Materials modeling and finite element simulation of isothermal forging of electrolytic copper

Isothermal forging of electrolytic copper is modeled using finite element simulation and materials models involving kinetic analysis and processing maps with a view to validate their predictions. Forging experiments were conducted on a rib–web (cup) shape in the temperature range of 300–800 °C and at speeds of 0.01–10 mm s⁻¹. The processing map for hot working of electrolytic copper revealed two domains in the temperature and strain ranges of (1) 400–600 °C and 0.001–0.01 s⁻¹, (2) 650–950 °C and 0.3–30 s⁻¹, where dislocation core diffusion and lattice self-diffusion are the rate-controlling mechanisms, respectively. Finite element simulation using the relevant experimental constitutive equations, predicted load–stroke curves that correlated well with the experimental data. The simulation has shown that there is a strain variation from about 0.4 to 4 in the web and rib regions of the forged component, although the dynamically recrystallized grain structure is fairly uniform, suggesting that dynamic recrystallization (DRX) is not sensitive to strain once the steady state flow is reached. The DRX grain size in the component is linearly dependent on Z and is similar to that predicted by the materials model after discounting for the longer time taken for the component removal.     

The size effect on micro deformation behaviour in micro-scale plastic deformation

When the geometry of metal deformed part is scaled down to micro-scale, the understanding and prediction of micro deformation behaviour becomes difficult. This is because the conventional material deformation models are no longer valid in micro-scale due to the size effect, which affects the deformation behaviour in micro plastic deformation, and thus leveraging the traditional knowledge of plastic deformation from macro-scale to micro-scale is not meaningful. In this paper, the size effect on micro-scale plastic deformation and frictional phenomenon are investigated via micro-cylindrical compression test, micro-ring compression test and Finite Element (FE) simulation. The experimental results show the occurrence of various size-effect related deformation phenomena, including the decrease of flow stress and the increases of: (a) irrational local deformation, (b) the amount of springback, and (c) the interfacial friction stress with the decreasing specimen size. The research further verifies that the established surface layer models, with the identified surface grain, the internal grain properties and the measured friction coefficients, are able to predict micro deformation behaviour. The research thus provides an in-depth understanding of size effect on deformation and frictional behaviours in micro-scale plastic deformation.     

Determination of critical strain for initiation of dynamic recrystallization

Using the work hardening rate–strain curves, an effective mathematical model has been developed to predict the stress–strain curves of alloy steel during hot deformation up to the peak stress regardless of the level of the strain, weather smaller or larger than the critical strain. This model is expressed in terms of peak stress, peak strain and one temperature-sensitive parameter, S. In addition, one new model, which is a function of peak strain, was proposed to predict the critical strain for the initiation of dynamic recrystallization using the second derivative of work hardening rate with respect to stress. Besides the theoretical study, the analysis is used to determine the stress–strain curves and critical strain of 304 austenitic stainless steel. The predicted results were found to be in accord with the experimental data.     

Constitutive base analysis of a 7075 aluminum alloy during hot compression testing

In the field of deformation process modeling, the constitutive equations may properly represent the flow behavior of the materials. In fact, these valuable relationships are used as a calculation basis to simulate the materials flow responses. Accordingly, in the present study a hot working constitutive base analysis has been conducted on a 7075 aluminum alloy. This has been performed using the stress–strain data obtained from isothermal hot compression tests at constant strain rates of 0.004, 0.04 and 0.4 s⁻¹ and deformation temperatures of 450, 500, 520, 550 and 580 °C up to a 40% height reduction of the specimen. A set of constitutive equations for 7075 Al alloy have been proposed employing an exponent-type equation. The related material constants (i.e., A, n and α) as well as the activation energy Q for each temperature regime have been determined. The correlation of flow stress to strain rate and temperature can be deduced from the proposed equations. Furthermore, a change in deformation mechanism has been realized in the semi-solid temperature range. This has been related to the onset of lubricated flow mechanism during processing.     

Materials modeling and simulation of isothermal forging of rolled AZ31B magnesium alloy: Anisotropy of flow

Isothermal forging of a rib–web shape in AZ31B magnesium alloy in the rolling direction was conducted at speeds of 0.01–10 mm s⁻¹ in the temperature range of 300–500 °C with the purpose of validating the results of materials models involving kinetic analysis and processing map. The process was also simulated using finite element method DEFORM to obtain the local values of strain and strain rate. Forging parallel to the rolling direction in the range 375–550 °C and 0.0003–0.3 s⁻¹ under the conditions of dynamic recrystallization (DRX) resulted in a symmetrical cup-shape while at other conditions an elliptical boat-shape was produced with the major axis coinciding with the transverse direction and the minor axis aligned with the normal direction. This anisotropy of flow has been attributed to the strong basal texture in the rolled plate and the dominance of prismatic slip at lower temperatures. In the DRX domain on the other hand, pyramidal slip dominates along with cross-slip as the recovery mechanism, which destroys the initial texture and restores the symmetry of flow. The grain size variation for forgings done in the DRX domain validated the predictions of the material models.     

Experimental and simulation study of deformation behavior in micro-compound extrusion process

In micro-forming process, the prediction of deformation behavior is difficult as the conventional material constitutive model is no longer valid when the part geometry is scaled down to micro-level. This is caused by the so-called “size-effect”. It is thus necessary to study the size effect and how it affects the deformation behavior in micro-forming process. In this research, a material constitutive model was established based on micro-compression test and its applicability was then studied. To facilitate the research, a flexible tooling set for micro-extrusion was designed and developed first. A modified micro-double cup extrusion test was proposed and the corresponding Finite Element Method (FEM) simulation was conducted. Through experiment and simulation, a set of deformation load curves were generated so as to provide a reference for calibration of flow stress–strain curve in modeling of micro-extrusion process. The applicability of the calibrated flow stress–strain curve was finally validated by the experimental and simulation results of micro-forward extrusion. It is therefore believed that the flow pattern, the material surface constraint and the material deformation mode are critical in determination of material flow stress curve. Furthermore, it was found that the change of cup height ratio of the extruded part is not caused solely by the change of friction when the part size is in micro-scale. The material flow stress significantly affects the cup height ratio. These findings provide a basis in understanding of micro-extrusion process.     

Hot compressive deformation behavior of a new hot isostatically pressed Ni–Cr–Co based powder metallurgy superalloy

The hot compressive deformation behavior of a new hot isostatically pressed Ni–Cr–Co based powder metallurgy (P/M) superalloy was studied in the temperature range of 950–1150 °C and strain rate range of 0.0003–1 s⁻¹ using Gleeble-1500 thermal simulator. The dynamic recrystallization-time–temperature (RTT) curve was developed and the constitutive equation of flow stress during hot deformation was established. The results show that the flow stress decreases with increasing deformation temperature and decreasing strain rate. The flow stress represents as the characteristic of dynamic crystallization with the increasing of strain at the deformation temperatures lower than 1100 °C and strain rates higher than 0.0003 s⁻¹. The beginning time of dynamic crystallization has no linear relationship with deformation temperature in the condition of strain rate lower than 0.01 s⁻¹. Besides, the experiments verify that the hyperbolic sine model including the variable of strain reflects the changing law of flow stress during the hot deformation process.     

Prediction of hot compression flow curves of Ti–6Al–4V alloy in α + β phase region

Prediction of material flow behavior is essential for designing the forming process of any material. In this research, experimental flow curves of Ti–6Al–4 V alloy were obtained using the isothermal hot compression test done at 750–950 °C with 50 °C intervals and constant strain rates of 0.001, 0.005 and 0.01 s⁻¹. For prediction of hot deformation flow curves two methods of modeling were applied. In the first method, an entire flow curve was modeled using Sellars equation. In the second one, modeling of a flow curve up to the peak point was carried out with Cingara model, and modeling beyond that was performed with a model developed based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory. The accuracy of each model was examined through a statistical method. Results showed that flow curve modeling using Cingara model and JMAK theory leads to results that are more consistent with the experimental data.     

Geometry and grain size effects on the fracture behavior of sheet metal in micro-scale plastic deformation

The demand on micro-parts is significantly increasing in the last decade due to the trend of product miniaturization. When the part size is scaled down to micro-scale, the billet material consists of only a few grains and the material properties and deformation behaviors are quite different from the conventional ones in macro-scale. The size effect phenomena occur in micro-scale plastic deformation or micro-forming and there are still many unknown phenomena related to size effect, including geometry and grain size effects. It is thus critical to investigate the size effect on deformation behavior, especially for the fracture behavior in micro-scale plastic deformation. In this research, tensile test was conducted with annealed pure copper foils with different thicknesses and grain sizes to study the size effects on fracture behavior. It is found that flow stress, fracture stress and strain, and the number of micro-voids on the fracture surface decrease with the decreasing ratio of specimen size to grain size. Based on the experimental results, dislocation density based models which consider the interactive effect of specimen and grain sizes on fracture stress and strain are developed and their accuracies are further verified and validated with the experimental results obtained from this research and prior arts.     

The limit drawing ratio and formability prediction of advanced high strength dual-phase steels

Dual phase (DP) steels, being among advanced high-strength steels (AHSS), have been successfully used in the sheet metal stamping of automotive components for its great benefit in reducing vehicle weight while improving car safety. In their practical application, one of the major challenges is related to formability prediction of onset crack. This paper first conducts limiting drawing ratio (LDR) experiments to identify the maximum blank diameter of SPFC340, DP600, DP800 and DP1000 with onset crack. The fracture modes of these four types of blanks are then compared and classified into two categories: necking crack and shear crack. Further for DP1000, appropriate hardening formula is determined to fit the flow curve derived by the tensile test. Three yielding models (Hill-48, Batlat-89 and Banabic-2005) are compared with each other in the numerical simulation of DP1000 LDR onset crack. The investigation shows that a Swift and Hockett–Sherby combined formula is in good agreement with the flow curve of the tensile test and Batlat-89 yield model successfully predicts the onset shear crack of DP AHSS.     

Springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes under bending

In this paper, the springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes subject to bending is explored. Rotary draw bending tests have been carried out and marked time-dependent springback has been observed. A novel model in which time-dependent springback is associated with strain hardening is presented as an attempt to analyze this behavior. Using this model, the formulae of time-dependent springback, time-independent springback and total springback are derived. In addition, finite element analysis has been performed to investigate the stress distribution as well as to calculate the magnitude of springback. Comparison between analytical and experimental results shows good agreement.     

A comparative analysis of constitutive behaviors of Mg–Mn alloys with different heat-treatment parameters

Mg–1.8Mn (wt.%) alloy was solution-treated by three regimes to obtain different initial microstructures. Isothermal hot compression tests were conducted in the temperature range of 250–450 °C and strain rate 0.01–1 s⁻¹ for each of the initial states. Constitutive constants for each initial state were obtained and compared. The results showed that homogenization of initial microstructure can significantly decrease the deformation resistance during hot working. It was also revealed that the dispersion of second-phase particles 1–1.5 μm in size with appropriate volume fraction (1–2%) and inter-particle spacing in initial microstructure can impart superior hot work deformation ability to the materials. Excessive amounts of particles resulted in an increase of the flow stresses and working-hardening degree. A large volume fraction of nano-sized particles also imposed difficulty in plastic deformation but with less harmful effects than the larger-sized particles. The influencing mechanism of the particle distribution on the constitutive behavior is discussed.     

A comparison of the deformation of magnesium alloys with aluminium and steel in tension, bending and buckling

A comparison was made between high pressure die cast and wrought magnesium alloys and formed mild steel and aluminium in tensile, bending and buckling deformation. It was found that the energy absorption properties of magnesium alloys were particularly good in bending and buckling, absorbing up to 50% more energy than the aluminium and over 10 times more energy than the mild steel. The primary reason for the good performance of Mg alloys was that the low density means that sections of increased thickness can be made without increasing weight. This is particularly beneficial in bending as the strength of a section in bending is proportional to the square of the thickness. However, it was also observed that the high rate of work hardening of Mg alloys is particularly important and this allows for considerably more energy to be absorbed. A simple analytical strut buckling model has been modified to incorporate work hardening and a good correlation has been observed between this model and the experimental results.     

Severe plastic deformation of copper and Al–Cu alloy using multiple channel-die compression

Severe plastic deformation studies of copper and Al–Cu alloy by multiple channel-die compression tests were investigated. The materials were tested under plane strain condition by maintaining a constant strain rate of 0.001/s. Extensive grain refinement was observed resulting in nano-sized grains after severe plastic deformation with concomitant increase in flow stress and hardness. The microstructural investigation of the severely deformed materials was investigated using optical microscope and scanning electron microscope. Shear band formation was identified as the failure mechanism in the two phase Al–Cu alloy. The results indicate difficulty in obtaining severe plastic deformation for alloys having two phase micro-structure.     

Microindentation study of Ti–6Al–4V alloy

In order to study the micromechanical behavior of Ti–6Al–4V alloy, microindentation experiments were performed with five different maximum loads of 100, 150, 200, 250 and 300 mN, and with three loading speeds of 6.4560, 7.7473 and 9.6841 mN/s respectively. The experimental results revealed that loading speed has little influence on microhardness and Young’s modulus. Microindentation hardness experiments showed strong indentation size effects, i.e. increase of indentation hardness with the decrease of indentation load or depth. Then microindentation constitutive equation that described the stress as a function of the strain was proposed through dimensional analysis. And the finite element simulation results showed that the predicted computational indentation data from developed constitutive equation can track the microindentation experimental data of Ti–6Al–4V alloy.     

Application of T-shape friction test for AZ31 and AZ80 magnesium alloys at elevated temperatures

T-shape side pressing experiment is a sort of friction test which, recently, is employed for evaluation of friction for bulk metal forming processes. One of important advantages of this experiment, compared with other friction tests such as the ring compression test, is the occurrence of appropriate surface enlargement during the deformation of the specimen. This paper is concerned with experimental and numerical studies on this test, when it is used for some magnesium alloys such as AZ31 and AZ80. Based on the experimental results, it was found that the friction sensitivity of T-shape experiment increased when the die edge radius decreased or the test temperature or ram velocity increased. Good repeatability of this test was also observed during experimental part of this research work. Finally, employing the flow curves gained from the compression tests and friction factors obtained from the T-shape experiments for the finite-element simulations of this test, resulted in a very good agreement between the numerical and experimental load curves.     

A parametric study on residual stresses and loads in drawing process with idle rolls

A comprehensive study of drawing process with flat idle rolls of round wires is presented through 3D mechanical finite element simulations. An elastic–plastic model is used for the wire material and contact behavior is simulated by a sliding–sticking friction model. The results of numerical simulations are compared with measurements on wires produced with a laboratory equipment. The comparison of drawing load and some geometrical characteristics of experimental samples with numerical model predictions allowed to establish a good correspondence of model with experimental findings, thus validating the numerical model. Residual stress of flat roll drawn wires, pressure distribution on the forming rolls and drawing load are studied. The effects of main process parameters such as initial workpiece diameter, forming rolls diameter and percentage of deformation are investigated. The results present a helpful insight into the process parameters effect in wire drawing with flat idle rolls thus furnishing the basic guidelines for process design and optimization.     

Development of ultrafine-grained Al 6063 alloy by cryorolling with the optimized initial heat treatment conditions

The effects of rolling temperature and rolling strain on the microstructural refinement of Al 6063 alloy are investigated in the present work by employing electron back scattered diffraction (EBSD) analysis, transmission electron microscope (TEM) investigations, and X-ray diffraction (XRD) analysis. The solution treated bulk Al 6063 alloy samples are subjected to cryorolling and room temperature rolling to produce sheets with different strain levels such as 0.4, 2.3 and 3.8, respectively. Prior to cryorolling and room temperature rolling, the initial conditions such as solution treatment temperature, and sample immersion duration time, in liquid nitrogen, before cryorolling are optimized by using EBSD analysis, TEM investigations, hardness test, and tensile test. It is observed that the formation of recrystallized ultrafine-grains with the high angle grain boundaries occurs at the strain value of 3.8. However, in case of room temperature rolled samples, the sub-grains are not recrystallized even up to the strain value of 3.8.     

Direct simulation of fatigue failure in solder joints during cyclic shear

A numerical finite element analysis is undertaken to directly simulate failure of solder joint caused by cyclic shear deformation. In the model the tin (Sn)-silver (Ag)-copper (Cu) solder and two copper substrates constitute a lap-shear testing configuration. A progressive damage model is incorporated into the rate-dependent elastic-viscoplastic response of the solder alloy, resulting in the capability of simulating damage evolution and eventual failure through crack formation. The study concerns three different applied shear strain rates, 1, 10 and 100 s⁻¹, under both the monotonic and cyclic loading conditions. It is found that, in the reference case of monotonic loading, the strain at failure can be influenced significantly by the fracture path in the solder. There is a tendency for cracking to occur closer to the interface during cyclic loading. The initiation of fatigue cracks is generally insensitive to the applied strain rate. However, the total fatigue life, in terms of the number of cycles to final failure, is seen to decrease significantly in the case of highest strain rate.