Cyclic Tension-compression Tests Research Articles

Finite element modeling for analyzing the production of high-strength steel sheets for automobile parts

Abstract An investigation was conducted on developing components from high-strength steel sheet grade 590, with a thickness of 2.40 millimeters, using finite element analysis. The focus was on predicting springback and deviation behavior during the manufacturing process of a Member C inner workpiece. The research comprised a comprehensive examination of chemical composition, microstructural analysis, and mechanical property testing to establish suitable material models for the forming process. Three material models were evaluated for accuracy, including the Barlat89 yield criteria, the Y-U model, and the Barlat89 yield criteria + Y-U model. Cyclic tension-compression tests were used to determine the parameters of the Barlat89 yield criteria + Y-U model, which were then confirmed using the 1-element model. The predicted bend angles for the manufactured samples were highly consistent with the experimental measurements. The three models were used to predict the strain distribution, springback and deviation behavior in the produced components. The results indicated that all three material models produced similar results in terms of strain distribution. However, the Barlat89 yield criteria + Y-U model exhibited the least inaccuracy when all seven sections were averaged, with angles θ1L of 93.66 degrees and θ1R of 93.13 degrees, underscoring its superior performance in predicting springback. The deviation behavior predicted by the three material model simulations was very comparable. Consequently, it can be concluded that the Barlat89 yield criteria + Y-U model represented the most precise and suitable choice for simulating the formation of the Member C inner component.

Advanced modeling of higher-order kinematic hardening in strain gradient crystal plasticity based on discrete dislocation dynamics

An extensive study of size effects on the small-scale behavior of crystalline materials is carried out through discrete dislocation dynamics (DDD) simulations, intended to enrich strain gradient crystal plasticity (SGCP) theories. These simulations include cyclic shearing and tension-compression tests on two-dimensional (2D) constrained crystalline plates, with single- and double-slip systems. The results show significant material strengthening and pronounced kinematic hardening effects. DDD modeling allows for a detailed examination of the physical origin of the strengthening. The stress–strain responses show a two-stage behavior, starting with a micro-plasticity regime with a steep hardening slope leading to strengthening, and followed by a well-established hardening stage. The scaling exponent between the apparent (higher-order) yield stress and the geometrical size h varies depending on the test type. Scaling relationships of h−0.2 and h−0.3 are obtained for respectively constrained shearing and constrained tension-compression, aligning with some experimental observations. Notably, the DDD simulations reveal the occurrence of the uncommon type III (KIII) kinematic hardening of Asaro in both single- and double-slip cases, emphasizing the relevance of this hardening type in the realm of small-scale plasticity. Inspired by insights from DDD, two advanced SGCP models incorporating alternative descriptions of higher-order kinematic hardening mechanisms are proposed. The first model uses a Prager-type higher-order kinematic hardening formulation, and the second employs a Chaboche-type (multi-kinematic) formulation. Comparison of these models with DDD simulation results underscores their ability to effectively capture the observed strengthening and hardening effects. The multi-kinematic model, through the use of quadratic and non-quadratic higher-order potentials, shows a notably better qualitative congruence with DDD findings. This represents a significant step towards accurate modeling of small-scale material behaviors. However, it is noted that the proposed models still have limitations, especially in matching the DDD scaling exponents, with both models producing h−1 scaling relationships (i.e., Orowan relationship for precipitate size effects). This indicates the need for further improvements in gradient-enhanced theories in order to guarantee their suitability for practical engineering applications.

Parameter identification of Yoshida–Uemori combined hardening model by using a variable step size firefly algorithm

Abstract The material behavior under cyclic loading is more complex than under monotonic loading and the usage of the sophisticated constitutive models is required to accurately define the elastoplastic behaviors of the advanced high-strength steels and aluminum alloys. These models involve the numerous material parameters that are determined from cyclic tests and accurate calibration of the variables has a great influence on the description of the material response. Therefore, the development of a precise and robust identification method is needed to obtain reliable results. In this study, a systematic methodology depending upon the firefly algorithm (FA) with variable step size has been developed and Yoshida–Uemori combined hardening model parameters of a dual-phase steel (DP980) and an aluminum alloy (AA6XXX-T4) are determined. The identified parameters are verified based on comparisons between the finite element simulations of the cyclic uniaxial tension-compression tests and experimental data and also the search performance of the variable FA is evaluated by comparing it with the standard FA. It is seen from these comparisons that variable FA can easily find and rapidly converge to the global optimum solutions.

Explicit and Implicit Integration of Constitutive Equations of Chaboche Isotropic-Kinematic Hardening Material Model

The proper selection of the material model and its parameters in numerical simulations of the material response under loading is a very important task. In the cyclic load one should assume different phenomena, e.g. ratchetting effect, the mean stress relaxation, creep, etc. The Chaboche kinematic hardening model is mainly applied in order to capture the Bauschinger effect due to its good description of the material behaviour under the cyclic loading. The modified Chaboche isotropic-kinematic hardening model is considered in this paper in order to simulate the strain-controlled and stress-controlled uniaxial cyclic tension-compression test. The implicit and explicit integration procedures are tested here, showing advantages and disadvantages of both methods. It is shown that both approaches provide similar results. The implicit integration method of constitutive equations is unconditionally stable and thus less calculation steps are required in comparison to the explicit procedure. The implicit and explicit integration of the Chaboche model including isotropic and kinematic hardening are then implemented for the 3D case in commercial ABAQUS program in the form of the user material procedure. The correctness of results obtained for the user material model is verified by comparison to results for commercially implemented Chaboche model.

Viscoelastic constitutive artificial neural networks (vCANNs) – A framework for data-driven anisotropic nonlinear finite viscoelasticity

The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications that typically cannot accurately capture the nonlinear viscoelastic behavior of materials. For example, the success of attempts to capture strain (rate)-dependent behavior has been limited so far. To overcome this problem, we introduce viscoelastic Constitutive Artificial Neural Networks (vCANNs), a novel physics-informed machine learning framework for anisotropic nonlinear viscoelasticity at finite strains. vCANNs rely on the concept of generalized Maxwell models enhanced with nonlinear strain (rate)-dependent properties represented by neural networks. The flexibility of vCANNs enables them to automatically identify accurate and sparse constitutive models of a broad range of materials. To test vCANNs, we trained them on stress-strain data from Polyvinyl Butyral, the electro-active polymers VHB 4910 and 4905, and a biological tissue, the rectus abdominis muscle. Different loading conditions were considered, including relaxation tests, cyclic tension-compression tests, and blast loads. We demonstrate that vCANNs can learn to capture the behavior of all these materials accurately and computationally efficiently without human guidance. Our source code is available at https://github.com/ConstitutiveANN/vCANN.

Research on the 2A11 Aluminum Alloy Sheet Cyclic Tension–Compression Test and Its Application in a Mixed Hardening Model

The increasing application of aluminum alloy, in combination with the growth in the complexity of components, provides new challenges for the numerical modeling of sheet materials. The material elastic–plasticity constitutive model is the most important factor affecting the accuracy of finite element simulation. The mixed hardening constitutive model can more accurately represent the real hardening characteristics of the material plastic deformation process, and the accuracy of the material property-related parameters in the constitutive model directly affects the accuracy of finite element simulation. Based on the Hill48 anisotropic yield criterion, combined with the Voce isotropic hardening model and the Armstrong–Frederic nonlinear kinematic hardening model, a mixed hardening constitutive model that considers material anisotropy and the Bauschinger effect was established. Analysis of the tension–compression experiment on the sheet using finite element method. Using the finite element model, the optimum geometry of the tension–compression experiment sample was determined. The cyclic deformation stress–strain curve of the 2A11 aluminum alloy sheet was obtained by a cyclic tensile–compression test, and the material characteristic parameters in the mixed hardening model were accurately determined. The reliability and accuracy of the established constitutive model of anisotropic mixed hardening materials were verified by the finite element simulation and by testing the cyclic tensile–compression problem, the springback problem, and the sheet in bending, unloading, and reverse bending problems. The tensile–compression experiment is an effective method to directly and accurately obtain the characteristic parameters of constitutive model materials.

In-situ analysis of the elastic-plastic characteristics of high strength dual-phase steel

Modeling the elastic behavior of dual-phase steels is complex due to the strain dependency of Young's modulus and high elastic nonlinearity. Since it is assumed that reasons for this are to be found in microstructural behavior, microscopic in-situ analysis are necessary, but due to the overlap of the martensite and ferrite peaks, the evaluation of diffraction profiles is highly complex. Within this work, CR590Y980T (DP1000) is investigated in a continuous cyclic tensile and tension-compression test under synchrotron radiation at High Energy Material Science beamline P07 in Petra III, DESY. On basis of additional EBSD measurements, an evaluation approach is shown to analyze the dual-phase diffraction profiles in such a way that martensite and ferrite can be separated for three lattice planes. The origin of the specific elastic-plastic behavior of dual-phase steels in terms of onset of yielding, anelasticity or early re-yielding is analyzed on the basis of lattice strains and interphase stresses. For this, the time-synchronously measured micro data is correlated with the macro stress-strain relationship and thermoelastic effect. The results help to better understand strain-dependent elastic-plastic behavior of DP steels on a micro level and provide great potential to improve characterization and modeling in terms of springback prediction.

Material Parameters Sensitivity on Springback Modelling of Simple Bending Process

Springback is one of the major defects that continuously concerns the sheet metal experts’ community. It is has long been known that the sheet thickness, the bending angle and the yield stress of the material primarily affect the angle change after the tools’ release. Besides, the consideration of the kinematic hardening (KH) model has powerful influence on the modelling results, too. In this study, we overviewed several possible factors on the springback with finite element modeling of a simple V-die bending operation, highlighting the effect of the material variables on the final shape. AutoForm® R7 software and the built-in theory of kinematic hardening were used for the material characterization, coupled with the Hockett-Sherby isotropic hardening rule as well as the Yld89 yield criterion. The material data for modeling kinematic hardening behavior were obtained by cyclic tension-compression tests, whilst the isotropic hardening and the yield surface parameters were acquired by simple uniaxial tension tests. The simulation results were compared to the experimental springback observations obtained by a CNC bending machine, without using springback compensation. A detailed parametric study was also carried out to highlight the level of criticality of the applied material variables on the final angle change.

Characterization of fatigue performance of cold mix recycled asphalt mixtures through uniaxial tension–compression testing

Cold recycling of pavements utilizes nearly 100% of the reclaimed asphalt pavement (RAP) for pavement rehabilitation. Due to the large amount of RAP, the cold recycled mixes would become prone to fatigue cracking, and hence evaluation of their fatigue performance becomes highly important. In this study, three cold recycled asphalt mixes were prepared using a regular cationic slow setting asphalt emulsions with hard base asphalt binder (CSS-1h) with and without Portland cement stabilization, and a polymer modified emulsion (CSS-1hp). The optimum emulsion and pre-mix water contents were determined using Superpave Gyratory compacted specimens through the mix design process by studying the air void levels and meeting minimum strength requirements. Fatigue properties of these three groups of mixes were then evaluated through a series of uniaxial cyclic tension–compression tests. The results were compared in terms of the modulus degradation, dissipated energy capacity, changes in phase angle, and number of cycles to failure, to determine the fatigue lives of the different mixes. The results indicated that adding 1% Portland cement to the cold recycled specimens significantly improved their fatigue performance as compared to the control scenario specimens prepared with regular CSS-1h emulsion. Using the polymer modified emulsion also led to a slightly improved fatigue resistance of the cold mix specimens as compared to the mixes prepared with regular emulsion. Furthermore, Multiple Stress Creep Recovery (MSCR) testing of the two residual emulsion binders indicated potential of improving the rutting resistance for the mixes prepared with the polymer modified emulsion.

Influence of Strain Gradient on Fatigue Life of Carbon Steel for Pressure Vessels in Low-Cycle and High-Cycle Fatigue Regimes.

This paper discusses how the strain gradient influences the fatigue life of carbon steel in the low-cycle and high-cycle fatigue regimes. To obtain fatigue data under different strain distributions, cyclic alternating bending tests using specimens with different thicknesses and cyclic tension–compression tests were conducted on carbon steel for pressure vessels (SPV235). The crack initiation life and total failure life were evaluated via the strain-based approach. The experimental results showed that the crack initiation life became short with decreasing strain gradient from 102 to 106 cycles in fatigue life. On the other hand, the influence of the strain gradient on the total failure life was different from that on the crack initiation life: although the total failure life of the specimen subjected to cyclic tension–compression was also the shortest, the strain gradient did not affect the total failure life of the specimen subjected to cyclic bending from 102 to 106 cycles in fatigue life. This was because the crack propagation life became longer in a thicker specimen. Hence, these experimental results implied that the fatigue crack initiation life could be characterized by not only strain but also the strain gradient in the low-cycle and high-cycle fatigue regimes.

Experimental and numerical study of springback effect of advanced high strength steel in a V-shape bending

Advanced high strength (AHS) steel sheets are increasingly used for the production of various automotive structural parts. The components of new lightweight vehicles have very complex Shapes, for which more precise forming procedures are required in order to achieve a desired geometry. Hereby, springback occurrences of such AHS parts are often the most critical concern. In this work, it aimed to investigate springback effects of the AHS steel grade 980 in a V-shape bending process. Experimental bending test and its corresponding FE simulations were conducted. The Hill’48 and Barlat89 yield criteria, and the Yoshida-Uemori (Y-U) kinematic hardening model were applied. The yield function parameters were obtained from the tensile tests of samples in various orientations. The Y-U model parameters were determined from a cyclic tension-compression test and were afterwards calibrated with the 1-element simulation. The resulted bend angles measured from the experiment and predicted by FE simulations using the different models were compared and evaluated. For the bending in this work, the Hill’48 and Barlat89 models showed the predictive errors of springback angle 1% and 2% higher than the Y-U model, respectively. The accuracy of springback prediction could be improved by the Y-U model using C1 and C2 parameters around 1%. In addition, effects of sheet thickness and punch radius on the springback were afterwards studied and discussed by using the Y-U model.

The cement-bone bond is weaker than cement-cement bond in cement-in-cement revision arthroplasty. A comparative biomechanical study.

This study compares the strength of the native bone-cement bond and the old-new cement bond under cyclic loading, using third generation cementing technique, rasping and contamination of the surface of the old cement with biological tissue. The possible advantages of additional drilling of the cement surface is also taken into account. Femoral heads from 21 patients who underwent a total hip arthroplasty performed for hip arthritis were used to prepare bone-cement samples. The following groups of samples were prepared. A bone—cement sample and a composite sample of a 6 weeks old cement part attached to new cement were tested 24 hours after preparation to avoid bone decay. Additionally, a uniform cement sample was prepared as control (6 weeks polymerization time) and 2 groups of cement-cement samples with and without anchoring drill hole on its surface, where the old cement polymerized for 6 weeks before preparing composite samples and then another 6 weeks after preparation. The uniaxial cyclic tension-compression tests were carried out using the Zwick-Roell Z020 testing machine. The uniform cement sample had the highest ultimate force of all specimens (n = 15; Rm = 3149 N). The composite cement sample (n = 15; Rm = 902 N) had higher ultimate force as the bone-cement sample (n = 31; Rm = 284 N; p <0.001). There were no significant differences between composite samples with 24 hours (n = 15; Rm = 902 N) and 6 weeks polymerization periods (n = 22; Rm = 890 N; p = 0.93). The composite cement samples with drill hole (n = 16; Rm = 607 N) were weaker than those without it (n = 22; Rm = 890 N; p < 0.001). This study shows that the bond between the old and new cement was stronger than the bond between cement and bone. This suggests that it is better to leave the cement that is not loosened from the bone and perform cement in cement revision, than compromising bone stock by removal of the old cement with the resulting weaker cement-bone interface. The results support performing cement-in-cement revision arthroplasty The drill holes in the old cement mantle decrease cement binding strength and are not recommended in this type of surgery.

Identification of Chaboche\u2013Lemaitre combined isotropic\u2013kinematic hardening model parameters assisted by the fuzzy logic analysis

A very good knowledge of material properties is required in the analysis of severe plastic deformation problems in which the classical material processing methods are accelerated by the application of the additional cyclic load. A general fuzzy logic-based approach is proposed for the analysis of experimental and numerical data in this paper. As an application of the fuzzy analysis, the calibration of Chaboche–Lemaitre model hardening parameters of PA6 aluminum is considered here. The experimental data obtained in a symmetrical strain-controlled cyclic tension–compression test were used to estimate the material’s hardening parameters. The numerically generated curves were compared to the experimental ones. For better fitting of numerical and experimental results, the optimization approach using the least-square method was applied. Unfortunately, commonly accepted calibration methods can provide various sets of hardening parameters. In order to choose the most reliable set, the fuzzy analysis was used. Primarily selected values of hardening parameters were assumed to be fuzzy input parameters. The error of the hysteresis loop approximation for each set was used to compute its membership function. The discrete value of this error was obtained in the defuzzification step. The correct selections of hardening parameters were verified in ratcheting and mean stress relaxation tests. The application of the fuzzy analysis has improved the convergence between experimental and numerical stress–strain curves. The fuzzy logic allows analyzing the variation of elastic–plastic material response when some imprecisions or uncertainties of input parameters are taken into consideration.

Identification of the anisotropic plasticity using the virtual fields method for 2024 aluminium alloy

In this work, the virtual fields method was applied to identify the anisotropic plastic constitutive parameters for the wrought 2024 aluminium alloy. First, low cyclic tension-compression tests were conducted for the specifically designed aluminium alloy specimens on a hydraulic universal testing machine and the full-field deformations measured by digital image correlation. Then, the measured experimental data were used to simultaneously identify the constitutive parameters of the Hill 1948 yield criterion and the nonlinear kinematic hardening model based on the virtual fields method. Reasonable identified parameters were obtained. The fitting curves of the virtual work during the minimization process verify the reliability of the identification results.

On the effect of detwinning-induced plasticity in compressive cyclic loading of NiTi shape memory alloys

A new inelastic mechanism, detwinning-induced plasticity (DIP), is proposed to model the response of NiTi SMAs to cyclic loading, based on thermodynamic considerations. DIP is incorporated into a constitutive framework for NiTi SMA. The constitutive framework also includes well-established inelastic mechanisms of phase transformation, transformation-induced plasticity, residual martensite, and detwinning. The model is constructed at the single crystal scale using the framework of thermodynamics and a crystal plasticity formulation. An explicit scale-transition rule is adopted for the simulation of polycrystalline materials, allowing direct comparison of the model predictions with published experimental test data. Thermodynamic considerations result in a strong contribution of DIP for cyclic loading regimes where compressive stress occurs during part of the loading cycle. However, the contribution of DIP is negligible for cyclic loading regimes that result exclusively in tensile stress. This predicted dependence of DIP on compression, but not on tension, is strongly supported by experimental cyclic loading results. Inclusion of DIP results in improved prediction of experimentally observed NiTi SMAs behavior, including strain-controlled cyclic compression-unloading and cyclic tension-unloading tests and stress-controlled cyclic tension-compression and tension-unloading tests. During the first loading cycle the contribution of DIP is not significant in any loading regimes. However, in cases where compressive stress occurs during part of the loading cycle, DIP contributes strongly to the material response from the second cycle onwards. In strain-controlled cyclic compression-unloading tests DIP leads to a less negative peak stress and a more negative residual strain following several loading cycles. In stress-controlled tension-compression cyclic loading DIP leads to a reduction of peak and residual strains.

Characterization of kinematic hardening with a hydraulic bulge test

The increase of the mapping accuracy in numerical simulations of sheet metal forming processes is an important field of research today. In this context, the modelling of the kinematic hardening plays a major role when it comes to nonlinear strain paths during the forming process. The kinematic hardening leads, beside other effects, to a lower increase of the hardening after a change of the linear strain path. Characterization of the Bauschinger coefficient, an indicator of the portion of kinematic hardening, is normally done with cyclic tension-compression tests. The testing setup is quite challenging in the strain measurement and the specimen handling due to the small geometry and the risk of buckling during compression. Thus, a hydraulic bulge test with an optimized geometry is used for the characterization of the kinematic hardening with a strain path change for the materials DC06 and DP600. According to literature, DC06 has no significant kinematic hardening, while the high strength steel DP600 is sensitive to this hardening mechanism. The strain path change is realized by a secondary element in the die. In the beginning of the test, a conventional circular die induces an equi-biaxial strain. After this preforming step, an elliptical geometry is used to induce plane strain in the specimen. The resulting strain path changes from equi-biaxial to plane strain. The flow curves out of the experiment show the kinematic hardening effect after the strain path change for the DP600 while no change is observable for the DC06. Numerical simulation with the identified kinematic factor should lead to a better mapping accuracy regarding the springback behavior.

Parameter Determination and Application Research of Mixed Hardening Model Based on Cyclic Tension-compression Test

Parameter Determination and Application Research of Mixed Hardening Model Based on Cyclic Tension-compression Test

A Comparative Study of Forming and Crash Behavior of High Strength Steels

Abstract Advanced high strength (AHS) steel sheets of various grades have been increasingly used in the automotive industries because of their advantageous mechanical properties. High strength and great energy absorption are desired for a structural component design. On the other hand, large formability and strain hardening are necessary for achieving an effective forming process. To apply eligible steel grades, precise understanding of their forming and crash characteristics is needed. In this work, AHS steels with varying strengths, namely grades 780, 980, and 1180, were investigated. First, tensile tests were performed, and mechanical properties, including r-values, of the examined steels were obtained for different loading directions. The forming limit curves (FLCs) and respective forming limit stress curves (FLSCs) were determined by means of a Nakajima forming test and finite element simulation. The cyclic tension-compression tests were conducted to characterize the elastic recovery and Bauschinger effect of steels. Afterward, forming processes of an automotive part were performed, and the forming and springback behaviors of steels were evaluated by using simulations coupled with Hill’48 and Yoshida-Uemori models, determined material parameters, FLCs, and FLSCs. In addition, crashworthiness of steels was numerically studied by means of a crash rectangle profile and simplified side impact pole test. The mechanical, forming, and crash performances of all the investigated AHS steels were evaluated and discussed so that the results can be applied for part design and manufacturing.

Characterization of Asphalt Mixes Behaviour from Dynamic Tests and Comparison with Conventional Cyclic Tension–Compression Tests

In the presented research, conventional cyclic tension–compression tests and dynamic tests were performed on two types of asphalt mixes (AM). For the tension–compression tests, the complex modulus was obtained from the measurements of the axial stress and axial strain. For the dynamic tests, an automated impact hammer equipped with a load cell and an accelerometer were used to obtain the frequency response functions (FRFs) of the specimens at different temperatures. Two methods were proposed to back-calculate the complex modulus from the FRFs at each temperature: one using the 2S2P1D (two springs, two parabolic elements and one dashpot) model and the other considering a constant complex modulus. Then, a 2S2P1D linear viscoelastic model was calibrated to simulate the global linear viscoelastic behaviour back calculated from each of the proposed methods of analysis for the dynamic tests, and obtained from the tension–compression test results. The two methods of analysis of dynamic tests gave similar results. Calibrations from the tension–compression and dynamic tests also show an overall good agreement. However, the dynamic tests back analysis gave a slightly higher value of the norm of the complex modulus and a lower value of the phase angle compared to the tension–compression test data. This result may be explained by the nonlinearity of AM (strain amplitude is at least 100 times smaller for dynamic tests) and/or by ageing of the materials during the period between the tension–compression and the dynamic tests.

DUSST: Development of a new stress sweep fatigue test for asphalt mixtures

Fatigue cracking is one of the main damage mechanisms that take place in asphalt pavements. However, its evaluation during the design asphalt mixtures is not usually considered due to the complexity of the tests required, their high costs and the long time required to perform them. As a consequence, several research teams are working on developing new test procedures to reduce the time related to fatigue characterization of asphalt mixtures. In this context, this paper presents the development of a new test procedure consisting of a cyclic uniaxial tension-compression test in which the stress applied increases every 5000 cycles. In this manner, it is possible to evaluate a mixture’s response under cyclic loading at different stress levels in one test. Also, failure of the mixture takes place in a shorter time period than that required by classical time sweep fatigue tests. This paper presents results obtained in the application of this new methodology to a mixture frequently used in Chilean pavement structures (type IV-A-12 by Chilean standards) with three different asphalt binders: a conventional binder (CA-24), a high modulus binder (CA-HM) and a polymer-modified binder (CA-PM). We evaluated three different types of aggregates obtained through two different shredding processes. Results achieved in the development of our Direct Uniaxial Stress Sweep Test (DUSST) show that it is an experimental method with great potential. This test can characterize fatigue behaviors of asphalt mixtures in a shorter time by using important parameters such as initial strain, failure strain, complex modulus and dissipated energy. In addition, we obtained a good sensitivity of the DUSST main parameters to variables evaluated.