Cyclic Plasticity Model Research Articles

Bayesian protocols for high-throughput identification of kinematic hardening model forms

Constitutive models are essential for assessing the mechanical response of complex materials, yet uncertainties in model forms and parameters persist due to the influence of micromechanisms and microstructural features. We develop Bayesian protocols to iteratively refine both model forms and the associated material properties for complex constitutive models. Our aim is to provide rigorous, probabilistically informed evaluations of improvements achieved with increasing model complexity. Leveraging high-throughput experimental microindentation data, the protocols involve three steps: (i) emulating FE simulations using multi-output Gaussian process surrogate models, (ii) calibrating an initial simple constitutive model against experimental data, and (iii) progressively enhancing model complexity by iteratively improving agreement between simulations and experiments. The various model forms are compared using model form probabilities and aggregate discrepancies. Sobol indices are used to quantify the identifiability of material properties, aiming to prevent parameter proliferation. We apply this protocol to identify the optimal form of cyclic plasticity models for duplex Ti-6Al-4V. Although tailored for cyclic plasticity models, these protocols hold promise for calibrating and refining nonlinear constitutive models across diverse material classes.

Enhanced Cyclically Stable Plasticity Model for Multiaxial Behaviour of Magnesium Alloy AZ31 under Low-Cycle Fatigue Conditions.

Magnesium alloys, particularly AZ31, are promising materials for the modern automotive industry, offering significant weight savings and environmental benefits. This research focuses on the challenges associated with accurate modelling of multiaxial cyclic plasticity at small strains of AZ31 under low-cycle fatigue conditions. Current modelling approaches, including crystal plasticity and phenomenological plasticity, have been extensively explored. However, the existing models reach their limits when it comes to capturing the complexity of cyclic plasticity in magnesium alloys, especially under multiaxial loading conditions. To address this gap, a cyclically stable elastoplastic model is proposed that integrates elements from existing models with an enhanced algorithm for updating stresses and hardening parameters, using the hyperbolic tangent function to describe hardening and ensure a stabilised response with closed hysteresis loops for both uniaxial and multiaxial loading. The model is based on a von Mises yield surface and includes a kinematic hardening rule that promises a stable simulation of the response of AZ31 sheets under cyclic loading. Using experimental data from previous studies on AZ31 sheets, the proposed model is optimised and validated. The model shows promising capabilities in simulating the response of AZ31 sheet metal under different loading conditions. It has significant potential to improve the accuracy of fatigue simulations, especially in the context of automotive applications.

Multiaxial ratcheting-fatigue evaluation of pressurized elbow pipe under strong cyclic loading using damage-coupled cyclic plasticity model

Continuous damage mechanics (CDM) is based on the theories of continuous medium mechanics and continuous medium thermodynamics, which considers damage is an irreversible dissipative process within the materials, and employs the field-theoretic approach of image-only science to study the internal macroscopic damage evolution law of the materials and its influence on the deterioration of the macroscopic mechanical properties of the materials. Hence, within the framework of CDM, a damage-coupled cyclic plasticity constitutive model is proposed based on combined isotropic and Chen-Jiao-Kim (CJK) kinematic hardening rule for evaluating the ratcheting-fatigue behavior of 90° elbow pipes under strong cyclic loading in this paper. Stress return mapping and numerical solution procedures of the proposed model are formulated based on the backward finite difference method. Formulation of the consistent tangent operator is presented for the Finite Element implementation of the plasticity model in ABAQUS UMAT. The FE analysis of non-pressurized and pressurized elbow pipes under cyclic displacement-controlled loading is respectively performed using the implemented constitutive model. The results reveal that the predicted results of the damage-coupled cyclic plasticity constitutive model are better than combined isotropic-kinematic hardening model, and well consistent with the experimental data.

Unconventional cyclic plasticity model implementation for shell and plane stress elements in UMAT/Abaqus

Finite element simulations are widely used in several industrial sectors (civil, aerospace, mechanical, naval, biomedical, etc.) to design components or structures. Often, the resolution of highly non-linear problems requires the recurse to dense meshes with the consequent increase in computation time. This aspect becomes particularly relevant for cyclic mobility problems where repeated loading might affect the computational cost. Therefore, the efficiency of finite elements represents a crucial aspect of speeding up the design process. Past works of the authors focused on developing the additive hypoelastic-based and multiplicative hyperelastic-based constitutive equations of the Extended Subloading Surface model for three-dimensional finite elements adopting fully implicit integration schemes. In this paper, the constitutive equations of the Extended Subloading Surface theory are reformulated for shell and plane stress elements, aiming to obtain an efficient computational tool suitable for cyclic mobility problems. The numerical implementation considers isotropic hardening, kinematic hardening, and material anisotropy. Numerical solutions obtained utilising shell/plane stress and solids elements are also discussed.

Characterizing the mechanical deformation response of AHSS steels: A comparative study of cyclic plasticity models under monotonic and reversal loading

This study evaluates the performance of a user-defined combined hardening modeling method for advanced high-strength steels (AHSS) under monotonic and reversal loading conditions. The plastic behavior of TWIP980 and TRIP980 AHSS sheet metals is investigated using a cyclic plasticity modeling approach. The model incorporates an isotropic von Mises yield criterion and a single-term Chaboche nonlinear kinematic hardening rule. Monotonic and reversal loading stress-strain curves are predicted and compared with experimental results. The model accurately captured the Bauschinger effect for both materials, but it needs help to effectively model the permanent softening behavior observed in TWIP980 steel. Overall, the proposed modeling method agrees well with experimental results for monotonic loading and accurately represents the Bauschinger effect and transient behavior during reversal loading. However, better improvements are needed to capture the permanent softening behavior of TWIP980 steel.

Validating cyclic plasticity material model for three materials subjected to asynchronous axial-torsion conditions

In the present work, a cyclic plasticity model based on Ohno-Wang kinematic hardening rule and Tanaka non-proportionality parameter, is proposed to simulate the cyclic stress strain response of three materials. The proposed model has been validated with respect to reported test results on two grades of steel (SA 333 Gr. 6 and E355) and one grade of austenitic stainless steel (X5CrNi18-10) under asynchronous axial-torsion loading conditions with a wide range of frequency ratios. The proposed model resulted in a comparable assessment of axial and shear stress–strain response with respect to the test loops for all three materials.

Effect of martensitic transformation on ratchetting in medium-manganese steel: Experiment and homogenized constitutive model

Transformation-induced plasticity (TRIP) behavior and related cyclic plasticity model of medium-manganese steel subjected to uniaxial cyclic loading were studied. Cyclic loading tests were conducted at different mean stresses and stress amplitudes. The results show that medium-manganese steel exhibits two different ratchetting evolution characteristics. Moreover, microscopic characterizations reveal that martensitic transformation occurs in medium-manganese steel during asymmetrical cyclic stressing, and the higher the applied stress amplitude, the greater the ratchetting strain and the more likely the martensitic transformation will occur. The interaction between TRIP and ratchetting leads to accelerated accumulation of plastic strain. Based on the existing meso-mechanics cyclic elastoplastic constitutive model, a kinetic equation for the strain-induced martensitic transformation and a modified nonlinear kinematic hardening equation are introduced. Subsequently, the two-leveled homogenization method was used to construct a homogenized cyclic plasticity model containing a three-phase microstructure of austenite, martensite, and ferrite. By comparing the predicted results with the experimental results, the proposed model can reasonably describe the evolutionary features of each phase and the effect of the phase transformation on the ratchetting of medium-manganese steel. Finally, ratchetting is further predicted and discussed for different austenite contents and phase transformation rates using the proposed model.

Constitutive modelling and damage prediction of AlSi10Mg alloy manufactured by SLM technology with emphasis on ratcheting in LCF regime

The present work has been aimed at developing an improved cyclic plasticity model in the framework of Ohno-Wang kinematic hardening formulation and evaluating the performance of the model with reference to the critical experimental investigation. LCF test specimens of the AlSi10Mg aluminium alloy have been fabricated through selective laser melting technology. The material shows strain-range dependent variation of modulus of elasticity under symmetric strain-controlled loading. The modulus of elasticity decreases with increasing strain amplitude. Stress–strain responses have been critically examined under multistep uniaxial ratcheting in the LCF regime with incremental mean stress and stress amplitude. Damage calculation considering ratcheting and LCF mechanisms as independent gives unconservative predictions. The linear damage accumulation rule taking the largest contribution of both is bringing much more accurate estimates. The proposed model incorporates effects of mean stress and stress amplitude under uniaxial multistep ratcheting in the LCF regime. All fatigue tests in the LCF regime have been simulated using the proposed improved model. Evolution of strain-range dependent elastic modulus has been incorporated in the formulation of the improved model through the memory history dependent parameter. The ratcheting parameter is newly formulated in this present work to account for the effects of accumulated mean plastic strain on the opening of stress strain hysteresis loops that results in a better prediction of the behaviour of cyclic plastic deformation. The proposed model has been validated by comparing simulated results with experimental observations and reference published simulation results.

Two Contributions to Rolling Contact Fatigue Testing Considering Different Diameters of Rail and Wheel Discs

Scaled rolling contact fatigue tests, used to practically simulate the wear of the wheel and rail material under laboratory conditions, are typically classified into two categories. Tests in the first category use twin-disc stands, while the second group of test rigs use two discs of different diameters considering the rail disc as the larger one. The latter setup is closer to the real situation, but problems can occur with high contact pressures and tractions. The focus of this paper is on two main contributions. Firstly, a case study based on finite element analysis is presented, allowing the optimization of the specimen geometry for high contact pressures. Accumulated plastic deformation caused by cycling is responsible for abrupt lateral deformation, which requires the use of an appropriate cyclic plasticity model in the finite element analysis. In the second part of the study, two laser profilers are used to measure the dimensions of the specimen in real time during the rolling contact fatigue test. The proposed technique allows the changes in the specimen dimensions to be characterized during the test itself, and therefore does not require the test to be interrupted. By using real-time values of the specimen’s dimensional contours, it is possible to calculate an instantaneous value of the slip ratio or the contact path width.

Mixed-mode crack growth analysis using a cyclic plasticity model

The effects of two singularity fields, namely, the HRR solution and modified form of the nonlinear kinematic hardening (NKH) solution, on the pure mode I and mixed mode I/II fatigue crack propagation were investigated. Experiments and computations were performed on compact tension shear (CTS) specimens of P2M steel, aluminium 7050, and Ti-6Al-4V with different monotonic and cyclic elastic–plastic properties. The analysis of the experimental data on the crack growth rate for all tested materials is given in terms of plastic stress intensity factors (SIFs) according to the HRR and NKH models. The elastic–plastic crack tip fields were obtained by FE computation as a function of the position along the curvilinear crack path for the monotonic condition and the first several cycles of fatigue deformation considering the Bauschinger effect. As a complement to the FE modelling, digital image correlation (DIC) measurements of the displacement and strain fields around the crack tip in the CTS specimens were performed. This study aimed to obtain more detailed information on the local cyclic strain ahead of the mixed mode crack tip by using DIC. From the sensitivity analysis, it was established that the DIC value depended significantly on the location along the crack direction of the pair of points selected before and behind the crack tip. In this study, acceleration or retardation of the crack growth rate in terms of the NKH plastic SIF with respect to the HRR model was observed because of the coupling effect of the mode mixity and cyclic plastic properties of the tested P2M steel, aluminium 7050, and Ti-6Al-4V.

Damage-Coupled Cyclic Plasticity Model for Prediction of Ratcheting–Fatigue Behavior under Strain and Stress Controlled Ratcheting for Two Different Nuclear Piping Steels

Damage-Coupled Cyclic Plasticity Model for Prediction of Ratcheting–Fatigue Behavior under Strain and Stress Controlled Ratcheting for Two Different Nuclear Piping Steels

Predicting the forming limits in the tube hydroforming process by coupling the cyclic plasticity model with ductile fracture criteria

This study presents a one-surface plasticity constitutive model combined with phenomenological and micromechanical damage models to be applied to the large plastic deformation during tube hydroforming. These factors lead to simulating the Bauschinger effect and transient behavior in large plastic strain ranges and predicting fracture onset. By using the integration approach, a numerical integration algorithm of implementation by explicit schemes was carried out. A comparison of several cyclic loading tests between experiments and numerical simulation was accomplished. The accuracy of these models is verified, which could be expanded to a large strain range forming process. Adopting the proposed models, finite element modeling is performed in the tube hydroforming process. The simulation and experimental results comparison showed that the proposed framework accurately predicted the tube formability in the hydroforming process.

Incorporating Dislocation Mechanisms into a Phenomenological Cyclic Plasticity Model for Structural Alloys

Incorporating Dislocation Mechanisms into a Phenomenological Cyclic Plasticity Model for Structural Alloys

Impact of the plasticity modeling on fatigue life prediction for steels showing modest non-proportional hardening

This study evaluated the influence of Tanaka parameter-based cyclic plasticity modeling on fatigue life estimation under multiaxial loading. The life predictions based on the experimental stress–strain data, simulated by the Chaboche cyclic plasticity model and Chaboche model with the implemented Tanaka parameter, were compared for this purpose. The fatigue life was then calculated using three popular prediction models for the two steel grades exhibiting moderate non-proportional hardening. Eleven multiaxial loadings were investigated, including proportional, 90° out-of-phase, and asynchronous cases. Modeling the cyclic material response using the coupled Chaboche and Tanaka models revealed to have improved all fatigue life predictions.

Strain‐controlled fatigue loading of an additively manufactured AISI 316L steel: Cyclic plasticity model and strain–life curve with a comparison to the wrought material

AbstractLow cycle fatigue (LCF) regime was experimentally studied for a 316L steel additively manufactured by laser‐powder bed fusion (L‐PBF), a material widely used in sectors that require a reliable durability analysis. Material cyclic elastoplastic behavior is described by the Chaboche–Voce combined plasticity model, which displayed a great degree of accuracy. The fatigue life was modeled by both invoking the Manson–Coffin curve and other simplified models derived from static properties of the material; some of which showed remarkably good accuracy. A quantitative comparison with a wrought‐processed 316L steel displayed a markedly different cyclic elastoplastic response but comparable fatigue strengths.

The role of accumulated plasticity on yield surface evolution in pearlitic steel

In this paper, we analyze one specific assumption used in many cyclic plasticity models: The dependence of the yield surface evolution on the accumulated plasticity, i.e., the time-integrated plastic multiplier. We measure this scalar variable in carefully designed experiments and track the yield surface evolution. Our results show that this variable is insufficient to describe the isotropic or distortional hardening of the investigated steel, invalidating the commonly used assumption. The results highlight requirements for developing and verifying new isotropic and distortional hardening laws.

Effects of recast layer on fatigue performance of laser-drilled holes in nickel-based superalloy

The effects of the recast layer on the fatigue performance of laser-drilled holes in Ni-based superalloy were experimentally and computationally investigated. It was found that millisecond-laser drilling leads to a recast layer of about 10 μ m , whereas no recast layer was observed in the picosecond-laser drilled hole. The recast layer was confirmed to reveal the Niobium segregation, the Laves phase precipitation and small lattice distortions, resulting in low yield stress. In-situ fatigue test results indicated that the recast layer does not show an obvious influence on the fatigue life of the holed structures in the low-cycle fatigue regime. With the help of the developed cyclic plasticity model, computational analysis verified that the recast layer significantly decreased the stress concentrations around the hole root. The shielding effects improved the fatigue performance of the mismatched material system. The investigations confirm that the millisecond-laser-drilled holes can be used in high-performance turbine blades sofar the recast layer does not dominate the fatigue process, which provides new insights into laser manufacturing.

An improved strain path dependent model under multiaxial cyclic loading for simulating material response of low C-Mn steel

In this work, a prominent cyclic plasticity model based on modified AbdelKarim-Ohno kinematic hardening rule and Calloch isotropic hardening is implemented and validated w.r.t. test results of low C-Mn steel. In reference to the shortcomings of the model, an improved model based on modified Ohno-Wang and Tanaka non-proportionality parameter is introduced. Since the precise assessment of stress–strain response is an essential precondition for carrying out fatigue life analysis, therefore hysteresis loop responses under various multiaxial LCF loading having different strain paths are compared. The simulation result with the proposed model resulted in improved assessment for non-proportional strain paths.

Modeling Bauschinger’s Effect in Planar Impact

Bauschinger’s effect was first noticed as a decrease of yield stress upon unloading from a plastic state in standard tension-compression tests. It was later established that Bauschinger’s effect is a rather general phenomenon in terms of materials and modes of loading. We may say that Bauschinger’s effect may be regarded as a manifestation of anisotropic plasticity caused by the plastic flow itself. Bauschinger’s effect was extensively researched as part of an ongoing effort to understand and model cyclic plasticity. Cyclic plasticity models found in the literature are usually based on concepts of kinematic hardening which are usually rather complex, and they contain many material parameters to be calibrated from tests. Here we’re concerned with modeling Bauschinger’s effect in dynamic situations, specifically in planar impact tests. In such tests Bauschinger’s effect is mainly manifested by the so called quasi-elastic response upon unloading from the shock plateau level. Our approach is based on ideas put forward since the 1930s. First, we show that our model, which we call effective grains model, is able to reproduce the main modes of response in the plastic range, including Bauschinger’s effect. We then apply it to planar impact situations, and show that it’s able to reproduce the so called quasi-elastic response.

Austenitic Stainless Steel EBF Subjected to Low and Extremely Low Cycle Fatigue

AbstractDissipative zones buildings, in which plastic hinges or plastic strains occur during, for instance, seismic episodes, have been studied for many different types of steel fuse elements. Stainless steel (SS), has attracted attention in this regard due to its high ductility and further studies are needed to determine its performance and usefulness as fuses.The use of SS in the construction industry has represented an advance due to its already known anticorrosive properties in addition to its strength and ductility. However, recent research on cyclic plasticity shows that SS has significant hardening properties, which can be exploited in the use of this material in structural elements to support cyclic loads, such as those occurring during earthquakes.The cyclic plasticity models in SS have been studied with some applications (fatigue, low‐cycle fatigue and extremely low cycle fatigue). Several studies carried out cyclic tests to obtain experimental data, which have been used for numerical models with the utilisation of a combined numerical model of kinematic/isotropic hardening. These studies recommend models to simulate the behaviour of SS under a cyclic load.This work presents an experimental study of the cyclic behaviour of SS when subject to low and extremely low cycle fatigue. Several protocols on tests such as companion, multiple step and arbitrary tests were carried out. The results inferred from the experimental program provide hardening parameters used to study one example of dissipative zones of eccentrically braced frames (EBFs).