CN117095773A - Method for establishing right-angle cutting equal-divided shearing area model characterization based on Oxley theory - Google Patents

Method for establishing right-angle cutting equal-divided shearing area model characterization based on Oxley theory Download PDF

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CN117095773A
CN117095773A CN202311070284.7A CN202311070284A CN117095773A CN 117095773 A CN117095773 A CN 117095773A CN 202311070284 A CN202311070284 A CN 202311070284A CN 117095773 A CN117095773 A CN 117095773A
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chip
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CN117095773B (en
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杨琳
刘佳良
张湘媛
张为
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Harbin University of Science and Technology
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Abstract

The application discloses a method for establishing a right-angle cutting equal-division shearing area model characterization based on an Oxley theory, which comprises the following steps: s1: analyzing the viscous behavior of an austenite phase and a ferrite phase from a microscopic dislocation angle, and establishing a viscous constitutive model of the S32760 duplex stainless steel based on the viscous effect of the two phases and a mixing rule; s2: establishing a right-angle cutting equal-division shearing area model based on an Oxley theory, and predicting the multi-physical-field distribution in the cutting process; s3: and carrying out reverse identification correction on the constitutive parameters based on a right-angle cutting experiment. The method comprehensively considers the influence of high temperature and high strain rate in the cutting process, analyzes the influence of the viscosity effect on the cutting process, and provides a basis for researching the viscosity effect in the cutting process. The method constructs a biphase stainless steel constitutive model considering the viscous effect, and researches the change rule of flow stress along with the strain rate. The problem that the accuracy of the constitutive model is affected by the fact that the viscous effect in the cutting process is ignored in the existing method is solved.

Description

Method for establishing right-angle cutting equal-divided shearing area model characterization based on Oxley theory
The application relates to a divisional application of application number 202310282401.X, application day 2023, 03 and 21, and the application name is 'a construction method of a double-phase stainless steel adhesive constitutive model'.
Technical Field
The application belongs to the technical field of construction of a biphase stainless steel viscosity constitutive model, and particularly relates to a characterization method for establishing a right-angle cutting equal-division shearing area model based on an Oxley theory.
Background
In high-speed cutting, the material is subjected to a process of large strain, high strain rate and high temperature, the influence of viscous behavior on the plastic deformation process of the material needs to be considered, and the existing constitutive model ignores the influence of viscous effect on the cutting process.
Because of the large number of parameters to be determined and the limitations of research means, the parameters are analyzed and researched by using a finite element method and a Hopkinson pressure bar experimental method in the early stage. While both methods can obtain constitutive equations for materials, the former requires extensive calculations and consumes a significant amount of time; the latter only can study the strain rate of the metal at 10 3 -10 4 s -1 And experimental data reliability and experimental condition adaptability are difficult to be completely ensured.
The existing constitutive parameter acquisition method is difficult to reveal the viscous behavior of the material under the condition of high strain rate in the cutting process, so that the application aims at the problems, analyzes the viscous effect of the duplex stainless steel under the condition of high strain rate, and establishes an constitutive equation of the S32760 duplex stainless steel based on the viscous effect of two phases and a mixing rule. The method is suitable for reversely identifying the constitutive parameters under the high strain rate condition based on the cutting theory, and discloses the viscous behavior of the duplex stainless steel under the high strain rate condition.
Disclosure of Invention
The application aims to provide a method for establishing a right-angle cutting equal-division shearing area model characterization based on Oxley theory, so as to solve the problems in the prior art.
In order to achieve the above purpose, the present application provides the following technical solutions: the method for establishing the right-angle cutting equal-divided shearing area model characterization based on the Oxley theory comprises the following steps:
s1: analyzing the viscous behavior of an austenite phase and a ferrite phase from a microscopic dislocation angle, and establishing a viscous constitutive model of the S32760 duplex stainless steel based on the viscous effect of the two phases and a mixing rule;
s2: establishing a right-angle cutting equal-division shearing area model based on an Oxley theory, and predicting the multi-physical-field distribution in the cutting process;
s3: and carrying out reverse identification correction on the constitutive parameters based on a right-angle cutting experiment.
1. The right-angle cutting aliquoting shear zone characterization method comprises the following steps:
(1) Under the conditions of plane strain and steady cutting, a theoretical relation between a right-angle cutting process variable and an output variable is established, the cutting force distribution state of a cutting area for representing right-angle cutting is shown in fig. 2, FEBA and ABCD are respectively the upper half part and the lower half part of the cutting area for dividing, AG is the contact length of a cutter and chips, and is expressed as h tc 。
(2) Shear plane analysis
Based on the balance conditions of the shear plane and the tool-chip interface, each cutting component and chip thickness t 2 The method can be obtained by the following formula:
F c ＝F R cos(λ-α) (1)
F t ＝F R sin(λ-α) (2)
F f ＝F R sinλ (3)
F n ＝F R cosλ (4)
wherein: alpha is the front angle of the cutter;is the shear angle; lambda is the friction angle; t is t 1 Is the undeformed chip thickness; w is the cutting width; θ is F R An included angle with AB; sigma (sigma) AB Representing the shear plane average flow stress.
Any particle velocity in the first deformation zone is related to the average shear strain rate in the shear zone:
wherein: v is the right angle cutting speed; ΔS 1 Is the thickness between the two parallel bands of the first deformation zone.
The equivalent strain and equivalent strain rate of any particle at shear plane AB are:
the chip material flow velocity V can be obtained from the velocity vector relationship of FIG. 2 c And material flow velocity V of shear plane s ：
Shearing angleAnd the included angle theta satisfies the following relationship:
C 0 for the modified strain rate constant, the expression is:
wherein: c (C) Oxley Shearing the ribbon aspect ratio for the first deformation zone; A. b and n are JC constitutive parameters respectively.
The average temperature expression of the shear plane AB is:
wherein: t (T) r Taking 0.9 in analysis, wherein eta is the average temperature coefficient of the workpiece; ρ w Is the density of the material; c (C) w Specific heat capacity, β is the heat distribution coefficient.
Wherein: k (K) w Is the thermal conductivity.
(3) Tool-chip interface analysis
The equivalent strain and equivalent strain rate of the tool-chip interface are
Wherein: h is a tc Is the cutter-chip contact length.
Average temperature T of tool-chip interface int Expressed as:
T int ＝T r +ΔT SZ +ψΔT M (19)
wherein: psi is a correction coefficient; delta T M Is the maximum temperature rise in the chip; delta T C Is the average temperature rise in the chip; delta T SZ The temperature rises for the first deformation zone.
2. Method for solving chip forming force:
and establishing a right-angle cutting equal-division shearing area model, and taking the material property, the geometric angle of the cutter and the cutting amount as independent variables. In the theoretical calculation process, the shearing angle value, the aspect ratio of the shearing band of the first deformation zone and the ratio of the thickness of the second deformation zone to the thickness of the chip are calculated in an iterative mode according to three balance conditions, and when the output variable meets the three balance conditions, the calculation is finished.
Assuming that the stress of the cutter-chip interface is uniformly distributed, obtaining the stress tau of the cutter-chip interface int And stress sigma at point B N The expression is:
the normal stress sigma 'of the point B near the tip position in FIG. 2' N Average shear of combinable shear planesThe flow stress is obtained:
3. the viscous constitutive model construction method comprises the following steps:
building a constitutive model considering the viscous effect, and dividing the equation into three parts:
wherein: sigma (sigma) a Is a non-thermal stress term;is an influencing factor of reaction strain rate and temperature effect; sigma (sigma) th Is a thermal stress term; sigma (sigma) c Is a viscous effect term.
Because of the biphase nature of the material, three stresses of ferrite and three stresses of austenite should be calculated respectively and the proportioning weights should be added up.
σ＝l 1 σ 1 +l 2 σ 2 (25)
(1) Non-thermal stress term
The non-thermal stress term in the ferrite and austenite constitutive equations, respectively, can be written as:
wherein: sigma (sigma) i1 Sum sigma i2 The total resistance to dislocation movement within ferrite and austenite, respectively; m is m 1 And m 2 Constants characterizing grain boundary strength for ferrite and austenite, respectively; d, d 1 And d 2 Ferrite and austenitic respectivelyGrain size of the body; k (K) 1 Is a ferrite hardening coefficient; epsilon is the true strain; n is n 1 Is a ferrite strain sensitivity index.
(2) Thermal stress term
The expression of the influencing factor is:
wherein: k is a Boltzmann constant; t is the temperature; g 0 Is the reference thermal activation energy;is the reference strain rate; p and q are barrier constants.
The ferrite thermal stress term is expressed as:
wherein:is a reference value for ferrite saturation threshold stress at t=0k; b is the Burgers vector of dislocation; e is the shear modulus of the material; a, a 0 Is constant.
The austenitic thermal stress term is expressed as:
wherein: k (K) 2 Is an austenite strain hardening coefficient; n is n 2 Is an austenite strain sensitivity index;is a reference value for the austenite saturation threshold stress at t=0k.
(3) Viscous effect term
The ferrite viscosity effect term is expressed as:
wherein: mu (mu) d1 Is a ferrite viscous damping coefficient; ρ d1 Dislocation density is moved for ferrite; b 1 Burgers vector, which is ferrite dislocation.
The austenite viscosity effect term is expressed as:
wherein: mu (mu) d2 Is an austenite viscous damping coefficient; ρ d2 Dislocation density for austenite movement; b 2 Is the Burgers vector of the austenite dislocation.
(4) S32760 adhesive mechanism
4. The viscosity constitutive parameter inverse solving method based on cutting force comprises the following steps:
(1) Constructing a right-angle cutting experiment platform;
(2) Measuring the cutting force using a load cell;
(3) The strain rate varies with cutting speed;
(4) A relationship between flow stress and cutting force component;
(5) A least square method principle objective function;
(6) Reversely solving a constitutive parameter flow chart based on the cutting force;
(7) The modified constitutive equation:
5. the verification method of the constitutive model parameters comprises the following steps: the predicted values are compared with the experimental values.
Unlike the already disclosed technology: the existing constitutive model building method is concentrated on the condition of low strain rate, and the influence of viscous effect under high strain rate in the cutting process is ignored; the viscosity effect of the duplex stainless steel is characterized, and a basis is provided for analyzing the viscosity behavior of the duplex material under the condition of high strain rate in the cutting process. The existing solving method of the constitutive model parameters is mainly focused on a finite element method and a Hopkinson pressure bar experimental method, but the former method needs to perform a large amount of calculation and consumes a large amount of time, and the latter method only can study that the strain rate of metal is 10 3 -10 4 s -1 And experimental data reliability and experimental condition adaptability are difficult to be completely ensured. The application provides a cutting theory-based constitutive parameter reverse identification method suitable for high strain rate conditions, and discloses viscous behavior of duplex stainless steel under the high strain rate conditions.
Compared with the prior art, the application has the beneficial effects that: the method for constructing the viscosity constitutive model of the duplex stainless steel comprehensively considers the influence of high temperature and high strain rate in the cutting process, analyzes the influence of the viscosity effect in the cutting process, and provides a basis for researching the viscosity effect in the cutting process. The method constructs a biphase stainless steel constitutive model considering the viscous effect, and researches the change rule of flow stress along with the strain rate. The problem that the accuracy of the constitutive model is affected by the fact that the viscous effect in the cutting process is ignored in the existing method is solved.
According to the method, the influence of cutting force on parameters of the constitutive model is considered, a right-angle cutting equally-divided shearing area model is established, and the change rule of multiple physical fields of the shearing area in the cutting process is analyzed. In combination with a cutting experiment, a resolving method for reversely identifying and correcting the constitutive parameters based on cutting force is provided. By comparing the model predictive value with the cutting experimental value, the average error of the cutting force is found to be within 3 percent, and the reliability and the accuracy of the simulation result are effectively improved by the reverse recognition algorithm and the constitutive model.
Drawings
FIG. 1 is a logical block diagram of the present application;
FIG. 2 is a graph showing the cutting force distribution of a right angle cutting equal shearing area according to the present application;
FIG. 3 is a flow chart of the calculation of the right angle cutting process of the present application;
FIG. 4 is a graph showing the strain rate versus cutting speed characteristic of the present application;
FIG. 5 is a flow chart of the present application constitutive model parameter optimization program;
FIG. 6 is a graph of F at a feed rate of 0.3mm/r in accordance with the present application c Cutting force comparison schematic;
FIG. 7 is a graph of F at a feed rate of 0.3mm/r in accordance with the present application t Cutting force comparison schematic;
FIG. 8 shows the present application 10 4 s -1 A schematic diagram of a true stress-strain curve under strain rate conditions;
FIG. 9 shows the present application 10 4 s -1 Fitting a result diagram of a non-thermal stress term under a strain rate;
FIG. 10 is a microstructure of the S32760 duplex stainless steel of the application under SEM observation;
FIG. 11 is a flow chart for inverse solving of constitutive parameters based on cutting force in accordance with the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The application provides a construction method of a double-phase stainless steel viscosity constitutive model as shown in fig. 1-11, which comprises the following steps:
s1: analyzing the viscous behavior of an austenite phase and a ferrite phase from a microscopic dislocation angle, and establishing a viscous constitutive model of the S32760 duplex stainless steel based on the viscous effect of the two phases and a mixing rule;
s2: establishing a right-angle cutting equal-division shearing area model based on an Oxley theory, and predicting the multi-physical-field distribution in the cutting process;
s3: and carrying out reverse identification correction on the constitutive parameters based on a right-angle cutting experiment.
Example 1. Right angle cut aliquoting shear zone characterization method:
(1) Shear plane analysis
The distribution diagram of the cutting component force of the right-angle cutting equal-divided shearing area is shown in figure 2, and the normal force F at the shearing surface N And the cutting force F at the shear plane s Is a combination of the resultant force of (F) and the normal force of the tool-chip interface n Friction force F of tool-chip interface f The sum is a pair of equilibrium forces, the chip forming force F R Is decomposed into F along the cutting direction and perpendicular to the cutting direction c And F t . The cutting force value can be determined by the balance conditions of the shearing surface and the cutter-chip interface, so that each cutting component and the chip thickness t 2 The method can be obtained by the following formula:
F c ＝F R cos(λ-α) (1)
F t ＝F R sin(λ-α) (2)
F f ＝F R sinλ (3)
F n ＝F R cosλ (4)
wherein: alpha is the front angle of the cutter;is the shear angle; lambda is the friction angle; t is t 1 Is the undeformed chip thickness; w is the cutting width; θ is F R An included angle with AB; sigma (sigma) AB Representing the shear plane average flow stress.
The following relationship exists between any particle velocity in the first deformation region and the average shear strain rate in the shear region in the Oxley model:
wherein: v is the right angle cutting speed; ΔS 1 Is the thickness between the two parallel bands of the first deformation zone.
Shearing angleAfter determination, the equivalent strain and equivalent strain rate of any particle at the shear plane AB can be expressed as follows according to von Mises stress yield criteria:
as is clear from the equation (9), the strain rate increases with the increase of the cutting speed, and when the cutting speed is known, the strain rate can be obtained by the cutting speed, and further, the strain rate can be controlled by the cutting speed, whereby the viscosity behavior under the high strain rate condition can be studied.
Assuming that the shear deformation occurs at the shear plane, the workpiece becomes a chip by the shear deformation, and the workpiece material that would otherwise move with the tool, due to the increase in cutting speed, causes the workpiece to rapidly pass through the shear zone to become a chip. From the velocity vector relationship of fig. 2, the chip material flow velocity V can be determined c And material flow velocity V of shear plane s ：
The friction angle calculation formula during cutting isThe coefficient of friction μ=tan λ can be obtained, according to Oxley theory the shear angle ++in fig. 2>And the included angle theta satisfies the following relationship:
corrected strain rate constant C 0 Considering the influence of material strain, the expression is:
wherein: c (C) Oxley Shearing the ribbon aspect ratio for the first deformation zone; A. b and n are JC constitutive parameters respectively.
Since shear stress is temperature dependent, it is necessary to iteratively calculate the temperature of the shear plane AB until steady state is reached. According to the bootroyd temperature model, the expression of the average temperature is:
wherein: t (T) r Taking 0.9 in analysis, wherein eta is the average temperature coefficient of the workpiece; ρ w Is the density of the material; c (C) w Specific heat capacity, β is the heat distribution coefficient.
Wherein: k (K) w Is the thermal conductivity.
In high speed cutting, the material undergoes a high strain, high strain rate, high temperature process. S32760 duplex stainless steel is 10 4 s -1 At strain rates above, a significant viscous effect is exhibited. So in order to take into account the viscous behaviour of the material being processed, in the Oxley theory model, the S32760 bi-phase constitutive model taking into account the viscous effect should be used to predict the flow stresses in the shear zone.
(2) Tool-chip interface analysis
In analyzing the second deformation zone, it is generally assumed that the thickness of the plastically deformed region of the tool-chip interface is constant: ΔS 2 ＝δt 2 δ is the ratio of the second deformation zone thickness to the chip thickness, and therefore the equivalent strain and equivalent strain rate resulting in the tool-chip interface is:
wherein: h is a tc For the tool-chip contact length, a moment balance formula for the shear plane can be used for calculation.
Average temperature T of tool-chip interface int Expressed as:
T int ＝T r +ΔT SZ +ψΔT M (19)
wherein: psi is a correction coefficient, and is taken as 0.6; delta T M Is the maximum temperature rise in the chip; delta T C Is the average temperature rise in the chip; delta T SZ The temperature rises for the first deformation zone.
And the flow stress of the cutter-chip contact interface is predicted by using an S32760 bi-phase constitutive model considering the viscosity effect, along with the characteristics of the flow stress at the shear band.
Implementation example 2. Solution method of chip forming force:
due to the shearing angle of the shearing zoneCoefficient of shear zone deformation C Oxley The ratio delta of the thickness of the second deformation zone to the chip thickness changes along with the cutting condition, the material property and the geometric angle of the cutter, so three variable ranges are set as the iterative ranges of the three, namely +.>C Oxley ∈[2,10]，δ∈[0.005,0.2]. When the output satisfies three equilibrium conditions, the calculation will terminate: first, stress balance at the tool-chip interface, where the tool-chip interface tangential stress (τ int ) Equal to the flow stress (sigma) in the chip chip ) The method comprises the steps of carrying out a first treatment on the surface of the Second, stress balance at the nose, i.e., nose interface normal stress (σ) calculated using the resultant force N ) Is equal to the normal stress (sigma 'calculated by the boundary condition of the tip' N ) The method comprises the steps of carrying out a first treatment on the surface of the Third, cutting force (F c ) Minimum principle.
Assuming that the stress of the cutter-chip interface is uniformly distributed, obtaining the stress tau of the cutter-chip interface int And stress sigma at point B N The expression is:
the normal stress sigma 'of the point B near the tip position in FIG. 2' N The average shear flow stress of the shear plane can be combined to obtain:
in a cutting force prediction model, when solving the temperature of a shearing area, determining the flow stress of the shearing area at a given initial temperature, updating the temperature of the shearing area according to the flow stress, replacing the temperature with the initial temperature, and starting new calculation, wherein the process is repeated until the difference between the initial temperature and the calculated temperature is smaller than the given value of 1 ℃; when the temperature of the cutter-chip interface is solved, the sum of the room temperature and the temperature rise of the first deformation zone is taken as an initial temperature, then the maximum temperature rise and the average temperature rise in the chip are taken as temperature increment to update the chip temperature, the chip temperature is replaced by the initial temperature, new calculation is started, and the process is repeated until the difference between the initial temperature and the calculated temperature is smaller than a given value of 1 ℃. The tangential stress (tau) of the tool-chip interface is determined int ) Flow stress (sigma) at tool-chip interface chip ) Comparing, taking the difference between the absolute values as the judgment basis, and cutting the angleTaking the position with the minimum absolute value of the two, repeatedly calculating various parameters of the shearing area at the shearing angle at the moment, and then solving the normal stress (sigma) of the tool nose interface N ) And a positive stress (sigma 'near point B at the tip position' N ) The difference between the absolute values is taken as the judgment basis, and the deformation coefficient C of the shearing area Oxley Taking the position with the minimum absolute value, repeatedly calculating various parameters of the shearing area by using the deformation coefficient of the shearing area at the moment, and finally comparing the cutting force (F c ) And selecting the minimum value to determine the ratio (delta) of the thickness of the second deformation zone to the thickness of the chip, taking the cutting force at the moment as the chip forming force, and calculating a flow chart of the right-angle cutting process as shown in figure 3.
Implementation example 3. Viscous constitutive model building method:
building a constitutive model considering the viscous effect, and dividing the equation into three parts:
wherein: sigma (sigma) a Is a non-thermal stress term;
is an influencing factor of reaction strain rate and temperature effect; sigma (sigma) th Is a thermal stress term; sigma (sigma) c Is a viscous effect term.
Because of the biphase nature of the material, three stresses of ferrite and three stresses of austenite should be calculated respectively and the proportioning weights should be added up.
σ＝l 1 σ 1 +l 2 σ 2 (25)
Wherein: l (L) 1 The proportion of ferrite is that of ferrite; l (L) 2 The proportion of austenite is calculated; sigma (sigma) 1 Ferrite phase stress; sigma (sigma) 2 Is the corresponding force of austenite.
(1) Non-thermal stress term
The non-thermal stress term reflects only the effect of strain changes independent of the effect of strain rate and temperature changes. Since the strain rate and temperature have negligible effect on the ferrite work hardening term, the flow stress added by ferrite work hardening is accounted for in the ferrite non-thermal stress term. The non-thermal stress term in the ferrite and austenite constitutive equations, respectively, can be written as:
wherein: sigma (sigma) i1 Sum sigma i2 The total resistance to dislocation movement within ferrite and austenite, respectively; m is m 1 And m 2 Constants characterizing grain boundary strength for ferrite and austenite, respectively; d, d 1 And d 2 Grain sizes of ferrite and austenite, respectively; k (K) 1 Is a ferrite hardening coefficient; epsilon is the true strain; n is n 1 Is a ferrite strain sensitivity index.
(2) Thermal stress term
The expression of the influencing factor is:
wherein: k is a Boltzmann constant; t is the temperature; g 0 Is the reference thermal activation energy;is the reference strain rate; p and q are barrier constants.
Since the thermal stress of the body-centered cubic structure is independent of strain, the thermal stress term of ferrite is equal to the ferrite saturation stress value, so:
wherein:is a reference value for ferrite saturation threshold stress at t=0k; b is the Burgers vector of dislocation; e is the shear modulus of the material; a, a 0 Is constant.
For austenite, the work hardening rate of austenite is high, so the influence of strain rate and temperature on the strain hardening of austenite needs to be considered: therefore, it is
Wherein: k (K) 2 Is an austenite strain hardening coefficient; n is n 2 Is an austenite strain sensitivity index;is a reference value for the austenite saturation threshold stress at t=0k.
(3) Viscous effect term
The viscous behavior of a material is related to the dislocation speed, the higher the dislocation speed, the more pronounced the viscous effect of the dislocation and the more pronounced the viscous effect of the material. The motion damping force of the dislocations is:
F v ＝μ d v d (31)
wherein: mu (mu) d A viscous damping coefficient; v d Is the dislocation movement speed.
The force required for dislocation movement is:
F＝τb (32)
wherein: τ is the shear stress on the dislocation and b is the Burgers vector of the dislocation.
The dislocation in the metal is caused by the stress generated by the external force, and the plastic strain rateRelationship with average dislocation motion velocity:
wherein: ρ d To move dislocation density.
When cutting, the dislocation speed is approximately equal to the cutting speed, and the dislocation is balanced with the resistance for preventing the dislocation from generating movement in the whole process from the sliding movement to the balance, so that the stable and smooth cutting process can be ensured, and the method can be used for obtaining:
F v ＝F (34)
from newton's law of internal friction, newton's fluid shear stress can be expressed as:
the viscous effects of ferrite and austenite are thus obtained with:
order the
The constitutive equation of the S32760 duplex stainless steel is obtained by arrangement:
the strain rate has no influence on the non-thermal stress item, the influence of the non-thermal stress item on the strain rate and the temperature change is independent, only the influence of the strain change is reflected, the influence of the strain rate on the thermal stress item is logarithmic, the influence is small, the influence of the strain rate on the viscosity effect item is one-time function, and the influence is large.
(4) Parameter identification
To obtain the flow stress values at high strain rates of S32760, an S32760 bi-phasic constitutive equation is fitted. Using a Hopkinson pressure bar apparatus at 10 4 s -1 The strain rate is compressed to obtain the stress-strain curve of the material, the experimental material is an S32760 cylinder phi 2 multiplied by 2mm, fig. 10 is a microstructure diagram of S32760 duplex stainless steel under SEM observation, and the obtained stress-strain curve is shown in fig. 8. The chemical composition of the S32760 duplex stainless steel is shown in table 1.
Table 1 chemical composition (mass fraction/%)
Since the rheological stress is not related to the temperature when the temperature is high enough, the experimental data at the moment can be used for carrying out least square curve fitting, 10 4 s -1 The fitting result of the non-thermal stress term under the strain rate is shown in fig. 9, and 3 undetermined parameters in the non-thermal stress term can be obtained:n 1 ＝0.07997。
since S32760 duplex stainless steel contains both BCC and FCC structures, the viscous effect terms for both structures are solved separately for summation. BCC reference Ta element structure μ=1.8x10 -3 The method comprises the steps of carrying out a first treatment on the surface of the FCC reference Al element structure μ=3.8x10 -3 . Analysis of fig. 10 using image J software shows 54% BCC structure and 46% FCC structure. From this, the S32760 duplex stainless steel viscosity effect term parameter is μ=2.72X10 -3 。
The parameters in the thermal stress term includen 2 、α、β、/>p, q is due to->Is not independent in the parameter fitting and both are contained in a logarithmic function, so that the change of both has less influence on the term than alpha, beta, and can be estimated as +.>In order to determine other parameters. The S32760 duplex stainless steel has both BCC and FCC structures, and the HCP metal constitutive equation can be regarded as a linear combination of both BCC and FCC structures, so the reference strain rate of the HCP metal can be used to determine the reference strain rate of S32760. />Wherein->Taking b=3×10 -10 m，l 0 ＝500b，p w ＝10 11 /cm 2 T=598k, y=0.25. Finally calculate +.>Due to->General ratio->Two orders of magnitude larger, so->
Determining completion ofThe remaining parameters can then be solved by means of a reverse identification method.
The purpose of parameter solving is to find a group of material parameters conforming to physical meaning, so that the curve solved by constitutive equation is as consistent as possible with the curve obtained by experiment. The least square method is utilized to define an objective function, the square sum of the difference between the stress value calculated by using the constitutive equation and the stress value measured by the experiment is used as the objective function, so that the objective function is as small as possible, and the objective function can be expressed as:
wherein x= [ x ] 1 ,x 2 ,…,x m ]Is a parameter to be optimized, N is the number of the sampling points, Y i Is the calculated value of the i-th point, Y i * Is the value measured by the i-th point experiment.
And (3) performing optimization calculation by using a MATLAB program, wherein a flow chart of the constitutive model parameter optimization program is shown in fig. 5. In addition, in order to ensure the accuracy of the calculation result, the theoretical range of each parameter needs to be determined.
And carrying out grouping determination on the rest unknown parameters.
(1)Is determined by: 1560 is taken as +.>The median of the range extends to both ends to giveThe temperature T is 77-998K, the strain epsilon is 0-0.6, and the temperature T can be estimated and determined
(2) Determination of alpha and beta: k is boltzmann constant, taking k= 1.3806506 ×10 -23 J/K, S32760 duplex stainless steel b=3×10 -10 m, shear modulus e=159.2gpa, a 0 ∈(0.2,2)，α＝k/(b 3 Ea 0 ) Alpha E (1.6X10) was estimated -6 ,1.6×10 -5 ) The upper and lower limits of the range are expanded to a certain extent, and the maximum variation range (1 multiplied by 10) allowed in theory can be taken -6 ,1×10 -4 ) Since α and β are constants of the same order, the ranges of α and β can be considered to be the same.
(3)n 2 Is determined by: n of the most FCC metals is generally considered 2 Taking 0.5, there may be a small range around 0.5 for individual metalsAnd the circumference changes. Therefore, on this basis, we consider n of S32760 2 The maximum range of variation theoretically allowed is (0, 1]。
(4) Determination of p and q: p and q are a pair of correlation constants determining the shape of the potential barrier, and p is generally 0 < 1, and q is generally 1 < 2 for single crystals. Several typical (p, q) values are: (2/3, 1) represents a rectangular barrier, (1/2, 2) represents a hyperbolic barrier, (1, 2) represents a sinusoidal barrier, and for most metals, (p, q) = (2/3, 1), (2/3, 2), (3/4, 4/3) and (1, 1), the transition forms between rectangular and sinusoidal can be considered. Although the p and q values described above are applicable to single crystal structures, they are equally applicable to S32760, since the terms of p and q in the constitutive model are the average of the homogeneous terms of the constitutive model of the BCC structure and the FCC structure.
And each parameter range in the constitutive model determined above is the parameter range of the genetic algorithm. And (3) carrying out parameter optimization by adopting a genetic algorithm, and calculating by utilizing a ga function in a MATLAB optimization tool box to obtain a group of constitutive model parameters, wherein the thermal stress item parameters of the constitutive model are shown in the table 2 of S32760.
Table 2S32760 constitutive model thermal stress term parameters
Therefore, a group of initial values of the S32760 duplex stainless steel constitutive parameters can be obtained as initial conditions, and the right-angle cutting experimental data is used as reference to form the reverse identification of the thermal stress item in the constitutive parameters, so that the constitutive parameters are continuously corrected until the difference between the experimental values and the simulation values is minimized.
According to the constitutive parameters obtained in Table 2, the initial S32760 constitutive model obtained is
Implementation example 4. Method for solving the viscosity constitutive parameters based on cutting force in reverse:
and constructing a right-angle cutting experiment platform, and observing the cutting force of the right-angle cutting S32760 duplex stainless steel. The right-angle cutting experiment platform is characterized in that the bar is clamped by a three-jaw clamp, the bar is centered, the outer circle is roughly turned once according to the feeding amount of 1mm, then a grooving cutter with the width of 3mm is used for grooving the bar, the groove depth is 3mm, the groove is repeatedly grooved, the groove spacing is 2mm, the type of the grooving cutter is MGGN300-V DH8532, the front angle is 18 degrees, the type of the cutter bar is MGEHR2525-3, and the outer circle and grooving operation is carried out by using a C6136HK lathe.
The adopted force measuring instrument is a KISTLER piezometer 9139AA, the force measuring instrument can measure cutting forces in three directions in the cutting process, and in order to ensure the accuracy of measurement results, each group of experiments are repeated three times and an average value is obtained. In order to verify the accuracy of the cutting force prediction model, the cutting amount of the right angle cutting experiment is shown in table 3.
TABLE 3 Right angle cutting experiment cutting amount
The cutting forces obtained by the right angle cutting test are shown in table 4.
Table 4 cutting force for right angle cutting experiment
S32760 the parameters required for the right angle cut equally divided shear zone model are shown in table 5.
TABLE 5 parameters required for equally dividing the shear zone model
The viscosity effect under high strain rate conditions is considered by the present applicationThe strain rate should be increased with increasing cutting speed, when the strain rate is increased to 10 4 s -1 In the above, the dislocation slip speed is controlled by viscous resistance of dislocation, and the cutting process shows a viscous flow process like a fluid. According to the model prediction of the equally divided shearing area, under the condition that the feeding amount is 0.3mm/r and the cutting speed is above 63m/min, the strain rate is 10 4 s -1 The characteristics of the strain rate change with cutting speed are shown in fig. 4.
From the formulas (1), (2) and (5), the relation between the flow stress and the cutting force component is:
wherein the angle of shearThe friction angle lambda and the included angle theta can be solved through the equal-division shearing area model iteration, parameters in table 3 and table 5 are input into the equal-division shearing area model, and the predicted value of the equal-division shearing area model can be obtained as shown in table 6.
TABLE 6 equally divided shearing area model predictors
Therefore, the constitutive parameters can be corrected by utilizing the least square method through the relation between the flow stress and the cutting component force, the square sum of the difference between the flow stress value calculated by using the constitutive equation and the flow stress value calculated by using the cutting component force is taken as an objective function, the objective function is as small as possible, and the objective function is expressed as:
wherein the method comprises the steps ofIs the parameter to be optimized, N is the number of points, sigma i Is the value, sigma, calculated by the ith point using the constitutive equation AB Is the value calculated at the i-th point using the cutting component. And (3) carrying out optimization calculation by utilizing a MATLAB program, and solving a constitutive parameter flow chart reversely based on cutting force, wherein the theoretical range of the parameters is as shown in the table 2.
The modified constitutive equation is:
implementation example 5. Verification method of constitutive model parameters:
the cutting force versus model predicted cutting force for the right angle cut test is shown in table 7.
Table 7 comparison of experimental cutting force to model predictive cutting force
The experimental observed force and model predicted force pairs for feed rates of 0.3mm/r are shown in figures 6-7. Analysis revealed that the cutting force F was 0.3mm/r c The maximum prediction error of (2) is 4.6%, the minimum prediction error is 1.2%, and the average prediction error is 2.7%; cutting force F t The maximum prediction error of the model is 3.8%, the minimum prediction error is 1.0%, and the average prediction error is 2.8%, so that the prediction of the cutting force by using the constitutive model constructed by the application is more accurate.
In summary, compared with the prior art, the method comprehensively considers the influence of high temperature and high strain rate in the cutting process, analyzes the influence of the viscosity effect on the cutting process, and provides a basis for researching the viscosity effect in the cutting process. The method constructs a biphase stainless steel constitutive model considering the viscous effect, and researches the change rule of flow stress along with the strain rate. The problem that the accuracy of the constitutive model is affected by the fact that the viscous effect in the cutting process is ignored in the existing method is solved.
According to the method, the influence of cutting force on parameters of the constitutive model is considered, a right-angle cutting equally-divided shearing area model is established, and the change rule of multiple physical fields of the shearing area in the cutting process is analyzed. In combination with a cutting experiment, a resolving method for reversely identifying and correcting the constitutive parameters based on cutting force is provided. By comparing the model predictive value with the cutting experimental value, the average error of the cutting force is found to be within 3 percent, and the reliability and the accuracy of the simulation result are effectively improved by the reverse recognition algorithm and the constitutive model.
Finally, it should be noted that: the foregoing description is only illustrative of the preferred embodiments of the present application, and although the present application has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described, or equivalents may be substituted for elements thereof, and any modifications, equivalents, improvements or changes may be made without departing from the spirit and principles of the present application.

Claims (2)

1. The method for establishing the right-angle cutting equal-division shearing area model characterization based on the Oxley theory is characterized in that the method predicts the multi-physical field distribution in the cutting process, establishes the theoretical relationship between the right-angle cutting process variable and the output variable under the conditions of plane strain and steady cutting, and comprises the following steps of: normal force F at shear plane N And the cutting force F at the shear plane s Is a combination of the resultant force of (F) and the normal force of the tool-chip interface n Friction force F of tool-chip interface f The sum is a pair of equilibrium forces, the chip forming force F R Is decomposed into F along the cutting direction and perpendicular to the cutting direction c And F t The method comprises the steps of carrying out a first treatment on the surface of the The cutting force value can be determined by the balance conditions of the shearing surface and the cutter-chip interface, so that each cutting component and the chip thickness t 2 The method can be obtained by the following formula:
F c ＝F R cos(λ-α) (1)
F t ＝F R sin(λ-α) (2)
F f ＝F R sinλ (3)
F n ＝F R cosλ (4)
wherein: alpha is the front angle of the cutter;is the shear angle; lambda is the friction angle; t is t 1 Is the undeformed chip thickness; w is the cutting width; θ is F R An included angle with AB; sigma (sigma) AB Represents the shear plane average flow stress;
the following relationship exists between any particle velocity in the first deformation region and the average shear strain rate in the shear region in the Oxley model:
wherein: v is the right angle cutting speed; ΔS 1 Is the thickness between the two parallel bands of the first deformation zone;
shearing angleAfter determination, the equivalent strain and equivalent strain rate of any particle at the shear plane AB can be expressed as follows according to von Mises stress yield criteria:
as can be seen from the formula (9), the strain rate increases with the increase of the cutting speed, and in the case that the cutting speed is known, the strain rate can be obtained by the cutting speed, and further, the strain rate can be controlled by the cutting speed, so that the study of the viscosity behavior under the condition of high strain rate can be realized;
assuming that the shearing deformation occurs on the shearing surface, the workpiece becomes the cutting chip through the shearing deformation, the workpiece material which moves along with the cutter originally is changed into the cutting chip through the shearing area due to the increase of the cutting speed, and the flowing speed V of the cutting chip material can be obtained according to the speed vector relation c And material flow velocity V of shear plane s ：
The friction angle calculation formula during cutting isThe coefficient of friction μ=tan λ can be obtained, shear angle ++according to Oxley theory>And the included angle theta satisfies the following relationship:
corrected strain rate constant C 0 Considering the influence of material strain, the expression is:
wherein: c (C) Oxley For the first variationShearing the strip length to width ratio in the shape region; A. b and n are JC constitutive parameters respectively;
since shear stress is temperature dependent, it is necessary to iteratively calculate the temperature of the shear plane AB until steady state is reached; according to the bootroyd temperature model, the expression of the average temperature is:
wherein: t (T) r Taking 0.9 in analysis, wherein eta is the average temperature coefficient of the workpiece; ρ w Is the density of the material; c (C) w Specific heat capacity, beta is a heat distribution coefficient;
wherein: k (K) w Is the heat conduction coefficient;
tool-chip interface analysis: the equivalent strain and equivalent strain rate of the tool-chip interface are:
wherein: h is a tc For the cutter-chip contact length, a moment balance formula of a shearing surface can be used for calculation;
average temperature T of tool-chip interface int Expressed as:
T int ＝T r +ΔT SZ +ψΔT M (19)
wherein: psi is a correction coefficient, and is taken as 0.6; delta T M Is the maximum temperature rise in the chip; delta T C Is the average temperature rise in the chip; delta T SZ Temperature rise is carried out for the first deformation zone;
method for solving chip forming force: and establishing a right-angle cutting equal-division shearing area model, taking material properties, a cutter geometric angle and cutting amount as independent variables, performing iterative calculation on a shearing angle value, a first deformation area shearing band length-width ratio and a ratio of a second deformation area thickness to a chip thickness according to three balance conditions in a theoretical calculation process, and ending calculation when an output variable meets the three balance conditions.
2. The method for modeling right angle cutting equally divided shear zone based on Oxley theory according to claim 1 wherein the three equilibrium conditions are first, stress balance at the tool-chip interface, wherein the tool-chip interface tangential stress equals the flow stress in the chip; secondly, the stress at the tool nose is balanced, namely the normal stress of the tool nose interface calculated by the resultant force is equal to the normal stress calculated by the tool nose boundary condition; third, the principle of minimal cutting force.
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