Elastic-plastic Finite Element Research Articles

Implementation and Application of Cell-Based S-FEM Based on the Object-Oriented Programming Framework

The object-oriented programming is widely used in different fields of finite element analysis (FEA). The commonly used object-oriented codes were almost written by C++. Due to the inability to automatically manage memory and the lack of gigantic standard library and a third-party library for C++, building matrix classes are needed and a strong programming ability for program developers is also necessary. The conventional FEM method still has many disadvantages such as poor accuracy, hard stiffness matrix, mesh dependence and lack of upper bound solution. The smoothed FEM (S-FEM) method proposed by Liu et al. can efficiently overcome these disadvantages and is therefore widely used in FEA. In this work, the elastic-plastic CS-FEM method is extended and implemented using Python programming based on the framework proposed [H. Li and Y. Xiao, Implementation and numerical simulation on object-oriented elastic-plastic finite element method based on Python, J. Syst. Simul. 36(5) (2024) 1107–1117] The resulting object-oriented elastic-plastic CS-FEM framework is then applied to FEA of elastic-plastic mechanics problems. The correctness of the resulting framework and the high computational accuracy and good mesh adaptability of CS-FEM models have been verified by comparing the corresponding results with an analytical solution or ABAQUS results. The object-oriented elastic-plastic CS-FEM framework provides a more efficient and adaptable approach to FEA, and can also overcome many limitations of the conventional FEM method and C++ programming. The use of Python and the CS-FEM method offers improved computational accuracy, mesh adaptability and development efficiency, and this will make it a valuable tool for solving practical problems in mechanics and engineering.

Probabilistic Modeling Geometric Tolerance and Low Cycle Fatigue Life of Gas Turbine Compressor Blade

Abstract This paper presents a probabilistic low cycle fatigue (LCF) assessment for geometric tolerances on high load contact surfaces of gas turbine compressor blades. The typical patterns of the geometric deviations for the root contact flank of the compressor blades are identified and characterized according to coordinate measurement machine (CMM) measurements of the blade root. These typical patterns are closely related to the root form manufacture tools and process. Finite element (FE) models for the typical geometric deviation patterns are created based on nodal coordinates transformation of the surface nodes on the blade root contact flanks and radius. An optimized blade root profile tolerance is established, which enables significant cost saving. The elastic-plastic FE analysis with nonlinear contact model, material strain-life test, response surface, and constrained Monte Carlo simulation are used to create a probabilistic LCF life model for the optimized tolerance. The model quantifies the effect of the geometric deviations, blade mass, and material property on the blade LCF life. The result shows that with the optimized tolerance, the probability of blade LCF failure is very low and acceptable. It is also shown that the strain life material property is the most critical factor for the LCF failure. The root profile tolerance and blade mass are seen to have a much weaker effect on the blade LCF life.

Theoretical Study of Asymmetric Bending Force on Metal Deformation in Cold Rolling

A three-dimensional elastic–plastic finite element model of a six-roll cold rolling mill has been developed using the finite element software ABAQUS. The actual parameters of the rolling mill have been incorporated into the finite element model, with the working conditions applied as boundary constraints and load conditions. Subsequently, a non-symmetrical bending force is introduced to the finite element model. Through simulation calculations, this study analyzes the patterns of change in the transverse pressure of the rolling mill and roller pressure during non-symmetrical bending, as well as the variations in strip thickness, crown, edge drop, and flatness. Additionally, the regulating function of the bending force is examined. Each adjustment of 5 t in the asymmetric bending force results in an increase of approximately 0.01 mm in the thickness of the positive bending side of the strip while causing a decrease of about 0.01 mm in the thickness of the negative bending side. Therefore, the application of asymmetric bending forces proves to be effective in controlling the shape of lateral wave defects on the edges of steel strips.

Detectability of residual stress anomalies in railway wheels with different geometries subjected to thermal overload based on back gauge change

Temperature increases of railway wheels due to frictional braking on the running surface (wheel tread) can lead to maintenance challenges such as tread wear and thermal cracking. While heating within the anticipated design range should not adversely affect the structural safety of the wheels, excessive temperature rises resulting from brake system failures can induce tensile residual stresses in the rim, potentially leading to wheel fracture. Detecting wheels with abnormal residual stresses is therefore crucial for railway safety, and monitoring residual displacements in the rim due to changes in circumferential residual stresses is an implementable approach. However, the shape of the wheel web varies, and the displacement response to thermal input differs depending on the wheel geometries. This study aims to explore general deformation behaviours related to wheel shape and elucidate the relationship between shape and heat resistance. The elastic-plastic finite element analysis employing simplified intense thermal input revealed that residual deformation after excessive thermal loading consistently results in back gauge expansion, although the deformation and stress responses differ based on the web geometry. Differences in heat resistance are indicated by the variation in the temperature at which compressive yielding due to thermal stress occurs, depending on the web shape. The residual stress detectability of each wheel is determined based on the principle that greater residual displacement at lower stress indicates higher anomaly detectability.

Error analysis for determining transverse tensile delamination strength of REBCO coated conductors by anvil test: numerical simulation demonstrations

RE–Ba–Cu–O (REBCO, where RE = Y, Gd, Sm, and other rare earth elements) coated conductor (CC) tapes exhibit considerable potential for application within the domains of high-energy physics and high-field science. Nevertheless, weak interfacial properties pose a significant obstacle, impeding the progress and practical implementation in high-field scenarios. The anvil tension method has been extensively employed for the assessment of transverse delamination strength of REBCO CC tapes. However, the outcomes derived from anvil tension exhibit severe dispersion, thereby impeding its efficacy in evaluating material performance. The underlying cause of this phenomenon remains unidentified. In this study, error analysis of anvil measurement method in determining the transverse tensile delamination strength (TTDS) of REBCO CC tapes was conducted based on finite element (FE) numerical simulations. A two-dimensional multilayer elastic-plastic delamination FE model with main layers of REBCO CC tapes, solder connecting layers and anvil materials were developed based on the bilinear cohesive zone model. The effects of anvil test conditions and the structural configuration of the conductor itself on the test results were discussed. Simulation results show that localized premature cracking of the interface due to stress concentration and plastic yielding of the CC tape around the loading boundary is the root reason for the discrepancy between the anvil test results and the true interfacial strength. Therefore, anvil test conditions (including top anvil dimensions, soldering conditions, loading eccentricity angle, and anvil material properties) as well as the structural configuration of the conductor itself (including edge initial crack length, edge encapsulation width, and stabilizer thickness) have a significant impact on anvil test-based TTDS results.

Influence of welding sequences and boundary conditions on residual stress and residual deformation in DH36 steel T-joint fillet welds

This paper aims to investigate the influence of welding sequences and boundary conditions on welding-induced residual stress and residual deformation of DH36 steel T-joint fillet welds through experimental and numerical methods. A series of typical experiments of successive and simultaneous double-sided welding conditions are conducted to explore both the magnitude and distribution of temperature field, residual stress and residual deformation. Meanwhile, thermal elastic-plastic finite element analysis based on a double ellipsoidal heat source model is performed to investigate the heat transfer and deformation mechanism during the welding process. The influencing factors are further explored to determine and quantify the residual stress and residual deformation induced by different welding sequences and boundary conditions. There is generally well agreement between the experimental and numerical results in terms of temperature field, residual stress, residual deformation and molten pool morphology. The results show that the welding sequences have an important influence on the magnitude and distribution of residual stress and residual deformation. Continuous simultaneous double-sided welding can significantly reduce residual stress and residual deformation to obtain better-quality welds. Boundary conditions have a significant effect on the distribution and magnitude of residual deformation and little effects on residual stress. Tightening the ends of the flange plate with bolts during the welding process can significantly reduce the deformation.

Experimental, numerical, and theoretical analysis of tapered belleville spring

Uniform thickness belleville springs(UBS) are a suitable replacement for coil springs in many applications due to their ability to take higher loads and their relatively small and compact size. This paper presents an experimental, numerical and theoretical analysis of the taper belleville spring(TBS). Experimental results on a normal taper belleville spring (NTBS), fabricated from stainless steel alloy (SS304), are presented. Non linear elastic-plastic finite element simulations support the experimental behaviour reasonably well. A correction factor based on Timoshenko’s theory of plates, to match the finite element analysis(FEA) results for NTBS, is presented. Reverse taper belleville spring (RTBS) analysis shows that it can store more elastic strain energy than UBS and NTBS. An optimisation study on TBS geometrical parameters is performed to attain maximum energy absorption for the null stiffness region.

Prediction of Welding Deformation Using the Thermal Elastic-Plastic Finite Element Method by Considering Welding Interpass Temperature.

In this study, we propose a method for predicting welding deformation caused by multi-pass welding using the thermal elastic-plastic finite element method (TEP-FEM) by considering the interpass temperature. This method increases the interpass temperature, which has not been considered in the existing TEP-FEM, from 200 °C to 1000 °C, and simultaneously performs thermal and mechanical analyses. In addition, this method can also evaluate temperature history and the time it takes to weld. By predicting the welding deformation using this method, angular distortion prediction was reduced from 16.75 mm to 10.9 mm compared to the case where the interpass temperature was cooled to room temperature. Additionally, the deformation error was significantly reduced from 6.14% to 2.92% compared to that of the strain as directed boundary method used in a previous study. Additionally, our research demonstrated that interpass temperatures above 800 °C can result in increased deformation errors. In conclusion, it is essential to select an appropriate temperature to minimize deformation error.

Seismic Response and Collapse Analysis of a Transmission Tower Structure: Assessing the Impact of the Damage Accumulation Effect

This paper delves into the impact of the damage accumulation effect, which leads to the degradation of material strength and stiffness, on the seismic resistance of transmission towers. Building upon the elastic–plastic finite element theory, a mixed hardening constitutive model is derived for circular steel tubes, standard elements in transmission towers, incorporating the damage accumulation effect. A user material subroutine, UMAT, is created within the LS–DYNA framework. The program’s validity and reliability are established through axial constant–amplitude loading tests on single steel tubes. The subroutine is employed to conduct the incremental dynamic analysis (IDA) of an individual transmission tower and to contrast it with the structure utilizing the Plastic Kinematic material model, assessing the discrepancies in tower top displacements and segment damage indices (SDIs) at both macroscopic and microscopic scales. The results shows that the Plastic Kinematic model inflates the seismic performance of the transmission tower. When considering the damage accumulation effect in structural failure, the damage index of the members increases, leading to a reduction in both the structural strength and stiffness. The dynamic response in the plastic phase becomes more pronounced, and the onset of structural failure is accelerated. Consequently, structural analysis under seismic conditions should account for the damage accumulation process. Through the delineation of member and segment damage, the extent of damage to transmission tower segments can be quantitatively assessed. Subsequently, the ultimate load–bearing capacity and the most vulnerable location of the transmission tower can be ascertained. Finally, this paper provides a detailed analysis of the transmission tower collapse process under seismic action and summarizes the mechanism of collapse for the structure.

Analysis of fracture damage mechanical properties of particle reinforced polymer composite film based on micro-macro finite element method

The particle reinforcement and related effect on fracture damage mechanical properties of polymers have been studied in this paper. Based on the uniaxial tensile test result of SiO2 particle reinforced polyvinylidene fluoride (PVDF) composites, the parameters of macro elastic-plastic finite element model and micro particle reinforced model are obtained. The effects of boundary conditions, shape and size of damage notch on fracture damage mechanical properties of PVDF composites are studied from macroscopic view. The uniaxial tensile mechanical properties and elastic modulus are increased with notch angle (0°, 30°, 60°, 120°). The damage analysis of the micro model shows that the mechanical properties of SiO2/PVDF composites are best when the content of SiO2 is 6%. Debonding between particles and matrix indicates have great effect on crack propagation. The micro-macro finite element model is effective tool to study the damage mechanical properties of particle reinforced polymers.

Local relaxation of residual stress in high-strength steel welded joints treated by HFMI

This research studies the influence of high-peak loads on local relaxation of residual stress and fatigue damage in high-strength steel welded joints treated by high-frequency mechanical impact (HFMI) treatment. The joint behavior is simulated with elastic–plastic finite element analyses that account for the combined effect of geometry, residual stress, and material properties. This simulation uses two treated geometry models: with or without surface roughness on HFMI groove, and two material properties: S690QL and AH36 structural steels. The results show that surface roughness and load history, including high-peak loads, significantly influence fatigue response. It is revealed that the model neglecting the surface roughness cannot represent the amount of residual stress change and fatigue damage at less than 100 µm depth from the surface. In addition, the local yield strength in the HFMI-treated zone affects the plasticity behavior near the surface imperfection under the high-peak loads, which provides comparatively different fatigue damage between S690QL and AH36 in some cases. As a result, this study provides the further understanding needed to develop a robust modeling approach to the fatigue life estimation of HFMI-treated welds subjected to high-peak loads.

Analysis of secondary makeup characteristics of drill collar joint and prediction of downhole equivalent impact torque of Well SDTK1

Based on the three-dimensional elastic-plastic finite element analysis of the 8” (203.2 mm) drill collar joint, this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions, as well as the downhole secondary makeup features, and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads. On the basis of verifying the correctness of the calculation results by using measured results in Well GT1, the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10 000 m in China (Well SDTK1). The results indicate that under complex loads, the stress distribution in drill collar joints is uneven, with relatively higher von Mises stress at the shoulder and the threads close to the shoulder. For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards, when the downhole equivalent impact torque exceeds 65 kN·m, the preload balance of the joint is disrupted, leading to secondary make-up of the joint. As the downhole equivalent impact torque increases, the relative offset at the shoulder of internal and external threads increases. The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment. It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque, and effectively prevent drilling tool failure.

Analysis of crack propagation of annular butt weld and distribution of weld-induced residual stress

The circumferential surface crack propagation and the effect of weld-induced residual stress were analyzed to comprehensively understand the mechanical behavior and fracture resistance of dissimilar girth welded joints of steel castings. The evaluation of stress intensity factors is conducted for circumferential cracks on internal surfaces, aiming to predict the fracture toughness of dissimilar welded joints. The distribution of weld-induced residual stress is obtained by thermal elastic-plastic finite element methods. The impact of residual stress on the propagation of cracks is investigated through the application of extended finite element theory. The high-stress intensity factors were found in such dissimilar welded joints due to the local bending and distortion caused by the asymmetrical weld geometry. The tensile residual stress and distortion were applied to the weld root area and its vicinity. Both the asymmetrical weld geometry and tensile residual stress contribute to the tensile distortion of the inner surface around the weld root, and enable the growth of internal surface cracks in the circumferential direction and radially from inside out of the welded joint. The fracture resistance decreases with the simultaneous influence of residual stress and welds’ asymmetry.

Numerical Study on Mechanical Behavior and Electromechanical Properties of Solder-Jointed REBCO-Coated Conductors.

As the second-generation high-temperature superconducting conductors, rare earth-barium-copper-oxide (REBCO) coated conductor (CC) tapes have good potential as high-field and high-energy superconductors. In superconducting applications, several joints are required for conjugating comparatively short REBCO CC tapes. Soldering lap joints are the simplest and most commonly applied REBCO CC joints. In addition to joint resistance, the mechanical behavior and electromechanical properties are also crucial for superconducting applications. In this paper, the electromechanical properties and mechanical behaviors of soldering lap joints at 77 K under a self-field were studied. The mechanical behavior was addressed by using a full three-dimensional multilayer elastic-plastic finite element model (FEM) with REBCO CC tape main layers and solder connecting layers. Then, the electromechanical properties were analyzed by using Gao's strain-Ic degradation general model on the basis of the FEM results. Both the mechanical behavior and electromechanical properties were verified by experimental results. The effects of soldering lap conditions including lap length, soldering thickness and lap style on the electromechanical properties and mechanical behaviors were discussed. The results indicate that shorter overlap lengths and a thinner solder can reduce the premature degradation of Ic due to stress concentrations nearby the joint edges; moreover, the irreversible critical strain is significantly higher in the back-to-back joint approach compared to the widely used face-to-face joint approach.

In-situ studies on environmental degradation in Al 7075 in saltwater environment under tensile loading

Abstract We report the crack growth on peak aged Al 7075 under tensile loading in a saltwater environment to investigate whether hydrogen plays a role in the initiation and the subsequent growth of the crack. As the hydrostatic stress is at a maximum ahead of the notch, it has been speculated that hydrogen would diffuse to region of maximum hydrostatic stress and initiate the crack. An elastic-plastic finite element (FE) model is developed to determine the stress distribution around the circular notch at the edge of the plate. The crack growth was monitored using a camera attached with an optical microscope, and various regimes corresponding to hydrogen evolution, pit formation and growth, crack nucleation and initial growth and rapid crack growth leading to failure have been identified. We observe the crack was nucleated in a region associated with the highest hoop stress instead of the maximum hydrostatic stress from the base of a pit at the circular notch. We demonstrated the crack growth rate in a salt water environment is governed mostly by the dissolution of grain boundary MgZn2 precipitate, rather than the hydrogen induced decohesion mechanism.

Deformation caused by T-shape expansion of existing metro station: complex challenges and strategies

This case study presents an investigation on existing metro station deformation characteristics during T-type expansion in Nanjing, China. A three-dimensional elastic-plastic finite element model is adopted to consider the interaction of soil, retaining structure, horizontal support system and existing station structure. The results indicate that coupling deformation of asymmetric uplift deflection and existing structure rotation occurs on existing structure. Moreover, the sensitivity of influencing factors is analyzed, including the dimension of retaining structure, the support spacing, the excavation method, the soil reinforcement depth in passive area, the width of retaining soil during excavation, the relative position between foundation pit and existing structure, the excavation depth, the existing structure rigidity. Furthermore, based on the analysis of difficulties in the T-shape expansion projects, the controlling measures for the deformation of existing metro station are proposed. The achievements of this case study can be used as a reference for similar underground expansion projects.

Prediction and control of profile for silicon steel strip in the whole tandem cold rolling based on PSO-BP algorithm

In the rolling process of silicon steel strip of the five-stand UCMW tandem cold rolling line, the quality of finished profile is the result of cooperative control of five stands, the exit profiles of the first four stands jointly decide the exit profile of the fifth stand, so it is necessary to accurately control the strip profile in the rolling process. However, the shapemeter is only typically equipped at the exit of fifth stand, making it impossible to obtain the strip profile of the first four stands. A profile prediction model for the whole tandem cold rolling based on PSO-BP algorithm is established, compared with the finite element method, this model can satisfy the demand for fast prediction of strip profile and quickly analyzing the profile change characteristics for five stands according to the adjustment of profile control parameters in the industrial field. Firstly, a 3D elastic-plastic finite element model of rolls and strip for five stands is built, and a large number of profile calculation data are as the training sample sets to build the PSO-BP model. Through the transfer calculation of strip profile between adjacent stands, the PSO-BP model of five stands is established, and the validity is verified by comparing with the actual measured data. Secondly, to improve the quality of product profile, focusing on the unreasonable setting of production parameters, many improvement schemes of WRB and WRS for five stands are designed, and the PSO-BP model is used to quickly calculate the strip profile, then comparing the result of each scheme, the optimum improvement scheme is selected, which is furtherly carried out rolling experiments in the industrial field, and the quality of strip profile is well improved. At present, the new scheme has been successfully applied to industrial production.

The flexural behavior and efficiency of RC beams strengthened with SNSM bars under the effect of several end conditions and material properties

In this paper, twelve strengthened, and one un-strengthened reinforced concrete (RC) beams were experimentally and numerically investigated in flexure. The strengthened RC beams were upgraded with steel or glass fiber reinforced polymer (GFRP) in the form of side-near surface mounted (SNSM) reinforcement. The tested parameters were the SNSM bar diameter, adhesive materials, SNSM end conditions, and materials of strengthening bars. The three-dimensional elastic-plastic finite element program (ABAQUS) was utilized to simulate numerically the tested beams in the experimental program. Finally, a parametric study was numerically conducted to show the effect of different parameters of the SNSM technique on the flexural response of the strengthened beams. The experimental findings demonstrated that the RC beams strengthened with SNSM steel bars generally had higher load capacity than those strengthened with GFRP. Bent ends of the SNSM steel bars were more efficient than in SNSM GFRP bars or end anchorage by GFRP sheets. The load-carrying capacity enhancement for strengthened beams with SNSM steel bars (10 and 12 mm in diameter) having end anchorage (wrapped by CFRP sheets) was 212.6% and 234.7% compared to the unstrengthened beam. In contrast, the enhancement decreased from 184.5 to 145% and 160.5 to 158.3% as the bond material changed from epoxy to grout for the beams strengthened by 10 mm and 12 mm diameters of SNSM steel bars, respectively. The numerical and experimental findings were in close agreement.

A deep neural network-based method to predict J-integral for surface cracked plates under biaxial loading

As surface cracks may cause potential failure for engineering structures, it is of vital significance to carry out the fracture assessment for cracked structures. The crack driving force in the form of J-integral is an important input parameter in fracture assessment. This paper focuses on the determination of J-integral for surface cracked plates under biaxial loading. A method for predicting the J-integral based on the deep neural network (DNN) is proposed to estimate J-integral efficiently and accurately. Firstly, extensive three-dimensional (3D) elastic–plastic finite element (FE) analysis is conducted to compute the J-integral along the crack front for developing a FE J-integral datasets containing 1600 cases. Various crack aspect ratios, crack depth ratios, strain hardening exponents, ratios of the loading perpendicular to the crack plane to yield stress, and biaxial ratios, are strategically considered. Secondly, DNN models for predicting the J-integral are constructed and trained according to the obtained datasets by FE analysis. Then, the evaluation criteria for DNN models and the grid search method are utilized to determine the optimal DNN model structure. Finally, test cases are employed to verify the feasibility and prediction accuracy of the determined DNN model. Based on validation results, the determined DNN model exhibits sufficiently accurate prediction performance. This research provides an idea for engineering applications, through building software based on continuously optimized DNN models, the J-integral for surface cracked plates under biaxial loading can be accurately and efficiently predicted for performing fracture assessments.

In-situ neutron imaging of delayed crack propagation of high strength martensitic steel under hydrogen embrittlement conditions

This paper presents an in-situ observation, using neutron imaging, of delayed crack propagation in a high-strength martensitic steel specimen. Delayed cracking is believed to be caused by hydrogen embrittlement occurring due to the slow diffusion and accumulation of hydrogen ahead of a crack front, causing decreased ductility and eventual cracking under constant load. The experiment involved mechanical loading of a single-edge-notch bend specimen while submerged in an electrolyte solution (H2O + 3.5% NaCl) under cathodic polarization to facilitate hydrogen ingress. Intermittent crack propagation was observed for 12 h after the environment had been removed. The stress state at each crack configuration was extracted from a three-dimensional elastic–plastic finite element simulation, which was tailored to match the quantitative information acquired from the neutron radiographs of the fracture process. To gain insight into the evolution of hydrogen concentration with crack propagation, a modeling scheme for stress-assisted hydrogen diffusion was also employed.