Flow Stress Model Research Articles

Implementation of Fracture and Flow Stress Models for AA5052-H32 Sheet Deformed Through Shock Tube–Based Forming Technique

Abstract Selection of flow stress models and fracture models to model sheet deformation at high strain rates is of great concern. The same is attempted in the present work during shock tube impact forming of 1-mm-thick AA 5052-H32 sheet using a rigid nylon striker. Lab scale experiments and finite element simulations using DEFORM 3D are conducted for the purpose. Johnson–Cook flow stress model and Modified Johnson–Cook flow stress model along with fracture models like normalized Cockcroft and Latham model, Rice and Tracey model, Oyane model, and McClintock model are tested for their accuracy and consistency. The fracture strain and fracture pattern evaluation suggest that the modified Johnson–Cook flow stress model and Rice and Tracey fracture model are suitable for fracture prediction, and it is better to use these together for fracture evaluation. An alternate method of evaluating rate-dependent tensile properties of sheet at higher strain rates is proposed and delivered acceptable fracture prediction results. Finite element simulations using Hollomon power law predict a strain rate of 1925/s at a striker velocity of 49.79 m/s, which is in the range of values in literature for explosive forming. Systematic shock tube forming experiments for calibrating the fracture models are acceptable.

Coupling effect of feature size and δ phase on compressive deformation of a nickel-based superalloy at the mesoscopic scale

Nickel-based superalloys have become essential materials due to their excellent comprehensive properties as the miniaturization of products in the aerospace and energy fields develops. The complex microstructure and various strengthening mechanisms of nickel-based superalloys make the plastic deformation behavior extremely complicated at the mesoscopic scale. In this paper, compression experiments of nickel-based superalloy samples with different feature sizes (i.e. the sample diameter to grain size ratio, D/d) and different aging times at the mesoscopic scale were carried out. The coupling effect of feature size and δ phase on the compressive deformation behavior was studied. The results show that the δ phase plays a role in precipitation strengthening during compressive deformation at the mesoscopic scale. When D/d is in the range of 9.7–10.9, the flow stress decreases significantly with the increase of grain size, and a “smaller is weaker” size effect appears. When D/d is less than 9.7, the flow stress increases with the grain size, and a “smaller is stronger” size effect appears. Considering grain boundary strengthening, solid solution strengthening, and precipitation strengthening, a size effect model of flow stress was established. The calculated values were in good agreement with the experimental values. The inhomogeneity of the end surface and side surface increases with the decrease of feature size and the decrease of aging time. The presence of the δ phase reduces the inhomogeneous deformation of nickel-based superalloys during compressive deformation at the mesoscopic scale.

Development of the Johnson-Cook flow stress and damage parameters for the impact response of polycarbonate: Experimental and numerical approach

The Johnson and Cook (JC) flow stress and damage model parameters of a polycarbonate (PC) plate were determined by the mechanical tests and numerical simulations of the tests. The experimental tests included quasi-static and high strain rate tension and compression, quasi-static notched-specimen tension, quasi-static indentation (QSI), low velocity impact (LVI) and projectile impact (PI). Initially, five different quasi-static flow stress-strain equations were extracted from the experimental and numerical tests. The flow stress equation determined from the experimental average true stress-true strain curve well agreed with the effective stress-strain obtained from the quasi-static numerical tension test. The numerical QSI force-displacement curve based on the experimental average true stress-true strain equation was further shown to be very similar to that of the experiment. The LVI and PI test simulations were then continued with the experimental average true stress-true strain equation using five different flow stress-strain rate relations: JC, Huh and Kang (HK), Allen-Rule and Jones (ARJ), Cowper-Symonds (CS) and the nonlinear rate approach (NLA). The rate sensitivity parameters of these relations were extracted from the quasi-static and high strain rate tests. The LVI test simulations using the stress-strain rate relations exhibited force-displacement curves higher than those of the experiments. The detected almost no strain rate sensitivity in the LVI tests was ascribed to low strain rate dependency of the flow stress at these intermediate strain rates and large strains involved. On the other side, all the stress-strain rate relations investigated nearly predicted the experimental damage types: dishing at 100 and 140 m s−1 and petalling at 160 m s−1, except the CS relation which predicted the fracture of the plate at 140 m s−1. The experimental average projectile exit velocity at 160 m s−1 was further well predicted by the used stress-strain rate relations while the experimental average petal thicknesses were under estimated by the models. The absorbed energy at 160 m s−1 PI test was determined 1.6 times that of the QSI test, which proved an increased energy absorption capability of the tested PC at the investigated impact velocities.

Modified Voce-Type Constitutive Model on Solid Solution State 7050 Aluminum Alloy during Warm Compression Process

The 7050 alloy is a kind of Al-Zn-Mg-Cu alloy that is widely used for aircraft structures. Although the deformation behavior of the solid solution state 7050 aluminum alloy is critical for engineering and manufacturing design, it has received little attention. In this study, the room and warm compression behavior of the solid solution-state 7050 alloy was researched, and a modified model with variable parameters was built for the flow stress and load prediction. The isothermal compression tests of the solid solution-state 7050 alloy were performed under the conditions of a deformation temperature of 333–523 K, a strain rate of 10−3–10−1 s−1, and a total reduction of 50%. The strain-stress curves at different temperatures were corrected by considering interface friction. The flow stress model of aluminum was established using the modified Voce model. For evaluating the modified Voce model’s prediction accuracy, the flow stresses calculated by the model were compared with the experimental values. Consequently, for assessing its prediction abilities in finite element applications, the whole compression process was simulated in the finite element analysis platform. The results sufficiently illustrated that the modified Voce-type model can precisely predict the complex flow behaviors during warm compression. This study will guide the prediction of the warm compression load and the optimization of the heat treatment process of the alloy.

A simulative study on the effect of friction coefficient and angle on failure behaviors of GLARE subjected to low-velocity impact

Abstract The aim of this paper is to study the effect of friction coefficient and impact angle on the failure behaviors of glass fiber reinforced aluminum laminates (GLARE) under the low-velocity impact (LVI) loading. A methodology is developed in commercial software ABAQUS/Explicit, and its accuracy is verified based on the results of comparison between simulation and experiment. In the simulation, Johnson–Cook flow stress model and surface-based cohesive behavior are carried out to simulate the damage evolution of aluminum alloy layers and delamination at the interface. Further, both the dynamic response history and damage mechanism characterization of these hybrid laminates are presented and compared carefully. Additionally, due to the advantage of simulation, it is accurate and easy to discuss on the evolution of the damage contour consisting of the damage degree of composite and metal layers as well as the interface between them. Finally, the influence rules of friction coefficient and angle on the failure behaviors of GLARE under LVI are drawn clearly.

Prediction of corrosion defect critical size and corrosion failure assessment study of SGTs

Alloy 690 is a common material for heat transfer tubes of steam generators (SGTs), and its corrosive properties affect service life. In this paper, a corrosion failure assessment diagram (CFAD) of SGTs is proposed for the first time based on the flow stress model and the "mechanical-electrochemical" (M-E) coupled model, and the critical value of defects for the failure of SGTs is predicted. The results show that the electrochemical reaction at both sides of the corrosion interface transforms from anodic to cathodic with increasing a/t, and the corrosion interface undergoes a transition from elastic deformation to plastic deformation. When a/t > 0.6, the SGTs undergo plastic deformation, the corrosion rate at the corrosion defect becomes more uniform with increasing b/t, and the "M-E" synergistic effect decreases. The critical size of the defect affected by the "M-E" coupling is a/t = 0.676, and the failure mode is transformed from electrochemical to "M-E" coupling failure mode. The anode current density at the corrosion defect was 400 times higher than that at the nondefective site. The "M-E" coupling resulted in a 9.03% increase in defect size for SGT failure. Plastic damage occurs when the depth of cracking under stress reaches 62% of the wall thickness. Corrosion is introduced into the structural integrity assessment of SGTs for the first time, which has a leading role in the prediction of the remaining life of different SGT materials under normal operating/accident conditions.

Practical approach for determining material parameters when predicting grain size after static recrystallization

The static recrystallization (SRX) behavior of 42CrMo steel was investigated by a non-isothermal hot compression test. The conventional empirical equation for SRX was applied to a finite element (FE) simulator using a nonconventional manner of parameter characterization. Parameter characterization was conducted by applying the FE-coupled optimization method to cylinder compression, which is an axisymmetric upsetting process. An accurate and practical flow stress model was used to precisely determine the critical strain value and define the instant when SRX occurred. The results revealed that the microstructural evolution during SRX was substantially influenced by temperature, strain rate, degree of deformation, and initial austenite grain size. The predicted recrystallized SRX grain sizes exhibited good agreement with the measured values when the model's parameters for the calculation of grain size were obtained using a FE-coupled optimization scheme.

Thermomechanical Treatment Performance and Flow Stress Model of a Fe–Mn–Al–C Low‐Density Steel

The flow stress curves of Fe‐31.7Mn‐11.5Al‐0.9C low‐density steel are obtained by a hot‐compression test with a Gleeble‐3500 thermomechanical simulator. It is shown in the results that the dynamic recovery and dynamic recrystallization (DRX) of δ‐ferrite occur preferentially under the same deformation condition, inducing a “yield point‐like” phenomenon in the true stress–strain curves. The Zener–Hollomon parameter is introduced to fit the characteristic parameters used to establish the flow stress model according to Arrhenius hyperbolic sine relationship and Avrami equation, and the DRX activation energy of austenite is 414.12 KJ mol−1. The hot‐processing maps at different true strains are simulated based on the dynamic material model to determine the suitable hot‐rolling process and the optimal hot‐working process selection of high strain rate and high deformation temperature combination, 1100–950 °C/1–0.2 s−1, is recommended.

The influence of natural aging of the AW-2024 aluminum sheet on the course of the strain hardening curve

Aluminum sheet drawpieces pressings with the ability to harden precipitation can be shaped from the sheet after annealing or heat treatment. In the second variant during the analysis and design of the technological proces, the change in the material properties of the shaped sheet due to natural aging should be additionaly taken into account. This article presents the results of research on the effect of the natural aging time after heat treatment of AW-2024 sheet material with a thickness of 1 mm on the course of the strain hardening curve. Strain hardening curves were determined on the basis of a uniaxial tensile test. The sheets were tested immediately after heat treatment and during natural aging, i.e. (20, 45, 90 and 120) minutes after heat treatment. The research showed a significant influence of natural aging in the tested range of times after heat treatment on the course of the deformation hardening curve of the sheet material. Based on experimentally determined in particular directions (0, 45 and 90 degrees to the rolling direction) the strain hardening curves, the values of material coefficients as a function of natural aging time were determined for four models of flow stress. Material coefficients in individual yield stress models were determined on the basis of approximation of strain hardening curves using the least squares method. On the basis of the analysis of approximation errors, the accuracy of the tested models of yield stress to describe the course of the hardening curve of the material of the tested sheet in the tested range of natural aging time was assessed.

Dislocation density and shear texture effects on grinding force during the grinding of maraging steel 3J33

This paper focuses on the change of dislocation density and shear texture generated in plastic deformation, and its effect on the grinding force during the grinding of maraging steel 3J33. The grinding force in a grinding arc is divided into three stages, i.e., rubbing, plowing and chip forming in turn, and each grinding arc is continuous. The large plastic deformation caused by the forming force of cutting has a significant effect on the nearest rubbing force in the next arc area by influencing the microstructure. However, it has little effect on the plowing force away from the cutting area. Therefore, a flow stress model with respect to the influence of dislocation density and texture was established to describe the relationship between the grinding forces of different grinding arcs and modify the total grinding force. The microstructure of the processed materials before and after grinding experiments was compared, and the corresponding shear texture, Taylor factor and dislocation density were analyzed. The analysis of the multi-stage forces composed elastic deformation and plastic deformation of offers a comprehensive understanding of dislocation density and shear texture evolution mechanisms during the grinding process that would be very beneficial for process optimization. At high wheel speed, lower workpiece speed and cutting depth could result in higher rubbing force, thereby achieving better polishing effect and lower surface roughness.

Hot workability characteristics of two A335 P92 steels for power plant application: A comparative study

The article reports on the workability of two P92 steels having a chromium content of 8.29 and 9.48 wt%. Constitutive equations were used to calculate material parameters describing the hot deformation flow stress. Hot deformation tests were conducted using the Gleeble® 3500 thermomechanical facility. Test conditions were: temperature of 850-1000°C and strain rate of 0.1-10s-1 to a strain of 0.5. The flow stress curve results show that dynamic recovery was the only softening mechanism. A comparative study of the two steels revealed that Cr content had a marginal significance on the flow stress behaviour. Constitutive analysis results of the material parameters were: a stress exponent of 9.0 (P92-A), and 11.0 (P92-B), while the activation energy was 369 kJmol-1 (P92-A), and 472 kJmol-1 (P92-B). A brief explanation of the material parameter results is in this article. A flow stress model was developed to predict the flow stress behaviour of the two P92 steels investigated. The results show that the model accurately predicts the flow stress at all the deformation conditions applied. The statistical parameters showed a good correlation between the predicted and the experimental data. Therefore, this model can be used to develop metal forming schedules for industrial applications.

Flow stress modeling of a new HSLA steel by Zerilli-Armstrong model

The selection of an appropriate constitutive model is vital for the design of thermo-mechanical treatment as it describes the flow patterns and governs the metallurgical transformations. In this research, the constitutive behavior of a newly developed high-strength steel has been studied employing a physical-based Zerilli-Armstrong model. For this purpose, the experimentally generated stress–strain data from isothermal compression tests performed over a wide range of temperatures (1073–1323 K) and strain rates (0.01–10 s−1) have been considered. The constitutive relationships of flow stress as functions of temperature, strain rate, and true strain have been developed for both original and modified Zerilli-Armstrong models. The comparison between the measured and predicted flow stresses demonstrates better predictability of the modified model with a higher correlation coefficient (R = 0.982) and a much lower average absolute relative error (AARE = 7.31%) since the values of R and AARE for the original model are 0.845 and 23.96%, respectively. The better accuracy of the modified Zerilli-Armstrong model is attributed to the fact that it additionally considers the coupled effects of temperature and strain, unlike the original Zerilli-Armstrong model.

Finite element analysis of the surface finishing of additively manufactured 316L stainless steel by ball burnishing

As additive manufacturing of metal components is becoming increasingly significant due to high levels of design freedom yet features insufficient surface quality, finishing processes need to be further developed. As an alternative to machining, investigating the ball burnishing of powder bed fusion (PBF) workpieces provides opportunities to advance fundamental research. Studying this method's capabilities, finite element analyses (FEA) were conducted based on a flow stress model parameterized with Split-Hopkinson Pressure Bar (SHPB) tests. The roughness smoothing and a macroscopic approach mapping residual stress distributions was modelled and validated. Improvements in surface integrity were confirmed in both the FEA and experimentally.

Tensile Behavior, Constitutive Model, and Deformation Mechanisms of MarBN Steel at Various Temperatures and Strain Rates.

To reduce harmful gas emission and improve the operational efficiency, advanced ultra-supercritical power plants put forward higher requirements on the high temperature mechanical properties of applied materials. In this paper, the tensile behavior and deformation mechanisms of MarBN steel are discussed at different strain rates (5 × 10-3 s-1, 5 × 10-4 s-1, and 5 × 10-5 s-1) under room temperature and 630 °C. The results show that the tensile behavior of the alloy is dependent on temperature and strain rate, which derived from the balance between the average dislocation velocity and dislocation density. Furthermore, observed dynamic recrystallized grains under severe deformation reveal the existence of dynamic recovery at 630 °C, which increases the elongation compared to room temperature. Finally, three typical constitutive equations are used to quantitatively describe the tensile deformation behavior of MarBN steel under different strain rates and temperatures. Meanwhile, the constitutive model of flow stress for MarBN steel is developed based on the hyperbolic sine law.

Comparative study on high temperature deformation behavior and processing maps of Mg-4Zn-1RE-0.5Zr alloy with and without in-situ sub-micron sized TiB2 reinforcement

Mg-4Zn-1RE-0.5Zr (ZE41) Mg alloy is extensively used in the aerospace and automobile industries. In order to improve the applicability and performance, this alloy was engineered with in-situ TiB 2 reinforcement to form TiB 2 /ZE41 composite. The high temperature deformation behavior and manufacturability of the newly developed TiB 2 /ZE41 composite and the parent ZE41 Mg alloy were studied via establishing constitutive modeling of flow stress, deformation activation energy and processing map over a temperature range of 250 °C - 450 °C and strain rate range of 0.001 s −1 - 10 s −1 . The predicted flow stress behavior of both materials were found to be well consistent with the experimental values. A significant improvement in activation energy was found in TiB 2 /ZE41 composite (171.54 kJ/mol) as compared to the ZE41 alloy (148.15 kJ/mol) due to the dispersed strengthening of in-situ TiB 2 particles. The processing maps were developed via dynamic material modeling. A wider workability domain and higher peak efficiency (45%) were observed in TiB 2 /ZE41 composite as compared to ZE41 alloy (41%). The Dynamic recrystallization is found to be the dominating deformation mechanism for both materials; however, particle stimulated nucleation was found to be an additional mode of deformation in TiB 2 /ZE41 composite. The twinning and stress induced cracks were observed in both the materials at low temperature and high strain rate. A narrow range of instability zone is found in the present TiB 2 /ZE41 composite among the existing published literature on Mg based composites. The detailed microstructural characterization was carried out in both workability and instability domains to establish the governing deformation mechanisms.

Double-machine-learning-based data-driven stochastic flow stress model for aluminium alloys at elevated temperatures

As a widely used metal, aluminium alloys take an important role in many engineering fields. Quantifying the stochastic flow behaviour of aluminium alloys at high temperatures is inevitable for performing the reliability design in structural fire engineering. This work proposes a double-machine-learning (DML) framework for modelling the stochastic flow stress of aluminium alloys at elevated temperatures directly from the dataset. The proposed framework extracts the mean and standard deviation of the flow stress from the dataset and describes them separately by two machine learning (ML) models. The experimental data of the 6061-T651 aluminium alloys is used to validate the DML-based stochastic flow stress model. By comparison between four popular ML models, the artificial neural network (ANN) model and the Gaussian process regression (GPR) model are the most appropriate choices for predicting the mean and the standard deviation, respectively, in the DML framework. The stochastic distribution of the flow stress estimated by the DML framework, which consists of the ANN model and GPR model, is in high agreement with the experimental results. The good agreement between predictions and experimental results demonstrates that the DML framework can accurately describe the stochastic flow stress of aluminium alloys at elevated temperatures and can be used in the reliability design processes of aluminium structures. • Double-machine-learning (DML) framework is proposed for stochastic flow stress at elevated temperatures • Established stochastic flow stress model is validated by experimental data of aluminium alloys • DML framework with ANN and GPR model is the most suitable choice for aluminium alloys • Probability distribution of aluminium alloys’ flow stress is accurately reproduced by DML framework

Analytical modeling of residual stresses in laser-assisted milling AerMet100 steel

Laser-assisted milling (LAM) is generally regarded as a promising method for machining hard-to-cut materials. The residual stress generated in LAM has a significant influence on the fatigue life, accuracy stability, and corrosion resistance of parts. An analytical model is presented in this paper to predict the residual stress distribution induced in the LAM process. The material softening behavior caused by laser heating and its effect on the distributed loads and mechanical stresses are considered. To achieve this, a flow stress model considering the comprehensive impacts of laser heating and plastic deformation is adopted. A series of LAM experiments are performed to verify the residual stress model. Reasonable agreement between the predicted and measured results indicates the proposed model is feasible. The effect of feed rate and radial cutting depth on surface residual stresses is then discussed theoretically. A moderate feed rate (about 100 mm/min) is recommended to obtain higher surface compressive residual stresses. The findings can be further used in process parameter optimization to improve the surface integrity and processing efficiency of LAM.

Research on the Relation between Slump Flow and Yield Stress of Ultra-High Performance Concrete Mixtures.

The relation between slump flow and yield stress of ultra-high performance concrete (UHPC) mixtures was studied with theoretical analysis and experimentation. The relational expression between slump flow and yield stress of UHPC mixtures was built and then verified with a rheological test. The results showed that the prediction model, as a function of cone geometry of dimensionless slump flow and dimensionless yield stress of the UHPC mixtures, was constructed based on Tresca criteria, considering the geometric relation of morphological characterization parameters before and after slump of the UHPC mixtures. The rationality and applicability of the dimensionless prediction model was verified with a rheological test and a slump test of UHPC mixtures with different dosages of polycarboxylate superplasticizer. With increase in polycarboxylate superplasticizer dosage, yield stress of the two series of UHPC mixtures (large/small binding material consumption) gradually decreased, leading to a gradual increase in slump flow. Based on the prediction model of dimensionless slump flow and dimensionless yield stress, the relational expression between slump flow and yield stress of the UHPC mixtures was built. The comparison result showed that the calculated data was consistent with the experimental data, which provided a new method for predicting yield stress of UHPC mixtures with a slump test.

Deformation and recrystallization behavior of the new Ni-Co based superalloy ingot material prepared by electron beam smelting layered solidification

The hot deformation behavior of a Ni-Co based superalloy prepared by electron beam smelting layered solidification (EBSL-Ni-Co superalloy) was studied by hot compression tests under the temperature range of 1070–1180 °C and the strain rate range of 0.001–1 s−1 with a true strain of 0.693. The results show that the flow stress increases with the increase of strain rate and the decrease of deformation temperature, and the friction effect and adiabatic heating effect make the measured value of material flow stress higher than the real value. The hyperbolic sine Arrhenius equation was developed based on the γ' phase solution temperature, and the plastic flow stress model of the EBSL-Ni-Co superalloy was established. The deformation activation energies of the alloy in the γ + γ′ dual-phase and γ single-phase regions were 621.6 kJ/mol and 368.6 kJ/mol, respectively. The processing map of the superalloy was constructed based on the dynamic material model (DMM). Combined with the variation of microstructure, the optimum hot deformation processing conditions of the superalloy were determined. The increase of strain rate and the decrease of deformation temperature, the proportion of low-angle grain boundaries (LAGBs), and the reduction of recrystallization. Additionally, the hot deformation behavior of the EBSL-Ni-Co superalloy was found to be greatly influenced by the coarsening of γ' phase solution temperature.

The Influence of Natural Aging of the AlCu4Mg1 Aluminum Sheet Alloy on the Constitutive Parameters of Selected Models of Flow Stress

The Influence of Natural Aging of the AlCu4Mg1 Aluminum Sheet Alloy on the Constitutive Parameters of Selected Models of Flow Stress