CN104636539A - Method for predicting sheet forming fractures based on damage fracture standard numerical value - Google Patents

Abstract

The invention discloses a method for predicting sheet forming fractures based on a damage fracture standard numerical value. The method includes the steps of obtaining the stress state distribution of a metal sheet cylindrical piece in the stamping process according to the thermodynamics irreversible law, obtaining a stress balance differential equation of the metal sheet cylindrical piece in the stamping process according to the stress state distribution, calculating the change rate, occurring when the metal sheet cylindrical piece is damaged, of the area of a small unit of the metal sheet cylindrical piece in the stamping process according to the continuum damage mechanics theory, obtaining the damage to the metal sheet cylindrical piece according to the change rate, calculating the relation between the damage and the strain of the metal sheet cylindrical piece, and finally deriving the relation between the damage value and the true stress, true strain and hydraulic stress of the metal sheet cylindrical piece under the unidimensional scale in the whole stamping process. By means of the method, the technical problem that when fractures during sheet forming are predicted through an existing numerical value method, errors are large can be solved.

Description

A kind of method based on the fracture of damage fracture criterion numerical prediction sheet forming

Technical field

The invention belongs to Plastic Forming field, more specifically, relate to a kind of method based on the fracture of damage fracture criterion numerical prediction sheet forming.

Background technology

Sheet forming is one of processing mode of a kind of very important metal forming, has and occupy sizable proportion in Aero-Space, automobile, boats and ships and civilian industry.In the past, the experience of sheet forming technique is very abundant, the improvement of technique and technology often derives from the repetition test of tens times even up to a hundred times, along with the complicated of processing parts and the sharp increase of work-piece throughput, the breakage problem in sheet forming is difficult point and the hot issue in metal forming field always.In Sheet metal forming process, not only contain the Plastic Flow of material, also along with the damage of material, and develop into the macroscopic cracking of material gradually along with the evolution of material damage, and the breakage problem of workpiece is the key factor affecting sheet metal formability, therefore, the Damage and Fracture behavior realizing Accurate Prediction material has important scientific meaning and construction value.

Finite Element Method is adopted to carry out to Sheet metal forming the effective tool that numerical simulation has become technological design and Design of Dies.By stress, strain, distribution law of temperature field in the measurable metal flow process of method for numerical simulation, the fracture behaviour even in material forming process, has very large reference value to technique and Design of Dies.For many years, many researchers have carried out large quantity research to the prediction that simulation plate forming interruption splits, achieve many achievements, but, sheet forming is a quite complicated mechanical process, be subject to the restricted influence of the problems such as the performance such as material constitutive relation, material anisotropy, geometrical large distortion and computing power, the fracture in sheet forming has very large error to adopt existing numerical method to predict.

Summary of the invention

For above defect or the Improvement requirement of prior art, the invention provides a kind of method based on the fracture of damage fracture criterion numerical prediction sheet forming, its object is to, solve the technical matters that existing numerical method prediction sheet forming Fracture has very large error, the damage fracture criterion of the inventive method can be used in instructing the forming quality improving sheet forming ability and part simultaneously, there is cost low, the feature that efficiency is high.

Based on a method for damage fracture criterion numerical prediction sheet forming fracture, comprise the following steps:

(1) obtain the stress distribution of metal blank cylindrical member punching course according to the irreversible law of thermodynamics, and obtain the balance differential equation of stress in metal blank cylindrical member punching course according to the distribution of this stress;

(2) when there is damage according to metal blank cylindrical member in continuum damage mechanics theory calculate metal blank cylindrical member punching course, the rate of change of the area of the junior unit of metal blank cylindrical member, and the damage of metal blank cylindrical member is obtained according to this rate of change, calculate the relation between the damage of metal blank cylindrical member and strain, finally and Mi Xisi yield criteria theoretical according to free energy derives impairment value under the unidimensional scale of metal blank cylindrical member in whole metal blank cylindrical member punching course and true stress, logarithmic strain, relation between hydrostatic stress, and the damage fracture criterion expanded under metal blank cylindrical member triaxiality yardstick,

(3) expression formula of the damage fracture criterion under the metal blank cylindrical member triaxiality yardstick obtained according to balance differential equation and the step (2) of stress in step (1) metal blank cylindrical member punching course, and the expression formula of impairment value in damage fracture criterion is write based on finite element software ABAQUS, and this expression formula is applied in Finite Element Simulation of Sheet Metal Forming model, to obtain the impairment value that the fracture moment appears in metal blank cylindrical member, and the impairment value of metal blank cylindrical member fracture position.

Preferably, in step (1), the balance differential equation of stress is as follows:

$\left\{\begin{array}{c}\frac{\∂{\mathrm{\σ}}_x}{\∂x}+\frac{\∂{\mathrm{\τ}}_{\mathrm{xy}}}{\∂y}+\frac{\∂{\mathrm{\τ}}_{\mathrm{xz}}}{\∂z}+f_{1x}=0\\ \frac{\∂{\mathrm{\τ}}_{\mathrm{yx}}}{\∂x}+\frac{\∂{\mathrm{\σ}}_y}{\∂y}+\frac{\∂{\mathrm{\τ}}_{\mathrm{yz}}}{\∂z}+f_{1y}+f_2=0\\ \frac{\∂{\mathrm{\τ}}_{\mathrm{zx}}}{\∂x}+\frac{\∂{\mathrm{\τ}}_{\mathrm{zy}}}{\∂y}+\frac{\∂{\mathrm{\σ}}_z}{\∂z}+f_{1z}=0\end{array}\right.$

Wherein x, y and z are the coordinate figure of junior unit in three directions of three-dimensional perpendicular coordinate system of metal blank cylindrical member, internal stress σ _tthe normal stress value of junior unit on t direction (t=x, y, z), τ _ijfor the shearing stress value of junior unit in ij plane (i, j=x, y, z, wherein i ≠ j), f ₂for the equal pressure load of punch adopted in metal blank cylindrical member punching course, f _1yfor the Y-direction compressive stress load of the blank holder of employing, f _1xand f _1zfor the friction force load of blank holder.

Preferably, step (2) comprises following sub-step:

(2-1) original section obtaining the junior unit of metal blank cylindrical member amasss S ₀;

(2-2) when obtaining metal blank cylindrical member generation damage in metal blank cylindrical member punching course, the sectional area S under the faulted condition of the junior unit of metal blank cylindrical member;

(2-3) S is amassed according to the original section of junior unit ₀the impairment value D of junior unit is calculated, the rate of change as the area of junior unit with the sectional area S under faulted condition:

$D=1-\frac{S}{S_0}.$

(2-4) the elastic strain ε of junior unit is obtained according to the impairment value D of the junior unit calculated _ewith plastic strain ε _p:

${\mathrm{\ϵ}}_e=\frac{{\mathrm{\σ}}_H}{(1-D)3K}$

${\mathrm{\ϵ}}_p={\left[\frac{{\mathrm{\σ}}^{\′}}{(1-D)(\mathrm{\λ}+2G)}\right]}^n.$

In formula, n is the material hardening exponent of metal blank cylindrical member, G is the metal blank cylindrical member plastic shear modulus relevant with plastic deformation degree, K is the metal blank cylindrical member bulk modulus relevant with cubic deformation, λ is that metal blank cylindrical member and elastic stress change relevant elastic modulus, and has:

$G=\frac{E}{2(1+v)}$

$K=\frac{E}{3(1-2v)}$

$\mathrm{\λ}=K-\frac{2}{3}G=\frac{\mathrm{vE}}{(1-2v)(1+v)}$

Wherein ν is the Poisson ratio of metal blank cylindrical member, and E is the elastic modulus of metal blank cylindrical member, therefore the damage elasticity strain of junior unit strain with damage plasticity can be expressed as:

${\widetilde{\mathrm{\ϵ}}}_e=\frac{{\mathrm{\σ}}_H}{{(1-D)}^{2}3K}$

${\widetilde{\mathrm{\ϵ}}}_p={\left[\frac{{\mathrm{\σ}}^{\′}}{{(1-D)}^2(\mathrm{\λ}+2G)}\right]}^n.$

The wherein deviatoric stress of the junior unit of σ ' expression metal blank cylindrical member:

(2-5) theoretical according to free energy, can draw:

$\mathrm{\ψ}={\mathrm{\ψ}}_e+{\mathrm{\ψ}}_p=\mathrm{\ρ}{\∫}_0^{{\mathrm{\ϵ}}_{\mathrm{ef}}}{\mathrm{\σ}}_{H}d{\widetilde{\mathrm{\ϵ}}}_e+\mathrm{\ρ}{\∫}_0^{{\mathrm{\ϵ}}_{\mathrm{pf}}}{\mathrm{\σ}}^{\′}d{\widetilde{\mathrm{\ϵ}}}_p$

In formula, ψ is the free energy of metal blank cylindrical member in sheet forming, and ρ is the density of metal blank cylindrical member, ψ _eand ψ _pbe respectively elastic free energy and the plasticity free energy of metal blank cylindrical member, t is the time of fracture, ε _effor elastic strain when metal blank cylindrical member ruptures, ε _pffor plastic strain when metal blank cylindrical member ruptures.

Then in conjunction with the result of above-mentioned steps (2-3) and (2-4), metal blank cylindrical member damage free energy is obtained:

$\frac{\∂\mathrm{\ψ}}{\∂{\mathrm{\ϵ}}_p}=\frac{{\mathrm{\σ}}^{\′2}}{2E{(1-D)}^2}[\frac{2n}{3}(1+v)+3(1-2v){\left(\frac{{\mathrm{\σ}}_H}{{\mathrm{\σ}}^{\′}}\right)}^2]$

Finally, the flow stress form of metal blank cylindrical member damage free energy is drawn according to Mi Xisi yield criteria.

$\mathrm{d\ψ}=\frac{S^2}{2E{(1-D)}^2}[\frac{2n}{3}(1+v)+3(1-2v){\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]d{\mathrm{\ϵ}}_p$

In formula, S is the Mi Xisi yield stress of metal blank cylindrical member, when metal blank cylindrical member is broken, supposes that the damage threshold of metal blank cylindrical member is the constant D relevant to material property _c, the breaking strain of metal blank cylindrical member is the constant ε relevant to material property _rwith metal blank cylindrical member just start occur damage strain be the constant ε relevant to material property _d, then in metal blank cylindrical member punching course metal blank cylindrical member unidimensional scale under fracture criterion can be expressed as:

$\mathrm{dD}=\frac{D_c{S}^2}{{\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}_t}^2}{E}\right)d{\mathrm{\ϵ}}_p=\frac{D_c{S}^2}{({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}_t}^2}{E}\right)d{\mathrm{\ϵ}}_p$

Wherein dD is the variable quantity of the impairment value of metal blank cylindrical member, d ε _pfor the variable quantity of the plastic strain of metal blank cylindrical member.

(2-6) citation form of damage fracture criterion is derived according to the metal blank cylindrical member damage free energy obtained in step (2-5).

Preferably, in step (2-4), the deviatoric stress σ ' of the junior unit of metal blank cylindrical member is:

${\mathrm{\σ}}^{\′}=\left[\begin{array}{ccc}{\mathrm{\σ}}_x-{\mathrm{\σ}}_H& {\mathrm{\τ}}_{\mathrm{xy}}& {\mathrm{\τ}}_{\mathrm{xz}}\\ {\mathrm{\τ}}_{\mathrm{yx}}& {\mathrm{\σ}}_y-{\mathrm{\σ}}_H& {\mathrm{\τ}}_{\mathrm{yz}}\\ {\mathrm{\τ}}_{\mathrm{zx}}& {\mathrm{\τ}}_{\mathrm{zy}}& {\mathrm{\σ}}_z-{\mathrm{\σ}}_H\end{array}\right]$

The wherein hydrostatic stress σ of the junior unit of metal blank cylindrical member _h=(σ _x+ σ _y+ σ _z)/3.

Preferably, the damage fracture criterion in step (2-6) under metal blank cylindrical member triaxiality yardstick is:

$\left[\begin{array}{c}{\mathrm{dD}}_x\\ {\mathrm{dD}}_y\\ {\mathrm{dD}}_z\end{array}\right]=\frac{D_c{S}^2}{{\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}^2}_t}{E}\right){\mathrm{d\ϵ}}_p=\frac{D_c{S}^2}{E({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\mathrm{d\ϵ}\left[\begin{array}{c}{{\mathrm{\σ}}_x}^2\\ {{\mathrm{\σ}}_y}^2\\ {{\mathrm{\σ}}_z}^2\end{array}\right]$

Wherein D _cfor the critical damage value size of metal blank cylindrical member, D _x, D _y, D _zbe respectively the impairment value of metal blank cylindrical member at three principal directions of stress.

Preferably, the damage fracture criterion of metal blank cylindrical member comprises measurement constant: the critical damage value size D of metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _d.

Preferably, the measurement constant in following steps calculating damage fracture criterion is adopted:

(2-6-1) carry out one directional tensile test to metal blank sample, to obtain material parameter, it comprises true stress, logarithmic strain, equivalent plastic strain and elastic modulus.

(2-6-2) the maximum tension length of unilateral stretching is divided into n equal portions, wherein n is positive integer, and mark the distance of each node stretching, with cupping machine sample is stretched to first demarcate distance time carry out load unloading, when unloading load and becoming 0 again to the distance of same sample unilateral stretching to next equal portions node, so carry out reverse cyclic loadings unloading test, till tensile sample breaks;

(2-6-3) on testing machine, derive the test findings of reverse cyclic loadings unloading, the result of derivation is converted into the relation of true stress and logarithmic strain, the elastic modulus of metal blank cylindrical member is calculated according to each section of loading curve, and calculate impairment value according to elastic modulus, obtain the relation of impairment value and average equivalent plastic strain;

(2-6-4) according to the stress state relation of the Sheet metal forming process in step 1, the stress area main in forming process when metal blank is in uniaxial stressed state, linear fit is carried out to the equal equivalent strain relation of impairment value peace of metal blank cylindrical member, elongated linear straight line obtains the intercept with ordinate, and the values of intercept obtained is the strain value ε just starting to occur damage of metal blank cylindrical member _dand obtain damage formula, when the main stress area of metal blank in forming process is in two-dimensional state of stress or multi-dimensional stress state, nonlinear function approximation is carried out to the equal equivalent strain relation of impairment value peace of metal blank cylindrical member, extended function curve obtains the intercept with ordinate, and the values of intercept obtained is the strain value ε just starting to occur damage of metal blank cylindrical member _d, and obtain damage formula;

(2-6-5) set up in finite element software ABAQUS and repeatedly add Unloading Model, wherein boundary condition and the material properties of modeling are all with above-mentioned repeatedly to add unloading experiment consistent, utilization repeatedly adds Unloading Model and carries out finite element analogy, and aftertreatment is carried out to finite element analogy result, with obtain metal blank cylindrical member breaking strain ε _r, finally by breaking strain ε _rsubstitute in damage formula, to obtain fracture threshold values D _c;

(2-6-6) by the critical damage value size D of obtained metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _dsubstitute in the damage fracture criterion of metal blank cylindrical member, obtain the expression formula of metal blank cylindrical member fracture criterion.

Preferably, step (3) is specially, set up metal blank cylindrical member punching press finite element model, in order to improve precision and the quality of calculating, the small cell size of fining metal plate cylindrical member, then the boundary condition of the drift loading speed that different metal blank cylindrical member is shaped is set, metal blank cylindrical member punching press finite element model is used to simulate on ABAQUS finite element software, obtain metal blank cylindrical member finite element analogy result, finally, under the drift loading speed that the different metal blank cylindrical member obtained is shaped, metal blank cylindrical member finite element analogy result derives, obtain the metal blank cylindrical member fracture maximum impairment value in moment and the maximum impairment value of metal blank cylindrical member fracture position.

In general, the above technical scheme conceived by the present invention compared with prior art, can obtain following beneficial effect:

1. the present invention is less at fracture prediction process medial error: the damage of the Macroscopic behavior in sheet forming and microcosmic combined and step 3 Subgridding method and Finite Element Method owing to have employed step 2, therefore use the rupture time of the prediction of damage fracture criterion of the present invention and fracture position comparatively accurate.

2., because the present invention mainly have employed the method that numerical simulation and experiment combine, and the time consumed is few, human resources and utilization factor high, can avoid experiment repeatedly, therefore the present invention can be cost-saving.

3. the result due to numerical method of the present invention is consistent with experimental result, and therefore of the present invention is a kind of reliable believable numerical method, and this damage fracture criterion can predict rupture time in sheet forming and position accurately.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the method that the present invention is based on the fracture of damage fracture criterion numerical prediction sheet forming;

Fig. 2 is round metal barrier part punching press stress state distribution plan;

Fig. 3 illustrates metal blank tensile sample;

Fig. 4 illustrates the relation of true stress and logarithmic strain in one way tensile test;

Fig. 5 illustrates trus stress in reverse cyclic loadings unloading test and true strain graph of a relation;

Fig. 6 illustrates the matched curve of impairment value and equivalent plastic strain;

Fig. 7 is metal blank cylindrical member punching press finite element model;

Fig. 8 illustrates the relation of metal blank cylindrical member impairment value and loading speed.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.In addition, if below in described each embodiment of the present invention involved technical characteristic do not form conflict each other and just can mutually combine.

The present invention proposes the method for damage fracture criterion numerical prediction sheet forming fracture.The method does not need a large amount of experimental results, be applicable to most sheet forming technique, the breakage problem of the damage problem of microcosmic and macroscopic view is combined, predict the fracture position in sheet forming and rupture time accurately, as shown in Figure 1, the method that the present invention is based on the fracture of damage fracture criterion numerical prediction sheet forming comprises the following steps:

(1) obtain the stress distribution of metal blank cylindrical member punching course according to the irreversible law of thermodynamics, and obtain the balance differential equation of stress in metal blank cylindrical member punching course according to the distribution of this stress; Specifically, as shown in Figure 2, cylindrical member is subject to the effect of three-dimensional stress state at flange region 2-1, punch-nose angle region 2-4 and die entrance region 2-5, and bottom section 2-3 is subject to the effect of plane stress state, and Zhi Bi region 2-2 is subject to the effect of uniaxial stressed state.In metal blank cylindrical member punching course, plate is subject to the effect of four face power, is respectively the friction force load of the equal pressure load of the punch adopted in metal blank cylindrical member punching course, the Y-direction compressive stress load of the blank holder of employing and the blank holder of employing.Therefore can show that the balance differential equation of stress is as follows:

$\left\{\begin{array}{c}\frac{\∂{\mathrm{\σ}}_x}{\∂x}+\frac{\∂{\mathrm{\τ}}_{\mathrm{xy}}}{\∂y}+\frac{\∂{\mathrm{\τ}}_{\mathrm{xz}}}{\∂z}+f_{1x}=0\\ \frac{\∂{\mathrm{\τ}}_{\mathrm{yx}}}{\∂x}+\frac{\∂{\mathrm{\σ}}_y}{\∂y}+\frac{\∂{\mathrm{\τ}}_{\mathrm{yz}}}{\∂z}+f_{1y}+f_2=0\\ \frac{\∂{\mathrm{\τ}}_{\mathrm{zx}}}{\∂x}+\frac{\∂{\mathrm{\τ}}_{\mathrm{zy}}}{\∂y}+\frac{\∂{\mathrm{\σ}}_z}{\∂z}+f_{1z}=0\end{array}\right.$

In formula, x, y and z are the coordinate figure of junior unit in three directions of three-dimensional perpendicular coordinate system of metal blank cylindrical member, internal stress σ _tthe normal stress value of junior unit on t direction (t=x, y, z), τ _ijfor the shearing stress value of junior unit in ij plane (i, j=x, y, z, wherein i ≠ j), f ₂for the equal pressure load of punch adopted in metal blank cylindrical member punching course, f _1yfor the Y-direction compressive stress load of the blank holder of employing, f _1xand f _1zfor the friction force load of blank holder.

Further, the deviatoric stress σ ' of the junior unit of metal blank cylindrical member can be expressed as:

${\mathrm{\σ}}^{\′}=\left[\begin{array}{ccc}{\mathrm{\σ}}_x-{\mathrm{\σ}}_H& {\mathrm{\τ}}_{\mathrm{xy}}& {\mathrm{\τ}}_{\mathrm{xz}}\\ {\mathrm{\τ}}_{\mathrm{yx}}& {\mathrm{\σ}}_y-{\mathrm{\σ}}_H& {\mathrm{\τ}}_{\mathrm{yz}}\\ {\mathrm{\τ}}_{\mathrm{zx}}& {\mathrm{\τ}}_{\mathrm{zy}}& {\mathrm{\σ}}_z-{\mathrm{\σ}}_H\end{array}\right]$

In formula, the hydrostatic stress σ of the junior unit of metal blank cylindrical member _h=(σ _x+ σ _y+ σ _z)/3.

(2) when there is damage according to metal blank cylindrical member in continuum damage mechanics theory calculate metal blank cylindrical member punching course, the rate of change of the area of the junior unit of metal blank cylindrical member, and the damage of metal blank cylindrical member is obtained according to this rate of change, calculate the relation between the damage of metal blank cylindrical member and strain afterwards, finally and Mi Xisi (Misses) yield criteria theoretical according to free energy derives impairment value under the unidimensional scale of metal blank cylindrical member in whole metal blank cylindrical member punching course and true stress, logarithmic strain, relation between the parameters such as hydrostatic stress, and the damage fracture criterion expanded under metal blank cylindrical member triaxiality yardstick.Specifically, this step comprises following sub-step:

(2-1) original section obtaining the junior unit of metal blank cylindrical member amasss S ₀;

(2-2) when obtaining metal blank cylindrical member generation damage in metal blank cylindrical member punching course, the sectional area S under the faulted condition of the junior unit of metal blank cylindrical member;

(2-3) S is amassed according to the original section of junior unit ₀the impairment value D of junior unit is calculated, the rate of change as the area of junior unit with the sectional area S under faulted condition:

$D=1-\frac{S}{S_0}.$

(2-4) the elastic strain ε of junior unit is obtained according to the impairment value D of the junior unit calculated _ewith plastic strain ε _p:

${\mathrm{\ϵ}}_e=\frac{{\mathrm{\σ}}_H}{(1-D)3K}$

${\mathrm{\ϵ}}_p={\left[\frac{{\mathrm{\σ}}^{\′}}{(1-D)(\mathrm{\λ}+2G)}\right]}^n.$

In formula, n is the material hardening exponent of metal blank cylindrical member, G is the metal blank cylindrical member plastic shear modulus relevant with plastic deformation degree, K is the metal blank cylindrical member bulk modulus relevant with cubic deformation, λ is that metal blank cylindrical member and elastic stress change relevant elastic modulus, and has:

$G=\frac{E}{2(1+v)}$

$K=\frac{E}{3(1-2v)}$

$\mathrm{\λ}=K-\frac{2}{3}G=\frac{\mathrm{vE}}{(1-2v)(1+v)}$

Wherein ν is the Poisson ratio of metal blank cylindrical member, and E is the elastic modulus of metal blank cylindrical member.Therefore the damage elasticity strain of junior unit strain with damage plasticity can be expressed as:

${\widetilde{\mathrm{\ϵ}}}_e=\frac{{\mathrm{\σ}}_H}{{(1-D)}^{2}3K}$

${\widetilde{\mathrm{\ϵ}}}_p={\left[\frac{{\mathrm{\σ}}^{\′}}{{(1-D)}^2(\mathrm{\λ}+2G)}\right]}^n.$

(2-5) theoretical according to free energy, can draw:

$\mathrm{\ψ}={\mathrm{\ψ}}_e+{\mathrm{\ψ}}_p=\mathrm{\ρ}{\∫}_0^{{\mathrm{\ϵ}}_{\mathrm{ef}}}{\mathrm{\σ}}_{H}d{\widetilde{\mathrm{\ϵ}}}_e+\mathrm{\ρ}{\∫}_0^{{\mathrm{\ϵ}}_{\mathrm{pf}}}{\mathrm{\σ}}^{\′}d{\widetilde{\mathrm{\ϵ}}}_p$

In formula, ψ is the free energy of metal blank cylindrical member in sheet forming, and ρ is the density of metal blank cylindrical member, ψ _eand ψ _pbe respectively elastic free energy and the plasticity free energy of metal blank cylindrical member, t is the time of fracture, ε _effor elastic strain when metal blank cylindrical member ruptures, ε _pffor plastic strain when metal blank cylindrical member ruptures.

Further, in conjunction with the result of above-mentioned steps (2-3) and (2-4), can obtain metal blank cylindrical member damage free energy can be expressed as.

$\frac{\∂\mathrm{\ψ}}{\∂{\mathrm{\ϵ}}_p}=\frac{{\mathrm{\σ}}^{\′2}}{2E{(1-D)}^2}[\frac{2n}{3}(1+v)+3(1-2v){\left(\frac{{\mathrm{\σ}}_H}{{\mathrm{\σ}}^{\′}}\right)}^2]$

Further, according to Misses yield criteria, the flow stress form of metal blank cylindrical member damage free energy can be drawn.

$\mathrm{d\ψ}=\frac{S^2}{2E{(1-D)}^2}[\frac{2n}{3}(1+v)+3(1-2v){\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]d{\mathrm{\ϵ}}_p$

In formula, S is the Misses yield stress of metal blank cylindrical member.When metal blank cylindrical member is broken, suppose that the damage threshold of metal blank cylindrical member is the constant D relevant to material property _c, the breaking strain of metal blank cylindrical member is the constant ε relevant to material property _rwith metal blank cylindrical member just start occur damage strain be the constant ε relevant to material property _d.Therefore in metal blank cylindrical member punching course metal blank cylindrical member unidimensional scale under fracture criterion can be expressed as:

$\mathrm{dD}=\frac{D_c{S}^2}{{\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}_t}^2}{E}\right)d{\mathrm{\ϵ}}_p=\frac{D_c{S}^2}{({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}_t}^2}{E}\right)d{\mathrm{\ϵ}}_p$

Wherein dD is the variable quantity of the impairment value of metal blank cylindrical member, d ε _pfor the variable quantity of the plastic strain of metal blank cylindrical member.

(2-6) citation form of damage fracture criterion is derived according to the metal blank cylindrical member damage free energy obtained in step (2-5).Specifically, because the impairment value of metal blank cylindrical member appears at after Misses surrender occurs material, equivalent plastic strain ε now _pmuch larger than elastic strain value ε _e, the equivalent plastic strain therefore when damage occurs material can substitute with logarithmic strain ε, and the damage fracture criterion that therefore can obtain under metal blank cylindrical member triaxiality yardstick is:

$\left[\begin{array}{c}{\mathrm{dD}}_x\\ {\mathrm{dD}}_y\\ {\mathrm{dD}}_z\end{array}\right]=\frac{D_c{S}^2}{{\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}^2}_t}{E}\right){\mathrm{d\ϵ}}_p=\frac{D_c{S}^2}{E({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\mathrm{d\ϵ}\left[\begin{array}{c}{{\mathrm{\σ}}_x}^2\\ {{\mathrm{\σ}}_y}^2\\ {{\mathrm{\σ}}_z}^2\end{array}\right]$

Wherein D _cfor the critical damage value size of metal blank cylindrical member, D _x, D _y, D _zbe respectively the impairment value of metal blank cylindrical member at three principal directions of stress.

Further, the damage fracture criterion of metal blank cylindrical member comprises three constants measured, the critical damage value size D of metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _d, adopt following steps to calculate:

(2-6-1) to metal blank sample (as shown in Figure 3, it has identical material properties with metal blank cylindrical member) carry out one directional tensile test, to obtain material parameter, it comprises true stress, logarithmic strain (as shown in Figure 4), equivalent plastic strain and various elastic modulus.

(2-6-2) the maximum tension length of unilateral stretching is divided into n equal portions (n span is the integer between 10 to 100), and mark the distance of each node stretching, with cupping machine sample is stretched to first demarcate distance time carry out load unloading, when unloading load and becoming 0 again to the distance of same sample unilateral stretching to next equal portions node, so carry out reverse cyclic loadings unloading test, till tensile sample breaks.

(2-6-3) on testing machine, derive the test findings of reverse cyclic loadings unloading, the result of derivation is converted into the relation (as shown in Figure 5) of true stress and logarithmic strain, the elastic modulus of metal blank cylindrical member is calculated according to each section of loading curve, and calculate impairment value according to elastic modulus, obtain the relation (as shown in Figure 6) of impairment value and average equivalent plastic strain, the ordinate of Fig. 6 is the axle of impairment value, and horizontal ordinate is the axle of equivalent plastic strain.

(2-6-4) according to the stress state relation of the Sheet metal forming process in step 1, the stress area main in forming process when metal blank is in uniaxial stressed state, linear fit is carried out to the equal equivalent strain relation of impairment value peace of metal blank cylindrical member, elongated linear straight line obtains the intercept with ordinate, and the values of intercept obtained is the strain value ε just starting to occur damage of metal blank cylindrical member _dand obtain damage formula, when the main stress area of metal blank in forming process is in two-dimensional state of stress or multi-dimensional stress state, nonlinear function approximation is carried out to the equal equivalent strain relation of impairment value peace of metal blank cylindrical member, extended function curve obtains the intercept with ordinate, and the values of intercept obtained is the strain value ε just starting to occur damage of metal blank cylindrical member _d, and obtain damage formula.

(2-6-5) set up in finite element software ABAQUS and repeatedly add Unloading Model, wherein boundary condition and the material properties of modeling are all with above-mentioned repeatedly to add unloading experiment consistent, utilization repeatedly adds Unloading Model and carries out finite element analogy, and aftertreatment is carried out to finite element analogy result, with obtain metal blank cylindrical member breaking strain ε _r, finally by breaking strain ε _rsubstitute in damage formula, to obtain fracture threshold values D _c.

(2-6-6) by the critical damage value size D of obtained metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _dsubstitute in the damage fracture criterion of metal blank cylindrical member, obtain the expression formula of metal blank cylindrical member fracture criterion.

(3) according to the expression formula of the damage fracture criterion under the balance differential equation of stress in step 1 metal blank cylindrical member punching course and the metal blank cylindrical member triaxiality yardstick of step 2 acquisition, and the expression formula of impairment value in damage fracture criterion is write based on finite element software ABAQUS, and this expression formula is applied in Finite Element Simulation of Sheet Metal Forming model (as shown in Figure 7), to obtain the impairment value that the fracture moment appears in metal blank cylindrical member, and the impairment value of metal blank cylindrical member fracture position.Concrete operations are as follows: first, set up metal blank cylindrical member punching press finite element model, in order to improve precision and the quality of calculating, and the small cell size of fining metal plate cylindrical member; Secondly, the boundary condition of the drift loading speed that different metal blank cylindrical member is shaped is set, uses metal blank cylindrical member punching press finite element model to simulate on ABAQUS finite element software, obtain metal blank cylindrical member finite element analogy result; Finally, under the drift loading speed that the different metal blank cylindrical member obtained is shaped, metal blank cylindrical member finite element analogy result derives, obtain the metal blank cylindrical member fracture maximum impairment value in moment and the maximum impairment value of metal blank cylindrical member fracture position, and contrast with metal blank cylindrical member damage threshold, as shown in Figure 8.

Example

Below by way of example, method step of the present invention is described:

(1) shock pressure experiments of metal blank cylindrical member is carried out on 1000kN servo-pressing machine, the diameter of metal blank is 180mm, thickness is 1mm, arranges the Y-direction compressive stress load f of servo-pressing machine to the blank holder that metal blank cylindrical member punching course adopts _1yalong with adopted punch pressure f ₂change and change, i.e. f _1y=0.3f ₂.Adopt parting speed to be 10mm/s, friction factor in the shock pressure experiments of metal blank cylindrical member is coated oil lubricating, is adjusted to 0.15, adopt convex mould diameter to be 98mm, institute's employing punch and adopt die profile radius be all 8mm, adopt die internal diameter to be 100mm.The material of the metal blank adopted is aluminium alloy 5052-O, and density is 2700kg/m ³, elastic modulus E is 70GPa, and Poisson ratio is 0.33.In metal blank cylindrical member punching course, plate is subject to the effect of four face power, can show that the balance differential equation of stress is as follows:

$\left\{\begin{array}{c}\frac{\∂{\mathrm{\σ}}_x}{\∂x}+\frac{\∂{\mathrm{\τ}}_{\mathrm{xy}}}{\∂y}+\frac{\∂{\mathrm{\τ}}_{\mathrm{xz}}}{\∂z}+0.063f_2=0\\ \frac{\∂{\mathrm{\τ}}_{\mathrm{yx}}}{\∂x}+\frac{\∂{\mathrm{\σ}}_y}{\∂y}+\frac{\∂{\mathrm{\τ}}_{\mathrm{yz}}}{\∂z}+1.3f_2=0\\ \frac{\∂{\mathrm{\τ}}_{\mathrm{zx}}}{\∂x}+\frac{\∂{\mathrm{\τ}}_{\mathrm{zy}}}{\∂y}+\frac{\∂{\mathrm{\σ}}_z}{\∂z}+0.063f_2=0\end{array}\right.$

(2) when there is damage according to metal blank cylindrical member in continuum damage mechanics theory calculate metal blank cylindrical member punching course, the rate of change of the area of the junior unit of metal blank cylindrical member, the rate of change of junior unit area is converted into the rate of change of the elastic modulus of junior unit, the damage of the junior unit of metal blank cylindrical member also can be expressed as the form of elastic modulus:

$D=1-\frac{\tilde{E}}{E}$

Wherein for the effective modulus of elasticity of junior unit, E is the initial elastic modulus of junior unit.

Use the test of the metal blank shown in Fig. 3 to carry out one directional tensile test, obtain the true stress of metal material in sheet forming and the relation of logarithmic strain.The constitutive relation obtaining metal material can be expressed as formula (7)

$\mathrm{\σ}=e^{4.4+5.42x-7.20x^2}$

Carry out the damage fracture criterion that method that reverse cyclic loadings unloading test and finite element analogy combine measures metal blank cylindrical member and comprise three constants measured, the critical damage value size D of metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _d, finally obtain when loading speed is 1mm/s, the critical damage value of metal blank cylindrical member is 0.60, and the breaking strain of metal blank cylindrical member is 0.33, metal blank cylindrical member just start occur damage strain value be 0.05.Damage fracture criterion under the triaxiality yardstick of therefore metal blank cylindrical member can be expressed as:

$\left[\begin{array}{c}{\mathrm{dD}}_x\\ {\mathrm{dD}}_y\\ {\mathrm{dD}}_z\end{array}\right]=0.22S^2[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}^2}_t}{E}\right){\mathrm{d\ϵ}}_p=\frac{D_c{S}^2}{E({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\mathrm{d\ϵ}\left[\begin{array}{c}{{\mathrm{\σ}}_x}^2\\ {{\mathrm{\σ}}_y}^2\\ {{\mathrm{\σ}}_z}^2\end{array}\right]$

(3) according to the expression formula of the damage fracture criterion under the balance differential equation of stress in step 1 metal blank cylindrical member punching course and the metal blank cylindrical member triaxiality yardstick of step 2 acquisition, and the expression formula of impairment value in damage fracture criterion is write based on finite element software ABAQUS, and this expression formula is applied in Finite Element Simulation of Sheet Metal Forming model (as shown in Figure 7), under the drift loading speed that different metal blank cylindrical member is shaped, draw out damage and the loading speed curve (as shown in Figure 8) of metal blank cylindrical member, the error of the maximum impairment value in metal blank cylindrical member damage threshold and metal blank cylindrical member fracture moment is less than 10%, the error of the maximum impairment value of metal blank cylindrical member damage threshold and metal blank cylindrical member fracture position is less than 10%.

Totally it seems, a kind of reliable during a kind of method based on the fracture of damage fracture criterion numerical prediction sheet forming of the present invention, feasible method for numerical simulation, the method may be used for the quality and the productive rate that improve sheet forming, has the advantages that cost is low, efficiency is high, the cycle is short.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1., based on a method for damage fracture criterion numerical prediction sheet forming fracture, it is characterized in that, comprise the following steps:

(1) obtain the stress distribution of metal blank cylindrical member punching course according to the irreversible law of thermodynamics, and obtain the balance differential equation of stress in metal blank cylindrical member punching course according to the distribution of this stress;

(2) when there is damage according to metal blank cylindrical member in continuum damage mechanics theory calculate metal blank cylindrical member punching course, the rate of change of the area of the junior unit of metal blank cylindrical member, and the damage of metal blank cylindrical member is obtained according to this rate of change, calculate the relation between the damage of metal blank cylindrical member and strain, according to free energy, theoretical and Mi Xisi yield criteria derives impairment value under the unidimensional scale of metal blank cylindrical member in whole metal blank cylindrical member punching course and true stress, logarithmic strain, relation between hydrostatic stress, and the damage fracture criterion expanded under metal blank cylindrical member triaxiality yardstick,

(3) expression formula of the damage fracture criterion under the metal blank cylindrical member triaxiality yardstick obtained according to balance differential equation and the step (2) of stress in step (1) metal blank cylindrical member punching course, and the expression formula of impairment value in damage fracture criterion is write based on finite element software ABAQUS, and this expression formula is applied in Finite Element Simulation of Sheet Metal Forming model, to obtain the impairment value that the fracture moment appears in metal blank cylindrical member, and the impairment value of metal blank cylindrical member fracture position.

2. method according to claim 1, is characterized in that, in step (1), the balance differential equation of stress is as follows:

$\left\{\begin{array}{c}\frac{{\∂\mathrm{\σ}}_x}{\∂x}+\frac{{\∂\mathrm{\τx}}_y}{\∂y}+\frac{{\∂\mathrm{\τ}}_{\mathrm{xz}}}{\∂z}+f_{1x}=0\\ \frac{{\∂\mathrm{\τ}}_{\mathrm{yx}}}{\∂x}+\frac{\∂{\mathrm{\σ}}_y}{\∂y}+\frac{{\∂\mathrm{\τ}}_{\mathrm{yz}}}{\∂z}+f_{1y}+f_2=0\\ \frac{{\∂\mathrm{\τ}}_{\mathrm{zx}}}{\∂x}+\frac{{\∂\mathrm{\τ}}_{\mathrm{zy}}}{\∂y}+\frac{\∂{\mathrm{\σ}}_z}{\∂z}+f_{1z}=0\end{array}\right.$

Wherein x, y and z are the coordinate figure of junior unit in three directions of three-dimensional perpendicular coordinate system of metal blank cylindrical member, internal stress σ _tthe normal stress value of junior unit on t direction (t=x, y, z), τ _ijfor the shearing stress value of junior unit in ij plane (i, j=x, y, z, wherein i ≠ j), f ₂for the equal pressure load of punch adopted in metal blank cylindrical member punching course, f _1yfor the Y-direction compressive stress load of the blank holder of employing, f _1xand f _1zfor the friction force load of blank holder.

3. method according to claim 2, is characterized in that, step (2) comprises following sub-step:

(2-1) original section obtaining the junior unit of metal blank cylindrical member amasss S ₀;

(2-2) when obtaining metal blank cylindrical member generation damage in metal blank cylindrical member punching course, the sectional area S under the faulted condition of the junior unit of metal blank cylindrical member;

(2-3) S is amassed according to the original section of junior unit ₀the impairment value D of junior unit is calculated, the rate of change as the area of junior unit with the sectional area S under faulted condition:

$D=1-\frac{S}{S_0}.$

(2-4) the elastic strain ε of junior unit is obtained according to the impairment value D of the junior unit calculated _ewith plastic strain ε _p:

${\mathrm{\ϵ}}_e=\frac{{\mathrm{\σ}}_H}{(1-D)3K}$

${\mathrm{\ϵ}}_p=[\frac{{\mathrm{\σ}}^{\′}}{(1-D)(\mathrm{\λ}+2G)}{]}^n.$

In formula, n is the material hardening exponent of metal blank cylindrical member, G is the metal blank cylindrical member plastic shear modulus relevant with plastic deformation degree, K is the metal blank cylindrical member bulk modulus relevant with cubic deformation, λ is that metal blank cylindrical member and elastic stress change relevant elastic modulus, and has:

$G=\frac{E}{2(1+v)}$

$K=\frac{E}{3(1-2v)}$

$\mathrm{\λ}=K-\frac{2}{3}G=\frac{\mathrm{vE}}{(1-2v)(1+v)}$

Wherein ν is the Poisson ratio of metal blank cylindrical member, and E is the elastic modulus of metal blank cylindrical member, therefore the damage elasticity strain of junior unit strain with damage plasticity can be expressed as:

${\widetilde{\mathrm{\ϵ}}}_e=\frac{{\mathrm{\σ}}_H}{{(1-D)}^{2}3K}$

${\widetilde{\mathrm{\ϵ}}}_p={\left[\frac{{\mathrm{\σ}}^{\′}}{{(1-D)}^2(\mathrm{\λ}+2G)}\right]}^n.$

The wherein deviatoric stress of the junior unit of σ ' expression metal blank cylindrical member:

(2-5) theoretical according to free energy, can draw:

$\mathrm{\ψ}={\mathrm{\ψ}}_e+{\mathrm{\ψ}}_p=\mathrm{\ρ}{\∫}_0^{{\mathrm{\ϵ}}_{\mathrm{ef}}}{\mathrm{\σ}}_{H}d{\widetilde{\mathrm{\ϵ}}}_e+\mathrm{\ρ}{\∫}_0^{{\mathrm{\ϵ}}_{\mathrm{pf}}}{\mathrm{\σ}}^{\′}d{\widetilde{\mathrm{\ϵ}}}_p$

In formula, ψ is the free energy of metal blank cylindrical member in sheet forming, and ρ is the density of metal blank cylindrical member, ψ _eand ψ _pbe respectively elastic free energy and the plasticity free energy of metal blank cylindrical member, t is the time of fracture, ε _effor elastic strain when metal blank cylindrical member ruptures, ε _pffor plastic strain when metal blank cylindrical member ruptures.

Then in conjunction with the result of above-mentioned steps (2-3) and (2-4), metal blank cylindrical member damage free energy is obtained:

$\frac{\∂\mathrm{\ψ}}{\∂{\mathrm{\ϵ}}_p}=\frac{{\mathrm{\σ}}^{\′2}}{2E{(1-D)}^2}[\frac{2n}{3}(1+v)+3(1-2v){\left(\frac{{\mathrm{\σ}}_H}{{\mathrm{\σ}}^{\′}}\right)}^2]$

Finally, the flow stress form of metal blank cylindrical member damage free energy is drawn according to Mi Xisi yield criteria.

$\mathrm{d\ψ}=\frac{S^2}{2E{(1-D)}^2}[\frac{2n}{3}(1+v)+3(1-2v){\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]d{\mathrm{\ϵ}}_p$

In formula, S is the Mi Xisi yield stress of metal blank cylindrical member, when metal blank cylindrical member is broken, supposes that the damage threshold of metal blank cylindrical member is the constant D relevant to material property _c, the breaking strain of metal blank cylindrical member is the constant ε relevant to material property _rwith metal blank cylindrical member just start occur damage strain be the constant ε relevant to material property _d, then in metal blank cylindrical member punching course metal blank cylindrical member unidimensional scale under fracture criterion can be expressed as:

$\mathrm{dD}=\frac{D_c{S}^2}{{\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}_t}^2}{E}\right)d{\mathrm{\ϵ}}_p=\frac{D_c{S}^2}{({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}_t}^2}{E}\right)d{\mathrm{\ϵ}}_p$

Wherein dD is the variable quantity of the impairment value of metal blank cylindrical member, d ε _pfor the variable quantity of the plastic strain of metal blank cylindrical member.

(2-6) citation form of damage fracture criterion is derived according to the metal blank cylindrical member damage free energy obtained in step (2-5).

4. method according to claim 3, is characterized in that, in step (2-4), the deviatoric stress σ ' of the junior unit of metal blank cylindrical member is:

${\mathrm{\σ}}^{\′}=\left[\begin{array}{ccc}{\mathrm{\σ}}_x-{\mathrm{\σ}}_H& {\mathrm{\τ}}_{\mathrm{xy}}& {\mathrm{\τ}}_{\mathrm{xz}}\\ {\mathrm{\τ}}_{\mathrm{yx}}& {\mathrm{\σ}}_y-{\mathrm{\σ}}_H& {\mathrm{\τ}}_{\mathrm{yz}}\\ {\mathrm{\τ}}_{\mathrm{zx}}& {\mathrm{\τ}}_{\mathrm{zy}}& {\mathrm{\σ}}_z-{\mathrm{\σ}}_H\end{array}\right]$

The wherein hydrostatic stress σ of the junior unit of metal blank cylindrical member _h=(σ _x+ σ _y+ σ _z)/3.

5. method according to claim 4, is characterized in that, the damage fracture criterion in step (2-6) under metal blank cylindrical member triaxiality yardstick is:

$\left[\begin{array}{c}{\mathrm{dD}}_x\\ {\mathrm{dD}}_y\\ d{D}_z\end{array}\right]=\frac{D_c{S}^2}{{\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\left(\frac{{{\mathrm{\σ}}^2}_t}{E}\right)d{\mathrm{\ϵ}}_p=\frac{D_c{S}^2}{E({\mathrm{\ϵ}}_R-{\mathrm{\ϵ}}_D)}[\frac{n}{3G}+\frac{1}{K}{\left(\frac{{\mathrm{\σ}}_H}{S}\right)}^2]\mathrm{d\ϵ}\left[\begin{array}{c}{{\mathrm{\σ}}_x}^2\\ {{\mathrm{\σ}}_y}^2\\ {{\mathrm{\σ}}_z}^2\end{array}\right]$

Wherein D _cfor the critical damage value size of metal blank cylindrical member, D _x, D _y, D _zbe respectively the impairment value of metal blank cylindrical member at three principal directions of stress.

6. method according to claim 5, is characterized in that, the damage fracture criterion of metal blank cylindrical member comprises measurement constant: the critical damage value size D of metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _d.

7. method according to claim 6, is characterized in that, adopts the measurement constant in following steps calculating damage fracture criterion:

(2-6-1) carry out one directional tensile test to metal blank sample, to obtain material parameter, it comprises true stress, logarithmic strain, equivalent plastic strain and elastic modulus.

(2-6-2) the maximum tension length of unilateral stretching is divided into n equal portions, wherein n is positive integer, and mark the distance of each node stretching, with cupping machine sample is stretched to first demarcate distance time carry out load unloading, when unloading load and becoming 0 again to the distance of same sample unilateral stretching to next equal portions node, so carry out reverse cyclic loadings unloading test, till tensile sample breaks;

(2-6-3) on testing machine, derive the test findings of reverse cyclic loadings unloading, the result of derivation is converted into the relation of true stress and logarithmic strain, the elastic modulus of metal blank cylindrical member is calculated according to each section of loading curve, and calculate impairment value according to elastic modulus, obtain the relation of impairment value and average equivalent plastic strain;

(2-6-4) according to the stress state relation of the Sheet metal forming process in step 1, the stress area main in forming process when metal blank is in uniaxial stressed state, linear fit is carried out to the equal equivalent strain relation of impairment value peace of metal blank cylindrical member, elongated linear straight line obtains the intercept with ordinate, and the values of intercept obtained is the strain value ε just starting to occur damage of metal blank cylindrical member _dand obtain damage formula, when the main stress area of metal blank in forming process is in two-dimensional state of stress or multi-dimensional stress state, nonlinear function approximation is carried out to the equal equivalent strain relation of impairment value peace of metal blank cylindrical member, extended function curve obtains the intercept with ordinate, and the values of intercept obtained is the strain value ε just starting to occur damage of metal blank cylindrical member _d, and obtain damage formula;

(2-6-5) set up in finite element software ABAQUS and repeatedly add Unloading Model, wherein boundary condition and the material properties of modeling are all with above-mentioned repeatedly to add unloading experiment consistent, utilization repeatedly adds Unloading Model and carries out finite element analogy, and aftertreatment is carried out to finite element analogy result, with obtain metal blank cylindrical member breaking strain ε _r, finally by breaking strain ε _rsubstitute in damage formula, to obtain fracture threshold values D _c;

(2-6-6) by the critical damage value size D of obtained metal blank cylindrical member _c, metal blank cylindrical member breaking strain ε _rwith the strain value ε just starting to occur damaging of metal blank cylindrical member _dsubstitute in the damage fracture criterion of metal blank cylindrical member, obtain the expression formula of metal blank cylindrical member fracture criterion.

8. method according to claim 7, it is characterized in that, step (3) is specially, set up metal blank cylindrical member punching press finite element model, in order to improve precision and the quality of calculating, the small cell size of fining metal plate cylindrical member, then the boundary condition of the drift loading speed that different metal blank cylindrical member is shaped is set, metal blank cylindrical member punching press finite element model is used to simulate on ABAQUS finite element software, obtain metal blank cylindrical member finite element analogy result, finally, under the drift loading speed that the different metal blank cylindrical member obtained is shaped, metal blank cylindrical member finite element analogy result derives, obtain the metal blank cylindrical member fracture maximum impairment value in moment and the maximum impairment value of metal blank cylindrical member fracture position.