Deformation of titanium alloys under dynamic compression



Deformation of titanium alloy Ti-6Al-4V under dynamic compression

Qite Zhaoa, Guoqing Wua, Wei Shab,*

aSchool of Materials Science and Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China

bSchool of Planning, Architecture and Civil Engineering, Queen’s University Belfast, Belfast BT7 1NN, UK

*Corresponding author.

Telephone +44-28-90974017; fax +44-28-90974278; e-mail w.sha@qub.ac.uk

Abstract

Deformation localisation is the main reason for material failure in cold forging of titanium alloys and is thus closely related to the production yield of cold forging. Recent research has revealed that the width of shear band of titanium alloys after dynamic compression is related with their static and dynamic mechanical properties and processing parameters. To explore the influences of these factors on titanium alloys in dynamic compression, the distributions of stress, strain, strain rate and temperature of the specimens over the macro and micro scales have been systematically studied. This work can be beneficial to process parameter optimisation and material designing for cold forging. In the study of the influence of process parameters on dynamic compression, considering material constitutive behaviour, physical parameters and process parameters, a numerical dynamic compression model for titanium alloys has been constructed. The entire dynamic compression process is simulated and a good agreement with experiments is observed. By extracting and comparing the stress, strain and temperature distribution under prescribed conditions, the effects of friction and compression velocity on the macro state and distribution of strain and stress of compression samples are studied. Friction and compression rate are important factors influencing the spread and the stress state of deformation localisation zone. When friction is reduced to a certain level, deformation localisation can be effectively alleviated. The increase of friction and compression rate can lead to early appearance of tension stress in the deformation localisation zone, which may explain the experimental finding that crack tendency increases with higher compression rate and poorer lubrication. By adjusting the process parameters, the severity of strain localisation and stress state in the localised zone can be controlled thus enhancing the compression performance of titanium alloys.

Keywords: forming; constitutive behaviour; elastic-plastic material; metallic material; finite elements

1. Introduction

Deformation of titanium alloys under dynamic compression is a topic under extensive research at present. Some very recent studies are by Cui et al. [1] and Gong et al. [2]. Friction is the cause of inhomogeneous deformation during metal forming, resulting in excessive wear of the forming tools such as dies and rollers. During compression process, depending on the distribution of friction force and the geometry of the material part being compressed, several deformation regions exist from mechanics analysis of the process. These are elastic, stiff region, active deforming region, and passive deforming region. The existence of these different types of regions within a work piece causes inhomogeneous deformation in it. The compression rate and degree (i.e. amount) are important. At high compression rate and degree, much heat is generated during compression, significantly changing the flow behaviour of the material. In addition, the compression rate affects the strain hardening behaviour of the material, again influencing the deformation. Titanium alloys have low thermal conductivity. Therefore, the temperature increase, and therefore material softening, due to deformation are more significant than in other alloys. These encourage localised deformation, which is the major mechanism of material failure during high rate deformation [3]. Therefore, it is vitally important to study and understand the effects of friction, and compression rate and degree during the dynamic deformation process of titanium alloys.

2. Analysis of existing work

There have been many experimental studies on the effect of friction coefficient on the materials behaviour during compression deformation and their formability. Concerning the effects of compression rate and degree, studies have been concentrated on the materials microstructure and resistance to deformation. Luo et al. [4] studied the effect of strain on the formability of titanium alloys at isothermal, elevated temperatures. Venugopal et al. [5] studied the effects of compression rate and degree on the formability of commercially pure titanium. Lee et al. [6] studied the influence of temperature and strain rate on the flow stress of titanium alloys. These experimental studies, however, did not conclusively elucidate the controlling factor of the compression processing parameters in the dynamic compressive deformation of titanium alloys. Because the localised deformation is the main mechanism of titanium alloy failure during dynamic processing, it is a major factor determining the formability of these alloys. Therefore, using computer modelling to investigate the effects of friction coefficient, and compression rate and degree on the extent of deformation localisation is potentially significant in that it can provide physical insight of the process over and above what can be revealed through different testing data.

Based on the constitutive testing data, this paper will establish a numerical model for the dynamic compression process of titanium alloys, using DEFORM software. Using the model, the evolution of the stress field, strain field, strain rate field, and the temperature field of the Ti-6Al-4V (Ti64) alloy during room temperature dynamic compression is simulated, for different processing parameters. Some outline of the modelling was given in a previous publication by Wu and Sha [7]. The aim is to reveal and evaluate the effects of different processing parameters on the compression process of the titanium alloys. The affecting patterns of the processing parameters on the dynamic compression are discussed, with the aim of providing a scientific basis for developing a technology of minimising the localised deformation and fracture of titanium alloys during cold deformation. This work is a continuation of the extensive modelling work on microstructure, properties and applications of titanium alloys [8].

3. Theory and calculation

Materials model setting up, in the main, requires knowledge of constitutive relations and materials property parameters. A constitutive model needs to include consideration of the effects of temperature and compression rate on the flow stress of the material, reflecting the dynamic nature of the compression. The chosen constitutive model in this work is the Khan-Huang-Liang (KHL) model. The materials property parameters under consideration include, as functions of the temperature, elastic modulus, heat capacity, and thermal conductivity. During simulation, the thermal expansion coefficient and the Poisson’s ratio were considered constants.

3.1. The constitutive model of titanium alloys under the condition of dynamic compression

The constitutive model shows the relationship among the flow stress, strain, and temperature of the deforming material. In practice, this model determines the choice of deformation temperature and loading parameters, and the capacity of the deformation equipment requirement. Two types of constitutive model have been applied for the deformation of titanium alloys, the Johnson-Cook (JC) model (Eq. 1) and the KHL model (Eq. 2):

[pic] (1)

[pic] (2)

where σ is the stress, ε is the plastic strain, Tm, Tr and T are melting point temperature, reference temperature (20 °C), and the local material temperature, and [pic]= 106 s-1. The other parameters need to be obtained through fitting.

For the fitting of the constitutive relations for the Ti64 alloy, we have adopted the KHL constitutive equation, following Khan et al. [9]. The fitted parameters from the present work are all within the ranges validated for this equation, and are given in Table 1. The fitting curves are shown in Fig. 1. This figure is reproduced from [9]. The solid lines are results of numerical simulation using material law of Eq. 2 and including the thermal properties. In the solid lines, adiabatic thermal softening is considered by converting the increment of temperature from the stress–strain curve using following equation:

[pic] (3)

where β, ρ, Cp are the fraction of heat dissipation caused by the plastic deformation, mass density and specific heat at constant pressure, respectively [9]. In this way, the temperature increase is computed numerically and not analytically, and is considered in Eqs. 1 and 2.

Table 1. KHL constitutive model parameters for the Ti-6Al-4V alloy

|Parameter |A (MPa) |B (MPa) |C |n1 |n0 |m |

|Value |1069 |874.8 |0.02204 |0.5456 |0.4987 |1.3916 |

[pic]

(a)

[pic]

(b)

Fig. 1. The KHL constitutive model fitting results for the Ti-6Al-4V alloy. Symbol: experiments; solid line: correlations with KHL model. (a) Varying strain rate at a fixed temperature of 23 °C; (b) varying deformation temperature at a fixed strain rate of 10-3 s-1 [9].

From the fitting results and their comparison with the experimental data, the KHL model fitted to the constitutive relations for Ti64 agrees well with the experiments in large data ranges, but the difference is big at low temperatures and high strain rates.

The present paper will carry out simulations of the Ti64 alloy in wide strain rate ranges. In the software, when inputting constitutive equation tables for this alloy, parameters within the DEFORM package were used for strain rates lower than 10 s-1. For higher strain rates, the KHL equation fitting data from the above fitting were inputted.

3.2. Material parameters of the titanium alloys

The material parameters for the Ti64 alloy used in the simulation are listed in Table 2.

Table 2. Thermal physical properties of the Ti-6Al-4V alloy [10].

|Temperature (°C) |Heat capacity |Thermal conductivity |Thermal expansion coefficient|Elastic modulus |Poisson’s ratio |

| |(J/kg.K) |(W/m.K) |(10-6 K-1) |(GPa) | |

|20 |- |8.37 |- |117.00 |0.31 |

|100 |678 |8.79 |7.89 |- |- |

|200 |691 |9.79 |9.01 |106.80 |- |

|300 |703 |10.47 |9.10 |- |- |

|400 |741 |12.56 |9.24 |95.08 |- |

|500 |754 |14.24 |9.39 |- |- |

|600 |879 |15.49 |9.40 |82.68 |- |

The low thermal conductivity of titanium alloys is the reason for localised deformation of these alloys. It is much lower than other materials, comparing with, for examples, the thermal conductivity of mild steel, aluminium and copper at, respectively, 48.5, 230 and 371 W/m.K, all at 300 °C.

3.3. The geometrical model and boundary conditions

In the model, cylindrical symmetry is assumed of the specimen, as an elastic-plastic body. The dies are assumed elastic bodies. The specimen dimension is 4 cm diameter and 6 cm in length. Due to the cylindrical symmetry, the model can be simplified to two dimensional, illustrated in Fig. 2. The loading direction is downward from the top die. The maximum penetration depth between the dies and the specimen is 2.5 μm.

[pic]

Fig. 2. Dynamic compression of the titanium alloys. I and III: die; II: specimen. “b” is the symmetry axis and “a” is free surface.

The mesh quality of the deforming body affects significantly the accuracy of the calculations. Therefore, this mesh quality must be maintained throughout the metal forming simulation process. The quality control is achieved through the initial mesh generation and regeneration. Due to the possibility of various and complex shapes of the forging parts and the large deformation capability of metals, regeneration of mesh during deformation is a research hot topic in finite element modelling of metal forming.

DEFORM is a finite element software package for analysing metal deformation, in particular cold, warm, and hot forging deformation coupled with heat conduction analysis. It contains a large data bank of material parameters, including steels, aluminium alloys, titanium alloys, and superalloys. Using a user-defined data bank, the user can input material parameters for materials not included in the package data bank. The software can be used to calculate material flow, mould filling, load bearing during forming, die stress, fibre flow direction, defect formation, and ductile fracture processes. Material models include rigid, elastic, and viscoplastic models, and thus the software is suitable for analysing large strain deformation processes. Mesh and node tracing allows the flow information and the field distribution inside the material to be followed. The field includes temperature, strain, stress, and damage. The easiest way to illustrate such distribution is usually using contour plots. Remeshing capability means that the simulation can be completed even after defects are formed in the material.

The DEFORM software has built-in rules and capability for automatic mesh regeneration, and it is convenient to set up model parameters through a user interface. When the mesh distortion exceeds any of the rules and the calculation cannot continue, the system can automatically regenerate a new set of mesh, and pass the solution information from the old mesh to the new mesh using automatic interpolation. For typical meshes, the software regenerates a mesh every 10 to 20 time-steps. In this work, because we are interested in localised straining, mesh regeneration is carried out once strain reaches just 4%. In the beginning, equal size mesh is used. In the subsequent automatic mesh regeneration, the total number of mesh remains unchanged, but the parameters are set such that the mesh density is increased in areas of high strain or high strain rate.

The first boundary condition is the temperature boundary condition. The top and bottom dies are assumed to be thermally conducting elastic bodies, and have the same initial temperature as the initial temperature of the specimen work piece. During metal plastic deformation, the specimen loses heat to the environment through its free surface, via convection as well as radiation. According to the heat transfer theories, convection heat can be expressed as:

qc = hc(T – T()

where hc is the heat transfer coefficient and T( is the environment temperature. During plastic deformation, the specimen may also dissipate heat to the air through radiation. Radiation heat exchange follows the Stefan-Boltzmann law:

qr = σε (T4 – T(4)

where σ is the Stefan-Boltzmann constant, ε is the emissivity of the grey body; if it is a perfect blackbody, ε = 1. During hot deformation, there should be temperature difference between the die and the work piece, so there is heat loss through the contact interface. This heat exchange at the interface includes the heat conduction through the real contacting points, heat conduction through contacting medium, and heat radiation through the gaps between contacting surfaces at the high temperature. These are very complicated heat transfer mechanisms. The present modelling work is concerned with room temperature compression, though the temperature inside the work piece can reach well above it. This source of heat exchange is simplified as following the formula:

qd = hlub(T – Td)

where hlub is the heat transfer coefficient of the lubricant. Td is the die temperature at the contact interface, taken as 20 °C in calculations. At the same time, there is relative sliding movement between the work piece and the dies, accompanied by friction forces. This friction force can convert to heat, and heat up the work piece. The heat due to friction is:

[pic]

where f is the friction force and vr is the relative sliding speed. In this paper, in the Ti64 alloy, the deformation strain energy can convert to heat, with a conversion efficiency of 0.9. The die-work piece friction induced heat is assumed to equally divide between the work piece (i.e., the specimen) and the dies.

The velocity boundary conditions are set as follows. In Fig. 2, side “b” is the symmetry surface and side “a” is the free surface. The bottom die III does not move during the deformation. The top die I is given a fixed speed. Dynamic compression involves heat conduction of the material, which is not a linear function of time. In the paper, we will use compression speed (also referred to as compression rate) rather than strain rate to quantify the deformation rate.

The friction is defined through the contacting face between the dies and the work piece.

4. Results and discussion

From mechanics analysis, the friction between the specimen and the dies leads to the change of specimen shape to drum-shape. On the equator of the drum shaped specimen, additional tensile stress will develop, leading to the coexistence of shear region and tensile region in the specimen. Dynamic loading results in temperature increase in the specimen, leading to its softening, which, in turn, makes the localised deformation more severe (Fig. 3) [11]. The diagonal region is the strain concentrated area. For cylindrical specimens, the localised deformation zone is along the diagonal region, which is also the material fracture location. Fig. 4 shows, in a macroscopic level, simulation result of titanium alloy specimens after dynamic compression. Good agreement is achieved with the experimental compression test results shown in a previous paper [7], which used carbon flake for lubricant. Its friction coefficient is approximately 0.3.

[pic]

Fig. 3. The stress distribution during dynamic compression [11]. Because there is cylindrical symmetry, the inclined plane, and thus the fracture direction, shown in the diagram can be in any direction along the circumference.

The effective strain is used in Fig. 4. The difference between effective stress and stress and between effective strain and strain will be explained here. There are six component of stress, σx, σy, σz, γxy, γyz, γzx. In tensile or compressive testing, these are usually used, which are obtained by dividing load by area. Sometimes true stress is used, considering the change of cross section area during deformation. The effective stress is usually used in the micro scale, and it represents the combined effect of these stresses. It is defined as σeffective = [pic]. The effective strain is defined in the same way.

[pic][pic]

Fig. 4. Effective strain contour distribution simulation result of Ti64 titanium alloy after dynamic compression. Cylindrical symmetry is maintained, which is only broken after destabilisation, i.e., at shear fracture. Shear fracture is not the subject of simulation in this paper, as this paper only simulates deformation before shear fracture. Compression rate 40 mm s-1, deformation degree 42.3%, friction coefficient 0.3.

Constant compression rate was used in the experiments. This, coupled with the fact that strain rate does not reflect the influence of the specimen dimension on the nonlinearity of thermal conduction, justify the choice of using compression speed and not the strain rate to quantify the speed of straining in the contents that follow in this paper. There are three blocks of the modelling work: the effect of friction coefficient on localised deformation; the effect of compression speed on localised deformation; and the effect of compression degree on localised deformation.

4.1. Effect of friction coefficient on the extent of localised deformation

Friction is the major cause of localised deformation, usually more significant than the effects of compression speed and degree. Therefore, it is important to understand its effect. In addition, friction is the cause of die wear during materials forming. In this section, based on the model, the effect of friction coefficient on the dynamic compression process of the Ti64 alloy is analysed. The friction coefficient is varied between 0.05 and 0.6 in the simulations, which are carried out for three different compression rates. The deformation degree is 42.3% unless otherwise specified.

In order to reveal of friction effect on the stress and the strain in the localised deformation zone, we will examine the simulated strain and strain rate in a specific location in the specimen. These are extracted from the three nodes in the specimen at approximately 4/5th in height having maximum effective strain, when the specimen deformation degree is 42.3%. Visually, the location is in the white box shown in Fig. 4. The averaging results from the three node points, as functions of friction coefficient, are shown in Fig. 5.

[pic]

Fig. 5. The extent of localised strain in the localised strain region as functions of friction coefficient.

As can be seen, with increasing friction coefficient, at the specific, fixed location, the degree of strain localisation increases rapidly in the beginning, reaching a maximum when the friction coefficient is 0.3, 0.2 and 0.15 for the compression rate of 250, 200 and 300 mm/s, respectively. This reduces slightly afterwards, but changes into a new fluctuation mode when the friction coefficient is greater than 0.4. If we examine the specimens with relatively large friction coefficients, two high strain rate bands are evident in the later stages of deformation. High strain rate occurs along both the new and the old diagonal directions (Fig. 6). This is confirmed by the experimental observation of titanium alloys after ambient temperature dynamic compression, which has found “double shear bands” in some samples under the same compression speed (Fig. 7). Also corresponding to Fig. 6, when the friction coefficient is relatively small, simulation results show only one high strain rate band (Fig. 8).

It should be noted that localisation has different stages, and what we are simulating here is the stable localisation process, i.e., before its eventual consequence of fracture. It should also be noted that the simulation is for tendency only, due to the difficulty in obtaining parameters needed for quantitative comparison, at this stage of the research. The double shear band has been observed experimentally, but is difficult to explain. It is usual for modelling work to start with qualitative simulation, and the numerical model should be judged in a qualitative sense. It should be noted that single shear band is more common, and double shear band only happens in certain conditions.

[pic] [pic] [pic] [pic][pic]

(a) (b) (c) (d)

Fig. 6. Strain rate bands distribution during dynamic compression, for friction coefficient of 0.3 and compression speed of 250 mm/s, at different deformation degrees: (a) 30%; (b) 33%; (c) 36%; (d) 42%.

[pic]

Fig. 7. Double shear bands phenomenon in a test sample of a Ti-3Al-4.6Mo-4.9V alloy. Friction coefficient approximately 0.3, compression speed 250 mm/s.

Here, we will discuss the difference between the high strain rate band and the high strain band. Strain is the integration of strain rate with respect to time. In this paper, in order to analyse the shear band, which is a high strain band, we differentiate the strain and analyse the resulting high strain rate band. The simulation results show that the high strain rate band moves during deformation. Therefore, the high strain rate band is not the same as the high strain band. The reason for the second shear band is the movement of the high strain rate band. Therefore, analysing high strain rate band in isolation, without considering its movement, cannot explain the entire shear band phenomenon.

Comparing Figs. 6 and 8, it can be seen that with a large friction coefficient, the second high strain rate band enlarges the strain concentration region. To a certain extent, this helps reducing the further strain concentration. The development of double high strain rate bands may the reason behind the double shear bands found in some test specimens.

[pic] [pic] [pic] [pic][pic]

(a) (b) (c) (d)

Fig. 8. Strain rate bands distribution during dynamic compression, for friction coefficient of 0.1 and compression speed of 250 mm/s, at different deformation degrees: (a) 30%; (b) 33%; (c) 36%; (d) 42%.

With increasing friction coefficient, the drum shape development of the specimen is stronger, because the deformation at the specimen contact face with the flat dies is more difficult. When the difference in the deformation degrees of the contact face and the cylinder specimen body is large enough, the deformation concentration region will move to the new diagonal lines. This reduces the extent of the localised deformation in the original deformation concentration region. Simulation has found that the new high strain rate band is always to the right hand side of the old high strain rate band. In order to study whether the strain concentrated region, as represented by the shear band, has a fixed diversion direction, we examine the strain-time curves at three locations in the deformation concentrated region in the specimen, from left to right at the same height of 4/5th of specimen height. The result is shown in Fig. 9.

[pic]

time (s)

Fig. 9. Strain as a function of deformation time at different locations at the same specimen height in the high strain band. Friction coefficient 0.2.

It can be seen that the sequence of effective strain occurring does correspond to the horizontal locations within the high strain band. The strain concentration regions spread from left to right. When the friction coefficient is relatively small, with the progress of deformation, the strain concentration regions moves to the right continuously. When the friction coefficient is relatively large, and when such gradual movement cannot satisfy the deformation stress condition and geometrical compatibility, it becomes possible to form a new high strain rate area along the new diagonal line, broadening the strain concentration region. When deformation reaches a certain level, even double shear band can happen. When the friction coefficient is greater than 0.4, possibly due to the effect of friction-generated heat on material deformation, some irregular fluctuation is apparent.

4.2. Effect of compression rate and degree on the extent of localised deformation

In the simulations shown below, the friction coefficient and the deformation degree are fixed at 0.2 and 42.3%, respectively, unless otherwise specified. The macroscopic simulation results of the Ti64 alloy when the compression rate varies between 0.5 and 350 mm/s are shown in Fig. 10.

[pic][pic] [pic][pic] [pic][pic]

(a) (b) (c)

[pic][pic] [pic][pic]

(d) (e)

Fig. 10. Effective strain distribution under different compression rate. Friction coefficient 0.3. (a) 0.5 mm/s; (b) 5 mm/s; (c) 25 mm/s; (d) 200 mm/s; (e) 350 mm/s.

As can be seen from the figure, the compression rate has a significant effect on the deformation at macroscopic level. The increase of compression rate causes increasing extent of localised deformation. This is because with the increase of compression rate, it is harder for the material deformation generated heat to dissipate. The accumulation of heat causes material softening, which in turn accelerates the localised deformation. However, because the Ti64 alloy has a relatively high strain-hardening rate, when the compression rate is over 100 mm/s, the localised deformation does not continue to increase with the compression rate, but instead is partially relieved.

In Fig. 10c, at the top and bottom edges of the specimen, small ears appear. This is because the material sliding along the strain concentration band resulted in the bending of the top and bottom of region II (Fig. 10d) at their contact with the dies. The formation process of the ears is shown in Fig. 11.

[pic] [pic] [pic] [pic]

(a) (b) (c)

[pic] [pic] [pic] [pic]

(d) (e) (f)

Fig. 11. The formation process of ears of Ti64 during dynamic compression. Compression rate 75 mm/s. Friction coefficient 0.2. Compression degrees are (a) 24.5%, (b) 27.9%, (c) 32.1%, (d) 37.2%, (e) 39.8%, and (f) 42.3%.

As shown in Fig. 11, the formation of the ears starts at the compression degree of 32%. No such ear structure is found when the compression rate is smaller than 20 mm/s or larger than 100 mm/s, confirming that localised deformation is under control in these two ranges.

In order to more fully examine the effects of compression rate on the material deformation behaviour especially the degree of localised deformation, we now compare the average effective strain values at three nodes having the maximum effective strain at 4/5th height (Fig. 12).

[pic]

compression rate (mm/s)

Fig. 12. The effect of compression rate and degree on the extent of localised deformation during compressive deformation of Ti64.

From Fig. 12, with increasing compression rate but within the range of 0-50 mm/s, the localised deformation rapidly intensifies. It can be reasoned that, within this range, the titanium alloy softening due to local temperature increase caused by compression dominates. However, with further increase of the compression rate, the extent of localised deformation first fluctuates at high levels, followed by a decreasing trend.

In order to find a reason for this phenomenon, we now analyse the strain rate of the different specimens under different compression rate, shown in Fig. 13. As can be seen from Fig. 13, at low compression rate conditions, there is only one high strain rate band. When the compression rate is relatively high, however, there are two high strain rate bands. This is similar to the effect of friction, albeit the latter effect is mainly on the shifting of the stress concentration regions. The expansion of region I in Fig. 10d causes the areas under both shear and tension to move towards the right. With increase in the compression rate, the stress concentrated areas will move. In addition, when the rate is large, the strain hardening effect of the material increases, strengthening the weak region in the original strain concentrated region. When these effects combine, at high compression rates, there will be two high strain rate bands in the specimen. After examining the distance separating the two high strain rate bands, it can be concluded that the effect of compression rate on the degree of strain concentration is much larger than the effect of the friction coefficient.

This last statement should be qualified from three aspects. Firstly, in practice, changing the range of friction coefficient is comparatively limited, once there is friction. The effect of friction would be very significant if comparing very large friction coefficient with little friction. The former can be achieved by using a coarse surface, but this would not be used in practice. In practice, i.e., real forging, the range of change of compression rate can be very large. This is also the case in the simulation. Therefore, the conclusion is corresponding to large change of compression rate compared to relatively small change of friction coefficient. Secondly, and more importantly, friction force is a function of friction coefficient and compression force. Compression force increases with increasing compression rate. Therefore, when increasing compression rate, friction increases as well (but hidden) though friction coefficient remains the same. Thirdly, and consequently, the effect of compression rate actually includes the effect of friction, though not friction coefficient.

[pic][pic] [pic][pic]

(a) (b)

Fig. 13. The distribution of effective strain rate at different compression rate of (a) 400 mm/s and (b) 50 mm/s. Compression degree 42.3%.

Around the compression rate of 175 mm/s, the extent of localised deformation bounces up with increasing compression rate. This can be explained with the temperature increase data around the localised deformation zone during compression. The compression rate is an important factor affecting the magnitude of deformation temperature increase in the specimen. If we ignore the interface heat dissipation and the heat exchange at the contact with the dies, extracting the simulated temperature in the centre of the specimen leads to the results shown in Fig. 14. The temperature in the centre of the specimen rapidly increases with strain rate increase in the beginning. Due to this, the material softens, making the weak region even weaker and causing the localised deformation. When the compression rate increases from 100 mm/s to 200 mm/s, because of the strain hardening and strain rate hardening of the material, the extent of localised deformation of the material has receded, and the temperature increase in the centre reduces at the same time. With further increase of the compression rate, the available time for the centre to dissipate heat to the surrounding, lower temperature region is shorter. Thus, the temperature starts to increase again. The localised temperature increase, in turn, facilitates the material localised deformation. The temperature increase reaches a maximum at about 200 mm/s, coinciding with the maximum localised strain at about 200 mm/s, showing the synergy between temperature increase and material softening.

[pic]

compression rate (mm/s)

Fig. 14. The relationship between temperature increase in the centre of the dynamic Ti64 specimen and the compression rate. Compression degree 42.3%.

It should be commented that neglecting the heat exchange between the sample and dies should have little effect. The whole compression process lasts shorter than 0.1 second. The temperature decrease during 0.1 second is about 10 °C during natural cooling when the specimen rests on a flat surface. Titanium alloys are poor in dissipating heat, having low thermal conductivity.

Corresponding to the simulation results in Fig. 14, 600 °C was reached by experimental observation. In the test specimen especially designed for this measurement, a hole was drilled in the specimen to measure the temperature in the middle of the specimen, but not accurately due to experimental difficulties for such measurements. The heat exchange during measurement is unavoidable [12]. The surface temperature of the specimen after compression reached approximately 200 °C.

From Fig. 12, we can also see the relation between compression rate and the extent of localised deformation. When the compression rate is relatively small, with increasing compression degree, the extent of localised deformation increases rapidly. This is especially the case for the rate interval of 25-125 mm/s. When the compression rate is higher than 150 mm/s, the increase of compression degree from 33% to 50% contributes little to the increase of the extent of localised deformation, because some deformation has already moved to the second high strain rate regions.

4.3. Effect of the extent of localised deformation and its spread on the stress state

Experimentally, increasing compression rate or friction will make titanium alloy fracture more likely. In the above simulation work, however, when over certain levels, the increase of the compression rate or friction ceases increasing the extent of localised deformation, but instead decreases it. This is because, although the localisation extent of the material is a major reason for material fracture, as long as the deformation concentrated region is under compressive stress, the localised deformation induced material weakening will not result in the fracture of the material. During some high strain rate experiments, it has been found that the material localised shear deformation even causes local melting of the material, but it does not fracture. Based on this knowledge, and the simulation result showing that the strain localisation region always enlarges with increasing rate and friction, in this section, we will examine the influence of the spread of localised deformation on the stress state of the material localised deformation region. The force analysis in the material between two high strain rate bands is shown in Fig. 15.

[pic][pic][pic]

Fig. 15. Force analysis schematics in the strain localised region after its spread.

The effect of the moment will cause the counter clockwise rotation of AB. B point will likely have displacement along the positive x direction. Because the strain localisation is a very strong process, this force can be rather large. At the same time, because the temperature increase in this region is very severe, if the force resultant is pointing towards the positive x direction and is greater than the alloy strength at that temperature, fracture of the titanium alloy during the compression will result. In order to compare the magnitude of the force along the x direction in the localised deformation region under different compression rate, we have extracted the x-direction force distribution diagrams at compression rates of 10 mm/s and 200 mm/s with a friction coefficient of 0.3. It may be noted that the x direction is the same as the R direction, i.e., the radial direction, under the cylindrical symmetry model constructed and used in this work. Results show that for the compression rate of 10 mm/s, the deformation-localised region is under compression along the x direction (Fig. 16). This becomes tensile when the compression rate is 200 mm/s (Fig. 17). If the tensile strength of the titanium alloy is reduced significantly enough due to temperature increase in the deformation-localised region, the fracture of the titanium alloy is quite likely. Fig. 18 shows the variation of the strain values when tension stress is generated in the strain concentrated areas during compression as a function of compression rate.

[pic] [pic] [pic]

Fig. 16. Effective strain distribution and x-direction stress contour diagrams of specimens after dynamic compression. Compression rate 10 mm/s, degree 42.3%. In the scale on the right, the unit is ksi and K represents the border between tension and compression stresses.

[pic] [pic] [pic]

Fig. 17. Effective strain distribution and x-direction stress contour diagrams of specimens after dynamic compression. Compression rate 200 mm/s, degree 42.3%. In the scale on the right, the unit is ksi and K represents the border between tension and compression stresses.

[pic]

compression rate (mm/s)

Fig. 18. The relation between the compression degree at the point of tension stress appearing in x direction in the localised deformation region and the compression rate in titanium alloy under dynamic compression. Friction coefficient 0.2.

The stress results obtained here are significantly different from the mechanics analysis result in static conditions. Especially in the centre of the specimen, mechanics analysis result would indicate tension, but the dynamic simulation gives compression. This is because the material strain hardens under static conditions. Under dynamic conditions, however, after considering the deformation induced temperature increase, the large deformation region in the specimen greatly softens. The deformation of softened part is constrained by the surrounding non-softened material, and is thus under compressive stress. Just below the contact interface between the specimen and the dies, simulation shows tension. This is because the friction force is a passive, induced force. Friction force can only form in the negative x direction when the material below the die is under tension stress in the x direction.

From Fig. 18, it can be seen that, with increasing compression rate, the tension stress in the x direction in the strain concentrated region appears earlier. This could be the reason for the experimentally observed phenomenon that the titanium alloy is more likely to fracture at larger compression rate. The x-direction tension force in the strain concentrated region does not remain permanently in subsequent deformation after appearing. Under the simulation conditions in this work, for relatively high compression rates, greater than 200 mm/s, it is only present in the subsequent deformation of 8-12% of the original specimen height. Using an example of the compression rate of 400 mm/s, this is shown in Fig. 19. The formation of this tension stress is possibly the cause of the deterioration of the formability of Ti64. The appearance and disappearance are thus the reason behind the experimentally observed significant change of the processing instability parameter of the Ti64 alloy as a function of compression degree.

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(a) (b) (c) (d)

Fig. 19. The evolution of x direction tension stress in the strain concentrated region during dynamic compression of titanium alloy. The K lines are zero stress contours, i.e., the boundary between tension and compression stresses. Compression degree (a) 28.7%, (b) 31.3%, (c) 34.7%, (d) 38.9%.

Simulation in Fig. 19 shows that the tensile stress disappears when the compression degree reaches about 40%. Venugopal et al. [5] showed an improvement of the compressibility of Ti64 within a range of compression degree after 40%, when the strain rate was 10 s-1, corresponding to the compression rate in this work of 250-600 mm/s. Here, the term compressibility represents the ability of the material to be deformed without fracture and being damaged.

5. Conclusions

Based on a finite element model for the dynamic compression of titanium alloys using the DEFORM 2D software package, the strain field, strain rate field and the temperature field in compression specimens are modelled, for different processing parameters and conditions. The influence of various processing parameters on the dynamic compression process of titanium alloys is discussed. The main conclusions are as follows.

(1) Friction has a quantifiable effect on the localised deformation during the dynamic deformation process of the Ti-6Al-4V alloy. A threshold value exists. From this work, when the friction coefficient is lower than a certain value, 0.1, the extent of localised deformation is minimal. When it is above this value, the effect of friction condition on localised deformation is almost constant.

(2) Compression rate has a quantifiable effect on the localised deformation during the dynamic deformation process of the Ti-6Al-4V alloy. A threshold value exists, 75 mm/s. When the compression rate is lower than this value, the extent of localised deformation increases rapidly with increasing compression rate. When it is higher, the extent of localised deformation does not change significantly when the compression degree is relatively small, lower than 33%. When the compression degree is larger, the localised deformation even reduces.

(3) Both friction and compression rate are important factors affecting the spread of the strain concentrated regions and the stress state during the deformation process. When they are above the threshold levels, increasing friction causes the shear stress region to move outwards during deformation. With the increase of compression rate, in addition to the outward shift of the shear stress region, the original stress concentrated region will strain harden and strain rate harden, therefore accelerating the spread of the strain concentrated region. Though this spread will help reducing the intensifying of the strain concentration, it causes a tension stress in the x direction within the strain concentrated region. This may be related to the increased likelihood of fracture tendency of titanium alloys during dynamic compression when friction and compression rate increase.

References

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