Non-uniform Stress Distribution Research Articles

Experimental and numerical study of shear-lag effect on low-ribbed steel-UHPC composite structure

Due to its excellent mechanical properties, the application of Ultra-High Performance Concrete (UHPC) in the field of civil engineering is rapidly increasing. Recently, a UHPC-based composite structure referred to as a low-ribbed slab steel-UHPC composite beam (SUHPC-LRSCS) is developed, which can reduce the structural self-weight significantly without compromising the mechanical performance of the structure. Because the shear-lag effect (non-uniform stress distribution) tends to cause localized damage to the structure, it is critical to consider this effect on the relatively new composite structure. In this paper, it numerically demonstrates that the shear-lag effect on this low-ribbed composite structure is greater than that of the composite beam with a traditional rectangular cross-section. To avoid the inaccuracy analysis in the structural design, this paper proposes a theoretical calculation approach for considering the shear-lag effect on that based on the bar simulation method. The effectiveness of the proposed method is verified by both the lab experiment and FE models. The proposed method presents high accuracy results showing a potential application in the engineering field. In addition, for the proposed method, the effects on both the determination of the bars quantity and separation ways for calculating the bar equivalent area are investigated. Finally, a suggested upper limit of the shear-lag coefficient for simply supported SUHPC-LRSCS is given for reference.

Methodology for testing the compressive strength of pultruded composites

Unidirectional (UD) composites with 0° fibre orientation have high axial strength along the direction of fibres. Hence, the axial compressive testing of 0° UD composites is extremely difficult due to associated issues like misalignment, buckling, non-uniform gripping and non-uniform stress distribution. These issues can intensify during fatigue testing, especially at higher load levels. The data available in the literature on the compressive response of unidirectional fibre reinforced composites is scarce. Many researchers have attempted designing a standard testing fixture for compressive testing of the fibre reinforced polymers (FRPs). Two most common fixtures are Boeing-modified ASTM D695 end loading fixture and ASTM D6641 combined loading compression (CLC) fixture. However, these fixtures are only feasible for compressive testing of the rectangular composite laminates. There is no standard fixture for compressive testing of cylindrical pultruded composites. This paper presents a methodology for testing the compressive strength of pultruded cylindrical composites. A fixture is designed and fabricated to conduct the tests. Different misalignment, gripping and stress concentration issues that could occur during the compression testing are addressed and a corresponding solution is provided. Unidirectional (UD) carbon/epoxy pultruded rods are used as test specimens. The test data of 21 specimens is presented and the failure modes are analysed using scanning electron microscope (SEM) images.

Engineered Interphase Mechanics in Single Lap Joints: Analytical and PINN Formulations

Adhesively bonded joints showcase non-uniform stress distribution, along their length as the load is transferred through layers of dissimilar stiffness. For efficient transfer of loads, the peak interfacial shear stress is required to be engineered. In this study, inspired by electric pulses, the interphase modulus is modified according to square, sinusoidal and triangular pulses. The variation in peak stresses with increased number of pulses up to four is also investigated. The developed analytical model is solved for the interfacial shear stresses as well as the peel stresses, using energy functional approach, through MAPLE software. The abrupt changes in modulus in square pulse graded interphase are observed to create highest interfacial shear stresses among the considered grading profiles. Furthermore, the peak interfacial stresses are observed to increase with increased number of pulses. An effective elastic modulus parameter is defined to indicate the area under the modulus profile curve. The effective modulus is found to be gradually increasing with increase number of pulses in square graded interphase. Whereas, it is constant for sinusoidal- and triangular-graded interphases. A deep machine learning-based physics informed neural network model is developed to quickly solve the developed governing differential equations. Therefore, results from the machine leaning model are compared to the analytical results.

Time-dependent modelling of steel-tube confined concrete columns considering confining and bonding effects

Steel tube confined reinforced concrete (STCRC) columns have been applied in high-rise buildings with a promising future due to its high load-bearing capacity and excellent seismic behaviour. Different from traditional reinforced concrete (RC) and concrete-filled steel tubular (CFST) columns, the concrete of STCRC columns is subjected to triaxial time-dependent varying stresses even at low sustained loads, and the stresses of the tube and concrete are non-uniformly distributed along the column length due to the interfacial bonding effects. In this context, available long-term research outcomes for RC or CFST columns cannot be implemented to STCRC columns directly. Hence, a confined concrete creep model for STCRC columns was determined based on the collected 56 creep tests on sealed confined concrete under multiaxial stress states. Subsequently, accounting for the time-dependent varying confinement effects and the influence of the non-uniform interfacial stress distribution, a refined numerical analysis method was established for the long-term behaviour prediction. A parametric study was then conducted with particular attention to the difference in the long-term behaviour of STCRC, RC and CFST columns and the determination of the key parameters. Results indicate that the uniaxial creep model (i.e. Eurocode 2) can be extended to the creep prediction of confined concrete with the effective Poisson's ratio of 0.187. Due to the longitudinal bonding effects, the slenderness ratio would significantly influence the long-term deformation of STCRC columns. The influence of the steel tube on the time effects is less noticeable when compared with the concrete strength, loading age and slenderness ratio.

Anchorage performance of straight rebars in UHPC with strain-hardening property

Bond and anchorage are the basis to conduct performance analysis on reinforced-concrete structures. The strain-hardening property makes the bond-slip behaviour of rebars in ultra-high-performance concrete (UHPC) different from that in ordinary concrete. This study investigates the anchorage performance of straight rebars in UHPC based on its material properties. First, the anchorage failure process is revealed using pull-out test combined with computed tomography scanning. Thereafter, a finite element model is established to analyze the effects of strain-hardening property on failure mechanism and anchorage performance. The regularity of bond stress distribution along the rebar is also obtained. Subsequently, parametric analyses are developed to analyze the effects on bond stress, including the embedded rebar length, concrete cover thickness, and tensile strength and ductility of UHPC. Expressions for the non-uniform distribution of bond stress are established. Finally, a calculation formula is proposed for the anchorage-bearing capacity considering the strain-hardening property of UHPC material.

Passive Earth Pressure on the Retaining Wall of Limited-width Backfill Based on Curvilinearly Layered

This study presents a new method to calculate the passive earth pressure on the rigid retaining wall of non-cohesive limited-width backfill. The proposed method considers the non-cohesive backfill behind the wall as the research object. It was assumed that under the translational mode of the retaining wall, the fracture surface was the plane passing through the heel of the wall and that the principal stress trajectory of the backfill was arc-shaped. The backfill was divided into several arc thin-layer elements by layering along the principal stress trajectory. The non-uniformity of stress distribution on the upper and lower surfaces of the elements was considered. The proposed method was validated with the data obtained from the model tests found in the literature. The results showed that compared with the common horizontal element layering method, the arc thin-layer element method can accurately consider the complex stress acting on the element and better reflect the variation law of the passive earth pressure on the retaining wall. The passive earth pressure of limited-width backfill presented a non-linear distribution along the height of the wall and increased with an increase in soil depth. With an increase in the aspect ratio of soil or a decrease in the internal friction angle, the resultant force of the passive earth pressure gradually decreased while the height of the action point of the resultant force gradually increased. When calculating the passive earth pressure on the retaining wall of limited-width backfill, the critical aspect ratio of limited-width to semi-infinite width was 3.

Dynamic instability analysis of perforated stiffened laminated composite panels subjected to non-uniform in-plane edge load under hygrothermal condition

A robust and computationally efficient finite element (FE) formulation has been developed in an effort to understand the parametric instability behaviour of a perforated stiffened composite panel subjected to a pulsating non-uniform edge load under a hygrothermal environment. The panel is modelled using a 9-noded heterosis element to avoid shear locking, whereas the stringer uses a 3-noded isoparametric beam element with a displacement compatibility condition employed at the skin–stringer​ interface. Due to the non-uniform distribution of stress in the perforated panel as a result of exposure to environmental and mechanical loading conditions, a unique dynamic technique has been implemented to account for the instability performance by employing two types of boundary conditions. In the current investigation, an unstiffened panel is initially obtained based on the highest value of the dynamic instability opening (DIO) and the unstable excitation frequency of the panel for different lamina schemes, cutout shapes, and loading conditions. The obtained unstiffened panel is further investigated for various stiffener configurations to determine a highly unstable perforated stiffened panel based on the DIO value and instability zone frequency range. Detailed parametric studies are then carried out considering the cutout sizes, cutout orientation, panel’s aspect ratio, and stiffener depth to understand the parametric instability behaviour of the panel in a hygrothermal environment. It is found that moisture significantly influences the dynamic instability behaviour of the perforated stiffened panel compared to the temperature exposure by shifting the instability zone towards the lower frequency. The width of the instability region of the stiffened panel broadens abruptly as the magnitude of the applied static in-plane edge load enhances. Also, for certain combinations of the dynamic and static load factors, the lower bound of the instability region reduces to zero, resulting in fluttering. In general, it is observed that stiffer the panel, wider is the instability zone with a higher unstable excitation frequency range.

Compressive behaviour of corroded thin-walled circular section steel stub columns

The influences of corrosion on the buckling behaviour and bearing capacity of the circular section steel tubular (CST) stub columns subject to axial compression were investigated experimentally and numerically. Seven CST stub columns with chloride corrosion were investigated. After the accelerated chloride corrosion test on CST stub columns, three methods were used to evaluate the corrosion degree of each specimen. A monotonic axial compression test was then carried out. Based on the test results, the influence of corrosion degree on failure mode, bearing capacity and deformation behaviour were analysed. In addition, the surface morphology of the corroded column was obtained by a 3D Scanner and processed by Geomagic Studio software. Then the reconstructed models were imported into finite element (FE) software ABAQUS. This novel method considering the natural morphology of surface corrosion was verified by comparing the FE solutions to the experimental result. Based on the verified FE model, the deterioration of the mechanical behaviour of corroded compression stub columns under the actual rusty surface was also studied. It was found that the rough surface of the corroded specimens cause non-uniform stress distribution and change buckling mode. Parametric analysis, therefore, was conducted to study the influences of the corrosion degree and steel grade on the yield load. Finally, the proposed design formula is able to predict the axial compression strength of the rusty stub column with reasonable accuracy.

Iterative method for obtaining nonuniform grinding-induced residual stress distribution of silicon wafers based on global deformation

Grinding as the main thinning process for silicon wafers is widely used in chip manufacturing. The residual stress distribution is desired to be known to optimize the grinding process. In this paper, an iterative method for obtaining the nonuniform residual stress of ground silicon wafers was proposed. The deformation of ground silicon wafers was divided into two parts in which one part was large spherical deformation and the other was a small out-of-sphere deformation. The spherical deformation which was in the nonlinear range corresponded to an average stress which was obtained using the bisection method. The small out-of-sphere deformation corresponded to the stress variation which was obtained using the regularization method with continuity constraints. An iterative successive approximation process was conducted to address the nonlinear problem which was transformed into a local linear problem. The residual stress distribution of a ground silicon wafer was obtained successfully using the proposed method. Although the overall shape of the wafer deformation was approximately spherical, the residual stress value varied a lot with the crystal orientation of the silicon wafer. The stress values in the <110> orientations were much larger than those in the <100> orientations. The method could be used to evaluate the grinding process independently of the dimension sizes of ground silicon wafers. The proposed method in this paper is non-destructive and could be used to track the residual stress changes in the grinding process and the process parameters could be optimized accordingly.

The perpetual shearing of granular soils under low stresses using the stadium shear device

The constitutive response of granular soils under indefinitely large shear deformation and low stress controls the dynamics of shallow landslides and offshore pipelines. Current testing devices, however, are either limited to small shear deformation or involve a non-uniform stress distribution across the sample being tested. This paper presents the development of an original stadium shear device (SSD) that is free from those issues. In the SSD, soil samples can deform perpetually within a closed stadium shaped container that is sheared continuously by a belt. The stress uniformity across the width of the device is validated using Discrete Element Method (DEM) simulations, which give insight into the relationships between the normal stresses acting on the material. The performance of the SSD is validated using experimental data obtained from tests on glass beads, which further disclose stress and void ratio relationship in soils. When applied to sub-angular natural sands with different degrees of polydispersity, the SSD reveals a weak rate hardening of friction coefficient and sample dilatancy that reaches the loosest possible density at critical state, regardless of the initial packing conditions.

Methodology of Leakage Prediction in Gasketed Flange Joints at Pipeline Deformations.

The paper presents the proposal of a leakage prediction method in flange joints, after pipeline deformation, based on FEM (Finite Element Methods). The stages of developing the design are discussed, and a complex, multi-stage method of applying the loads is presented in detail. Moreover, the gasket material data obtained in experiments were used. The paper also presents the results of calculations on a non-uniform stress distribution in the radial direction of the gasket. In addition, it has been shown that the deflection of the pipeline with a minor displacement causes an increase in the diversification of the circumferential pressure of the gasket, and also has a significant influence on the determination of the actual state of stress to which the gasket is subject. Moreover, it was found that the distribution of contact pressure on the deflection of the pipeline has a significant influence on the level of leakage. The results of tests are compared to the results of the numerical calculations of the stress in bolts. By comparing the bolt tension changes obtained by numerical and experiment analyses, it has been shown that the assumptions made in developing the numerical model are correct.

Flexible Equivalent Strain Sensor with Ordered Concentric Circular Curved Cracks Inspired by Scorpion.

Slit sensillum, a unique sensing organ on the scorpion's legs, is composed of several cracks with curved shapes. In fact, it is just its particular morphological distribution and structure that endows the scorpions with ultrasensitive sensing capacity. Here, a scorpion-inspired flexible strain sensor with an ordered concentric circular curved crack array (CCA) was designed and fabricated by using an optimized solvent-induced and template transfer combined method. The morphology of the cracks can be effectively controlled by the heating temperature and the lasting time. Instead of the nonuniform stress distribution induced by disordered cracks, ordered concentric circle curved structures are introduced to generate a uniform stress distribution and larger deformation, which can significantly improve the performance of the strain sensor. Thus, the CCA sensor exhibits ultrahigh sensitivity (GF ∼ 7878.6), excellent stability (over 16 000 cycles), and fast response time (110 ms). Furthermore, the CCA sensor was demonstrated to be feasible for monitoring human motions and detecting noncontact vibration signals, indicating its great potential in human-health monitoring and vibration signal detection applications.

Thermophysical and thermomechanical properties of basalt-phenolic FRP rebars under high temperature

An experimental investigation was conducted on the thermophysical and thermomechanical properties of phenolic-basalt fiber-reinforced polymer (P-BFRP) rebars subjected to high temperature. As a comparison, vinyl-BFRP (V-BFRP) and epoxy-BFRP (E-BFRP) rebars were also investigated within the same program. The mass variation of all BFRP rebar types was similar in air atmosphere while P-BFRP rebars decomposed more slowly in nitrogen atmosphere. All BFRP rebar types were found to have a similar specific heat and thermal conductivity up to 350 °C. P-BFRP rebars exhibited a much higher glass transition temperature compared with the other two types of BFRP rebars. Three failure modes could be differentiated for all BFRP rebar types according to three temperature ranges, the latter were shifted to higher values for P-BFRP rebars. No reduction in tensile strength occurred in P-BFRP rebars up to 300 °C, while V-BFRP and E-BFRP rebars experienced a significant degradation of tensile strength at around 100 °C already. This advantage of P-BFRP rebars was mainly caused by the much higher Tg which delayed the initiation of interfacial bonding failure up to 300 °C. The elastic modulus of all BFRP rebar types exhibited a similar degradation, which was caused by progressive fiber and fiber bundle failure due to non-uniform stress distributions.

Assessment of deformation in bridge bearing areas using measurements and welding simulation

Deformations of bottom flanges in the vicinity of bridge bearings, i.e., in bearing areas, due to manufacturing and loading can result in serious problems in service life and damages in bridge superstructures and structural bearings coming from nonuniform stress distribution. The paper focuses on the out-of-flatness measurement of bearing areas using Coordinate Measuring Machine (CMM) in typical steel and composite bridges having box and open cross-sections. Advanced manufacturing simulations are also carried out in addition to site measurements to analyse imperfections due to welding during assembly and strengthening of a typical bridge superstructure. A qualitative comparison is made with measurement results showing that the magnitudes of simulated and measured distortions are in good agreement. Results are evaluated in accordance with the permitted total deformation limit in EN 1337–2 recommended for spherical structural bearings. The current study uses a novel approach in the field of bridge engineering; the analogy of Abbott-Firestone curve is applied for describing the deformed shape and evaluating the extent of defects in the contact area since the magnitude of out-of-flatness imperfection is not inevitably sufficient for classifying the surfaces. Based on the obtained results it is demonstrated that using additional transverse bearing stiffeners for strengthening the superstructure can result in large distortions. Even the magnitude of out-of-flatness due to welding of transverse bearing stiffeners can exceed the permitted limit resulting in nonuniform stress distribution in the sliding elements affecting wear resistance and service life of spherical structural bearings.

A new incremental variational micro-mechanical model for porous rocks with a pressure-dependent and compression–tension asymmetric plastic solid matrix

In this paper, we shall formulate a new micro-mechanical model for describing both local and macroscopic elastic–plastic behavior of porous rocks with a pressure-sensitive and tension–compression asymmetric solid matrix. For this purpose, a new incremental variational mean field homogenization (IVMFH) method is first established. The novelty lies in the fact that the new formulation allows considering solid matrix obeying a nonlinear plastic yield criterion rather than the linear Drucker–Prager one adopted in the previous work Zhao et al. (2019). To this end, a new optimization procedure is proposed to estimate the effective incremental potential involving a stress-dependent relation between volumetric and deviatoric parts of local plastic strain field of solid matrix. The proposed incremental variational model takes into account the effect of non-uniform distribution of local stress and strain fields in solid matrix by incorporating their first and second moments in the homogenization process. The proposed model is able to provide not only macroscopic but also local mechanical responses of porous rocks. Its efficiency is assessed by a series of comparisons with full-field finite element calculations. Application examples are also presented through comparisons with experimental data for two typical porous rocks: Vosges sandstone and Lixhe chalk.

Measurement and simulation of residual stresses in laser welded CFRP/steel lap joints

In light of the demand for reducing the emission of climate-damaging gases such as CO2, it is very important to apply lightweight materials in the aerospace and automotive industries. In the past years, hybrid structures made of carbon fiber reinforced plastics (CFRP) and metals received high attention from numerous industries. Laser welding is an advanced approach for bonding dissimilar materials. However, in the welding process, residual stresses are induced in the joined part, which influence the mechanical performance of the bonded components. In the present work, residual stresses in laser welded CFRP and steel joints are experimentally determined using the hole drilling method (HDM) and numerically analyzed by thermal elastic–plastic finite element analysis. The non-uniform residual stress distribution through the thickness direction of the CRRP and steel plates can be successfully measured when the anisotropic material properties in CFRP are considered. Moreover, a numerical simulation was carried out for analyzing the residual stresses in the laser welded CFRP/steel joints, particularly their distribution characteristics at the CFRP/Steel interface. Specific discussions focus on the residual stress formation mechanism and the effect of laser welding process parameters on the residual stresses through experimental tools and numerical simulations.

Non-linear necking behaviour of S275 to S960 structural steels under monotonic tension

For cylindrical coupons of structural steels under tension, gradual reductions in their cross-sections, commonly known as necking, occurred at an elongation that the maximum force is attained. Non-uniform stress and strain distributions in the critical cross-sections of the necking regions have been known for more than 70 years; however, the values of these stresses cannot be directly measured in experiments so far. This paper presents a systematic investigation into the post-necking structural responses of the S275 to S960 steels under monotonic tension forces through the Instantaneous Area (iArea) Method proposed by the authors. In order to examine post-necking deformation characteristics of structural steels up to fracture, a total of 15 standard tensile tests on proportional cylindrical coupons of these steels were carried out carefully to obtain their force–elongation (F – e) curves while precision measurements were made to obtain their instantaneous dimensions. Complementary advanced finite element models are then established to predict non-linear stress and strain distributions at the critical cross-sections of the necking regions. Through a process of successive approximation, a series of correction factors are obtained to allow for the effects of these non-uniform stress and strain distributions respectively onto the post-necking structural responses of the coupons. Hence, the predicted force–elongation (F - e) curves of the coupons are demonstrated to follow the measured curves closely throughout the entire deformation ranges. More importantly, the predicted instantaneous diameters dgi are shown to have a good agreement with the measured values at various deformation stages up to fracture.

Equivalent stress-strain model of half grouted sleeve connection under monotonic and repeated loads: Experiment and preliminary application

The half grouted sleeve connection (HGSC) is widely adopted in the construction of precast concrete (PC) structures. So far, a few studies have been developed on the mechanical behavior of HGSC, however, efficient load-deformation models of HGSC are still scarce, which limits the numerical analysis of PC structures. In this study, therefore, an experimental study is undertaken to propose equivalent stress-strain models of HGSC under monotonic and repeated loads. The effect of rebar diameter, as well as the spliced length of rebar in the sleeve on the load-deformation behavior of HGSC is investigated with 60 specimens. Based on the test results, the failure mode, load capacity and strain of the spliced rebar is discussed. The results show that the failure mode of HGSC is mainly related to the spliced length of rebar. The capacity of HGSC is affected by the failure mode rather than the loading type. Moreover, a non-uniform distribution of bond stress of the spliced rebar is observed from the measured strains in the rebar. Finally, equivalent stress-strain models are proposed for the HGSC under monotonic and repeated loads. The model is established by revising the bi-linear stress-strain model of bare rebar, thus can be applied in the numerical study of PC members with high computational efficiency. The parameters of the models are calibrated with the test data obtained in the current study. A numerical simulation of a PC column with HGSC is developed to preliminarily verify the proposed model. The results show that the prediction of member deformation can be greatly improved by using the proposed model.

Similarity Simulation on the Movement Characteristics of Surrounding Rock and Floor Stress Distribution for Large-Dip Coal Seam.

The question of how to mine safely in close multi coal seams is the main concern for coal operators, in particular for large-dip coal seams with complex geological and mechanical conditions. This paper presents a detailed similarity simulation on the movement characteristics of the overburden and the stress distribution of underlying strata in terms of a specific coal mine in the Tielieke mining area of the Kubai coalfield via a three-dimensional photogrammetry system and a high-speed static resistance analyzer. The results show that the overburden strata are asymmetrically deformed around the coal pillar and the fracture area is perpendicular to the longwall with an “M” shape when deeper coal is mined. Moreover, the asymmetric movement of overburden results in the non-uniform distribution of stress on the floor of the coal pillar and ribs. In particular, stress is closely related to the location of the longwall, and stress of the coal pillar is much larger when it is closer to the deep side. The floor stress relief degree of the longwall in the deep zone is higher than that of its counterparts, providing a theoretical foundation for a reasonable layout and a support technique for roadways. The main contribution of this research that it can be used as a reference in maintaining the integrity of surrounding rock for large-dip coal seams with close distances.

Experimental analysis of shear-lag effect in reinforced concrete T-beams

The non-uniform distribution of normal stresses within wide flanges of beam sections is typically referred to as shear-lag effect. Shear lag is a result of the interaction of normal and tangential stresses or correspondingly by the influence of shear strains on longitudinal strains. In structural engineering, the shear-lag effect has been a concern in the flanges of thin-walled metallic structures or the slab of composite steel–concrete elements, among others. Though existing codes of practice provide a simplified way to address shear lag by means of the effective width concept, such provisions can be insufficient for concrete structures, for which a deeper knowledge on the real influence of shear lag is necessary due to the current trend to design wide concrete bridge girders, with geometric configurations of the cross-sections which can be sensitive to shear lag (i.e. box- or T-sections). Moreover, the influence of the behaviour of structural concrete (cracking, rheology, yielding of reinforcement) has not been dealt with in detail so far. In the present paper, an experimental campaign on two reinforced concrete T-beams is presented. The beams have been subjected to two types of tests: firstly, to time-dependent effects governed by concrete shrinkage and creep; secondly, to the application of increasing direct loads to cover the whole concrete behaviour (uncracked, cracked and ultimate stage). The strain distribution at the top slab of the T-sections has been studied with extensive strain measurements at different cross-sections. The experiments have shown a distinct intensity of shear-lag effect depending on the load type. Moreover, the shear-lag impact varies longitudinally for each cross-section. In case of direct load tests, it has been also found that the strain distribution on the top slab changes as a function of the load level, which indicates that the different behavioural stages of concrete affect the shear lag, especially cracking. The experimental results have been analyzed with the help of analytical and numerical models, which have allowed understanding the progressive modification of the strain distribution within the top slab and the shear-lag intensity.