CN109918785B - Method for predicting and controlling hot forming wrinkling of large complex thin-wall titanium alloy component - Google Patents
Method for predicting and controlling hot forming wrinkling of large complex thin-wall titanium alloy component Download PDFInfo
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Abstract
The invention discloses a method for predicting and controlling hot forming wrinkling of a large complex thin-wall titanium alloy component, which belongs to the field of basic non-cutting treatment of metal plates and comprises the following steps of establishing a hot forming wrinkling prediction theory of the titanium alloy thin-wall component; predicting a wrinkling area possibly generated in the sheet forming process; step three, establishing a finite element simulation model of the hot forming of the sheet metal part; step four, determining a wrinkling area and a wrinkling reason; fifthly, optimizing the shape of the original plate and the structure of the die, and then carrying out analog simulation analysis; sixthly, repeating the third, fourth and fifth steps, and performing actual sheet metal part hot forming production after the simulation result meets the technical requirements of the product; seventhly, further optimizing the actual production result, and producing again; the method can predict and control the wrinkling of the large complex thin-wall hot-formed titanium alloy component, reduce the rejection rate, improve the production efficiency and reduce the production cost.
Description
Technical Field
The invention belongs to the field of basic non-cutting machining or treatment of metal plates, pipes, bars or profiles, relates to a metal plate hot sizing process, and particularly relates to a prediction and control method for hot forming wrinkling of a large complex thin-wall titanium alloy component.
Background
The titanium alloy has excellent properties of high specific strength, high temperature resistance, corrosion resistance and the like, so the titanium alloy is widely applied to the field of aerospace. However, the titanium alloy has poor plasticity at normal temperature, large deformation resistance and difficult cold forming of the plate; therefore, the hot press forming is the most common process method for manufacturing titanium alloy sheet metal parts, and particularly can manufacture large-scale sheet metal parts with high precision and complex structures.
However, in the hot press forming process of sheet metal parts, when the material is deformed under the action of the male die, part of the material is subjected to radial material supplementing, and part of the material is subjected to radial compressive stress, and at the moment, if the pressure of the die on the sheet material cannot effectively inhibit displacement caused by the compressive stress, the sheet material is wrinkled.
Although many researchers analyze wrinkling and establish a mechanical model of wrinkling instability, the wrinkle prediction and control is still a great problem in forming thin-wall components, and particularly in the process of hot forming of titanium alloy plates, the strength of materials is significantly influenced by factors such as the strain rate and the temperature of the materials, so that the wrinkling phenomenon of complex thin-wall titanium alloy parts is more difficult to predict and control.
Disclosure of Invention
The invention discloses a method for predicting and controlling hot forming wrinkling of a large complex thin-wall titanium alloy component.
The invention is realized by the following steps:
step one, establishing a titanium alloy thin-wall component hot-press forming wrinkling prediction theory;
step two, acquiring material mechanical parameters, obtaining a critical buckling stress function of wrinkling of a blank plate by combining a wrinkling prediction theory, and predicting an area which is possibly wrinkled in the plate forming process according to the actual plate forming process;
step three, establishing a finite element simulation model for the hot forming of the sheet metal part based on the material parameter model and the sheet metal mould digifax;
comparing the theoretical prediction area with the wrinkling area of the sheet metal part subjected to the simulated forming, and determining the wrinkling area and the wrinkling reason;
fifthly, optimizing the shape of the original plate and the structure of the die based on the transfer characteristics of the material, and then carrying out analog simulation analysis;
sixthly, repeating the third, fourth and fifth steps, and performing actual sheet metal part hot forming production after the simulation result meets the technical requirements of the product;
and seventhly, further optimizing the shape of the original plate and the structure of the die according to the actual production result, and producing again.
Further, the first step specifically comprises:
1.1, setting the plate to be subjected to in-plane compressive stress in one direction and to be subjected to in-plane tensile stress and blank holding force p under the action of common constraint force in the other direction, and loading the buckling plate and the intact plate through monotonous and proportionally increased boundary displacement u x Of the stress σ in the tensile direction z And compressive stress σ in the x direction x Proportional, i.e. sigma z /σ x = α, wherein the stress ratio α is assumed to be constant; assuming the case of neglecting shear stress, i.e. σ 3 /σ 1 ＝σ z /σ x = α, the following stress states are therefore described in terms of principal stress and strain; assuming that the buckling plate and the flat plate have the same strain increment delta epsilon in the third direction under the action of tension 3 ；
1.2, modeling the material as plane anisotropy, wherein the anisotropy is expressed by a parameter R, and the parameter is the ratio of width plastic strain on a sheet plane to thickness plastic strain in a simple tensile test; the equivalent stress and equivalent strain are as follows:
the strain hardening behaviour of a material is described by the formula of dove @:
wherein K is the material strength coefficient, n is the strain hardening exponent, ε 0 Is pre-strained;
for a flat panel, at a given edge displacement u x at/L, corresponding strain component
Can be expressed as:
we can get the strain increase Δ ∈ compared to the case without lateral tension, i.e. α =0 3 ：
The equivalent strain of the plate is obtained by substituting the formula:
wherein
Thus, the strain energy per unit width E on the plate under edge compression and lateral tension 0 Can be expressed as:
1.3 strain energy E per unit width of buckled plate, respectively w Can be obtained by the following method:
at a given edge displacement u x at/L, the deformed shape of the buckled plate can be assumed to be a sine wave:
y＝δ(1+cos(mx))
wherein m is the frequency in the corresponding mode;
based on the assumption of incompressibility of the material and no thickness variation, a volume per unit width of:
by simplified processing of the taylor expansion, we can obtain a projection amplitude of the modal shape as:
1.4 continuous element finite element analysis with simplified integration, displacement u without transverse tension z Is considered to be homogeneous and therefore the corresponding strain epsilon z Is constant at zero, under tension, assuming the same strain increase Δ ε on the bent sheet and on the flat sheet 3 For large deformations of the bending plate, the external strain ε z Radial strain epsilon r And circumferential strain ε θ Comprises the following steps:
ε z ＝Δε 3
ε θ ＝ln(r/r u )
ε r ＝-Δε 3 -ln(r/r u )
is generally considered to be 3 ＜＜ε θ The equivalent strain of the buckling plate can be simplified as follows:
wherein, the first and the second end of the pipe are connected with each other,
wherein r is the radius of curvature, r u Is the radius of curvature of the unstretched surface; let r i And r 0 Respectively representing the radii of curvature of the inner and outer surfaces of the curved plate; also, r can be obtained from the non-deformation of the volume u Comprises the following steps:
wherein
r 0 ＝r i +t
The unstretched sheet material is superposed with the middle surface of the bent sheet material under the assumption of no thickness change;
1.5, by using the theory of deformation, the strain energy E of the bending plate per unit width under the action of edge compression and transverse stretching is researched w Can be expressed as:
approximated by a taylor expansion as:
by calculating E 0 ，E W And δ, the critical buckling stress can be obtained as:
to find out
Are respectively connected with L 1 、L 2 The following relation is established:
therefore, we can quantitatively determine the displacement at the transfer edge
The following critical buckling stresses are:
it can be seen that the critical stress of wrinkling depends on the pressure to which the sheet is subjected, the stress state and the mechanical parameters of the material, namely:
σ cr ＝f(p,α,n,K,R,ε 0 )。
further, the second step is specifically as follows:
2.1, establishing a hardening model corresponding to the titanium alloy component;
2.2, establishing FLD strain forming limit failure criterion of the titanium alloy component;
2.3, establishing a critical buckling stress function of wrinkling of the titanium alloy blank plate;
and 2.4, predicting the area which is possible to wrinkle in the sheet forming process and improving the sheet wrinkling behavior according to the actual sheet forming process.
Further, the fourth step is specifically: obtaining a failure form of forming according to the forming result of the part; the degree of wrinkling is evaluated by comparing the shape of the deformed central symmetry axis of the plate with the shape of the digital model central line of the theoretical part, and the wrinkling area and the wrinkling reason are determined according to the wrinkling shape.
Further, the titanium alloy is a large-size complex TA32 titanium alloy skin piece.
Compared with the prior art, the invention has the beneficial effects that: the invention establishes a non-uniformly stressed sheet wrinkling instability mechanical model and a wrinkling prediction theory of hot-press forming, establishes a simulation model based on the theory, provides basis for guiding and optimizing the actual production in the early stage, and further predicts and controls wrinkling of a large complex thin-wall hot-formed titanium alloy component.
Drawings
FIG. 1 is a flow chart of a wrinkle prediction and control method for a large complex thin-walled hot-formed titanium alloy component;
FIG. 2 is a diagram of an appearance of a large-size complex skin part;
FIG. 3 is a schematic view of the plate material being pressed under the action of the blank holder;
FIG. 4 is a schematic view of a bent sheet;
FIG. 5 is a large-scale complex skin finite element model;
FIG. 6 is a simulation result of large-size skin forming;
FIG. 7 is a schematic view showing a modification of the mold structure;
FIG. 8 shows the simulation result of the mold after modification of the mold structure.
Detailed Description
In order to make the objects, technical solutions and effects of the present invention more clear, the present invention is further described in detail by the following examples. It should be noted that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method aims at hot forming of a large-size complex TA32 titanium alloy skin piece, and the part appearance digital model is shown in figure 2;
the wrinkle prediction and control method for large-size complex titanium alloy skin piece is described in detail below with reference to the accompanying drawings 1-8, wherein the flow chart of the method is shown in fig. 1, and the steps are as follows:
step one, establishing a titanium alloy thin-wall component hot-press forming wrinkling prediction theory;
step two, acquiring material mechanical parameters, obtaining a critical buckling stress function of wrinkling of a blank plate by combining a wrinkling prediction theory, and predicting an area which is likely to wrinkle in the plate forming process according to the actual plate forming process;
establishing a finite element simulation model for the hot forming of the sheet metal part based on the material mechanics parameter model and the sheet metal mold digital analogy;
comparing the area which is predicted by theory and is possible to wrinkle with the wrinkling area of the sheet metal part after the simulated forming, and determining the wrinkling area and the wrinkling reason;
fifthly, optimizing the shape of the original plate and the structure of the die based on the transfer characteristics of the material, and then carrying out analog simulation analysis;
sixthly, repeating the third, fourth and fifth steps, and performing actual sheet metal part hot forming production after the simulation result meets the technical requirements of the product;
and seventhly, further optimizing the shape of the original plate and the structure of the die according to the actual production result, and performing secondary production, which is specifically described as follows.
The problem of wrinkling areas on each material point during thermoforming can be reduced to analysis of rectangular sheet wrinkling as shown in figure 3. The sheet is subjected to in-plane compressive stress in one direction and edge pressing force p under the action of in-plane tensile stress and ordinary restraining force in the other direction. For the buckled and intact sheets in FIG. 3, the loading was by a monotonically and proportionally increasing boundary displacement u x Of the stress in the tensile direction σ z Proportional to compressive stress in the x-direction, i.e. sigma z /σ x = α, wherein the stress ratioAlpha is assumed to be constant. It is assumed that the normal stress is identical to the principal stress, i.e. σ, ignoring the shear stress 3 /σ 1 ＝σ z ,/σ x = α, so the following stress state is described in terms of principal stress and strain. The sheet is elongated to different degrees in all three directions under lateral tension as a result of boundary constraints in this direction. Assuming that the buckling plate and the flat plate have the same strain increment delta epsilon in the third direction under the action of tension 3 。
The material was modeled as a planar anisotropy, which is expressed as a parameter R. This parameter is the ratio of the width plastic strain at the plane of the sheet to the thickness plastic strain in a simple tensile test. The secondary yield criterion for Hill's 1948 standard anisotropic materials is used here. The equivalent stress and equivalent strain are as follows:
the strain hardening behaviour of a material is described by the svvitt formula:
wherein K is the material strength coefficient, n is the strain hardening exponent, ε 0 Is pre-strained.
For a plate, at a given edge displacement u x at/L, corresponding strain component
Can be expressed as:
we can get the strain increase Δ ∈ compared to the case without lateral tension, i.e. α =0 3 ：
The equivalent strain of the flat plate is obtained by substituting a formula
Wherein
Thus, the strain energy per unit width E on the plate under edge compression and lateral tension 0 Can be expressed as
Accordingly, strain energy E per unit width of the buckling plate w Can be obtained in the following manner. At a given edge displacement u x at/L, the deformed shape of the buckled plate can be assumed to be a sine wave:
y＝δ(1+cos(mx))
where m is the frequency in the corresponding mode.
Based on the assumption of incompressibility of the material and no thickness variation, a volume per unit width of:
by simplifying the processing of the Taylor expansion, we can obtain a projection amplitude of the modal shape
By adopting continuous unit finite element analysis of simplified integral, through observation of strain and stress output, the shearing stress and strain are ignored, and the normal stress and strain in the plane of the bending plate are ignored. These simplifications make the problem of buckling of the sheet a pure bending problem. In the absence of lateral tension, the displacement u z Is considered to be homogeneous and therefore the corresponding strain epsilon z Is constant at zero. Under tension, assume the same strain increase Δ ε in a bent sheet and in a flat sheet 3 . For large deformations of the bent plate, external strain ε z Radial strain epsilon r And circumferential strain ε θ Is composed of
ε z ＝Δε 3
ε θ ＝ln(r/r u )
ε r ＝-Δε 3 -ln(r/r u )
Is generally considered to be 3 ＜＜ε θ The equivalent strain of the buckling plate can be simplified to
Wherein, the first and the second end of the pipe are connected with each other,
wherein r is the radius of curvature, r u Is the radius of curvature of the unstretched surface, the curved sheet material is shown in figure 4. Let r i And r 0 Respectively, the radii of curvature of the inner and outer surfaces of the curved plate. Also, r can be obtained from the non-deformation of the volume u Is composed of
Wherein
r 0 ＝r i +t
The unstretched sheet material coincides with the middle surface of the curved sheet under the assumption of no thickness variation.
By utilizing the deformation theory, the strain energy E of the bending plate per unit width under the actions of edge compression and transverse stretching is researched w Can be expressed as
Approximated by Taylor expansion as
By calculating E 0 ，E w And δ, a critical buckling stress of
To find out
Are respectively connected with L 1 、L 2 The following relation is established:
thus, we can quantitatively determine the displacement at the transfer edge
A critical buckling stress below of ^ 5>
It can be seen that the critical stress of wrinkling depends on the pressure to which the sheet is subjected, the stress state and the mechanical parameters of the material, namely:
σ cr ＝f(p,α,n,K,R,ε 0 )
establishing a hardening model of the TA32 titanium alloy, wherein the yield function expression of the TA32 is as follows:
in which it is known that:
A＝A(ε)
n＝n(ε)
α＝α(ε)
therefore, in isothermal hot forming, the strain and strain rate are biased by:
establishing FLD strain forming limit failure criterion of the TA32 titanium alloy:
ε max ＝-0.0001536ε min 3 +0.00658ε min 2 +0.1031ε min +30.36
establishing a critical buckling stress function of wrinkling of a TA32 titanium alloy blank plate;
quantitatively determining displacement at transfer edge
Lower critical buckling stress of
Wherein R of the TA32 titanium alloy is about 0.8 at the hot forming temperature, and the relation between the value of the strain hardening exponent n and the temperature and the strain rate is as follows:
it can be known from theory that the critical buckling stress of the thin-wall part with a larger size is lower, and particularly in the hot forming process, the softening of the material is aggravated under the high-temperature condition, so that the critical buckling stress is further reduced. In the forming process, the periphery of the plate is not restrained, so that the materials around the part inevitably flow to the middle, a pressure-pressure stress state is easily formed near the central point, and the wrinkle degree is increased.
Aiming at the hot forming of a large-size complex TA32 titanium alloy skin piece, the wrinkling theory prediction result shows that the method changes sigma 3 /σ 1 ＝σ z /σ x And = α and increasing the pressure, i.e. changing the central area compressive-compressive stress state to a compressive-tensile stress state, can significantly improve the wrinkling behavior of the board, and thus remove wrinkles.
Compiling the material parameter constitutive model into a FORTRAN code based on the material parameter model and the plate mould digital-analog, and compiling by referring to the format of the VUHARD subprogram interface of ABAQUS, namely using the material parameter constitutive model in an Explicit solver of ABAQUS; inputting the elastic modulus of a material, a Poisson ratio, an FLC curve model, a critical buckling stress function and the like; dividing a grid, setting load, boundary conditions and the like to complete the establishment of a finite element simulation model of the thermal forming of the variable-curvature special-shaped thin-wall titanium alloy skin part, wherein the finite element model is shown in FIG. 5;
the part forming results are shown in fig. 6 (a), and are shown by stress cloud graphs, the part is mainly formed without obvious local plastic deformation, and the failure mode of the forming is mainly wrinkling instability. The degree of occurrence of the wrinkle is evaluated by comparing the shape of the deformed central symmetry axis of the plate with the shape of the digital-analog central line of the theoretical part, as shown in (b) in fig. 6, which shows that the wrinkle mainly originates from the junction of the areas I and II of the part, and then is uniformly diffused and distributed to the area II with less deformation, and the wrinkle extends rightwards like a wave shape. As the area I firstly contacts the punch of the die to force the plate to bend, the bending center pushes the inner side material to the junction central point of the areas I and II, so that the material is gathered at the junction point of the areas I and II, and the bifurcation point is firstly reached, and wrinkling and instability are easy to occur.
According to the wrinkle instability theory, the critical stress of the pressure-tension state is two times that of the pressure-pressure state, and the stability of the sheet material in the forming process can be improved by modifying the method of the die to restrict the boundary conditions, so that the wrinkle degree of instability is reduced. Therefore, the stress state of the plate at each point in the forming process can be changed by modifying the structure of the die, so that the wrinkling degree in the forming process is reduced. The schematic diagram of the modified mold structure is shown in fig. 7. The modification of the die structure is mainly in a circle area in the drawing, the die structure is changed into a sunken die structure, and meanwhile, the boundary size of a blank is increased. The forming simulation result after the die structure is modified is shown in fig. 8, and the sheet near the boundary and the die rub against each other due to the bending at the sheet boundary in the forming process, so that the material is limited from flowing to the central point. The modification measure is equivalent to the restriction of the plate boundary, and when the central point deforms, the boundary condition in the width direction is changed from free movement to displacement restriction. Therefore, the infinitesimal stress state is changed from pressure-pressure to pressure-tension when critical instability is caused near the central point, and the wrinkle defect after forming is improved. In general, simulation results show that varying the boundary conditions effectively suppresses the degree to which buckling occurs.
As a result of the primary forming, the central region of the formed part is wrinkled. Materials around the part inevitably flow to the center in the primary forming process, so that a pressure-pressure stress state is easily formed near the center point, and the wrinkle degree is increased. The forming result is basically consistent with the simulation prediction result. The result also shows that the corrugated grain wave crest is large, and the shape precision of the part is seriously influenced. After the process optimization, the wrinkling degree can be inhibited, the wrinkling area of the part becomes small, and the use requirement of the part is basically met.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications can be made without departing from the principle of the present invention, and these modifications should also be regarded as the protection scope of the present invention.
Claims (4)
1. A large complex thin-wall titanium alloy component hot forming wrinkling prediction and control method is characterized by comprising the following specific steps:
step one, establishing a titanium alloy thin-wall component hot-press forming wrinkling prediction theory; the first step is specifically as follows:
1.1, setting the compression stress in a plane on the plate in one direction, the tensile stress in the plane and the blank pressing force p under the action of common constraint force on the plate in the other direction, and loading a bent plate and a perfect plate through monotonous and proportionally increased boundary displacement u x Of the stress σ in the tensile direction z And compressive stress σ in the x direction x Proportional, i.e. sigma z /σ x = α, wherein the stress ratio α is constant; in the case of neglecting shear stress, i.e. σ 3 /σ 1 ＝σ z /σ x = α, and is therefore described below in terms of principal stress and strainStress state of the face; under the action of tension, the buckling plate and the flat plate have the same strain increment delta epsilon in the third direction 3 ；
1.2, modeling the material as plane anisotropy, wherein the anisotropy is expressed by a parameter R, and the parameter is the ratio of width plastic strain on a sheet plane to thickness plastic strain in a simple tensile test; the equivalent stress and equivalent strain are as follows:
the strain hardening behaviour of a material is described by the formula of dove @:
wherein K is the material strength coefficient, n is the strain hardening index, ε 0 Is pre-strained;
for a plate, at a given edge displacement u x at/L, corresponding strain component
Expressed as:
the strain increase Δ ∈ is obtained compared to the case without transverse tension, i.e. α =0 3 ：
The equivalent strain of the plate is obtained by substituting the formula:
wherein
Thus, the strain energy per unit width E on the plate under the action of the compression of the edge and the transverse tension 0 Expressed as:
1.3 strain energy E per unit width of buckled plate, respectively w Obtained by the following steps:
at a given edge displacement u x at/L, the deformed shape of the bent plate is a sine wave:
y＝δ(1+cos(mx))
wherein m is the frequency in the corresponding mode;
based on the incompressibility of the material and the absence of thickness variation, the volume per unit width is given by:
through the simplified processing of the taylor expansion, the projection amplitude of the obtained modal shape is:
1.4, continuous element finite element analysis with simplified integration, in the absence of transverse tension, displacement u z Is considered to be homogeneous and therefore the corresponding strain epsilon z Is constant at zero, has the same strain increment delta epsilon on a bent plate and a flat plate under the action of tension 3 For large deformations of the bending plate, the external strain ε z Radial strain epsilon r And circumferential strain ε θ Comprises the following steps:
ε z ＝Δε 3
ε θ ＝ln(r/r u )
ε r ＝-Δε 3 -ln(r/r u )
Δε 3 ＜＜ε θ and the equivalent strain of the buckling plate is simplified as follows:
wherein the content of the first and second substances,
wherein r is the radius of curvature, r u Is the radius of curvature of the unstretched surface; let r i And r 0 Respectively representing the radii of curvature of the inner and outer surfaces of the curved plate; also, from the absence of volume deformation, r is obtained u Comprises the following steps:
wherein
r 0 ＝r i +t
The unstretched sheet material is superposed with the middle surface of the bent sheet material under the condition of no thickness change;
1.5, using the theory of deformation, the strain energy E of the bent plate per unit width under the action of edge compression and transverse stretching is researched w Expressed as:
approximated by a taylor expansion as:
by calculating E 0 ，E w And δ, obtaining a critical buckling stress of:
to find out
Are respectively connected with L 1 、L 2 The following relation is established:
thus, it is quantitatively confirmedFixed on the transfer edge displacement
The following critical buckling stresses are:
it can be seen that the critical stress of wrinkling depends on the pressure to which the sheet is subjected, the stress state and the mechanical parameters of the material, namely:
σ cr ＝f(p，α，n，K，R，ε 0 )；
step two, acquiring material mechanical parameters, obtaining a critical buckling stress function of wrinkling of a blank plate by combining a wrinkling prediction theory, and predicting an area which is possibly wrinkled in the plate forming process according to the actual plate forming process;
step three, establishing a finite element simulation model for the hot forming of the sheet metal part based on the material mechanics parameter model and the sheet metal mould digifax;
comparing the area which is predicted by theory and is possible to wrinkle with the wrinkling area of the sheet metal part after the simulated forming, and determining the wrinkling area and the wrinkling reason;
fifthly, optimizing the shape of the original plate and the structure of the die based on the transfer characteristics of the material, and then carrying out analog simulation analysis;
sixthly, repeating the third, fourth and fifth steps, and performing actual sheet metal part hot forming production after the simulation result meets the technical requirements of the product;
and seventhly, further optimizing the shape of the original plate and the structure of the die aiming at the actual production result, and producing again.
2. The method for predicting and controlling hot forming wrinkling of large complex thin-wall titanium alloy components according to claim 1, wherein the second step is as follows:
2.1, establishing a hardening model corresponding to the titanium alloy component;
2.2 establishing FLD strain forming limit failure criterion of the titanium alloy component;
2.3, establishing a critical buckling stress function of wrinkling of the titanium alloy blank plate;
2.4, predicting the areas where the sheet forming process may wrinkle and improving the sheet wrinkling behavior according to the actual sheet forming process.
3. The method for predicting and controlling hot forming wrinkling of large complex thin-wall titanium alloy components according to claim 1, wherein the fourth step is as follows: obtaining a failure form of forming according to the forming result of the part; the degree of wrinkling is evaluated by comparing the shape of the deformed central symmetry axis of the plate with the shape of the digital model central line of the theoretical part, and the wrinkling area and the wrinkling reason are determined according to the wrinkling shape.
4. The method as claimed in claim 1, wherein the titanium alloy is a large-sized complex TA32 titanium alloy skin.
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