Hardening Model Research Articles

Thermal-structural analysis for reusable thrust chamber using temperature-dependent CuZr alloy model adapted to cryogenic to elevated temperature

The inner liners of reusable regeneratively-cooled thrust chambers endure significant thermal and mechanical loads, resulting in doghouse deformation and even cracks during cyclic operations. To correctly reveal the failure mechanism of the thrust chamber inner liner, this study investigates the material properties for CuZr alloy and develops a temperature-dependent material model spanning from cryogenic to elevated temperatures. Firstly, we experimentally obtain the thermal and mechanical properties of the material in the temperature range from 77 K to 900 K. The experimental data reveal that the material properties vary considerably with temperature. Then, to precisely characterize the mechanical behavior of CuZr alloy under cyclic loading across a wide temperature range, a material model that combines Voce nonlinear isotropic hardening model with Chaboche nonlinear kinematic hardening model is proposed, and temperature-dependent parameters of this model are calibrated and verified. Finally, the developed material model is applied to perform the thermal-structural analysis on a reusable thrust chamber, with the aim of investigating its failure mechanism. The results demonstrate the capability of the developed model to accurately replicate the doghouse deformation of the inner liner and quantitatively capture the ratcheting effect.

Creep Behavior of the Clay Cores at the Bougdoura Dam Using Ansys Software

Abstract The creep of fine soils is due to the viscous properties of the assembly of mineral particles accompanied of adsorbed water which forms intergranular skeleton. It is evident during the secondary consolidation that the effective stresses are constant, the deformation extends over time. Rock fill dams with clay sealing cores deformed during exploitation. During commissioning of the core, clay undergoes. Creep is a major characteristic of the nonlinear behaviour of materials, in which the material continues to become deformed under a constant load. It can cause considerable deformations of the works (two to three times instantaneous strain in three years). This study presents a prediction of the creep behavior of a clay core in a rock dam subjected to constant hydrostatic loading for 20000 h and describes a procedure for modeling the primary and secondary creep law simulation using ANSYS software APDL In this aims, we have applied the finite element method based on a model shown in equation 8 called (Strain Hardening Model) in order to simulate a creep behavior of clay core.

Numerical Simulation of the Effect of Fusion Welding Processes on Residual Stress in Stainless Steel Pipe Weld Joints Used in Fast Reactors

The main structural material used in the building of Fast Breeder Reactors (FBR) is stainless steel of type 316L(N). Finite Element Model (FEM)-based simulations were carried out to understand the effect of various welding processes on the residual stresses induced in 316L(N) stainless steel primary sodium-carrying pipes with an inner diameter of 208 mm and a wall thickness of 5.6 mm. The welding processes considered include multi-pass Tungsten Inert Gas (TIG) welding, A-TIG, laser, hybrid laser-TIG, and Hybrid laser-Metal Inert Gas (MIG). First, single or hybrid heat sources are chosen based on the welding process, and then weld bead profiles obtained during simulation are made to match with that of the actual weld bead profiles obtained during experiments. Then, the optimised heat source is employed for the thermal analysis. The thermal analysis output is then successively linked and provided as input to the mechanical analysis, which uses an isotropic hardening model to predict hoop and axial residual stresses in pipe weld joints. The results show that the A-TIG weld joint exhibited lower hoop stress (165 MPa at inner diameter and -2 MPa at outer diameter) in comparison with that of the other weld joints. The lower residual stress is attributed due to the straight-sided weld bead, lower peak temperature, and slower cooling rate of the A-TIG welding. Therefore, A-TIG welding is recommended among the chosen fusion welding processes for welding of 316L(N) stainless steel primary sodium carrying pipes to minimise the residual stresses and mitigate the premature failure of the pipe weld joints.

Verification of Classical Models of Hardening by the Method of Molecular Dynamics in the Case of Magnesium Deformation by Compression

Verification of Classical Models of Hardening by the Method of Molecular Dynamics in the Case of Magnesium Deformation by Compression

Hardening Behavior and Model of a 316L Sheet Considering Macro and Micro Size Effects

316L stainless steel is often used as the metal bipolar plate, which is a key component of fuel cells. For the thinner metal bipolar plates, the mechanical properties may be different for different specimen sizes. In this paper, the mechanical properties, metallographic structure, and hardening behavior of 316L stainless steel sheets with different grain sizes and specimen thickness were studied. Several mathematical models were selected to describe the hardening behavior of 316L stainless steel sheet. A correlated hardening model of 316L stainless steel was established, considering the specimen and grain size effect. The results show that the specimen thickness has no effect on the microstructure and grain size, but the austenite grain size increases gradually with an increase in holding time. With a decrease in plate thickness and an increase in grain size, the strength decreases. Compared to the 0.1 mm sheet, the yield strength and tensile strength for the 0.9 mm sheet are increased by 48% and 24%, respectively. The yield strength and tensile strength are decreased by nearly half after 20 min heat treatment due to the grain size growth. The thicker the sample and higher the grain size is, the higher the hardening rate is. The predicted stress–strain by established correlated hardening model has a good agreement with the experiment curves.

Elastic-viscoplastic model for coarse-grained soil considering particle breakage

This paper presents a novel elastic-viscoplastic constitutive model for reproducing the time-dependent behaviour of coarse-grained soil considering particle breakage, by integrating the Unified Hardening (UH) model, the elastic-viscoplastic (EVP) model and the overstress theory. The relationship between the degree of particle breakage and the loading rate is established, and the state variables associated with the critical state of coarse-grained soil are derived to jointly consider both time and particle breakage. A new three-dimensional elastic-viscoplastic constitutive model is then constructed through combining the one-dimensional viscoplastic hardening parameter with a secondary consolidation coefficient considering particle breakage. The proposed model requires 19 parameters and it can well describe the influence of time-dependency and particle breakage to the shear, dilatancy, and compression behaviours of coarse-grained soil with various confining pressures or initial void ratios. Comparisons between the model predictions and experimental data are employed to validate the capability of the proposed model to replicate the time-dependent behaviour of coarse-grained soil.

Temperature-dependent behavior of CP-Ti interpreted via self-consistent crystal plasticity simulation

A commercially-pure titanium sample was investigated using an elasto-visco-plastic self-consistent polycrystal model. Temperature-dependent plastic deformation behavior was described by a dislocation density-based hardening model. The model reasonably reproduced various experimental behaviors, including stress vs. strain curves, diffraction lattice strains, twin volume fraction, and crystallographic texture. The temperature-dependent behavior was interpreted based on the dislocation evolution rules comprised of dislocation generation and recombination in accordance with the Kocks-Mecking rule. The modeling results successfully provided an in-depth interpretation of mechanical behavior of α-titanium under a wide range of temperatures.

Modelling of shakedown, ratcheting and liquefaction of saturated granular soils using kinematic hardening with memory surface

The present paper proposes a kinematic hardening model with a memory surface to more accurately reproduce cyclic hardening and the behaviour of saturated granular soils subjected to cyclic loads. The new cyclic hardening law offers improved accuracy in predicting soil ratcheting in drained conditions and failures due to liquefaction in undrained conditions. Simulating these two aspects has been challenging due to issues such as significant loss of accuracy and numerical instability, particularly under extended (or a large number of) cyclic loads. To deal with the challenge, in addition to the novel theoretical framework, we also developed a robust sub-stepping algorithm based on an explicit stress integration scheme with automatic error control. The proposed model is compared with several existing models and its performance is evaluated by conducting sensitivity analyses and performing validations against a wide range of laboratory test results.

The Effect of Viscous Drag on the Maximum Residual Stresses Achievable in High-Yield-Strength Materials in Laser Shock Processing.

In this paper, the experimentally observed significant increase in yield stress for strain rates beyond 104 s-1 (viscous regime) is explicitly considered in laser shock processing (LSP) simulations. First, a detailed review of the most common high-strain-rate deformation models is presented, highlighting the expected strain rates in materials subject to LSP for a wide range of treatment conditions. Second, the abrupt yield stress increase presented beyond 104 s-1 is explicitly considered in the material model of a titanium alloy subject to LSP. A combined numerical-analytical approach is used to predict the time evolution of the plastic strain. Finally, extended areas are irradiated covering a squared area of 25 × 25 mm2 for numerical-experimental validation. The in-depth experimental residual stress profiles are obtained by means of the hole drilling method. Near-surface-temperature gradients are explicitly considered in simulations. In summary, the conventionally accepted strain rate range in LSP (106-107 s-1) is challenged in this paper. Results show that the conventional high-strain-rate hardening models widely used in LSP simulations (i.e., Johnson Cook model) clearly overestimate the induced compressive residual stresses. Additionally, pressure decay, whose importance is usually neglected, has been found to play a significant role in the total plastic strain achieved by LSP treatments.

Research on the constitutive relation of different material zones of weathering steel Q355GNHB

To research the mechanical properties and low cycle fatigue performance of Q355B structural steel and Q355GNHB weathering steel, this study performs monotonic and cyclic tests on the base metal, welded metal and heat-affected zone (HAZ) of Q355GNHB welded connections and Q355B. The monotone and cyclic constitutive model parameters are calibrated using the true stress-strain relationship and the Chaboche hybrid strengthening model, and their accuracy is verified by ABAQUS. To streamline the calibration process, a simplified calibration method is established for the Chaboche combined hardening model. Compared to the traditional calibration method, the proposed method uses the stress-strain data obtained from the monotonic tests. The applicability of the calibrated model is verified by simulating the tests via ABAQUS. The research results show that both Q355B structural steel and Q355GNHB weathering steel have excellent bearing capacity and plastic deformation capacity. The Q355GNHB weathering steel has better ductility, while the Q355B structural steel has higher bearing capacity and stronger strength reserve capacity. The strength of Q355GNHB varies according to different zones: the yield strength of the base metal material is the lowest, while the tensile strength and the plastic deformation capacity of the welded metal material is the lowest. Besides, the Chaboche combined hardening model and simplified combined hardening model can capture the cyclic fatigue performance of Q355B and Q355GNHB steel. The research results provide effective data support for the in-depth study of the constitutive relations and mechanical properties of weathering steel materials and the accurate simulation of the properties of weathering steel structures.

Constitutive Model-Based Efficient Creep-Fatigue Damage Computation Technique for Steam Turbine Rotors to Enhance Flexible Operational Capabilities

Abstract In the new era of renewable energy, flexible operation of conventional power plants is inevitable, causing high creep-fatigue life consumption. Conventional life assessment methods are deemed to be conservative to address the current requirements. The use of unified constitutive models for the analysis of damage evolution in steam turbine rotors in the past decade has shown promising results and is closely related to experimental data. However, identification of large number of material constants and high computational time hinder the widespread use of such models. In this paper, the latter is addressed using a novel representative input cycle (RIC) concept together with the noniterative asymptotic numerical method (ANM). Various startup shutdown sequences of a typical steam turbine rotor are studied using a unified constitutive model based on Chaboche's kinematic hardening including the damage parameter, Chaboche–Rousselier's isotropic hardening model including the damage parameter, Norton's viscoplastic flow model, Lemaitre's damage potential function and Kachanov–Rabotnov's creep damage law. First, a conventional finite element method (FEM) technique is used and then the proposed RIC method is used to study the evolution of inelastic variables. The reduction in computational time and the compromise in accuracy using the proposed method are studied.

Machining hardening and dislocation modeling of magnesium alloys based on Fields-Backofen equation

Abstract Magnesium alloys are now widely used, and the Fields-Backofen equation is combined with an investigation of the properties of common magnesium alloys in order to be able to better analyze them. In this paper, some properties, applications and superiority of magnesium alloys are first analyzed, in which the plastic deformation mechanism slip and twinning of magnesium alloys are particularly explored in detail. Focusing on the stages and model of machining hardening dislocations of magnesium alloy, and combined with Fields-Backofen equation, a model of machining hardening and dislocations of magnesium alloy based on Fields-Backofen optimization is constructed. Then the constructed model was applied to stage III of machining hardening dislocations in magnesium alloy for performance testing. The predicted and actual maximum values of the model were 132MPa and 30MPa, which were in basic agreement with 130MPa and 32MPa. The saturation stresses ranged from 50 MPa to 6 MPa for temperatures from 100°C to 500°C when the strain rate of the dislocation processing stage was 10−2 s−1, and from 55 MPa to 10 MPa for temperatures from 100°C to 500°C at a strain rate of 10−3 s −1. Finally, only basal slip and twin initiation with higher saturation stresses were obtained at lower temperatures. As the temperature continues to increase, the dislocation density decreases, plastic deformation becomes easier, and then the saturation stress decreases.

Using XFEM technique to predict the crack growth in the notched plate under high loading cyclic conditions

Our study delves into analyzing fatigue damage in notched structures, an essential field in structural mechanics. We aim to understand how geometric and dimensional variations in the notches affect fatigue damage under different modes and amplitudes of cyclic loading, focussing on the behavior of steel. Our research methodology integrates experimental and numerical approaches. Experimental validation encompasses material properties, mesh selection, and boundary conditions. The finite element method is tailored to address steel’s elastoplastic behavior, employing calibrated parameters for kinematic and isotropic cyclic hardening models within the numerical realm. Specific findings elucidate the cyclic response of notched structures, tracking damage progression to critical thresholds, including the number of cycles to failure (Nf) and the critical crack length ( Lc ). Hysteresis curves vividly depict stress–strain relationships, offering insight into material behavior under cyclic loading. Implications span engineering domains, focussing on reliability and durability in the aerospace, automotive, and civil engineering sectors. Future directions include real-world applications and advanced techniques such as the Extended Finite Element Method (XFEM). In conclusion, this research enriches our understanding of fatigue damage analysis in notched structures, poised to impact safety and robust engineering design.

Constitutive Modeling of Annealed OFHC with Wide Strain-Rate and Temperature Effects: Incorporating Dislocation Dynamics and Normalized Microstructural Size Evolution.

The flow stress of face-centered cubic (FCC) metals exhibits a rapid increase near a strain rate of 104 s-1 under fixed-strain conditions. However, many existing constitutive models either fail to capture the mechanical characteristics of this plastic deformation or use piecewise strain-rate hardening models to describe this phenomenon. Unfortunately, these piecewise models may suffer from issues such as discontinuity of physical quantities and difficulties in determining segment markers, and struggle to reflect the underlying physical mechanisms that give rise to this mutation phenomenon. In light of this, this paper proposes that the abrupt change in flow stress sensitivity to strain rate in FCC metals can be attributed to microstructural evolution characteristics. To address this, a continuous semiempirical physical constitutive model for FCC metals is established based on the microstructural size evolution proposed by Molinari and Ravichandran and the dislocation motion slip mechanism. This model effectively describes the mutation behavior of strain-rate sensitivity under fixed strain, particularly evident in an annealed OFHC. The predicted results of the model across a wide range of strain rates (10-4-106 s-1) and temperatures (77-1096 K) demonstrate relative errors generally within ±10% of the experimental values. Furthermore, the model is compared with five other models, including the mechanical threshold stress (MTS), Nemat-Nasser-Li (NNL), Preston-Tonks-Wallace (PTW), Johnson-Cook (JC), and Molinari-Ravichandran (MR) models. A comprehensive illustration of errors reveals that the proposed model outperforms the other five models in describing the plastic deformation behavior of OFHC. The error results offer valuable insights for selecting appropriate models for engineering applications and provide significant contributions to the field.

Combined rate-temperature effects in postnecking plasticity of A2-70 stainless steel

In this paper, a comprehensive study that integrates theoretical, experimental and FE analyses, elucidates the combined effect of strain, strain rate, and temperature on the mechanical response of A2-70 stainless steel. A wide series of tensile experiments on cylindrical specimens is presented, including low to high temperatures and quasi-static to dynamic rates. Opportune combinations of temperatures and strain rates are imposed in order to possibly separate and identify their respective effects on the flow curve of the material. The adopted experimental procedures based on neck-related measurements revealed the onset of secondary phenomena affecting dynamic tensile tests. Classical material models were found not suitable to correctly predict the complex elastoplastic deformation of this material. Thus, a new general material model is presented and used to account for the complex interplay between strain, temperature, and rate-dependent effects. Finite element simulations are conducted using both the proposed constitutive model and another classical model of dynamic hardening, to investigate and compare their predictive capability over the entire experimental campaign.

Mechanical Characterization of Fatigue and Cyclic Plasticity of 304L Stainless Steel at Elevated Temperature

BackgroundThe mechanical characterization of the cyclic elastoplastic response of structural materials at elevated temperatures is crucial for understanding and predicting the fatigue life of components in nuclear reactors.ObjectiveIn this study, a comprehensive mechanical characterization of 304L stainless steel has been performed including metallography, tensile tests, fatigue tests, fatigue crack growth tests and cyclic stress-strain tests.MethodsIsothermal tests were conducted at both room temperature and 300 °C for both the rolling direction and the transverse direction of the hot rolled steel. Mechanical properties were extracted from the uniaxial experiments by fitting relevant material models to the data. The cyclic plasticity behavior has been modelled with a radial return-mapping algorithm that utilizes the Voce nonlinear isotropic hardening model in combination with the Armstrong-Frederick nonlinear kinematic hardening model. The plasticity models are available in commercial FE software and accurately capture the stabilized hysteresis loops, including a substantial Bauschinger effect.ResultsThe material exhibits near isotropic properties, but its mechanical performance is generally reduced at high temperatures. Specifically, in the rolling direction, the Young’s modulus is reduced by 16 % at 300 °C, the yield strength at 0.2 % plastic strain is lower by 23 %, and the ultimate tensile strength is lower by 30 % compared to room temperature. Fatigue life is also decreased, leading to an accelerated fatigue crack growth rate compared to room temperature. A von Mises radial return mapping algorithm proves to be effective in accurately modelling the cyclic plasticity of the material. The algorithm has also been used to establish a clear correlation between energy dissipation per cycle and cycles to failure, leading to the proposal of an energy-based fatigue life prediction model.ConclusionsThe material exhibits reduced mechanical performance at elevated temperatures, with decreased monotonic strength, compared to room temperature. Fatigue life is also compromised, resulting in accelerated fatigue crack growth. The material’s hardening behavior differs at room temperature and elevated temperature, with lower peak stress values observed at higher temperatures. The radial return mapping algorithm can be used to determine the dissipated energy per cycle which together with fatigue testing has been used to propose a low cycle fatigue life prediction model at both temperatures.

Formability prediction of high‐strength steel sheet using experimental, analytical and theoretical analysis based on strain and stress forming limit curves and its application to automotive forming parts

AbstractIn this work, the high‐strength steel (HSS) sheet dual‐phase 440 (DP440) were conducted to establish the forming limit curve (FLC) and analytical forming limit stress curve (FLSC) obtained from experimental forming limit curve. First, the Nakajima stretch forming examination was carried out to obtain forming limit curve of investigated sheet. Afterwards, the theoretical Marciniak–Kuczinsky (M–K) model was developed and calculated to evaluate localized necking limits both in strain and stress spaces combination with anisotropic yield criteria. Then, the analytical forming limit stress curves were plastically calculated by using experimental forming limit curve data combination with Swift hardening model and anisotropic yield criteria namely, Hill’48 and Yld2000‐2d for representing anisotropic plastic deformation behavior on examined steel sheet. Finally, automotive stamping parts were performed in order to verify an applicability of all developed curves. It was observed that the analytical forming limit stress curves could more precisely predict the formability of automotive parts better than the forming limit curve based on strain. Particularly, the one based on Yld2000‐2d predict better than the one based on Hill’48. Simultaneously, the experimental forming limit curve and analytical forming limit stress curve were also evaluated comparing with the theoretical calculated forming limit curve and forming limit stress curve using the Marciniak–Kuczinsky model. It should be noted again that the experimental forming limit curve and analytical forming limit stress curve are the best one. Therefore, the Yld2000‐2d yield function better represented the anisotropic behavior of the high‐strength steel sheet dual‐phase 440 than Hill′ 48 yield function, and can suitable be used for the analysis prediction and design of bumper automotive parts under forming processes.

Design and industrial implementation of a multi-functional part produced by powder bed fusion

The use of robot end-effectors programmed to perform handling tasks in industrial environments has expanded in several sectors as a consequence of the rapid digital transformation seen in recent years. With such growing demands, additive manufacturing is evolving in the robotics field with more efficient, innovative, and customer-specific solutions owing to its design flexibility. Thus, this work presents a robot end-effector developed and produced by powder bed fusion (PBF) to execute palletizing operations in the automotive electronics industry, where electrostatic discharge interference is a critical concern. To guarantee the functionality of the developed robot end-effector under real conditions of implementation, prototypes of polyamide 12 (PA12) and PA12 incorporating graphene nanoplatelets were fabricated and characterized. This included the assessment of the mass, electrical surface resistance, and mechanical properties under tensile and compressive loads using biaxial strain gauges coupled to the prototypes for local strain monitoring. The experimental data were then used to define multilinear isotropic hardening models needed to numerically characterize the robotic system. At last, the final product was validated in an industrial environment at Bosch Car Multimedia S.A. Through the applied methodology, valuable insights in guiding process parameters optimization and materials selection for functional PBF parts depending on the technical requirements demanded by industrials are provided.

Monotonic and Cyclic Modelling of Structural Steel for Finite Element Analysis

Nowadays, as a response to the promoted concept of performance-based seismic design, the finite element method (FEM) has become an omnipresent practice that supports the simulation of structural elements. This approach requires constitutive numerical models, which could reproduce both elastic and plastic behaviour of steel. Looking forward to a reliable FEM simulation, the modelling and calibration of steel undergoing monotonic and cyclic loading tests is investigated in this paper. With respect to monotonic tensile test, a sensitivity analysis regarding mesh refinement and finite element type is developed. Another inspected issue, such as high-strength steel modelling, taking into consideration low ductility and absence of yield plateau, is also presented. And finally, a model for structural steel, using the combined isotropic-kinematic hardening model, is introduced to simulate metal non-linear behaviour under ultra-low-cycle fatigue regime. All these numerical simulations are processed via Abaqus software package, and are validated by a set of experimental tests.

Fatigue crack initiation life prediction using different plasticity models in cold expanded AL-alloy plates utilized in double shear lap joints

Cold expansion of fastener holes is a recognized technique for enhancing the fatigue life of holed plates utilized in detachable joints. This method involves introducing compressive residual stress around the holes, which has proven to be effective in improving the structural integrity and longevity of such components. In this research, the role of using different plasticity models in finite-element simulations of cold expansion (CE) in determining residual stress distribution and predicting the fatigue life of lap joints was investigated. Finite-element simulations were conducted to analyze the distribution of residual stress in cold-expanded Al-alloy 2024-T3 plates utilized in double-shear lap joints. Three time-independent plasticity models, specifically multilinear kinematic hardening, multilinear isotropic hardening (M.L.I.H) based on monotonic tensile tests, and nonlinear combined hardening models derived from saturated hysteresis stress and strain loops, were employed in the simulations. These models allowed for an accurate determination of the residual stress distribution in the plates. In finite-element simulations, two CE sizes of 1.5% and 4.7% were employed to create residual stresses. In the simulations, after creating residual stress by CE, remote sinusoidal loads are applied to the joints corresponding to the previously conducted fatigue tests in order to obtain stress and mechanical strain distributions. In order to predict the fatigue life, four different multiaxial fatigue criteria (Smith–Watson–Topper, Glinka, Kandil–Brown–Miller, and Fatemi–Socie) were employed, using the stress and strain distributions obtained from the finite element simulations with the different plasticity models. The simulations yielded varying stress and strain distribution results for the multilinear kinematic and M.L.I.H models, while the results of the nonlinear combined hardening model fell between the other two models. Notably, the fatigue life prediction based on the nonlinear combined hardening plasticity model closely matched the experimentally observed fatigue lives, with an absolute percentage deviation of 24.8%.