Effect Of Biaxial Loading Research Articles

Compression softening of textile CFRP reinforced concrete (CRC): Biaxial testing of cracked CRC panels and derivation of constitutive laws

Due to its insensitivity to corrosion, textile CFRP (carbon fibre reinforced polymer) reinforcement enables the construction of thin-walled concrete structures such as shells, vaults and girder webs with minimal concrete cover. In contrast to tensile and flexural behaviour, strutting and compressive membrane action of cracked thin-walled carbon reinforced concrete (CRC) elements and the interaction of compressive stresses with transverse tensile loading have not yet been investigated. While for steel reinforced concrete components, extensive biaxial testing has shown a significant reduction of concrete compressive strength as a function of the lateral tensile stress (compression softening), the effect of biaxial loading on CRC structures has not been quantified yet. However, a different behaviour is expected due to different bond properties of steel and CFRP in concrete, smaller crack spacings and the tendency of the CFRP reinforced concrete for in-plane splitting. This paper presents an extensive experimental campaign for investigation of the influence of transverse tension and cracking on the compressive strength of CRC with refined measurement techniques. Based on a literature review on compressive softening behaviour and conventional test setups for steel reinforced concrete, a novel test setup was developed. The phenomenology of compression softening in CRC as well as the main factors influencing compressive membrane behaviour are highlighted. Based on the experimental findings a constitutive law for compression softening behaviour of CRC is proposed.

Thoughts on the Importance of Similitude and Multi-Axial Loads When Assessing the Durability and Damage Tolerance of Adhesively-Bonded Doublers and Repairs

Adhesively bonded doublers and adhesively bonded repairs are extensively used to extend the operational life of metallic aircraft structures. Consequently, this paper focuses on the tools needed to address sustainment issues associated with both adhesively bonded doublers and adhesively bonded repairs to (metallic) aircraft structures, in a fashion that is consistent with the building-block approach mandated in the United States Air Force (USAF) airworthiness certification standard MIL-STD-1530D and also in the United States (US) Joint Services Structural Guidelines JSSG-2006. In this context, it is shown that the effect of biaxial loads on cohesive crack growth in a bonded doubler under both constant amplitude fatigue loads and operational flight loads can be significant. It is also suggested that as a result, for uniaxial tests to replicate the cohesive crack growth seen in adhesively bonded doublers and adhesively bonded repairs under operational flight loads, the magnitude of the applied load spectrum may need to be continuously modified so as to ensure that the crack tip similitude parameter in the laboratory tests reflects that seen in the full-scale aircraft.

A detailed study of short fatigue crack directions for carbon steel specimens with circular holes subject to cyclic biaxial loads

The effect of notches and biaxial fatigue loading on the crack paths was studied in detail for thin-walled tube specimens with a passing-through hole, paying special attention to the short-crack period. The study was focused on the high cycle fatigue regime. The material was a carbon steel and the tests were under load control, at Rσ=−1. The crack initiation point on the notch surface and the crack direction were studied with an optical microscope on the specimen outer surface and with a scanning electron microscope and a non-contact 3D optical profilometer on the fracture surface. The crack direction was analyzed for several crack lengths, ranging from the length of one average grain to the length of twenty average grains, all lengths within the short-crack regime, in order to carefully observe the evolution of the crack direction in the Stage I and during the transition from Stage I to Stage II. A statistical analysis of the crack initiation point and the experimental crack directions was carried out. In general, the crack initiation point was close to the maximum principal stress point. The crack direction during the first grains was approximately the Mode I direction. There was no initiation in Mode II. The crack continued in the Mode I direction as it got longer, within the short-crack period. The experimental fatigue limits were compared with the predictions calculated with two models from the literature. The direction of the straight lines used by the models to make the predictions were compared with the average crack directions measured experimentally. The goodness of the models, not only from the point of view of the fatigue limit value prediction but also from the closeness of the direction of the line used for the prediction to the experimental crack direction, was discussed.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

Non-linear analysis of CFRP-wrapped steel box sections under biaxial load

The effect of biaxial compressive loading on hollow steel box column (HSBC) and concrete-filled steel box column (CFSBC) sections wrapped with low-modulus carbon-fibre-reinforced polymer (CFRP) was studied. The CFSBC and HSBC sections were simulated using Abaqus finite-element software and validated using available experimental data. Biaxial compressive loading was considered for different eccentricities (i.e. eccentricity to depth ratio (e/D) ratio of zero to 0.32). The results indicated that, for CFRP-wrapped HSBCs at low eccentricity (e/D = 0.08), compact and non-compact sections were effective at carrying higher load, while a slender section was effective for concentric loads. For the CFRP-wrapped CFSBCs, compact and non-compact sections were effective for all the eccentric loads (e/D = 0–0.32). It was also found that the low-modulus CFRP layer wrapping the CFSBC sections had no significant effect on strength. An empirical relationship was developed based on trend analysis, which gives the load-carrying capacity of any section. For the CFSBC sections, axial compression–uniaxial moment (P–M) interaction curves are presented to validate the simulation results under biaxial loading.

Effect of Dynamic Biaxial Loading of Car Seats

The aim of this article is to determine the effect of the biaxial loading of a car seat, in vertical and horizontal directions, on seating comfort. We measured the transfer characteristic in the vertical direction with a free load. The method of laboratory testing of the car seat was chosen due to the simple repetition of the tests, ensuring the same test conditions, with high accuracy of their reproduction. To determine the effect, tests with uniaxial loading were compared with tests with biaxial loading. The resulting characteristic was the transfer characteristic in the vertical direction. The effect of horizontal loading on the transfer characteristic of a car seat was determined.

A numerical analysis on the behavior of CFRP laminates under biaxial loads

The study of the failure mechanisms of a composite material is essential for the efficient design of structures. The analysis of the effect of transverse biaxial loads, both at micromechanical and macromechanical level, is required for an integral vision of the whole mechanism of damage. In a previous work by the authors a transverse biaxial testing campaign was performed on cruciform specimens; in the present work a FEM model that successfully reproduces the coupons elastic state is presented in order to understand the failure occurrence and to make failure predictions avoiding the complexity of the experimental process.

On Experimental Procedure Development for Evaluating the Effect of Biaxial Loading on the Static Crack Resistance Characteristics of Reactor Vessel Steels

On Experimental Procedure Development for Evaluating the Effect of Biaxial Loading on the Static Crack Resistance Characteristics of Reactor Vessel Steels

Numerical analysis of in- and out-of-plane coupling effects on angle bracket connections in CLT structures

Angle bracket connections are commonly used to transfer shear loads in cross laminated timber (CLT) structures. In reality, these connections may experience multiple-direction loads simultaneously in the wind and seismic events. A two-phase numerical program was carried out to assess the coupling effect of biaxial loading on the performance of CLT wall-to-floor angle bracket connections. In phase I, a 3D finite element model of connections was developed using ABAQUS software and verified with the data from experimental tests previously carried out by the authors. In Phase II of the study, the verified model was used to simulate the performance of connections under three biaxial loads, i.e., in-plane shear and uplift, in-plane shear and out-of-plane outward shear, and in-plane shear and out-of-plane inward shear. The coupling effect on the performance of the connections was evaluated in terms of strength, stiffness, ductility, and failure modes under biaxial loads, and compared with the scenario where the connection was only loaded in in-plane shear. Results show that the application of biaxial loading may considerably decrease the in-plane shear performance of the angle bracket connections when the secondary load is more than 50% of its monoaxial resistance, while the effect of biaxial loading is limited when the secondary load is less than 25% of its monoaxial resistance.

Design of biaxially loaded external slab column connections

The paper investigates the influence of biaxial loading on punching resistance at square and elongated edge columns of flat slabs which is virtually neglected in the literature. In the absence of experimental data, the influence of biaxial loading is determined using nonlinear finite element analysis (NLFEA) with 3D solid elements. The resulting baseline punching resistances are compared with the predictions of various implementations of the Critical Shear Crack Theory (CSCT) including a Joint Shell Punching Model (JSPME) in which punching failure is simulated using nonlinear joint elements inserted between the nodes of nonlinear shell elements located around the punching control perimeter. The failure criterion of the JSPME, which is most suited for structural assessment, implicitly accounts for the effect of biaxial loading unlike the original (classic) and closed form versions of the CSCT. The classic CSCT indirectly accounts for loading eccentricity by reducing the punching control perimeter by a multiple ke which is determined in this paper using shear field analysis. Conversely, the closed form CSCT, which is adopted in the draft for the next generation of Eurocode2 (EC2), enhances the design shear force by a multiple β. The paper uses experimental data to determine an expression for β for edge column connections subject to inwards eccentricity normal to the slab edge. Subsequently, shear field analysis on representative flat slab to edge column connections is used to extend this expression for β to edge column connections subject to biaxial eccentricity. NLFEA simulations with 3D solid elements are used to validate the predictions of the JSPME, the shear field methodology used to determine ke in the classic CSCT and the proposed expression for β in the closed form CSCT. Reasonable agreement is achieved between all these analysis methods. The main advantage of the JSPME over NLFEA with 3D solid elements is its increased computational efficiency which makes it more suitable for the assessment of large structures.

Predictive model for bidirectional shear strength of reinforced concrete columns subjected to biaxial cyclic loading

Corner columns are subjected to bidirectional lateral loading in three-dimensional framed structures during seismic events, which can deteriorate their shear strength. The majority of the design codes do not consider the effect of biaxial lateral loading in the calculation of the column shear strength, and hence an accurate formulation that can predict the bidirectional shear strength is still lacking. Gene Expression Programming (GEP) was used in this research to predict the bidirectional shear strength of columns subjected to biaxial cyclic loads based on a database collected from different experimental studies found in the literature. Based on the previous experimental studies, it is found that the biaxial shear strength of RC columns are predominantly controlled by the column axial load, cross-sectional area of the columns, column shear reinforcement area, concrete compressive strength, and the height of the column. These parameters were used to develop the GEP models in this research. The models were statistically evaluated in order to ensure their applicability, and then they were compared to the ACI-318 formulation of the uniaxial shear strength. The R2 value obtained using the ACI-318 formulations is low compared to that obtained using the GEP models, where the R2 value obtained using the ACI formulation is 0.35, and that obtained using the first and second GEP models are 0.87 and 0.73, respectively. This confirms that the GEP models are more fitting to the experimental results compared to the ACI-318 formulation.

Biaxial Loading Effects on Strain Energy Release Rate and Crack-Tip Strain Field in Elastic Hydrogels

We characterized the strain energy release rate and local crack-tip strain field for elastic hydrogels under several types of biaxial loading: planar, unequal biaxial, and equibiaxial extensions. The strain energy release rate (G) in each type of biaxial strain is characterized via two different approaches. One evaluates G from the change in strain energy with respect to the notch length (Xc) using single-edge notched specimens with various Xc values. The other estimates G from the difference in strain energy density between the two regions far behind and ahead of the crack tip. The excellent agreement between the G values obtained by the two methods demonstrated their reliability. We also revealed the features of the local crack-tip strain field in biaxial loading, including crack-tip opening displacement, strain field area, strain magnitude resulting from crack opening, and strain singularity exponent for strain growth near the crack tip. Importantly, these properties are governed exclusively by G, independent of the biaxial loading type. The results provide an important basis for a comprehensive understanding of the fracture behavior of elastic soft materials under complicated deformations.

Dynamic behaviour of perforated laminated panels under biaxial non-uniform edge loads based on FE approach

Buckling loads of laminated panels are calculated by analytical approaches are usually based on the assumptions that the panels are subjected to uniform in-planes edge loads without cutouts, despite of the fact that real structural components are subjected to various kinds of non-uniform in-plane edge loads along with the different sized cutouts. The aim of this work is to investigate the effect of biaxial non-uniform in-plane edge loads on the vibrations and buckling behaviour of panel with and without circular cutouts by using finite element technique. Further, the effect of different ply-orientations, boundary conditions and cutout sizes are also addressed in this work. Towards this, a nine-noded heterosis plate element has been adopted to model the panel by incorporating the effect of shear deformation and rotary inertia. Finally, it is shown that the non-uniform edge loading, boundary condition and cutout sizes have a remarkable effect on the vibration and buckling behavior of panel.

Smooth Nonlinear Hysteresis Model for Coupled Biaxial Soil-Pipe Interaction in Sandy Soils

Pipelines as infrastructure components are very vulnerable to geohazard-induced ground deformation and failure. Soil–pipe interaction (SPI) thus is very important for the assessment and design of resilient pipeline systems. Previous work on SPI modeling has been based on crude assumptions, such as representation of the soil as uncoupled three-dimensional bilinear springs, and quasi-static loading conditions. This paper proposes a simplified macroelement designed to capture the effects of dynamic SPI in cohesionless soils subjected to arbitrary loading normal to the pipeline axis. First, we present the development of a uniaxial hysteresis model that can capture the smooth nonlinear reaction force-relative displacement curves (FDCs) of SPI problems. Using the unscented Kalman filter, we derived the model parameter κ that controls the smoothness of transition zone from linear to plastic using published empirical and experimental data. We extended this uniaxial model to biaxial loading effects, and showed that the macroelement can capture effects such as pinching and shear–dilation coupling. The model input parameters were calibrated using finite-element (FE) analyses validated by experiments. The FDCs of the biaxial model were verified by comparison with FE and smoothed-particle hydrodynamic (SPH) simulations for different loading patterns: cyclic uniaxial, 0-shaped, 8-shaped, and transient loading. Accounting for smooth nonlinearity, hysteresis, pinching, and coupling effects, the proposed biaxial macroelement showed good agreement with FE and SPH analyses, while maintaining the computational efficiency and simplicity of beam on nonlinear Winkler foundation models, as well as a small number of input parameters.

Fracture-mechanics-based evaluation of failure limit on pre-cracked and hydrided Zircaloy-4 cladding tube under biaxial stress states

ABSTRACTTo better understand the failure limit of fuel cladding during the pellet-cladding mechanical interaction (PCMI) phase of a reactivity-initiated accident (RIA), pre-cracked and hydrided cladding samples with base metal final heat-treatment status of cold worked (CW) and recrystallized (RX) were tested under biaxial stress conditions (strain ratios (εz/εθ) of 0 and 0.5). Displacement-controlled biaxial-expansion-due-to-compression (biaxial-EDC) tests were performed to obtain the hoop strain at failure (failure strain) of the samples. The conversion of the failure strains to J-integrals at failure (JIC) by finite-element analysis involving data of stress-relieved (SR) cladding specimens from our previous study revealed that the failure limit in the dimension of JIC unifies the effects of pre-crack depth. About 30–50% reduction in the JIC value was observed as the strain ratio increased from 0 to 0.5 irrespective of the annealing type, pre-crack depth, and hydrogen content. The rate of fractional decreases of JIC with increase of hydrogen content is in the order of CW>SR>RX, which are essentially independent of strain ratio for the CW and SR samples. The results were incorporated into the failure prediction model of the JAEA’s fuel performance code in the form of a correction factor that considers the biaxial loading effect.

The effect of bi-axial in-plane loads on nonlinear dynamics of micro-plates under harmonic excitation

Based on the theories of the first-order shear deformation (FSDT) plate and the modified couple stress, a nonlinear micro-plate model is developed for steady state dynamics of harmonically excited micro-plates subjected to two-sided in-plane tension or compressive loads. The governing equations of motion and corresponding boundary conditions are derived using Hamilton's principle. The semi-analytical method of Galerkin's is utilized to discretize the governing equations of motion into ordinary differential equations. By performing complexification-averaging method and arc-length continuation techniques, semi-analytical approximations for nonlinear steady-state response is developed. For micro-plate with post-buckling deformation coexisting attractors are observed. These attractors have different nonlinear behaviors such as multi frequency, period doubling, intermittency, quasi-periodic and chaotic behaviors. The effects of different parameters such as in-plane load, load ratio, the material length scale parameter and aspect ratio on the nonlinear forced vibration are examined.

Experimental evaluation of the effect of the internal pressure and flaw size on the tensile strain capacity of welded X42 vintage pipelines

Pipelines exposed to geo-hazards such as moving slopes, discontinuous permafrost, and other ground movements may be subjected to displacement-controlled loading, which may lead to significant plastic strains. This can potentially impact pipeline structural capacity and their leak-tight integrity. Traditional stress-based design methods may become uneconomical in the design of pipelines subjected to large plastic strain. In view of the extensive use of such pipelines, reliable calibration of the tensile strain capacity (TSC) plays a critical role in strain-based design (SBD) methodology. Recent studies were focused mostly on high toughness modern pipelines with limited research performed on lower-grade vintage pipelines. However, the effects of biaxial loading due to internal pressure and bending stresses imposed on pipelines as a result of interactions with geo-hazards were not properly addressed in previous studies. This paper investigates the effect of internal pressure and flaw size on the TSC of X42 welded vintage pipelines using experimental testing. Eight full-scale pressurized four-point bending tests were conducted on 22 inches (558.8 mm) diameter X42 grade welded vintage pipes with D/t ratio of 44 to examine the effect of the influential parameters on the TSC. Biaxial strain gauges and a digital image correlation (DIC) system were major instrumentations used for measuring strain. The results were used to examine the crack growth rate by estimating the crack mouth opening displacement (CMOD) at failure and the effects of internal pressure and flaw size on the TSC. The TSC obtained from the tests were compared with those predicted using TSC predictive models proposed by ExxonMobil and Pipeline Research Council International (PRCI).

Characterization of Mismatch Constraint Effect for the Central Crack Plate under Biaxial Loading

The effects of biaxial loading and creep mismatch on creep fracture parameter C(t) and constraint effect are investigated for the plane strain central crack plate. The studied biaxialities in this paper are limited to the range of [-1,1]. Based on the three-term asymptotic solution for creep crack tip field, the higher-order terms coefficient parameter A2(t) is introduced to characterize the creep mismatch constraint effect. The impacts of loading level on the parameter A2(t) for different biaxialities and creep mismatch factors are also examined in this paper. The result shows that the steady creep fracture parameter C* decreases with the increments of mismatch factor and biaxiality B. The creep constraint parameter A2(t) is insensitive to loading level for the creep mismatch crack plate under biaxial loading. The steady creep constraint parameter increases with the increments of biaxialities and decreases as m increases, which indicates the higher under-match plate with higher biaxiality has higher creep constraint effect.

Couple effects of mixed mode biaxial loading and crack tip configuration on plastic stress intensity factor behavior at small and large scale yielding

In this paper the plastic stress intensity factor (SIF) approach is used to study the coupling effects of loading biaxiality, material properties and crack tip configuration in both the small- and large-scale yielding ranges. For comparison between small-scale and large-scale yielding solutions, a rectangular plate with a centered line crack subjected to biaxial loading and three types of test specimens under mixed mode loading were analysed by using a finite element method. Numerical analysis was performed for two types of steel and titanium and aluminum alloys with different elastic–plastic properties. Both the mathematical notch type crack tip and the crack tip with finite radius of curvature were considered. The governing parameter of the elastic–plastic crack-tip stress field In-integral, J-integral, and the plastic SIF were calculated as functions of loading biaxiality and applied stress levels. Special emphasis was put on an ambivalent J-integral and the plastic SIF behavior for specified the crack tip geometries. Contrary trends of biaxiality effects on J-integral behavior were established depending on crack tip configuration. Nonlinear fracture resistance parameters in the form of J-integral, In-integral and the plastic SIF were calculated as a function of the material properties and mode mixity for specified test specimen geometries. Finally, the applicability of the plastic stress intensity factor approach to large-scale yielding analysis of mixed mode crack tip stress fields was demonstrated.

Constraint Assessment for Specimens Tested Under Uniaxial and Biaxial Loading Conditions

In structural integrity analysis of reactor pressure vessels (RPVs), a postulated shallow crack is subjected to biaxial far-field stresses. However, the fracture toughness Kc or Jc, which is an important material property for the structural integrity assessment of RPVs, is usually obtained from testing deeply cracked compact tension (C(T)) or single-edged bending (SE(B)) specimens under uniaxial loading. Thus, the fracture toughness data do not reflect the biaxial loading state that cracks in a RPV are subjected to. Cruciform bending specimen was therefore developed to simulate the biaxial stress state. In this paper, a series of finite element (FE) simulations of the cruciform specimens containing different crack geometries and of different material properties are conducted. The crack tip stress fields are analyzed, and the constraint is investigated using the J–A2 theory. The results show that the biaxial effect is material property dependent which could be useful for the optimization of the test method and the better design of cruciform specimens. The trends about the biaxial loading effect revealed in this study would also be helpful in estimating the safe operating life of RPVs.