Force-displacement Relationship Research Articles

Mechanical properties of structural metallic alloys for nuclear applications deduced by small punch test

Small Punch Test (SPT) techniques are becoming a popular tool for the characterization of the irradiation damage effects in nuclear materials thanks to a number of advantages as compared to conventional test methods. As of today, there are two standards available (ASTM and EN) and several methods are developed to extract the tensile properties from the SPT force-displacement relationship. Here, we carry a set of benchmark tests using SPT and conventional uniaxial tensile tests on a number of metallic materials commonly applied in nuclear facilities. The investigation includes reactor pressure vessel steel, high-Cr ferritic martensitic steel, copper-chromium-zirconium alloy, nickel based super alloy, austenitic stainless steel and titanium. The SPT sample geometry and setup is designed according to the requirements of the EN10371 norm. As a result, we have deduced the tensile properties using both techniques and thus have revealed the accuracy/reliability of the currently available standards for the determination of the yield stress and ultimate tensile strength by the SPT.The study has revealed that in an overwhelming number of tests, the yield stress extracted from the SPT (for both EN and ASTM standards) is systematically overestimated as compared to the value measured from the uniaxial tensile test. However, the prediction for the ferritic and austenitic steels is close to the uniaxial stress, for both standards. In the case of Inconel material, the yield stress is underestimated. The ultimate tensile strength extracted by either of the existing methods is in a good agreement with the value otherwise measured from the uniaxial tests for all the materials except the titanium. Based on the obtained results and discussion, a number of recommendations for the evaluation of yield and ultimate tensile stress from the small punch test is given.

A Half-Cycle Negative-Stiffness Damping Model and Device Development

This paper proposes a novel damping model with negative stiffness known as the half-cycle negative-stiffness damping model. Analysis of a single degree of freedom (SDOF) system demonstrated that the half-cycle negative-stiffness damping model has negative stiffness and energy dissipation. The equivalent negative stiffness of the model was derived from the frequency response analysis of the system. An alternating transmission system and a one-way friction system were developed to assemble a half-cycle negative-stiffness damping device (HCNSDD), which can generate a half-cycle negative-stiffness damping model. A mechanical model was developed to represent the force-displacement relationship of the proposed HCNSDD. A HCNSDD specimen was manufactured and examined using experimental tests. The HCNSDD exhibits half-cycle negative-stiffness damping and stable mechanical properties, demonstrating the feasibility and effectiveness of the proposed HCNSDD. Finally, a finite element simulation approach for HCNSDD was presented, and the performance of seismic vibration control of HCNSDD was evaluated using a multidegree-of-freedom system.

Estimation of the residual bearing strength of corroded bridge girders using 3D scan data

The main cause of structural deficiency in steel bridges is corrosion damage at girder ends caused by the leakage of bridge joints. This localized corrosion damage reduces steel girders’ bearing strength and affects bridge structures’ overall load-carrying capacity. Accurate estimation of the residual strength of corroded elements is critical for prioritizing repair projects and allocating funding and resources. However, due to the varied environment around the metal surface, corrosion damage on bridge girders is highly variable in severity and shape. The inspection results could vary greatly from inspector to inspector using the current methods. The accuracy of the inspection cannot be ensured. To address this limitation, this study proposes a methodology for creating a computationally efficient finite element (FE) model of a steel plate girder end with the exact representation of the geometry of the corroded region using 3D scan data. The point cloud data from a high-resolution structured-light 3D scanner is used to obtain geometric features such as plate boundaries, connectivity between plates, and thickness variations across plates. This information is used to automatically create a FE model of the damaged girder using shell elements. The applicability and accuracy of the proposed methodology were evaluated using the results from the load testing of a full-scale girder with corrosion damage. The agreement between the experimental and analytical failure mode, force–displacement relationship, and strain distribution on the plates demonstrated the accuracy of the method for estimating the residual bearing strength of plate girders with corrosion damage.

Tests of double-stage SMA slip friction damper

This study presents a new type of self-centering damper, termed the double-stage shape memory alloy (SMA) slip friction damper, which mainly comprises of the grooved center and cap plates, stacked disc springs, and SMA bars. The double-stage behavior is realized by the serial connection of the stacked disc springs and the SMA bars, with the purposes of adjusting stiffness and damping for varied seismic hazard levels. The configuration and working mechanism are firstly presented, along with the analytical equations governing the force-displacement relationship. As the key components, the SMA bar, the friction mechanism, and the disc springs were tested separately. And then, the proof-of-concept tests of the reduced-scale damper were conducted. From the testing results, the damper exhibited a symmetric double-stage self-centering damping behavior. Some hysteretic parameters of interest were then quantified. Three-dimensional numerical models were established and were further used for parametric analysis. Both the analytical method and numerical model agree well with the experimental data.

Experimental characterization and modelling of adhesive bonded joints under static and non-monotonic fracture loading in the mode II regime

Understanding and predicting the behaviour of bonded joints under different loading conditions is certainly an aspect of primary importance. Although numerous experimental studies have been carried out over the last few decades, the shear behaviour of bonded joints under cyclic loading has not been investigated in detail. To fill this gap, an extensive experimental and numerical program of double lap shear bonded joints has been carried out. The double lap shear joints were tested under static and cyclic loading to evaluate and compare the influence of external forces on the adhesive performance. The results are discussed in terms of the force-displacement relationship, shear stress, stiffness, residual displacement, and initial damage. Finally, a method is presented for predicting the actual behaviour of double lap shear bonded joints under different loading conditions using an imperfect interface model with damage evolution. The numerical results are in good agreement with the experimental results for all loading conditions. This work has provided and validated an interesting design tool for adhesive structures.

Quasi-static experimental study on seismic performance of exterior shear key with different failure modes

The shear key with horizontal failure mode manifests secondary stiffness-strengthening capacity comparing to the diagonal and slide shear modes. It is more suitable for protecting bridges that sustain multiple hazard actions. However, the seismic performance of shear keys with horizontal failure mode has seldom been addressed. This study designed and manufactured ten RC exterior shear key models involving 1:3 geometrical scaling to achieve three failure modes with specific reinforcement layouts. A quasi-static experiment was performed to investigate the seismic performance of shear keys, including crack observation, force–displacement relationship, rotation and stress distribution characteristics. The experiment results indicate that the failure mode depends on the proportion of reinforcement capacity, and can affect the maximum resistance of shear keys. The shear key with horizontal failure exhibits apparent secondary stiffness strengthening characteristics, whereas the diagonal and sliding failure modes suffer persistent reduction under large deformations. Furthermore, the diagonal shear key exhibits the highest residual capacity under severe damage. The measured data are compared with the existing analytical models in terms of both peak capacity and envelope curves, showing the models are more applicable to diagonal failure shear key than the others.

Mechanical model of the casing sidetracking tool system considering weight on bit and axial displacement

It is of practical interesting to investigate the mechanical behaviors of sidetracking tool system and describe the sidetracking window profile with its influencing factors, because it can provide an important basis for optimizing the sidetracking tool system and controlling the shape of sidetracking window effectively. A load-displacement equation of sidetracking tool system, which describes the force-displacement relation of grinding shoes, is established using the piecewise rigidization method. Stress equations of sidetracking tool system are derived to describe the stress distribution characteristics and their influencing factors more effectively, in which the weight on bit (WOB) is considered. An axial displacement function of flexible joint is obtained through numerical simulation and data fitting, and then a profile equation of sidetracking window is established to express the influences of axial displacement. It should be emphasized that the established profile equation can predict the casing sidetracking window shape more accurately because the influence of the axial displacement of the flexible joint is considered. The load-displacement equation, stress equations, axial displacement function and window profile equation, which have been mentioned above, compose a mechanical model of sidetracking tool system. Using the mechanical model, the influence laws of flexible joint length and thickness and construction WOB on window shape are calculated and analyzed, and then the operation parameters of sidetracking window are optimized. Some useful findings are as follows. The sidetracking window profile resembles an inverted tear drop shape. The window width is mainly affected by the size of casing and grinding shoe, while the window length is mainly affected by the angle of whipstock and the combined deformation of sidetracking tool. The adjustable range of window width is less than that of the window length. The length of the window increases with the reduced length of the flexible joint, or the increased thickness of the flexible joint, or the increased WOB. This work can become a theoretical basis and calculation tool for designing a sidetracking tool system which produces the sidetracking window shape more effectively and accurately.

Analytical approach for force-displacement behavior of deformed reinforcing bars embedded in concrete

Component-based joint model suggested by Eurocode is a simple yet efficient approach to evaluating the joint behavior of composite beam-column subassemblies. The reinforcing bars in this approach play an instrumental role, especially for progressive collapse analysis where the ultimate resistances and structural ductility of beam-column subassemblies are significantly influenced and in some extreme cases directly governed by the reinforcing bars. This paper describes an analytical approach for predicting the force-displacement characteristics of deformed reinforcing bars that are embedded in concrete blocks. In contrast to previous studies that roughly predefined the profiles of bar and bond stresses in tension, this paper utilizes an iteration method to provide a more accurate and simpler description of such non-uniform local behavior. This approach has greater flexibility to account for the variations in the embedment length of reinforcing bars, lateral restraints and failure modes. The proposed approach is verified using four groups of published reinforcing bar pull-out tests. The predicted force-displacement relationships, distributions of local slips, bond stresses, and bar stresses along the length are shown in reasonable agreement with the test results. Finally, component-based joint models are established for composite beam-column subassemblies under progressive collapse scenarios, in which the force-displacement relationships of the reinforcing bar components are determined through the proposed approach.

Development of numerical model capturing cyclic behavior of Two-Side clamped infill plates

This study aims to propose a simple numerical model methodology for two-side clamped infill steel plates with various aspect ratios, slenderness ratios and even different steel grades. The modeling element constructed using the methodology expects to be directly implemented into computer structural software for nonlinear time-history analyses of structures employing two-side clamped infill plates. The suggested model is constructed with their force–displacement relation including nonlinear and cyclic effects which can be defined by modeling parameters evaluated from empirical equations. The empirical equations are developed using regression analyses to agree with the parametric analysis results with detailed finite element models of two-side clamped infill plates. A proposed numerical model including the hysteretic characteristics was validated by comparison with existing experimental results conducted by other studies. It is confirmed to utilize the proposed numerical model that can accurately represent cyclic behavior over entire response ranges including buckling, tension field action representing the post-buckling behavior, and fracture of steel plates.

Influence of transverse beams on seismic behavior of a reinforced concrete beam-column joint

In this study, an interior reinforced concrete (RC) beam-column joint from the ground storey of a generic 3-storey building, has been studied for the lateral load carrying capacity. Four instances of the interior joint have been considered: a two-dimensional joint and a joint with transverse beams, each with their combination of, with and without joint hoops. Finite element (FE) modelling package, ABAQUS has been used for the numerical modelling of the joint specimens. Quasi-static cyclic lateral loading was applied to the specimens to develop the force–displacement relations, which could eventually determine the effectiveness of including joint hoops and transverse beams to the joint. It has been found that, in a seismically designed joint, inclusion of transverse beams has negligible effect on the behaviour of the joint, whereas it improved significantly in a non-seismically designed joint.

Development of a novel tuned negative stiffness inerter damper for seismic induced structural vibration control

Recently, inerter-based devices have been widely explored for possible applications to both civil and mechanical engineering structures for effective vibration control. The control force-displacement relationship of an inerter is related to the vibration frequency, which may lead to excessive force under high-frequency excitation. A negative stiffness element, on the other hand, is effective for the shear force and acceleration response mitigations. The combined use of inerter and negative stiffness element therefore has the potential to further improve the control performance compared to a single device in terms of controlling both the displacement and acceleration responses. In this paper, a novel tuned negative stiffness inerter damper (TNSID) integrating negative stiffness and inerter elements is proposed for seismic induced structural vibration control. A physical realization of the proposed device is developed, and its working mechanism is analysed. The closed-form expressions for its optimal parameters are attained based on the fixed-point theory by minimizing its maximum displacement amplification factor. The proposed TNSID is then implemented to control the vibrations of a single-degree-of-freedom structure and a five-storey building subjected to different excitations to evaluate its feasibility and effectiveness. For comparison, the systems without control, with a tuned viscous mass damper, a tuned inerter damper and a negative stiffness amplifying damper are also investigated. The results reveal that the combination of the negative stiffness and inerter elements endows TNSID with the capacity to attain dual mitigation effects on both the displacement and acceleration responses and widen the effective frequency bandwidth, therefore achieve the most evident control effectiveness compared to the other devices investigated in this study.

Local wrinkles of van der Waals heterostructures under nanoindentation

Probing van der Waals (vdW) heterostructures to characterize their properties, especially the stability and durability is of vital importance due to the weak interactions between two-dimensional materials. However, the wrinkling behavior of vdW heterostructures under nanoindentation is still unclear, which hinders the accuracy and development of probing methods at the nanoscale. Herein, the wrinkles of vdW heterostructures composed of graphene and molybdenum disulfide (MoS2) under indentation are studied through molecular simulation and theoretical analysis. It is found that wrinkles occur when the hoop strain of the upper layer reaches the critical value for the graphene film-single layer MoS2 substrate system. By fitting the force–displacement relationship, we estimate the predicted elastic modulus of the vdW heterostructure, and uncover that the wrinkling phenomena have ignorable effect on the probing results. It is interesting to find a transition from a sinusoidal wrinkling to a period-doubling bifurcation of vdW heterostructures with the increase of indentation depth. What is more, the wrinkling morphology of vdW heterostructures can be tuned through choosing suitable indentation depth, indenter size, upper film size as well as applied pretension. The present findings should be useful for the developing probing methods of vdW heterostructures, and serve as a guide for their blooming applications.

Improvement of size effect simulation based on an energy-balanced exponential softening bond model and fracture energy regularization

Although the Mode I fracture of rock demonstrates a noticeable size effect, current contact models in the discrete element method cannot simulate the size effect very well. An exponential softening bond model is proposed to address this issue based on an exponential damage law and an elliptic yield criterion. Its basic formulas are established on energy balance to ensure that the total fracture energy of the normal and shear springs always equals the fracture energy dissipated by the resultant contact force. The simulations of uniaxial tensile and three-point bending tests were conducted to demonstrate the performances of the proposed model on the fracture simulations. The particle size dependency is successfully eliminated by fracture energy regularization, in which the force–displacement relationship is adjusted based on fracture energy and particle size. The simulation results show that the exponential softening bond model effectively simulates the whole load–displacement curves of experimental tests. It also demonstrates a perfect energy balance among external work, internal energy, and fracture energy. Besides, compared with the other two bond models, the exponential softening bond model is more precise in representing the fracture toughness, the fracture process zone, and the size effect of the Mode I fracture of limestone.

Improved identification of stiffness coefficients of non intrusive nonlinear geometric reduced order models of structures

Significant, successful efforts have been devoted in recent years to the non intrusive construction from finite element software of reduced order models of the nonlinear geometric response of structures. A key assumption in these models is that the elastic restoring forces can be represented as cubic polynomials of their generalized coordinates. However, there has been only very limited discussion of whether this representation is appropriate, how deviations from this polynomial form affect the identification of its coefficients and ultimately the prediction of the structural response, and how current identification strategies can be improved.These questions are the focus of the present investigation which considers first a simple structural model that exhibits the potential for snap-through and thus represents an interesting validation case with strongly nonlinear geometric behavior. It is shown that the force–displacement relationship which can be derived in closed form is not exactly a cubic polynomial but can be very closely modeled by one. However, the match between exact curve and polynomial fit is very sensitive to small changes in the linear, quadratic, and cubic stiffness coefficients and thus the prediction of the response may range from excellent to significantly in error depending on how the identification of the coefficients is performed. In particular, it is found that a cubic approximation obtained by Taylor series around the undeformed configuration is not very accurate post snap-through.Based on these findings, two strategies are proposed to improve the identification of the stiffness coefficients of these reduced order models. The first one is a tuning procedure in which a limited number of key coefficients of the model are adjusted to fit additional static response data. The second approach performs the identification of the stiffness coefficients at a series of different levels, as opposed to one as currently performed, and seeks the most appropriate value of each coefficient based on a “small change” criterion.The applicability of these two novel strategies is demonstrated on several challenging structural models: a clamped–clamped curved beam undergoing snap-through as well as a curved panel and a hat stiffened one. It is found that the reduced order models identified via the tuning or multi-level strategies not only lead to more accurate predictions of the structural response as compared to the original finite element model but also are more computationally stable than their counterparts identified with the current single-level strategy.

Development and experimental validation of finite element models for a prestressed lead extrusion damper

The emerging trend in earthquake-resistant structural design is to dissipate some part of the seismic input energy through energy-dissipating devices (EDDs). A prominent candidate to serve this purpose is the lead extrusion damper (LED), which dissipates seismic energy by the extrusion of lead through the displacement of a bulged shaft. The LEDs should be designed as they meet the demands of the host structural system. Hence, predicting the force–displacement relation and energy dissipation characteristics of the LED is essential. To serve this purpose, comprehensive three-dimensional finite element models (FEMs) were developed in this study to simulate the cyclic behavior of a prestressed LED. The methodology consisted of performing coupon tests, the development of FEMs, and experimental verification. Coupon tests were performed for lead and steel to simulate the nonlinear material behaviors better. The models were validated against the experimental results of the LED and a steel beam-to-column connection. In general, the adapted model satisfactorily captured the experimental results. The maximum differences in the maximum force and dissipated energy predictions were about 7.5% for the generated FEMs. In addition, the mean relative difference in predicting damper forces for eight LEDs selected from the literature was about 6%. The low relative differences between the models and experiments demonstrated that the adapted FEM could reliably estimate the cyclic response of the LEDs. It can be stated that the adapted three-dimensional finite element modeling strategy can be utilized robustly for design purposes.

Experimental Behavior and Modelling of Steel Bolted T-Stub Connections

The paper comprehensively investigates the tension performance of Q355 steel T-stubs, whose nonlinear mechanical behavior is modelled by spring-slider elements. First, tension tests were conducted on seven specimens to explore the tension performance of Q355 steel T-stubs. T-stub connections were discussed in terms of their tension characteristics. Second, a numerical simulation was performed to analyze the stress distribution of T-stub components during deformation. Finally, on the basis of the tension characteristics of the T-stub connections, we constructed the constitutive model’s density function. The constitutive model’s force–displacement relationship was derived mathematically. A method for determining parameters was also developed. With the proposed model, the entire tensile behavior of T-stub connections can be described accurately while reducing the degrees of freedom at the contact interfaces, resulting in more efficient computing. Four parameters are defined physically in the model, and their values can be determined directly by macroscopic experiments.

Experimental and theoretical research on a shear-bending-metallic-damper with a double-phased yield mechanism

Aiming at improving the performance and practicability of metallic dampers, this paper proposes a novel shear-bending metallic damper with a double-phased yield mechanism (SBD-DY) by setting bending and shear plates with different yield strengths in parallel. The double-phased yield mechanism enables the damper to provide proper energy dissipation ability and stiffness for the primary structures during various earthquakes. Design methods of SBD-DY, including the elastic stiffness, the yield strength, the yield displacement, the force-displacement relationship and the membrane effect, are proposed. Ten SBD-DY specimens are tested under monotonic and cyclic loading to verify the workability of the bending and shear plates. The test results reveal that the SBD-DY specimens demonstrate satisfactory plastic development with full hysteresis curves, favorable energy dissipation ability and good ductility. Two types of failure modes, namely the weld failure of bending plates and fracture of strips, are summarized. Test specimens with fracture of strips exhibit better residual load capacity and energy dissipation ability than specimens with weld failure of bending plates. The effects of parameters including width of bending plates (B), height of bending plates (H) and width of the strips (S) are compared and analyzed. The theoretical results agree well with the experimental results, clearly revealing the double-phased mechanism of SBD-DY. Finally, potential improvements are also proposed to avoid premature weld failure of SBD-DY.

Experimental investigation and load-deformation analysis of reinforced concrete bridge columns under various loading cycles

Twenty reinforced concrete (RC) bridge columns were tested under constant axial compressive as well as cyclic lateral loading, to explore the effect of loading cycle numbers (3, 10, 20 cycles for a given displacement amplitude) on the seismic behavior of RC bridge columns. Test results demonstrate that the bridge column specimens under cyclic loading failed in flexural-shear mode, which was evident by the presence of diagonal cracks, buckled longitudinal reinforcement, fractured stirrup, as well as saliently pinched lateral force–displacement hysteretic curves. As the axial compression ratio increased from 0.05 to 0.15 at the aspect ratio 1.6, there was about 50% increase in their yield and peak strengths, significant decrease in ultimate displacement, and about 30% decrease in the displacement ductility in the RC bridge columns. As the aspect ratio decreased from 2.3 to 1.6 at the axial compression ratio 0.05, there was about 35% increase in their yield and peak strengths, about 40% increase in the displacement ductility in the RC bridge columns. Additionally, the effect of loading cycle numbers on the seismic behavior of RC bridge column specimens is investigated. The effect of the number of loading cycles on seismic behavior is more significant after peak load than prior to the attainment of peak strength, and the deformation capacity is significantly reduced. During post-peak loading stage increasing the loading cycle numbers accelerates damage accumulation and impairs the seismic behavior of the specimens due to substantial reduction of their energy dissipation capacity and seismic ductility. Based on the analysis of test results under varied loading cycles and monotonic lateral force–displacement curves, a calculation model of lateral force–displacement relationship considering the influence of loading cycle numbers is developed, and its effectiveness and accuracy is verified. The objective of this paper is to investigate the effect of the number of loading cycles on the seismic behavior of RC bridge columns through experimental testing. The research results would improve seismic assessment of RC bridge columns exposed to such hazards that flexural-shear failure caused by cyclic degradation.

Mechanical Behaviors of a Buckling-Plate Self-Centering Friction Damper

In order to improve the resilience of structures subjected to strong earthquakes, a buckling-plate self-centering friction damper (BPSCFD) with low post-yielding stiffness is proposed, which consists of a group of post-buckling plates and a self-centering variable friction mechanism. The damper is intended to not only reduce the peak and residual deformation of structures, but also to limit the additional internal force of the structural elements. Through theoretical derivation and finite element simulation, the hysteretic damping and self-centering characteristics of BPSCFDs are studied. In order to examine the seismic performance of the BPSCFDs, the dampers are employed to retrofit a double-columns bridge bent, and the corresponding elastic-plastic time history analysis is conducted. The results show that the force-displacement relationships of BPSCFDs with different parameter combinations are characterized by typical flag-shaped self-centering hysteretic loops and low post-yielding stiffness, and the dampers can effectively reduce the peak and residual deformation of the bridge bent without increasing the peak acceleration and base shear. The research results could supply a guideline for the design and application of the damper.

Blast response of cantilever retaining wall: Modes of wall movement

For the past few decades, there has been an increase in awareness regarding the safety of highway bridges from blast loads. Since abutments/Retaining walls (RWs) are portions of bridges, investigating abutments/RW or RW behaviour under blast loads is important. As there have not been any studies investigating the dynamic response of retaining walls due to blast loading, an experimental study was conducted to examine the influence of blast loads on the dynamic behaviour of reinforced concrete retaining wall (RCRW) with sand as a backfill material. A shock tube was used to generate blast loads on the soil-RW model. The influence of the relative density, backfill saturation, blast load intensity, and traffic load equivalent surcharge on the blast behaviour of RCRW with sand backfill was studied. The results showed that the modes of wall movement were affected by the backfill relative density, blast load intensities, and degree of saturation. Under the same load conditions, an increase in the wall movement was noticed in loose backfill, and a translation response mode was evident in this condition. A relationship between wall relative movements and mobilized earth pressure coefficients was determined. The mobilized passive resistance of the RW backfill induced by blast load was used to determine the force–displacement relationship. Acceleration time histories for RW/backfill were found for all conditions. The findings of this research will help to properly evaluate and design bridges’ abutment and to develop resilient transportation infrastructure systems.