Softening Stage Research Articles

High-temperature tensile deformation behavior and microstructure evolution of Ti55 titanium alloy

High temperature tensile and electron backscatter diffraction (EBSD) techniques were combined to perform a systematic investigation for the hot deformation behavior and microstructure evolution of the Ti55 alloy. Under temperatures ranging from 885 to 935°C and stain rates of 8.3×10−4 s−1−1.33×10−2 s−1, all the flow curves of the Ti55 alloy exhibit similar behaviors: after reaching the peak flow stress, the curves enter into a softening stage and then remain a steady level, where the maximum superplastic elongation of 987% indicates good superplasticity. Detailed microstructure characterizations under different deformation stages show that the grain aspect ratios decrease greatly and the fractions of high angle boundaries (>15°) increase rapidly at the softening stage. These observations are attributed to the dynamic recrystallization, in which low angle grain boundaries (<5°) evolve into high angle boundaries and the formation of equiaxed grains is accelerated. In contrast, no obvious changes in either the grain aspect ratios or the fractions of high angle boundaries occur at the steady flow stage, while the initial texture gradually disappears and the Schmid factor increases with the further straining. At this stage, the deformation mechanism is grain boundary sliding and grain rotation would accommodate the process of grain boundary sliding. Moreover, the main softening mode responsible for the flow behaviors has been identified as discontinuous dynamic recrystallization, which completely neutralized the effect of work hardening at the quasi stable deformation stage.

Nano-structure evolution of secondary Al3(Sc1−xZrx) particles during superplastic deformation and their effects on deformation mechanism in Al-Zn-Mg alloys

The nano-structure evolution of secondary Al3(Sc1−xZrx) particles during high-strain-rate (0.01 s−1) superplastic deformation at 500 °C was investigated by high resolution transmission electron microscopy. The results show that by increasing the true stains from 0.69 to 2.40, the mean radii of spheroidal secondary Al3(Sc1−xZrx) particles increase from 9.8 ± 3.4 nm to 16.4 ± 6.8 nm, and the lattice misfit value increases from 1.04% to 1.30%. Before deformation, Al3(Sc1−xZrx) nano-particles are completely coherent with Al(α) matrix. As the deformation proceeds, the accumulated sever plastic deformation introduces misfit dislocations at the interface between particles and matrix. Superplastic flow deformation data indicate that with the increase of true strains, the strain rate sensitivity of Al-Zn-Mg alloy decreases from 0.29 to 0.19, and the deformation activation energy increases from 112 to 121 kJ/mol. However, for Al-Zn-Mg alloy with secondary Al3(Sc1−xZrx) nano-particles, the strain rate sensitivity increase from 0.33 to 0.45, and the deformation activation energy decreases from 107 to 84 kJ/mol. Based on the microstructural results and the established constitutive equations at different strains, it can be concluded that at the working hardening stage, two kinds of alloys are both controlled by dislocation viscous glide creep mechanism. At the dynamic softening stage, dislocation creep mechanism operates in Al-Zn-Mg alloy, whereas grain boundary sliding mechanism is dominant in Al-Zn-Mg-Sc-Zr alloy. Secondary Al3(Sc1−xZrx) nano-particles play an important role in accelerating the cooperative grain boundary deformation and only affect dynamic softening deformation mechanism of Al-Zn-Mg alloys.

An analytical model for particulate reinforced composites (PRCs) taking account of particle debonding and matrix cracking

In this work, a simple micromechanics-based model was developed to describe the overall stress–strain relations of particulate reinforced composites (PRCs), taking into account both particle debonding and matrix cracking damage. Based on the secant homogenization frame, the effective compliance tensor could be firstly given for the perfect composites without any damage. The progressive interface debonding damage is controlled by a Weibull probability function, and then the volume fraction of detached particles is involved in the equivalent compliance tensor to account for the impact of particle debonding. The matrix cracking was introduced in the present model to embody the stress softening stage in the deformation of PRCs. The analytical model was firstly verified by comparing with the corresponding experiment, and then parameter analyses were conducted. This modeling will shed some light on optimizing the microstructures in effectively improving the mechanical behaviors of PRCs.

Effects of particle size ratio on the macro- and microscopic behaviors of binary mixtures at the maximum packing efficiency state

The effects of particle size ratio on the mechanical behaviors of binary mixtures are investigated using three-dimensional discrete element method. The samples with three types of particle size ratios (SR, $$\hbox {SR}=3.0$$ , 4.5 and 6.0) are prepared at the maximum packing efficiency state, which appears at 70 % of the large particle volume content. The results demonstrate that the maxima of peak deviator stress are obtained at the sample with $$\hbox {SR}=4.5$$ . The initial elastic modulus, $$E_{0}$$ , increases with increasing SR. The value of deviator stress increases with increasing SR at the softening stage, whereas an opposite trend is observed at the critical state. The evolutions of the effective particle ratio can capture the differences among the evolutions of the deviator stress of different samples during the softening stage and the critical state to some degree. In addition, different SRs generate different packing structures of the binary mixtures and have apparent influences on the force chain networks in the binary mixtures. With increasing SR, the strong force chains become stronger, and the weak force chains become weaker. The deviator stress contributed by the contacts between large particles and between large and small particles constitutes a major part of the overall deviator stress of the binary mixtures at the maximum packing efficiency state. Furthermore, the positions of the critical state lines of binary mixtures in the $$p-q$$ plane and $$v-\ln p$$ plane are sensitive to SR, and the lubrication effect of small particles in the binary mixtures is enhanced with increasing SR.

Studying recovery processes in a strain-hardened Al–Mg–Mn–Fe–Si alloy

The material of a shell structure subjected to 20-year use under ambient conditions has been studied. The structure and mechanical characteristics of a strain-hardened AMg6 alloy, as well as the effect of subsequent holdings of this alloy for 10–3000 h at temperatures of 50, 70, 80, 100, 130, 150, 180, and 220°C, on changes in its dislocation structure and mechanical characteristics have been investigated. It has been shown that, in the structures under study, the AMg6 alloy has a cellular structure with a high density of dislocations and the ultimate strength σu = 445.5 ± 2.5 MPa, the proof stress σ0.2 = 326.5 ± 3.5 MPa, and the relative elongation δ = 11.7 ± 0.5%. Polygonization in the alloy occurs at a temperature of 220°C and the initial stage of the recovery process corresponds to a temperature range of 50–100°С in which the softening process can be divided into two stages, i.e., stage (1) of active softening due to the interaction of point defects with each other and stage (2) of the stabilization of the characteristics of the alloy.

Constitutive Model Based on Dynamic Recrystallization Behavior during Thermal Deformation of a Nickel-Based Superalloy

The thermal deformation and dynamic recrystallization (DRX) behavior of a nickel-based superalloy were investigated by the thermal compression test. The experimental results show that the process parameters have great influence on the flow stress of the superalloy. In addition, there is an inflection point on the DRX softening stage of the work-hardening rate versus stress curve. DRX under the conditions of higher temperatures and lower strain rates easily occurs when the strain reaches a critical level. Based on the classical dislocation density theory and the DRX kinetics models, a two-stage constitutive model considering the effect of work hardening-dynamic recovery and DRX is developed for the superalloy. Comparisons between the predicted and experimental data indicate that the values predicted by the proposed constitutive model are in good agreement with the experimental results.

Investigation of the micro-cracking behavior of asphalt mixtures in the indirect tensile test

The micro-cracking behavior of asphalt mixtures in the indirect tensile test (IDT) was studied by the discrete element modeling in this paper. A user-defined discrete element model was constructed and verified by the laboratory test results. The material mechanical behavior, the micro-cracking mode, the crack initiation and propagation, and the energy consumption during the IDT of asphalt mixtures were investigated. Firstly, the mechanical behavior of asphalt mixtures during the IDT was studied. The simulation results indicate that the bearing capacity of the sample is controlled by the micro-crack development. According to this feature, the mechanical behavior of asphalt mixtures during the IDT was divided into five stages. Secondly, the micro-cracking mode during the IDT was analyzed. The results show that the majority of micro-cracks are caused by normal tensile forces. And the crack initiation and propagation in asphalt mixture mainly happen between aggregates and asphalt mastic and in asphalt mastic. Thirdly, the crack initiation and propagation during the IDT were investigated. The simulation results show that the micro-cracks appear first at the top and bottom of the sample before peak load due to the local compression by the loading platens. And at the softening stage, the micro-cracks propagate rapidly, which causes apparent macro-cracks in the middle of the sample. Finally, the energy consumption during the IDT was explored. The results indicate that at a temperature of −10°C the majority of energy is consumed by crack initiation and propagation during the IDT.

Tensile flow and work hardening behaviors of ultrafine-grained Mg-3Al-Zn alloy at elevated temperatures

Tensile flow behavior of ultrafine-grained Mg-3Al-Zn alloy processed via mechanical milling, hot-press consolidation followed by extrusion has been determined in the temperature range from 300K to 523K and strain rate range from 10−2 to 10−4s−1. The effects of temperature and strain rate on the work hardening behavior are successfully analyzed by the derived Lukáč and Balík expression. The microstructure evolution shows that the dislocation density increases from 1.59×1016m−2 to 3.04×1016m−2 in work hardening stage and decreases to 3.97×1015m−2 in work softening stage, which is in accordance with Lukáč and Balík expression. The apparent activation energy value of 66.71kJ/mol in the strain rate range from 10−2 to 10−4s−1 at 523K suggests that the dominant mechanism is GBS accommodated by slip controlled by grain boundary diffusion, which is further proved by the formation of cavities and filaments during tensile test. The analysis of work hardening behavior indicates that dislocation multiplication contributes to the hardening process, while cross slip and climb of dislocations as well as GBS play a role in the softening process.

Application of TBM operational parameters to estimate the drop modulus, case study: Karaj–Tehran water conveyance tunnel of Iran

The drop modulus is an important parameter to estimate the post peak behavior of rock mass. It is the slope for the softening stage of rock mass that related to quality of rock mass and confinement stress as increasing in the quality of rock mass and decreasing in the confinement stress can increase the drop modulus and it is true inversely. One of the most important applications of this parameter is to predict the rock burst, squeezing and etc because the mentioned phenomena are directly related to post peak behavior of rock mass. In this study, a new empirical method is proposed to estimate the drop modulus using the double shield TBM specifications of Karaj–Tehran water conveyance tunnel in Iran. It is estimated based on the penetration rate of TBM, the equivalent thrust per cutter and the torque of TBM. The result shows that there are inverse relations between the drop modulus of rock mass with the penetration rate and the torque of TBM and a direct relation between the drop modulus and the equivalent thrust per cutter. In this study, new power equations are proposed to estimate the drop modulus using the penetration rate and the equivalent thrust per cutter respectively. Also a new linear equation is suggested to estimate the drop modulus using the torque of TBM. Finally, the most useful equation to estimate the drop modulus is achieved using the ratio of the equivalent thrust per cutter to product of TBM penetration rate on torque of TBM because it is a function of three parameters.

An improved ductile fracture model for structural steels considering effect of high stress triaxiality

This study presents results of experimental investigation and ductile fracture model for ductile crack initiation, propagation and final failure in structural steels subjected to high stress triaxiality. To this end, uniaxial tension tests on smooth flat bars, U-notched specimens and V-notched specimens are conducted. Nonlinear finite element analysis of the notched specimens is carried out to obtain the stress triaxiality distributions and histories of notch tip and center of specimens. Based on the previous three-stage and two-parameter ductile fracture model proposed by the authors, the equivalent plastic displacement at element failure during simulations is obtained by notched specimen tests, and an improved ductile fracture model is presented considering the effect of high stress triaxiality during both the plastic stage and the softening stage. The relationship between the equivalent plastic displacement at element failure and nonuniform ratio (nonuniform ratio is the ratio of the average value of stress triaxiality of notch tip and center) is determined by a series of tests and analyses. Detailed finite element analyses that employ the improved ductile fracture model are shown to predict ductile fracture behavior under high stress triaxiality with good accuracy across the mesh sizes, notch radii, and notch degree in terms of ductile crack initiation point, ultimate load point and load-displacement curve.

Three dimensional quantification of anisotropic void evolution in deformed semi-crystalline polyamide 6

The evolution of voids has been used as an efficient indicator of the volume changes occurring during deformation for polymers which undergo high levels of plasticity. This has to be taken into account in determining the constitutive models for these polymers. Void growth during uniaxial stretching of a semi-crystalline polyamide 6 has been studied using 3D image analysis of tomography data. Tests on axi-symmetrical notched round bars have been stopped at: (i) the maximum net stress; (ii) the end of the stress softening stage; (iii) the onset of the final failure. Local synchrotron tomography has been performed so as to observe voids in a predetermined volume of interest around the minimum net section. The shape of the voids was found to be cylindrical. Mathematical morphology analysis was used to identify 3D voids, allowing the void diameter and height histograms to be obtained. An anisotropic shape factor parameter was defined as the ratio between the void diameter and the void height. This shape factor was found to evolve with the degree of deformation. The principal strain components of the voids were calculated and plotted, showing anisotropy and a heterogeneous distribution. The irreversible void growth noted as plastic dilation was also found to be heterogeneous in the deformed net section.

Explicit, comprehensive modeling of multi-axial finite strain pseudo-elastic SMAs up to failure

A new elastoplastic J 2 − flow model with nonlinear combined hardening is proposed for the purpose of achieving an explicit, comprehensive simulation of pseudo-elastic SMAs over the whole range of strain up to failure. To this goal, a new, explicit methodology based on any given uniaxial data is introduced to obtain multi-axial expressions for the constitutive quantities incorporated in this model, in such a unified sense that all three successive deformation stages may be simultaneously represented, including a pseudo-elastic stage with perfect strain recovery, a hardening stage with partial strain recovery, and a softening stage up to failure. As such, any given shapes of uniaxial stress–strain curves from both loading and unloading in these three stages may be automatically reproduced from the proposed model, without involving usual complicated numerical procedures in treating nonlinear rate constitutive equations with a number of switching conditions. Numerical examples with test data are supplied to simulate a complete process including all three stages.

Microstructure Evolution and Constitutive Modeling Based on Flow Behavior of 2297 Al-Cu-Li Alloy

Flow behavior and microstructure evolution of 2297 Al-Cu-Li alloy were investigated by isothermal compression tests conducted at the deformation temperature of 300-500°C and strain rates of 0.001-10s-1. The results demonstrate that the characteristics of stress-strain curves depended on the interaction of work hardening and dynamic softening. The true stress increased with the decreasing of temperature and the increasing of the strain rate. At a given deformation condition, the flow curve consisted of three stages: stage I (work hardening stage), stage II (softening stage) and stage III (steady stage). Deformation temperature and strain rate had a great influence on microstructure evolution. 2297 alloy deformed at low temperature (300°C) and high strain rate (10s-1) showed a DRV characteristic. As deformed at high temperature (500°C) and low strain rate (0.001s-1), DRX gradually become the main softening mechanism. The measured flow stress was friction corrected and then employed to develop constitutive equations on the basis of the Arrhenius-type equation by considering the effect of the strain on material constants by a sixth orders polynomials. Flow stress value of 2297 alloy predicted by the proposed constitutive equations shows a good agreement with experimental results, thereby confirming the validity of the developed constitutive relation.

High temperature deformation behavior of an optimized Nb–Si based ultrahigh temperature alloy

The high temperature deformation behavior of an optimized Nb–Si based ultrahigh temperature alloy was investigated by isothermal compression. The constitutive equation as well as the deformation microstructure has been evaluated and discussed. The activation energy of deformation during the steady softening stage is 366–437kJ/mol. Dynamic recovery of Nbss, brittle fracture of large silicide blocks and refinement of small silicide particles have been recognized as the softening mechanisms of the Nb–Si based alloy under present deformation conditions.

Hot compressive deformation behaviors of Mg–10Gd–3Y–0.5Zr alloy

In this paper, the hot compressive deformation characteristics of a Mg–10Gd–3Y–0.5Zr (GW103K) alloy have been investigated by isothermal compression test at the temperature range of 350–450°C and strain rate range of 0.0001–0.1s−1. True stress–strain relationships at various strain rates showed the typical strain hardening and softening stage which is indicative of dynamic recrystallization during deformation. The results showed that the peak stress was obviously dependent on temperature and strain rate. A constitutive equation to describe the deformation process was established based on the hyperbolic sine function. The stress exponent n and apparent activation energy Q were determined to be 3.018 and 203.947 kJ/mol, respectively. Microstructure investigation showed that dislocation slipping was the dominant deformation mechanism during the hot deformation at all conditions. However, at the temperatures lower than 400°C and strain rates higher than 0.01s−1, twinning was observed to be activated, which indicated another deformation mechanism. Dynamic recrystallization and dynamic precipitation were found to occur simultaneously under such deformation condition.

Microstructure Evolution of a Medium Manganese Steel During Thermomechanical Processing

An as-cast Fe-0.2C-10Mn-3Si-3Al medium manganese steel with a ferrite plus austenite duplex microstructure was subjected to hot compression tests at deformation temperatures within two-phase (α + γ) range and various strain rates. The microstructure evolution of the experimental steel during hot deformation was investigated. The flow curves were characterized by a discontinuous yielding at the beginning of plastic deformation, followed by a weak work hardening to a peak and a subsequent mild softening stage. Two restoration processes took place during hot deformation, namely dynamic recrystallization (DRX) of austenite and continuous dynamic recrystallization of ferrite. The DRX of austenite was believed to dominate the softening stage of the flow curves. The discontinuous yielding stemmed from the existing Kurdjumov–Sachs (K–S) orientation relationship between ferrite and austenite in the initial undeformed microstructure, which gradually weakened during subsequent deformation.

The Superplastic Properties and Microstructures Evolution of High Nb Ti&lt;sub&gt;3&lt;/sub&gt;Al Based Alloy

The superplasticity of high Nb Ti3Al based alloy - Ti-23Al-17Nb (at.%) alloy sheet under the conditions of 940~1000°C and 5.5×10-5s-1~1.7×10-3s-1are studied. The results show the elongation changes as a parabola with the deformation temperature increasing, and the maximum elongation obtained at 960°C and 5.5x10-5s-1 is 1447.5%. Work hardening stage increases much more than softening stage when strain rate is decreased due to the increasing of element Nb. Compared with primary microstructure, the lath-like α2 grains gradually disappeared, the α2 grains became more equiaxed, and the content and size of α2 grains are decreasing with increasing of deformation temperature. The volume fraction ratio of α2 and β phase at the optimum deformation condition is 50:50%. The cavities mechanism at the fracture tip was discussed; it can be defined that the cavities could be avoided when deformation temperature is higher than 940°C.

Mechanical Behavior and Microstructure Evolution during Superplastic Deformation of the Fine-Grained AlCoCrCuFeNi High Entropy Alloy

Characteristics of mechanical behavior during superplastic flow and associated microstructural evolution in the wrought AlCoCrCuFeNi high-entropy alloy were studied. The alloy had complex microstructure with fine grain/particle size of ≈2.1 μm. 4 different phases with volume fractions from 7% to 46% and different deformation characteristics were found in the alloy. Very high tensile elongations of up to 1240% were observed during deformation at temperatures of 800°C–1000°C and at strain rates of 10-4 s-1–10-1 s-1 despite presence of pronounced softening stage followed by steady state flow stage. Microstructure of the alloy after tensile testing was studied in detail. Phase transformations were analyzed employing thermodynamic modeling and their role in strain accommodation is discussed.

Adhesively Bonded Blanks for Local Reinforcements in Body-in-White Manufacturing

Adhesively bonded blanks are manufactured using a method for combined forming and bonding of locally reinforced parts for body-in-white in the automotive and truck industry. The method allows lightweight constructions with steel sheets by generally reducing the thickness of body parts and compensates stiffness as well as strength by steel grades of higher yield points and locally applied reinforcement sheets where necessary. Applying adhesive bonding in the body-in-white shops implies certain boundary conditions, such as bonding on oiled surfaces and curing at cataphoretic burn-in after coating. Adhesive bonding, with the forming process being employed between, was successfully applied with film adhesives based on different polymer families and works the best in two steps, as the formation of already bonded and cured parts causes much damage to the bond lines. Due to the early softening stage in the electro coat (EC) burn-in oven, the adhesive in most cases needs the assistance of an additional fixation technique to avoid negative results of unwanted spring-back behaviour (especially with reinforcement sheets with higher yield points). Efficient auxiliary techniques for fixation are usually not based on adhesive technology because of a process-related short time frame. Three different fixation techniques additionally to the adhesive bonding of the reinforcement sheets were investigated in a research project. This paper discusses options and results on the complex interaction between forming and adhesive bonding.

Effect of ultrasound on the characteristics of superplastic deformation

The deformation of aluminum–lithium alloy 1420 is investigated in the region of temperatures of its superplasticity T = 320–395°C under the simultaneous action of stretching load and axial ultrasonic vibrations. The estimates of the activation parameters of deformation show that the activation energy of deformation during stretching with ultrasonic vibrations and without them are close both at the stage of hardening and at the stage of softening. It is concluded that the ultrasonic vibrations facilitate intragranular deformation at the hardening stage and promote an increase in its contribution to the total deformation without changing the deformation mechanisms.