Equivalent Stress-strain Relationship Research Articles

Axial compressive behaviour of ultra-high performance concrete filled steel tube stub columns at elevated temperatures

Ultra-high performance concrete (UHPC) has many advantages such as high strength, good plasticity and toughness, and excellent durability. However, it is more likely to experience explosive spalling at high temperatures than ordinary concrete due to its low porosity. The ultra-high performance concrete-filled steel tubes (UHPCFSTs), where steel tubes are placed outside of UHPC to reduce its high-temperature spalling, could be an effective structural type to make full use of the advantages of both steel and UHPC. Most of the existing fire protection design codes for concrete-filled steel tube structures are based on ordinary concrete, and the performance and failure mechanisms of UHPCFSTs under high temperatures are still unclear. On this basis, an experimental study on the axial compressive performance of UHPC filled circular steel tube stub columns at constant elevated temperatures was carried out. The effects of temperature, steel tube thickness and coarse aggregate content on the compressive properties and failure modes of UHPCFST members were analysed. The results have shown that the UHPCFST mainly suffered from the overall pier coarse type and drum type failure modes. The failure characteristics were highly influenced by temperature magnitude, and 400℃ was the critical temperature where the structural performance change significantly beyond this point. The constraint effect of the steel tube on UHPC increased with the increase of thickness of steel tube, but it would be weakened with the increase of temperature or the coarse aggregate content. Finally, based on the average temperature method, a formula for calculating the ultimate load bearing capacity and equivalent stress–strain relationship of an UHPCTST stub column under a constant high temperature was proposed.

Study on the Dynamic Mechanical Properties of Ultrahigh-Performance Concrete under Triaxial Constraints.

To confirm the effect of confining pressure on the dynamic mechanical behavior of ultrahigh-performance concrete (UHPC), this study used a true triaxial split Hopkinson pressure bar test system to perform dynamic compression tests on UHPC under triaxial constraints. The confining pressure range considered was 5~10 MPa, the strain rate range was 35~80 s-1, and the steel fiber contents were 0.5%, 1% and 2%. The three-dimensional dynamic engineering stress-strain relationship and equivalent stress-strain relationship of UHPC under different confining pressures and different strain rates were obtained and analyzed in detail. The results show that under the confinement condition, the dynamic peak axial stress-strain and dynamic peak lateral stress-strain of UHPC have strong sensitivity to the strain rate. In addition, the dynamic peak lateral stress-strain is more sensitive to the confining pressure than the dynamic axial stress. An empirical strength enhancement factor (DIFc) that considers the strain rate effect and confining pressure was derived, and the impact of the coupling between the enhancement caused by the confining pressure and the strain rate effect on the dynamic strength of the UHPC under triaxial confinement was discussed. A dynamic strength failure criterion for UHPC under triaxial constraint conditions was established.

Improvement of fracture assessment method for pipe girth weld based on failure assessment diagram

The increasing demand for oil and gas resources in China has promoted the rapid construction and development of oil and gas pipeline networks. With an increase in the mileage of high-grade pipeline, the intrinsic safety of pipeline girth weld faces serious challenges, and the existing fracture assessment methods have many shortcomings. The failure assessment diagram of the commonly used fracture assessment method in engineering is taken as the research object. Aiming at deficiency that it cannot accurately consider the strength matching characteristics of girth welds. Based on the failure assessment diagram theory and the equivalent stress-strain relationship method, the influence of crack size, pipeline diameter-thickness ratio, and material parameters on the fracture assessment accuracy of the girth weld is studied. The calculation method of optimized limit load and reference stress is established. Moreover, the improved fracture assessment process of pipeline girth weld is proposed, which makes up for the lack of conservative assessment results in traditional methods and improves the accuracy of fracture assessment girth weld under high-stress conditions.

Analysis of horizontal cyclic bearing capacity of pile based on cyclic strain wedge finite element strip method

This paper proposes a cyclic strain wedge finite element strip model to analyze of the cyclic bearing characteristics of pile foundation. First, the strain wedge body is meshed by every soil element, which can assign the stress-strain relationship to each soil element of the wedge body. Then, the equivalent substitution stress‒strain relationship of each wedge layer can be obtained from the stress‒strain relationship of the soil element by the principle of the stress‒strain equivalent substitution method. It can truly reflect the stress-strain relationship of the soil to the stress-strain relationship of the wedge layer and the p-y curve. At the same time, the equivalent cyclic creep constitutive of soil is applied to the strain wedge finite element strip model for the cyclic bearing characteristics of the wedge layer and the cyclic p‒y curve. Finally, the cyclic strain wedge finite element strip model is verified by some tests. The results from the proposed method agree reasonably well with the measured results. It can provide a new method for analyzing the horizontal cyclic bearing characteristics of pile.

A new design method of the equivalent stress–strain relationship for hybrid (FRP bar and steel bar) reinforced concrete beams

Hybrid reinforced concrete (hybrid-RC) beams consisting of fiber-reinforced polymer (FRP) bars and steel bars can provide high strength, serviceability, and durability. However, based on a review of the literature, the design methods for hybrid-RC beams fail to effectively predict the flexural failure mode of these structures. Therefore, an equivalent constitutive relationship is proposed, which considers the FRP bar and steel bar as a new material with a bilinear constitutive relationship. Two balanced reinforcement ratios were introduced in the design method, which can accurately predict the failure mode of both the hybrid-RC structure and FRP strengthened RC structure. The feasibility of the proposed method was then confirmed by experimental testing.

Modelling of stay cables with large earthquake-induced force variations in cable-stayed bridges

The present study proposes a practical yet reliable model for stay cables in cable-stayed bridges considering large force variation under seismic actions. The proposed model is capable of approximating the nonlinear equivalent stress-strain relationship of cables, taking into account the variation of equivalent modulus of cables during the earthquake as well as possible cable loosening. The cable performance based on the proposed method shows an overall good agreement with the actual response of cables. Then, the model is applied to a case cable-stayed bridge under seismic actions and the structural response is compared with the conventional method which models the cables with a constant equivalent modulus derived at dead load state. Comparing to the proposed model, the conventional method fails to accurately describe the cable force at the low stress level and shows discrepancies in time histories of the structural response in terms of amplitude and phase angle. Moreover, conventional method might lead to underestimation of the bending moment at the tower bottom and longitudinal displacement at deck end for most cases, resulting in unconservative seismic design. Such result highlights the importance of applying the proposed model in seismic design of cable-stayed bridges.

Experimental study on low-strength concrete joint core strengthened with steel meshes for connecting PFCC column and RC beam

This paper presented a new joint core strengthened with multi-layer steel meshes for connecting the PVC-FRP Confined Concrete (PFCC) column and Reinforce Concrete (RC) beam. Seven specimens were tested under concentric compression and the effects of several parameters including the height, diameter of specimen and volume ratio of steel mesh on the compressive behaviors were investigated. Test results showed that all the reinforcement yielded successively and eventually the crushing of the concrete dominated the failures of specimens. The ultimate bearing capacity and ultimate equivalent axial strain decreased as the height of specimen increased, while they increased as the diameter of specimen or the volume ratio of steel mesh increased. The ultimate strains of all the reinforcement and concrete increased as the height of specimen increased while they decreased as the diameter of specimen or the volume ratio of steel mesh increased. Considering the influence of height of specimen, a modified formula for conveniently predicting the ultimate bearing capacity of the joint core strengthened with steel meshes was proposed based on the theory of confined concrete and superposition principle of multiple confinement. The predicted results were in good agreement with the experimental data. Additionally, an equivalent stress–strain relationship model of the joint core strengthened with steel meshes was suggested based on the experimental research. The predicted curves agreed well with the measured equivalent stress–strain curves. Moreover, a validated Finite Element (FE) model for the joint core strengthened with steel meshes was developed to conduct parametric studies, which broadened the available experimental results about the mechanical performances of the joint.

Behavior of FRP-confined ultra-high performance concrete under eccentric compression

This paper presents an investigation on the eccentric compressive behavior of fiber-reinforced polymer (FRP)-confined ultra-high performance concrete (UHPC). Twenty specimens with varied tube thicknesses and loading eccentricities were tested. The results indicated that nearly all specimens showed a strain-hardening behavior, except that several specimens with a very large loading eccentricity showed a strain-softening behavior. With the increase of the loading eccentricities, the load-carrying capacity and deformability exhibited a substantial reduction, while the tube thickness only showed a significant effect in concentric or small eccentricity cases. A finite element model was established, where UHPC was treated as a two-phase material and simulated with UHPC matrix and explicitly modeled steel fibers. An equivalent stress–strain relationship derived from the single fiber pullout test was proposed for the embedded steel fibers to provide a more accurate prediction for the fiber–matrix interfacial behavior. Based on a regression analysis of the experimental and numerical results, a design equation was developed to predict the ultimate load-carrying capacity of FRP-confined UHPC under eccentric compression.

Local compressive behavior of joint core reinforced with ring beam for connection of polyvinyl chloride fiber‐reinforced polymer confined concrete column and reinforced concrete beam

AbstractIn this paper, seven specimens were designed to study the influence of the height (h), width (b), and reinforcement ratio (ρ) of ring beam on the failure mode, bearing capacity, deformation, and equivalent stress–strain relation of joint core reinforced with ring beam for connection of polyvinyl chloride fiber‐reinforced polymer confined concrete column and reinforced concrete beam. The experimental results indicated that the crushing of concrete in the joint core dominated the failure of specimens. The ultimate, yield bearing capacity and axial strain decreased with the increase of height, while raised with the improvement of width or reinforcement ratio. The growth of the strains of reinforcement and concrete accelerated with the increment of height, while decelerated with the rise of width or reinforcement ratio. Subsequently, based on the local compression theory, confined concrete theory, and the principle of superposition of multiple confinement, considering the influence coefficient of joint height βh and the enhancement coefficient of stirrups αs, a new formula was proposed to estimate the ultimate bearing capacity of specimens under axial local compression. Then, on the basis of Mander's model, taking the correction parameter η into consideration, a new model of equivalent stress–strain relationship was established. Verification results showed that the models proposed in this research agreed well with the experimental results.

Determination of Constitutive Relationships of Tubular Materials at Various Strain Rates Using Hydro-Bulging Experiments

Liquid impact forming (LIF) is a rapid tube hydroforming technique. The deformation behaviour of a metal tube may be different in LIF from that in tube hydroforming. A constitutive equation or equivalently an equivalent stress-strain relationship is generally used to describe the deformation behaviour of metals. The purpose of this work is to model the deformation behaviour of tubular materials in LIF using the Johnson-Cook (JC) structural model. LIF hydro-bulging experiments combined with the analytical approach based on the membrane theory and the force equilibrium equation were used to determine the model coefficients A, B, C, and n in the equations for SS304 stainless steel tubular materials. Finite element (FE) simulations of hydro-bulging under various impact velocities were carried out to validate the resultant JC model. The relationship between the strain rates and impact velocities was determined, the bulging heights between the equivalent stress-strain curves at different impact velocities were analysed, and the bulging heights obtained by FE simulations and experimental results were compared. The results show that the proposed approach using the JC model is suitable to define the stress-strain behaviour of tubular materials in LIF.

Fracture assessment of mismatched girth welds in oval-shaped clad pipes subjected to bending moment

This paper provides an engineering assessment of an oval-shaped clad pipes with a circumferential part-through surface crack subjected to bending moment based upon equivalent stress-strain relationship method (ESSRM) in conjunction with EPRI J-estimation procedure. Plastic limit load equations are developed specially to determine the equivalent stress-strain relationship of the welded clad pipe. Then, the conventional EPRI J-estimation procedure is extended to calculate J values of the equivalent configuration with oval cross-section converted from the welded clad pipe using the ESSRM. The validation of the ESSRM/EPRI estimation framework mentioned in the above is carried out by comparing with the results obtained from 3-D elastic-plastic finite element (FE) analysis.

Development of a strain based fracture assessment procedure for undermatched pipe girth welds subjected to bending

Structural integrity assessment of pipeline girth welds subjected to high strain levels which arises from the reel-lay method relies on precise crack driving force estimation procedures. Recent developments in subsea technology favor the use of high strength carbon steel pipelines with an internal corrosion resistant layer to increase protection against corrosive fluids. In contrast to homogeneous structural components, the bimetal configuration may induce the occurrence of weld strength undermatch, with a strong impact on the relationship between remote applied load and crack tip constraint. This work explores the development of a crack driving force estimation procedure based on a strain-based version of the EPRI J estimation scheme coupled with the equivalent stress-strain relationship method (ESSRM) and a weld geometry simplification procedure. The proposed framework takes advantage of the displacement controlled nature of the reeling process. Extensive 3D analyses provide a large set of fracture parameters applicable to the strain-based EPRI methodology followed by parametric analyses conducted to assess the accuracy of the new procedure. Subsequently, a case study is performed to determine the tolerable crack sizes in an idealized pipe installation. The procedure shows an overall good agreement to the benchmark analyses and increased accuracy when compared to the recommended approach proposed by DNV.

Surface mechanical property and residual stress of peened nickel-aluminum bronze determined by in-situ X-ray diffraction

As one of the most important surface strengthening method, shot peening is widely used to improve the fatigue and stress corrosion crack resistance of components by introducing the refined microstructure and compressive residual stress in the surface layer. However, the mechanical properties of this thin layer are different from the base metal and are difficult to be characterized by conventional techniques. In this work, a micro uniaxial tensile tester equipped with in-situ X-ray stress analyzer was employed to make it achievable on a nickel-aluminum bronze with shot peening treatment. According to the equivalent stress-strain relationship based on Von Mises stress criterion, the Young’s modulus and yield strength of the peened layer were calculated. The results showed that the Young’s modulus was the same as the bulk material, and the yield strength corresponding to the permanent plastic strain of 0.2% was increased by 21% after SP. But the fractographic analysis showed that the fracture feature of the surface layer was likely to transform from the dimple to the cleavage, indicating the improved strength might be attained at the expense of ductility. The monotonic and cyclic loading were also performed via the same combined set-up. In addition, the specific relaxation behavior of compressive residual stress was quantified by linear logarithm relationship between residual stress and cycle numbers. It was found that the compressive residual stress mainly relaxed in the first few cycles, and then reached steady state with further cycles. The relaxation rate and the stable value were chiefly depended on the stress amplitude and number of cycles. The retained residual stress kept in compressive under all given applied stress levels, suggesting that the shot peening could introduce a more stable surface layer of compressive residual stress other than the elevated strength of nickel-aluminum bronze alloy.

Characterization of Multiaxial Stress-Strain Response of Tube Metal from Double-Sided Hydro-Bulging Test Based on Hosford’s 1979 Yield Criterion

To further explore the characterization of the multiaxial stress-strain responses of anisotropic tube metal from double-sided hydro-bulging tests, an analytical model for the equivalent stress and equivalent strain calculation was derived based on Hosford’s 1979 yield criterion. Furthermore, thin-walled 5052-O aluminum alloy tubes were used to conduct the bulging experiment with an external pressure of 85 MPa. After the experimental data were substituted into the above analytical model, the Voce equation was used to fit the equivalent stress-strain relationship. It is concluded that the stress versus strain curves of the 5052-O tubes are strongly dependent on the loaded stress states, the adopted yield criteria, and the anisotropy coefficients. The external pressure of 85 MPa had little or no effect on the stress versus strain curves of the tubes, but the locations of the multiaxial stress versus strain curves were lower than that of the uniaxial stress versus strain curve. Moreover, the curve from Hosford’s 1979 yield criterion not only had a higher saturation stress and material constant value than the curve from Mises and Hill’s 1948 yield criteria but also had a dependence on the anisotropy coefficient.

Deformation behaviours of SS304 tubes in pulsating hydroforming processes

Tube hydroforming (THF) under pulsating hydraulic pressures is a novel technique that applies pulsating hydraulic pressures that are periodically increased to deform tubular materials. The deformation behaviours of tubes in pulsating THF may differ compared to those in conventional non-pulsating THF due to the pulsating hydraulic pressures. The equivalent stress-strain relationship of metal materials is an ideal way to describe the deformation behaviours of the materials in plastic deformation. In this paper, the equivalent stress-strain relationships of SS304 tubes in pulsating hydroforming are determined based on experiments and simulation of free hydraulic bulging (FHB), and compared with those of SS304 tubes in non-pulsating THF and uniaxial tensile tests (UTT). The effect of the pulsation parameters, including amplitude and frequency, on the equivalent stress-strain relationships is investigated to reveal the plastic deformation behaviours of tubes in pulsating hydroforming. The results show that the deformation behaviours of tubes in pulsating hydroforming can be well described by the equivalent stress-stain relationship obtained by the proposed method. The amplitude and frequency of pulsating hydraulic pressure have distinct effects on the equivalent stress-strain relationships-the equivalent stress becomes augmented and the formability is enhanced with the increase of the pulsation amplitude and frequency.

A framework for fracture assessments of dissimilar girth welds in offshore pipelines under bending

This work describes the development of a framework for structural integrity assessments of dissimilar girth welds in clad and lined pipes subjected to high levels of bending load for a wide range of pipe geometries, crack configurations, weld grooves and weld strength mismatch levels based upon an EPRI estimation scheme for crack driving forces coupled with a weld groove simplification procedure and the equivalent stress–strain relationship. Systematic validation of the method is provided and the crack driving force estimation accuracy is demonstrated through comparisons with numerical tools and 3-D finite element analyses for reeled pipelines.

Fiber-Element Modeling for Seismic Performance of Square RC Bridge Columns Retrofitted with NSM BFRP Bars and/or BFRP Sheet Confinement

This paper presents an analysis of the seismic performance of square RC bridge columns retrofitted with near-surface-mounted (NSM) basalt fiber-reinforced polymer (BFRP) bars and/or BFRP sheet confinement based on fiber element modeling. An axial stress versus loaded-end displacement model of NSM FRP bars, including both elastic elongation and bond-slip effects, is proposed to account for the significant slippage of FRP bars in the plastic hinge region of strengthened columns. The simplified FRP bar model is then converted into the equivalent stress-strain relationship for easy implementation in fiber-based analysis. Moment-curvature analysis is performed based on the proposed FRP bar model, and the analytical moment versus fixed-end rotation relationship of a strengthened column is calculated and assigned to the rotational spring in the fiber element model. The proposed method avoids the nested iterations in sectional analysis that require force equilibrium and deformation compatibility. Comparisons between the numerical simulations and experimental results indicate that the proposed method is appropriate for predicting pushover curves and the hysteretic response of strengthened columns. Furthermore, the mechanism of the hybrid effect of combining NSM FRP bars with externally bonded FRP sheets can be interpreted after the analytical study; that is, confining the column with FRP sheets improves the bond conditions for NSM FRP bars, while the bond-slip effect mitigates the premature fracturing of the FRP bars, leading to more effective utilization of the NSM reinforcement and a more ductile column behavior.

CTOD estimation procedure for clad pipe girth welds subjected to bending load

This work describes a crack driving force estimation procedure applicable for structural integrity assessments of dissimilar girth welds in clad pipes subjected to high levels of bending load. The purpose of this study is to explore the application of the equivalent stress-strain relationship approach coupled with a weld bevel simplification scheme and the EPRI procedure to evaluate the CTOD for defects located at the weld centerline, including the effects of the weld strength mismatch, weld bevel geometry and the clad layer thickness. Parametric 3D finite element analyses of pipes with circumferential part-through cracks are performed to validate the weld joint simplification and to assess the accuracy of the crack driving forces predictions. Finally, the results show that the estimations using the proposed methodology are in close agreement to those obtained directly from finite element analyses

Calculation of Ductility of Square CFT Stub Columns with Binding Bars Subjected to Eccentric Load

Based on the equivalent uniaxial stress-strain relationship for the encased concrete in the square steel tube with binding bars, the fiber element analysis technique is used to conduct the load versus curvature curves for the square concrete-filled steel tubular (CFT) stub columns with binding bars subjected to eccentric load, and the results predicted by the program agree well with the experimental ones. The fiber element analysis program developed is then used to investigate the effects of varied parameters on the curvature ductility of square CFT stub columns with binding bars subjected to uniaxial or biaxial eccentric load, and the corresponding simplified formulas to predict the curvature ductility of the columns are put forward, respectively. The results predicted by the simplified formulas agree well with those predicted by the program.

Establishment of a cutting force model and study of the stress–strain distribution in nano-scale copper material orthogonal cutting

This article focuses on the establishment of a cutting force calculation model in terms of nano-scale orthogonal cutting, and investigates the stress–strain distribution of single-crystal copper that occurs in terms of nano cutting. The cutting force that occurs during the nano-scale cutting of single-crystal copper, and also its changes under different situations, can be found in this study. The molecular dynamics (MD) model was proposed to evaluate the displacement components of the atom in any temporary situation on the nano-scale cutting. The atom and lattice were regarded as the node and element, respectively. The shape function concept of the finite element method (FEM) is used to calculate the equivalent strain of the nodal atom and element. The equivalent stress–strain relationship equation was acquired by nano-scale thin-film tensile simulation in this study, and was used to further calculate the equivalent stress that occurs under the equivalent strain. Subsequently, a stress–strain distribution during nano-scale orthogonal cutting can be acquired.