CN105243195A - Prediction method for micro-milling and work-hardening nickel-based superalloy - Google Patents

Abstract

The present invention discloses a prediction method for micro-milling and work-hardening nickel-based superalloy, belongs to the micro-milling working field, relates to the micro-milling and work-hardening nickel-based superalloy, and uses simulation modeling and theory to derive the prediction method for work-hardening. The prediction method comprises: carrying out three-dimensional macroscopic modeling on a workpiece and a tool; taking consideration of an elastoplastic constitutive relationship to establish a nickel-based superalloy model, a tool workpiece friction model, and a metal cutting separation model; outputting a strain value under different cutting parameters of finite element simulation; and combining a relationship between strain and hardness, obtaining a hardness prediction value under the different cutting parameters, and predicting work-hardening conditions. The prediction method numerically predicts work-hardening condition by using a modelling mode, and saves manpower and reduces a cost by comparison with test and measurement hardness. According to the utilization of the prediction method, hardness verification is simple and accuracy is good.

Description

The Forecasting Methodology of a kind of micro-milling nickel base superalloy work hardening

Technical field

The invention belongs to micro-cutting manufacture field, relate to a kind of micro-Milling Process nickel base superalloy, by the Forecasting Methodology of simulation modeling and theory deduction work hardening.

Background technology

Along with the progress of science and technology, all there is micro-structure/part in the fields such as Aero-Space, energy source and power, biomedicine, this type of micro-structure/element precision requires high, there is three-dimensional geometrical structure shape as step surface, deep hole, thin-walled etc., there are larger depth-to-width ratio and length-diameter ratio, wherein part not only requires to bear higher working temperature, and needs to possess higher intensity and decay resistance.Nickel base superalloy Inconel718 has the premium properties such as high strength, antifatigue, corrosion-resistant, high temperature resistant, inoxidizability, is the ideal material manufacturing aeromotor, turbo blade, engine thermal end pieces.The micro-milling technology of nickel base superalloy is the high efficiency technical means preparing nickel base superalloy micro parts.But because nickel base superalloy has the features such as intensity is high, viscosity is large, heat-conductive characteristic is low, large deformation can be produced at micro-milling process, thus produce lattice distortion distortion, cause work hardening phenomenon.Work hardening for parts with microstructure appropriateness can improve the intensity of workpiece, hardness and wearing quality, and excessive work hardening is processed further to workpiece and is caused difficulty, particularly in the Precision Machining such as micro-milling, cutter is small is easy to wearing and tearing, work hardening causes cutter Fast Wearing, have a strong impact on cutter life, crudy, excessive work hardening also can cause that workpiece cracks, size changes, so extremely important for the research of work hardening.In cutting field, for work hardening research, there is certain scale, but great majority research is the forecast model based on test, generally can consider the effect tendency of many factors to work hardening and the degree of depth of hardened layer, but the hardness after materials processing is carried out the prediction that quantizes by few people.And test method wastes time and energy, poor universality.Due to the development of soft project, modern analysis software forms scale, a lot of people has been had to use the method for finite element software to emulate working angles, wherein have the situation of change of stress, strain, temperature, tool wear in human simulation working angles, but use emulation mode to hardness after cut quantize prediction research be little.The paper " Numericalandexperimentalanalysisofresidualstressandplast icstraindistributionsinmachinedstainlesssteel " that the people such as such as N.BenMoussa deliver for 2012 in periodical " InternationalJournalofMechanicalSciences ", by the prediction plastic strain of two dimensional finite element emulation mode and with testing measurement plastic strain verification model rationality, then by relation between test matching hardness and plastic strain, and after reality processing, not simple for hardness measurement for material plasticity strain measurement, plastic strain verification model rationality is used not use hardness to verify simple, accuracy is poor, and the numerical relation do not set up between plastic strain and hardness.

Summary of the invention

The present invention is in order to overcome the defect of prior art, consider micro-Milling Process scale effect, carry out the finite element three-dimensional artificial of micro-Milling Process, use finite element technique and sclerosis, theory relation between strain and hardness, set up the model of micro-milling nickel base superalloy prediction work hardening.First Forecasting Methodology uses finite element simulation technology, three-dimensional macro modeling is carried out to workpiece and cutter, consider the elastic-plastic constitutive relation of material, set up nickel base superalloy model, tool work piece friction model, borings disjunctive model, thus the micro-Milling Processes finite element simulation of nickel base superalloy under obtaining different cutting parameter.Then, according to hardening curve and the Vickers hardness test philosophy of nickel base superalloy, the relational model of flow stress and Vickers hardness is set up.Export on the basis of strain at finite element simulation, contact strain and the relation of hardness, realize the Hardness Prediction on the micro-Milling Process surface of nickel base superalloy.Adopt the checking of Forecasting Methodology hardness simple, accuracy is better.

The technical solution used in the present invention is the Forecasting Methodology of a kind of micro-milling nickel base superalloy work hardening, adopt finite element simulation technology, it is characterized in that, Forecasting Methodology is by carrying out three-dimensional macro modeling to workpiece and cutter, consider material elastic-plastic constitutive relation, set up nickel base superalloy model, tool work piece friction type, metal cutting disjunctive model, strain value under the different cutting parameter of output finite element simulation, again by the relation of contact strain with hardness, obtain Hardness Prediction value under different cutting parameter, prediction work hardening situation; The concrete steps of Forecasting Methodology are as follows:

Step 1: set up micro-milling cutter model, takes into picture by scanning electron microscope by the micro-milling cutter of test, uses software picture to be depicted as micro-milling cutter solid model, imports in ABAQUS;

Step 2: consider the condition such as milling cutter size and cutting parameter, choose suitable dimension and set up workpiece to be machined three-dimensional model;

Step 3: carry out stress and strain model to micro-milling cutter and workpiece, arranges micro-milling cutter and workpiece rigid body type, selects stress and strain model mode and cell type;

Step 4: material property parameter is arranged, cutter is considered as rigid body, workpiece material type definition is elastoplasticity, adopts the essential equation of flow stress and strain in the true cutting material of J-C modeling, using the chip separation criterion of J-C model as criterion simulation cutting fragment forming process;

Wherein, the constitutive model of described material is:

${\mathrm{\σ}}_Y=\[A+B{\left({\stackrel{\‾}{\mathrm{\ϵ}}}^P\right)}^n\]\[1+Cln\left(\frac{{\stackrel{\·}{\stackrel{\‾}{\mathrm{\ϵ}}}}^p}{{\stackrel{\·}{\mathrm{\ϵ}}}_0}\right)\](1-{\hat{T}}^m)---\left(1\right)$

In formula, σ _yfor flow stress, A is reference temperature and with reference to the yield strength under strain rate, and B is strain hardening coefficient, for equivalent plastic strain, n is strain hardening exponent, and C is strain rate hardening coefficient, for equivalent plastic strain rate, for reference rate of strain, m is thermoplastic index, for nondimensional value, relevant with temperature;

The separation criteria adopted is J-C fracture failure criterion, and its failure model is based on the equivalent plastic strain on element integral point, and its invalid coefficient ω is defined as follows:

$\mathrm{\ω}=\mathrm{\Σ}\left(\frac{\mathrm{\Δ}{\stackrel{\‾}{\mathrm{\ϵ}}}^p}{{\stackrel{\‾}{\mathrm{\ϵ}}}_f^p}\right)---\left(2\right)$

In formula, for equivalent plastic strain increment, for there is strain value during fracture,

${\stackrel{\‾}{\mathrm{\ϵ}}}_f^p=\[d_1+d_2\exp \left(d_3\frac{p}{q}\right)\]\[1+d_4\ln \left(\frac{{\stackrel{\·}{\stackrel{\‾}{\mathrm{\ϵ}}}}^p}{{\stackrel{\·}{\mathrm{\ϵ}}}_0}\right)\](1+d_5\hat{T})---\left(3\right)$

In formula, d ₁~ d ₅for lower than the inefficacy constant recorded under reference temperature, p/q is pressure deviatoric stress ratio, p is compressive stress, q is Von-Mises stress, and when failure parameter ω is greater than 1, element integral point reaches failure criteria, the all stress of unit is all set to 0, unit is deleted from grid, and namely workpiece material ruptures, and starts to be formed to cut chip;

Step 5: import cutter and part model, assemble; Adjust the relative position of micro-milling cutter and workpiece, determine cutting depth and feeding distance;

Step 6: defined analysis step and output step, ABAQUS/Explicit is used to carry out explicit state analysis, insert Machining Analysis step, withdrawing analysis step, Changeover constraint analysis step successively, arrange analysis step time and incremental step type respectively, output variable is set to equivalent plastic strain;

Step 7: definition surface and contact property, arrange cutter constrained type at contact modules, contact type is selected to penalize model, and friction factor is set to 0.4, then defines cutter set and reference point set;

Step 8: definition boundary condition, first define tool speed amplitude of variation curve, then tool feeding speed and the speed of mainshaft are set in reference point set, definition workpiece bottom and side node set, hard constraints freedom of workpiece, arranges constraint condition respectively in each analysis step;

Step 9: creation task also submits computing, the micro-milling nickel base superalloy realistic model submitting to different cutting parameter to combine respectively, thus obtain the lower material plasticity strain of different cutting parameter combination;

Step 10: after emulation terminates, several points of Stochastic choice on working groove bottom surface, the equivalent plastic strain of characterization of surfaces after averaging;

Step 11: adopt Hollomon formula to obtain strain-stress relation, emulation gained equivalent plastic strain is substituted into formula and obtains micro-milling nickel base superalloy groove bottom stress value, Hollomon formula is as follows:

σ＝Kε ⁿ(4)

In formula, σ is plasticity trus stress, and ε is plasticity true strain, and K is strength factor, and n is work-hardening exponential; σ=K ε ⁿσ=K ε ⁿ

Step 12: adopt indentation test gained discriminant Δ to judge material elastic-plastic deformation, discriminant is as follows:

$\mathrm{\Δ}=\frac{Etan\mathrm{\β}}{{\mathrm{\σ}}_Y(1-v^2)}---\left(5\right)$

In formula, E is Young modulus, and v is Poisson ratio, σ _ybe flow stress, β is the angle that in indentation test, penetrator and non-textured surface are formed; When Δ≤3, there is small plastic yield in material, must carry out flexibility analysis; When 3≤Δ≤30, plastic yield is expanded; As Δ > 30, no longer have any impact to hardness for most metals or alloy elastic, hardness number becomes strict direct ratio with flow stress value, can obtain thus:

H＝Cσ _e(6)

In formula, H is hardness number, and C is constant, is determined, get 2.4 in the calculation by the geometric configuration of penetrator; σ _efor stress and, when using Durometer measurements, σ _e=σ _repr+ σ _res, σ _reprfor the stress that penetrator causes, σ _resfor original stress;

Step 13: to be derived strain and hardness relation by formula (4) and formula (6) and Inconel718 stress-strain curve, obtain hardness number computing formula as follows,

H＝Cσ _e＝C(σ _repr+σ _res)＝CK(ε _repr+ε _res) ⁿ(7)

In formula, ε _reprfor the overstrain that pressure head is introduced, its value is retrieved as 0.08, ε by indentation test _resfor original overstrain;

Step 14: substitute into emulation gained bottom land plastic strain value and related coefficient, obtain micro-milling nickel base superalloy bottom land hardness number.By setting up limit element artificial module and stress hardness relation model, realize nickel base superalloy micro-Milling Process sclerosis prediction.

The invention has the beneficial effects as follows and first solve for micro-structure parts such as precision machined micro-raceway grooves, because its raceway groove or bottom land are of a size of micron order, penetrator cannot be pressed into the problem carrying out measuring.And to the problem that some workpiece sidewalls cannot use sclerometer directly to measure.And when using Durometer measurements, generation impression length and the degree of depth are micron order, with micro-Milling Machining size at the same order of magnitude, destroy can not ignore micro-structure/part machined surface., by setting up work hardening forecast model, workhardness value under different cutting parameter being predicted meanwhile, reference can be provided for selecting rational cutting parameter to combine.To quantize prediction work hardening by the mode of Modling model, with test with measures hardness and compares and can save manpower, minimizing cost.

Accompanying drawing explanation

Nickel base superalloy stress-strain curve when Fig. 1 is cold-drawn state, wherein, horizontal ordinate is strain, and dimensionless, ordinate is stress, and unit is Mpa.

Fig. 2 be hardness STRESS VARIATION and based on indentation test discriminant between relation, wherein, horizontal ordinate is discriminant Λ logarithm value, and ordinate is hardness and flow stress ratio, I-elastic deformation stage, II-plasticity extension phase, III-plastic period.

Embodiment

Specific embodiment of the invention is described in detail below in conjunction with technical scheme and accompanying drawing, use finite element analysis software ABAQUS, threedimensional FEM is carried out to micro-milling nickel base superalloy process, the plastic strain of prediction bottom land, then according to theory deduction strain and hardness relation, obtain the rear hardness number of processing by the plastic strain of emulation gained, set up micro-milling nickel base superalloy prediction work hardening situation model, concrete operation step is as follows:

(1) in threedimensional FEM, cutter model uses cutter modeling, the micro-milling cutter MX230 adopting Japanese NS to produce in modeling process of the present invention, tool diameter D=1mm, rounded cutting edge radius 0.002mm, helixangleβ=30 °, the long L=2mm of sword with reference to test.For ensureing that geometric model is identical with parameter with real tool shape, scanning electron microscope is adopted to take micro-milling cutter image.Use CAD to copy image, proportionally chi converts, and obtains actual parameter.Use Inventor spiral to scan instrument to cutter three-dimensional modeling, helical edges line equation is as follows:

In formula, r is milling cutter cylindrical radius, for angle of revolution, β is lead angle;

Substitute into data, r=0.5mm, z=2mm, β=30 °,

(2) workpiece geometric model is set up according to tool dimension and cutting parameter.The CAE function adopting ABAQUS to carry sets up the rectangular workpiece model being of a size of 2mm × 1.5mm × 1mm.

(3) stress and strain model is carried out to micro-milling cutter.Micro-milling cutter is set to discrete rigid body, no longer consider distortion, reduce calculated amount, subregion grid division is carried out to cutter, for arranging overall seed amount except cutting edge, for cutting edge being arranged seed on limit, whole cutter uses triangular element, adopt free mesh technology, choosing rigid unit is cell type.

(4) stress and strain model is carried out to workpiece.Selection arranges seed on limit, suitably encrypts within the workpiece, and the seed for both sides is suitably dredged, to reduce calculated amount.Due to workpiece shapes rule, select hexahedron structure dividing elements technology, select the cell type in explicit.

(5) material property parameter is set.Input density is 8190Kg/m ³, elastic modulus 2.1e+11, Poisson ratio is 0.3.Use the plastic yield of J-C constitutive model simulation cutting process, input model parameter A is 700Mpa, B be successively 1798Mpa, C be 0.0312, n be 0.9143, m is 1.3.Adopt J-C separation criteria simulation cutting forming process, input inefficacy constant d in formula (3) successively ₁~ d ₅, be respectively 0.239,0.456 ,-0.3,0.07,2.5.

(6) importing workpiece and cutter model assemble.The relative position of micro-milling cutter and workpiece is adjusted according to cutting depth and feeding distance.

(7) defined analysis step and output step.In Step module, insert micro-Milling Process analysis step, withdrawing analysis step, constraints conversion analysis step, procedural type selects Dynamics, Explicit.

(8) between definition cutter and workpiece, contact property is for penalizing model, and friction factor is set to 0.4, and friction pair is cutter outside surface and workpiece surface.

(9) define tool speed amplitude of variation curve, reference point set arranging speed of feed and the speed of mainshaft, in order to limit the movement of workpiece, constraint being set in the bottom surface of workpiece and side.In Milling Process analysis step, micro-milling cutter rotating speed n and speed of feed v is set _f, along direction of feed milling groove, workpiece movable speed and rotational speed are set to 0, Workpiece clamping, and the analysis step time is t=l/f (l is feeding distance, and f is speed of feed); In withdrawing analysis step, arranging the speed of mainshaft is 0, and speed of feed is still v _f, clamping constraint continues, and the analysis step time is 0.001s; In constraints conversion analysis step, Workpiece clamping state stops, and speed of feed and the speed of mainshaft are set to 0, and workpiece movable speed and rotational speed are set to 0, and the analysis step time is 1.Arranging output variable is equivalent plastic strain.

(10) in Job module, data are created.Spindle speed 60000r/min, cutting depth is 30 μm, and feed engagement is respectively 0.5 μm/z, 0.9 μm/z, 1.1 μm/z, 1.3 μm/z.Check errorless after submit task, carry out finite element analysis.

(11) after having emulated, the equivalent plastic strain of Stochastic choice 40 points, the equivalent plastic strain of characterization of surfaces after averaging.

(12) judge material elastic-plastic deformation according to test gained discriminant (5), substitute into nickel-base high-temperature alloy material correlation parameter, E=205Gpa, σ _y=1290MPa, β=22 °, v=0.30:

According to the relation of stress hardness and discriminant, see Fig. 2, obtain Δ and fall into plastic yield III stage, hardness number and flow stress value are directly proportional.

Substitute into parameter by formula (7) and namely obtain hardness number, be 0.5 μm/z with feed engagement, the speed of mainshaft is 60000r/min, and cutting-in 30 μm is example, and now simulation data equivalent strain is 0.31, and hardness calculation is as follows,

H＝CK(ε _repr+ε _res) ⁿ＝2.4×2487×(0.310+0.08) ^0.153＝4952MPa＝495.2kg/mm ^2。

Claims (1)

1. the Forecasting Methodology of micro-milling nickel base superalloy work hardening, adopt finite element simulation technology, it is characterized in that, Forecasting Methodology is by carrying out three-dimensional macro modeling to workpiece and cutter, consider material elastic-plastic constitutive relation, set up nickel base superalloy model, tool work piece friction type, metal cutting disjunctive model, strain value under the different cutting parameter of output finite element simulation, again by the relation of contact strain with hardness, obtain Hardness Prediction value under different cutting parameter, prediction work hardening situation, the concrete steps of Forecasting Methodology are as follows:

Step 1: set up micro-milling cutter model, takes into picture by scanning electron microscope by the micro-milling cutter of test, uses software picture to be depicted as micro-milling cutter solid model, imports in ABAQUS;

Step 2: consider the condition such as milling cutter size and cutting parameter, choose suitable dimension and set up workpiece to be machined three-dimensional model;

Step 3: carry out stress and strain model to micro-milling cutter and workpiece, arranges micro-milling cutter and workpiece rigid body type, selects stress and strain model mode and cell type;

Step 4: material property parameter is arranged, do not need to arrange material because cutter is considered as rigid body, workpiece material type definition is elastoplasticity, adopt the essential equation of flow stress and strain in the true cutting material of J-C modeling, using the chip separation criterion of J-C model as criterion simulation cutting fragment forming process;

Wherein, the constitutive model of described material is:

${\mathrm{\σ}}_Y=\[A+B{\left({\stackrel{\‾}{\mathrm{\ϵ}}}^P\right)}^n\]\[1+Cln\left(\frac{{\stackrel{\·}{\stackrel{\‾}{\mathrm{\ϵ}}}}^p}{{\stackrel{\·}{\mathrm{\ϵ}}}_0}\right)\](1-{\hat{T}}^m)---\left(1\right)$

In formula, σ _yfor flow stress, A is reference temperature and with reference to the yield strength under strain rate, and B is strain hardening coefficient, for equivalent plastic strain, n is strain hardening exponent, and C is strain rate hardening coefficient, for equivalent plastic strain rate, for reference rate of strain, m is thermoplastic index, for nondimensional value, relevant with temperature;

The separation criteria adopted is J-C fracture failure criterion, and its failure model is based on the equivalent plastic strain on element integral point, and its invalid coefficient ω is defined as follows:

$\mathrm{\ω}=\mathrm{\Σ}\left(\frac{\mathrm{\Δ}{\stackrel{\‾}{\mathrm{\ϵ}}}^p}{{\stackrel{\‾}{\mathrm{\ϵ}}}_f^p}\right)---\left(2\right)$

In formula, for equivalent plastic strain increment, for there is strain value during fracture,

${\stackrel{\‾}{\mathrm{\ϵ}}}_f^p=\[d_1+d_2\exp \left(d_3\frac{p}{q}\right)\]\[1+d_{4}ln\left(\frac{{\stackrel{\·}{\stackrel{\‾}{\mathrm{\ϵ}}}}^P}{{\stackrel{\·}{\mathrm{\ϵ}}}_0}\right)\](1+d_5\hat{T})---\left(3\right)$

In formula, d ₁~ d ₅for lower than the inefficacy constant recorded under reference temperature, p/q is pressure deviatoric stress ratio, p is compressive stress, q is Von-Mises stress, and when failure parameter ω is greater than 1, element integral point reaches failure criteria, the all stress of unit is all set to 0, unit is deleted from grid, and namely workpiece material ruptures, and starts to be formed to cut chip;

Step 5: import cutter and part model, assemble; Adjust the relative position of micro-milling cutter and workpiece, determine cutting depth and feeding distance;

Step 6: defined analysis step and output step, ABAQUS/Explicit is used to carry out explicit state analysis, insert Machining Analysis step, withdrawing analysis step, Changeover constraint analysis step successively, arrange analysis step time and incremental step type respectively, output variable is set to equivalent plastic strain;

Step 7: definition surface and contact property, arrange cutter constrained type at contact modules, contact type is selected to penalize model, and friction factor is set to 0.4, then defines cutter set and reference point set;

Step 8: definition boundary condition, first define tool speed amplitude of variation curve, then tool feeding speed and the speed of mainshaft are set in reference point set, definition workpiece bottom and side node set, hard constraints freedom of workpiece, arranges constraint condition respectively in each analysis step;

Step 9: creation task also submits computing, the micro-milling nickel base superalloy realistic model submitting to different cutting parameter to combine respectively, thus obtain the lower material plasticity strain of different cutting parameter combination;

Step 10: after emulation terminates, several points of Stochastic choice on working groove bottom surface, the equivalent plastic strain of characterization of surfaces after averaging;

Step 11: adopt Hollomon formula to obtain strain-stress relation, emulation gained equivalent plastic strain is substituted into formula and obtains micro-milling nickel base superalloy groove bottom stress value, Hollomon formula is as follows:

σ＝Kε ⁿ(4)

In formula, σ is plasticity trus stress, and ε is plasticity true strain, and K is strength factor, and n is work-hardening exponential;

Step 12: adopt indentation test gained discriminant Δ to judge material elastic-plastic deformation, discriminant is as follows:

$\mathrm{\Δ}=\frac{Etan\mathrm{\β}}{{\mathrm{\σ}}_Y(1-v^2)}---\left(5\right)$

In formula, E is Young modulus, and v is Poisson ratio, σ _ybe flow stress, β is the angle that in indentation test, penetrator and non-textured surface are formed; When Δ≤3, there is small plastic yield in material, must carry out flexibility analysis; When 3≤Δ≤30, plastic yield is expanded; As Δ >30, no longer have any impact to hardness for most metals or alloy elastic, hardness number becomes strict direct ratio with flow stress value, obtains thus:

H＝Cσ _e(6)

In formula, H is hardness number, and C is constant, is determined, get 2.4 in the calculation by the geometric configuration of penetrator; σ _efor stress and, when using Durometer measurements, σ _e=σ _repr+ σ _res, σ _reprfor the stress that penetrator causes, σ _resfor original stress;

Step 13: to be derived strain and hardness relation by formula (4) and formula (6) and nickel base superalloy stress-strain curve, obtain hardness number computing formula as follows,

H＝Cσ _e＝C(σ _repr+σ _res)＝CK(ε _repr+ε _res) ⁿ(7)

In formula, ε _reprfor the overstrain that pressure head is introduced, its value is retrieved as 0.08, ε by indentation test _resfor original overstrain;

Step 14: substitute into emulation gained bottom land plastic strain value and related coefficient, obtain micro-milling nickel base superalloy bottom land hardness number; By setting up limit element artificial module and stress hardness relation model, realize nickel base superalloy micro-Milling Process sclerosis prediction.