Global Trends and Challenges in Design and Manufacturing- Proc. of the 3rd Intl. & 24th AIMTDR Conf. 2010 Beela Satyanarayana and Koona Ramji (Eds) Copyright ©2010 AUCE (A), Vishakhapatnam, INDIA
Evaluation of the effect of process parameters on various stresses in EDMed AISI D2 tool Steel components 1
M. K. Pradhan & 2C. K. Biswas 1
Assistant Professor, Department of Mechanical and Industrial Production Engineering, Maulana Azad National Institute of Technology, Bhopal-462051, M.P. India Email:
[email protected],
[email protected] (Corresponding author) 2
Associate Professor, Department of Mechanical Engineering, National Institute of Technology, Rourkela-769 008, India Email:
[email protected] Abstract: - In this research, a Finite Element Modeling of the Electric Discharge Machining (EDM) process is presented. An axisymmetric non-linear transient Finite Element model has been developed to predict the thermal stress and residual stress of a single-pulse discharge on AISI D2 steel machined by EDM have been depicted. The effect of input variables such as discharge current and pulse duration, on the temperature distribution on the component, thermal stress and residual stresses have been examined and reported. The model has been validated using experimental data for residual stresses using X-ray diffraction method and found that the general trend of the data match very well.
Keywords: Electrical Discharge Machining, Finite Element Method, ANSYS Thermal Stress, Residual Stress.
1.
INTRODUCTION
Electrical discharge machining (EDM) is a most primitive non-conventional machining process, which is best suitable for machining those materials which are characterized by extremely tough tolerances and circumstances that would be really difficult or unattainable to handle with other method of machining [1]. It is used widely in machining conductive “difficult to machine” and hard metals as well as alloys in aerospace, automotive, die and mould making industries. EDM is regarded as the “last resort” and most conventional non-conventional machining process. In EDM material is removed by a sequence of discrete electrical discharges occurring between an electrode and a work piece in the presence of dielectric. Moreover, there is no physical contact between electrode and workpiece thus it is well suited for making frail or fragile parts that cannot take the stress of machining. The duration of the
spark in EDM is of the order of micro-seconds and during this very short period of time a plasma channel is formed between the tool and the workpiece. The plasma channel produces very high thermal energy during machining results in very high local temperature (close to the vaporization temperature) of the work piece. This leads to the thermal erosion and also produces recast layer with micro-cracks on machined surface. Further, because of this non-uniform heating of material during this EDM process generates a multi-layered heat affected zone in the sub surface of the work piece; the layers are of different temperature contracts and thus generate thermal stress. If these stresses overpass the yield stress of the material, they will remain as residual stress in the work piece during subsequent cooling, which play a key role in fatigue crack growth, crack closure, and fracture. Usually, residual stresses are self-equilibrating stress exists within a component when no external tractions are applied to it. The state of the residual stress typically comes up
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M. K. Pradhan & C. K. Biswas as a cumulative effect of the processes it has undergone, and the material properties. The residual stresses are particularly detrimental when they are tensile in nature, as it instigates the crack and become critical if subjected to fatigue load. Prediction and measurement of residual stress in engineering components have been a pursuit of researchers as residual stresses not only have an effect on the initiation and onset of the propagation of surface crack but also change the path/growth of the crack as it grows below the surface. Due to the complexity and highly stochastic nature of the EDM process that involve relations of thermal, mechanical, chemical, plasma and electrical phenomena simultaneously, thus the mechanism of this process is not completely understood yet. In consequence, the modeling of EDM process is indispensable to understand this rapid process and the developed model should be able to predict the temperature generated in the workpiece surface, thermal stresses and the residual stresses induced in the workpiece. Also, experimental trials are required to validate the model the understanding the conditions for an EDM operation. Efforts are made to model the process to understand the behavior of process and influence of the machining parameters on the responses in order to trim down the experimental cost associated The electric spark among the anode and the cathode produces huge heat over a tiny area of the work piece. A fraction of the produced heat is conducted through the cathode (8%), a fraction is conducted through the anode (18%), and the rest is dissipating by the dielectric [2, 3, and 4]. The formation of surface cracks has attributed to the differentials of high contraction stresses exceeding the material’s ultimate tensile stress within the white layer [5]. Mamalis et al. [6] experimentally investigated on low-carbon steel St37, medium carbon steel C45 and alloyed steel 100Cr6 work piece and found that the peak stresses are almost independent of the discharge energy and approach the ultimate tensile strength of the material. Rebelo et al. [7] in his investigation using XRD methodology found that the residual stress of steel work piece increases from the bulk material to a maximum and decreases again approaching the surface. Also the peak stresses are almost independent of the discharge energy and the greater the discharge energy, the greater the depth at which the maximum value of residual stress occurs. A qualitative relationship with the operating parameters was presented by Ekmekci et al. [8] using DIN 1.2738 (AISI P20) work piece material. For solving these problem present trends of most of
the research work are devoted to numerical models based the finite element method. Yadav et al. [9] applied FEM to investigate the thermal stress generated by a single spark in EDM of Cr die steel. Though several attempts have been made to model the EDM process and the influence of machining parameters on these responses are analyzed, a little research has been reported relating to finite element modeling of residual stresses on AISI D2 tool steel using ANSYS software. Also, the work piece material AISI D2 steel was selected in this research due to its emergent range of applications in the field of manufacturing, tools and in mould making industries. An attempt has been made to model the EDM process using ANSYS software, and to investigate the effects of most significant machining parameters (pulse current and pulse duration) on the temperature and the stresses developed in the beneath the spark produced by a single spark. The foremost aim of developing this model is to predict the nature of residual and thermal stresses occurring during EDM. The FEA model is then used to study the relation between these parameters and maximum temperature attended and thermal stresses generated at the end of heating cycle along with residual stress produced at the end of cooling cycle. To establish the thermal and residual stresses in the work piece during EDM, the temperature distribution at the end of pulse duration in the work piece has to be estimated first, latter on after cooling the residual stress is determined. In addition, residual stress which is the main aspect responsible for component failure, and the location of tensile peak stress, at the end of cooling cycle are investigated and verified experimentally.
2.
THEORY AND FORMULATION
For the transient thermal analysis, a single-spark cycle is considered that comprises pulse current of 1A and 9 A with pulse duration of 20µs and 100 µs. The thermal diffusion differential equation for the heat transfers of the axisymmetric workpiece: ρC p
1 ∂ ∂T ∂ ∂T ∂T = (1 ) k + k ∂t r ∂r ∂r ∂z ∂z
Where T is temperature, t is time, ρ is density, k is thermal conductivity, C is specific heat capacity of workpiece material in solid state and r and z are coordinate axes as shown in Fig. 1. If the total power which is used only by one single spark with the radius (R) is known, then the heat flux qw (r) at radius r is given by
Global Trends and Challenges in Design and Manufacturing- Proc. of the 3rd Intl. & 24th AIMTDR Conf. 2010 Beela Satyanarayana and Koona Ramji (Eds) Copyright ©2010 AUCE (A), Vishakhapatnam, INDIA 2 3.1. BOUNDARY CONDITION r 4 .55 P f U b I p r = − ( ) exp 4 . 5 ( 2 ) qw Fig. 2 demonstrates a schematic diagram of the Rp π R 2p thermal model with the applied boundary conditions during heating cycle. During the spark on-time Where Pf is the percentage of heat input distributed (heating cycle) on the top surface 1, the energy to the work piece, Ub the breakdown discharge transfer to the work piece is represented by a voltage (different from the applied voltage), Rp the Gaussian heat flux distribution up to spark radius Rp. spark radius and Ip is the current. The Pf value has Beyond Rp, the heat loss to the coolant is modeled been previously determined by Yadav et al. [9] to be using convective boundary conditions. However, 0.08 for their theoretical work of conventional during cooling cycle, on the entire top surface 1, the EDM. convection heat transfer takes place due to the cooling effect caused by the dielectric fluid. No heat transfer occurs across surfaces on 2 and 3, because they are consider to be sufficiently far away for any heat transfer to take place as the duration of spark is very small. The boundary 4 is the axis of symmetry, hence the heat flux has been taken as zero as there is no net heat gain or loss across this boundary. 4.
Figure 1 Schematic sketch of the physical model. 3.
THERMAL MODEL
The domain of the model is treated as a semiinfinite object in considering the microcosmic characteristics of the single discharge. The upper surface of the cylinder is the machining surface and its centre is the focus of the ionized channel. When a single spark is incident in to the work piece, the heat propagates symmetrically in all direction, so taking advantage of its symmetry a small cylindrical portion of the work piece around the spark is used as the domain as shown in Fig. 1. A convective heat transfer boundary conditions are applied on the surface that is exposed to the dielectric. All of the equations in this study are based on the cylindrical coordinate system, as shown in Fig. 2.
Figure 2 An axisymmetric model for the EDM process simulation.
METHODOLOGY
For modeling and simulate the process a finite element based model is used to estimate the temperature, thermal stress and residual stresses distribution developed due to EDM. Commercial finite element software ANSYS 12 is used for the purpose of modeling in which the Gaussian heat input model is used to approximate the heat from the plasma. The radial co ordinate depicted as x axis and axial coordinate is y-axis. For this purpose, the thermo-physical properties of the workpiece were considered temperature dependent, and the convection phenomenon was also considered external surface which are exposed to the dielectric. A direct thermal-structural analysis is performed in this investigation. Conduction heat transfer within the workpiece is governed by the diffusion equation. Results are obtained by using thermal-structural coupled field elements and all of the boiled material and a fraction of melted material are removed from the domain at the end of pulse duration. Following assumptions are made due to the random and complex nature of EDM. • The domain is considered axisymmetric. • Material is homogenous and isotropic. • Workpiece material is stress-free before EDM. • Heat transfer to the workpiece is by conduction. • Gaussian heat flux distribution on spark incident surface of the workpiece material during pulse time period. • Inertia and body force effects are negligible during stress development. A tiny cylindrical portion of the workpiece beneath of the spark is taken as the domain. Energy portion (8%) transmits to the workpiece as heat input and pressure serve the thermal and solid boundary
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M. K. Pradhan & C. K. Biswas conditions respectively. The heat loss due to dielectric liquid on the non-spark incident surface is modeled using convective boundary conditions. Other boundaries are such distances away from the heat source where there is no heat transfer across them. 5.
EFFECT OF MACHINING PARAMETERS ON TEMPERATURE PROFILE
The variation of temperature along the line of symmetry with respect to the depth of the work piece has been presented before material ejection in this section for different pulse current and pulse duration. The peak temperature and its distribution depends upon the amount of spark energy supplied to work piece and hence the pulse current and pulse duration has a significant impact on the temperature profile which are explained in the subsequent section. 5.1. Effect of current: The variation of temperature at the end of spark with depth of the work piece has been plotted presented in Fig.3. From these plots, it can be observed that with the increase in Ip the peak temperature goes on increasing. This is due to the fact that, with the increase in Ip the magnitude of the heat energy transferred to the work piece increases. From the figure, it is observed that temperature shows inverse exponential relation with respect to the axial distance.
Figure 3 The effect of Ip on the temperature variation with depth 5.2. Effect of pulse duration: The effect of pulse duration is presented along the depth for Ip = 9A for Ton = 20 µs and 100 µs. It could be noted that if Ton is higher, the spark radius R will also be larger and the heat will be distributed to a larger area, (as the plasma channel becomes wider with increase of Ton, the heat flux distribution becomes less steep), which may not
produce the higher peak temperature, but will remove more material. In this figure presented, it can be clearly seen that the profile of Ton =100 µs, though more heat is produced, but the peak temperature approaches 4000K. However, the profile of Ton=20 µs with lower heat supplied to a radius of 75 µm for a very short time, thus produces a peak temperature of slightly higher than 4000K. This may be attributed to, though less amount of heat is produced and the heat is concentrated to smaller area, produce slightly higher peak temperature, than that for larger Ton. 6.
EFFECT OF MACHINING PARAMETERS ON THERMAL STRESS
Gaussian heat source, believed to be closer to the real life situation, is showing steep temperature gradients within the spark radius zone. These steep gradients are considered to be the main source of induced thermal stresses in the work piece just after the material ejection. However, it was not possible to validate the thermal stress distributions in the work piece, as no results (experimental/theoretical) are available for thermal stresses developed during EDM. Fig.4. corresponds to the nature of the thermal stress variation in radial direction along the centerline of work piece. The machining conditions are stated in the plot. It is noted that the thermal stresses obtained for all cases are compressive in nature near the crater with the maximum values of the stress are -348 MPa for Ip=1A and Ton=20µs, and the value gradually becomes tensile and then asymptotically become stress free with the increases in depth. The trends of thermal stresses in other machining parameter setting are similar. It could be clearly noticed that the profile is shifting outwards (depth where maximum compressive stress occure varies from 7.59 µm to 16.05 µm for 20 µs and from 10.95 µm to 40.78 µm for 100 µs) indicating that with the increase in Ip, as the spark energy increases, produces higher gradient of heat flux that propagates to more depth. Similar trend is also observed for Ton (corresponding depth varies from 7.59 µm to 10.95 µm for 1 A and 16.04 µm to 40.78 µm for 9A) where with the increase of pulse on time, the stresses propagate to more depth. Fig.4. represents the thermal stress directly following the heat flux in axial direction. Similar trend has been observed for the thermal stress distributions in radial direction. The maximum compressive stresses are located on the surface of the newly created crater and the magnitude is comparatively low. Also, with the increase in Ip from 1A to 9A the depth of maxi- mum thermal stress increases from 30.33 to 48.11 µm and 43.79 to 122.92µm for 20µs and 100 µs, respectively. Similarly, with the increase of Ton from 20 µs to 100 µs the depth of maximum thermal stress increases
Global Trends and Challenges in Design and Manufacturing- Proc. of the 3rd Intl. & 24th AIMTDR Conf. 2010 Beela Satyanarayana and Koona Ramji (Eds) Copyright ©2010 AUCE (A), Vishakhapatnam, INDIA from 30.33 to 43.79 µm and 48.11 to 122.92 µm for Fig. 5 illustrates the residual thermal stress in the 1A and 9A, respectively, confirming the claim that axial direction. Around the crater, tensile stresses are with the increase in both Ip and Ton, the depth of present, but they are not as large as those beneath the maximum thermal stress increases. The shear stress adjacent surface. There stresses reach a maximum in the line of symmetry is found to be zero. value and then gradually decreases as the depth rz increases and become compressive in nature. On further increase of depth, this stress asymptotically diminishes to a zero value.
8.
Figure 4 Effect of Ip and Ton on thermal stress 7.
EXPERIMENTAL VALIDATION
The graph shows the experimental results of residual stress obtained by X-ray diffraction and plotted along the depth of the workpiece. The effect of Ip and Ton are indicated. The magnitude of peak of the residual stresses increases with increase both Ip and Ton. The experimental results denote that there is a considerable rise in the residual stress as Ip or Ton increases resulting in a greater peak.
EFFECT OF MACHINING PARAMETERS ON RESIDUAL STRESS
Investigating the plot in Fig. 5 minutely, it is found that radial components of the residual stresses in EDM are predominantly tensile in nature. The magnitude starts to increase from the top surface to its maximum value. It is very interesting to observe that the magnitudes of the residual stress for all four cases are found to be approximately 600 Map. Thus, it can be concluded from this observation that the intensity of the peak stresses is found to be unaffected with respect to the magnitude of the spark energy produced. This peak intensity of the stress indicates the hot strength of the material machined. However, it is observed that as the spark energy increases, the depth at which the residual stress reaches maximum, has been found to be increase. Subsequently, residual stresses fall rapidly to fairly low values of compressive residual stresses.
Figure 5 Effect of Ip and Ton on residual stress
Figure 6 Experimental residual stress in radial direction ( rr) along symmetric path. The results imply that the stress levels reaches its maximum values close to the surface but diminish very rapidly in the sub-surface area, which is analogous with the FEM simulation results. Even though the values of stresses do not match exactly with the order of magnitude but the general trend of the data match very well. This is obvious because the simulation results are considered for single spark, whereas, these results are for multiple spark. This is a clear indication that estimation of residual stresses within the recast layer fails since this portion of the material actually liquefy and hence relief its stresses during sparking that is not take into consideration in FEM analysis. Besides, cracks also work as a stress relieving mechanism. Once crack occur, they reduce the stress level of residual stresses in the neighborhood. Hence, the actual stress level of recast portion of the material differs from FEM analysis.
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M. K. Pradhan & C. K. Biswas 9.
CONCLUSION
In the present analysis, a two-dimensional axisymmetric model was developed to predict the temperature, thermal and residual stresses. Wellknown finite element commercial software ANSYS 12.0 is used to simulate the effects of a single spark for AISI D2 steel. The important features of the process such as temperature-dependent material properties, shape and size of heat source (Gaussian heat distribution), percentage fraction of heat contribution to the work piece, pulse on/off time, material ejection fraction are taken into account in the development of the model. The temperature profiles and material transformations that occur in the work piece material due to high temperature, deformations and transient operation are analyzed. In this study it is assumed that 50% of the molten material is ejected from the material and rest is recast on the work piece. There is a sharp temperature rise during the heating cycle and then it falls rapidly during quenching. It is observed that the compressive thermal stresses are developed beneath the crater and the tensile stresses are occur away from the axis of symmetry. FEM results show that the peak temperature sharply increases with pulse current whereas, with lower pulse on time, it is slightly higher than that of higher pulse on time. The work piece is severely affected by the thermal stresses to a larger depth with increasing pulse energy. The nature of residual stresses is predominantly tensile. It is very interesting to observe that the magnitudes of the radial component of the residual stresses acquired from FEM are dominant than other components for all the machining parameter combinations. The axial component of residual stresses is however, minimum on the surface path and increase as the path rotating towards the symmetry path. The experimental results signify that the stress levels reaches its maximum values close to the surface but diminish very rapidly to comparatively low values of compressive residual stresses in the sub-surface area and the trend of these stresses with depth has an excellent agreement with theoretical results. The magnitude of tensile and compressive residual stresses as well as the depth, at which they occur, increases with the pulse energy however, the pattern of residual stress does not change with regard to the machining parameters.
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