Post-yield Range Research Articles

Experimental observations and data analysis of a commercially grade aluminium alloy (6082T6) for large elastoplastic deformation

Large elastoplastic deformation generally occurs in sheet-metal forming processes during stretching, blanking, punching, stamping, bending, bending-unbending, reverse bending and deep drawing. In today’s world, due to very high competition and swift development of products in metal forming industries, there is a growing demand in high precision end products to be manufactured in short duration. It is very essential and important to have a knowledge of an in-depth understanding of material behaviour in all these metal forming steps. Therefore, to predict material behaviour, an accurate material modelling is required by considering the simultaneous effects of strain and strain rate. Classical flow rules are generally used to predict the material behaviour in the post yield range. Overall material deformation can be represented as the change in size, change in shape and their rates. A new generalised relation is developed to represent the material behaviour from elastic range to failure. This relation involves eight material parameters which includes two classical material constants like bulk modulus and shear modulus, two material viscosity terms and four in the form rule which relates elastic strain rate to plastic strain rate. All these material parameters can be obtained from uniaxial tension experiments. The material deformation is 3-D in nature and therefore classical yield criteria is avoided while formulating the relation. Instead, concept of activation energy is used. In the present work, experimental observations and data analysis on the commercial grade aluminium (6082T6) was discussed. The material behavior in the post yield region with new understanding of the material model was presented here for uni-axial loading case. Based on the experimental observations and the results obtained it was found that the both the elastic moduli and the viscosities remain constant throughout the large deformation.

Formulation of Localized Damping Models for Large Displacement Analysis of Single-Degree-of-Freedom Inelastic Systems

ABSTRACT Issues with traditional implementations of tangent-stiffness-proportional damping model are associated with negative damping forces that develop in the post-yield range when the system stiffness becomes negative and with unrealistic damping forces arising at degrees of freedom undergoing second-order movements only. To overcome these issues, this paper proposes a localized formulation of the tangent-stiffness-proportional damping model which can be used in nonlinear dynamic analysis of simple inelastic systems. Results show the consistency of the local and global damping formulations in small displacements and the effectiveness of the localized tangent-stiffness-proportional damping model in the presence of material and geometrical nonlinearities.

Parameters Affecting the Local Buckling Response of High Strength Linepipe

The local buckling response and post-buckling mechanical performance of high strength linepipe subject to combined loading state was evaluated using the finite element (FE) simulator abaqus/standard v6.12. The constitutive model parameters were established through laboratory tests and the numerical modeling procedures were verified with large-scale experiments investigating the local buckling response of high strength linepipe. The numerical predictions demonstrated a high level of consistency and correspondence with the measured experimental behavior with respect to the peak moment, strain capacity, deformation mechanism, and local buckling response well into the postyield range. A parametric study on the local buckling response of high strength plain and girth weld pipelines was conducted. The loading conditions included internal pressure and end rotation. The pipe mechanical response parameters examined included moment–curvature, ovalization, local strain, and modal response. The magnitude and distribution of the characteristic geometric imperfections and the end constraint, associated with the boundary conditions and pipe length, had a significant influence on the predicted local buckling response. The importance of material parameters on the local buckling response, including the yield strength (YS), yield strength to tensile strength ratio (Y/T), and anisotropy, was also established through the numerical parameter study. For girth weld linepipe, the study demonstrated the importance of the local high/low misalignment, associated with the circumferential girth weld, on the local buckling response.

Curving structural steel girders by two-point bending

Point bending is often used for cambering and curving steel girders to large radii. In this method, a fabricated straight girder is bent by concentrated loads applied at the third points using hydraulic jacks. The required geometric profile develops from permanent residual deformations induced upon removing the loads. The resulting shape is not circular but closer to a parabolic shape. The goal of this paper is to evaluate the profiles of structural steel girders curved by point bending in the post-yield range and explore alternative loading configurations that result in the fabrication of specimens that better approximate circular curves. Limits are developed on the minimum radius of curvature that can be achieved to ensure accuracy of the idealization and on the induced strain to avoid damaging the steel section or adversely affecting the physical properties of steel. The accuracy of the proposed analysis is established by comparing predictions against available experimental results from a full-scale test. Further validation is also provided based on comparisons with results from 3-D finite element analysis incorporating initial residual stresses and geometric imperfections.

Evaluating the Behavior of Anchor Rod Foundations for High-Mast Light Poles Using Nonlinear Finite-Element Analysis

AbstractThis study examines the behavior of high-mast lighting pole (HMLP) foundations through the use of nonlinear finite-element modeling. HMLPs utilize nuts and threaded rods to clamp the light pole structure’s base plate to the foundation. Inspections by the Alaska Department of Transportation and Public Facilities (AKDOT&PF) have revealed widespread loosening of the nuts used on HMLPs over time. The threaded rods used are F1554 Grade 55, which are heat treated from mild steel rods, Fy=248 MPa (36 ksi) to gain additional yield strength. This study briefly highlights the difference in postyield behavior in mild steel and high-strength steel, and proposes a probable mechanism behind the clamp-load loss experienced by Alaska’s HMLPs. Because the HMLPs are much taller than traditional lighting poles, they experience larger external wind loading. This wind load is potentially stressing threaded rods into the postyield range. A previous study shows that the current tightening procedure is likely not undert...

조립형 프리캐스트 콘크리트 보강재를 가지는 비좌굴가새의 이력특성

The conventional brace system is generally accepted as the lateral load resisting system for steel structures due to efficient story drift control and economic feasibility. But lateral stiffness of the structure decreases when buckling happens to the brace in compression, so that it results in unstable structure with unstable hysteresis behavior through strength deterioration. Buckling restrained brace(BRB) system, in which steel core is confined by mortar/concrete-filled tube, represents stable behavior in the post-yield range because the core`s buckling is restrained. So, seismic performance of BRB is much better than that of conventional brace system in point of energy absorption capacity, and it is applied the most in high seismicity regions as damper element. BRBs with various shaped-sections have been developed across the globe, but the shapes experimented in Korea are now quite limited. In this study, we considered built-up type of restraining member made up of precast reinforcement concrete and the steel core. we experimented the BRB according to AISC(2005) and evaluated seismic performances and hysteresis characteristics.

Bond Strength Deterioration of Reinforced and Prestressed Concrete Members at Reversed Cyclic Loads

The bond strength of concrete members at reversed cyclic loads is quite different from that of the concrete members at monotonic loads. Reversed cyclic loads produce a progressive bond deterioration that can lead to failure at cyclic stress levels lower than the ultimate stress at monotonic loads. In addition, the structural behavior of concrete members at dominant reversed loads reveals a dramatic reduction of energy dissipation in the hysteresis region due to a severe pinch effect. A method was proposed to predict the structural behavior of concrete members failing in bond after flexural yielding. The method takes into account the bond deterioration due to the degradation of concrete in the postyield range. To verify the bond behavior by the proposed method, predicted results were compared with the experimental data for concrete members at reversed cyclic loads, cited in the literature. Comparison of the experimental and calculated bond behavior of examined concrete members showed reasonable agreement.

Methods of analysis of a reinforced concrete section under bending with axial force in the post-yield range

Predicting the behaviour of plastic hinges subjected to large inelastic deformations caused by extreme loads such as earthquakes plays an important role in assessing maximum stable deformation capacities of framed concrete structures. This paper presents the analytical procedure for analysing the behaviour of a reinforced concrete section under bending with axial force in the post-yield range. The following stages of section behaviour are defined: the uncracked, first cracked, yielding, cover crushing, cover spalling, buckling of bars and limit stages. The relationship between the moment and curvature in these stages, including the effects of concrete confinement, the spalling of the concrete cover, and the inelastic buckling of the reinforcing bars, is considered. The presented method makes it possible to estimate the ductility of reinforced concrete members with various longitudinal and transverse reinforcement.

An elastoplastic model for structured clays

An elastoplastic model for structured clays, which is formulated based on the fact that the difference in mechanical behavior of structured and reconstituted clays is caused by the change of fabric in the post-yield deformation range, is present in this paper. This model is developed from an elastoplastic model for overconsolidated reconstituted clays, by considering that the variation in the yield surface of structured clays is similar to that of overconsolidated reconstituted clays. However, in order to describe the mechanical behavior of structured clays with precision, the model takes the bonding and parabolic strength envelope into consideration. Compared with the Cam-clay model, only two new parameters are required in the model for structured clays, which can be determined from isotropic compression and triaxial shear tests at different confining pressures. The comparison of model predictions and results of drained and undrained triaxial shear tests on four different marine clays shows that the model can capture reasonable well the strength and deformation characteristics of structured clays, including negative and positive dilatancy, strain-hardening and softening during shearing.

Bond-slip analysis via a cohesive-zone model simulating damage, friction and interlocking

A recently proposed cohesive-zone model which effectively combines damage, friction and mechanical interlocking has been revisited and further validated by numerically simulating the pull-out test, from a concrete block, of a ribbed steel bar in the post-yield deformation range. The simulated response is in good agreement with experimental measurements of the bond slip characteristics in the post-yield range of deformed bars reported in the literature. This study highlights the main features of the model: with physically justified and relatively simple arguments, and within the sound framework of thermodynamics with internal variables, the model effectively separates the three main sources of energy dissipation, i.e. loss of adhesion, friction along flat interfaces and mechanical interlocking. This study provides further evidence that the proposed approach allows easier and physically clearer procedures for the determination of the model parameters of such three elementary mechanical behaviours, and makes possible their interpretation and measurement as separate material property, as a viable alternative to lumping these parameters into single values of the fracture energy. In particular, the proposed approach allows to consider a single value of the adhesion energy for modes I and II.

Seismic shear strength and deformation of RC columns failed in flexural shear

This paper investigates the seismic shear strength and deformation capacity of flexural shear critical columns in the post-yield range of longitudinal reinforcement. In total, 24 reinforced concrete (RC) column specimens with span-to-depth ratios ranging from 1·63 to 6·16 and volumetric ratios of transverse reinforcement of 0·77% and 1·54% were tested under constant axial load ratios of 0·2 and 0·5 and cyclically reversed horizontal load. Of these 24 RC column specimens, seven failed in flexure, two failed in shear and 15 failed in flexural shear. Based on the test results, simple models are proposed to predict the shear strength and displacement capacity of columns failed in flexural shear mode. The proposed shear model includes the effects of span-to-depth ratio, axial load ratio, transverse reinforcement and displacement ductility. Analytical results from the proposed model were compared with test data and consistent agreement was achieved.

Post-yield bond behaviour of deformed bars in high-strength self-compacting concrete

Self-compacting concrete (SCC) has gained substantial attention since its advent for its ability to compact without the need for either internal or external vibration even in areas of highly congested reinforcement such as beam-column joints. During the past two decades, extensive research has been conducted on both the fresh and hardened properties of normal strength SCC; however, only recently has interest in high-strength self-compacting concrete (HSSCC) gained momentum.This study investigates bond properties between reinforcement and HSSCC as well as conventionally vibrated high-strength concrete (CVHSC). Appropriate mix designs for both HSSCC and CVHSC were first developed to achieve comparable concrete compressive strength of about 90MPa. The effects of bar grade, diameter, bond length, and concrete type were investigated by means of pull-out tests for both concrete types; where, special attention was paid to the post-yield slip behaviour of different steel grades. It was found that the difference in ductility of bars with different grades results in different rate of diameter reduction due to axial tensile stress which consequently affects their bond performance; especially in the post-yield range. Available bond models were applied to the experimental outcomes of this study and modifications and/or new expressions are suggested where possible.

The method of analysis of a reinforced concrete section under bending in the post-yield range

Predicting the behavior of plastic hinges subjected to large inelastic deformations caused by extreme loads such as earthquakes plays an important role in assessing maximum stable deformation capacities of framed concrete structures. This paper presents an analytical procedure for analysing the behaviour of a reinforced concrete section under bending in the post-yield range. The following stages of section behaviour are defined as the uncracked; first cracked; yielding; cover crushing; cover spalling; buckling of bars; and limit stages. The relationship between the moment and curvature in these stages, including the effects of concrete confinement, the spalling of the concrete cover, and the inelastic buckling of the reinforced bars, are considered. The results obtained from analytical calculations have are compared to the results obtained from a computer analysis. The presented method makes it possible to estimate the ductility of reinforced concrete members with various longitudinal and transverse reinforcement.

휨항복 후 부착파괴하는 철근콘크리트 부재의 부착 연성 평가

A general earthquake resistant design philosophy of ductile frame buildings allows beams to form plastic hinges adjacent to beam-column connections. In order to carry out this design philosophy, the ultimate bond or shear strength of the beam should be greater than the flexural yielding force and should not degrade before reaching its required ductility. The behavior of RC members dominated by bond or shear action reveals a dramatic reduction of energy dissipation in the hysteretic response due to the severe pinching effects. In this study, a method was proposed to predict the deformability of reinforced concrete members with short-span-to-depth-ratios, which would result in bond failure after flexural yielding. Repeated or cyclic loading produces a progressive deterioration of bond that may lead to failure at lower cyclic bond stress levels. Accumulation of bond damage is caused by the propagation of micro-cracks and progressive crushing of concrete in front of the lugs. The proposed method takes into account bond deterioration due to the degradation of concrete in the post yield range. In order to verify bond deformability of the proposed method, the predicted results were compared with the experimental results of RC members reported in the technical literature. Comparisons between the observed and calculated bond deformability of the tested RC members showed reasonably good agreement.

Behavior of T-shaped reinforced concrete beams partially confined by structural steel

External confinement of reinforced concrete (R/C) members with structural steel sections or fiber reinforcing wraps is commonly used to improve the flexural behavior of structural members. Flexural strengthening of R/C beams by external steel members is among the most effective and convenient techniques. A study is presented in this paper investigating the flexural behavior of R/C beams having T cross-sections partially confined (P/C) by a combination of various steel members connected together by intermittent batten plates. Four R/C specimens, representing dropped beams in solid slabs, were tested. One control beam had no confinement whereas the three other beams had four steel angles simply wrapped and tied around the stem by batten plates, two angles at the bottom corners of the stem and the other two angles at the stem-flange junctions. Two plates were placed on the top surface of the flange and connected by studs to the two angles at the bottom of the flange. The resulting P/C beams are categorized as partial composite beams because no shear connectors were used between the R/C beam and the jacketing bottom-tension steel angles as in the case of conventional composite beams. All specimens were tested in positive bending under two points loading. Test results revealed an enhancement in the flexural behavior, particularly in the post-yield range of loading, and ductility due to the proposed strengthening and partial composite effect. The number and spacing of the intermittent battens played a significant role in the behavior of the strengthened specimens. Analytical values of loads and deformations at yield and ultimate loading showed good agreement with the measured values.

Low-Cycle Fatigue Damage of Circular Concrete-Filled-Tube Columns

Under seismic actions, the induced damage in critical regions of a concrete-filled steel tube (CFT) column could be attributed to cumulative damage of the steel tube caused by repeated cyclic loading in the post-yield strain range. An experimental study was undertaken to develop an analytical model of cumulative damage for circular CFT columns subjected to cyclic loading. The low-cycle fatigue behavior of CFT columns was investigated and a relationship between fatigue life and normalized displacement amplitude was established for typical controlling parameters. A total of 12 large-scale model column specimens, representing two types of circular CFT columns with different steel tube diameter-to-thickness ratios were tested under quasistatic loading with either constant drift amplitude or standard cyclic loading histories with increasing peak drift displacement. Test results indicate that the low cycle fatigue behavior of CFT columns depends on the thickness of the steel tube. Fatigue life expressions useful for application in damage-based seismic design are developed and used to predict the damage index for additional CFT columns based on experimental data reported in the literature.

Effect of second-order forces on seismic response

In a building structure subjected to seismic forces, the gravity loads acting through the lateral displacements lead to additional shears and moments. This is generally referred to as the P–Δ effect; it tends to reduce the capacity of the structure to resist the seismic forces and may lead to instability. It has been suggested that an increase in structural strength, in stiffness, or in both would mitigate the P–Δ effect and ensure stability of the structure. It is shown here that instability results when the P–Δ effect causes the stiffness of the structure to become negative in the post-yield range, in which case increasing the strength, the stiffness, or both does not ensure stability. In a single-storey structure, stability can be ensured if there is sufficient strain hardening that the post-yield stiffness is positive even in the presence of the P–Δ effect. For a multistorey building the vulnerability of the structure to P–Δ instability can be judged by obtaining a pushover curve. It is shown that as long as the maximum displacement produced by the design earthquake lies in the region of positive slope of the pushover curve, the structure will remain stable.Key words: seismic response, P–Δ effect, dynamic instability, stability coefficient, amplification factor, pushover analysis, nonlinear analysis.

Poisson Effect in Reinforced Concrete Membrane Elements

RC shear elements behave very differently before vs. after cracking. The Poisson effect before cracking is characterized by the Poisson's ratio, but after cracking is characterized by 2 Hsu/Zhu ratios. In the postyield range, the Hsu/Zhu ratio v-sub-12 (tensile strain caused by perpendicular compressive strain) was found to be a constant of 1.9, and the Hsu/Zhu ratio v-sub-21 (compressive strain caused by perpendicular tensile strain) was measured to be 0. This study describes the experiments performed to measure these 2 Hsu/Zhu ratios, which provide the basis for the establishment of the softened membrane model (SMM). This new theory, reported in a companion paper, can predict the entire shear stress vs. shear strain curves of membrane elements, including the postpeak descending branches.

Testing and Analysis of Steel Pipe Segments

Steel pipelines buried in cold regions are subject to thermally induced axial loads, hoop stresses caused by the action of the fluids they convey, and differential settlements caused by such factors as thaw settlements, frost heave, and landslides. Due to these loads, pipelines may experience localized deformations well into the plasticity range of the pipe material. In this paper, an experimental program consisting of 7 tests conducted to research and document the deformational behavior of full-scale pipes subjected to loads similar to those in the field is presented. The specimens and loading conditions were carefully selected to match those in the field. A finite-element model was developed using the finite-element simulator ABAQUS to predict the local buckling behavior of pipes. The finite-element model was based on a large displacement, large rotation, finite-membrane-strain formulation, and included material nonlinearity effects. The comparison between the numerical and experimental results shows the ability of the analytical model to predict the local buckling behavior of pipes when deformed well into the postyield range.

Shear failure and ductility of RC columns after yielding of main reinforcement

During the Hanshin-Awaji Earthquake, catastrophic shear failure accompanying plenty of diagonal shear cracks was experienced in RC structures and bridge piers serving transportation facilities. In this paper, shear capacity and ductility of RC columns in the post-yield range of longitudinal reinforcement are discussed for seismic-resistant-design. First, the shear failure of large-scale RC columns is computationally simulated for an understanding of the mechanism of shear collapse of bridge piers. FEM computational results on ductility are compared with the experiments and a parametric study is conducted concerning factors that affect the post-yield deformability of RC columns. Finally, a simple formula for ductility is presented for summarizing the sensitivity of influential factors.