A method for predicting fracture toughness and yield strength of a tough, difficult-to-machine material by milling

Abstract

The application discloses a method for predicting fracture toughness and yield strength of a tough difficult-to-machine material by milling, which comprises the following steps: firstly, a prediction model of the fracture toughness and yield strength of the tough difficult-to-machine material in the process of forming a sawtooth chip by an oblique cutting saw is established; then, a milling test is carried out; and finally, the fracture toughness and yield strength are calculated by combining the prediction model and the test data. The method can avoid the problem that the predicted values of the fracture toughness and yield strength are unreasonable due to the crack blunting of the tough difficult-to-machine material in a standard mechanical test, so that the values of the fracture toughness and yield strength of the tough difficult-to-machine material in a dynamic cutting process can be simply, conveniently, feasibly and universally predicted at the same time.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for predicting the fracture toughness and yield strength of tough-to-machine materials in the process of saw-tooth chip formation by widely used milling machining method, and in particular to a method for predicting the fracture toughness and yield strength of metal and alloy materials with high hardness and high toughness in the process of dynamic cutting machining. BACKGROUND

[0002] Tough-to-machine materials are widely used in aerospace, consumer electronics and medical devices, etc. due to their high strength and hardness at high temperature. However, in the actual cutting process, they tend to produce saw-tooth chips at a wide range of cutting speed and feed rate, which makes the cutting process unstable, leading to accelerated tool wear and poor machined surface quality. Both yield strength and fracture toughness are control factors affecting the deformation of removed material and the finish of machined surface. In addition, a high ratio of fracture toughness to yield strength is beneficial to the controllability of workpiece material removal process and improves the integrity of machined surface. However, due to the fact that tough-to-machine materials cannot meet the linear elastic fracture mechanics conditions, they tend to produce crack blunting in standard mechanical tests, so that their effective values of yield strength and fracture toughness cannot be obtained through traditional experiments. Therefore, it is of great scientific research significance and engineering application value to explore a simple and feasible method to predict the yield strength and fracture toughness of tough-to-machine materials in the process of actual cutting saw-tooth chip formation.

[0003] The document "Y. Patel, B. R. K. Blackman, J. G. Williams, Determining fracture toughness from cutting tests on polymers, Engineering Fracture Mechanics 76(18) (2009) 2711-2730." relies on a built orthogonal cutting test platform to obtain cutting data, and discloses a test method based on orthogonal cutting machining to predict the yield strength and fracture toughness of tough polymers. Although this method uses cutting machining to avoid the problem of crack blunting of workpiece materials in standard mechanical tests, this method is carried out under orthogonal conditions, which requires special equipment and tools to ensure plane cutting, and measures the cutting force and undeformed chip thickness in machining, so that this method has certain limitations and is not convenient and universal.

[0004] The document “B. Wang, Z. Q. Liu, Q. B. Yang, Investigations of yield stress, fracture toughness, and energy distribution in high speed orthogonal cutting, International Journal of Machine Tools and Manufacture 73 (2013) 1-8.” discloses a method to predict the yield strength and fracture toughness of a ductile metal in the serrated chip formation process using the milling force and the average thickness of the serrated chip for the machining of carbon steel AISI 1045. However, the straight end mill is used in this method and the tool rake angle is 0 degree. Therefore, the milling process can also be regarded as a two-dimensional orthogonal cutting process.

[0005] The document “L. Liang, G. Z. Lin, H. H. Tan, J. D. Yuan, L. He, C. C. Jiang, X. Q. Li, Prediction of critical cutting condition for onset of serrated chip in ductile metallic material using dynamic yield stress, Journal of Manufacturing Processes 64 (2021) 927-936.” discloses a method to predict the yield strength and fracture toughness of a ductile metal in the dynamic cutting process using the milling force and the chip thickness for the machining of ductile metals silicon brass and titanium alloy Ti6Al4V. Although the external work done by the tool on the workpiece is considered to be concentrated at the tool tip in this method to promote the growth of sharp natural cracks in the workpiece material and does not cause excessive blunting of the cracks, the straight end mill is also used in the experiment and the workpiece material is a thin plate to ensure that it is subjected to plane stress. Therefore, although the milling process is commonly used in this method, the straight end milling process in the experiment is still a two-dimensional orthogonal cutting process.

[0006] The typical feature of the above-mentioned references is that the cutting process is used to replace the prediction of the yield strength and fracture toughness of the ductile material, thereby avoiding the problem of crack blunting encountered in standard mechanical tests, so that the yield strength and fracture toughness of the ductile material can be effectively obtained. However, the experiments essentially use two-dimensional orthogonal cutting, which requires special equipment and tools to ensure plane cutting, making the material processing method not simple and not universal. SUMMARY

[0007] In order to overcome the limitations of the prior art, that is, the need for special equipment and tools to ensure orthogonal cutting, so that the prediction method is inconvenient, there is no universality, the present application proposes a widely used milling method to predict the yield strength and fracture toughness of the tough difficult-to-machine material, thereby avoiding the problem of crack blunting encountered in standard mechanical tests. Referring to the accompanying Figure 4 (b), first, the end mill cutting edge is divided along the tool axis into an infinite number of micro elements, and each micro element cutting is regarded as an oblique angle cutting process; then the cutting force model related to chip generation is established for a single blade micro element, and the cutting force in the oblique angle cutting is projected into the plane perpendicular to the cutting edge, and the fracture toughness is introduced at the tool tip, and then the orthogonal cutting theory and method are used for cutting force analysis, so as to deduce the equation for predicting the fracture toughness and yield strength in the dynamic milling process, and the yield strength and fracture toughness of the tough difficult-to-machine material are calculated by combining the test cutting force data and the average thickness of the sawtooth chip.

[0008] The technical effect is that the present application provides a modeling method for predicting the fracture toughness and yield strength of the tough difficult-to-machine material based on the cutting force and the average thickness of the sawtooth chip in the ordinary milling process, which can avoid the problem of unreasonable prediction of the fracture toughness and yield strength caused by crack blunting in the standard mechanical test of the tough difficult-to-machine material, so as to more simply, conveniently, feasibly and universally predict the values of the fracture toughness and yield strength of the tough difficult-to-machine material in the dynamic cutting process.

[0009] The technical solution adopted by the present application to solve the technical problem is: first, a prediction model of the fracture toughness and yield strength of the tough difficult-to-machine material in the process of forming sawtooth chip in oblique angle cutting is established, then a milling test is carried out, and finally the fracture toughness and yield strength are calculated by combining the prediction model and the test data. The characteristics include the following steps:

[0010] Step one, combining Figure 1 (a) and (b), according to the chip generation geometry model and the cutting force analysis model in the oblique angle cutting process, the following equation can be derived to calculate the plastic shear flow direction angle δ of the material in the first deformation zone, the chip flow direction angle β of the chip, and the normal friction angle λ between the chip and the rake face of the tool n .

[0011]

[0012]

[0013]

[0014] Where φ nis the first deformation zone normal shear angle, a is the tool rake angle, γ is the inclination angle of the cutting edge in oblique cutting, F c is the main cutting force, F t is the transverse force, F l is the side force.

[0015] Step two, project each cutting force in oblique cutting to the plane perpendicular to the cutting edge, and calculate the projection component of each cutting force according to the following equation:

[0016] F' c = F c cos γ

[0017] F' s = F s cos δ

[0018] F' f = F f cos β

[0019] wherein F' c , F' s , F' f are the projection components of the main cutting force F c , the first deformation zone shear force F s , and the friction force F f between the chip and the tool rake face in the plane perpendicular to the cutting edge.

[0020] Step three, according to the cutting force balance on the tool rake face, the equation is obtained, and the Coulomb friction law, i.e. F f = μF N is used, wherein the following two equations are obtained:

[0021]

[0022] wherein μ is the friction coefficient when the chip slips on the tool rake face, λ is the friction angle when the chip slips on the tool rake face, t1 is the thickness of the undeformed chip, w1 is the width of the undeformed chip, G c is the fracture toughness of the workpiece material at the tool tip in oblique cutting, σ Y is the yield strength of the workpiece material in the first deformation zone shear plane in oblique cutting.

[0023] Step four, according to the cutting force balance on the first deformation zone shear plane, the equation is obtained, and the derivative of tan φ n is taken, the following two equations are obtained, and then the linear fitting of the experimental data between the cutting force and the undeformed chip thickness can be carried out respectively.

[0024]

[0025] Step five, comparing the cutting force equation set obtained in step three and step four, the first deformation zone normal shear angle φ n and the relationship expression between the normal friction angle λ n between the chip and the rake face of the tool can be obtained:

[0026]

[0027] Step six, according to the shear force balance on the shear plane of the first deformation zone, the equation is obtained. Using the expression of τ s , the first deformation zone normal shear angle φ n is derived, and the expressions of and in step three are combined to obtain the following equation, and then the planning solving method is used to simultaneously solve the two unknowns of the left and right sides of the equation, i.e. the fracture toughness G c and the yield strength σ Y .

[0028]

[0029] Where τ s is the critical shear stress on the shear plane of the first deformation zone, and the Tresca yield criterion is followed.

[0030] The beneficial effects of the present application are: the method first establishes a continuous chip generation geometric model and a cutting force analysis model in the oblique angle cutting process, and establishes equations to calculate the normal friction angle λ n of the contact surface between the tool and the chip in the chip generation process, the shear flow direction angle δ of the first deformation zone, the flow direction angle β of the chip on the rake face of the tool and the first deformation zone normal shear angle φ n ; then the geometric model of the sawtooth chip generation is extended, equations are established to calculate the projection of the cutting force in the plane perpendicular to the cutting edge, and the fracture toughness G c is introduced for cutting force balance analysis to establish equations to predict the fracture toughness G c of the material at the tool tip in the oblique angle cutting process and the yield strength σ Y of the material on the shear plane of the first deformation zone. Finally, the fracture toughness G c of the material at the tool tip and the yield strength σ Y of the material on the shear plane of the first deformation zone are solved by using the above equations and combining the milling cutting force data and the average thickness of the sawtooth chip. Compared with the given literature, the present application uses ordinary milling machining method to establish the fracture toughness G c of the material at the tool tip in the sawtooth chip generation in the oblique angle cutting process.σ Y , the prediction model of σ c , and σ Y , can avoid the problem of unreasonable calculation of the value of σ c , σ Y , and σ c_max .

[0031] The present application is described in detail below with reference to the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is a schematic diagram of a slant angle cutting geometry model and a cutting force analysis model.

[0033] Figure 2 is a geometry and a cutting force analysis model of regular saw tooth type chip generation.

[0034] Figure 3 is a schematic diagram of a side milling force analysis geometry model.

[0035] Figure 4 is a top view of the side milling force analysis geometry model and a front view of the end mill geometry model.

[0036] Figure 5 is the saw tooth chip morphology under different milling speeds.

[0037] Figure 6 are the test results and the fitted straight lines under different milling speeds. DETAILED DESCRIPTION

[0038] The following examples are used to illustrate the present application.

[0039] The test uses a four-tooth flat bottom carbide end mill with a radius of 8 mm, a helix angle of 35 degrees, a rake angle of 10 degrees, and a relief angle of 6 degrees. The tool coating is AlCrN, and the milling method is down milling. The cutting parameters used are a radial depth of cut of 0.1 mm, an axial depth of cut of 2 mm, and a feed per tooth of 0.01 mm / tooth.

[0040] Step one, refer to the attached Figure 2 and the attached Figure 5 , measure the maximum thickness t c_max , and the minimum thickness t c_min of the regular sawtooth segment of the sawtooth chip under a microscope. Figure 5The serration size is irregular at a cutting speed of 80 m / min, and the serration profile morphology is irregular at 110 m / min, so the maximum and minimum thickness of the serration section is not measured.

[0041] Step two, calculate the average thickness t of the serration chip according to the following equation chip :

[0042]

[0043] Step three, set the initial value of the normal shear angle of the first deformation zone [φ n ] ini , and calculate the average thickness t of the serration section of the chip at this position according to the following equation chip :

[0044]

[0045] Where r c is the ratio of the undeformed chip thickness before and after machining and the deformed chip thickness.

[0046] Step four, solve the instantaneous tool intrusion angle φ at the undeformed workpiece material thickness h according to the following equation

[0047] h-f' z sin(φ ex -φ)=0

[0048] Where f' z is the actual feed per tooth (f' z can approach the nominal feed per tooth f z ), φ ex is the angle of the cutting end position when the tool cuts out the workpiece material.

[0049] Step five, calculate the cutting forces F c , F t and F l at the instantaneous tool intrusion angle φ according to the following equation

[0050]

[0051] Where F x , F y , F z are the X, Y, Z direction cutting force components measured by the dynamometer at the instantaneous tool intrusion angle φ.

[0052] Step six, calculate the normal friction angle λ n of the tool and chip contact surface according to the above equation .

[0053] Step seven, according to the above equation Calculate the normal shear angle φ of the first deformation zone n .

[0054] Then compare the calculated normal shear angle [φ n ] cal with the initial value [φ n ] ini set for it, and calculate the relative error ε If ε is within the allowable error range, the calculated result of the normal shear angle [φ n ] cal is considered reasonable, i.e., acceptable; if ε is not within the allowable error range, return to step three, reset the initial value of the normal shear angle [φ n ] ini , and recalculate until a satisfactory result is obtained, where the initial value of the normal shear angle [φ n ] ini is in the range of 0 degrees to 45 degrees. Some results obtained from experimental data are shown in Table 1.

[0055] Table 1 Calculated results of t chip , t1, φ n , β and δ under different cutting speed conditions

[0056]

[0057]

[0058] Step eight, according to the milling test data, i.e., the cutting force and the average thickness of the sawtooth-shaped chip, calculate the longitudinal coordinate and the transverse coordinate respectively, and calculate the longitudinal coordinate and the transverse coordinate respectively according to the cutting force equation obtained from the cutting force balance described above. Then perform linear fitting respectively, and the fitting results are shown in Figure 6 . Then use the slope and intercept of the fitting straight line to calculate the yield strength σ Y and the fracture toughness G c of the workpiece material in the generation process of the oblique angle cutting sawtooth-shaped chip, and the calculated results are shown in Tables 2 and 3:

[0059] Table 2 Predicted yield strength σ Y and fracture toughness G c values of the workpiece material from the fitting straight line between and under different cutting speed conditions

[0060]

[0061] Table 3. Conditions under different cutting speeds and The yield strength σ of the workpiece material predicted by the fitted straight line. Y value

[0062]

[0063]

[0064] Step 9: Based on the above equation Similarly, combining milling test data, namely cutting force and average thickness of serrated chips, the yield strength σ of the workpiece material during bevel cutting is calculated using a problem-solving approach. Y and fracture toughness G c The calculation results are shown in Table 4:

[0065] Table 4. Yield strength σ of the workpiece material obtained by programming solution under different cutting speeds. Y Value and fracture toughness G c value

[0066]

[0067] Step 10: The yield strength σ of the workpiece material during the milling process of the tough, difficult-to-machine nickel alloy Inconel 718, obtained from Tables 2, 3, and 4 above, is compared with that of the Inconel 718. Y and fracture toughness G c By comparing the results respectively, we found that the predicted yield strength σ of the workpiece material under different cutting speed conditions in Tables 2, 3, and 4 was... Y Value and fracture toughness G c The similar values ​​demonstrate the rationality of this milling modeling method. This is because the yield strength σ varies under different cutting speeds. Y Differences between values ​​and fracture toughness G cThe differences between the values can be explained by the combined effects of strain rate hardening encountered during the generation of a sawtooth chip in the cutting process and the softening of the workpiece material caused by high temperatures, and by comparing the yield strength and fracture toughness values of the nickel-based superalloy Inconel 718 in the literature "B. Wang, Z. Q. Liu, Acoustic emission signal analysis during chip formation process in high speed machining of 7050-T7451 aluminum alloy and Inconel 718 superalloy, Journal of Manufacturing Processes 27 (2017) 114-125." and "C. Liu, M. Wan, C. J. Shen, Y. Yang, Determination of the yield strength and the energy distribution in the milling of Inconel 718 considering fracture toughness, Journal of Manufacturing Processes 82 (3) (2022) 347-361.", it is found that they can better match the results of the present milling test, thus proving the effectiveness of the modeling method of the present application for predicting the fracture toughness and yield strength of the workpiece material of the tough-to-machine material in the sawtooth chip generation process by milling.

Claims

1. A method for predicting fracture toughness and yield strength of tough, difficult-to-machine materials by milling, characterized in that, Includes the following steps: Step one, according to the oblique angle cutting process chip generation geometry model and cutting force analysis model, can be derived as follows equation, to calculate the first deformation zone material plastic shear flow direction angle delta, chip in the rake face flow direction angle beta, chip and tool rake face between normal friction angle lambda n ; where φ n is the first deformation zone normal shear angle, a is the tool rake angle, g is the inclination of the cutting edge angle during cutting, F c is the main cutting force, F t is the transverse force, F l is the side force; Step 2: Project each cutting force during the bevel cutting process onto a plane perpendicular to the cutting edge, and calculate the projected components of each cutting force according to the following equations: F' c =F c cosγ In s =F s cosδ In f =F f cosβ Where F' c , F' s , F' f The main cutting force F c Shear force F in the first deformation zone s The frictional force F between the chip and the rake face of the tool f The projection component in the plane perpendicular to the cutting edge; Step 3: Based on the cutting force balance on the tool's rake face, the equation is obtained. And using Coulomb's law of friction, i.e. F f =μF N ,in The following two equations can be obtained: Where μ is the coefficient of friction when the chip slides on the rake face of the tool, λ is the friction angle when the chip slides on the rake face of the tool, t1 is the thickness of the undeformed chip, w1 is the width of the undeformed chip, and G... c σ represents the fracture toughness of the workpiece material at the tool tip during bevel cutting. Y The yield strength of the workpiece material within the shear plane of the first deformation zone in oblique cutting; Step 4: Based on the cutting force balance on the shear plane of the first deformation zone, the equation is obtained. And for tanφ n By taking the derivative, we obtain the following two equations, and then we can perform linear fitting of the experimental data between the cutting force and the thickness of the undeformed chip. Step 5: By comparing the cutting force equations obtained in Step 3 and Step 4, the normal shear angle φ of the first deformation zone can be obtained. n The normal friction angle λ between the chip and the rake face of the tool n Relational expressions between the two: Step 6: Based on the shear force balance on the shear plane of the first deformation zone, the equation is obtained. Using τ s The expression for t1 represents the normal shear angle φ of the first deformation zone. n Perform differentiation and combine it with step three. and From the expression, we obtain the following equation, and then use the solver method to simultaneously calculate the fracture toughness G on both sides of the equation. c and yield strength σ Y Two unknowns; Where τ s It is the critical shear stress within the shear plane of the first deformation zone, and Follow the Tresca yield criterion.

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