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A physics-based constitutive model for machining simulation of Ti-6Al-4V titanium alloy

Today, simulation of cutting processes still relies, in most cases, on the phenomenological representation of flow stress properties of workpiece materials. This investigation presents a physics-based (dislocation-based) constitutive model to simulate the flow stress properties of Ti6Al4V titanium alloy at elevated temperatures and a large range of strain rates. The Split Hopkinson Pressure Bar (SHPB) data and inverse modelling of orthogonal cutting tests are combined using a novel approach to obtain flow stress properties and to calibrate the damage and friction models. The applicability of the presented model for cutting simulation is critically discussed.

Neural network modeling of the flow stress of the AlMg6/10% SiC metal matrix composite under deformation at high temperatures

A neural network is constructed to describe flow stress curves for the AlMg6/10% SiC metal matrix composite (MMC) at temperatures ranging from 300 to 500 °С and strain rates ranging from 0.1 to 5 s−1. The metal matrix composite was produced by powder metallurgy technologies from the AlMg6 alloy (the 1560 aluminum alloy according to GOST 4784-97) with the addition of 10% SiC powder having a fraction of F1500. The obtained flow stress curves of the AlMg6/10% SiC MMC in the studied temperature–rate range have several sections (stages). At the first stage, the material hardens, then it softens, and a peak of deformation stress appears on the flow stress curve. After the softening stage, a steady section begins, at which the hardening and softening rates almost coincide. This is expressed in the constancy of the flow stress value with an increase in strain. The obtained flow stress curves are described by a neural network. The study shows that the constructed neural network can predict with acceptable engineering accuracy the behavior of flow stress curves for temperatures and strain rates that are not used in its training.

Stepwise modelling method for post necking characterisation of anisotropic sheet metal

Modelling and simulation are important tools during design and development processes. For accurate predictions of, e.g. manufacturing processes or final product performance, reliable material data is needed. Usually, the applied material models are calibrated by utilising direct methods such as conventional uniaxial tensile/compression tests but also inverse methods are occasionally applied. Recently, an effective inverse method, the stepwise modelling method (SMM), was presented. By using SMM, the flow stress from initial yielding, beyond necking to final fracture, can be determined. However, the method is developed for sheet materials having isotropic von Mises hardening. In this paper the SMM is extended for post necking characterisation of anisotropic sheet metals using the Barlat yield 2000 criterion. The novel method was applied to analyse the post necking plasticity of the widely used aluminium alloy AA6016 in T4 condition and the aluminium alloy AA5754 in H111 condition. The latter alloy has reported to show serrated yielding, also known as the Portevin–Le Chatelier effect. The obtained flow stress curves agree well with the curves form conventional uniaxial tensile tests up to the point of necking and show credible post necking predictions to final fracture. Furthermore, SMM showed that it could handle the effect of serrated yielding for AA5754-H111. Hence, the novel approach can be used to characterise the post necking hardening of a variety of anisotropic sheet metals and thereby contributes to efficient and reliable material model calibration.

Hot Deformation Behaviors in Ti-6Al-4V/(TiB + TiC) Composites

Thermal compression testing was investigated using the Gleeble 3800 thermal simulator, and thermal deformation behavior of particle-reinforced titanium matrix composites (TMCs) was studied under deformation temperatures of 750–900 °C, strain rates of 0.001–1 s−1, and experimental deformation of 60%. According to obtained flow stress curves, the hot deformation characteristics were analyzed. Based on the Arrhenius hyperbolic sinusoidal model, the constitutive equation at high temperature was established. Based on the theory of dynamic material models, a hot processing map of TMCs at high temperature was established, and the peak region of power dissipation rate and the instability region in the hot processing map were both determined. At the same time, the corresponding microstructures in the peak power dissipation rate and rheological instability regions were observed. The results showed that flow stress decreased with increasing deformation temperature and increased with increasing strain rate. The thermal deformation activation energy of titanium matrix composites was 301.8 kJ/mol. The Ti-6Al-4V/(TiB + TiC) composites possessed only one instability zone under high-temperature compression at a strain of 0.5, with corresponding temperatures at 750–840 °C and strain rates at 0.1–1 s−1. The optimal thermal deformation parameters included corresponding temperatures of 830–880 °C and strain rates of 0.001–0.05 s−1. The microstructures corresponding to optimal hot working parameters in processing maps were more homogeneous than the microstructures in the instability zone, including the distribution uniformity of reinforcement and the degree of dynamic recrystallization, and no instability phenomena including abnormal grain growth, microcracks or intensive fracture of reinforcements were found, indicating that the hot processing map had a positive guiding effect on the option of desirable material thermal-working parameters.

Flow characterization of magnesium alloy ZK61 during hot deformation with improved constitutive equations and using activation energy maps

The present study aimed at characterizing the flow characteristics and workability of an as-extruded magnesium alloy ZK61 by isothermal compression tests performed at temperatures of 523–673 K and strain rates of 0.001–1s−1. The flow stress curves were analysed via considering the mechanism of microstructure evolution. Using the obtained flow stress data, both of the conventional and improved Arrhenius constitutive equations were developed to predict the flow characteristics, and the 3D activation energy maps were constructed to propose the optimal deformation conditions and reveal the effects of deformation parameters on microstructure evolution. It can be found that the strain factor plays an important role in determining the shapes of the flow stress curves, which exhibit three types of variation tendencies due to the flow softening and hardening behaviour as the strain increases. The improved constitutive equations resulted in excellent predictability of the peak flow stress within all the deformation conditions. Combining with the activation energy maps, the dominant deformation mechanisms, i.e., dynamic recrystallization and flow localization in different deformation regions were identified, and the optimal processing window of the alloy can be obtained at strain rate and temperature range of 0.001–0.01s−1 and 623 ~ 673 K under a strain of 0.9.

Rheological behavior and dynamic softening mechanism of AA7075 sheet under isothermal tensile deformation

Rheological behavior and dynamic softening mechanism of high-strength AA7075 sheet were investigated by performing isothermal uniaxial tensile tests at deformation temperatures of 573−723 K and strain rates of 0.01–10 s−1. On the basis of the obtained flow stress, response surface models for the ultimate tensile stress (UTS) and fracture strain were developed as a function of temperature and strain rate, respectively. Error analysis certified the reliability of the models. Besides, a constitutive model coupling with dislocation evolution was built to predict the deformation behavior of the alloy, and the dislocation evolution law was revealed based on the established constitutive model. In addition, the dynamic softening mechanism of the alloy during hot deformation was exposed according to the Zener-Hollomon parameter map, microstructural observation and apparent activation energy. Owing to precipitates pinning effect on the motion of dislocation and migration of subgrain boundaries, the dominant softening mechanism is concluded to be dynamic recovery (DRV), relating to cross-slip of screw dislocation.

New Phenomenological Model to Predict High-Temperature Flow Stress Curves at High Strain Rates

Abstract In this study, a new phenomenological equation has been presented to predict high-temperature flow stress curves of metallic materials at industrially relevant deformation conditions with negligible flow softening. To this end, a nonlinear estimation of strain-hardening rate versus strain curves was employed to obtain flow stress as a function of strain. To prove the validity and competency of the presented model, flow stress curves of Alloy 800 H obtained at temperatures from 850°C to 1,050°C and at strain rates of 5 s−1 and 10 s−1 were used. The evaluation of the mean error of flow stress revealed that the presented model can give a precise estimation of stress-strain curves of Alloy 800 H at high strain rates. The Johnson-Cook and logarithmic power models were also used to show the accuracy of the presented model at different deformation conditions. It was discovered that the presented model can provide a more accurate estimation of flow stress curves for the alloy of this study.

알루미늄 5083 주조재를 이용한 실린더형 블레이드 루트 열간 자유 단조 공법에 관한 연구

The blade cylinder root is a key component connecting the blade and pitch bearing of a wind turbine and is 20% of the blade’s manufacturing cost. Blade cylinder roots are manufactured using the open die forging method with steel alloy. However the blade cylinder root for 750 KW class wind turbine is manufactured using AA5083 cast material to reduce weight. The purpose of this study is to develop a hot open die forging method, through experiment and FEA, using AA5083 material manufactured by continuous casting. The forging process was designed using the mandrel forging method. Hot compression tests were conducted to obtain flow stress of cast microstructure at different temperatures and strain rates. Control parameters of each forging process were analyzed/compared to predict adaptability of the mandrel forging process. High productivity, good internal quality, shapes, and dimension were verified by prototypes manufactured by the proposed forging process.

Microstructure based modeling of deformation and failure of spot-welded advanced high strength steels sheets

Microstructures and hardness of different weld zones of spot-welded high strength steel grade 1000 and press-hardened 22MnB5 steel were characterized. Tensile shear and cross tension test of welded specimens were conducted, in which load responses and fracture developments were identified. Then, samples with microstructures of each weld zone in all examined joints were generated by specific heat treatment processes. 2D representative volume elements (RVEs) for these microstructures were modelled. Flow stress curves of the individual phases were described by micromechanics based models under consideration of local chemical compositions and phase constituents. It was clearly shown that predicted overall stress-strain responses of all weld regions were well in accordance with the tensile test results of heat-treated samples. Furthermore, fracture criteria were determined for each weld zone by using samples having varying geometries for a wide range of stress triaxialities along with the digital image correlation technique. Finally, FE simulations of the tensile shear and cross tension tests of all investigated joints were carried out, in which the obtained flow stress curves and fracture criteria were defined for the individual weld regions. The experimental force-displacement curves up to fracture and observed failure occurrences could be correctly described by the simulation results.

A Study at the Workability of Ultra-High Strength Steel Sheet by Processing Maps on the Basis of DMM

AbstractThe hot workability of the ultra-high strength steel BR1500HS has been investigated by processing maps. A series of hot deformation tensile tests were carried out on a Gleeble-3500 thermal simulator in the deformation temperature range of 773–1,223 K and strain rate range of 0.01–10 s–1. The obtained flow stress curves reveal that the peak stress increases with the rising of strain rate and decreases with the rising of temperature. Based on dynamic materials model (DMM), the processing maps at the strains of 0.05, 0.10 and 0.15 were developed, and the optimum hot working conditions were recommended as the temperature range of 1,200–1,223 K and the strain rate range of 0.01–0.1 s–1, where the peak power dissipation efficiency is about 37 % revealing the occurrence of typical dynamic recrystallization (DRX). The main instability defects are deformation twinning and micro-crack occurring mainly at the temperature range of 773–873 K with the strain rate higher than 1 s–1. In order to deeply understand the microstructure mechanisms, the Zener–Hollomon parameter is solved, and then the self-diffusion activation energy is compared with the apparent activation energy Q at different deformation temperatures and strain rates.

Digital material representation concept applied to investigation of local inhomogeneities during manufacturing of magnesium components for automotive applications

AbstractMulti-scale computer aided design of manufacturing processes of a magnesium bracket for the automotive industry is the main goal of the present paper. Tensile tests at various deformation conditions (temperatures, strain rates etc.) were performed to obtain flow stress data necessary for the macro-scale finite element analysis. The digital material representation concept was used to create a micro-scale model and to evaluate the influence of local microstructural features in the form of twins on material behaviour. An algorithm based on the cellular automata method capable of replicating microstructural morphology with twins was proposed to provide the digital material representation model. The bracket made of AZ31 magnesium alloy was formed at an elevated temperature of 200 °C. Description of the study as well as results obtained at two length scales are presented in the paper.

Effect of Purity Levels on the High-Temperature Deformation Characteristics of Severely Deformed Titanium

In the present investigation, high-temperature compression tests were conducted at strain rates of 0.001 to 0.1 s−1 and at temperatures of 873 K to 1173 K (600 °C to 900 °C) in order to study the hot deformation characteristics and dynamic softening mechanisms of two different grades of commercial purity titanium after severe plastic deformation. It was observed that the effects of deformation rate and temperature are significant on obtained flow stress curves of both grades. Higher compressive strength exhibited by grade 2 titanium at relatively lower deformation temperatures was attributed to the grain boundary characteristics in relation with its lower processing temperature. However, severely deformed grade 4 titanium demonstrated higher compressive strength at relatively higher deformation temperatures (above 800 °C) due to suppressed grain growth via oxygen segregation limiting grain boundary motion. Constitutive equations were established to model the flow behavior, and the validity of the predictions was demonstrated with decent agreement accompanied by average error levels less than 5 pct for all the deformation conditions.

Crystal plasticity modeling of irradiation effects on flow stress in pure-iron and iron-copper alloys

The mechanistic modeling of irradiation induced embrittlement of reactor pressure vessel steels strongly depends on the precise evaluation of flow stress behavior. This requires accurate characterization of change in both the yield strength as well as the strain-hardening capacity. A dislocation-density based crystal plasticity model is thus developed in this work to quantify these variations with irradiation. The model considers the interaction between dislocations and irradiation induced defects such as self-interstitial atomic loops, vacancy clusters and precipitates to obtain flow stress variations in irradiated ferritic alloys. The model is calibrated and validated for polycrystalline pure-iron and iron-copper alloys, neutron-irradiated to different dose levels under typical pressure vessel operating conditions. A comparison with experimental results show that the model is able to quantify the changes in flow stress behavior accurately. At 0.2 dpa a loss of strain-hardening capacity beyond 2% strain is also obtained from the model. The yield strength increase with irradiation obtained from the model is also compared with analytical strengthening models based on Orowan’s equation.

Flow stress identification of tubular materials using the progressive inverse identification method

Purpose – The purpose of this paper is to propose a progressive inverse identification algorithm to characterize flow stress of tubular materials from the material response, independent of choosing an a priori hardening constitutive model. Design/methodology/approach – In contrast to the conventional forward flow stress identification methods, the flow stress is characterized by a multi-linear curve rather than a limited number of hardening model parameters. The proposed algorithm optimizes the slopes and lengths of the curve increments simultaneously. The objective of the optimization is that the finite element (FE) simulation response of the test estimates the material response within a predefined accuracy. Findings – The authors employ the algorithm to identify flow stress of a 304 stainless steel tube in a tube bulge test as an example to illustrate application of the algorithm. Comparing response of the FE simulation using the obtained flow stress with the material response shows that the method can accurately determine the flow stress of the tube. Practical implications – The obtained flow stress can be employed for more accurate FE simulation of the metal forming processes as the material behaviour can be characterized in a similar state of stress as the target metal forming process. Moreover, since there is no need for a priori choosing the hardening model, there is no risk for choosing an improper hardening model, which in turn facilitates solving the inverse problem. Originality/value – The proposed algorithm is more efficient than the conventional inverse flow stress identification methods. In the latter, each attempt to select a more accurate hardening model, if it is available, result in constructing an entirely new inverse problem. However, this problem is avoided in the proposed algorithm.

Hot deformation behavior of Zr-2.5Nb alloy: A comparative study using different materials models

Dynamic materials model (DMM), modified dynamic materials model (MDMM) and α-parameter were used to develop processing maps of Zr-2.5Nb alloy. Gleeble-3800® thermo-mechanical simulator was used to obtain flow stress at different temperatures and strain rates in the range of 700–925 °C and 0.01–10 s−1 respectively. Suitability of the three models in predicting the hot deformation behavior of Zr-2.5Nb alloy was evaluated by microstructural studies. DMM was found appropriate to delineate different deformation conditions for this alloy.

Prediction of the True Stress of ZE20 Magnesium Alloy at Different Temperatures and Strain Rates

Compression tests were performed to obtain flow stress curves of a newly developed magnesium ZE20 alloy for automobile applications. The experiments were performed in a temperature range from 200 °C to 425 °C and the strain rates from 0.01 to 15 s-1 to examine the material responses at various processing conditions. Artificial neural network (ANN) and gene expressing programming (GEP) were used for the estimation of the true stress curves obtained from the experimental tests. Recently, a few studies were performed to estimate the true stress of different magnesium alloys by using ANN modelling method. However, this method has not yet been applied for the ZE20 alloy; therefore, it was the subject in this study. Furthermore, this study is the first attempt of using a GEP model to predict the true stress of a magnesium alloy. Both developed ANN and GEP models successfully predicted the true stress of ZE20 alloy.

A novel approach to determine plastic hardening curves of AA7075 sheet utilizing hydraulic bulging test at elevated temperature

Precise estimation of various mechanical properties of sheet metal with strong non-linearities has always been a major problem in process simulation by Finite Element Method (FEM). The hydraulic bulge test as prescribed in ISO standard 16808 is well-known for its capability of obtaining flow stress at higher strain levels compared to uniaxial tensile test, but a more applicable method is also needed to calculate the flow stress properties of bulge test especially at elevated temperature. In this study, a set of explicit integral format formulas based on the classical plastic flow rules were deduced to calculate thickness distribution from the aspect of the mechanics analysis. Afterwards an iterative method combined with integration formulas was established to evaluate hardening curves for specimen. Finally, A group of hydraulic bulge tests were performed using sheet metal of AA7075 alloy at room and elevated temperatures with a constant pressure increasing rate, supplementary tensile tests were also carried out at corresponding conditions to compare with the stress–strain curves from the bulge tests. Result shows that the proposed method can evaluate the flow stress curves of the test specimen with reasonable accuracy and with higher strain range over the temperatures ranging from cold to elevated values.

Dynamic precipitation of nickel-based superalloys undergoing severe deformation below the solvus temperature

Abstract The authors performed uniaxial compression tests of nickel-based superalloys: single crystal CMSX–4, also precipitation hardened; Inconel 718 and X750, at temperatures below the γ′ solvus, in order to study the effect of temperature and strain rate on their flow stress and microstructural development. On the basis of the obtained flow stress values, the activation energy of a high-temperature deformation process was estimated. Microstructural observations of the deformed samples at high temperatures, previously solution heat treated and aged CMSX–4 and Inconel alloys revealed non-uniform deformation effects. Distribution of either molybdenum- or niobium-rich carbides was found to be affected by localized flow within the investigated strain range at relatively low deformation temperatures, 720–850 °C. Microstructural examination of the alloys also showed that shear banding and cavity growth were responsible for the decrease in flow stress and a specimen fracture at larger strains.

Development of High-speed Shearing Method to Obtain Flow Stress under High Strain Rate

Development of High-speed Shearing Method to Obtain Flow Stress under High Strain Rate

Modeling the Constitutive Relationship of Powder Metallurgy Ti-47Al-2Nb-2Cr Alloy During Hot Deformation

In the present work, the isothermal compression tests of PM alloy Ti-47Al-2Nb-2Cr were carried out in the temperature range of 950-1200 °C. A Gleeble 1500D thermosimulation machine was used, and samples were tested at strain rates ranging from 10−3 to 10−1 s−1. Based on the obtained flow stress curves, the hot deformation behavior was presented. The constitutive relationship of powder metallurgy (PM) Ti-47Al-2Nb-2Cr alloy was developed using an Arrhenius-type constitutive model that involves strain compensation in addition to an artificial neural network model. The accuracy and reliability of the developed models were quantified in terms of statistical parameters such as correlation coefficient and absolute value of relative error. It was found that deformation temperature and strain rate have obvious effects on the flow characteristics, and the flow stress increases with the increasing strain rate and the decreasing temperature. Moreover, the proposed models possess excellent prediction capability of flow stresses for the present alloy during hot deformation. Compared with the traditional Arrhenius-type model, the backpropagation neural network model is more accurate when presenting the isothermal compressing deformation behavior at elevated temperatures for PM Ti-47Al-2Nb-2Cr alloy.