Equivalent Strain Distribution Research Articles

Modeling of equivalent strain in 2D cross-sections of open die forged components using neural networks

Open die forging is one of the oldest manufacturing methods known to remove defects in the ingot resulting from the casting process. The improved properties of the final component are highly dependent on the strain distribution. Although sinusoidal equations and empirical formulations have been already used to estimate the strain, they have been applied only to the core of the workpiece. In this work, a novel approach is presented to model the equivalent strain distribution in 2D cross-sections, in the direction of the press, of open die forged components using neural networks. The proposed method efficiently combines a parametric sinusoidal function with a neural network to learn the complex relationships between the process parameters and the resulting local strain. The neural network is trained on a dataset of finite element (FE) simulations of rectangular geometries that cover a wide range of aspect ratios, bite ratios, and height reductions. The presented methodology with near real-time prediction capabilities shows good agreement with FE results. Moreover, the parametric function captures the characteristic pattern of the strain distribution and reveals certain physical relationships affecting the deformation of the material. These patterns are later examined by analyzing the parameters identified in the parametric sinusoidal function.

Research of interlayer dip angle effect on stability of salt cavern energy and carbon storages in bedded salt rock

In order to clean and decarbonize energy, large-scale underground energy storage in salt caverns can be utilized. The construction and safety evaluations for these caverns are crucial, especially for salt caverns with significant interlayer dip angles. Aimed at the bedded salt rocks for energy and carbon storage, this study focuses on the impact of different interlayer dip angles on the stability of underground energy and carbon storage caverns in bedded salt rock formations in China. Four salt caverns with varying interlayer dip angles of 0–30° were established for stability comparison. Numerical simulations reveal that caverns with high interlayer dip angles demonstrate low volume shrinkage, general deformation resistance and small equivalent strain, while exhibiting a larger volume of plastic zones compared to caverns with lower interlayer dip angles. It is important to consider the deformation of the cavern wall rock in the down-dip direction for caverns with high interlayer dip angles. The presence of inclined interlayers affects the symmetry of the contour distribution of deformation, safety factor and equivalent strain. Furthermore, recommendations are provided for the construction of salt caverns in salt rock formations with high interlayer dip angles.

Research on the Dynamic Softening Mechanism of Dual‐Phase Structure During Warm Forming of Fe–8.5Mn–1.5Al Medium‐Manganese Steel

In this article, Fe–8.5Mn–1.5Al medium‐manganese steel is taken as the research object, and Gleeble 3500 thermal simulation testing machine is used to conduct isothermal compression at different deformation temperatures, strain rates, and strains in its austenite ferrite two‐phase zone. A constitutive model and a dynamic recrystallization volume fraction model for materials are established, and finite‐element method is used to simulate the temperature, equivalent strain, and dynamic recrystallization volume fraction distribution in different regions of the workpiece under different deformation conditions. By comparing and analyzing the microstructure, finite‐element simulation results, and hot working diagrams obtained from the experiment, the microscopic mechanism of dynamic softening of the material when ferrite and austenite coexist is explained; the transformation of the dynamic softening mechanism of the two phases with the hot deformation process is also explained. Early deformation mainly occurs in softer ferrite, which preferentially undergoes continuous dynamic recrystallization. Austenite has a lower stacking fault energy, and discontinuous dynamic recrystallization (DDRX) occurs when the dislocation density reaches a certain critical value. At the same time, when the strain reaches a certain level, the dynamic softening behavior of ferrite will also transform into DDRX. The optimal deformation conditions for Fe–8.5Mn–1.5Al medium‐manganese steel during warm processing in the two‐phase zone are a temperature of 720 °C, a strain rate of 0.01 s−1, and a large deformation zone.

The effect of friction characteristics on electromagnetic impact deformation mechanism of 2A10 aluminum alloy bars

Purpose The purpose objective of this study is to identify the friction coefficient and friction effect in electromagnetic upsetting (EMU) high-speed forming process. Design/methodology/approach Based on numerical simulation and upsetting experiment of 2A10 aluminum alloy bar, the friction coefficient between contact surfaces is obtained by combining the fitting displacement distribution function and the electromagnetic-mechanical coupling numerical model, and the influence of friction effect is analyzed. Findings The maximum impact velocity and acceleration during EMU are 13.9 m/s and −3.3 × 106 m/s2, respectively, and the maximum strain rate is 7700 s−1. The functional distribution relationship between friction coefficient combination (FS, FD) and characteristic parameters [upper diameter (D1) and middle diameter (D2)] is established. The values of FS and FD are 0.1402 and 0.0931, respectively, and the maximum relative error is 2.39%. By analyzing the distribution of equivalent stress and strain, it is found that plastic deformation has obvious zoning characteristics and there is serious failure concentration in the strong shear zone. Originality/value Friction coefficient significantly affects stress or strain distributions in material forming process, but it is difficult to obtain friction coefficients through experimental tests in the high-speed forming process. In this paper, a multi-field coupling numerical model is proposed to determine friction coefficients and applied to the electromagnetic impact loading process (a high-speed forming process). Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0154/

A Multipath Process-Based Inherent Strain Method for Prediction of Deformation of Hull Plate for Integrated Heating and Mechanical Rolling Forming Process

Integrated heating and mechanical rolling forming (IHMRF) has recently been introduced for manufacturing complex curvature hull plates. It fabricates the target curved plate by sequential loading along the multipath. Accurate and efficient prediction of the deformation of the plate is the basis for developing the process planning and ensuring the quality of the forming. The inherent-strain method is ideal for this purpose, but its prediction accuracy needs to be improved. This paper proposes a multipath process-based inherent-strain method (MPISM), which considers the effect of the sequential loading process of the multipath on plate deformation. First, the effect of loading paths near the plate edge was investigated, which in turn clarified the rationale for obtaining the inherent strain only in the plate center. Secondly, a strain correction strategy was established by analyzing the variation pattern of the inherent strain caused by the crossing or proximity of the previous path and the subsequent path. This allowed the effects of the loading process to be taken into account in the elastic analysis. Based on the plate-and-shell theory, the idea of an equivalent inherent strain distribution is also presented. This makes the loading of inherent strains more accurate in the elastic finite-element model. MPISM predictions and experimental results show good agreement. Compared with the thermo-elastic–plastic finite element method, the MPISM substantially improves efficiency while maintaining accuracy. Compared with the original inherent-strain method, the MPISM is more accurate in terms of deformation magnitude prediction.

The Development of a Continuous Constitutive Model for Thin-Shell Components with A Sharp Change in the Property at Welded Joints.

Large-dimension complex integral thin-shell components are widely used in advanced transportation equipment. However, with the dimensional limitations of raw blanks and the manufacturing process, there are inhomogeneous geometric and mechanical properties at welded joints after welding, which have a significant effect on the subsequent forming process. Therefore, in this paper, the microstructure of welded joints with a sharp property change was accurately characterized by the proposed isothermal treatment method using the BR1500HS welded tube as an example. In addition, an accurate constitutive model of welded tubes was established to predict the deformation behavior. Firstly, the heat-treated specimens were subjected to uniaxial tensile tests and the stress-strain curves under different heat treatment conditions were obtained. Then, the continuous change in flow stress in the direction of the base metal zone, the heat-affected zone and the weld zone was described by the relationship between the microhardness, flow stress and center angle of the welded tube. Using such a method, a continuous constitutive model of welded tubes has been established. Finally, the constitutive model was compiled into finite-element software as a user material subroutine (VUHARD). The reliability of the established constitutive model was verified by simulating the free hydro-bulging process of welded tubes. The results indicated that the continuous constitutive model can well describe the deformation response during the free hydro-bulging process, and accurately predicted the equivalent strain distribution and thickness thinning rate. This study provides guidance in accurately predicting the plastic deformation behavior of welded tubes and its application in practice in hydroforming industries.

Heat-assisted friction stir incremental sheet forming of thermoplastics

Incremental sheet forming (ISF) has been attracting increasing interests for customised manufacture of thermoplastics, but the application in high-performance and hard-to-form thermoplastics is still a challenge. This paper develops a new heat-assisted friction stir incremental sheet forming (HAFS-ISF) process to form polyether ether ketone (PEEK) and polymethyl methacrylate (PMMA, acrylic). Flexible heating tapes and tool rotational friction heat the thermoplastic sheet on both bottom and top surfaces, which maintain the sheet material at high temperature and reduce the through-thickness temperature gradient. Results are given for the effect of key parameters on forming temperature, force, accuracy and thickness distribution. Spindle speed has the most significant effect on all the studied aspects, followed by the pre-heating temperature, while feed rate and step size have less effect. With lower spindle speed of 100 rpm, the through-thickness temperature gradient is improved. Compared with PEEK parts, more uniform forming temperature and smaller forming force can be observed for PMMA parts. But the material brittleness causes worse formability, and the severer twist and stretching effect affect the forming accuracy of PMMA parts. Forming accuracy, fracture and twist are discussed by developing analytical models. The model for forming accuracy considers the initial bending effect and springback. The fracture is discussed by modelling the stress triaxiality and equivalent strain distribution under contact. While the model for twist considers effect of the applied torque on shear strain energy and continuous accumulation of twist along the tool path. By comparing analytical models and testing observations, the effectiveness of the models is confirmed to understand the underlaying mechanisms and to address a few challenges.

Comparative Study of the Life Prediction and Failure Analysis of Metal Powder (Vanadium-V) Coated on Crankshaft

The crankshaft plays a crucial role in the efficient operation of internal combustion engines, converting piston reciprocating motion into rotary motion. This study aims at the life prediction and failure analysis of metal powder (Vanadium-V) coated on crankshaft using numerical method. It was modelled with SOLIDWORDS version 2019 and imported to ANSYS 2020 RI environment for static structural analysis. Numerical results of total deformations obtained from ANSYS are shown with the minimum value and maximum for propose material 7.3172e-5 and 0.00065855 respectively, and for the existing material value having 0.00014795 and 0.0013316 as well. Maximum and minimum values are 0.018841 and 2.9158e-7 in crankshaft equivalent elastic strain distributions in the existing material respectively. Results also show that maximum equivalent elastic strain is observed in propose with 0.097538 and minimum 3.1017e-7. The maximum value is 1.3933e9 and minimum value is 26418 of the stress found around the crankshaft of the propose and is stretched where there is concentration of pressure. The maximum stress intensity is observed in existing material with 1.5139e9 with minimum value of 30833. Results reveal significant improvements in total deformations, elastic strain distributions, and stress values for the proposed vanadium-coated material compared to the existing one. Despite a mere 0.0003mm thickness, the vanadium coating offers cost-effectiveness, better performance with cheaper lubricants, reduced friction, and enhanced dimensional tolerance at higher pressures. Results therefore proposed vanadium incorporated to inhibit grain growth to enhance strength and toughness of hardened steel.

Direct modeling of non-uniform strain field of heterogeneous materials

Engineering materials have a heterogeneous microstructure that induces non-uniform deformations (NUDs) even under uniform stress. Therefore, the development of NUDs in heterogeneous materials under a macroscopically non-uniform stress is characterized by the interactions between micro- and macroscopic NUDs. In this study, we attempt to directly describe microscopic NUDs by introducing a constitutive equation for the strain field. Using polycrystalline metal, which is a well-known heterogeneous material, we performed the uniaxial tensile tests on specimens with curved gauge sections. During modeling, the constitutive equation without nonlocal effect was first fitted based on the distribution of the local equivalent stress and strain. The strain calculated using the fitted equation was regarded as the strain for the homogeneous material, whereas the strain deviating from the fitted equation was assumed to be induced by the microscopic heterogeneity of the material. The respective strains were represented using different constitutive models, and the parameters employed in the models were fitted separately using the experimentally measured strain field. The plastic compliance gradient was employed as a material parameter quantifying the microscopic NUDs. Subsequently, a multiaxial elastoplastic nonlocal constitutive equation was formulated based on the nonlocally extended J2 flow theory. Finite element method simulations introducing the proposed nonlocal effect indicated that a scale-dependent NUD characterized by the interactions between micro- and macro-NUDs could be represented using the proposed model. Furthermore, the proposed model could predict the experimentally observed strain field characterized by a polycrystalline microstructure, such as the dispersion of the strain concentration at the curved gauge section and the appearance of NUDs even under uniform stress.

Biomechanical comparison of all-polyethylene total knee replacement and its metal-backed equivalent on periprosthetic tibia using the finite element method

BackgroundTotal knee arthroplasty (TKA) with all-polyethylene tibial (APT) components has shown comparable survivorship and clinical outcomes to that with metal-backed tibial (MBT). Although MBT is more frequently implanted, APT equivalents are considered a low-cost variant for elderly patients. A biomechanical analysis was assumed to be suitable to compare the response of the periprosthetic tibia after implantation of TKA NexGen APT and MBT equivalent.MethodsA standardised load model was used representing the highest load achieved during level walking. The geometry and material models were created using computed tomography data. In the analysis, a material model was created that represents a patient with osteopenia.ResultsThe equivalent strain distribution in the models of cancellous bone with an APT component showed values above 1000 με in the area below the medial tibial section, with MBT component were primarily localised in the stem tip area. For APT variants, the microstrain values in more than 80% of the volume were in the range from 300 to 1500 με, MBT only in less than 64% of the volume.ConclusionThe effect of APT implantation on the periprosthetic tibia was shown as equal or even superior to that of MBT despite maximum strain values occurring in different locations. On the basis of the strain distribution, the state of the bone tissue was analysed to determine whether bone tissue remodelling or remodelling would occur. Following clinical validation, outcomes could eventually modify the implant selection criteria and lead to more frequent implantation of APT components.

Research on the deformation characteristics of small module tooth during current-assisted splitting spinning of small module tooth-shaped part

Aiming at the problems such as low material utilization, poor strength and toughness of workpiece during manufacturing of small module tooth-shaped parts (SMTSPs) by traditional gear hobbing and shaping method, a current-assisted splitting spinning forming (CASSF) method was proposed to form SMTSPs with high performance requirements. A coupled electrical-thermal-mechanical finite element (FE) model was established based on the ABAQUS software, and the distribution of equivalent stress and equivalent strain, and deformation characteristics of small module tooth were investigated. The results show that the equivalent stress and equivalent strain decrease from tooth groove arc to the tooth crest arc and centre of the tooth groove at tooth profile surface. The distribution of equivalent stress and equivalent strain in the internal deformation region follows the same trend as the tooth profile surface from the centre of the tooth groove to the tooth groove arc, but increases from the tooth groove arc to the tooth crest. The material of small module tooth experiences three-directional stress state. The material in the gear tooth undergoes radial and axial elongation, and tangential compression, while in the tooth groove it undergoes radial compression, tangential and axial elongation.

The Influence of Materials on Footwear Behaviour: A Finite Element Simulation Study.

The objective of this study was to analyse the influence of materials and their position within the upper assembly on the behaviour of casual footwear using finite element simulation tools. The study was carried out on three models of casual footwear, which are identical in terms of design lines, varying only in the materials of the upper assembly, namely calfskin leather (M1), knitted fabric (M2), and combination of knitted fabric and calfskin leather (M3). The footwear models were designed according to the design constraints specific to casual footwear. The foot was reconstructed based on the shoe last obtained based on anthropometric data. Material definition, 3D models editing, setting up analysis conditions, and constraints were performed using the Ansys 17.2 software. Gait biomechanics were taken into account to define the loading model, force distribution, force values, and constraints. The study evaluates footwear behaviour in terms of directional deformation (Z axis), equivalent von Mises stress, and equivalent elastic strain distribution. This paper explores a methodology that has the potential to enhance the footwear design and manufacturing process, providing designers with information about the deformations and stress distribution on upper parts of the footwear product.

Thermal deformation behavior and microstructure evolution of GH141 superalloy during double-cone gradient compression

Thermal deformation behavior and microstructure evolution of GH141 alloy were researched efficiently by a high-throughput double-cone (DC) gradient compression to provide support for the formulation of forging process and gaining ideal microstructure. A wide gradient equivalent strain distribution was obtained for the DC specimens under different compression temperatures. The flow stress during DC gradient compression increased rapidly at the beginning of deformation, then decreased rapidly after reaching a certain peak, and finally tended to steady with the increase of deformation. The obvious gradient microstructure was obtained when compressing at 1050 °C, 1075 °C and 1100 °C. But when compressing at 1125 °C and 1150 °C, the grains were uniformly equiaxed inside the DC specimens with gradient strains. Continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) existed simultaneously in the DC specimen compressed at 1050 °C. The dynamic recrystallization (DRX) mechanism shifted towards the DDRX with the rising of compression temperature. In short, increasing the deformation temperature can obtain uniform equiaxed grain microstructure inside a GH141 superalloy with different strains, which has an important guiding role the fabrication of GH141 ring rolled parts.

Hardness prediction in the upsetting process of Al%ZrO2—an approach to machine learning using regression and classification models

The current study focuses on the prediction of metal hardness distribution in upsetting tests for different compositions of ZrO2 embedded with an aluminum matrix using machine learning algorithms and finite element (FE) analysis. The mass fraction of the ZrO2 particles varied from 4% to 8%, and three sets of solid cylindrical rods with Al4%ZrO2, Al6%ZrO2, and Al8%ZrO2 were prepared using the stir casting method. The upsetting process was simulated, and an equation for predicting hardness was developed from the equivalent strain distributions. Artificial neural networks (ANNs), multilinear regression (MLR) along with equations developed from FE analysis were used to train the model for regression analysis, considering the principal stresses, friction factor, anisotropy ratio, effective strain, and hoop strain as input and the magnitude of hardness as output parameters. Regression analysis reveals that ANN (tri-layer network), XGBoost, and MLR algorithms are the best suitable for the given data sets with a root mean square ( R2) greater than 0.95. XGBoost, ANN (narrow), and SVM are linear and are the most recommendable classifier algorithms for the current investigation. Hardness data from ring compression tests were used to validate the results obtained from the trained models with the test results.

Numerical and experimental investigation on cold drawing process of high spiral angle tube

A novel method of cold drawing process of high spiral angle tube made of 304 stainless steel is proposed. Forming principles of high spiral angle tube are calculated. New drawing dies are designed and manufactured. Numerical simulation and corresponding experiments are carried out. Forming quality and defects of cold drawing are discussed. Various factors affecting metal flow during cold drawing process are studied in detail. Finite element model of cold drawing process is established. The variation of drawing load is presented. The distributions of equivalent stress and equivalent strain in different directions during cold drawing process are analyzed. Displacements of points in axial direction and circumference direction during cold drawing process are compared respectively. The evolutions of microstructure during cold drawing process are studied.

Experimental and Numerical Studies on Hot Deformation of Graphene-reinforced Aluminum Matrix Composite

Graphene/Al composite materials have excellent comprehensive properties and can be used under extreme environmental conditions such as high temperature, high pressure, high vacuum, strong corrosion, and irradiation. The thermal deformation behavior of 0.5 wt.% graphene/Al6061 composites at T=300 °C, T=350 °C, T=400 °C, T=450 °C, and , was studied by isothermal compression tests and numerical simulation methods. The experimental data show that the flow stress of graphene/Al6061 composites gradually rises as the temperature reduces. When the strain rate reduces, the flow stress of graphene/Al6061 composites gradually decreases. A constitutive equation based on the Arrhenius equation is established, and the maximum error between the calculated stress value got from the constitutive equation and the measured stress value is less than 15%. The equivalent stress and strain distributions of graphene/Al6061 composites at distinct deformation temperatures and strain rates were simulated by using the finite element method. It is found that the spread of equivalent strain is related to the transmutation zone. The equivalent stress is uneven. The simulated equivalent stress is close to the experimental value.

The effect of rolling temperature on the microstructure and properties of multi pass rolled 7A04 aluminum alloy

The current research on 7-series aluminum alloys mainly focuses on solid solution and aging treatments, as well as the flow stress during the deformation process. There are limited researches on the influence of thermal deformation temperature on the microstructure and properties of the aluminum alloy during multi-pass hot rolling process. In this study, the as-cast 7A04 aluminum alloy was subjected to homogenization treatment, followed by multi-pass hot rolling. The effects of different deformation parameters on dislocation density were analyzed. Microstructural characterization of the deformed alloy was performed using optical microscopy (OM), scanning electron microscopy (SEM) with energy-dispersive spectroscopy (EDS), X-ray diffraction (XRD), and micro-hardness tester. The optimal microstructure of the deformed alloy was selected based on the size of recrystallization. Subsequently, the Deform–3D finite element simulation software was used to analyze the multi-pass hot rolling process. The influence of deformation parameters on the uniformity of equivalent strain distribution within the samples was investigated. The results showed that at the deformation temperature of 430 °C, a significant amount of recrystallized microstructure appeared in the alloy, resulting in the lowest dislocation density and a significant reduction in the quantity of coarse precipitates. Finite element numerical simulation revealed that the deformation temperature had a certain influence on the uniformity of strain distribution within the alloy. However, this influence was mostly eliminated when the deformation temperature exceeded 380 °C. Meanwhile, the distribution of strain within the alloy was found to be related to the temperature distribution.

Equivalent strain distribution at high pressure torsion extrusion of pure copper: Finite element modeling and experimental validation

Equivalent strain distribution at high pressure torsion extrusion of pure copper: Finite element modeling and experimental validation

Stability Analysis of Wind Turbine Blades Based on Different Structural Models

In order to better simulate the actual working conditions of wind turbines more realistically, this paper adopts the two-way fluid–structure coupling method to study the NREL 5 MW wind turbine, considering the blade coupling deformation and equivalent stress and strain distribution of the blades with different internal structures under different working conditions. The results show that the maximum equivalent stress and strain distribution of the beam–structure wind turbine blade was near the leading edge of the blade. The maximum equivalent stress and strain distribution of the shell structure wind turbine blade was near the leading edge of the blade root, and the dangerous area is obvious but smaller than that of the beam-type wind turbine. The coupled deformation of a wind turbine model with a shell structure blade with a web is significantly reduced, and the equivalent stress and strain distribution of the skin is similar to that of the shell structure, but the numerical value and the maximum equivalent stress distribution area are significantly smaller. From the comparison of the three, the shell structure blade with a web is the best.

INVESTIGATING THE EFFECT OF HEAT TREATMENT ON THE COLD FORGING OF 27MNB4 STEEL VIA CALPHAD METHODOLOGY AND FEM

As a material forming method, cold forging is preferred due to the reasons like absence of a heating step and high surface quality. Recently, the finite element method (FEM) has received growing attention for controlling and predicting final material properties for cold forging applications. FEM combines microstructure evolution models with failure criteria, thus providing solutions to complicated problems in the modern cold forging industry. The fastener industry extensively utilizes cold forging, in which manganese and boron-containing steels like 27MnB4 can be formed to obtain high mechanical properties. The current study investigates the effect of two different heat treatments, namely softening and spheroidizing annealing, on the formability of 27MnB4 bolts. Softwares such as Thermo-Calc 2022a and Forge NxT 3.2 were used to predict the microstructure of the wire rod and evaluate the cold forming process of the same rod under two different heat treatment conditions. Therefore, the current study also provides a relationship between microstructural features and the cold formability of 27MnB4 steel. The microstructure of 27MnB4 is predicted by CCT diagrams. The predicted microstructure corresponds to the microstructure of 27MnB4 samples taken from the production line. In addition, temperature, von Mises stress, and equivalent strain distributions for 27MnB4 steel in the hot rolled state were calculated higher than in annealed states due to the differences in the microstructure. These results demonstrate that computational material engineering methods and simulation techniques could be practical tools for cold forming processes.