Effect of discharge accumulation on wire breakage in WEDM process

In recent years, WEDM has been adopted in precision machining as an important alternative machining method because of its greater flexibility and lower wear cost compared with traditional machining, whereas wire breakage during WEDM is an unignorable problem that influences the machining quality and efficiency. Therefore, it has been a research topic of considerable interest. This work focuses on exploring the reason for the wire breakage. Firstly, by observing the wire after discharges and using the finite element method, a complete thermal model considering both latent heat and flushing efficiency was built. With this model, the simulation of the crater on the wire was finished. Then based on the result gotten from the simulation and experiment, the heat partition ratio to the wire was found as 46.74% by inverse fitting. After that, a wire breakage experiment was done and through locating the position of 50 discharges before wire breakage it is found that 34% of discharges were located within a range of 2 mm, and the minimum area in the wire cross-section only remained 41.88% compared with the original wire. This kind of decrease in the cross-section area made the stress higher than the UTS of the wire and caused the wire breakage. The findings of this work allow for a more in-depth understanding of the effect of discharge accumulation on wire breakage.


Introduction
In recent years, both industry and academia have shown an increasing interest in the wire electrical discharge machining (WEDM) process. The development and advances of WEDM machines in the last 20 years have been impressive, and this now constitutes a key technology for advanced sectors such as the aerospace, automotive, and biomedical industries, and is also critical for traditional fields such as tool and die manufacturers. Therefore, more and more researchers focus on enhancing the quality and efficiency of machining. Such as the work of Rohilla et al. [1], a study on the composition of dielectric fluid was finished for improving the surface roughness in WEDM. Moreover, in the work of Goyal et al. [2], a methodology was presented for analyzing the cutting rate and the thickness of the recast layer. Furthermore, a crucial problem that cannot be ignored in the process of WEDM is wire breakage and it has become a topic of considerable interest for decades. The reliability of WEDM machines during the early years of their development depended on the possibility of wire breakage, which limited machine productivity.
The earliest researchers of the process found that wire breakage was in some way related to excessive temperatures. Dekeyser et al. [3] concluded that the thermal load was probably the main reason for wire breakage. Then, by building a 2D finite element model, Saha et al. [4] found the existence of internal thermal stresses resulting from nonuniform heating of the wire. However, they also confirmed that 2D model is not enough to reflect the process of wire breakage fully and still needs improvement. Then in the work of Fedorov et al. [5], by considering the tensile force imposed by the machine, the thermal stresses were derived from the non-even temperature distribution on the wire, and accounting for the amorphization of the wire surface. They reached the conclusion that actual stresses on the wire during normal processing are approximately 50% of the actual tensile strength of the wire. It has also been shown that the Rehbinder effect, combined with wire damage and process loads, does not significantly affect wire breakage.
In addition, Okada et al. [6] found that wire breakage always occurred at a particular short kerf length. Through the combination of experimental results and fluid dynamic model simulation, they found that at the particular short kerf length the wire deflection due to the flushing flow made the debris accumulation easier and the frequency of wire breakage higher. Next, in the work of Bredgauer et al. [7], they adopted fractographic analysis to study the wire breakage. They found that the wire is subjected to mechanical tension until the ductile fracture appeared and they proposed that was possibly caused by the decrease in wire cross-section, whereas there is still no research work to verify this. For further investigating the decrease of a cross-section of wire in the process of WEDM, the craters generated by discharges become important and the thermal model building is an essential method to learn about this. Klocke et al. [8] presented a complete review of the strengths and weaknesses of the existing thermal models, together with proposals for future research directions. The electrode erosion thermal model commonly used is based on solving the transient state of the Fourier heat conduction equation. Solving this problem requires knowledge about the growth and shape of the plasma channel, along with the heat distribution between the electrodes. However, this technical report includes no information about critical aspects such as the nature and size of the heat source, the heat partition to the wire, or the flushing efficiency. Therefore, the accuracy of the simulation still needs to be confirmed.
Even in recent years, with the rapid development of artificial intelligence, it has also been adopted in the study of wire breakage. Such as in the work of Abhilash and Chakradhar [9], the artificial neural network was used to predict the wire breakage. With the input of discharge energy, spark frequency, open-spark ratio, and short-circuit ratio, their prediction system can reach an accuracy of 90%. Abhilash and Chakradhar [10] used an adaptive neuro-fuzzy inference system to predict the wire breakage with the indicator of mean gap voltage variation and they found that when the mean gap voltage variation was higher than the threshold value the wire breakage occurred.
For further developing the reason for wire breakage, the research plan is designed as shown in Fig. 1. In this work, a complete thermal model of the wire considering both latent heat and flushing efficiency is proposed in Sections 2 and 3. With the result gotten from the simulation and experiment, the precise heat partition ratio to the wire was found for the first time through the inverse fitting. In Section 4, a wire breakage experiment was done and through discharge locating, the position of the last 50 discharges before wire breakage was found. Then a novel 3D finite element model for studying the craters of consecutive discharge on the wire was built. Through studying the change of cross-section area of the wire due to the consecutive discharge and comparing the stress and ultimate tensile strength (UTS), the effect of discharge accumulation on wire breakage was further understood.

Description of the numerical model
As explained in Section 1, the conceptualization of the material removal process in WEDM focuses primarily on the thermal phenomenon. Wire and workpiece are then seen as tool electrode and work electrode respectively, which are immersed in a dielectric medium (deionized water in most commercial machines). The digital machine generator controls every single discharge in terms of voltage, current, and duration, with a discharge period of some microseconds. The discharge occurs where local dielectric conductivity is reduced, possibly due to the presence of a higher debris concentration, or because of a shorter gap at that time and location. Thus, generated heat is transferred to the workpiece, wire, debris, and dielectric, as shown in Fig. 2.
Special interest is focused on the heat flux towards the wire in order to further understand the wire breakage. When studying the nature of the heat flux, it is important to consider the generation and growth of a plasma channel inside the dielectric medium, which will be addressed later in this paper. Provided that the nature of the heat source is known, the heat flow -and therefore the calculation of thermal fields inside the wire -can be essentially expressed as a three-dimensional transient heat transmission problem (Eq. 1, given in partial derivatives), that needs to be solved, taking into account the boundary conditions of the problem: where ρ is the material density, C p is the specific heat capacity, K t is the thermal conductivity, T is the temperature, and r and z are the coordinates describing the distances to the center of the heat source, as shown in Fig. 3.
The solution of the above equation implies certain assumptions, which have already been validated by previous researchers: (1) Wire material properties are temperature dependent [11]. (2) Plasma channel can be considered a cylindrical column [11]. (3) Wire materials can be considered isotropic and homogeneous [11,12]. (4) In the process of heat transfer, heat radiation is neglected [13]. (5) Despite the intrinsic stochastic nature of the WEDM process, all pulses are assumed as equal. In other words, pulse duration, voltage, and current are the same for all the discharges, and the occurrence of abnormal pulses is ignored [13].
As stated previously, modeling the heat source is a critical issue. Patel et al. [14] proposed a Gaussian heat distribution equation which is shown in Eq. 2: where f c is the heat partition ratio to the wire, U is the voltage, I is the discharge current, r is the distance to the center of heat source, and R p is the radius of the plasma channel (assumed to be cylindrical). As this function describes more precisely the change in heat according to the distance to the center of the source, it is closer to the real situation. This expression has been widely used in the scientific literature in recent years. The determination of R p is also a controversial issue. The literature shows that existing models for R p can be divided into two large groups. The first one assumes that R p is dependent on process parameters. The model proposed by Ikai et al. [15] (Eq. 3) deserves special attention, which considers R p as a function of the pulse current (I) and pulse duration (t on ). The second group assumes R p to be dependent on time. The previously mentioned work by Spur and Schönbeck [16] provides evidence to suggest that a time-dependent model could be more accurate for short on-times (about 2 µs) such as those used in WEDM. Their results can be expressed using Eq. 4: Figure 3 illustrates graphically the fundamentals of the thermal model, including the coordinate reference system and boundary conditions.
During the discharge process, boundary conditions are time-dependent: (i) During on-time (which is approximately 2 µs in commercial state-of-the-art WEDM machines), part of the energy is transferred towards the wire through the plasma channel. Equation 5 expresses mathematically this part of the problem: Hayakawa et al. [17] found that although the working gap was immersed in the dielectric liquid, it was mostly occupied by air bubbles. Therefore, during on-time inside the plasma channel, the assumption of convection in air will be used. Outside the plasma channel, forced convection due to flushing of deionized water can be considered; (ii) during off-time (as much as 5 times longer than ontime), forced convection acts over the complete modeling region. As explained above, the effect of heat loss by radiation is negligible. Equation 6 expresses heat transfer by convection: where K t is the thermal conductivity, h is the convection transfer coefficient (that depends on the described boundary conditions), and T 0 is the initial temperature.
Finally, attention must also be paid at the properties of the material. It is known that in the process of WEDM, the maximum temperature will be higher than the melting point of metal, and sometimes it could also even exceed the boiling point. Chen et al. [11] pointed out that the latent heat during the state change from solid to liquid and from liquid to vapor cannot be ignored. Therefore, in this work, the equivalent specific heat capacity of the material is optimized by Eq. 7 and Eq. 8, where C p , C melting , and C evaporation are respectively the equivalent specific heat capacity when the material is in the state of solid to liquid and the state of liquid to vapor. T melting and T evaporation are melting point and boiling point, T ref is the ambient reference temperature, and L melting and L evaporation are the latent heats in the process of fusion and evaporation.

Experimental and simulation setup
Controlled experiments allow for extracting relevant information from the numerical model. The experiments were carried out on an industrial ONA AV35 WEDM machine and the brass wire (Cu63%/Zn37%, UTS 960 N/mm 2 ) with a diameter of 0.25 mm was adopted. Part material was Sverker21 tool steel which is widely used in the industry because of its high wear resistance [18] and the chemical  Table 2.
Numerical simulation was then programmed in ANSYS. The thermal transient problem with the boundary conditions described in Section 2 is solved using APDL, which was also used to filter and calculate the elements whose temperature was higher than the melting point. For the simulations, the thermal properties of the wire are required, as displayed in Table 3.

Results of the experiment and simulation
WEDM experiments using the industrial conditions given in Table 2 were conducted to measure the average crater volume removed from the wire surface. After cutting, the wires were collected for measuring their length. In order to increase the accuracy of the experiment, the procedure was carried out three times. The wire length of each experiment is shown in Table 4 and in that, the discharge number (N dis ) was recorded by ONA AV35 WEDM machine. Furthermore, it is known that in the process of WEDM, each of the two electrodes melts, and the debris fills the gap. When the flushing stream takes away the debris, it will also form part of that which adheres to the surface of the wire and workpiece, which is known as the recast layer.
For measuring the thickness of this layer, the cross-section of the wire with the crater needs to be observed. In this work, the used wire collected previously is fixed vertically and constructed as a capsule. After polishing, the chemical attack is conducted with liquid ferric nitrate. The observation is then completed with the Hitachi S-3400 N Scanning Electron Microscope (SEM). In Fig. 4, the recast layer can be clearly recognized. Also, the composition of the recast layer was analyzed by X-ray diffraction and the result is shown in Table 5. From this result, it is known that in the composition of the recast layer on the wire, there are a few elements from the workpiece and this result coincides with the research work on the recast layer on the workpiece in WEDM which was finished by Newton et al. [19]. They found that in the composition of the recast layer on the workpiece, there was only 0.06% of copper and no zinc which are the elements from the wire. Therefore, in the study of the recast layer on the wire, the impact of the workpiece can be ignored.
In addition, the profile of the wire is obtained as shown in Fig. 5a. According to the part without craters, the original    profile of the wire was marked as Fig. 5b. It is clear that discharge occurs at approximately 68% of the total wire perimeter. Further, the area without damage is obtained with the software of ImageJ. Using this, the removed area (A remove ) and the recast layer area (A recastlayer ) can be measured as shown in Table 6. Furthermore, in each experiment, the removal volume of each discharge (v crater ) can be established using Eq. 9. In addition, the flushing efficiency (F) was calculated as 44.98% through Eq. 10.
Once the value of crater volume on the wire is available, the experimental results can be compared with numerical simulations, so that it is possible to obtain a value of heat partition ratio to the wire. The transient thermal problem was then solved on the wire using ANSYS. Under the assumption of a cylindrical plasma channel, a similar value of R p can be used for both the heat source on the workpiece and the wire electrode. Following experimental results by Spur and Schönbeck [16], a value of R p of 81 μm after 2 μs will be used. In addition, a value of heat partition to the workpiece of 40% has been taken from Xia et al. [20]. This latter value helps set the feasible variation range of f c , which has been established below 60%. The validity of the above values for WEDM conditions reported in the literature has recently been confirmed in Wang et al. [21]. Mathematical simulations were then carried out using the numerical model described in Section 2. The results for crater volume removed from the wire per discharge have been plotted in Fig. 6 for the different values of f c . It can be observed that in the range of 40 to 50% of f c , the volume of crater increases from 51,933.21 to 72,441.65µm 3 . To obtain a more precise estimate of this value to match the real crater obtained previously, the curve fitting tool in Matlab was applied. The inverse fitting allows for achieving a precise value for the heat partition ratio to the wire. The value obtained is 46.74%. After this, a verifying simulation was conducted with this percentage and the error was 0.53%, as calculated by Eq. 11.

Exploration the reason for wire breakage
In the study of wire breakage, the local accumulation of discharges is worth to do further understanding. Local accumulation of discharges is attributed to the impossibility of effectively removing the debris generated by one or several previous discharges. The origin of this can be related to   . 6 Simulation of crater volume on the wire causes such as too short t off , which hinders debris removal and wire cooling. Thus, local conductivity in a region close to the previous discharges then becomes higher and the probability of a new discharge occurring in that region increases. The hypothesis is that, if discharge accumulation in a region is sufficiently high, the local thermal load on the wire increases in such a way that the active load bearing section of the wire is reduced. If this reduction is sufficiently high, the section of the wire cannot withstand the axial force, and, consequently, ductile failure of the wire occurs. For verifying this hypothesis, the position of several discharges just before wire breakage needs to be found.

Experimental setup for determining spark position
For further exploring the effect of discharge accumulation on wire breakage, the position of the sparks that cause the wire breakage should be located. In the work of Kunieda et al. [22], they proposed that with the change of spark position, the part of wire included in the upper circuit and lower circuit respectively will also change. Since the wire is seen as the resistance in the circuit, it means that the current value is distinct depending on the spark position. Also, later in the work of Boccadoro et al. [23], they used this method for monitoring the machining contour. As shown in Fig. 7 when the discharge occurs the wire can be seen as divided into two parts (upper part and lower part). Meanwhile, two closed circuits (upper circuit and lower circuit) are formed which include respectively relative parts of wire. In order to verify the feasibility of this method, several experiments were done on ONA AV35 WEDM machine with the machining parameters listed in Table 7. In this experiment, a Sverker21 sheet workpiece of 2-mm thickness was selected. As shown in Fig. 8, the distance between two nozzles (H) was 70 mm and 7 kinds of placement heights of the sheet workpiece (H 1 ) were chosen. Meanwhile, two CWT Rogowski current transducers were used for detecting the current of the upper circuit and the lower one and a Tektronix 5034B Digital Oscilloscope for collecting current signals.
After the measurement of 400 discharges in each height, the relation (k) between the upper circuit current (I upper ) and the lower circuit current (I lower ) was calculated by Eq. 12. As shown in Fig. 9, the relation between k and H 1 is relatively close to linear. Therefore, the linear tendency equation is obtained as Eq. 13. For further verifying the accuracy of this equation, another two kinds of H 1 (28 mm and 42 mm) were selected to do the same experiment and for each H 1 the relation Fig. 7 Schematic diagram of spark location system Then another experiment with the workpiece thickness of 50 mm was finished and for easier getting the wire breakage, 2 µs of t off was adopted. In the process of cutting, I upper and I lower were also measured. Finally, the last 50 sparks before the wire breakage were picked out to further process. The relation k was calculated by Eq. 12 and then H 1 was predicted by Eq. 13. As a result, the position of the last 50 discharges before wire breakage is shown in Fig. 10. It can be known that 34% of discharges concentrated between 2 and 4 mm.
In addition, the broken wire was also observed with Hitachi S-3400 N SEM; the result is shown in Fig. 11. The failure mode is clearly that of a ductile failure and the cupand-cone shape which is typical of ductile materials can clearly be observed. The fast fracture region occurs at 45°  to the plane of the tensile load, the angle at which the largest shear stress appears. Considering the proposal of Bredgauer et al. [7], this kind of ductile failure is possibly caused by a decrease in the cross-section area of the wire. For further exploring the reason, finite element simulation was considered to further understand the influence of discharge accumulation on the decrease of wire cross-section area.

Simulation of discharge accumulation
Through the experimental result in the previous part, the position with the STD range of the last 50 sparks before wire breakage was obtained. For realizing the simulation of consecutive sparks, COMSOL was selected to do the corresponding work. Firstly, according to the spark position result, the coordinate of the center of each spark was generated by MATLAB randomly in the range of STD. Then, based on the thermal model obtained in the previous section and the setting experimental parameters, the simulation was finished on the wire. As the result shown in Fig. 12a, after each spark, the part material whose temperature is higher than the melting point was removed. The craters on the wire are not uniform because of the overlap of craters. For the workpiece, a similar result was gotten by Liu and Guo [24].
It is found that concentrated discharges cause a local temperature to increase to make a removal volume increment. Next, the minimum area of the cross-section of the wire was obtained in Fig. 12b. It is learned that after the continuous discharges before wire breakage the remaining area was measured as 20,549µm 2 and it was only 41.88% compared with the original wire cross-section area. The decrease in cross-section area made the stress higher than the UTS of the wire and the ductile failure which is shown in Fig. 11 happened. This simulation result matches the experimental result. It further reveals the wire damage from the discharge accumulation and the caused decrease of the area in crosssection is the essential reason for the wire breakage.

Conclusions
In this work, the principle of thermal transfer to the wire in WEDM was studied. For detecting the effect of accumulative discharges on wire breakage in the WEDM process, several experiments and simulations were conducted in this study. Based on the results obtained, the following conclusions can be drawn:  Fig. 12 a Simulation of consecutive craters on the wire. b Minimum cross-section of wire in simulation -Complete observation of the wire after discharges has been carried out. The recast layer can be clearly identified, and discharge occurs at 68% of the total wire circumference. In addition, the flushing efficiency is learned as 44.98%. -Numerical simulations considering latent heat and flushing efficiency were conducted using the finite element method with different values of f c . The inverse fitting allows for achieving a precise value for the heat partition ratio to the wire. The value obtained is 46.74%, with a calculated error of 0.53%. -Spark locating was realized through the current ratio of the upper circuit and lower circuit. The tolerance range of this scheme was verified as 2 mm. Based on this, with the workpiece thickness of 50 mm, the position of the last 50 discharges before wire breakage was found and as the result, 34% of discharges were located within a range of 2 mm. -A novel 3D finite element model for studying the craters of consecutive discharge on the wire was built. Through the simulation of consecutive discharges before wire breakage, it is found that the minimum area in the wire cross-section only remained 20,549µm 2 and it was only 41.88% compared with the original wire cross-section area. This kind of decrease made the stress higher than the UTS of the wire and ductile failure happened. It further reveals the wire damage from the discharge accumulation and the caused decrease of the area in cross-section is the essential reason for the wire breakage.
Author contribution All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Jun Wang. The first draft of the manuscript was written by Jun Wang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding This work received funding support from the Spanish Ministry of Economy and Competitiveness and the FEDER operation program for funding the project "Scientific models and machine-tool advanced sensing techniques for efficient machining of precision components of Low-Pressure Turbines" (DPI2017-82239-P).

Competing interests
The authors declare no competing interests.