Axisymmetric Conditions Research Articles

Damage Prediction in the Wire Drawing Process

In this study, the prediction of damage in the wire drawing process of 2011 aluminum alloy was investigated through both experimental and numerical methods. A comprehensive experimental setup was designed involving 20 cases of wire drawing with varying die angles (10°, 15°, 21°, 27°, and 34°) and reductions (21%, 29%, 31%, and 38%). Each case was tested three times, and the drawing forces, as well as occurrences of wire breakage, were recorded. The mechanical behavior of the material was firstly characterized using uniaxial tensile tests, whose results were used to determine the material parameters of both the hardening Voce law and those of uncoupled and coupled damage models. Then, the numerical simulations of the wire drawing process were performed using a finite element model, accounting for axisymmetric conditions and mesh convergence analysis to ensure accuracy. The previously characterized damage models were applied to evaluate their fracture prediction capabilities. A novel presentation method using three-dimensional graphs was employed to indicate the level of damage for each angle and reduction, providing greater sensitivity and insight into the damage values. Good agreement between the experimental and numerical data was demonstrated for the bilinear coupled damage model, validating its effectiveness. This study contributes to a better understanding of damage prediction in the wire drawing process, with implications for improving industrial practices and material performance evaluations.

The Coefficient of Earth Pressure at Rest K0 of Sands up to Very High Stresses

The mechanical behaviour of soils subjected to any stress path in which deviatoric stresses are present is heavily characterised by non-linearity, irreversibility and is strongly dependent on the initial state of stress. The latter, for the majority of geotechnical applications, is normally determined by the at-rest earth pressure coefficient K0, even though this state is valid, strictly speaking, for axisymmetric conditions and for zero-lateral deformations only. Many expressions are available in the literature for the determination of this coefficient for cohesive and granular materials both for normal consolidated and over-consolidated conditions. These relations are available for low to medium stress levels. Results of an extensive experimental investigation on two sands of different mineralogy up to very high stress (120 MPa) are reported in the paper. For reach very high vertical stresses, a special oedometer has been realised. In the loading phase (normal consolidated sands), the coefficient K0n depends on the stress level. It passes from values of about 0.8 to values of about 0.45 in the range of effective vertical stress σ′v = 0.5–4 MPa. Subsequently, K0n is about constant and varies between 0.45 to 0.55 up to very high vertical effective stresses (120 MPa). For the sands employed in the tests, Jaki’s relation did not lead to reliable results at relatively low pressures, while at high pressures, the same relationship seems to lead to reliable predictions if it refers to the constant volume angle of shear strength. For the over-consolidated sands, K0C strongly depends on the OCR, and for very high values of OCR, K0C could be greater than Rankine’s passive coefficient of earth pressure, Kp. This result is due to the very locked structure of the sands caused by the grain crushing, with intergranular contact of sutured and sigmoidal, concavo-convex and inter-penetrating type, that confer to the sand a sort of apparent cohesion and make it similar to weak sandstone.

Analytical solutions of combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam‐Clay

AbstractThis paper presents an analytical solution for combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam‐Clay. The governing partial differential equations for the cylindrical cavity are established in the polar coordinate. The problem is formulated as a set of first‐order differential equations by using the axisymmetric condition, equilibrium equations, and elastic‐plastic constitutive relationship. The influence of the second shear loading on the initial shear strain is considered in the plastic state. Then the stress‐strain distributions can be calculated by integrating within the elastic and plastic zones around the cavity. A finite element method simulation of the cavity under combined shear loading is established to verify the proposed approach, and the results are in good agreement with the proposed analytical solution. Parametric analyses are carried out on the effects of clay overconsolidation ratios and in situ stress coefficients under different loading paths and loading ratios. The results show that the combined shear loading on the cavity wall has a significant effect on the stress distribution of the surrounding soil, and the influence of the loading path cannot be neglected.

Rotationally induced ingress in rotor–stator systems

The presence of a rotating disk adjacent to a stationary disk forms a rotor–stator cavity known as a wheel-space. It is necessary for gas turbine wheel-spaces to be purged with sealing flow bled from the compressor to counteract the harmful effects of ingress. This paper presents a combined experimental, theoretical, and computational study of rotationally induced ingress in rotor–stator systems. Measurements were made in a wheel-space with an axial clearance rim seal under axisymmetric conditions in the absence of a mainstream annulus through-flow. Ingress was quantified using a gas concentration technique and the flow structure in the cavity was explored with static and total pressure measurements to determine the swirl ratio. A low-order theoretical model was developed based on the boundary layer momentum-integral equations. The theory gave excellent results when predicting the effects of ingress and purge flows on the radial pressure and swirl gradients. Unsteady Reynolds-Averaged Navier–Stokes computations were conducted to provide greater fluid dynamic insight into the wheel-space flow structure and ingress through the rim seal. The computational results demonstrated some of the closest agreement with experimental measurements of ingress available in the literature, showing that rotationally induced ingress is dominated by unsteady large-scale structures in the rim seal gap instead of the previously ascribed disk-pumping effect. The study serves as an important validation case for investigations of ingress in rotor–stator systems in more complex environments.

A physically consistent 2D residual stress model for approximating 3D effects in welding

Welding-induced residual stresses play a critical role in fitness-for-service evaluation of pressure equipment as stipulated by codes and standards, e.g., BS 7910 and API 579 RP-1/ASME FFS-1. Due to the complex residual stress evaluation process, two-dimensional (2D) residual stress modeling is most often exercised for supporting the development of the residual stress prescriptions in these FFS codes. Two major limitations exist in such a 2D modeling approach. One is the lack of heat sink effects in the third direction, resulting in a missing linkage to the actual welding linear heat input. The other is the over-simplifications of the mechanical restraint effects on the residual stress development process by imposing generalized plane-strain or axisymmetric conditions. This paper presents a physically consistent 2D residual stress model, with which actual welding linear heat input can be consistently interpreted for use in a 2D thermal model and 3D mechanical restraint effects can be approximated through a set of closed-form expressions that can be readily implemented in available finite element procedures. The effectiveness of the proposed 2D modeling procedures is then validated against a few well-documented residual stress case studies on which experimental data are available.

Improving sensible heat storage in a vertical annular pipe subject to variable inlet boundary condition using TiO2/water nanofluid: Numerical study

A computational fluid dynamics (CFD) analysis is conducted to investigate the thermal performance of unsteady free convection of TiO2/water nanofluids. The study process within a coaxial heat exchanger system. The model is based on the mixture Buongiorno approach. Due to the axisymmetric conditions, the study is carried out in two dimensions, and the conservation equations are reformulated in dimensionless form. The obtained PDE system is Discretized using the finite element method. The TiO2 concentration heterogeneity, resulting from thermophoresis and Brownian motion is considered. The presentation of the results encompassed isotherms, nanoparticle volume fraction distributions, and streamlines. The validation of the model shows a good agreement with the experimental results. The impact of the mass fraction’s nanoparticles ( 0.01 ≤ ϕ ≤ 0.04 ) and the Rayleigh number ( 10 3 ≤ Ra ≤ 10 8 ) on the heat transfer performance are analyzed. The parametric study shows that an increase in the Rayleigh number has no effect on heat transfer enhancement. Unlike for Ra = 10 6 where an increase in Nusselt number is observed. It was found also that the effect of nanofluid concentration on the Nusselt number was more noticeable in high Rayleigh cases due to the convection-driven heat transfer.

Unit cell consolidation of a PVD incorporated soft soil: Comparative of 2D axisymmetric and plane strain analysis considering ideal and actual drain

The paper presents two-dimensional (2D) finite element-based study of a surcharge-induced consolidating unit cell model comprising fully saturated soft soil. Radial drainage in the unit cell is ensured through a single prefabricated vertical drain (PVD) along with vertical drainage through the top surface. Finite element based 2D axisymmetric and plane strain modelling has been conducted by considering the smearing of cohesive medium. The PVD is represented by both 1D drain element (ideal drain) and through geometric modelling considering well resistance. The parameters for the ‘Soft Soil’ model for the cohesive medium are adopted from the subsurface data at Krishnapatnam Ultra Mega Power Project (KUMPP), India. Comparative assessment of unit-cell consolidation is carried out between the 2D axisymmetric and equivalent plane strain condition based on Hird’s permeability compatibility approach. The two approaches yielded noticeable disparity in the time rates of consolidation for time factor ≤ 0.4, beyond which the disparity decreases, and the two methods lead to identical results beyond time factor = 4. Further, the influence of permeability of a geometrically modelled PVD and the height of unit cell on the time-rate of consolidation is elucidated, thereby manifesting the importance of well resistance and drainage length in such analyses.

Adiabatic Compressed Air Energy Storage system performance with application-oriented designed axial-flow compressor

Medium and long-duration energy storage systems are expected to play a critical role in the transition towards electrical grids powered by renewable energy sources. ACAES is a promising solution, capable of handling power and energy ratings over hundreds of MW and MWh, respectively. One challenge with ACAES is achieving the required highly efficient operation in the compressor over the range of conditions encountered in the system as the pressure in the air store changes. In this paper, an application-oriented axial-flow compressor is designed, aiming towards efficient operation throughout the operation range, whilst also associating the performance prediction to a practical compressor geometry. A two-step design methodology based on inviscid, axisymmetric flow conditions has been implemented, leading to the flowtrack, blade-row geometries and the compressor performance map. The compressor model is integrated into an ACAES model, including two compression spools, two expansion stages with preheat, a constant volume high pressure storage operating between 5.5 and 7.7 MPa and two separate Thermal Energy Storage units. While the existing ACAES literature either ignores the transient off-design operation or uses generic numerical correlations (which are not associated to a particular geometry), the key novelty of this paper is the application of a detailed design method for turbomachinery to ACAES. The results indicate that the designed compressor requires 33 stages over the two spools, and is able to operate efficiently over the storage pressure range, showing that if the application-oriented design procedure is applied to the compressor, it does not stop ACAES reaching 70% round-trip efficiency, outputting 35MW for approximately 15 h. Importantly, the specific ACAES requirement of conserving heat at higher temperatures has been fulfilled by decreasing the number of intercoolers. Finally, it is recommended that a similar level of scrutiny is applied to the other components (i.e. expanders, heat exchangers and TES units), keeping in mind the unique set of operational requirements of ACAES. This work is an important step towards removing the common misconception that off-the-shelf components can be easily be used in typical ACAES designs.

Semi‐analytical solution for ultimate bearing capacity of smooth and rough circular foundations on rock considering three‐dimensional strength

AbstractThis paper proposes a semi‐analytical solution for the ultimate bearing capacity qu of both smooth and rough circular shallow foundations on rock mass. Specifically, a three‐dimensional (3D) Hoek–Brown (HB) is adopted, in conjunction with equilibrium equations under axisymmetric conditions, to derive the governing equations. The method of characteristics is utilized to solve the stress and failure characteristics mesh to determine the qu. The proposed solution is verified by using it to analyze test foundations. Comparison with an HB criterion‐based solution is performed to highlight the importance of 3D strength. Furthermore, parametric studies are performed to investigate the effects of rock mass properties (intact rock constant , geological strength index GSI, intact rock unconfined compressive strength σc) and foundation diameter (B) on the qu, failure surface size, and vertical stress distribution on the foundation base. The results indicate that ignoring the 3D strength and the rock mass weight would lead to underestimation of qu. Besides, the ultimate bearing capacity factor (ratio of qu to σc) increases with , GSI and B but decreases with . The failure surface size is significantly affected by , GSI, B, and rock mass unit weight. The stress distribution on the foundation base has higher variance (higher possibility of stress concentration) at smaller , GSI, and larger B, rock mass unit weight.

Load Test on Combined Pile and Cap / Pad Foundation System on Compressible Calcareous Sand and Comparison with FEM Modelling

An optimum type of foundation is expected to support 2 – 3 stories residential house on reclamation area to avoid deep foundation. The foundation will sit on engineering fill that constructed with calcareous sand which is classified as compressible sand. Below that part, at the original ground medium density sand and very soft marine clay is found stratified. Typical column in the residential building will have about 100 tons load intensity and based on this project, the design load for a single pile is 32 ton. Since no additional compression on soft clay layer is expected after building construction, than combine cap/pad foundation with short pile 6.5 m length is proposed. Load test with stress cell for this combine pile and cap/pad foundation was performed. The load test result show that interpretation using Chin’s and Mazurkiewicz’s Method obtained that the combined pile and cap/pad foundation’s ultimate bearing capacity of 112 – 119 tons. Analysis using stress cell data shows that the cap/pad carry about 31.8 % of the total load. Finite element analysis with axisymmetric condition conducted to study load distribution on combine pile and cap/pad foundation system. Analysis result was show that the cap or pad can carried about 38.1% of design load during testing. The 6.3% deviation between the stress cell and FEM results could be attribute by the assumption when calculating the load acting on cap/pad foundation. The stress cell analysis used the assumption that the load carried by the cap/pad foundation was uniform while the FEM results showed a non-uniform load.

Finite Element Formulation and Computation of Superplastic Metal Forming Processes with Optimized Rate of Deformation Control

Superplastic forming (SPF) is a material forming technique that uses superplastic exceptional elongations and deformation characteristics to form superplastic materials into certain shapes. The combination of superplastic forming with diffusion bonding (SPF/DB) gives rise to an almost unlimited extension of superplastic forming since more integral lightweight cellular structural components can be manufactured. This paper discusses numerical modelling of the mechanism of superplasticity in metallic materials. The SPF computational method based on the finite element technique augmented with the controlling rate of deformations is developed to examine a range of design or operating conditions leading to more economical forming processes. The non-Newtonian ‘viscous flow’ material is used to model the constitutive of superplastic material during the forming period. The contact mechanics between the sheet material and the mold surface and the intersheet material contact mechanics are imposed using the penalty control method, in which the sticking contact boundary conditions are employed. The space discretization is carried out using the membrane element under plane strain and axisymmetric flow stress conditions, while the implicit time integration technique is utilized to follow the shape changes of the formed sheet material. The validation of the SPF finite element formulation was performed by comparing it with the available analytical solution of Hydraulic Free Bulging of Thin strips. The SPF of a hemispherical dome made of 7475 aluminum sheet alloy was performed to demonstrate the forming process as well as to validate the results obtained between the SPF finite element numerical simulation and the experimental results. The SPF/DB of the multicell component section is considered in the final part.

Ground stability of ellipsoidal cavity due to pipeline defects

The problem of road-related sinkhole stability has long been one of the main safety concerns to pavement engineers. Collapse and blowout failures are two typical types of pipeline-related sinkhole failures. Although much research on sinkhole stability analyses can be found in the literature, most of them assume a simple circular or rectangular shape of a cavity. In this study, the problem of sinkhole stability in an ellipsoidal cavity is investigated under both blowout and collapse conditions using advanced finite element limit analysis with adaptive meshing in an axisymmetric condition. A dimensionless pressure ratio is defined to represent sinkhole stability that is a function of many design parameters such as depth ratio, elliptical shape ratio, and soil strength ratio. Selected results are compared with published solutions, and comprehensive solutions of the parametric study are presented in the form of charts for use by design engineers. The present study contributes to the understanding of sinkhole stability under an ellipsoidal cavity, and it should be of interest to the road engineering community.

Role of grain boundary crystallography on void growth in FCC metals

The growth of an isolated spherical void at and near a grain boundary or a triple junction is studied by means of full-field crystal plasticity simulations with explicit representation of the void. To examine the fundamental aspects of void/grain boundary interactions in these cases, a three-dimensional large-strain elasto-viscoplastic fast-Fourier transform (LS-EVP-FFT) model with axisymmetric tensile periodic boundary conditions was developed. We employ this model to reveal the role of crystallography (grain orientations, grain boundary misorientation and inclination angle with respect to the largest component of the applied stress) and type of loading on void growth. It was found that grain orientation was the primary crystallographic feature governing void growth in strain-rate controlled simulations. For strains small enough to not significantly alter the local geometry, the overall growth of the void in bicrystal boundaries was not strongly affected by grain boundary inclination angle. The relative amount of void growth experienced within each grain in a bicrystal or tri-crystal was strongly dependent on the grain boundary inclination angle. We found a subset of orientations that exhibit faster void growth in bicrystal boundaries than inside the constituent single crystals. Last, we show that when placed primarily in one grain but near the grain boundary, void growth was similar to void growth when placed at the grain boundary. The growing void remained in the original grain and did not grow into the other grain, regardless of crystallographic character.

Two-dimensional Axisymmetric Modeling of the Magnetic Field for High-voltage Gas Circuit Breakers

High fidelity numerical analyses of high-voltage gas circuit breakers have been conducted at Hitachi Energy Research with an in-house CFD-based arc simulation tool. The tool extends the capability of a commercial flow solver (ANSYS Fluent) to represent physical phenomena at play in a high voltage circuit breaker during a breaking operation, such as magnetostatics, polymeric and metal evaporation, and arc-network interaction. This work describes the implementation of the Biot-Savart law for computing the magnetic field generated by an electric arc under the magnetostatic approximation and in two--dimensional axisymmetric conditions. The implementation is compared to the reference one based on the magnetic vector potential formulation of the Amp`ere’s law in the Coulomb gauge. The limitations of the two formulations are discussed and their numerical accuracy compared.

Underground storage tank blowout analysis: Stability prediction using an artificial neural network

Most geotechnical stability research is linked to “active” failures, in which soil instability occurs due to soil self-weight and external surcharge applications. In contrast, research on passive failure is not common, as it is predominately caused by external loads that act against the soil self-weight. An earlier active trapdoor stability investigation using the Terzaghi's three stability factor approach was shown to be a feasible method for evaluating cohesive-frictional soil stability. Therefore, this technical note aims to expand “active” trapdoor research to assess drained circular trapdoor passive stability (blowout condition) in cohesive-frictional soil under axisymmetric conditions. Using numerical finite element limit analysis (FELA) simulations, soil cohesion, surcharge, and soil unit weight effects are considered using three stability factors (Fc, Fs, and Fγ), which are all associated with the cover-depth ratio and soil internal friction angle. Both upper-bound (UB) and lower-bound (LB) results are presented in design charts and tables, and the large dataset is further studied using an artificial neural network (ANN) as a predictive model to produce accurate design equations. The proposed passive trapdoor problem under axisymmetric conditions is significant when considering soil blowout stability owing to faulty underground storage tanks or pipelines with high internal pressures.

A MATLAB finite element toolbox for the efficient nonlinear analysis of axisymmetric shells

AbstractShells of revolution under axisymmetric conditions exhibit a circumferentially uniform pre‐buckling stress state and are important fundamental systems which often serve as reference systems for those under more complex conditions. Given this status, work is continuing on a careful and complete characterization of their buckling response with the aid of the Reference Resistance Design (RRD) framework for the ultimate benefit of the EN 1993‐1‐6 Eurocode on the strength of stability of metal shells. The situation is greatly complicated by the fact that while modern finite element software packages offer axisymmetric shell elements in an efficient 2D modelling plane, these are not capable of detecting bifurcation buckling into non‐axisymmetric modes which are often critical for slender systems. Reverting to a full 3D plane is possible, but grossly inefficient and the explicitly modelled circumferential direction is parasitic and detrimental to the overall solution quality. AQUINAS is an accessible and intuitive toolbox developed by the Authors in MATLAB for the efficient analysis of axisymmetric shell structures, aiming to reintroduce a modelling capability that was once standard in the field. Data input is entirely object‐oriented and matrix assembly is parallelized with pre‐compiled C++ routines, with users being able to take direct advantage of MATLAB's visualization properties. The software natively supports the LA, LBA, MNA, GMNIA etc. Eurocode analysis taxonomy. This paper demonstrates the current capabilities of the toolbox, describes the extensive programme of verification against existing established solutions that has been performed, and illustrates its ability to efficiently compute very detailed capacity curves using the EN 1993‐1‐6 capacity curve framework.

A rigorous analytical approach to the pile-soil interaction of torsionally loaded piles in saturated SANICLAY soils

The paper proposes a rigorous analytical approach to predict interaction between torsionally loaded piles and saturated clay soils. The soil deformation mechanism around the pile is determined using the non-associated and anisotropic constitutive model, SANICLAY, along with the axisymmetric condition, equilibrium equation, and boundary conditions. By solving the derived governing equations, the hoop shear stress against rotation curve is obtained, including elastic, elastoplastic, and critical state processes. Taking advantage of the finite-difference method, the torque-rotation behavior of the pile and the stress-strain state of the soil around the pile are figured out. The proposed approach is compared with a FEM simulation and a parametric analysis is conducted to investigate the effect of overconsolidation ratio and in-situ coefficient. Model pile tests and field tests are used to manifest the validity and capacity of the model. The results demonstrate that the present approach can well predict the torque-rotation response of the pile and can reflect some important phenomena observed in pile tests.

Tailoring superelastic and transformation-induced plastic response of shape memory multilayers with wavy architectures

The finite-volume direct averaging micromechanics (FVDAM) has been extended to simulate the superelastic and plastic response of shape memory composites. The homogenized stress–strain response and local field variables generated with FVDAM were first validated vis-à-vis the exact solution under axisymmetric loading conditions. Furthermore, an in-house finite-element code was developed to assess the FVDAM theory’s accuracy for simulating wavy multilayers. Parametric studies were conducted to quantify the effect of microstructural parameters on the nonlinear response of multilayers. The common mechanism is responsible for the differences in the nonlinear stress–strain response of multilayers is rooted in the effective stress differences that alter the phase transformation.

Application of Physics-Informed Neural Networks for forward and inverse analysis of pile–soil interaction

The application of the Physics-Informed Neural Networks (PINNs) to forward and inverse analysis of pile–soil interaction problems is presented. The main challenge encountered in the Artificial Neural Network (ANN) modeling of pile–soil interaction is the presence of abrupt changes in material properties, which results in large discontinuities in the gradient of the displacement solution. Therefore, a domain-decomposition multi-network model is proposed to deal with the discontinuities in the strain fields at common boundaries of pile–soil regions and soil layers. The application of the model to the analysis and parametric study of single piles embedded in both homogeneous and layered formations is demonstrated under axisymmetric and plane strain conditions. The performance of the model in parameter identification (inverse analysis) of pile–soil interaction is particularly investigated. It is shown that by using PINNs, the localized data acquired along the pile length –possibly obtained via fiber optic strain sensing–can be successfully used for the inversion of soil parameters in layered formations.

Pattern identification of the non-stationary laminar flow of a viscous fluid in the round pipe inlet section

The study of the patterns of change in the hydrodynamic parameters under the conditions of non-stationary flow at the entry of the cylindrical pipe and the initial arbitrary distribution of velocities in the entry section was conducted based on the boundary layer equations. A boundary problem was formed under the axisymmetric change conditions in the flow. The boundary conditions were chosen in accordance with the pattern of an arbitrary distribution of velocities in the entry section. A general solution of the approximating Navier-Stokes equations is presented depending on the initial conditions and the Reynolds number. In accordance with the type of flow, the boundary conditions of the problem are established, and the boundary-value problem is formulated. Regularities for the change in velocities lengthwise in the entrance region have been obtained for a constant and parabolic velocity distribution in the inlet cross-sections. Analytical solutions have been obtained, allowing to obtain patterns of changes in velocities and pressures toward flow at any section and at any time. For the mentioned cases, the composite graphs of velocity changes in different sections along the length of the entrance transition area were constructed by computer analysis, for different time conditions. With the obtained composite graphs, the patterns of change over the entire length of the transition area of the entrance region were constructed, enabling to obtain fluid flow velocity at any point of the section. The length of the transition zone can be estimated based on the condition of reaching a certain percentage (99%) of the maximum velocity of the flow. The proposed solutions create the conditions for correctly constructing separate units of hydromechanical equipment