Mixed Isotropic-kinematic Hardening Research Articles

Mastering the art: Proficient finite element implementation and robust evaluation of a strain-hardening porous ductile material crack growth prediction model at finite strain

Accurate prediction of crack extension is crucial for ensuring the structural integrity of metal components exposed to diverse loads. While the Gurson model and its extensions are widely accepted for delineating ductile fracture stages, especially in porous materials with a rigid-perfectly plastic matrix, their efficacy diminishes in the presence of strain-hardening matrices. To address this limitation, our study introduces a robust numerical implementation and assessment of Perrin's model. In contrast to Gurson's approach, Perrin's model incorporates two distinct strain-hardening parameters derived from an intricate analysis of a strain-hardening hollow sphere subjected to axisymmetric loading.Moving beyond theoretical discussions, this paper actively engages in the rigorous evaluation of Perrin's model under various scenarios, encompassing isotropic, kinematic, and mixed isotropic-kinematic hardening conditions. The model's effectiveness is convincingly demonstrated through meticulous comparisons between numerical simulations and real-world experimental observations conducted on pre-cracked specimens.Facing challenges related to achieving global elastic-plastic convergence in large-scale simulations, our research introduces a sophisticated approach. Leveraging stiffness tangent moduli ensure the maintenance of quadratic convergence in global Newton method iterations. This not only enhances the reliability of our simulations but also underscores the practical applicability of our findings.The study also focuses on the necking and crack propagation of a cylindrical specimen through meticulous computational modeling. Our mesh captures intricate details and addresses stress gradients, revealing coplanar crack propagation contrary to prior beliefs. The confirmation of the cup-cone fracture effect challenges previous interpretations, emphasizing the critical role of void nucleation. This reinforces the credibility and applicability of our approach in advancing the understanding of material fracture behavior.In summary, this study significantly contributes to existing knowledge in fracture prediction models, offering a robust framework for predicting ductile fracture under substantial deformations. The presented findings pave the way for advancements in structural engineering, providing invaluable insights for optimizing the performance and resilience of metal structures in real-world applications.

Instrumented indentation for determining stress and strain levels of pre-strained DC01 sheets

In classical mechanical testing, determining the stress and strain states of complex shape specimens turns out to be very challenging, especially in the most deformed regions. In the latter case, when not enough material is present, non-destructive testing is needed for determining the corresponding mechanical state. In this study, a novel approach, based on the local quasi-non-destructive instrumented indentation technique (IIT) coupled with the inverse analysis technique (IAT), is used to determine the stress and strain levels of pre-strained DC01 specimens using monotonic and non-monotonic loading paths. Monotonic and cyclic shear tests as well as Marciniak tests, in both plane and equi-biaxial strain states, are used to apply different pre-strain levels. For monotonic loading paths, i.e. monotonic shearing and Marcianiak tests, the applied methodology showed very satisfying results in determining the stress and strain states of the pre-strained specimens, especially for pre-strain values close to the representative indentation strain values. A maximum stress error of less than 15% was obtained in the case of the highest applied pre-strain value (29.04%). The purely isotropic Voce hardening law was adopted for determining the hardening behavior of the studied specimens in both cases: as-received and pre-strained. In the case of cyclic shear, a mixed isotropic-kinematic hardening law is to be used to determine the stress and strain states of the pre-strained specimens. Adopting a mixed isotropic-kinematic Chaboche hardening law led to satisfying results where the estimation errors of the applied pre-strain value and corresponding yield stress didn't exceed 6% and 1.3%, respectively. The obtained results show that the proposed indentation-based method can be very useful in estimating the work-hardening level and corresponding plastic deformation of pre-strained parts under various loading paths

Geometric and Material Nonlinear Analyses of Trusses Subjected to Thermomechanical Loads

In this article, geometric and material nonlinear analyses of planar and space trusses subjected to thermo-mechanical loads are performed using the Total Lagrangian formulation. The material properties are Thermally InDependent (TID). By obtaining the equilibrium path of these structures, their buckling and post-buckling behaviors are predicted under thermal and mechanical loads. To consider material nonlinearity, a mixed isotropic–kinematic hardening criterion is developed in this formulation. The behavior of material is assumed to be bilinear. To solve nonlinear equations iteratively, the Generalized Displacement Control Method (GDCM) is used. The authors’ scheme is general and can be employed for different types of planar and spatial truss structures having complicated geometries and behaviors. Several popular benchmarks are considered to show the accuracy and correctness of the proposed formulation. Corresponding equilibrium paths and stress–strain curves are reported for each problem.

Notch fatigue analysis and crack initiation life estimation of maraging steel fabricated by laser beam powder bed fusion under multiaxial loading

This paper deals with the notch fatigue behaviour and crack initiation life estimation in maraging steel fabricated by laser beam powder bed fusion under multiaxial loading. Tests are conducted in tubular geometries with lateral holes considering different normal stress to shear stress ratios and multiaxial loading levels. The cyclic stress–strain response at the notch-controlled process zone is simulated numerically using two alternative approaches: a generalised isotropic plasticity model with mixed isotropic-kinematic hardening, and a linear-elastic model. Both approaches demonstrated to be suitable for predicting the crack initiation sites, the directions of crack growth, and the fatigue life. Fatigue life was calculated from a SWT-based model combined with the Theory of Critical Distances. Elastic-plastic predictions led to smaller errors but slightly shifted to the non-conservative side.

Validated prediction of weld residual stresses in austenitic steel pipe girth welds before and after thermal ageing, part 2: Modelling and validation

An extensive finite element simulation campaign was undertaken to examine the complete manufacturing history and high temperature thermal ageing of thick-walled girth-welded austenitic steel pipes fabricated from Esshete 1250 austenitic steel. The simulations examined the impacts of prior quenching of pipe material, fabrication of closely adjacent welds, and axial restraint during welding. The simulations considered both simple isotropic and kinematic hardening behaviour, and a large matrix of Lemaitre-Chaboche mixed isotropic-kinematic hardening material constitutive models, with a focus on examining the most accurate evolutionary hardening behaviour for weld metal. High temperature (650 °C) service exposure was modelled using an RCC-MR type creep model, and the sensitivity of the predicted relaxation to variability in the model parameters was assessed. The predicted residual stresses were validated using measurements made with the deep hole and incremental deep hole drilling techniques and the contour method.

A non-associated anisotropic plasticity model with mixed isotropic–kinematic hardening for finite element simulation of incremental sheet metal forming process

This paper focuses on numerical simulation of single point incremental forming (SPIF) process. Via a user-defined material (VUMAT) subroutine is employed to implement a non-associated mixed isotropic–kinematic hardening material model. The accuracy of the proposed non-associated flow rule model to predict the material behavior and the anisotropy in sheet metal forming simulations is examined by comparing numerical results with experimental measurements. The suggested model shows good agreement with experimental results compared to the associated Hill_R and Hill_S models. The proposed non-associated flow rule demonstrates a good efficiency to simulate the springback after sheet metal forming and to predict the thickness variation during incremental sheet metal forming process. The present non-associated model can improve the prediction of both anisotropic and hardening behaviors of material used in numerically controlled sheet metal forming technology.

Damage characterization in a ferritic steel sheet: Experimental tests, parameter identification and numerical modeling

The Gurson–Tvergaard–Needleman (GTN) model includes several parameters of different nature. Some of them have micromechanical roots while others are strictly phenomenological. Hence, a methodology should be developed in order to obtain a robust set of parameters with both numerical and physical meaning. The material parameters of the GTN model are found using an identification methodology based on experimental-numerical results. The method is applied on a DC01 ferritic steel sheet. An extended version of the Gurson model, incorporating plastic anisotropy, mixed isotropic-kinematic hardening, void nucleation, growth, coalescence and shear is used. Material parameters are obtained based on an inverse optimization and a sensitivity analysis on specimens with different geometries. The onset of coalescence, reflected as the loss of load carrying capacity in the force-displacement curve, is correctly predicted by the extended GTN model. The strain distribution, obtained by digital image correlation, is also correctly simulated. Nevertheless, the model does not to predict the increase of strain observed experimentally, because of the decoupling between hardening and the damage variable. In this respect, the article provides experimental evidence of the limitations of a GTN model based on a strain-controlled nucleation law with heuristic extensions of hardening.

On Residual Stress and Relief for an Ultra-Thick Cylinder Weld Joint Based on Mixed Hardening Model: Numerical and Experimental Studies

Residual stress distributions as welded and after local postwelding heat treatment (PWHT) of butted weld joint of a huge cylinder with ultra-thick wall were investigated by finite element (FE) simulations and measurement. Sequential coupling thermal-mechanical analyses were conducted with a generalized plane strain two-dimensional (2D) model to simulate the welding procedure bead by bead, combining with three-dimensional (3D) double-ellipsoid moving heat source and mixed isotropic–kinematic hardening plastic model. The simulation was validated by X-ray diffraction (XRD) measurements. Simulation results showed that local PWHT with heated band width of 0.5Rt can significantly reduce the residual stress on the outer surface of weld joint, but bring about harmful high tensile stress on inner surface due to bending moment induced by local radial thermal distortion. For the purpose to find out the appropriate heated band width of local PWHT, relations between stress relief and size of heated band were studied. Results show that the stresses on the inner surface reach a maximum value when the heated band width is less than 1Rt. Based on the simulation results and from the view point of lowering the stress level on the inner surface, the optimum width of 3Rt for heated band was proposed.

The NeT Task Group 4 residual stress measurement and analysis round robin on a three-pass slot-welded plate specimen

Accurate prediction and measurement of residual stresses in welds is an important part of assuring their short and long-term structural performance in high value, safety critical engineering components and structures. However, both measurements and predictions of weld residual stresses often exhibit high levels of variability that are not widely appreciated. The mission of the European Network on Neutron Techniques Standardization for Structural Integrity (NeT) is to develop experimental and numerical techniques and standards for the reliable characterisation of residual stresses in structural welds.The NeT Task Group 4 project examined residual stresses in a three-pass slot-welded plate specimen fabricated from AISI 316L(N) austenitic stainless steel plate. Several nominally identical specimens were fabricated under closely controlled conditions, with detailed records kept of the manufacturing history, weld process parameters, transient temperatures during welding, and the resulting geometric distortions. Comprehensive stress-strain material property characterisation was then undertaken, extending to the isothermal cyclic tests necessary to calibrate the mixed isotropic-kinematic material hardening models required for accurate weld residual stress prediction. Parallel residual stress measurement and simulation round robins were performed by a large number of participants from around the world.Residual stresses were measured using neutron and high energy synchrotron diffraction, surface X-ray diffraction, surface and deep hole drilling, the contour method, and ultrasonics. Neutron diffraction measurements were made at eight different instruments. The diffraction measurements database alone is large enough to generate reliable mean profiles, to identify clear outliers, and to establish that there is no statistically significant difference in the residual stress field in the specimens used for the non-destructive measurements. NeT Task Group 4 gives a unique insight into the real-world variability of diffraction-based residual stress measurements, and forms a reliable foundation against which to benchmark other measurement methods.NeT Task Group 4 is also a unique test bed for the development and validation of weld residual stress simulation techniques in austenitic stainless steel. Its combination of extensive materials characterisation, accurately characterized welding temperature transients, and reliable residual stress and distortion measurements is currently unrivalled. About thirty finite element simulations were submitted to the network over the course of the project, giving insights into the required accuracy of welding thermal solutions, the mechanical solution accuracy achievable using optimized material constitutive models, and the level of acceptable error in finite element residual stress simulation results for use in structural integrity assessments of high integrity engineering components.

Springback Prediction of Stretching Process using Finite Element Analysis for DP600 Steel Sheet

Abstract Springback phenomenon is well predicted for some mild steel materials, but not for steels with higher strength. One of the most used tools to stamping optimization is usage of finite element analysis. In order to accurate describe the real behaviour of the materials for stamping of vehicle panels, the application of proper hardening rule seems to be crucial. Due to higher accuracy of predicted results, high strength steel sheets are usually modelled by means of kinematic or mixed isotropic-kinematic hardening models. In this paper the springback prediction of advanced high strength steel DP600 by numerical simulation was investigated. Through cyclic tension-compression tests, the material characterization has been performed for DP600 steel sheet. Different hardening models (isotropic, kinematic and mixed isotropic-kinematic) used in the simulations were compared with expreriment. The Yoshida–Uemori model succesfully describe the kinematic behaviour of the material and provided more accurate results than others.

A mixed hardening model combined with the transformation-induced plasticity effect

A mixed isotropic–kinematic hardening model considering the transformation-induced plasticity (TRIP) effect was proposed for TRIP steels in this study. Besides the nonlinear Chaboche backstress and linear Prager–Ziegler backstress, a third backstress that depicts the contribution of TRIP effect to the kinematic hardening was presented. The TRIP effect was modeled using an equivalent plastic strain and a stress triaxiality coefficient as the variant. Forward–reverse shear experiments were performed for a cold rolled TRIP780 steel. A new clamper was designed to reduce the buckling during reverse shear. Cyclic loading–unloading–reloading uniaxial tension experiments were conducted and the degradation of elastic modulus with the plastic strain was discussed. Micro-indentation tests were performed to check the true elastic modulus. U-bending springback simulation was performed with the new hardening model combined with the Yoshida’s elastic modulus. The results showed that the investigated TRIP780 steel has prominent kinematic hardening behavior, Bauschinger effect, transient hardening and permanent softening during forward–reverse shear deformation. The percentage of the third backstress component due to the TRIP effect in the total backstress reaches 31% at 0.25 plastic strain. Springback simulation with the proposed hardening model combined with the degradation of elastic modulus is more precise than the isotropic model.

A model of one-surface cyclic plasticity with Lemaitre damage criterion for plastic instability prediction in the incremental forming process

The precise prediction of plastic deformation instabilities during the incremental forming process is quite complex because of the complex stress state and extremely large plastic strain. Until now, most elasto-plastic constitutive models are only suitable within a small strain range and describe the isotropic behavior. However, for extremely large plastic deformation under complex loading processes such as an incremental forming process, these models are ineffective and ill-conceived. This paper presents an elasto-plastic constitutive model which combines a mixed isotropic-kinematic hardening model with the Lemaitre damage model. This model can predict the Bauschinger effect, transient behavior, permanent softening and fractures over a large plastic strain range. By using explicit integration schemes, an integration algorithm of numerical implementation is proposed using simple expressions. A cyclic loading test comparison between experiments and numerical analysis is carried out to validate these models. The model is also applied to FE analysis of incremental forming. The deformation and the prediction of thickness are consistent with experimental results and thus verify the accuracy of the model.

Comparison of the hardening behaviour of different steel families: From mild and stainless steel to advanced high strength steels

Although steel has been used in vehicles from the automotive industry׳s inception, different steel grades are continually being developed in order to satisfy new fuel economy requirements. For example, advanced high strength steel grades (AHSS) are widely used due to their good strength/weight ratio. Because each steel grade has a different microstructure composition, they show different behaviours when they are subjected to different strain paths in forming processes. Materials with high yield strength tend to be influenced by phenomena of cyclic plasticity such as the Bauschinger Effect, while low yield strength materials tend to harden when they are subjected to cyclic loading.Different steel grades are used in different forming processes, which are usually optimised by numerical tools such as Finite Element Models. This method requires proper hardening rules in order to correctly predict the real behaviour of the materials. For instance, AHSS are usually well modelled by means of mixed isotropic–kinematic hardening models.The methodology for developing a mixed hardening model to be implemented in finite element codes and simulate sheet forming processes requires three steps: (i) an appropriate experimental test to obtain stress–strain curves, (ii) a model able to predict accurately the behaviour of the material and (iii) a parameter identification method. Currently, there are few studies which analyse and model the hardening behaviour of different steel families following the same methodology. In this work, a wide range of steels from low to high yield strengths were characterised and their hardening behaviour modelled with the same methodology so as to provide comparative data.In particular, the Chaboche and Lemaitre hardening model was successfully fitted to the experimental stress–strain curves obtained from a tension–compression test. The test was performed at low cyclic deformations (±2%) due to the limitation of the test to achieve higher deformations during the compression without buckling. Therefore, this modelization is useful for low deformation processes such as the roll levelling process (Silvestre; 2013, Silvestre et al. Steel Res Int; 2012, 1295), in which the maximum deformations achieved are lower than 2%.

Development of a Global Indicator to Assess Mechanical Tests

Full-field measurement methods have emerged in the last years and these methods are characterized by directly providing displacement and strain fields for all points over the specimen surface. Thus, the design of heterogeneous tests can be performed for material parameter identification purposes since the inhomogeneous strain fields can be measured. However, (i) no defined criterion yet exists for designing new heterogeneous tests, (ii) it is rather difficult to compare and rate different tests and (iii) a quantitative way to define the best test for material behavior characterization of sheet metals has yet to be proposed. Due to this, the goal of this work is the development of a global indicator able to assess mechanical tests. The proposed indicator quantifies the strain state range, the deformation heterogeneity and the strain level achieved in the test, based on a continuous evaluation of the strain field up to rupture. This global indicator was applied to rank some classical tests, such as uniaxial tensile, simple shear, plane strain and biaxial tensile tests. These tests were carried out numerically by reproducing the virtual behavior of DC04 mild steel. A constitutive model composed by the non-quadratic Yld2004-18p yield criterion combined with a mixed isotropic-kinematic hardening law and a macroscopic rupture criterion was used. The performance of the tests was compared with the indicator and a ranking was established. The results obtained show that biaxial tension is the test providing more information for the mechanical behavior characterization of the material. It was also verified that plane strain test presents a better performance than simple shear and uniaxial tensile tests.

An improved implicit numerical integration of a non‐associated, three‐invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials

SummaryThe Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high‐performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large‐scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright © 2015 John Wiley & Sons, Ltd.

Material parameter identification within an integrated methodology considering anisotropy, hardening and rupture

The main focus of the present work is the development of a global procedure for a complete characterization of sheet metal behavior, including anisotropy, evolution of hardening and rupture. This efficient procedure involves the mechanical characterization, at room temperature and in quasi-static conditions, of the material up to large strains by evaluating the local strain field. The initial anisotropy, hardening and rupture of DC04 mild steel are characterized using a complex phenomenological model composed by the non-quadratic Yld2004-18p yield criterion combined with a mixed isotropic-kinematic hardening law and a macroscopic rupture criterion. For this purpose, an inverse methodology for material parameter identification is implemented based on several experimental tests considered as homogeneous and also, a mixed experimental-numerical approach to calibrate the rupture criterion is performed. In order to validate the obtained results, a deep drawing test, leading either to full drawing or rupture of the blank, is carried out. Digital image correlation is used to acquire additional data information in the deep drawing test. Strain fields at several stages of the deep drawing experiment are evaluated leading to a better comparison between the experimental observations and the results of the numerical simulation.

Influence of Kinematic Hardening during Machining of ARMCO Iron

The simpler implementation of isotropic hardening begs the question, if modelling kinematic hardening is necessary, especially if the hardening is nonlinear and temperature dependent. This question not only depends on the material, but also on the modelled load case, which varies with different manufacturing processes. To answer this, thermo-mechanically coupled elasto-plastic materials were used in an implicit material model in ABAQUS/Standard for a two-dimensional cutting simulation. The nonlinear hardening in the models varies from isotropic to mixed isotropic-kinematic hardening. The two-dimensional cutting simulation uses a two-dimensional continuous remeshing technique. A slow machining process was simulated leaving out strain rate and temperature dependencies and focussing purely on the kinematics of deformation. The necessity of a kinematically translated yield surface is concluded for iron, by comparing the purely isotropic to the mixed isotropic-kinematic hardening results. A comparison with experimental data illustrates the conformance quality of the different hardening modes.

The Role of Plasticity Theory on the Predicted Residual Stress Field of Weld Structures

Constitutive plasticity theory is commonly applied to the numerical analysis of welds in one of three ways: using an isotropic hardening model, a kinematic hardening model, or a mixed isotropic-kinematic hardening model. The choice of model is not entirely dependent on its numerical accuracy, however, as a lack of empirical data will often necessitate the use of a specific approach. The present paper seeks to identify the accuracy of each formalism through direct comparison of the predicted and actual post-weld residual stress field developed in a three-pass 316LN stainless steel slot weldment. From these comparisons, it is clear that while the isotropic hardening model tends to noticeably over-predict and the kinematic hardening model slightly under-predict the residual post-weld stress field, the results using a mixed hardening model are quantitatively accurate. Even though the kinematic hardening model generally provides more accurate results when compared to an isotropic hardening formalism, the latter might be a more appealing choice to engineers requiring a conservative design regarding weld residual stress.

Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach

In this paper we present a non-associated plane stress anisotropic constitutive model with mixed isotropic-kinematic hardening. The quadratic Hill 1948 and non-quadratic Yld-2000-2d yield criteria [Barlat F, et al. Int J Plasticity 2003;19: 1297–1319.] are considered in the non-associated flow rule (non-AFR) model to account for anisotropic behavior. To predict accurate hardening in cyclic loading conditions, a modification of the hardening model proposed by Chun et al. [Chun BK, et al., Int J Plasticity 2002; 18: 571–595.] is adopted. This one-surface non-linear mixed isotropic-kinematic hardening model does not require loading criterion and can predict Bauschinger effect, transient behavior and permanent softening. The developed model was implemented as a user-defined material subroutine (UMAT) into the commercial finite element code ABAQUS/Standard based on fully implicit backward Euler's method. Cup drawing simulation results for an automotive sheet metal AA5754-O show that the implemented hardening model avoids under- and over-estimation of the cup height respectively generated by kinematic and isotropic hardening laws. Moreover, as will be seen in the results of highly textured AA2090-T3, both cup height and earing profile generated by non-associated flow models are in better agreement with experimental results. Finally, the Yld2004-18p and non-AFR Yld2000-2d models are compared in terms of prediction of directional Lankford coefficients and yield stresses. It is shown that a same order of accuracy that is obtained by Yld2004-18p can be achieved by the non-AFR Yld2000-2d.

Failure of high strength steel sheets: Experiments and modelling

Failure in sheet metal structures of ductile material is usually caused by one of, or a combination of, ductile fracture, shear fracture or localised instability. In this paper the failure of the high strength steel Docol 600DP and the ultra high strength steel Docol 1200M is explored. The constitutive model used in this study includes plastic anisotropy and mixed isotropic-kinematic hardening. For modelling of the ductile and shear fracture the models presented by Cockroft–Latham and Bressan–Williams have been used. The instability phenomenon is described by the constitutive law and the finite element (FE) models. For calibration of the failure models and validation of the results, an extensive experimental series has been conducted including shear tests, plane strain tests and Nakajima tests. The geometries of the Nakajima tests have been chosen so that the first quadrant of the forming limit diagram (FLD) were covered. The results are presented both in an FLD and using prediction of force–displacement response of the Nakajima test employing element erosion during the FE simulations. The classical approach for failure prediction is to compare the principal plastic strains obtained from FE simulations with experimental determined forming limit curves (FLCs). It is well known that the experimental FLC requires proportional strains to be useful. In this work failure criteria, both of the instability and fracture, are proposed which can be used also for non-proportional strain paths.