage model can consider all energy aspects, including kinematic energy, strain energy, hysteresis energy, damping energy, and input energy. Additionally, the effect of ground motion duration, amplitude, and frequency content is appropriately considered in this damage model. For this purpose, the damage limit state bounds for two empirical RC bridge piers are statistically evaluated under the 22 far‐field ground motion sets of FEMA‐P695 for simulation of strong‐earthquake motion and consideration of record‐to‐record variability. First of all, appropriate validation between empirical and numerical fiber element models is implemented to estimate accurate results. Then, damage data at each performance level through strain limit states are collected by developing energy incremental dynamic analysis curves. Statistical results on collected damage data are presented in all performance levels to determine damage index bounds by the convolution of fragility curve distribution. Hence, five damage index bounds at five performance‐level are suggested, including very slight, slight, moderate, extensive, and complete damage. Finally, the effect of the other damping ratios on the modified energy damage model is carried out by using the beta coefficient in the formula. In the end, the modified energy damage model is compared with other damage indices to investigate the efficiency of the proposed damage model.

Experimental Study On the Critical Current of CORC Cable Under Cyclic Bending-straightening

To develop the application potential of conductor on round core (CORC) cables in the next generation of fusion magnets and accelerator magnets, fully automatic mechanized winding technology is required for the long CORC cables manufacturing. Meanwhile, the manufacturing and usage of the CORC cable are both limited by the strain sensitivity of the wound ReBCO tape on the CORC cable, because the processes may cause the superconducting layer of the ReBCO tape damaged when the strain limit is exceeded. The strains can arise from the manufacturing, bending, cooling, and operation of the cable and magnet, especially for the needed cyclic bending-straightening procedure for a long and multilayer cable winding layer by layer. Thus in this manuscript, a 1-m-long 12-layer CORC cable was manufactured to study the influence of cyclic bending on the critical current carrying performance of the CORC cable. It is consisted of 28 ReBCO tapes from Fujikura with 4 mm width and 0.05mm substrate thickness. The central core has an outer diameter of 3.85 mm. The cyclic bending-straightening experiment was conducted with a bending diameter of 900 mm and 700 mm, the Ic was tested at 77 K and self-field. After the cyclic bending test, the sample was bended to a diameter of 95 mm, which is planned to be used for the following insert solenoid coil, and has been verified no influence on the critical current carrying performance if bended without cyclic bending-straightening treatment. The results show that the required diameter for the reel experiencing cyclic bending-straightening procedure for ReBCO cable winding is suggested to be larger than 700 mm, especially for the equipment used for multilayer cables winding.

Influence of geometric and material nonlinearities on the behaviour and design of stainless steel frames

Material nonlinearity affects the stiffness and consequently the distribution of internal forces and moments in indeterminate structures. This has a direct impact on their behaviour and design, particularly in the case of stainless steel, where material nonlinearity initiates at relatively low stress levels. A method for accounting for the influence of material nonlinearity in stainless steel frames, including making due allowance for the resulting amplified second order effects, is presented herein. Proposals have been developed for austenitic, duplex and ferritic stainless steels. The method was derived based on benchmark results calculated through second order inelastic analysis with strain limits, defined by the Continuous Strength Method, using beam finite element models. A comprehensive set of frames was modelled and the proposed assessment of second order effects in the plastic regime was also verified against the results of four full-scale stainless steel frame tests. The proposed method is due to be included in the upcoming revision to Eurocode 3 Part 1.4

Experimental study on a new method to forecasting goaf pressure based key strata deformation detected using optic fiber sensors

The spatial distribution of rock mass stress in goaf seriously affects the stable operation of underground reservoir. Measurement of stress distribution in the goaf of coal mines is difficult due to the complex internal environment and other restrictive conditions of goaf. This paper presents a new method of monitoring the deformation of key stratum in overburden by optical fiber sensing, and then characterizing the pressure of goaf. The internal mechanism of key stratum breakage and the variation of goaf stress is investigated by physical model with the geometric dimension of 3 (length) × 1.3 (height) × 0.4 (width) m), in which the Brillouin Optical Time Domain Analysis (BOTDA) fiber-optic sensing technology and Fiber Bragg Grating (FBG) technology are used to monitor the stability of key stratum and the non-contact Digital Image Correlation (DIC) technique is employed to provide real-time deformation measurements. Combining the fracture mechanics model of key strata with the parabolic function model of subsidence trajectory, the stress evolution model of coal seam mining space is established for the first time, the goaf pressure change and the corresponding relation between the key layer breakage was quantitatively characterized. The research results show that: The fracture location of the key strata is consistent with the peak stress location of the goaf. The breaking limit strain threshold value of the key strata based on optical fiber sensing detection is 4000 με. Through the inversion of optical fiber monitoring results, the fracture degree and range of overburden rock in goaf are obtained, thus reflecting the position and change of the peak pressure in goaf. The consistency between key layer deformation and goaf pressure variation is verified.

Out-of-plane stability design of steel beams by second-order inelastic analysis with strain limits

An accurate and consistent approach to the out-of-plane stability design of steel beams and structures utilising second-order inelastic analysis with strain limits is proposed. The method is implemented using computationally efficient beam elements, with the ultimate structural resistance defined either by (i) the ultimate load factor or (ii) the load factor at which a strain limit, determined on the basis of the continuous strength method (CSM), is attained, whichever occurs first. Thus far, the method has been established for the in-plane design of steel structures and structural components; in the present paper, its scope is extended, for the first time to the scenarios in which out-of-plane stability effects, with a focus on lateral–torsional buckling (LTB), govern. The accuracy and safety of the method are assessed against the results of nonlinear shell finite element (FE) modelling. It is shown that the proposed method consistently provides more accurate results than the traditional LTB design method of prEN 1993-1-1. In addition to its accuracy, the proposed approach also streamlines the design process by eliminating the need for cross-section classification and member design checks.

Developing Mix Proportions for Class C Fly Ash-Based Alkali-Activated 3D-Printed Concrete Mixtures

This study investigated the use of class C fly ash (FA) as a precursor for alkali-activated mortar (AAM) for 3D-printed concrete (3DPC). AAMs with different water-to-FA (W/FA), alkaline activator-to-FA (Alk/FA), and sodium silicate-to-sodium hydroxide (SS/SH) ratios were examined to develop mixtures that can be tailored for different structural applications of 3DPC. The fresh properties, including extrudability and buildability, were evaluated through the open time (OT) and immediate deformation tests, respectively. Different cycle times (CTs) were applied to achieve a strain limit state necessary to maintain the printed shape. The strength of AAMs in different directions at different CTs was examined. Scanning electron microscopy (SEM) was carried out on AAM specimens having different CTs for a better understanding of the bond area. OTs ranging from 2.5 min to 31 min and axial strains ranging from 0.17% to 11.2% were achieved depending on the proportions of the AAMs and CT, which offers flexibility in optimizing the speed of printing and strength of concrete for different projects. The 3DPC specimens displayed anisotropic behavior compared with full-height specimens, where the compressive strength of full-height specimens was higher by 0.2% to 18% and 0.9% to 28% than 3DPC specimens when tested parallel and normal to the printing directions, respectively. SEM images and line scan indicated an approximately even intensity of the element concentration at the interfacial zones of AAMs having short CTs, which explained the relatively high compressive strength of those specimens. For AAMs having long CTs, there was a significant change in the intensity of the element concentration at the interfacial bond zone, and voids were observed resulting in low compressive strength of those specimens.

Determination of Strain Limits for Dimensioning Polyurethane Components.

Within the scope of this contribution, a method for the determination of a strain limit for designing components made of elastomeric polyurethane systems is presented. The knowledge of a material-specific strain limit is essential for the structural-mechanical calculation of plastic components in the context of component design. Compared to a commonly used component design, based on a simplified dimensioning approach taking only linear viscoelastic deformations into account, the strain limit determined in this study allows an improved utilisation of lightweight construction potential in the dimensioning of technical components made of polyurethanes through the consideration of permissible nonlinear viscoelastic deformations. The test method comprises a sequence of quasi-static loading and unloading cycles, with a subsequent load-free recovery phase, allowing the relaxation of the viscoelastic forces. Standardised tensile and simple shear test specimens and a dynamic mechanical thermal analyser (DMTA) are used within the tests. The strain limit is determined by means of the so-called residual energy ratio, which is a characteristic quantity for the evaluation of hystereses of load–unload cycles. These hystereses are increasingly formed by deformations outside the range of linear viscoelastic deformations. The residual energy ratio relates the proportion of deformation energy recovered during unloading to the deformation work that is applied. In this contribution, the residual energy ratio is successfully used to detect a significant evolution of loss energy under increasing load and to correlate this transition to a characteristic strain. The latter is used as a dimensioning parameter for the design of components made of elastomeric polyurethane materials for quasi-static load cases. The determination of this strain limit is performed under consideration of the criterion of reversibility of deformation.

High-temperature superconducting CORC® wires with record-breaking axial tensile strain tolerance present a breakthrough for high-field magnets

Cuprate high-temperature superconductors (HTS), such as RE-Ba2Cu3O7−δ (REBCO, RE = rare earth), (Bi,Pb)2Sr2Ca2Cu3O10−x and Bi2Sr2CaCu2O8−x , have enabled the development of high-field superconducting magnets capable of generating magnetic fields far exceeding 20 T. The brittle nature of HTS requires elaborate means to protect them against the high stresses and strains associated with high-field magnet operation, and so far, has prevented reliable high-field HTS magnets from becoming a reality. Here we report a more than tenfold increase in the irreversible strain limit under axial tension (ϵ irr) to over 7% in optimized high-current conductor on round core (CORC®) conductors, compared to the REBCO tapes from which the CORC® conductor is wound. Minimizing the tape winding pitch of the helical wind mechanically decouples the brittle REBCO film from the overall conductor. The REBCO tapes behave as springs, limiting the rate at which applied strain is transferred to the ceramic film. In addition, high-strength alloy cores allow the critical stress (ϵ crit) under axial tension at which initial degradation of CORC® conductors occurs to exceed 600 MPa, making them one of the strongest superconductors available. Mechanically decoupling the ceramic REBCO films from the overall CORC® conductor allows effective protection against the high operating stresses in high-field magnets. This breakthrough presents a monumental shift for HTS magnet technology, bringing reliable high-field superconducting magnets for compact fusion machines, the next generation of particle accelerators, and 40–60 T research solenoids within reach.

Ultimate strain capacity assessment of local buckling of pipelines with kinked dents subjected to bending loads

A dent is a typical defect found in oil and gas pipelines and poses a significant threat to their safety and integrity. In this study, the buckling behavior and limit strain capacity of pipelines with kinked dents under bending moment loads were investigated. First, four-point bending tests of full-scale pipelines with kinked dents were conducted in a laboratory, and the critical buckling load and strain response of the pipelines during buckling failure were tested. The test results revealed that the existence of kinked dents, specifically those with large depths, could weaken the bending resistance of the pipelines. During the buckling process of the pipeline, a considerable compressive strain was generated at the bottom center of the dent, which was considerably higher than the strain value at the corresponding position of the intact pipeline. However, the strain at both axial sides of the dent gradually changed from compressive strain at the initial bending stage to tensile strain after buckling failure. Then, nonlinear finite element (FE) models of buckling failure for pipelines with kinked dents under bending moment loads were developed, and the reliability of the FE models was verified through comparison with the test results. In addition, a parametric sensitivity study was conducted to determine the effect of parameters, such as dent depth, dent angle, diameter-to-thickness ratio of the pipe, and yield ratio of the pipe steel, on the compressive strain capacity of the pipeline. Finally, based on a large number of FE simulation results, a model for predicting the buckling compressive strain capacity of pipelines with kinked dents was developed, which can be used for evaluating buckling instability failure of pipelines with kinked dents subjected to bending moment loads.

The Effect of Steel Strength on the Behavior of a K‐Joint in a Slim‐floor Truss

AbstractThis paper studies the applicability of the strain‐limit criterion in the Eurocode 3 to defining the limit load for a K‐type truss joint, which connects two tubular braces to a plate chord. The joint is used in a novel Finnish slim‐floor system with integrated load‐bearing members of High‐Strength Steel (HSS). The Finite‐Element Model (FEM) of the joint is validated by the experimental results of scaled‐down, isolated joint specimens made of S420 and S700 steel. The validated FEM is used to study the failure of the joint and the effect of steel strength on the failure mode. For the specific geometry of this joint, the criterion based on the 5% strain limit proposed by the Eurocode 3 was found to be well justified for the steel grades S235 and S355 and reasonably applicable to the steel grades S460 and S550. However, the results indicated that the value of 5% for the strain limit was too large, if the joint was made of the S690 steel grade.

Partial shear diagram of slim‐floor beams

AbstractSlim‐floor beams which have the steel sections fully or partially integrated into the concrete slab lead to a significant reduction of the construction height. Due to its flat lower surface, it provides favourable solution for technical installation. According to EN1994‐1‐1, for composite beams plastic moment resistance is assumed. In the case of slim‐floor sections, due to the reduced construction height by the integration of the steel beam in the concrete and its extended bottom flange, a large compression zone height may be expected, thus concrete failure in the compression zone may happen before reaching the plastic moment resistance Mpl,Rd. Here, strain limit resistance becomes decisive. For design with partial shear connection, EN1994‐1‐1 provides the partial shear diagram based on the plastic bending resistance Mpl,Rd which is not always suitable for slim‐floor beams. Based on strain limited method, the more suitable partial shear diagram of different slim‐floor beams can be developed. From parametric studies of different types of slim‐floor beams, the impacts of critical parameters on the design are highlighted, and the limitations of the current plastic resistance based partial shear diagram are suggested. A simplified calculation method for situation beyond the limitation are also proposed to guarantee an economical design of those beams.

Nematic liquid crystalline elastomers are aeolotropic materials.

Continuum models describing ideal nematic solids are widely used in theoretical studies of liquid crystal elastomers. However, experiments on nematic elastomers show a type of anisotropic response that is not predicted by the ideal models. Therefore, their description requires an additional term coupling elastic and nematic responses, to account for aeolotropic effects. In order to better understand the observed elastic response of liquid crystal elastomers, we analyse theoretically and computationally different stretch and shear deformations. We then compare the elastic moduli in the infinitesimal elastic strain limit obtained from the molecular dynamics simulations with the ones derived theoretically, and show that they are better explained by including nematic order effects within the continuum framework.