Biaxial Behavior Research Articles

Characterizing the biaxial compressive deformation behavior of epoxy polymer through cruciform experiment and finite element analysis

The multiaxial deformation behaviors of amorphous epoxy polymers were characterized using planar biaxial compression tests and finite element (FE) analyses of cruciform specimens. The multiaxial limit of elastic deformation was investigated considering buckling instability of the planar biaxial compression tests. An offset-based yield criterion was proposed to determine the initial yield surface considering the nonlinear elastic deformation characteristics observed in the deformation tests. An FE analysis confirmed using the results of the tests revealed that the proposed method captured the initial multiaxial yielding in the central gauge of the specimen, demonstrating that existing pressure-dependent classical yield functions, such as the paraboloidal and conical yield functions, cannot appropriately describe the initial yield surface of the epoxy polymer. The yield function previously customized from molecular dynamics (MD) data exhibited a relatively good agreement with the initial yield surface. The determined shape of the initial yield surface and its agreement with the MD data–driven yield function were not consistently maintained during subsequent yielding. The results indicate that a new customized yield function properly describing the broader initial yield surface than those of the classical yield functions and its shape transition to plastic behavior is necessary to accurately reflect the entire multiaxial deformation behavior.

Energy-based critical plane fatigue methods applied to additively manufactured 18Ni300 steel

In this work, the uniaxial and biaxial fatigue behaviour of maraging steel (18Ni300) obtained by additive manufacturing was studied. The material was evaluated using several biaxial load paths and different load levels. The predictive capacity of the fatigue life and crack initiation angle of the critical plane methods of Liu (I and II), and Chu, Conle, and Bonnen (CCB) were evaluated. The results obtained showed that normal stresses had a strong effect on the fatigue life. In general, the best estimates of the useful life and initial crack angle prediction were obtained with the CCB method.

Mechanical Behaviour and Induced Microstructural Development upon Simultaneous and Balanced Biaxial Stretching of Poly(ethylene furandicarboxylate), PEF.

The biaxial behavior of PEF has been analyzed for equilibrated and simultaneous biaxial stretching. The ability of PEF to develop an organized microstructure through strain induced crystallization (SIC) has been described. Upon biaxial stretching, SIC can be difficult to perform because the stretching is performed in two perpendicular directions. However, thanks to the time/temperature superposition principle and an accurate heating protocol, relevant stretching settings have been chosen to stretch the material in its rubbery-like state and to reach high levels of deformation. By the protocol applied, the mechanical behavior is easily transposable to the industry. This work has shown that PEF can, as in uniaxial stretching, develop well-organized crystals and a defined microstructure upon biaxial stretching. This microstructure allows the obtention of improved mechanical properties and thermal stability of the biaxially stretched samples. The crystals induced upon biaxial stretching are similar to the one that has been developed and observed after uniaxial stretching and upon static crystallization. Moreover, the furan cycles seem to appear in a state similar to the one of a sample crystallized upon quiescent condition. The rigidity is increased, and the α-relaxation temperature is increased by 15 °C.

Biaxial deformation behaviour of duplex stainless steels: Experiments and crystal plasticity based stress predictions

Biaxial tensile tests are performed on two phase duplex stainless steel using a newly developed multiaxial testing rig integrated with a digital image correlation mapping facility. A cruciform-shaped specimen geometry is subjected to equibiaxial tensile (EBT) loading, and the load–strain response is captured. Unlike uniaxial tensile testing, a well-defined gauge area is absent in biaxial specimens; hence, stress cannot be estimated directly. Finite element analysis is used to calculate the stress state. The phenomenological finite element model failed to capture the inherent anisotropy of the material; hence, a crystal plasticity finite element based method is used to estimate the stresses. It is observed that the 0.2% proof stress increased, but the strain to failure remained constant in comparison with uniaxial tensile properties. The work hardening behaviour is isotropic similar to that observed during uniaxial testing. The goss and rotated goss orientations in austenite accommodated most of the strain along RD and TD, respectively. During EBT, the change in austenite and ferrite textures is minimal and similar to their single phase counterparts reported in the literature. The EBT test results indicate that the influence of micromechanical interactions between the phases on the work hardening behaviour and texture evolution is weak.

A review of in-plane biaxial fatigue behavior of metallic materials

Aerospace components, such as aircraft fuselage panels, pressurized container and turbine blades are exposed to in-plane biaxial fatigue loading in service. Assessment of the effect of biaxial stress state is of great importance in structural reliability analysis. In this paper, the current state of understanding and development of the fatigue behavior of metallic materials under in-plane biaxial loading is reviewed. The fatigue properties in cruciform specimens were examined under in-phase and out-of-phase biaxial loading as well as in-phase biaxial loading with overloads. The effect of stress biaxiality on the fatigue behavior, including crack initiation, crack trajectory, crack growth rate and fatigue life, were presented. The fracture morphology analysis was shown to clarify the mechanism of biaxial fatigue damage. Furthermore, several models that have been used to predict the biaxial fatigue behavior were analyzed. The applicability of these models in correlating biaxial experimental data were evaluated.

Deformation behavior and formability of friction stir processed DP600 steel

Abstract The effect of friction stir processing (FSP) on the formability of DP600 steel was experimentally investigated and the basic relationships between biaxial deformation behavior and FSP-induced evolutions in microstructural and mechanical properties were established. FSP formed a microstructure that consists of lath martensite with increased volume fraction compared to as-received (AR) microstructure that mainly consisted of well-distributed fine martensite particles in a ferrite matrix. Consequently, AR yield strength (301 MPa) and ultimate tensile strength (621 MPa) increased to about 811 and 1054 MPa, respectively. This strength enhancement achieved accompanied by adequate uniform elongation and elongation to failure values of 6.3 and 13.0%, respectively. Under biaxial loading conditions, good strain hardenability of the AR DP600 steel brought about a large membrane stretching regime leading to high punch force for biaxial flow. After FSP, both punch displacements within the membrane stretching regime decreased due to the increased volume fraction of lath martensite leading to higher cracking tendency. In result, cup depth and peak punch force of FSPed DP600 decreased from 8.7 mm and 33.2 kN to 7.1 mm and 28.1 kN, respectively. The obtained results simply indicate that FSP can be employed to enhance the strength of dual-phase steels with a reasonable level of formability.

Structural and biomechanical characterizations of acellular porcine mitral valve scaffolds: anterior leaflets, posterior leaflets, and chordae tendineae.

Mitral valve (MV) tissue engineering is still in its early stage, and one major challenge in MV tissue engineering is to identify appropriate scaffold materials. With the potential of acellular MV scaffolds being demonstrated recently, it is important to have a full understanding of the biomechanics of the native MV components and their acellular scaffolds. In this study, we have successfully characterized the structural and mechanical properties of porcine MV components, including anterior leaflet (AL), posterior leaflet (PL), strut chordae, and basal chordae, before and after decellularization. Quantitative DNA assay showed more than 90% reduction in DNA content, and Griffonia simplicifolia (GS) lectin immunohistochemistry confirmed the complete lack of porcine α-Gal antigen in the acellular MV components. In the acellular AL and PL, the atrialis, spongiosa, and fibrosa trilayered structure, along with its ECM constitutes, i.e., collagen fibers, elastin fibers, and portion of GAGs, were preserved. Nevertheless, the ECM of both AL and PL experienced a certain degree of disruption, exhibiting a less dense, porous ECM morphology. The overall anatomical morphology of the strut and basal chordae were also maintained after decellularization, with longitudinal morphology experiencing minimum disruption, but the cross-sectional morphology exhibiting evenly-distributed porous structure. In the acellular AL and PL, the nonlinear anisotropic biaxial mechanical behavior was overall preserved; however, uniaxial tensile tests showed that the removal of cellular content and the disruption of structural ECM did result in small decreases in maximum tensile modulus, tissue extensibility, failure stress, and failure strain for both MV leaflets and chordae.

Experimental tests and numerical modeling of full-scale unbonded fiber reinforced elastomeric isolators (UFREIs) under bidirectional excitation

Unbonded fiber reinforced elastomeric isolators (UFREIs) can be used for the seismic protection of structures as a lower-cost alternative to conventional laminated rubber bearings, by replacing internal steel shims with fiber reinforcement and exploiting the frictional mechanism at the rubber-concrete interface to avoid anchorage bolts. In this paper, the hysteretic behavior of full-scale (diameter 620 mm) UFREIs is investigated in both an experimental and a numerical framework when subjected to triaxial loading (i.e., simultaneous imposed displacement along two horizontal directions with concurrently applied vertical load), to account for the inherent multi-directional nature of a real earthquake scenario. Experimental results of UFREIs tested under two bidirectional orbits involving different velocities and amplitudes up to 100% shear strain are presented, and peculiar effects ascribed to the lateral coupling of the devices are identified by comparison with monodirectional test results. Then, an efficient nonlinear phenomenological model is proposed to simulate the isotropically coupled biaxial hysteretic behavior of UFREIs detected from the experiments. This model consists of a set of nonlinear springs arranged in a circular configuration and governed by just three parameters with clear mechanical significance. Novel analytical (closed-form) expressions for the model calibration are ad-hoc developed in this paper. This modeling approach is used to quantify the impact of biaxial coupling of UFREIs on the structural performance of base-isolated structures under bidirectional seismic excitation. To this aim, the seismic response of a three-dimensional reinforced concrete building isolated with UFREIs is numerically simulated. Numerical results show that isolator displacements and superstructure accelerations tend to be higher by using an uncoupled model, calibrated upon monodirectional tests and that neglects bidirectional interaction, as usually performed in practice.

Investigation of Fatigue Crack Growth in TA2 Cruciform Specimen with an Inclined Crack, Considering Stress Ratio and Biaxial Load Ratio

The biaxial fatigue crack growth behavior of commercial pure titanium TA2 of cruciform specimens with different crack inclination angles (β = 90°, 60°, 45°) under various biaxial load ratios (λ = 0, 0.5, 1) and different stress ratios (R = 0, 0.1, 0.3) is studied by an IPBF-5000 biaxial testing machine. The test results prove that the maximum tangential stress criterion is suitable for predicting the initiation angle of uniaxial and biaxial mixed-mode I–II fatigue cracks. The fatigue crack growth rate of a cruciform specimen with mode I and mixed-mode I–II cracks decreases with the increase of biaxial load ratio and increases with the stress ratio. The Walker model and Kujawski model have better compression effects on fatigue crack growth data than the Paris model.

Analysis-oriented model for FRP tube-confined concrete: 3D interpretation of biaxial tube behaviour

Filament-wound fibre-reinforced polymer (FRP) tubes are an emerging FRP product employed in various FRP-concrete composite structures, such as concrete-filled FRP tubes (CFFTs). Due to the fibre orientations in the tube wall, the filament-wound FRP tube exhibits biaxial behaviour under simultaneous axial compression and hoop expansion, causing relaxation of the confining stress. Therefore, the conventional hoop tension test may result in overestimation of the confining stiffness. In this paper, the biaxial behaviour of FRP tubes is theoretically investigated using classical laminate theory in conjunction with an analysis-oriented model for FRP-confined concrete. The geometrical meaning of the biaxial tube behaviour is interpreted intuitively using the 3D geometrical approach previously proposed by the authors. For the convenience of analysis and design, this paper proposes a simplified approach to rectify the confining stiffness that considers both elastic and nonlinear biaxial effects. The predicted results show good agreement with the collected test data.

Strain-dependent stress relaxation behavior of healthy right ventricular free wall

The increasing evidence of stress-strain hysteresis in large animal or human myocardium calls for extensive characterizations of the passive viscoelastic behavior of the myocardium. Several recent studies have investigated and modeled the viscoelasticity of the left ventricle while the right ventricle (RV) viscoelasticity remains poorly understood. Our goal was to characterize the biaxial viscoelastic behavior of RV free wall (RVFW) using two modeling approaches. We applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) theories to experimental stress relaxation data from healthy adult ovine. A three-term Prony series relaxation function combined with an Ogden strain energy density function was used in the QLV modeling, while a power-law formulation was adopted in the NLV approach. The ovine RVFW exhibited an anisotropic and strain-dependent viscoelastic behavior relative to anatomical coordinates, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. From the QLV fitting, the relaxation term associated with the largest time constant played the dominant role in the overall relaxation behavior at most strains from early to late diastole, whereas the term associated with the smallest time constant was pronounced only at low strains at early diastole. From the NLV fitting, the parameters showed a nonlinear dependence on the strain. Overall, our study characterized the anisotropic, nonlinear viscoelasticity to capture the elastic and viscous resistances of the RVFW during diastole. These findings deepen our understanding of RV myocardium dynamic mechanical properties. Statement of significanceAlthough significant progress has been made to understand the passive elastic behavior of the right ventricle free wall (RVFW), its viscoelastic behavior remains poorly understood. In this study, we originally applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) models to published experimental data from healthy ovine RVFW. Our results revealed an anisotropic and strain-dependent viscoelastic behavior of the RVFW. The parameters from the NLV fitting showed nonlinear relationships with the strain, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. These findings characterize the anisotropic, nonlinear viscoelasticity of RVFW to fully capture the total (elastic and viscous) resistance that is critical to diastolic function.

Biaxial Elongation Behavior in Partially Molted State of Two-Layer Sheets Containing Postconsumer Material

Due to the lack of raw material and forced by political demand, an increasing percentage of postconsumer materials (PCR) shall be used in all processing methods in polymer technology. Thermoforming, as one of the oldest polymer-processing methods, has special requirements regarding the melt stability at high temperatures. Low melt stability affects the thermoforming in a negative manner, as the low stiffness leads the sheet to sag during the heating phase. In this study, two-layer sheets are used in order to improve melt stability of PCR material. The focus is placed on the influence of rheological properties on the biaxial stretching behavior of mono- and two-layer sheets in partially molted state. In order to create a stabilizing layer, two different thermoformable virgin materials with a melt flow rate (MFR) of 3 g/10 min and 6 g/10 min were chosen. The second layer consists of instable PCR materials with a MFR of 16 g/10min and 50 g/10 min. Rheological investigations, molecular characterization and biaxial stretching tests are used to show the benefit of two-layer sheets for processing PCR material under elongational stress. The results show that the use of two-layer sheets can improve the biaxial stretching properties, so that two-layer sheets can offer a significant potential in the processing of PCR materials in thermoforming.

Measurement of Biaxial Deformation Behavior and Material Modeling for HI-PVC Using Multiaxial Tube Expansion Test

This study investigates the biaxial deformation behavior of the High Impact Polyvinyl Chloride (HI-PVC) used as a water pipe material. Multiaxial tube expansion test (MTET) was performed on the HI-PVC circular tube, and the stress-strain curves were measured for nine linear stress paths. The contours of plastic work and the directions of the plastic strain rates were also measurd. The experimental results show that the test sample has a strong anisotropy. Anisotropic hardening behavior was also confirmed from the evolution of the work contours. It was confirmed that the Yld2000-2d yield function had a better agreement with the measued work contour than Hill’s quadratic and the von Mises yield functons. Moreover, it was found that the test sample follows the normality rule with the Yld2000-2d yield function.

Measurement and Analysis of Deformation Behavior of Polyethylene Tube Subjected to Linear Loading and Unloading Stress Paths with Large Strain

A material testing apparatus for measuring the biaxial deformation behavior of a polymer tube has been developed to quantitatively evaluate the deformation behavior of polymeric materials. The testing apparatus can apply axial force and internal pressure to a tubular specimen. A noncontact strain measurement system was also developed, and the biaxial strain components and the radius of curvature in the axial direction of the bulging specimen are continuously measured to control the stress path applied to the specimen. Polyethylene tube with an outer diameter of 17 mm and a thickness of 2 mm are used as a test sample. The tubular specimens were subjected to linear stress paths with stress ratios of σΦ:σθ =1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1, where σΦ and σθ are the axial and circumferential stress components, respectively, applied to the central area of the bulging specimen. Loading and unloading tests were performed to determine the biaxial true stress-logarithmic plastic strain curves. The strain rate was 1×10-3s-1. From these test results, contours of plastic work and the directions of the plastic strain rates were measured to identify a proper material model for the test sample using the Yld2000-2d yield function (Barlat et al., 2003).

Compressive stress-strain relationships of concrete exposed to elevated temperatures based on mesoscopic damage method

Damage evolution in concrete after high temperature is a complicated procedure, in which the pre-peak strain hardening behaviour, the post-peak strain softening behaviour and the impact of high temperature play key roles. Uniaxial and biaxial compression damage models of concrete considering high temperature degradation effect are proposed based on damage theory and experimental phenomena. They consider that the destruction of concrete is actually the cumulative evolution course of the two meso-damage modes, rupture and yield. High temperature changes the mechanical performance in microstructure of concrete and the generation and propagation of microcracks. It could be described by adjusting the probability distributions which characterize the mesoscopic damage evolution. The damage constitutive model is employed to determine the stress-strain behaviour of concrete under uniaxial compression, and the calculated results are compared with the experimental results under different high temperature levels. Results indicate that the proposed model can not only predict the stress-strain behaviour with acceptable accuracy in macroscopic scale, but also reveal the damage evolution mechanism in mesoscopic scale. Finally, the constitutive behaviour under biaxial compression is also simulated to investigate the influence of high temperature on biaxial stress-strain behavior and strength envelope.

Numerical parametric study on the uniaxial and biaxial compressive behavior of H-shaped steel reinforced concrete composite beam-columns

As a follow-up work of previous experimental efforts, this paper aims to further explore the compressive behavior of Steel Reinforced Concrete (SRC) composite beam-columns with assistance of nonlinear Finite Element Analysis. The FE model was developed in ABAQUS software and it delivered desirable accuracy after calibrating against the dataset collected from published literatures. The validated FE model was then employed to evaluate the fundamental performance of SRC beam-columns under uniaxial eccentric compression and biaxial eccentric compression. On top of that, the fiber section analysis was adopted to build the three-dimensional axial force-bending moment (N-M) interaction diagrams, followed by a parametric study to investigate the effect of material grade, steel ratio, cross-section geometry, load eccentricity and load inclination on the load-carrying capacity of SRC beam-columns, and disclose the complex biaxial interaction mechanism that is not well-considered in current design codes. Based on the numerical data generated from parametric study, the Support Vector Machine method is utilized to intelligently estimate the biaxial moment contours under varying load levels, which exhibits improved accuracy and consistency than the code-specified method and conventional empirical formulae.

Cryogenic deformation behavior of 6061 aluminum alloy tube under biaxial tension condition

Cryogenic forming has been proposed for the fabrication of complex aluminum alloys tubular components to overcome the shortcomings of traditional forming processes. It is difficult to evaluate the cryogenic biaxial deformation behavior. In this study, a novel cryogenic hydro-bulging device was established to evaluate cryogenic deformation behavior and verify the feasibility of the new forming process. The cryogenic biaxial stress-strain relations were determined using a new analytical model to quantitatively characterize the hardening behavior. The cryogenic deformation mechanism was revealed by microstructure characterization. It is found that the maximum expansion rate of 6061 aluminum alloy tube at − 196 ℃ increases to 34.0% ± 0.6%, being 99.8% higher than that at room temperature. The obtained cryogenic biaxial flow curve exhibits the significantly improved plasticity and hardening ability with a strain hardening exponent of 0.43 at − 196 ℃. The high cryogenic strain hardening rate contributes to the stable uniform deformation. The improved cryogenic plasticity is associated with the diminished dislocations accumulation at grain boundaries. The enhanced cryogenic hardening ability is attributed to the impeded movable dislocations slip. The research demonstrates that cryogenic medium pressure forming has great potential for the fabrication of complex aluminum alloy tubular components. • A novel cryogenic hydro-bulging device was established for evaluating the cryogenic biaxial deformation behavior oftubes. • The cryogenic biaxial mechanical properties and hardening behavior were quantitatively evaluated by a new analytical model. • Excellent cryogenic biaxial formability can be obtained, contributing to the fabrication of complex tubular parts. • Microstructure was characterized to reveal the cryogenic deformation mechanism.

A study on texture stability and the biaxial creep behavior of as-hydrided CWSR Zircaloy-4 cladding at the effective stresses from 55 MPa to 65 MPa and temperatures from 300 °C to 400 °C

The creep rupture of high burnup used nuclear fuel (> 45 GWD/MTU) cladding is regarded as one of the failure mechanisms during long-term dry storage. A high amount of zirconium hydride in the cladding matrix would degrade the mechanical properties of the cladding especially leading to delayed hydride cracking. To better understand the influence of zirconium hydride on the biaxial thermal creep performance and the crystalline texture stability of Zircaloy-4 cladding, the pressurized tube technique is applied to test the durability of the as-hydrided material. Tests were performed on as-received Zircaloy-4 tubular specimens as well as-hydrided ones with targeted 300 wt parts per million (wppm) or 750 wppm hydrogen. The biaxial creep experiments were conducted at temperatures from 300 °C to 400 °C and at equivalent stresses at mid-wall from 55 MPa to 65 MPa. The hydridation process prior to creep tests induces the formation of FCC δ-hydride platelets along the circumferential direction of the tube. This alignment and phase structure of hydride show no significant change after biaxial creep tests. The creep strain-rate negatively depends on the hydrogen content. The synchrotron wide-angle X-ray diffraction (WAXD) technique and electron backscatter diffraction (EBSD) analysis were applied for the study of the crystallographic orientation relationship. zirconium-to-hydride grain orientation follows Shoji–Nishiyama crystallographic relationship. This relationship is stable before and after creep deformation. These results of creep performance and texture stability of Zircaloy-4 claddings can help support the design basis of interim and long-term dry storage facilities.

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading.

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors KI and KII for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.

Behavior of Confined Concrete using Prestressing Skew Bars

This paper presents the results of an experimental study on the biaxial compression behavior of concrete prism confined using pre-stressed bars. The pre-stressed bars could provide passive confinement stress, that preventing the lateral strain of the prism from increasing leading to an increase in both the initial modulus of elasticity and prism compressive strength. The confined concrete had a higher compressive strength that was directly proportional to the confinement bar pressing force and lower ductility than the plain prisms. The concrete initial modulus of elasticity is directly proportioned to the confinement lateral pressure of the prestressing bar and inversely proportion with the spacing between prestressing bars. It was simple to find out that the best pre-stressing stress was 10 N/mm2, also the compressive strength of the confined concrete with pre-stressed skew bars was greater than the compressive strength of the unconfined concrete by more 3.3 times.