Hot deformation behavior and strain compensation constitutive model of equiaxed fine grain diffusionwelded micro-duplex TC4 titanium alloy

Can LI, Imran SARDAR MUHAMMAD, Lihui LANG, Yingjian GUO,Xiaoxing LI, Sergei ALEXANDROVA, Dexin ZHANG

School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

KEYWORDSConstitutive models;Deformation;Diffusion bonding;Micro-duplex;Titanium alloys

AbstractIn this work, two-stage diffusion bonding of micro-duplex TC4 titanium alloy was carried out to study the flow behavior and constitutive models of the bonding joint and the base metal after the same thermal cycling during the hot forming process.Microstructure and mechanical properties test were used to verify the good quality of the equiaxed fine grain diffusion-welded TC4 alloy.Quasi-static tensile experiment was carried out at temperatures ranging from 750–900°C and strain rates of 0.0001–0.1 s-1.The joint showed the weak dynamic recovery at strain rates of 0.01–0.1 s-1and temperatures of 750–850 °C.At strain rates of 0.0001–0.001 s-1and temperatures of 850–900 °C, the flow stress of joint presented steady-state characteristics.Different deformation conditions lead to the remarkable difference of dynamic softening performance between the joint and heat-treated base metal,but the flow stress in elastic and strain hardening stages exhibited similar behavior.The strain compensated Arrhenius-type constitutive models of TC4 joint and heat-treated base metal were developed respectively.The fifth-order polynomial functions between the material property correlation coefficients and strain were obtained.The models have shown good correlation, with correlation coefficient values of 0.984 and 0.99.The percentage average absolute relative error for the models were found to be 10% and 9.46%, respectively.

1.Introduction

Superplastic Forming and Diffusion Bonding (SPF/DB) process is one of the most important research subjects in the area-space engineering field.1–4The titanium alloy multi-layer hollow structure is an important application in SPF/DB for its high specific strength,light weight and integrated structure,especially titanium alloy hollow wide chord fan blade.5–7However, the traditional SPF/DB process still has some disadvantages, such as uncontrollable internal deformation, and excessive deformation in the superplastic process.8–9The failures of wide chord hollow titanium alloy fan blade frequently occurred in the service of aeroengines, most of which were related to metal fatigue.Some of the failures were due to fatigue cracks, originated in acute corners between the internal membrane and the convex panel10, which indicated the low fatigue strength of the joint.A new hybrid manufacturing process was proposed to get blank with internal cavity structure by diffusion welding and then conventional hot forming,creep forming.11–14This hybrid technology can fully reflect the advantages of easy control of shape and performance of titanium alloy in forming complex components.15

Diffusion bonding technology is increasingly used in aeroengines and various load-bearing components of aircraft.16The essence of diffusion bonding is that the interfacial pores are closed by atomic diffusion.Residual micropores with different size distributions on the interface are unavoidable.They are generally spherical holes with a radius of less than 1 um.At present,the best and most common method is to test the joint quality by strength and plasticity property test.17–19Researchers have focused on the diffusion welding process of titanium alloy.20–22The mechanical properties of the diffusion welded joint were also discussed.Zhao et al.23investigated the static strength and fatigue performance at different loading levels of the TC4 alloy double lap joint.Zhang et al.24investigated the strength and toughness of TC4 alloy diffusion bonding joint by tensile test and Charpy impact test.Du et al.25studied the interface characteristic and mechanical properties of diffusion bonding joint by nanoindentation and shear tests.Xu et al.26studied the microstructure evolution and hightemperature mechanical properties of laser-welded TC4/TA15 dissimilar alloy joint.

The material after diffusion bonding needs to undergo several heating and pressurizing cycles.Deformation and damage of diffusion-welded structure may occur during hot forming,which leads to reliability problems during the service life.It is worth emphasizing that most of the research are focused on the hot deformation behavior of TC4 alloy for different processing conditions and the constitutive models.27–28Intelligent modeling aims to perceive the relationship between input processing parameters and output forming results.It is the foundation for intelligent decision-making during the forming process.29The phenomenological constitutive equations,where the instantaneous stress can be calculated as a function of deformation parameter and material property,especially the Arrhenius-type constitutive equation, are widely used.30Lin et al.31investigated the deformation mechanisms and dynamic softening behavior of TC4 alloy with thick lamellar microstructures by uniaxial hot tensile tests.Feng et al.32studied the formability and flow behavior of the TC4 alloy via isothermal hot compression tests,and established the constitutive equations in different phase regions.Xia et al.33investigated the hot deformation behavior of Ti-6Al-4V-0.1Ru titanium alloy by isothermal compression tests,and developed the Arrhenius-type constitutive models for temperature ranges of α-β dual phase at strain of 0.1.

Although the Arrhenius-type equation in the form of hyperbolic sinehas been proved to have high accuracy, it ignored the influence of the strain on the flow stress, which is an important factor for determining the hot processing parameters.34Lin et al.35compensated the influence of strain by defining the Arrhenius-type model parameters as higherorder polynomial functions of strain.Xiao and Guo36added an exponential function of strain with Arrhenius model to compensate the effect of the strain.Liu et al.37investigated the elevated-temperature flow behavior of damage-tolerant Ti-6Al-4V (TC4-DT) titanium alloy by conducting isothermal hot compression tests and established Arrhenius constitutive equation considering the strain.Yang et al.38established the flow stress prediction model considering strain compensation during isothermal compression in α-β phase field of TC4 alloy.Lypchanskyi et al.39established the strain compensation model and analyzed the hot deformation behavior of β titanium alloy.

Few research on hot deformation behavior of diffusionwelded sheet was reported until now.Wang et al.40studied the formability and microstructure evolution of welding seam and matrix material in the hot gas forming of TA15 titanium alloy tubes.Yang41established the stress–strain relationship of diffusion welded joint of TC4 titanium alloy by nanoindentation combined with dimensional analysis and finite element simulation.Tang et al.42conducted a comprehensive study on the compressive deformation behavior and the microstructure evolution of the bonding interface of TiAl/Ti2-AlNb alloy joint.However, none of these studies investigated the hot deformation behavior of diffusion-welded TC4 titanium alloy for generating hollow structures, making it a focus of this study.The influence of welded joint on the forming and the performance of welded joint after hot deformation need to be carefully analyzed.If it is assumed that the distribution of micropore defects and the mechanical properties at the diffusion bonding interface are the same, the finite element simulation analysis of the forming process of the diffusion-welded hollow parts can be realized by establishing the constitutive model.43In this paper, the evolution of microstructure and mechanical properties of aviation-grade TC4 titanium alloy after diffusion welding as well as the complex hot deformation behavior were studied.Strain compensation constitutive model was established.It is of great significance to optimize the plastic deformation process and evaluate the mechanical properties of titanium alloy diffusion-welded hollow components.

2.Material and experimental procedures

The annealed and forged blocks of TC4 alloy were used as test material, being called base metal.The alloy was forged using plate die forging at 985 °C to a deformation of 40%.It was then annealed at 720 °C for 1 h followed by air cooling.The chemical composition (mass fraction) is shown in Table 1.

The two bonding blocks with the dimensions of 35 mm × 75 mm × 150 mm were prepared.The bonding surfaces were ground, ultrasonically cleaned in ethanol, and then dried.The bonding surfaces were connected with spot welding in advance to fix the relative positions of specimens to prevent staggered movement.Then, the assembled specimens were placed in the vacuum furnace.Diffusion bonding experiments were conducted in a vacuum of 5.0 × 10–3Pa and the blocks were heated to 900 °C for 1 h, then heated to 930 °C for 2 h.The bonding pressure of 2 MPa was applied.The average grain size of diffusion-welded micro-duplex TC4 titanium alloy was approximately 20 μm, as shown in Fig.1(a).The diffusionwelded part for hot forming consists of two areas, as shownin Fig.1(b).An additional group of TC4 base metal after the same thermal cycling condition during the diffusion welding process was prepared, which was called heat-treated base metal.

Table 1 Chemical composition of experimental alloy (mass fraction/%).

Fig.1 Equiaxed fine grain diffusion-welded micro-duplex TC4 titanium alloy.

Microstructures of the base metal materials and welded joint were observed by using an optical microscope (OM).The base metal specimens were cut from the TC4 titanium alloy annealed forging blocks.The joints were taken from the diffusion bonding specimens in the region that excludes the edge.The specimens were mechanically ground, polished,then etched with Keller reagent before the microstructural examination.Mechanical properties of the base metal and welded joint were tested at room temperature and 750°C/0.1 s-1.The tensile tests were conducted on an INSTRON SANS-100 KN universal machine.Three samples were prepared for each condition, and the test results were averaged.The fracture morphology was observed with a SU8020 scanning electron microscope (SEM).

To study the hot deformation behavior of the diffusionwelded joint and the heat-treated base metal, the hightemperature tensile tests were performed at temperatures of 750–900 °C and strain rates of 0.0001–0.1 s-1.The geometric dimensions of tensile specimens are shown in Fig.2(a) and the machined samples are shown in Fig.2(b).The tensile specimens were held at the testing temperature for about 10 min before the test.The temperature (T), strain rate (˙ε) and specimen elongation were used to obtain true stress–strain curves,which were automatically controlled and recorded by the computer system.

3.Results and discussion

3.1.Original microstructures

Fig.3 shows the duplex microstructure of the base metal and diffusion welded joint.It can be seen from Fig.3(a) that the TC4 base metal was an α-β duplex titanium alloy, composed of white elliptic or short clubbed α phase,and black strip intergranular β phase with interleaved distribution.The SEM image shows that the α phase was mainly distributed in the β phase, and the secondary α phase was distributed in the β phase matrix in Fig.3(b).It can be seen from Fig.3(c) that the volume fraction of the equiaxed α phase in the material after diffusion welding increased by more than 50%, while the short rod α phase decreased.The interface of the weld zone was analyzed.It can be seen that the weld grains were combined in metallurgical form and the trigonal grain boundary was formed.The metallography of other regions also shows the same phenomenon.

3.2.Mechanical properties and fracture morphology

As shown in Fig.4(a)and(b),at room temperature,the tensile strength (σb) and elongation of base metal were 1049.7 MPa and 5.1%, respectively.The tensile strength and elongation of welded joints were 1023 MPa and 4.8%, respectively.At 750 °C, the tensile strength and elongation of the base metal were 379.5 MPa and 9.6%, respectively.The tensile strength and elongation of the welded joint were 372.3 MPa and 4.4%, respectively.

Fig.5(a) and (b) show the tensile fracture morphology of the base metal and welded joint at room temperature, which consisted of fiber zone, radiation zone and shear lip zone.The fibrous area was rough and uneven with many fibrous peaks.The SEM images show a mass of round dimples of different sizes distributed on the fracture surface.The failure mode was a typical ductile fracture in the fiber zone for both the materials according to Fig.5(c) and (d).

The tensile mechanical properties of the joint at room temperature were close to those of the base metal.At present, the quality of welded joints was evaluated by the metallographic structure and mechanical properties at room temperature.So, it can be concluded that the diffusion welded joints show good bonding quality.The diffusion welding went through a process of close contact,plastic deformation,element diffusion and reaction, and micropore elimination at the interface.

Fig.2 Uniaxial tensile specimen (unit: mm).

Fig.3 Microstructure images.

The tensile fracture morphology under 750°C/0.1 s-1of the base metal and welded joint are shown in Fig.6.The plasticity of the base metal was greatly improved with increasing the deformation temperature.The cross-sectional necking area in Fig.6(a) was far less than that in Fig.5(a), and the shear lip area almost disappeared.It can be seen in Fig.6(b) that the dimples of the fracture were large and deep.

It can be observed from Fig.6(c),(d)that the fracture morphology was smooth and almost had no necking in the thermal environment for the welded joint.The weak joint zone with elliptic depression was discovered on the section, with only a few shallow dimples, and the plasticity decreased compared with that at room temperature.This is due to the residual micropores that could not be completely avoided on the interface after diffusion welding.At the final stage of the diffusion bonding, grains are formed across bonding interface because of the grain boundary migration and volume diffusion.There are still some small and round voids at the interface,as shown in Fig.7(a).Some very few and tiny voids at the bonding interface were found, as shown in Fig.7(b) and (c).Actually, it is difficult to observe all these voids because of the sizes less than 1 um.Maybe the effect of these tiny voids on mechanical properties at room temperature is negligible.However,its influence on high temperature mechanical properties is obvious, and stress concentration is more easily formed in the voids area under thermal activation.It can be seen that thermal loading has great influence on the plasticity of the weld, and the weld seam of the diffusion welded joint can be the weak zone of diffusion bonding sheet at high temperature.Therefore, it is necessary to study the flow stress behavior of diffusion welded joints during hot forming and service after hot forming.

3.3.Flow behavior of TC4 diffusion welded joint and heattreated base metal

Fig.4 Tensile properties of TC4 alloy before and after diffusion welding (strain rate 0.1 s-1).

Fig.5 Tensile fracture morphology at room temperature of TC4 base metal and welded joint.

Fig.8 shows the true tensile stress–strain curves of microduplex TC4 diffusion welded joint and heat-treated base metal at temperatures ranging from 750–900 °C and strain rates of 0.0001–0.1 s-1.It can be seen that the flow curve can be roughly divided into elastic and strain hardening stage before peak stress and softening stage after peak stress.The flow stress abruptly increased to the peak at hardening stage,which might result from the rapid accumulating dislocation.The sufficient driving force for flow softening can be provided by accumulating dislocation energy, i.e., via dynamic recovery and dynamic recrystallization mechanisms.44Temperature and strain rate have a significant effect on the flow stress of joint and heat-treated base metal.Under all deformation conditions, the flow stress curves of the joint at the hardening stage are close to that of the heat-treated base metal,indicating that the influence of the joint interface can be ignored in the hardening process.

Fig.6 Tensile fracture morphology at high temperature of TC4 base metal and welded joint.

At the strain rates of 0.01–0.1 s-1and the temperatures of 750–850 °C, the curves of the joint showed an obvious strain hardening phenomenon before reaching the peak, and broke soon with almost no necking effect, as shown in Fig.8(a)–(c).Because the micropores left during diffusion welding were easy to form stress concentration when the strain accumulated to a certain extent at lower temperatures and higher strain rates.The polymerization directly led to the deformation can not continue, and the tensile parts fractured at the welding interface.At the temperature of 900 °C and the strain rates of 0.01–0.1 s-1, the stable deformation stage began owing to the occurrence of small neckings, as shown in Fig.8(d).At the strain rate of 0.001 s-1, the stable flow softening stage appeared until the temperature reached 850 °C.It is worth mentioning that the softening flow stage can be maintained for a long time at the strain rate of 0.0001 s-1under all temperatures for the joint as shown by the green lines in Fig.8.With the increasing temperature and the decreasing strain rate, the influence of strain hardening gradually decreased,and the softening effect became dominant.It should be explained according to the competition mechanism between hardening and softening of titanium alloy during hot deformation.It is the same for the joint and heat-treated base metal.This is because higher temperatures supply higher mobilty at boundaries for the nucleation and the growth of dynamically recrystallized grains and dislocation annihilation and thus result in the flow softening.45Lower strain rate slowed down the dislocation velocity and provided enough time for the deformation energy storage.The softening effect was greater than the hardening effect,and the flow stress was reduced.The steady-state of flow stress appeared as strain increasing due to the banlance between strain hardening and dynamic softening.

The above analysis of tensile behaviors suggests that the deformation behavior of the joint is different from the normal heat-treated base metal.The experimental curves show that the cross-sectional shrinkage caused by the necking of the joint was far less than that of the heat-treated base metal, which showed weak plastic processing performance.So it is not recommended to carry out hot forming of diffusion-welded sheet at strain rates ranging from 0.0001–0.1 s-1at 750 °C and 800°C.When the deformation temperature was 850 °C, the dynamic softening curve of the diffusion welded joint was closer to that of the heat-treated base metal at the strain rates of 0.0001–0.001 s-1.Based on the shapes of all the true stress-true strain curves at 900°C,it can be observed that the distribution of these curves of joint almost coincided with that of the heattreated base metal under different strain rates.The effect of interface on thermal deformation behavior of diffusionwelded TC4 alloy can be completely ignored.

To further analyze the elastic and strain hardening stages before reaching peak stress of the base metal and diffusion welded joint, the comparison curves of Young’s modulus(E), yield strength (σ0.2) and tensile strength are shown in Fig.9(a)–(d).It can be seen that the values of the aforementioned properties of both materials gradually decreased with the increasing deformation temperature and the decreasing strain rate.Even at lower temperatures and higher strain rates,there are only small differences in the material properties.

Fig.10 shows the optical microstructure of the area near the fracture of the diffusion welded joint and heat-treated base metal at 750 °C, 0.1 s-1.It can be seen that the grains had almost no deformation in Fig.10(a).This further explains the weak plasticity of the joint.But the heat-treated TC4 base metal still showed obvious grains deformation in Fig.10(b).The grains were elongated along the direction of deformation.

Fig.7 Residual micropores after diffusion welding.

3.4.Constitutive model and error analysis

3.4.1.Polynomial strain compensated Arrhenius-type model

In general,the TC4 diffusion welded joint was considered as a single unit under classical deformation conditions,46ignoring the contributions of the interface.However, the important characteristics of the joint,such as the hot deformation behavior and the impact induced by the bonding interface, will be covered up if taking the joint as a single in the phenomenological model.To get an overall consideration of the deformation behaviors of TC4 base material and interface in the joint during the hot tensile process, the constitutive model was proposed and validated in the present work.

According to Zener and Hollomon,47the Zener-Hollomon parameter (Z) can be expressed as.

where the deformation temperature T（K ）=T（C ）+273.15,ΔH (J ?mole-1) is the hot deformation activation energy, and Rgis the universal gas constant with value 8.314J ?mole-1K-1.Sellars and McTegart48established the relationship between flow stress (σ), temperature, and strain rate using Arrhenius-type equation as follows:

where X1, X2, X3, n1, n2and α are the fitting parameters.β characterizes the stress level, and is defined as β=α/n1.The hyperbolic sine form of Eq.(2)is applicable over a wide range of stress conditions, and is used to determine the flow stress.49Combining Eqs.(1)–(2) and rearranging, flow stress can be related to Zener-Hollomon parameter as.

Lin et al.35incorporated the effect of strain rate into Arrhenius-type equation by defining the material constants β, X3, n2and ΔH as higher-order polynomial functions of strain,obtained from the fitting of experimental data.For this study,the fifth-order polynomial, defined by Eq.(4), was chosen as it represented the influence of strain(ε)on material constants with very good correlation and generalization.

The parameters of Arrhenius-type constitutive model (β,X3, n2and ΔH) were determined for the strains ranging from 0.03 to 0.20.The Arrhenius model parameters were given in Table 2.Using the polynomial fitting approach to the data in Table 2, the coefficients of polynomial Eq.(4) were determined which are given in Table 3.

Combining the stress–strain results of micro-duplex TC4 welded joint and the heat-treated base metal shown in Fig.8,the Arrhenius-type constitutive models were established,respectively.Fifth-order polynomial functions of equiaxed fine grain TC4 diffusion welded joint are given by.

Fig.8 True stress–strain curves of TC4 diffusion welded joint and heat-treated base metal at various strain rates and temperatures.

Fifth-order polynomial functions of the heat-treated base metal are also given by.

3.4.2.Model validation

The modified Arrhenius-type constitutive equation considering the compensation of strain, strain rate and temperature was used to predict the flow behavior of TC4 diffusion welded joint in the process of hot forming.The experimental and predicted true stresses against the true strain at different temperatures and strain rates are plotted in Fig.11.Standard statistical parameters such as average absolute relative error (AARE)and correlation coefficient (R) to quantify the validation of the model can be expressed as.

where Eiand Piare the experimental and predicted flow stresses,respectively.E-and P-are the mean values of Eiand Pi.N is the total number of data points used in the study.R defines the linear correlation between experimental and predicted curves with possible values ranging from –1 to 1.A higher value closer to 1 would mean a better correlation.

Fig.9 Mechanical properties of TC4 diffusion welded joint and heat-treated base metal at various strain rates and temperatures.

Fig.10 Optical microstructure of TC4 diffusion welded joint and heat-treated base metal at 750 °C, 0.1 s-1.

As can be seen from Fig.11(a)–11(d), the model has successfully predicted the influence of strain rate, temperature and strain on deformation behavior of the diffusion welded joint, under different deformation conditions except at 800 °C-0.01 s-1, 800 °C-0.001 s-1and 850 °C-0.01 s-1.The model has shown a good correlation, with an R-value of 0.984.However, a higher value does not necessarily mean a better model performance as the tendency of the equation could be biased towards higher or lower values.46The AARE,which is an unbiased statistical parameter for determining the model’s predictability, was found to be 10%.As can be seen from Fig.12(a)–(d), for the model of the heat-treated base metal, the R-value was found to be 0.99, showing a good correlation between the experimental and predicted flow stress.The AARE was 9.46%.So, the polynomial strain compensated Arrhenius-type models established for TC4 diffusionwelded joint and heat-treated base metal exhibited good predictability, especially at lower strain rates under all deformation temperatures.

Table 2 Values of β, lnX3, n2and ΔH at different strains for the joint.

Table 3 Fifth-order polynomial coefficients for β, lnX3, n2and ΔH for the joint.

Fig.11 Comparison between experimental and predicted true stress–strain curves for welded joint.

Fig.12 Comparison between experimental and predicted true stress–strain curves for heat-treated base metal.

4.Conclusions

(1) The average static tensile strength and elongation of the equiaxed fine grain micro-duplex TC4 diffusion-welded joint at room temperature were 1023 MPa and 4.8%,reaching 97.5%, 94.1% of the base metal respectively.However, at elevated temperatures, the weld seam become the weak fracture zone.

(2) At 750 °C/0.1 s-1, the TC4 diffusion welded joint had almost no plastic deformation compared to the obvious grain elongation of the heat-treated TC4 base metal.The joint showed weak dynamic softening performance at 750–850 °C/0.01–0.1 s-1, and presented steady-state characteristics at 850–900 °C/0.0001 s-1.Increasing the deformation temperature and decreasing the strain rate,the dynamic softening curve of the joint comes closer to that of the heat-treated base metal.

(3) Under all deformation conditions,the flow stress curves and mechanical property parameters of the joint at the hardening stage were close to that of the heat-treated base metal, indicating that the influence of the joint interface can be ignored in the hardening process.

(4) The strain-compensated Arrhenius constitutive equation is used to describe the hot deformation behavior of the TC4 welded joint and the heat-treated base metal.The models have shown good correlation between the experimental and predicted flow stress.For the prediction model of the welded joint, the R value was 0.984, and the AARE was found to be 10%.For the model of the heat-treated base metal, the R value was 0.99, and the AARE was 9.46%.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (No.51675029).