Biaxial State Research Articles

Conceptualisation of biaxial tensile test setup for sheet metal forming application using fuzzy analytical network process

ABSTRACT An accurate selection of a concept among all available alternatives is one of the critical and challenging task for the designers. The overall success of commercial products is largely dependent on accurate evaluation and selection of concepts. The present work is mainly focuses on the selection of appropriate concepts for biaxial tensile test setup on uniaxial tensile test machines for sheet metal forming applications. Since biaxial states of stresses are developed in a sheet metal forming process, therefore, uniaxial tensile test is inadequate to provide complete stress strain curves and formability parameters. A more feasible biaxial test setup concept will also help in understanding the behaviour of other anisotropic materials. The available methods for concept selection like Pugh Method, Analytical Hierarchy Process are not able to capture the ambiguity related to the human’s appraisal related to Multi Criteria Decision Making (MCDM). Analytical Network Process (ANP) does take into account the interdependencies of different attributes and key enablers. A hybrid approach to concept selection has been done using fuzzy logic using an analytical network process. Parameters for cost efficiency and usability effectiveness have been considered to zero down upon the best concept. The final judgement was made using weights derived from the FANP.

A Dynamic Semi-Circular Bending Configuration for the Rheological Characterization of Asphalt Mixtures

Many experimental procedures have been proposed for the determination of the rheological properties of asphalt mixtures. Among them, the indirect tensile test (ITT) has gained a lot of attention because of its relative simplicity and advantages. However, a biaxial state of stress is developed into the sample and then, the Poisson ratio must be estimated or measured for the calculations of the dynamic modulus. Looking for a testing configuration with the same simplicity and advantages, this paper proposes the Semi-Circular Bending (SCB) geometry with dynamic loading conditions in order to characterize the rheological properties (dynamic modulus and phase angle) of asphalt mixtures. Samples compacted in the laboratory or cored from in-service pavements can be used. A uniaxial state of stress is developed in the lower plane surface of the sample doing negligible the influence of the Poisson ratio on the dynamic modulus calculations. A specific experimental configuration was adopted and a 2D-FEM model has been used for the development of an equation for the calculation of the dynamic modulus. Two different asphalt mixtures were tested at diverse testing temperatures and loading frequencies. The obtained results have been analyzed and compared with those acquired with the more conventional testing configuration in uniaxial compression. An excellent agreement has been found for either the dynamic modulus or the phase angle with both sets of results. It could be concluded that the SCB configuration has been validated as a simple and promising methodology for the characterization of the viscoelastic response of asphalt mixtures.

Energy landscapes of graphene under general deformations: DFT-to-hyperelasticity upscaling

Profound investigation of the unsurpassed mechanical properties of suspended graphene motivates the link between classical continuum mechanics (where the notions of “mechanical strength”, “mechanical stiffness”, and “elastic energy” have actually been coined) and density functional theory (DFT) rooted in quantum mechanics. Namely, the latter quantifies the energetic ground states of systems consisting of atomic nuclei and electrons; and these ground states, in turn, are directly linked to the elastic energy. While the corresponding state-of-the-art typically concerns graphene mechanics under uniaxial or equally biaxial strain states, we here present a fully anisotropic free (strain) energy function reflecting DFT-simulations associated with tens of thousands of arbitrary biaxial strain states. The latter are realized as sets of primitive unit cell vectors spanning a rhomboid unit cell hosting two carbon atoms. The position of the latter follows from internal energy minimization through the Vienna ab initio simulation package (VASP). As corresponding continuum mechanical representation we employ hyperelastic, structure tensor-based polynomial models up to the fifth order. The corresponding stress-strain relations are of concave nature, and hence, they provide access to the failure limits of the 2D material undergoing arbitrary loading situations. This is expected to introduce a new level of precision in the growing field of the structural mechanics of graphene.

Powder metallurgy and process induced residual stress states: A case distinction by X-ray diffraction

The classical sin²Ψ-method has been applied to investigate the main processing steps of a powder manufacturing route. For this investigation the hexagonal metal rhenium has been chosen to study the residual stress evolution within powder densification and the subsequent sintering. Despite the small penetration depth of the X-ray beam into rhenium it will be demonstrated that, the analysis of the sample on the basis of a biaxial residual state (σ33=0) can lead to physically totally unrealistic results within the sin²Ψ-technique. Even in those cases, where the appearance of the results derived by standard evaluation procedures (slopes within the sin²Ψ-plots) seems to be clear at a first glance, the uncritical acceptance can lead to serious errors. The differentiation demands a very detailed investigation of the sample in different diffraction geometries. More complex analysis routines, like the Rietveld based “combined analysis”, can clear without ambiguity concerning the stress state and enable the doubtless distinction between compressive/tensile and biaxial/triaxial.

Evolution on deformation behaviour of brazilian test under different contact area using particle image velocimetry and finite element modelling

Abstract This paper presents a study on the deformational behaviour of homogeneous material using Particle Image Velocimetry (PIV) and the Finite Element Method (FEM). For the initial stage, as to eliminate the inhomogeneity characteristic of rock material, homogenous acrylic material, were tested for its tensile strength using Brazilian test, under different contact area. Later, the test was carried out using a sandstone sample. It was found, with increases in the contact area, the tensile strength decreases. Based on the displacement vector of the PIV and stress concentration in the FEM, it is proven that the failure initiates from the center of the sample, which describes the bi-axial state of stress experienced in the sample. The FEM has successfully simulated that with increasing contact area, the vertical stress act in compression increases. It concentrated at the center of the sample, and move outward from the sample horizontally in lower tensile stress, which caused the diametrical fracture. In conclusion, FEM and PIV are effective tools for a better understanding of the failure behaviour samples under tensile load, particularly with varying contact area between sample and loading platen.

The stressed-deformed state of slab reinforced-concrete hollow structures considering the biaxial compression of concrete

In order to significantly reduce the weight of flat monolithic reinforced concrete floors, foundations, and other slab structures, construction operations have increasingly involved effective inserts as the separate articles made from relatively light and cheap materials that are placed in the midsection and left in the slabs after concreting.The inserts made from relatively light and cheap materials, with respect to concrete, have the strength and rigidity that are orders of magnitude less and are essentially used to form hollows. The inserts considered in this paper are prismatic. When the inserts are arranged in two directions, which is typical for most slab structures, we obtain the I-sections, whose calculation involved the analysis of the impact exerted by the general and local strength factors. Under such conditions, slabs must be calculated taking into consideration the biaxial work of concrete. In this paper, we have examined the stressed-strained state of the slab reinforced concrete structures with a bidirectional location of inserts and have substantiated the estimation schemes and calculation dependences related to the procedure for calculating the floors and other slab reinforced concrete structures with a bidirectional location of inserts. The paper gives an example of the calculation of a monolithic flooring slab based on the proposed procedure, which demonstrated that accounting for the biaxial stressed-strained state of concrete significantly increases the strength of concrete and the rigidity of a flooring slab, by 19.3 %.Thus, the consideration of biaxial compression of concrete is an important factor in the design of slab structures with a bidirectional arrangement of inserts

Strain Effects on the 2D van der Waals Heterostructure C3B/C3N: A Density Functional Theory and a Tight‐Binding Study

The 2D van der Waals (vdW) heterostructure C3B/C3N is a prototype of the 2D pn junction. To understand the effects of the built‐in electrical field on the properties of this heterostructure and the evolvement of properties under different strain states, the electronic structure of the system is systematically calculated and analyzed, using the first‐principle method and the tight‐binding (TB) Hamiltonian. Two stable structures and two saddle points in the potential surface are identified, between which the potential barriers along different sliding paths are compared. A TB model with 13 parameters is constructed, and it gives a reasonable potential difference when the heterostructure is under different strain states. Moreover, three distinct features are observed, namely the bandgap variation, metal–semiconductor transition, and band inversion under biaxial compressive strain states. By analyzing the work function change and capacitance variation, it is explained as to why the band spectrum changes as observed. This work deepens the understanding of the properties of the 2D vdW heterostructure, especially the effect of the built‐in electrical field on the band spectrum.

On the Determination of Forming Limits in Polycarbonate Sheets.

By proposing an adaptation of the methodology usually used in metal forming, this paper aims to provide a general procedure for determining the forming limits, by necking and fracture, of polymeric sheet. The experimental work was performed by means of Nakajima specimens with different geometries to allow to obtain strains in the tensile, plane, biaxial and equibiaxial states for Polycarbonate sheet with 1 mm of thickness. The application of the time-dependent and flat-valley approaches used in metals has been revealed appropriate to characterize the onset of necking and obtain the forming limits of polycarbonate, despite the stable necking propagation typical of polymeric sheets. An analysis of the evolution of the strain paths along a section perpendicular to the crack allowed for a deeper understanding of the steady necking propagation behaviour and the adoption of the methodology of metals to polymers. The determination of the fracture strains was enhanced with the consideration of the principal strains of the DIC system in the last stage, just before fracture, due to the significant elastic recovery typical of polymeric sheets. As a result of this analysis, accurate formability limits by necking and fracture are obtained for polycarbonate sheet, together with the principal strain space, providing a general framework for analysing incremental sheet forming processes where the knowledge of the fracture limits is relevant.

TO THE QUESTION OF THE STANDARD OF MECHANICAL STRESSES

The results of a study of a biaxial stress-strain state using neutron diffraction, standardized in the field of stress measurement, and the Barkhausen effect method are presented. The possibility of using a device with a biaxial load as a standard of stress is evaluated. The article gives an assessment of an error in measuring voltage using strain gauges in relation to measurements made by the neutron diffraction method. The Barkhausen effect method is used as one of the non-destructive testing methods that are sensitive to the stress-strain state. The studies describe the possibility of adapting this method to the proposed stress standard.

Mathematical modeling of area boundary of biaxial absolutely elastic states of wood

In the paper, the mathematical model for determination of the region boundary of biaxial elastic states of orthotropic materials is synthesized and the system of nonlinear algebraic equations for identification of its parameters is obtained. Using the continuous method of solution continuation concerning the best parameter and the Runge-Kutta method, the demarcation curves of absolutely elastic and non-elastic deformation regions for pine trees are depicted. The analysis of the obtained curves is carried out and on its base, it is shown that the proposed model makes possible to determine and substantiate the ultimate stress states of materials whose the asymmetry coefficients of the boundaries of proportionality in some anisotropy directions are greater, and in others less than one.

Numerical analysis of vhcf cruciform test specimens with non-unitary biaxiality ratios

With the development of new materials, it is now known that there is no such thing as a fatigue endurance limit, i.e., materials do not have infinite life when the stress level is such that there is no fracture up to 10 million (1E7) cycles. The problem of testing materials above this number of cycles is that most testing equipment operates well below 150 Hz, making testing up to 1 billion (1E9) cycles or above an impracticality. The recent developments of ultrasonic testing machines where frequencies can go as high as 20 kHz or above enabled tests to be extended to these ranges in just a few days. This is now known as Very High Cycle Fatigue (VHCF). On the other hand, critical components used in Engineering applications are usually subjected to multi-axial loads, as is the case of the fuselage and wings of aircrafts which are subjected to biaxial states of stress. In this paper, VHCF cruciform test specimens purposely designed to develop orthogonal biaxial stresses with different biaxiality ratios will be analysed. The specimens are composed from Aluminium 6082-T651, a medium strength alloy used in many highly stressed engineering applications, including trusses, cranes, bridges and transportation. The specimens work as tuning forks with determined mode shapes at 20±0.5 kHz, where maximum principal stresses are developed at the centre of the specimen. Finite Element Analysis (FEA) is used to assess the dynamic behaviour of the specimens. The framework on how to design and manufacture cruciform specimens with different biaxiality ratios will be explained in a clear way so it can be used by other engineers in the field.

Nonlinear Finite Element Analysis Formulation for Shear in Reinforced Concrete Beams

This study suggests a novel beam-column element formulation that utilizes an equilibrium-driven shear stress function. The beam shear is obtained from the bi-axial states of micro-planes, through matrix condensation and zero vertical traction assumptions. This properly remedies the shear stiffening of a one-dimensional beam-column element, keeping its degrees of freedom to a minimum. For verification of the proposed method, a total of seven shear test results of reinforced concrete (RC) beams were collected from the literature, in which the key variables were the reinforcement ratio, the presence of shear reinforcement, and section shape. The advantages are clearly shown in the shear stresses distributions being accurately described and the global load-displacement relations being successfully obtained and matching well with various test results. The proposed model shows satisfactory descriptions of the monotonic load-displacement response of the RC beams failing in multiple modes that vary from diagonal-tension to flexural-compression. In addition, more accurate and reliable information of sectional responses including sectional shear deformation and stresses is collected, leading to better prediction of a potential shear failure mode. Finally, the advantages of the proposed model are demonstrated by comparing the analysis results of an RCT-beam by using the different shear assumptions that include the constant and parabolic shear strains, constant shear flow, and the proposed shear stress function.

Investigation on shear strain of reinforced concrete membrane panels subjected to pure shear

Hsu recently conducted a shear test on nine reinforced concrete panel elements subjected to applying pure shear using a shear testing device. Modern truss models (i.e. modified compression field theory and a rotating angle softened truss model) are used to perform a complex nonlinear analysis through a trial and error method based on a double loop. This analysis is conducted by employing equilibrium conditions, compatibility conditions, and a ductile stress–strain relationship of a reinforced concrete membrane panel in a biaxial state. In this study, an effective algorithm that uses a revised Mohr compatibility method based on the failure criteria of struts and ties is proposed. This algorithm is used to improve the convergence rate in the analysis of shear history, which was performed in the experiment of Hsu. The result of the analysis indicates that the shear strain energy in a state of extended shear strain is influenced by the relationship between principal compressive stress and strain (crushing failure).

Cruciform specimens' experimental analysis in ultrasonic fatigue testing

AbstractIn this paper, two special aluminium cruciform specimens are designed and tested in an ultrasonic fatigue machine. They were designed based on Single‐Input‐Multiple‐Output (SIMO) modal analysis to induce in‐plane biaxial stress combinations (in‐phase tension‐tension [T‐T] and out‐of‐phase compression‐tension [C‐T]) when at resonance at 20 kHz. The geometries were subjected to both numerical analysis and experimental testing to understand if they can indeed create the intended biaxial state of stresses. Both numerical and experimental results showed an impact of nearby resonant modes of noninterest on the correct functioning of the specimens, especially regarding the T‐T specimen where a large deviation from the mode of interest was measured. This means that future work includes re‐designing T‐T specimens taking into account these mode shapes. Only out‐of‐phase specimens demonstrated to work properly and tests until failure were conducted. The first failure results showed to be consistent with literature when out‐of‐phase biaxial stress is applied cyclically.

Shear Design of High Strength Concrete Beams in MRFs

This paper presents the criteria for the shear design of high strength concrete (HSC) beams in moment resisting frames (MRFs). The formulation of an analytical model is provided for the case of beams with longitudinal reinforcement in the presence of transverse stirrups. The model is of additive type, in the meaning that the shear resistance of the beam is evaluated as the sum of several contributions. In particular, the contribution of concrete, longitudinal rebars and transversal reinforcement are taken into account. Furthermore, for assessing the concrete contribution, a classical approach is followed, according to which two effects arise in the shear mechanism: the arc and the beam effect. The features of these two resisting mechanisms are particularized to the case of HSC in steel reinforced beams and the maximum concrete contribution is limited to the maximum compressive strength of the concrete strut in biaxial state of stress. Moreover, for the evaluation of the resistance contribution of the longitudinal steel rebars in tension, the model takes into account the residual bond adherence between HSC and steel reinforcement and the spacing between subsequent cracks. The results are compared with the prescriptions currently provided in the main building codes and with different analytical models existing in the literature. For the comparison, the analytical expressions are applied to a set of experimental data available in the literature and design observations are made on the geometrical percentage of steel bars, the resistance of materials, the residual bond stress and the depth-to-shear span ratio.

A unified analytical solution for elastic–plastic stress analysis of a cylindrical cavity in Mohr–Coulomb materials under biaxial in situ stresses

This paper presents a unified analytical solution for elastoplastic stress analysis around a cylindrical cavity under biaxial in situ stresses during both loading and unloading. The two-dimensional solution is obtained by assuming that the connected plastic zone is statically determinate and using the complex variable theory in the elastic analysis. It is shown that the biaxial state of initial stresses applies significant influences on the stress distribution around the inner cavity. Under biaxial far-field stresses, the asymptotic conformal mapping function predicts that the outer boundary of the statically determinate plastic zone is in oval shape in Mohr–Coulomb materials. The major axis of the elastic–plastic interface lies in the direction of the greatest far-field compression pressure during loading, whereas it is along the perpendicular direction during unloading. The loading and unloading solutions are validated by comparing with the results of numerical simulation and other analytical solutions. In the assumed states, the new solution provides an accurate analytical method to capture the biaxial in situ stress effect in the prediction of the plastic failure zone and calculations of the static stress field and the elastic displacement field around a cylindrical cavity within an infinite medium.

Device and Methods for Measuring of Acoustic Anisotropy and the Residual Stress in the Main Gas Pipelines’ Metal

One of the main conditions of safe operation of gas pipelines is the use of non-destructive diagnostic methods. Particularly important problem is the earlier operational diagnosis of pipes’ material of main gas pipelines based on the evaluation of the stress-strain state, elastic moduli and properties anisotropy by acoustic methods. The aim of the work is to develop methods for acoustic assessment of the stress-strain state, the elastic moduli and the properties anisotropy of pipeline material and to study these characteristics in different sections of main pipelines using a device based on contactlessEMAtransducers.Methods are implemented using specialized equipment (the structurescopeSEMA) and non-contact electromagnetic acoustic transducers. As an object of research, we used fragments – the cuttings of gas pipelines with circumferential welds both after fabrication and removed from service with stress corrosion cracking, including ones with corrosion damage and without visible damage.The method of determining the plane stress-strain state of pipeline elements is based on the phenomenon of acoustoelasticity – the dependence of the propagation velocity of ultrasonic waves on mechanical stresses. The method for determining the elastic characteristics of materials and the anisotropy of their properties is based on the relationship between the velocities of ultrasonic waves and the elastic properties of the medium. Both techniques are implemented by sounding the sample in one section using a longitudinal wave and two shear waves with mutually perpendicular polarization planes coinciding with the main stresses, and measuring their propagation times.It is shown that the stress state distribution both in the circumferential direction and along the generatrix is uneven which is caused by the peculiarities of samples (presence of a welded joint, stress corrosion cracking, long-term operation). The smallest acoustic anisotropy is observed for the Young's modulus. The anisotropy of the properties of most samples is in the range of 12–14 % for shear modulus, 9–10 % for Young’s modulus, 13–15 % for Poisson’s ratio. For samples with stress corrosion cracking a sharp decrease in the anisotropy coefficient is observed which makes it possible to use the indicated characteristics as informative parameters in detecting stress corrosion cracking.A feature of the proposed methods is high accuracy, due to the absence of necessity to determine the material density and precision measurement of its thickness, the measurement error of which is significant by known methods.Keywords:main gas pipeline, elastic moduli, acoustic anisotropy of properties, the biaxial stress-strain state, longitudinal and transversal waves.

Biaxial elasto-plastic strain-stress state implementation in the case of the simple tension

Biaxial stress state obtaining in the flat tensile specimen is the main subject of this paper. Numerical simulation is the main method of investigation. All calculations were performed in ANSYS. The specimens with different geometry and location of the pairs of raisers stresses are considered. The choices of small plastic strains are shown. The interrelation of actual geometry of the specimen and the shape and size of advanced biaxial area is investigated. The experimental verification of the numerical simulation results is presented.

Strain effects on collagen proteolysis in heart valve tissues

Collagen is at the heart of any and all questions concerning semilunar valvular leaflet composition, structure, and function. Whether during development, physiological homeostasis, or pathological degeneration, it is the structural-mechanical state of the heart valve leaflet collagen network that ultimately confers valvular function, and the difference between health and disease. In the current study, the effects of physiologically relevant strain states on collagen catabolism are investigated in porcine aortic and pulmonary valve leaflets. Application of bacterial collagenase to the tissues which acts to simulate collagen degradation by endogenous matrix metalloproteinases, biaxial stress relaxation, and histology are all used to serve as measures of functional and compositional collagen catabolism. Current stress-relaxation results are used in conjunction with previous equibiaxial testing to confirm that a mechanism exists to prevent collagen catabolism when stretched at physiologically relevant strain states. Collectively, these in vitro results indicate that biaxial strain states are capable of impacting the susceptibility of valvular collagens to catabolism, and that at physiological strain states, a protective mechanism exists to effectively block collagen catabolism. The results of the study will be broadly applicable to clarify the roles of tissue microarchitecture and load transmission in a variety of other developmental, homeostatic, or pathogenic tissue processes such as tumor growth, embryogenesis, thrombi formation, and atherogenesis.

Spectra of Collective Excitations and Low-Frequency Asymptotics of Green’s Functions in Uniaxial and Biaxial Ferrimagnetics

The paper studies the dynamic description of uniaxial and biaxial ferrimagnetics with spin s=1/2 in alternative external field. The nonlinear dynamic equations with sources are obtained, on basis on which low-frequency asymptotics of two-time Green functions in the uniaxial and biaxial cases of the ferrimagnet are obtained. Energy models are constructed that are specific functions of Casimir invariants of the algebra of Poisson brackets for magnetic degrees of freedom. On their basis, the question of the stable magnetic states has been solved for the considered systems. These equations were linearized, an explicit form of the collective excitations spectra was found, and their character was analyzed. The article studies the uniaxial case of a ferrimagnet, as well as biaxial cases of an antiferromagnet, easy-axis and easy-plane ferrimagnets. It is shown that for a uniaxial antiferromagnet the spectrum of magnetic excitations has a Goldstone character. For biaxial ferrimagnetic materials, it was found that the spectrum has either a quadratic character or a more complex dependence on the wave vector. It is shown that in the uniaxial case of an antiferromagnet the Green function of the type Gsα,sβ(k,0), Gsα,nβ(k,0) and Gsα,sβ(0,ω) have regular asymptotic behavior, and the Green function of type Gnα,nβ(k,0)≈1/k2 and Gsα,nβ(0,ω)≈1/ω, Gnα,nβ(0,ω)≈1/ω2 have a pole feature in the wave vector and frequency. Biaxial ferrimagnetic states have another type of the features of low-frequency asymptotics of the Green's functions. In the case of a ferrimagnet, the “easy-axis” of the asymptotic behavior of the Green functions Gsα,sβ(0,ω), Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,sβ(k,0), Gsα,nβ(k,0), Gnα,nβ(k,0) have a pole character. For the case of the “easy-plane” type ferrimagnet, the asymptotics of the Green functions Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,nβ(k,0), Gnα,nβ(k,0), have a pole character, and the Green function Gsα,sβ(k,ω) contains both the pole component and the regular part. A comparative analysis of the low-frequency asymptotics of Green functions shows that the nature of magnetic anisotropy significantly effects the structure of low-frequency asymptotics for uniaxial and biaxial cases of ferrimagnet. Separately, we note the non-Bogolyubov character of the Green function asymptotics for ferrimagnet with biaxial anisotropy Gnα,nβ(k,0)≈1/k4.