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J-Integral Analysis of PCBN Tool Crack Propagation in Hybrid Machining of Advanced Materials
Journal ofJournal Manufacturing ProcessesProcesses of Manufacturing Vol. 6/No.2 Vol. 6/No. 2 2004 2004
J-Integral Analysis of PCBN Tool Crack Propagation in Hybrid Machining of Advanced Materials Z.Y. Wang, Nevada Manufacturing Research Center, Dept. of Mechanical Engineering, University of Nevada, Las Vegas, Nevada, USA K.P. Rajurkar and J. Fan, Industrial and Management Systems Engineering Dept., University of Nebraska–Lincoln, Lincoln, Nebraska, USA G. Petrescu, Nevada Manufacturing Research Center, Dept. of Mechanical Engineering, University of Nevada, Las Vegas, Nevada, USA
Abstract
chining most commonly used materials, such as alloy steels. Because in a machining process more than 90% of the energy consumed is eventually converted into heat (Trent 1984), cutting temperatures are high in machining advanced materials. However, the thermal conductivities for ceramics, titanium alloys, and Inconel are low. Therefore, high temperatures are concentrated in a narrow area close to the cutting edge (Komanduri and von Turkovich 1981). Tool cutting edges bear high forces and high temperatures, which quickly leads to crack initiation and propagation in the tool and results in rapid tool wear and early fracture. Many attempts have been reported in improving tool life and surface finish in machining advanced materials. Baker and Krabacher (1956) at the Cincinnati Milling Machine Co. pioneered hot machining in their research. Their work was further extended by Uehara and Takeshita (1986) and Shin and Kim (1996) in the machining of ceramics and Inconel, respectively. The reductions of cutting forces and improvement in workpiece machinability were observed in both of these papers. However, further research is needed to stabilize the cutting tool life affected by the heat generation during machining. Lindeke et al. (1991) adapted a different approach by applying high-pressure coolants to the cutting insert while machining titanium alloys and achieved promising results. To further strengthen the cooling effects, Hong and Zhao (1992) and Wang, Rajurkar, and Murugappan (1996) investigated the effect of cryogenic cooling on turning titanium alloys, low carbon steels, and ceramics by applying liquid nitrogen to the cutting tool. In both of these tests, cutting
Failure of polycrystalline cubic boron nitride (PCBN) cutting tools, resulting from microcrack development, is one of the major causes of tool replacement in the machining of advanced materials. In this research, the J-integral method is applied to study the relationship between crack growth in a cutting tool and tool life in a hybrid machining process. Results show that with the decrease of the cutting temperature and its gradient in the cutting tool, the J value decreases and the tendency for micro crack propagation in the tool declines. Therefore, tool wear and early fracture rates are remarkably reduced.
Keywords: J-Integral Analysis, Tool Failure, Advanced Materials
Introduction As the automotive, aerospace, electronics, and many other industries adapt more advanced materials, such as titanium alloys, Inconel, ceramics, and metal matrix composites (MMC), to improve the quality of their products, the machining of these materials both efficiently and economically becomes more and more challenging (Shaw 1984; Jahanmir et al. 1992). The surface finish of these materials is usually poor after being machined. Low cutting speeds are often used to reduce high wear rate and potential early tool fracture (Trent 1984). Cutting forces and temperatures are two major causes contributing to rapid tool wear and early tool fracture in machining advanced materials (Trent 1984). In general, more energy is consumed in machining advanced materials due to their excellent mechanical properties. Therefore, the specific force on a cutting edge is much higher compared to ma196
Journal of Manufacturing Processes Vol. 6/No. 2 2004
tool life was improved significantly because the heat generated in cutting was partially absorbed by the liquid nitrogen coolant applied to the cutting insert. Inspired by the experimental results, a technique called hybrid machining was proposed by a group of researchers headed by Rajurkar, Wang, and Fan (1996) and Shin and Kim (1996). This method applies plasma heating to soften the workpiece materials and also applies liquid nitrogen to cool the cutting insert. Extensive experimental results show that cutting forces and temperature-dependent tool wear are reduced considerably in machining ceramics, titanium alloys, Inconel, and tantalum (Rajurkar, Wang, and Fan 1996). This paper presents the theoretical part of the investigation of hybrid machining. A J-integral analysis is introduced to study the effect of hybrid machining on cutting tool life.
Figure 1 J-Integral Path
Here E is the modulus of elasticity, ␣ is the coefficient of linear thermal expansion, is Poisson’s ratio, T is the temperature, and
Model Development
⎡1 ∂ ⎤ E ⋅α (T ⋅ ε ii ) − ε ii ⋅ ∂T ⎥dA ⋅ ∫⎢ ⋅ 1 − 2 ⋅ ν A0 ⎣ 2 ∂x1 ∂x1 ⎦
is the temperature
gradient with respect to the x1 direction. In general, the value of a J-integral over a closed path is not zero if thermal stresses are present in the region. This indicates that for thermal stress induced crack problems the stress intensity factor at a crack tip cannot be determined directly from a J-integral calculation over a path surrounding the crack tip. To solve the problem, the procedure needs to be modified by considering the closed paths ⌫1 + s1 + ⌫2 + s2. Therefore, Eq. (1) is transformed into
The J-integral concept was originally used to define nonlinear elastic materials as a path independent line integral around a crack tip (Rice 1968). Later on, the concept was extended as a fracture criterion for elastic-plastic materials (Sumpter and Turner 1975). For a PCBN cutting tool, it is virtually impossible to avoid the presence of micro voids/cracks on or under its surfaces due to the nature of how the material was processed. When a PCBN insert is used for machining advanced materials, dynamic cutting forces and heat cause the voids/cracks to propagate to the insert surfaces and lead to tool fracture. In the meantime, the growth of the voids/cracks to cutting tool surfaces deteriorates cutting-edge integrity and therefore results in rapid tool wear. It is true that many other factors also result in tool wear. However, the research reported here is focused on the effects of hybrid machining on crack development in a cutting tool. Figure 1 illustrates a crack located at an arbitrary position in a PCBN cutting insert surface during a hybrid machining process. When thermal effects are considered, Wilson and Yu (1979) found that the Jintegral is equal to an integral over the area a0 inside the closed path. It has the form of J=
∂T ∂x1
1 − ν2 2 ⋅ K1 = J Γ2 − E ⎡1 ∂ ∂U ∂T ⎤ E ⋅α Ti ⋅ i ds − ⋅∫⎢ ⋅ (T ⋅ εii ) − εii ⋅ ⎥dA ∫ 1 2 2 ∂ x1 ⎦ ν ∂ x − ⋅ ∂ x 1 1 s2 + s2 A0 ⎣ J1 =
(2)
where J Γ is the J-line integral calculated over the path ⌫2. Taking the crack surface to be traction free, the above equation becomes 2
1 − ν2 2 ⋅ K1 = J Γ2 − E ⎡1 ∂ E ⋅α ∂T ⎤ ⋅∫⎢ ⋅ (T ⋅ εii ) − εii ⋅ ⎥dA 1 − 2 ⋅ ν A0 ⎣ 2 ∂x1 ∂x1 ⎦ J1 =
(3)
If J* is defined as
(1)
J * = ∫ W * ⋅ dx2 − Ti Γ
197
∂Ui ⋅ ds ∂x1
(4)
Journal of Manufacturing Processes Vol. 6/No.2 2004
where E ⋅α W =W − ⋅ T ⋅ ε ii 1 − 2 ⋅ν *
J1 =
E
(5)
F
1 −ν 2 ∂T E ⋅α ⋅ K 12 = J Γ*2 − ⋅ ∫ ε ii ⋅ dA (6) 1 − 2 ⋅ ν A0 ∂x1 E B
If is a constant, then it can be moved out from the integral sign. The area integral then becomes ii
Tool
G
∂T ∂x1
∫ε
D
Crack
A
C
Work
Figure 2 Edge Crack Strip and Boundary Condition
dA
A0
Physically, this integral is equal to the volume change of the material over the area a0. Using Green’s theorem, this integral can be transformed back to a line integral over the path of . The final equation becomes J1 =
⎡ ⎤ ∂U 1 − ν2 2 ⋅ K1 = ∫ ⎢W * ⋅ dx2 − σij ⋅ n j ⋅ i ⋅ ds ⎥ + E ∂ x 1 ⎦ Γ2 ⎣
q⋅E ⋅α ⋅ (U1 ⋅ dx2 − U 2 ⋅ dx1 ) 1 − 2 ⋅ ν Γ∫2
(7)
Here
q=
∂T ∂x1
Figure 3 Stress Distribution Due to Temperatures and Forces
FEA Results
heat sources, and both of them are assumed to generate heat during machining. CD and DE are far away from the cutting edges; they are assumed to be at room temperature, i.e. 25°C. Heat loss to the air by convection is considered on edge AC. EF is a special convective boundary; it breaks into two parts, with EF convecting heat to the liquid nitrogen and FG convecting heat to the air. For mechanical stress analysis, CD and DE are considered as rigid in both directions due to their long distances away from the cutting forces. The other two edges, AC and AE, are free of rotation and translation. Figure 3 is an example of stress distribution due to temperatures and forces. The results for J calculated from Eq. (7) are presented in Figures 4 and 5. Figure 4 reveals the relationship between J values and the temperature changes at a crack tip. The initial temperature at a crack tip used in the J value calculation was 275°C,
The J-integral values were calculated using Eq. (7) developed above. FEA software MSC.Patran™/ Nastran™ was used to obtain the values of stress, strain, and displacement needed in Eq. (7). The FEA model was composed of 29 connected surfaces, which were divided into 202,254 elements (triangular or quadrilateral) for the crack case and 202,089 elements (triangular or quadrilateral) for the non-crack case. Because the area of interest is at the tool tip, this is the region where high mesh density was used. The properties of PCBN tool material used in the J-integral calculations were the following: coefficient of –6 –1 linear thermal expansion = 4.9 10 K , Young’s modulus = 680 GPA, and Poisson’s ratio = 0.22. An edge crack located on the insert flank face was used in the calculation. Boundary conditions are shown in Figure 2. For the thermal analysis, AB and AG are
198
Journal of Manufacturing Processes Vol. 6/No. 2 2004
4
80 J-value Ratio
J - Value Ratio
5
3 2 1 0 200
60 40 20 0
300
400
500
600
0
700
25 50 75 100 125 150 175 200 225 Temperature Gradient (0C/mm)
0
The Temperature at Crack Tip C
Figure 4 J-Value Ratio vs. Temperature at a Crack Tip
Figure 5 J-Value Ratio vs. Temperature Gradient
and this J value was used as a benchmark for the rest of calculations. When the temperature at the crack
In the hybrid machining experiments, tool wear and fracture were reduced significantly when a workpiece material was softened by an external heat source and the tool insert was cooled by liquid nitrogen to a lower temperature range. Similar findings were also reported in previous publications (Wang, Rajurkar, and Murugappan 1996 and Wang and Rajurkar 2000) when machining was carried out with liquid nitrogen cooling only with no external heat source applied. The analyses presented in this paper reveal that when cutting forces, cutting temperatures, and temperature gradients in a tool reduce—i.e., the J value decreases—the stresses at the pre-existing crack tips reduce, leading to a slowing in the cutting tool wear rate, and the risk of tool fracture reduces accordingly. The relative importance of internal cracks versus tool edge surface cracks as a cause for tool wear has been debated for decades. Experimental evidence has proven to some extent that surface cracks cause fracture and expedite wear in cutting tools. However, some researchers still believe that the internal cracks are the cause of tool fracture. Because internal cracks are all started inside a cutting tool, it is very difficult to identify them before significant tool fracture occurs. Even after a tool fracture occurs, it is often difficult to say which crack started internally or externally due to wear marks on the fractured surface caused by the machining process. The J-integral analysis presented in this paper may influence that debate. Our calculation shows that the temperatures and temperature gradients in the cutting insert are always lower than those on cutting edge surfaces. The further a crack is away from an insert
⎛J
⎞
at 400°C ⎟ became tip reached 400°C, the J value ratio ⎜ J ⎝ at 275°C ⎠ 1.84. When the temperature reached 500°C, the J value ratio became 2.72, and when the temperature became 650°C, the J ratio was 4.69. Figure 5 shows the relationship between J values and temperature gradients in the PCBN cutting tool. The initial temperature gradient in the calculation was 18.75°C/mm, and the J value was used as benchmark for the rest of the calculations. When the temperature gradient reached 37.5°C/mm, 62.5°C/mm, 87.5°C/mm, 125°C/mm, and 200°C/mm, respectively, the J value increased to 2.89, 6.81, 12.39, 23.81, and 57.76 accordingly.
Validation and Discussion The assumption was made in the model development section that
∂T ∂x1
is a constant, which was based
on careful analysis of the FEA results obtained in this study. Figure 4 shows that temperature at a crack tip has great influence on J values. With temperature increases, the J value increases rapidly. Hence, the tendency for crack propagation increases. Figure 5 reveals another important factor that affects the J value and tool failure. When temperature gradients in the tool go up, the J value also increases quickly. Therefore, the cutting tool is more prone to fracture in these cases.
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Journal of Manufacturing Processes Vol. 6/No.2 2004
edge surface, the lower the J value is. Therefore, the J value at any point in the cutting insert is less than the J value on the surface. Thus, the tendency for micro-crack propagation inside the insert becomes less. Based on the J-integral analyses, it is reasonable to say that surface cracks and cracks adjacent to surfaces are more likely to cause tool fractures.
Lindeke, R.R.; Schoenig, F.C.; Khan, A.K.; and Haddad, J. (1991). “Machining of titanium with ultra-high pressure through the insert lubrication/cooling.” Transactions of the North American Manufacturing Research Institution of SME (v19). Dearborn, MI: Society of Manufacturing Engineers, pp154-161. Rajurkar, K.P.; Wang, Z.Y.; and Fan, J. (1996). “Hybrid machining.” Workshop on Hybrid Machining, MT-AMRI, Purdue Univ., West Lafayette, IN. Rice, J.R. (1968). “A path independent integral and the approximate analysis of strain concentration by notches and cracks.” Journal of Applied Mechanics (v6), pp379-386. Shaw, Milton C. (1984). Metal Cutting Principles. New York: Oxford Univ. Press. Shin, Y.C. and Kim, J. (1996). “Plasma enhanced machining of Inconel 718.” Mfg. Science and Engg. (ASME MED-v4), pp243-249. Sumpter, J.D.G. and Turner, C.E. (1975). “Method for laboratory determination of Jc.” Proc. of 9th Nat’l Symp. on Fracture Mechanics, Pittsburgh, ASTM STP-601, pp3-18. Trent, X.M. (1984). Metal Cutting. London: Butterworths. Uehara, K. and Takeshita, H. (1986). “Cutting ceramics with a technique of hot machining.” Annals of the CIRP (v35/1), pp55-58. Wang, Z.Y.; Rajurkar, K.P.; and Murugappan, M. (1996). “Cryogenic PCBN turning of ceramic (Si3N4).” Int’l Journal of Wear (v196), pp16. Wang, Z.Y. and Rajurkar, K.P. (2000). “Cryogenic machining of hard-tocut materials.” Int’l Journal of Wear (v239), pp168-175. Wilson, W.K., and Yu, I.W. (1979). “The use of the J-integral in thermal stress crack problems.” Int’l Journal of Fracture (v15, n4).
Conclusions This paper established a relationship between Jintegral values and cutting tool fracture in machining. It is found that when the temperature rises at a crack tip in a cutting insert, its J value increases also, and the tendency for micro crack propagation increases accordingly. It is also found that when temperature gradients in a cutting insert increase, the J value increases and the tendency for micro crack propagation increases as well. Hybrid machining reduces temperatures and temperature gradients in the cutting inserts. Therefore, it reduces early tool fracture and tool wear in machining advanced materials, and consequently, it improves surface finish of machined surfaces.
Authors’ Biographies Dr. Z.Y. Wang is the director of Nevada Manufacturing Research Center at the University of Nevada, Las Vegas. His research areas are manufacturing process improvements, lean manufacturing, and agile manufacturing.
Acknowledgment The authors are grateful for support from Nebraska Research Initiative funds and UNLV grants.
Dr. K.P. Rajurkar, Mohr Professor of Engineering, University of Nebraska, is the founder and director of the Nontraditional Manufacturing Research Center. For the last three years, he also served as a program director at the National Science Foundation. His research and teaching interests include advanced manufacturing processes.
References Baker, W.R. and Krabacher, E.J. (1956). “New techniques in metal-cutting tesearch.” Trans. of ASME (v78), pp1497-1505 Gdoutos, E.E. (1990). Fracture Mechanics Criteria and Application. Kluwer Academic Publishers. Hong, S.Y. and Zhao, Z.B. (1992). “Cooling strategies for cryogenic machining from materials viewpoint.” Journal of Materials Engg. & Performance (v1, n5). Jahanmir, S.; Ives, L.K.; Ruff, A.W.; and Peterson, M.B. (1992). “Ceramic machining: assessment of current practices and research needs in the United States.” NIST Special Publication 834. Gaithersburg, MD: NIST. Komanduri, R. and von Turkovich, B.F. (1981). “New observations on the mechanics of chip formation when machining titanium alloys.” Wear (v69), pp179-188.
Ms. Jun Fan, senior engineer with AVAYA Inc., is responsible of several ExchangeMax and SystiMax products. She received her master of science degree in manufacturing systems engineering from the University of Nebraska-Lincoln in 1998, where she was a research assistant with the Nontraditional Manufacturing Research Center. Her primary research interests are in cryogenic cooling and enhanced machining of ceramic and titanium alloys. George Petrescu received a BSc degree from the Technical University of Constructions, Bucharest, Romania, and a MSc degree from the University of Nevada, Las Vegas. His research interests include machining of hard-to-cut materials, cryogenic and hybrid machining, and crack propagation in tooling materials (PCBN), as well as path planning of redundant robots. Currently, he lives and works as a mechanical engineer in Toronto, Ontario.
200
J-Integral Analysis of PCBN Tool Crack Propagation in Hybrid Machining of Advanced Materials Z.Y. Wang, Nevada Manufacturing Research Center, Dept. of Mechanical Engineering, University of Nevada, Las Vegas, Nevada, USA K.P. Rajurkar and J. Fan, Industrial and Management Systems Engineering Dept., University of Nebraska–Lincoln, Lincoln, Nebraska, USA G. Petrescu, Nevada Manufacturing Research Center, Dept. of Mechanical Engineering, University of Nevada, Las Vegas, Nevada, USA
Abstract
chining most commonly used materials, such as alloy steels. Because in a machining process more than 90% of the energy consumed is eventually converted into heat (Trent 1984), cutting temperatures are high in machining advanced materials. However, the thermal conductivities for ceramics, titanium alloys, and Inconel are low. Therefore, high temperatures are concentrated in a narrow area close to the cutting edge (Komanduri and von Turkovich 1981). Tool cutting edges bear high forces and high temperatures, which quickly leads to crack initiation and propagation in the tool and results in rapid tool wear and early fracture. Many attempts have been reported in improving tool life and surface finish in machining advanced materials. Baker and Krabacher (1956) at the Cincinnati Milling Machine Co. pioneered hot machining in their research. Their work was further extended by Uehara and Takeshita (1986) and Shin and Kim (1996) in the machining of ceramics and Inconel, respectively. The reductions of cutting forces and improvement in workpiece machinability were observed in both of these papers. However, further research is needed to stabilize the cutting tool life affected by the heat generation during machining. Lindeke et al. (1991) adapted a different approach by applying high-pressure coolants to the cutting insert while machining titanium alloys and achieved promising results. To further strengthen the cooling effects, Hong and Zhao (1992) and Wang, Rajurkar, and Murugappan (1996) investigated the effect of cryogenic cooling on turning titanium alloys, low carbon steels, and ceramics by applying liquid nitrogen to the cutting tool. In both of these tests, cutting
Failure of polycrystalline cubic boron nitride (PCBN) cutting tools, resulting from microcrack development, is one of the major causes of tool replacement in the machining of advanced materials. In this research, the J-integral method is applied to study the relationship between crack growth in a cutting tool and tool life in a hybrid machining process. Results show that with the decrease of the cutting temperature and its gradient in the cutting tool, the J value decreases and the tendency for micro crack propagation in the tool declines. Therefore, tool wear and early fracture rates are remarkably reduced.
Keywords: J-Integral Analysis, Tool Failure, Advanced Materials
Introduction As the automotive, aerospace, electronics, and many other industries adapt more advanced materials, such as titanium alloys, Inconel, ceramics, and metal matrix composites (MMC), to improve the quality of their products, the machining of these materials both efficiently and economically becomes more and more challenging (Shaw 1984; Jahanmir et al. 1992). The surface finish of these materials is usually poor after being machined. Low cutting speeds are often used to reduce high wear rate and potential early tool fracture (Trent 1984). Cutting forces and temperatures are two major causes contributing to rapid tool wear and early tool fracture in machining advanced materials (Trent 1984). In general, more energy is consumed in machining advanced materials due to their excellent mechanical properties. Therefore, the specific force on a cutting edge is much higher compared to ma196
Journal of Manufacturing Processes Vol. 6/No. 2 2004
tool life was improved significantly because the heat generated in cutting was partially absorbed by the liquid nitrogen coolant applied to the cutting insert. Inspired by the experimental results, a technique called hybrid machining was proposed by a group of researchers headed by Rajurkar, Wang, and Fan (1996) and Shin and Kim (1996). This method applies plasma heating to soften the workpiece materials and also applies liquid nitrogen to cool the cutting insert. Extensive experimental results show that cutting forces and temperature-dependent tool wear are reduced considerably in machining ceramics, titanium alloys, Inconel, and tantalum (Rajurkar, Wang, and Fan 1996). This paper presents the theoretical part of the investigation of hybrid machining. A J-integral analysis is introduced to study the effect of hybrid machining on cutting tool life.
Figure 1 J-Integral Path
Here E is the modulus of elasticity, ␣ is the coefficient of linear thermal expansion, is Poisson’s ratio, T is the temperature, and
Model Development
⎡1 ∂ ⎤ E ⋅α (T ⋅ ε ii ) − ε ii ⋅ ∂T ⎥dA ⋅ ∫⎢ ⋅ 1 − 2 ⋅ ν A0 ⎣ 2 ∂x1 ∂x1 ⎦
is the temperature
gradient with respect to the x1 direction. In general, the value of a J-integral over a closed path is not zero if thermal stresses are present in the region. This indicates that for thermal stress induced crack problems the stress intensity factor at a crack tip cannot be determined directly from a J-integral calculation over a path surrounding the crack tip. To solve the problem, the procedure needs to be modified by considering the closed paths ⌫1 + s1 + ⌫2 + s2. Therefore, Eq. (1) is transformed into
The J-integral concept was originally used to define nonlinear elastic materials as a path independent line integral around a crack tip (Rice 1968). Later on, the concept was extended as a fracture criterion for elastic-plastic materials (Sumpter and Turner 1975). For a PCBN cutting tool, it is virtually impossible to avoid the presence of micro voids/cracks on or under its surfaces due to the nature of how the material was processed. When a PCBN insert is used for machining advanced materials, dynamic cutting forces and heat cause the voids/cracks to propagate to the insert surfaces and lead to tool fracture. In the meantime, the growth of the voids/cracks to cutting tool surfaces deteriorates cutting-edge integrity and therefore results in rapid tool wear. It is true that many other factors also result in tool wear. However, the research reported here is focused on the effects of hybrid machining on crack development in a cutting tool. Figure 1 illustrates a crack located at an arbitrary position in a PCBN cutting insert surface during a hybrid machining process. When thermal effects are considered, Wilson and Yu (1979) found that the Jintegral is equal to an integral over the area a0 inside the closed path. It has the form of J=
∂T ∂x1
1 − ν2 2 ⋅ K1 = J Γ2 − E ⎡1 ∂ ∂U ∂T ⎤ E ⋅α Ti ⋅ i ds − ⋅∫⎢ ⋅ (T ⋅ εii ) − εii ⋅ ⎥dA ∫ 1 2 2 ∂ x1 ⎦ ν ∂ x − ⋅ ∂ x 1 1 s2 + s2 A0 ⎣ J1 =
(2)
where J Γ is the J-line integral calculated over the path ⌫2. Taking the crack surface to be traction free, the above equation becomes 2
1 − ν2 2 ⋅ K1 = J Γ2 − E ⎡1 ∂ E ⋅α ∂T ⎤ ⋅∫⎢ ⋅ (T ⋅ εii ) − εii ⋅ ⎥dA 1 − 2 ⋅ ν A0 ⎣ 2 ∂x1 ∂x1 ⎦ J1 =
(3)
If J* is defined as
(1)
J * = ∫ W * ⋅ dx2 − Ti Γ
197
∂Ui ⋅ ds ∂x1
(4)
Journal of Manufacturing Processes Vol. 6/No.2 2004
where E ⋅α W =W − ⋅ T ⋅ ε ii 1 − 2 ⋅ν *
J1 =
E
(5)
F
1 −ν 2 ∂T E ⋅α ⋅ K 12 = J Γ*2 − ⋅ ∫ ε ii ⋅ dA (6) 1 − 2 ⋅ ν A0 ∂x1 E B
If is a constant, then it can be moved out from the integral sign. The area integral then becomes ii
Tool
G
∂T ∂x1
∫ε
D
Crack
A
C
Work
Figure 2 Edge Crack Strip and Boundary Condition
dA
A0
Physically, this integral is equal to the volume change of the material over the area a0. Using Green’s theorem, this integral can be transformed back to a line integral over the path of . The final equation becomes J1 =
⎡ ⎤ ∂U 1 − ν2 2 ⋅ K1 = ∫ ⎢W * ⋅ dx2 − σij ⋅ n j ⋅ i ⋅ ds ⎥ + E ∂ x 1 ⎦ Γ2 ⎣
q⋅E ⋅α ⋅ (U1 ⋅ dx2 − U 2 ⋅ dx1 ) 1 − 2 ⋅ ν Γ∫2
(7)
Here
q=
∂T ∂x1
Figure 3 Stress Distribution Due to Temperatures and Forces
FEA Results
heat sources, and both of them are assumed to generate heat during machining. CD and DE are far away from the cutting edges; they are assumed to be at room temperature, i.e. 25°C. Heat loss to the air by convection is considered on edge AC. EF is a special convective boundary; it breaks into two parts, with EF convecting heat to the liquid nitrogen and FG convecting heat to the air. For mechanical stress analysis, CD and DE are considered as rigid in both directions due to their long distances away from the cutting forces. The other two edges, AC and AE, are free of rotation and translation. Figure 3 is an example of stress distribution due to temperatures and forces. The results for J calculated from Eq. (7) are presented in Figures 4 and 5. Figure 4 reveals the relationship between J values and the temperature changes at a crack tip. The initial temperature at a crack tip used in the J value calculation was 275°C,
The J-integral values were calculated using Eq. (7) developed above. FEA software MSC.Patran™/ Nastran™ was used to obtain the values of stress, strain, and displacement needed in Eq. (7). The FEA model was composed of 29 connected surfaces, which were divided into 202,254 elements (triangular or quadrilateral) for the crack case and 202,089 elements (triangular or quadrilateral) for the non-crack case. Because the area of interest is at the tool tip, this is the region where high mesh density was used. The properties of PCBN tool material used in the J-integral calculations were the following: coefficient of –6 –1 linear thermal expansion = 4.9 10 K , Young’s modulus = 680 GPA, and Poisson’s ratio = 0.22. An edge crack located on the insert flank face was used in the calculation. Boundary conditions are shown in Figure 2. For the thermal analysis, AB and AG are
198
Journal of Manufacturing Processes Vol. 6/No. 2 2004
4
80 J-value Ratio
J - Value Ratio
5
3 2 1 0 200
60 40 20 0
300
400
500
600
0
700
25 50 75 100 125 150 175 200 225 Temperature Gradient (0C/mm)
0
The Temperature at Crack Tip C
Figure 4 J-Value Ratio vs. Temperature at a Crack Tip
Figure 5 J-Value Ratio vs. Temperature Gradient
and this J value was used as a benchmark for the rest of calculations. When the temperature at the crack
In the hybrid machining experiments, tool wear and fracture were reduced significantly when a workpiece material was softened by an external heat source and the tool insert was cooled by liquid nitrogen to a lower temperature range. Similar findings were also reported in previous publications (Wang, Rajurkar, and Murugappan 1996 and Wang and Rajurkar 2000) when machining was carried out with liquid nitrogen cooling only with no external heat source applied. The analyses presented in this paper reveal that when cutting forces, cutting temperatures, and temperature gradients in a tool reduce—i.e., the J value decreases—the stresses at the pre-existing crack tips reduce, leading to a slowing in the cutting tool wear rate, and the risk of tool fracture reduces accordingly. The relative importance of internal cracks versus tool edge surface cracks as a cause for tool wear has been debated for decades. Experimental evidence has proven to some extent that surface cracks cause fracture and expedite wear in cutting tools. However, some researchers still believe that the internal cracks are the cause of tool fracture. Because internal cracks are all started inside a cutting tool, it is very difficult to identify them before significant tool fracture occurs. Even after a tool fracture occurs, it is often difficult to say which crack started internally or externally due to wear marks on the fractured surface caused by the machining process. The J-integral analysis presented in this paper may influence that debate. Our calculation shows that the temperatures and temperature gradients in the cutting insert are always lower than those on cutting edge surfaces. The further a crack is away from an insert
⎛J
⎞
at 400°C ⎟ became tip reached 400°C, the J value ratio ⎜ J ⎝ at 275°C ⎠ 1.84. When the temperature reached 500°C, the J value ratio became 2.72, and when the temperature became 650°C, the J ratio was 4.69. Figure 5 shows the relationship between J values and temperature gradients in the PCBN cutting tool. The initial temperature gradient in the calculation was 18.75°C/mm, and the J value was used as benchmark for the rest of the calculations. When the temperature gradient reached 37.5°C/mm, 62.5°C/mm, 87.5°C/mm, 125°C/mm, and 200°C/mm, respectively, the J value increased to 2.89, 6.81, 12.39, 23.81, and 57.76 accordingly.
Validation and Discussion The assumption was made in the model development section that
∂T ∂x1
is a constant, which was based
on careful analysis of the FEA results obtained in this study. Figure 4 shows that temperature at a crack tip has great influence on J values. With temperature increases, the J value increases rapidly. Hence, the tendency for crack propagation increases. Figure 5 reveals another important factor that affects the J value and tool failure. When temperature gradients in the tool go up, the J value also increases quickly. Therefore, the cutting tool is more prone to fracture in these cases.
199
Journal of Manufacturing Processes Vol. 6/No.2 2004
edge surface, the lower the J value is. Therefore, the J value at any point in the cutting insert is less than the J value on the surface. Thus, the tendency for micro-crack propagation inside the insert becomes less. Based on the J-integral analyses, it is reasonable to say that surface cracks and cracks adjacent to surfaces are more likely to cause tool fractures.
Lindeke, R.R.; Schoenig, F.C.; Khan, A.K.; and Haddad, J. (1991). “Machining of titanium with ultra-high pressure through the insert lubrication/cooling.” Transactions of the North American Manufacturing Research Institution of SME (v19). Dearborn, MI: Society of Manufacturing Engineers, pp154-161. Rajurkar, K.P.; Wang, Z.Y.; and Fan, J. (1996). “Hybrid machining.” Workshop on Hybrid Machining, MT-AMRI, Purdue Univ., West Lafayette, IN. Rice, J.R. (1968). “A path independent integral and the approximate analysis of strain concentration by notches and cracks.” Journal of Applied Mechanics (v6), pp379-386. Shaw, Milton C. (1984). Metal Cutting Principles. New York: Oxford Univ. Press. Shin, Y.C. and Kim, J. (1996). “Plasma enhanced machining of Inconel 718.” Mfg. Science and Engg. (ASME MED-v4), pp243-249. Sumpter, J.D.G. and Turner, C.E. (1975). “Method for laboratory determination of Jc.” Proc. of 9th Nat’l Symp. on Fracture Mechanics, Pittsburgh, ASTM STP-601, pp3-18. Trent, X.M. (1984). Metal Cutting. London: Butterworths. Uehara, K. and Takeshita, H. (1986). “Cutting ceramics with a technique of hot machining.” Annals of the CIRP (v35/1), pp55-58. Wang, Z.Y.; Rajurkar, K.P.; and Murugappan, M. (1996). “Cryogenic PCBN turning of ceramic (Si3N4).” Int’l Journal of Wear (v196), pp16. Wang, Z.Y. and Rajurkar, K.P. (2000). “Cryogenic machining of hard-tocut materials.” Int’l Journal of Wear (v239), pp168-175. Wilson, W.K., and Yu, I.W. (1979). “The use of the J-integral in thermal stress crack problems.” Int’l Journal of Fracture (v15, n4).
Conclusions This paper established a relationship between Jintegral values and cutting tool fracture in machining. It is found that when the temperature rises at a crack tip in a cutting insert, its J value increases also, and the tendency for micro crack propagation increases accordingly. It is also found that when temperature gradients in a cutting insert increase, the J value increases and the tendency for micro crack propagation increases as well. Hybrid machining reduces temperatures and temperature gradients in the cutting inserts. Therefore, it reduces early tool fracture and tool wear in machining advanced materials, and consequently, it improves surface finish of machined surfaces.
Authors’ Biographies Dr. Z.Y. Wang is the director of Nevada Manufacturing Research Center at the University of Nevada, Las Vegas. His research areas are manufacturing process improvements, lean manufacturing, and agile manufacturing.
Acknowledgment The authors are grateful for support from Nebraska Research Initiative funds and UNLV grants.
Dr. K.P. Rajurkar, Mohr Professor of Engineering, University of Nebraska, is the founder and director of the Nontraditional Manufacturing Research Center. For the last three years, he also served as a program director at the National Science Foundation. His research and teaching interests include advanced manufacturing processes.
References Baker, W.R. and Krabacher, E.J. (1956). “New techniques in metal-cutting tesearch.” Trans. of ASME (v78), pp1497-1505 Gdoutos, E.E. (1990). Fracture Mechanics Criteria and Application. Kluwer Academic Publishers. Hong, S.Y. and Zhao, Z.B. (1992). “Cooling strategies for cryogenic machining from materials viewpoint.” Journal of Materials Engg. & Performance (v1, n5). Jahanmir, S.; Ives, L.K.; Ruff, A.W.; and Peterson, M.B. (1992). “Ceramic machining: assessment of current practices and research needs in the United States.” NIST Special Publication 834. Gaithersburg, MD: NIST. Komanduri, R. and von Turkovich, B.F. (1981). “New observations on the mechanics of chip formation when machining titanium alloys.” Wear (v69), pp179-188.
Ms. Jun Fan, senior engineer with AVAYA Inc., is responsible of several ExchangeMax and SystiMax products. She received her master of science degree in manufacturing systems engineering from the University of Nebraska-Lincoln in 1998, where she was a research assistant with the Nontraditional Manufacturing Research Center. Her primary research interests are in cryogenic cooling and enhanced machining of ceramic and titanium alloys. George Petrescu received a BSc degree from the Technical University of Constructions, Bucharest, Romania, and a MSc degree from the University of Nevada, Las Vegas. His research interests include machining of hard-to-cut materials, cryogenic and hybrid machining, and crack propagation in tooling materials (PCBN), as well as path planning of redundant robots. Currently, he lives and works as a mechanical engineer in Toronto, Ontario.
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