Isotropic Hardening Model Research Articles

FE thermo-mechanical simulation of welding residual stresses and distortion in Ti-containing TWIP steel through GTAW process

Abstract The effect of residual stresses can be beneficial or harmful depending on their magnitude, type and distribution. This research work applied the isotropic and kinematic hardening models with different strain rates (0.001-100 s−1) to simulate the non-linear mechanical behavior of Twinning Induced Plasticity (TWIP) steel microalloyed with titanium. A finite element (FE) thermo-mechanical model was employed to analyze the welding thermal cycle in the TWIP-Ti steel. The numerical prediction of residual stress was validated by X-ray diffraction (XRD) measurements in welding critical regions. Furthermore, a residual stress critical zone (SCZ) was defined as a function of the maximum tensile residual stress and hardness in the fusion zone (FZ) and heat affected zone (HAZ). The magnitude of residual stresses estimated in the SCZ was lower than the TWIP-Ti steel yield strength. The weld joint preparation and the mechanical constraint provided a control to mitigate both residual stress and distortion. Quantitatively, the results provided good weldability of the TWIP-Ti steel in higher plate thickness through the Gas Tungsten Arc Welding (GTAW) process at low heat input.

Crack tip fields at crack initiation and growth under monotonic and large amplitude cyclic loading: Experimental and FE analyses

In this paper, experiment and FE analyses are performed to investigate crack tip deformation and stress fields under monotonic and large amplitude cyclic loading. Fracture tests using C(T) specimens made of SA508 Gr.1a and TP316 are performed under monotonic and cyclic loading. Using the debonding analysis, it is found that the isotropic hardening model is relevant for monotonic loading, the kinematic hardening for SA508 Gr.1a under cyclic loading, and the Chaboche combined hardening for TP316 under cyclic loading. Using the relevant hardening model, crack tip deformation and stress fields at crack initiation and growth are presented.

Utilization of Advanced Computational Methods to Predict Spring-back of Aluminium Alloys in Automotive Industry

The automotive industry is one of the most dynamically developing segments of the industrial production worldwide. The introduction of still increasingly stringent emission limits for newly developed cars forces car producers to still reduce the fuel consumption of cars. One option is to use hybrid drive units in combination with a redesign of the automobile body while maintaining the highest possible level of vehicle safety. For these reasons, the automotive industry has been increasingly demanding to apply and process low density (lightweight) alloys, including aluminium-based alloys. These materials are subject to high demands both in terms of mechanical properties and technological workability in the mass production process. The utilization of mathematical modelling (numerical simulations) of production processes is now one of the standards in all phases of design and production the car-body and allows the implementation of variable designs in a relatively short time scale and the detection of potential production problems as well. In this paper, the influence of the kinematic hardening model on the accuracy of spring-back prediction is shown in comparison with the commonly used isotropic hardening model. For deformation analysis, a simple workpiece having ?U-shape? of EN AW 6111 material was used. Such aluminium alloys is used for production car-body panels in the automotive industry. Achieved accuracy of numerical simulation results is evaluated by the comparison shape obtained by numerical simulations and shape of experimentally bended workpiece.

The influence of strain hardening of copper on the crack path in Cu/Al2O3/Cu direct bonded copper substrates

In automotive applications, Cu/Al2O3/Cu compounds are widely used as substrates in electronic power devices due to their high thermal and electrical conductivity.The significance of this research are Vickers hardness measurements that reveal the hardening of Cu in Cu/Al2O3/Cu compounds under thermal cycling for the first time. A key finding was that the Cu hardening dictates the characteristics of the observed crack propagation path. Using a kinematic and isotropic Cu hardening model in finite element simulations and a fracture mechanical modeling methodology, we were able to predict the crack path in very good agreement with experimental observations.

Combined hardening parameters of steel CK45 under cyclic strain-controlled loading: Calibration methodology and numerical validation

This study is to indicate the methodology of investigating the behavior of materials in the plastic domain while bearing cyclic loading i.e. low cycle fatigue. Materials under such loading, which experience huge amount of plastic deformation, are affected by the hardening or softening effects of loading which should be taken into account in all applications and numerical simulations as well. This work investigates the methodology of obtaining the nonlinear isotropic and kinematic hardening of steel CK45. To find the parameters of the above mentioned combined nonlinear isotropic/kinematic hardening one tensile test as well as three strain-controlled low cycle fatigue tests are carried out to extract the monotonic stress/strain curve and three diagrams of hysteresis curves, respectively. Then, four parameters necessary to simulate the nonlinear isotropic/ kinematic behavior of the material are extracted by means of curve fitting technique using MATLAB software. Afterwards, the accuracy of the data extracted from the experimental tests using the proposed methodology, are verified in a finite element package, ABAQUS, through implementing two user defined subroutines UMAT written in FORTRAN. It is indicated that the computed constants draw stress-strain curves much closer to experimental responses than isotropic hardening model does. Eventually, the numerical results acquired by simulating the behavior of the sample under cyclic loading with importing the constants, calculated via combined hardening model, to ABAQUS reflects results highly close to the experimentally obtained response of the sample. It means that the procedure used to find the constants is accurate enough and consequently the constants computed are able to be used in both ABAQUS and subroutines.

Modeling differential permanent softening under strain-path changes in sheet metals using a modified distortional hardening model

In this study, a modified distortional hardening model is proposed based on the homogeneous yield-function based anisotropic hardening (HAH). An improvement is made to capture differential permanent softening (DPS) under strain-path changes in sheet metals, whereas the other anisotropic hardening features such as the Bauschinger effect, transient behavior, and cross hardening phenomenon are retained as they are in the original HAH model.The modified HAH (M-HAH) model is implemented in a commercial finite element software using the user-defined material subroutine, and validated well by reproducing the flow stress behaviors after differently programmed strain-path changes for dual-phase steel, extra deep drawing quality steel, and ferritic stainless steel. Additionally, the M-HAH can simulate the DPS in two-step tension tests, which cannot be accurately modeled by the original HAH. Finally, the V-bending springback tests with pre-tensioned specimens are evaluated with different modeling schemes including the classical isotropic hardening, kinematic hardening and distortional hardening models.

Size effect on the subsequent yield and hardening behavior of metal foil

With the growing demand for miniaturized and integrated products, the metal foils have been extensively applied in the field of aerospace, electronics, medical equipment, and microsystem technology. However, the deformation process is usually under the complex stress status for the fabrication of the micropart. In addition, size effect dramatically impact the microforming process and therefore the well-developed metal forming theory established at macroscale is inapplicable at the grain level. To further investigate the size effect on the subsequent yield and hardening behavior, the biaxial tests of stainless-steel foils with diverse grain sizes and thicknesses were conducted under different stress states. The initial and subsequent yield loci are computed under various loading histories according to the plastic work per unit volume principle. It is found that the evolution of yield loci from initial to the subsequent state shows a remarkable difference for metal foils with different grain sizes. Based on Yld2000-2d yield criterion, the theoretical yield loci based on three different hardening models, including isotropic, kinetic, and isotropic-kinetic mixed hardening models, were acquired to explore and evaluate their applicability at microscale. Results indicated that the isotropic-kinetic mixed hardening model can better describe the evolution of subsequent yield locus than the individual hardening model. In addition, the back stress is shifted down with the increase of grain size for the foils with a certain thickness. Based on the Taylor-Bishop-Hill (TBH) polycrystal plasticity model, the evolution of subsequent yield surface is interpreted by the transformation of grain orientation.

Enriched finite element modeling in the dynamic analysis of plane frame subject to random loads

This work contributes to the generalized finite element approach in free vibration, dynamic elastic, and elastoplastic analysis of plane frame subjected to random excitation generated by the wind action. The wind velocity is modeled mathematically by using power spectral density method in combination with Shinozuka’s model, along with the commonly employed wind spectra. From these spectra, the dynamic wind loading is determined from the sum of the mean and floating wind velocities. The governing equation is formulated by Euler–Bernoulli beam theory, and it is discretized by using the enriched beam element. The enrichment is done by employing enriched finite element shape function to construct the enriched mathematical space. This strategy is constituted by the enrichment space, which is constructed by trigonometric functions, and the conventional space, which is constructed by conventional two-node Lagrange–Hermite shape function. The time increment procedure is carried out by Hilber-Hughes-Taylor algorithm and the material nonlinearity is modeled by von Mises isotropic hardening model, solved by the Newton–Raphson algorithm. A flowchart is presented to summarize the proposed numerical modeling procedure. Finally, several applications are presented, and the results obtained by the generalized finite element method are compared with those obtained by conventional beam element. Natural frequencies are determined in a one-story plane frame and are compared with reference results. The relative error in displacement is determined in h-refine strategy for quadratic beam element (FEM3), while the generalized finite element method adopts the enrichment increment strategy. The results demonstrate the competitiveness and numerical stability of generalized finite element method in this type of application. Even in comparison to the quadratic beam element, the generalized finite element method presents good performance and accuracy in numerical modeling.

Effect of Temperature on Deformation and Fatigue Behaviour of A356-T7 Cast Aluminium Alloys Used in High Specific Power IC Engine Cylinder Heads.

Aggressive downsizing of the internal combustion engines used as part of electrified powertrains in recent years have resulted in increasing thermal loads on the cylinder heads and consequently, the susceptibility to premature thermo-mechanical fatigue failures. To enable a reliable computer aided engineering (CAE) prediction of the component lives, we need more reliable material deformation and fatigue performance data. Material for testing was extracted from the highly loaded valve bridge area of specially cast cylinder heads to study the monotonic and cyclic deformation behaviour of the A356–T7 + 0.5% Cu alloy at various temperatures. Monotonic tensile tests performed at different temperatures indicate decreasing strength from 211 MPa at room temperature to 73 MPa at 300 °C and a corresponding increase in ductility. Completely reversed, strain controlled, uniaxial fatigue tests were carried out at 150, 200 and 250 °C. A dilatometric study carried out to study the thermal expansion behaviour of the alloy in the temperature range 25–360 °C shows a thermal expansion coefficient of (25–30) × 10−6 °C−1. Under cyclic loading, increasing plastic strains are observed with increasing temperatures for similar load levels. The experimental data of the cyclic deformation behaviour are calibrated against a nonlinear combined kinematic–isotropic hardening model with both a linear and non-linear backstress.

Numerical Simulation of Temperature Field and Residual Stresses in Stainless Steel T-Joint

T-joint, an important type of welding joint, is widely used in automobiles, ships, aerospace, and other industries. The variation in the temperature field and the stress field for T-joint is more complicated than that in other joint methods, and it is difficult to control the welding quality. The temperature field and stress field in 316L stainless steel T-joint were analyzed in this research by using simulation software, considering the thermal–metallurgical–mechanical coupling behavior, the isotropic hardening model and moving heat source condition. In the end, the simulation results were verified by the test results, and it was shown that the numerical simulation results agreed with the test results, which proved the reliability of the simulation results in 316L T-joint. The simulation results showed that the temperature distribution of T-joint cross section changed from a fan shape to an elliptical shape and the temperature distribution range increased with time. The temperature field was distributed symmetrically along the center of the weld. There was a large temperature difference between the weld zone and the base metal. The peak temperature was obtained in the second pass, and the peak temperature in the web plate was significantly higher than that in the flange plate; with farther away from the weld, a little variation happened in the thermal cycle curve. Whether it was longitudinal residual stress or transverse residual stress presented a hat-like distribution trend along the weld direction. The maximum tensile longitudinal residual stress appeared in the middle, while the maximum transverse residual stress appeared near the middle. In the vertical weld, the larger tensile stress in longitudinal and transverse direction appeared near the weld zone.

Modeling material behavior during continuous bending under tension for inferring the post-necking strain hardening response of ductile sheet metals: Application to DP 780 steel

Continuous bending under tension (CBT) testing can stretch ductile sheet metals significantly more than simple tension (ST) testing. Strength and plastic strain levels increase with the number of CBT cycles and substantially exceed those achieved in ST. Taking advantages of the improved elongation-to-fracture (ETF) achieved by CBT, samples of DP 780 steel are pre-deformed to several strain levels by interrupting their CBT testing. Sub-size specimens are machined from the CBT interrupted specimens and tested in ST. The flow curves from these secondary ST tests are then shifted according to the axial strain accumulated during pre-deformation by CBT to determine a large strain (post-necking) flow curve of the material. The identified large strain flow curve is validated with two approaches. First, the large strain flow curve is used to simulate the load versus displacement curve during CBT to large number of CBT cycles. Second, the curve is used to simulate the flow curves based on the secondary ST testing. The simulations are performed using isotropic hardening (IH) and combined isotropic-kinematic hardening (CIKH) material models. The latter model is calibrated using a set of large strain cyclic tension-compression data. An automated procedure is developed for the creation of sub-size specimens from the finite element (FE) mesh of the interrupted CBT specimen to facilitate efficient secondary ST simulations. The procedure involves cutting of the FE mesh into the sub-size specimen shape by Boolean operations in Abaqus software followed by generation of volume FE mesh and mapping of the state variables. The state variables are mapped to simulate deflection of the specimens, as the residual stress field from the prior CBT simulation evolves to reach a new equilibrium. It is found that the model reproduces the experimental load versus displacement curve, including the succession of spikes and plateaus typical of CBT, very closely. The model also predicts yielding of the interrupted sub-size specimens further verifying the identified curve. The predictions demonstrate the utility of the developed methodology for inferring the post-necking strain hardening behavior of sheets.

Microstructure topology optimization by targeting prescribed nonlinear stress-strain relationships

In this paper, we proposed a new material design method by microstructure topology optimization. Novelty of the proposed method is to target the whole nonlinear volume-averaged effective stress-strain curve of microstructure representative volume element (RVE) rather than aiming specific values such as strength, stiffness or Poisson ratio. J2 plasticity model with a linear isotropic hardening model was chosen for local residuals. Global residuals are computed within nonlinear finite element framework for the topology optimization. Sensitivities of the objective function augmented with the residuals and adjoint response vectors with respect to design variables are derived with details and their numerical computational procedures were also presented. Microstructure topologies showing two different targeted stress-strain curves under uniaxial and biaxial loadings were obtained by using the method of moving asymptotes (MMA) optimization algorithm. Accuracy of the sensitivity computations was verified and numerical examples demonstrated a potential of the proposed method in applications to multiscale topology optimization.

Effect of different welding parameters on residual stress and deformation of 20/0Cr18Ni9 dissimilar metal arc-welding joint

Pipelines used for the petrochemical, energy, and other industries contain 20 steel and 0Cr18Ni9. This paper based on the finite element simulation software Simufact Welding, the residual stress field and deformation results for 6-mm-thick 20/0Cr18Ni9 plates were examined by combining numerical simulation with experimental verification and performing an orthogonal experiment of three factors on different welding parameters. Herein, the thermodynamic coupling, isotropic hardening model, viscoplastic model, moving heat source are considered, and the experiments confirm the welding residual stress and deformation. The experimental results show that the stress distribution of each model is similar and the maximum stress appears in the fusion zone. Furthermore, the longitudinal residual stress is substantially greater than the transverse residual stress, whereas the minimum stress distribution is observed in paramaters of heat input 13493 J (welding layer 1) and 22400 J (welding layer 2), interpass temperature 50 °C, ambient temperature 65 °C. The minimum deformation occurred in paramaters of heat input 5913 J (welding layer 1) and 9200 J (welding layer 2), interpass temperature 250 °C, ambient temperature 65 °C, whereas the maximum deformation occurred in paramaters of heat input 13493 J (welding layer 1) and 22400 J (welding layer 2), interpass temperature 250 °C, ambient temperature 20 °C. Finally, the paramaters of heat input 7077 J (welding layer 1) and 11440 J (welding layer 2), interpass temperature 50 °C, ambient temperature 20 °C were selected to conduct the actual experiment and verify the residual stress and deformation. The results showed that the simulation results agreed with the actual results, thereby confirming the model’s reliability.

Finite element modeling of girth welded pipe with multiple defects

Due to the expansion of the pipeline network in the transportation of petroleum and its derivatives, it has been essentialto develop studies to evaluate and guarantee the safety condition, as well as the reliability of such facilities. Weldedpipelines have been widely used, and they are susceptible to corrosion. Since the heating at the welded point may leads tostructural and compositional modifications in the material, which may generate corrosion. The present paper presents anonlinear computational model burst pressure assessment in API X70 girth welded pipes with multiple defects, created bycorrosion, which may represent a great risk for gases and fuel leakage during transportation. In this study, the computationalmodel has been developed by the finite element method considering the isotropic hardening model and contact conditionsbetween different materials involved in the analysis, with corrosion simulated as a rectangular defect. The corroded pipe andthe efficiency of the computational model have been analyzed by varying the width of the heat-affected zone (HAZ), and thedepth of single and multiple defects. The results obtained by using the finite element analysis have been compared with thesemi-empirical methods and literature results. The computational model developed by the present work has presentedsatisfactory results.

The Effect of Strain Rate and Temperature on Forming Limit Diagram for DKP-6112 and AZ31 Materials

Forming limit diagrams (FLDs) are used in sheet metal operations widely for predicting blank fracture and forming characteristics of materials. There are three approaches for building forming limit diagrams which are the experimental, theoretical and numerical methods. Experimental method, which includes Nakazima formability test, is generally preferred for determining forming limit diagrams, although it requires complex experimental setup and effort. This study, firstly, compares the experimentally determined FLD results with the numerically obtained ones by using the constitutive models formed through the use of von Mises criteria with isotropic, kinematic and combined hardening models, and Hill48 yield criterion at quasi-static loading and room temperature conditions. The stress-strain relations are obtained by applying the Johnson-Cook phenomenological model for DKP-6112 and AZ31 materials. Then, the constitutive relation that gives closest results to experimental data is chosen to evaluate the effects of the variations of strain rate and temperature values on the FLDs for both materials. Nakazima tests, with 8 different blank specimens, are simulated by using a finite element software to present and compare the numerical forming limit diagrams. For determining the necking time in numerical FLDs maximum strain acceleration strain localization method is used. It is observed that forming limit diagram shifts downwards with strain rate increase and shifts upwards with temperature increase for both materials.

A study on experiment and simulation to predict the spring-back of SS400 steel sheet in large radius of V-bending process

The spring-back phenomenon is one of the key problems in sheet metal forming process, especially with a complex shape. In this paper, the experiments of spring back have been first carried out to study the effect of punch strokes (different bending angles) on the spring-back angle for 6 (mm) thickness of SS400 sheet steel by V-bending process. The experimental results are then validated by finite element analysis (FEA) of ABAQUS software. To simulate spring-back of V-bending, deformed results of V-shape from a dynamic forming simulation in Abaqus/Explicit would be imported into Abaqus/Standard, and then a static analysis will calculate the spring-back of V-bending. Simulation studies have shown that there are different variations in the initial bending angle and the spring-back angle after the removal of the bending force based on isotropic and kinematic hardening models. Therefore, the combined hardening model has been proposed to overcome the mismatch between prediction results and the corresponding experiments. Based on the accuracy of FEM simulation, this study also verifies the effect of parameters such as a thickness of the sheet, punch radius and punch stroke on the spring-back angle in order to select the optimum input parameters by using Taguchi method.

Evaluation of strength of stainless steel bolt without heat treatment considering Bauschinger effect during manufacturing process

Abstract Isotropic hardening models for elastic-plastic materials are often used to simulate cold forging processes, although it cannot represent the Bauschinger effect. However, the Bauschinger effect must be considered for precise simulation of the strength in service of cold-forged components without heat treatment, as well as their geometry. A cold-forged bolt made of stainless steel is a typical example. In this report, finite element analysis of the forming process and the strength was performed for two multi-stage cold forging processes of non-heat-treated stainless steel bolts. The Yoshida-Uemori model was used as a kinematic hardening model that takes into consideration the Bauschinger effect of a material. The Yoshida-Uemori model was modified so that they can represent the strain hardening behavior in a large strain region appropriately for applying the model to cold forging process. As a result, it was possible to account for the Bauschinger effect during the forming process. Moreover, it was possible to estimate the difference in strength between the isotropic and kinematic hardening models by analysis of the tensile test results. Furthermore, the impact of the forming process on the strength of the cold-forged bolt was also evaluated.

Return-mapping algorithms for associative isotropic hardening plasticity using conic optimization

We present a mathematical programming approach for elastoplastic constitutive initial value problems. Consideration of the associative plasticity and a linear isotropic hardening model allowed us to formulate the local discrete constitutive equations as conic programs. Specifically, we demonstrate that implicit return-mapping schemes for well-known yield criteria, such as the Rankine, von Mises, Tresca, Drucker-Prager, and Mohr–Coulomb criteria, can be expressed as second-order and semidefinite conic programs. Additionally, we propose a novel scheme for the numerical evaluation of the consistent elastoplastic tangent operator based on a first-order parameter derivative of the optimal solutions.

Finite element approach of the buried pipeline on tensionless foundation under random ground excitation

This work presents an investigation in the numerical performance of finite element approach in the dynamic elastoplastic analysis of buried pipeline, which is subjected to random ground motion. The surrounding soil is modeled by Winkler and Pasternak type foundation, while the random ground motion is generated synthetically by generalized nonstationary Kanai–Tajimi model. The governing equation is formulated by Euler–Bernoulli beam theory and discretized by beam-pipe element. Moreover, the von Mises isotropic hardening model is employed for material behavior modeling. The Hilber–Hughes–Taylor (HHT) method and the Newton–Raphson method are adopted as the time incremental iterative algorithm to solve the global equilibrium equation. Several applications are carried out to investigate the numerical performance of the present numerical model in dealing with the dynamic elastoplastic analysis of buried pipe. The norm L2 of stress and displacement error are determined for different time intervals and the factors that contribute to the error reduction are investigated in present work.

Determination of Model Parameters for the Hardening Soil Model

The Hardening Soil model, an elasto-plastic second-order hyperbolic isotropic hardening model, in Plaxis has seen many applications in finite element analysis of various earth structures. This technical note presents a protocol for determination of the model parameters of the Hardening Soil model from a set of triaxial compression tests. The technical note also describes details about how to determine the Mohr-Coulomb strength parameters c and ϕ for well-compacted fills (with and without cohesion), of which the failure envelopes are typically curved. The motivation for preparing this technical note came from a study on analysis of field-scale soil–geosynthetic composites in which the soil model and model parameters deduced from triaxial tests were able to predict with very good accuracy “all” measured results of five field-scale soil–geosynthetic composites under increasing applied vertical loads up to 1000 kPa (approximately five times the load level commonly used in design of reinforced soil bridge abutments). The model parameters were determined by a well-defined protocol. The protocol should be of value to researchers and engineers who use the soil model for sophisticated finite element analysis and design of earth structures.