Robust Constitutive Model Research Articles

Analysis of Cement Sheath–Rock Damage Mechanism—A Case Study on Water Injection Wells

In the field of water injection wells within oilfields, comprehending the intricate mechanics of water channeling and the resulting rock damage on the external cemented surface holds paramount significance for the efficient management of reservoirs. This paper presents a comprehensive study aimed at illuminating the complex nature of rock damage on the external cemented surface of casings and deciphering the underlying mechanisms that underpin water channeling occurrences. To this end, a robust constitutive model is established and refined to capture the multifaceted interactions inherent in rock damage on the cemented surface. This model introduces a modified bonding force approach to enhance shear stress precision and thoughtfully accounts for the profound effects of elastic–plastic behavior, cracking damage, and elastic-cracking coupling damage on damage progression. Subsequently, the refined model is employed to investigate rock damage on the external cemented surface of water injection wells, encompassing variations in confining pressure, rock width on the cemented surface, and the ratio of Young’s modulus between the cement sheath and the rock. The research findings emphasize the interplay between cracking and elastic damage as the catalyst for rock damage on the cemented surface. Impressively, the accuracy of the refined constitutive model for the cemented surface has advanced by over 5% compared to prior studies. The manipulation of confining pressure and the Young’s modulus ratio enhances peak fracture water pressure, signifying substantive strides in comprehending damage propagation mechanics. Furthermore, the study discerns the negligible influence of rock width on the cemented surface regarding damage patterns. These findings have important implications for the effective management of water injection wells, providing insights for the restoration of water channeling wells and proactive measures against water channeling phenomena. They also contribute to the refinement of well cementing practices and the proficient management of water channeling and water flooding in oilfields. The research findings have profound implications for the domain of water injection wells, offering novel insights into the restoration of water channeling wells and the implementation of preemptive measures against water channeling phenomena. These findings hold the potential to guide the refinement of well cementing practices and the adept management of water channeling and water flooding wells within the studied oilfield.

Design and validation of a heterogeneous interior notched specimen for inverse material parameter identification

Nowadays, virtual manufacturing, digitalisation and simulation predictions are essential for the design and the development of engineering parts and components, as well as companies’ productivity. The implemented constitutive model and the accuracy of the determined material parameters influence the reliability of these predictions. It is necessary to calibrate multiple parameters of a complex and robust constitutive model. This is a very time-consuming task and involves high costs when using a classical approach, in which several different homogeneous mechanical experiments are performed. The non-homogeneous mechanical tests can provide a larger variety of mechanical information in just one experiment, reducing the number of required tests for material characterisation. The aim of this work is to numerically design a specimen with an interior notch for a uniaxial loading test that presents strain heterogeneity. The shape of the interior notch is optimised to maximise the strain heterogeneity. The optimisation procedure is guided by a cost function established by several strain heterogeneity indicators. The best specimen shape exhibits numerically uniaxial tension and compression, pure shear and plane strain tension in the plastic region. The identifiability of Swift’s hardening law parameters was quantitatively investigated based on the partial derivative of the strain fields with respect to the sought parameters. Results show that the proposed design strategy enables to increase in strain heterogeneity. It is shown that the optimised specimen has significantly better identifiability compared to a tensile specimen with a circular hole. Finally, a comparison between a classical Finite Element Model Updating (FEMU) methodology and a FEMU-based approach that uses a DIC-levelling strategy was conducted in order to inversely identify the Swift hardening law parameters and validate the designed specimen. It was confirmed that the DIC-levelling method finds more accurate results than the classical approach, with the compromise of the computational time. It was also shown that the optimum designed specimen is adequate for inverse identification strategies. • Optimised heterogeneous specimen to test in standard tensile test machine. • Better hardening parameters’ identifiability than circular perforated specimen. • The strain states observed in FEA are exhibited in the virtual experiment. • Parameter identification using a DIC-levelled approach is more accurate than the classical. • On the reduction of time, resources and costs in the development of engineering parts.

A 3D finite-strain beam model for thermo-mechanical deformations of 2D shape memory alloys in 3D space

In this paper, a robust constitutive model adapted to a 3D beam theory in the finite strain regime is proposed to simulate thermo-mechanical behaviors of shape memory alloys (SMAs) under triaxial normal-shear loadings. For the first time, four internal parameters are considered to capture martensitic transformation, orientation/reorientation of martensite variants, normal-shear deformation coupling, and asymmetric/anisotropic strain generation in polycrystalline SMAs. Solution algorithms of the model are presented for stress- and strain-control cases based on the elastic-predictor inelastic-corrector return mapping process. To develop the Cauchy-Green deformation tensor, a 3D exact displacement field is proposed based on the centroid movements and rotations of the cross-section. A finite element formulation along with the Newton-Raphson and Riks techniques is also established to trace the non-linear equilibrium path of 3D SMA beam structures in the large defamation regime. Higher-order shape functions are also considered to avoid shear and membrane locking issues. To explore and demonstrate the capabilities of the proposed model, the results of the triaxial and 3D SMA constitutive models are compared with existing experimental results on uniaxial tension, and combined tension-torsion tests. Afterwards, the results of 3D solid element and proposed 3D beam element are compared with experimental results of deep stretch SMA helical springs under three loading/unloading cycles. An excellent qualitative and quantitative correlation is observed between numerical and experimental results verifying the model accuracy and the solution procedure. The combination of the proposed triaxial SMA constitutive model with 3D beam theory leads to a significant reduction in computational time and storage requirements without any accuracy loss. Extra simulations are then conducted for a simplified model of a 3D biomedical vascular SMA stent under various loading/unloading conditions. The simulations reveal that the new 3D finite-strain SMA-beam element is well appropriate for modeling of 3D spatial lattice-based stents. Due to simplicity and accuracy, the 3D SMA beam model could serve in future efforts for a computationally efficient modeling of large defamations of complicated 3D SMA structures with 2D members (e.g., SMA lattices). • A robust constitutive model is developed to simulate behaviors of SMAs under triaxial normal-shears loadings. • The solution algorithms combined is extended to trace the non-linear equilibrium path of 3D SMA beam structures. • The results of present 3D Beam model has been compared with existing experimental results as well as 3D solid elements. • A good qualitative and quantitative correlation is observed between numerical and experimental results. • The proposed triaxial SMA beam model leads to a significant reduction in computational time without loss inaccuracy.

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

A Physical Mechanism-Based Model of CoCrFeMnNi High Entropy Alloy Considering Adiabatic Heat Effect for Hot Bulk Forming Processes

Fabrication of a newly developed high entropy alloy is an essential step to enable it to be used as an industrial structure for its potential applications, such as billets, frames and tubes. Bulk forming processes at high temperatures are preferably used requiring the hot flow behavior of the HEA, which needs to be thoroughly investigated for accurate construction of a robust constitutive model and, hence, reliable process simulation and optimizations. In this study, to compensate for the lack of modelling microstructure using conventional phenomenological models, a novel physical mechanism-based model of CoCrFeMnNi high-entropy alloy was established. Particularly, the adiabatic heat effect was taken into account for modelling the HEA for the first time. The hot flow behavior, as well as grain evolution of this alloy under different forming conditions, are well modelled. The modelling predictions obtain great agreement with the experimental results, the calculated R-value (all higher than 0.95) and AARE (all smaller than 0.05) because the different conditions provide validity to the accuracy of the model prediction. In addition, the temperature increase due to deformation heat was well predicted to further evident to the accuracy of model. Furthermore, the hardening behavior during hot deformation was also compared, enabling the provision of useful guides for process designers of hot bulk forming HEAs.

A three-parameter structurally motivated robust constitutive model for isotropic incompressible unfilled and filled rubber-like materials

A structurally motivated three-parameter strain energy function W is presented in this paper for application to the constitutive modelling of various types of incompressible isotropic rubber-like materials, from unfilled to filled rubbers, polymers and soft tissues. A particular objective of the current work is to achieve another step towards devising a comprehensive model for application to an assortment of incompressible isotropic hyperelastic materials, not limited only to a specific subset type of rubbers or polymers. To this end, the application of the model to extant datasets from various types of rubber-like materials is presented, via simultaneous fitting of the model to the considered deformation modes. The modelling results are then compared with those of a selected set of established three-parameter models in the literature, including a generalised neo-Hookean strain energy function and another two models which include an I2 term. It will be shown that the proposed model most favourably captures the datasets for all unfilled, filled rubber and polymer specimens considered. Finally, the model is applied to the deformation datasets of a soft tissue, namely the human brain, for which the (one-term) Ogden model is currently known to provide the best fit. It will be demonstrated that the application of the Ogden model will lead to loss of convexity, while our proposed model provides a better fit, with lower relative errors, and remains convex over the deformation domain. By way of the presented examples and applications, it is concluded that the proposed model provides a reliable degree of robustness for a suitable application to constitutive modelling of various types of rubber-like materials.

Differential equation model of shape memory alloy spring and its application in heat engines

In order to use low-grade thermal sources more efficiently, different types of Shape Memory Alloy (SMA) heat engines have been proposed and studied, but the lack of a robust constitutive model is still an open issue. In the current paper, the SMA spring model is constructed by combining the mechanical spring theory and the SMA differential equation model. This model can describe the characteristics of SMA springs well, so it is used for SMA heat engine modeling. The state of the SMA heat engine under different loads is calculated, and the output of the SMA heat engine can also be calculated and compared with its experimental value. The calculated rotation speed and output power of the SMA heat engine are in good agreement with the experimental values, which illustrates the superiority of the proposed model and provides a method for the simulation, design, and optimization of the SMA heat engine.

Experimental and modeling study of the viscoelastic-viscoplastic deformation behavior of amorphous polymers over a wide temperature range

The deformation behavior of amorphous polymers in the post-yield region is viscoelastic-viscoplastic (VE-VP) as it exhibits both viscoelastic and viscoplastic characteristics. However, a systematic experimental and modeling study for it is lacking. In this paper, the VE-VP deformation behavior of an amorphous polymer was experimentally investigated over a wide temperature range. It was found that some of the observed deformation behaviors cannot be reasonably explained by the common assumptions of the thermally-activated segmental motions and the formation of a topologically-entangled rubbery network. With the assumption that there is a glassy network formed from weak linkages in the polymer, the observed deformation behaviors over a wide temperature range can be well explained by considering the stretch and relaxation of the glassy network. The glassy network assumption was first proposed by one of our coauthors and employed for modeling the VE-VP deformation behavior of amorphous polymers at room temperature. In this paper, the glassy network assumption was further examined at different temperatures and employed to establish a constitutive model for simulating the VE-VP deformation behavior of amorphous polymers over a wide temperature range. The model was validated by corroboration with experiments. It was demonstrated that a constitutive model based on the glassy network assumption is capable of representing the loading, strain recovery, and stress relaxation behaviors simultaneously, in contrast to most of the existing constitutive models. Hence, this work not only proposes a reasonable physical picture for understanding but also provides a robust constitutive model for simulating the VE-VP deformation behavior of amorphous polymers and its temperature dependence.

Multi-axial creep-fatigue analysis of a cracked groove structure subjected to cyclic thermal loading

The aim of this study is to analyze the local change in stress–strain and damage behavior in an inlet groove structure of a power plant component under the effect of the crack geometrical constraint. A robust constitutive model is used to describe the inelastic behavior of advanced 9–12% Cr heat-resistant steels at high temperature. Steam temperature and loading profiles corresponding to the idealized startup, holding and shutdown sequence of the structure are assumed. Thirteen cycles of this sequence are chosen for the loading conditions. Transient heat transfer analysis is conducted to estimate the thermal field throughout the structure. Structural analysis is then performed using the material constitutive model. The results show that the crack geometrical constraint not only changes the stress–strain behavior, but also the damage distribution. Compared to the results without the crack effect, the damage locations demonstrate a major change. Specifically, the damage starts underneath the surface of the groove structure. This is attributed to the more complex multi-axial features in the regions close to the surface of the structure.

Fractional-Order Elastoplastic Modeling of Sands Considering Cyclic Mobility

Seabed soil may experience a reduction in strength or even liquefaction when subjected to cyclic loadings exerted by offshore structures and environmental loadings such as ocean waves and earthquakes. A reasonable and robust constitutive soil model is indispensable for accurate assessment of such structure–seabed interactions in marine environments. In this paper, a new constitutive model is proposed by enriching subloading surface theory with a fractional-order plastic flow rule and multiple hardening rules. A detailed validation of both stress- and strain-controlled undrained cyclic test results of medium-dense Karlsruhe fine sand is provided to demonstrate the robustness of the present constitutive model to capture the non-associativity and cyclic mobility of sandy soils. The new fractional cyclic model is then implemented into a finite element code based on a two-phase field theory via a user subroutine, and a numerical case study on the response of seabed soils around a submarine pipeline under cyclic wave loadings is presented to highlight the practical applications of this model in structure–seabed interactions.

Multiscale modeling of coupling mechanisms in electrically assisted deformation of ultrathin sheets: An example on a nickel-based superalloy

Electrically assisted (EA) forming has ubiquitous merits over room-temperature (RT) forming and thermally aided forming for the fabrication of difficult-to-form microscale products. However, it is difficult to predict the material deformation behavior in the EA microforming process owing to the coupling between the electric current and microstructural size effect. To develop a robust constitutive model that considers the interplay between the electric and grain size effects, RT and EA quasi-static uniaxial tensile tests were performed on ultrathin nickel-based superalloy sheets with a thickness of 0.2 mm and grain sizes ranging from 27.2 to 79.4 μm. The experimental results demonstrated that the Joule heating effect and the normalized flow stress reduction were non-monotonically related to the grain size of the superalloy. The grain size effect in the polycrystalline superalloy was suppressed by the enhanced current density. A multiscale constitutive model that considered multiple strengthening mechanisms was proposed to describe the EA deformation behavior of ultrathin superalloy sheets. The multiscale model was proven to have a desirable predictive ability for the EA drawing force of thin-walled superalloy capillaries. Furthermore, the model revealed that the weakening of the grain size effect with increasing current density in the polycrystalline superalloy was caused by the combined variations in dislocation interaction, shear modulus, and strengthening mechanisms. The abnormal evolution of the surface effect with the current density was captured by the proposed constitutive model, which demonstrates that the electric current can promote the grain size effect in the multicrystalline superalloy.

Long-term deformation of railway tracks considering train-track interaction and non-linear resilient behaviour of aggregates – a 3D FEM implementation

Railway track designers and maintenance entities have long been pursuing for a robust and reliable method to predict the track’s long-term behaviour. The complexity of this railway system, in terms of its changing structural and material behaviour throughout its life cycle, have hindered that quest. This paper presents a novel computer implementation focused on the estimation of the ballast and sub-ballast long-term deformation that provides a realistic reproduction of the actual behaviour of the structures because (i) it considers the three-dimensional aspect of the problem, (ii) incorporates accurate non-linear resilient material laws for the granular layers, (iii) uses a robust constitutive high-cycle strain accumulation model specifically devised for railway tracks that accounts for the three-dimensional stress conditions to determine both the volumetric and deviatoric permanent deformations and (iv) explicitly considers the dynamic train-track interaction. After calibration and validation with the results from an experimental case study comprising a physical model, a simulation scenario, considering different train types, is presented to demonstrate the potential of this approach. This implementation allows the construction of sufficiently extensive and elaborate representations of the railway track, allowing the study of geometrically complex cases and of the influence of many other aspects on its long-term behaviour.

Insights into the passive mechanical behavior of left ventricular myocardium using a robust constitutive model based on full 3D kinematics

Myocardium possesses a hierarchical structure that results in complex three-dimensional (3D) mechanical behavior, forming a critical component of ventricular function in health and disease. A wide range of constitutive model forms have been proposed for myocardium since the first planar biaxial studies were performed by Demer and Yin (J. Physiol. 339 (1), 1983). While there have been extensive studies since, none have been based on full 3D kinematic data, nor have they utilized optimal experimental design to estimate constitutive parameters, which may limit their predictive capability. Herein we have applied our novel 3D numerical-experimental methodology (Avazmohammadi et al., Biomechanics Model. Mechanobiol. 2018) to explore the applicability of an orthotropic constitutive model for passive ventricular myocardium (Holzapfel and Ogden, Philos. Trans. R. Soc. Lond.: Math. Phys. Eng. Sci. 367, 2009) by integrating 3D optimal loading paths, spatially varying material structure, and inverse modeling techniques. Our findings indicated that the initial model form was not successful in reproducing all optimal loading paths, due to previously unreported coupling behaviors via shearing of myofibers and extracellular collagen fibers in the myocardium. This observation necessitated extension of the constitutive model by adding two additional terms based on the I8(C) pseudo-invariant in the fiber-normal and sheet-normal directions. The modified model accurately reproduced all optimal loading paths and exhibited improved predictive capabilities. These unique results suggest that more complete constitutive models are required to fully capture the full 3D biomechanical response of left ventricular myocardium. The present approach is thus crucial for improved understanding and performance in cardiac modeling in healthy, diseased, and treatment scenarios.

Constitutive Behavior and Deep Drawability of Three Aluminum Alloys Under Different Temperatures and Deformation Speeds

In the present work, uniaxial tensile tests were carried out to evaluate the stress–strain response of AA2014, AA5052 and AA6082 aluminum alloys at four temperatures: 303, 423, 523 and 623 K, and three strain rates: 0.0022, 0.022 and 0.22 s−1. It was found that the Cowper–Symonds model was not a robust constitutive model, and it failed to predict the flow behavior, particularly the thermal softening at higher temperatures. Subsequently, a comparative study was made on the capability of Johnson–Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-ARR) and artificial neural network (ANN) for modeling the constitutive behavior of all the three aluminum alloys under the mentioned strain rates and temperatures. Also, the improvement in formability of the materials was evaluated at an elevated temperature of 623 K in terms of cup height and maximum safe strains by conducting cylindrical cup deep drawing experiments under two different punch speeds of 4 and 400 mm/min. The cup heights increased during warm deep drawing due to thermal softening and increase in failure strains. Also, a small reduction in cup height was observed when the punch speed increased from 4 to 400 mm/min at 623 K. Hence, it was suggested to use high-speed deformation at elevated temperature to reduce both punch load and cycle time during the deep drawing process.

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.

Consistent treatment and automation of the incremental Mori\u2013Tanaka scheme for\xa0elasto-plastic composites

A consistent algorithmic treatment of the incremental Mori–Tanaka (MT) model for elasto-plastic composites is proposed. The aim is to develop a computationally efficient and robust micromechanical constitutive model suitable for large-scale finite-element computations. The resulting overall computational scheme is a doubly-nested iteration-subiteration scheme. The Newton method is used to solve the nonlinear equations at each level involved. Exact linearization is thus performed at each level so that a quadratic convergence rate can be achieved. To this end, the automatic differentiation (AD) technique is used, and the corresponding AD-based formulation is provided. Excellent overall performance of the present MT scheme in three-dimensional finite-element computations is illustrated.

Unified viscoplasticity modeling for isothermal low-cycle fatigue and fatigue-creep stress–strain responses of Haynes 230

• A constitutive model for combustor liner material Haynes 230 is developed. • A broad set of isothermal low-cycle fatigue and fatigue-creep responses are simulated. • Static recovery feature simulated stress relaxation in rate-independent regime. • Simulation of mean stress evolution needs additional modeling feature. • Strain range modeling features are essential to simulate hysteresis loop shapes. A robust cyclic viscoplasticity model is developed for simulating a broad set of isothermal, low-cycle fatigue and fatigue-creep responses of Haynes 230 (HA 230) under uniaxial loading. High temperature components experiencing thermo-mechanical fatigue failures can be designed considering their failure responses such that their fatigue life is predictable. Hence, design of high temperature components in aerospace, automobile, nuclear power, and chemical industries should be based on viscoplastic nonlinear analysis using a robust constitutive model. A unified viscoplasticity model based on the nonlinear kinematic hardening rule of Chaboche with several added features for strain-range dependence, rate-dependence, static recovery, and mean stress evolution is developed and evaluated against a broad set of HA 230 responses. Robustness of the constitutive model is demonstrated against predicting fatigue and dwell period stress relaxation responses under uniaxial strain-controlled loading for a broad temperature range of 25–982 °C and strain rate range of 1.1×10 −2 to 2.6×10 −5 /s. Parameter determination of such an advanced model is discussed showing the importance of a well thought out experimental database and thereby providing physical meaning to model parameters.

Local Mechanical Response of Superelastic NiTi Shape-Memory Alloy Under Uniaxial Loading

In this paper, we focus on the local mechanical response of superelastic NiTi SMA at different temperatures under uniaxial loading. In situ DIC is applied to measure the local strain of the specimen. Based on the experimental results, two types of mechanical response, which are characterized with localized phase transformation and homogenous phase transformation, are identified, respectively. Motivated by residual strain accumulation phenomenon of the superelastic mechanical response, we conduct controlled experiments, and infer that for a given material point, all (or most) of the irreversibility is accumulated when the transformation front is traversing the material point. A robust constitutive model is established to explain the experimental phenomena and we successfully simulate the evolution of local strain that agrees closely with the experimental results.

Multi-axial thermo-mechanical analysis of power plant components from 9–12% Cr steels at high temperature

The aim of this paper is to analyze local changes of stress and strain states in a power plant component under a transient thermal environment. A robust constitutive model is developed to describe inelastic behavior of advanced 9–12% Cr heat-resistant steels at high temperature and in a multi-axial stress state. The model includes the constitutive equation for the inelastic strain rate tensor, the evolution equation for a tensor-valued state variable to reflect hardening/recovery processes and two evolution equations for two scalar-valued variables that characterize softening and damage states. The model is calibrated against experimental creep curves and verified for inelastic responses under different isothermal and non-isothermal loading paths. Steam temperature and loading profiles that correspond to an idealized start-up, holding and shut-down sequence of a power plant component are assumed. To estimate the thermal fields, transient heat transfer analysis is performed. The results are applied in the subsequent structural analysis using the developed inelastic constitutive model. The outcome is a multi-axial thermo-mechanical fatigue loop which can be used for damage assessment.

Numerical implementation of a constitutive model for simulation of hot stamping

In order to increase the accuracy of numerical simulations of the hot stamping process, an accurate and robust constitutive model is crucial. During the process, a hot blank is inserted into a tool where it is continuously formed and cooled. For the steel grades often used for this purpose, the initially austenitized blank will decompose into different product phases depending on the cooling and mechanical history. As a consequence, the phase proportions change will affect both the thermal and mechanical properties of the continuously formed and cooled blank. A thermo-elastic–plastic constitutive model based on the von Mises yield criterion with associated plastic flow is implemented into the LS-Dyna finite element code. Models accounting for the austenite decomposition and transformation induced plasticity are included in the constitutive model.The implemented model results are compared with experimental dilatation results with and without externally applied forces. Further, the calculated isothermal mechanical response during the formation of a new phase is compared with the corresponding experimental response for two different temperatures.