JP3945876B2 - Superplastic forming system and recording medium storing superplastic forming analysis program - Google Patents

Description

【００３７】
ここでｒ_１は、要素１４ｉの曲率半径であり、変形形態及び接触形状から幾何学的に決定される。すなわち、図３（ｂ）、図４（ａ）に示すように、成形初期であって、材料１４の全要素が非接触の状態では、前記曲率半径ｒ_１は、型の幅寸法ｂ及び成形される円筒面の中心角α_１により、次式で表される。
【００３８】
【数２】

【００３９】
また、要素１４ｉｊに生じる円周方向応力をσ_θｉｊとし、板厚をｔ_ｉｊとすると、前記円周方向力Ｆ_ｉｊは、次式のように表される。
【００４０】
【数３】

【００４１】
ここで、σ_θｉｊは平面ひずみの定義から相当応力σ_ｅｑｉｊにより次のように表される。
【００４２】
【数４】

【００４３】
要素１４ｉｊの板厚ｔ_ｉｊは、板厚方向のひずみ速度ｖ_εｔｉｊの時間積分で表され、
【数５】

【００４４】
ただし、相当ひずみ速度ｖ_{εｅｑｉｊ}と板厚方向ひずみ速度ｖ_εｔｉｊの関係は、平面ひずみの定義より、
【数６】

【００４５】
とする。
【００４６】
次に接触部１４ｂについての考え方を図４（ｂ）を参照して説明する。
【００４７】
材料１４の一部に、この図に示すような接触部１４ｂが生じると、この接触部１４ｂの各要素は成形圧力Ｐにより成形面１３ａに押し付けられ、摩擦力を受ける。従って、この接触部１４ｂと非接触部１４ａとのつりあいから、円周方向力Ｆは次のように表される。
【００４８】
【数７】

【００４９】
ここで、μは摩擦係数である。またＬ_ｉｊは、接触部１３ｂと非接触部１３ａとの境界点から、解析する接触要素１４ｉまでの距離である。接触部１３ｂでは、成形圧力Ｐによる板厚方向応力σ_ｔｉｊが相当応力の因子として影響してくるため、σ_θｉｊは次のように表される。
【００５０】
【数８】

【００５１】
ただし、仮定からσ_ｔｉｊは下記のようになる。
【００５２】
【数９】

【００５３】
また、ひずみの関係については式（５）、（６）と同じである。
【００５４】
したがって、この適正成形圧力算出部４は、材料１４が型１３に接触するまでは式（１）〜（６）に基づいて計算を行い、材料１４の一部に接触部１４ｂが生じた後は前記式（７）〜（９）を加味して、非接触部１４ａと接触部１４ｂの内部応力及びひずみを各要素毎に求めるようにする。
【００５５】
（ひずみ速度の算出（ステップＳ４））
次に、ひずみ速度の算出について説明する。
【００５６】
まず、前述したようにステップＳ１で仮に与えられた圧力Ｐを用いて、各要素１４ｉｊに生じる内部応力σ_θｉｊ及びひずみε_ｉｊを求める。そして、前記応力−ひずみ関係格納部１０から、当該材料１４に応じた応力−ひずみ関係を取り出し、これに前記内部応力及びひずみを適用してひずみ速度を求める。
【００５７】
この応力−ひずみ関係は、予め当該材料１４について引っ張り試験を行うことにより図５（ａ）、（ｂ）に示すようにして求めたものである。
【００５８】
まず、当該材料１４の引っ張り試験を行い、図５（ａ）に実線で示すように超塑性変形に最も適したひずみ速度（ｖ_ε＝２・１０^−４／ｓｅｃ）となるような応力−ひずみ線図を求める。そして、この線図の直線部を延長して応力０を示す横軸との交点Ｇを求める。このことで、図５（ｂ）に１６で示すような基準応力−ひずみ線（傾き＝ｖ_ε＝２・１０^−４／ｓｅｃ）を得る。
【００５９】
そして、この基準線１６を基準として、異なるひずみ速度を求める。
【００６０】
例えば、ある要素１４ｉｊの内部応力σ_θｉｊ及びひずみε_ｉｊを、図５（ｂ）に示す応力−ひずみ線図上にプロットしたところ点Ｈであったとする。この場合、この点Ｈと頂点Ｇとを結ぶ直線１７を求め、前記基準線１６の傾きに対するこの直線１７の傾きの内分比から、前記直線１７が示すひずみ速度ｖ_εを求めるようにする。
【００６１】
このような応力−ひずみ関係を用いることで、一点（例えば点Ｈ）のみを与えることで、ひずみ速度を求めることが可能になる。
【００６２】
そして、適正成形圧力算出部４は、このようにして得られたひずみ速度が最適のひずみ速度ｖ_ε＝２・１０^−４／ｓｅｃでない場合、前記ステップＳ５、Ｓ６において、与える圧力を変更して当該最適のひずみ速度を得られるようにする。
【００６３】
ついで、この適正成形圧力算出部４は、前記ひずみ速度及び前記時間カウンタにより得られた経過時間から、その間に生じた要素毎のひずみ量を求め、前記変形解析部５に出力するようにする。
【００６４】
（変形解析（ステップＳ７〜Ｓ１０））
次に、変形解析部５における変形解析について説明する。
【００６５】
この変形解析部５は、ステップＳ７において、変形後の各要素の長さを算出する。すなわち、各要素の変形前の長さに、前記適正成形圧力算出部４から受け取ったひずみ量を加算することで、荷重Ｐによって変形された各要素の変形後の長さを求める。そして、各要素の変形後の長さを材料１４の全長に亘って積算することで変形後の材料全体長を求める。ついで、この変形解析部５は、ステップＳ８において、前記材料全体長に基づき材料１４の変形後の形状を求めるようにする。
【００６６】
具体的には、例えば、図６（ａ）、（ｂ）に示すようにして求める。すなわち、まず、図６に点線で示すように、材料１４全体が型１３の成形面１３ａと接触していないもの（非接触）として変形後の材料形状を求める。この実施形態では、非接触状態においては前記材料１４は一定の曲率をもって変形すると仮定しているから、全長が求まれば変形後の形状を求めることができる。
【００６７】
このようにして求めた材料１４の形状が、型１３の成形面１３ａと干渉していなければ、未だ非接触であるとして、この形状を変形後の材料形状として確定する。
【００６８】
しかしながら、図６（ａ）に示すように、型１３と非接触であるとして求めた材料１４の形状が型１３の成形面１３ａと干渉している場合には、図６（ｂ）に示すようにして材料１４の形状を補正する。なお、非接触部１４ａは、前述したように一定の曲率半径を有するものとする。このような補正は幾何学的に行う。
【００６９】
このようにして、ステップＳ７で求めた各要素の変形量に基づき、ステップＳ８で型１３の形状を考慮した材料１４の変形後の形状を求めるようにする。
【００７０】
また、ステップＳ９において、この変形解析部５は、前記形状に基づき、前記材料１４の各要素のうち、接触・非接触の各要素１４ａ、１４ｂを特定する。そして、これに基づき、ステップＳ１０において成形が終了したかを判断する。すなわち、前記材料１４の各要素のすべて若しくは略すべてが型１３と接触する場合には、材料１４の成形が終了したものと判断し、そうでない場合には、成形が終了していないものと判断する。
【００７１】
成形が終了していない場合には、再度適正成形圧力算出工程（Ｓ１〜Ｓ６）及び変形解析工程（Ｓ７〜Ｓ１０）を再度行い成形を続行する。すなわち、前記適正成形圧力算出部４は、前記変形解析部５から各要素の接触・非接触の情報を受け取り、適宜前記つりあい式（７）を用いてひずみ及び内部応力を求める。そして、最大のひずみ速度が適正ひずみ速度（ｖ_ε＝２・１０^−４／ｓｅｃ）となるような圧力を求めるようにする。
【００７２】
このような構成によれば、ステップＳ１〜Ｓ１０を繰り返すことで、材料１４と型１３との接触を考慮し、成形圧力を所望のひずみ速度が得られるような適正な値に調整しつつ超塑性成形を行うことができる。
【００７３】
（発明の効果）
以上述べたような構成によれば、以下の効果を得ることができる。
【００７４】
第１に、型１３と材料１４との接触を考慮して正確な応力−ひずみ関係を求め、これに基づいて適正な圧力を求めることができるから、良好な超塑性加工を行うことができる。
【００７５】
すなわち、超塑性材料の応力−ひずみ関係は、一般に、ひずみ速度感受性指数ｍにより
【数１０】

【００７６】
と表され、変形の解析に多く用いられている。しかし実際には、ひずみの大きさに対してｍ値が大きく変化することが知られており、また、ひずみ応じて加工硬化も進むため、式（１０）のみでは正確な応力−ひずみ関係を表すことができない。
【００７７】
そこで、この発明では、内部応力σ、ひずみε及びひずみ速度ｖ_εが、応力−ひずみ関係に関して各要素毎に個別に定義されるとする。すなわち、要素１４ｉの時間ｊでの内部応力（変形抵抗）σ_ｉｊが、ひずみε_ｉｊ及びひずみ速度ｖ_εｉｊの関数として表されるとし、
【数１１】

【００７８】
とする。この関係を示したのが図５（ｂ）に示した応力−ひずみ線図である。
【００７９】
応力−ひずみ関係をこのように定義し、かつ、接触部１４ｂと非接触部１４ａとのつりあいを考慮し演算を実行することによって、正確な応力−ひずみ関係を求め、これに基づいて適正な成形圧力を求めることができるから、良好な超塑性加工を行うことができる。
【００８０】
第２に、この発明によれば、要素毎のひずみ速度を求める場合、一対の内部応力とひずみとを求めるだけで、対応するひずみ速度を演算することができる。このことで、ひずみ速度の演算を迅速に行うことができ、より正確な処理を行える効果がある。
【００８１】
なお、この発明は、前記一実施形態に限定されるものではなく、発明の要旨を変更しない範囲で種々変形可能である。
【００８２】
たとえば、前記一実施形態で用いた応力−ひずみ線図は、図５（ｂ）に示すように直線であったが、曲線であっても良い。曲線であっても同様の手法でひずみ速度を決定するようにすれば良い。
【００８３】
また、前記一実施形態においては、この発明は「システム」として構成されていたが、汎用コンピュータシステムにこの一実施形態と同様の処理を行わせるためのプログラム（プログラムが格納された記憶媒体）として提供することも可能である。
【００８４】
【発明の効果】
第１に、型１３と材料１４との接触を考慮して正確な応力−ひずみ関係を求め、これに基づいて適正な圧力を求めることができるから、良好な超塑性加工を行うことができる。
【００８５】
第２に、この発明によれば、要素毎のひずみ速度を求める場合、一対の内部応力とひずみとを求めるだけで、対応するひずみ速度を演算することができる。このことで、ひずみ速度の演算を迅速に行うことができ、より正確な処理を行える効果がある。
【図面の簡単な説明】
【図１】この発明の一実施形態を示す概略構成図。
【図２】同じく、処理工程を示すフローチャート。
【図３】同じく、型と材料の関係を示すための説明図。
【図４】同じく、材料の変形を拡大して示す説明図。
【図５】同じく、応力−ひずみ関係を示すチャート。
【図６】同じく、変形後の材料形状の算出方法を説明するための説明図。
【符号の説明】
４…適正成形圧力算出部、５…変形解析部、９…超塑性材料情報格納部、１０…応力−ひずみ関係格納部、１１…型情報格納部、１３…型、１３ａ…成形面、１４…材料、１４ａ…非接触部、１４ｂ…接触部、１６…基準線（応力−ひずみ線図）[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a superplastic forming system suitable for analyzing a deformation of a material in superplastic forming and calculating a forming pressure for obtaining an appropriate superplastic deformation, and a storage medium storing a program used for the system. It is.
[0002]
[Prior art]
In the field of component processing, “superplastic forming” has recently attracted attention. Superplastic forming is capable of obtaining significantly larger plastic deformation than normal plastic deformation by continuously deforming a superplastically deformable material (hereinafter referred to as “superplastically deformable material”) at an appropriate strain rate. This is a material molding method focusing on the above. For example, a superplastic deformable material can be deformed into a desired shape by being superplastically deformed by applying a load to the mold with a high-pressure gas or the like and closely contacting the mold.
[0003]
In such superplastic forming, a complicated shape can be integrally formed with a thin material. Since the assembly work can be omitted, the number of processing steps can be reduced, the cost of jigs and tools and other costs can be reduced, and the weight of the structure can be reduced by integral molding. For this reason, it is attracting attention and being adopted especially in the field of aircraft parts molding.
[0004]
[Problems to be solved by the invention]
By the way, in order to obtain the superplastic deformation, as described above, it is necessary to control the molding load and maintain the appropriate strain rate so that the superplasticity appears. If the proper strain rate cannot be maintained, there will be defects inside the molding material and the risk of significantly degrading the material properties after molding. Furthermore, there may be a case where the material breaks during molding and the product cannot be obtained.
[0005]
Therefore, the control of the strain rate is the key to whether good superplastic forming can be performed. Also, in product design, accurately predicting the thickness distribution after forming is an important key in applying superplastic forming.
[0006]
In the conventional technique, a load that can obtain an appropriate strain rate for each material is obtained by experiment or the like, and the load applied to the material on the assumption that the same strain rate can be obtained with the same load throughout the entire process. Generally, a method of controlling the above is adopted.
[0007]
However, the strain rate of the material varies depending on various conditions. A particularly significant factor is the contact between the material and the mold. When the material begins to come into contact with the mold, the strain of the material is regulated by the frictional force generated therebetween, and the strain rate fluctuates.
[0008]
The present invention has been made in view of such circumstances, and an object of the present invention is to provide a superplastic forming system capable of controlling the strain rate more accurately and obtaining good superplastic forming. It is.
[0009]
[Means for Solving the Problems]
In order to solve the above-described problems, the means of the present invention is a superplastic forming system for determining a forming pressure of a superplastic material, and is deformed based on a strain history of the material and a shape of a mold for forming the material. Based on the deformation analysis means for determining the later material shape and determining the non-contact element and the contact element for the mold among the elements constituting the material, and the balance of the material component including the non-contact element and the contact element, each element And a proper molding pressure calculating means for obtaining a molding pressure so that the maximum strain rate is suitable for a strain rate suitable for superplastic deformation.
[0010]
The appropriate molding pressure calculation means includes strain rate calculation means for specifying the strain rate of each element based on a reference curve that defines a stress-strain relationship for a predetermined strain rate. It is preferable that the strain rate of each element is obtained using the stress-strain relationship of each element obtained based on the balance of the material constituent elements including the non-contact element and the contact element.
[0011]
In addition, this system preferably includes a superplastic forming device that performs superplastic forming, and preferably forms a final product while controlling the forming pressure in real time.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the drawings.
[0013]
(Configuration of the embodiment)
FIG. 1 is a block diagram showing a schematic configuration of the present invention, and FIG. 2 is a flowchart showing its processing steps.
[0014]
As shown in FIG. 2, the processing process of this invention is roughly divided into an appropriate molding pressure calculation process (steps S1 to S6) and a deformation analysis process (steps S7 to S10).
[0015]
In this embodiment, the molding material is handled by being divided into fine elements. First, in the appropriate molding pressure calculation step (steps S1 to S6), the strain and internal stress are obtained based on the shape of the material, thereby calculating a molding pressure that can obtain a strain rate suitable for superplastic molding. .
[0016]
On the other hand, in the deformation analysis step (steps S7 to S10), the deformed material shape is obtained based on the strain obtained in the appropriate molding pressure calculation step. Since the contact between the material and the mold affects the subsequent strain rate of the material, in this process, the element that is in contact with the mold (contact part) and the element that is not in contact (non-contact part) are determined. To do.
[0017]
Then, while repeating the appropriate molding pressure calculation step (steps S1 to S6) and the deformation analysis step (steps S7 to S10), a strain rate corresponding to the shape of the material is obtained, and the material is maintained while maintaining an appropriate strain rate. Try to deform.
[0018]
In such superplastic forming, management of the strain rate is very important, and this strain rate is greatly influenced by the contact between the mold and the material. The present invention is characterized in that a load capable of obtaining an appropriate strain rate is obtained based on the contact between the material and the mold.
[0019]
In order to perform such a function, the system of this embodiment is configured as shown in FIG.
[0020]
That is, in this system, a processing unit 6 having an appropriate pressure calculation unit 4 and a deformation analysis unit 5 and a data storage unit 7 for storing data necessary for processing are stored in a bus 3 to which a RAM 1 and an input / output device 2 are connected. Is connected. The data storage unit 7 stores a main program storage unit 8 for storing a main program, a superplastic material information storage unit 9 for storing various information of a superplastic material to be analyzed, and a stress-strain relationship for each material. A stress-strain relationship storage unit 10 and a mold information storage unit 11 for storing the shape of the mold are provided.
[0021]
This system is connected to a superplastic forming / forming apparatus indicated by 12 in the figure. This superplastic forming / forming apparatus actually performs superplastic forming of a material based on the forming pressure output from the input / output unit.
[0022]
(Molding condition)
Hereinafter, the configuration of this system will be described in detail along with its processing steps.
[0023]
First, in this embodiment, a case where the material 14 is molded using a mold 13 having a rectangular cross section as shown in FIG. 3A will be described as an example. That is, by applying a uniform molding pressure (gas pressure or the like) as indicated by an arrow (P) in the figure from above the material 14, as shown in FIGS. The deformation of the material 14 is advanced along the molding surface 13a.
[0024]
In this embodiment, the material characteristics and the deformation characteristics are based on the following assumptions.
[0025]
The portion of the material 14 that is not in contact with the mold 13 (the non-contact portion 14a shown in FIGS. 3B and 3C) is deformed in accordance with the film theory, and an arc as shown in FIGS. 3B and 3C Deformation proceeds while maintaining the shape.
[0026]
-The volume of the material 14 is unchanged before and after molding.
[0027]
As shown in FIG. 3 (c), a contact portion 14b with the mold 13 is generated in the molding process, and the contact portion 14b is pressed against the molding surface 13a of the mold 13 by the molding pressure P. Deforms while being affected by Coulomb friction.
[0028]
As described above, the material 14 is a continuum of a large number of elements 14i (i is an integer).
[0029]
Each element 14i has an individual stress-strain relationship, and represents independent strain, internal stress, and strain rate (hereinafter, strain is represented by ε, the corresponding strain rate is represented by v _ε , and the internal stress is represented by σ). Have.
[0030]
Individual material information, for example, the type and thickness of the material 14, and the friction coefficient μ with the mold 13 are stored in the superplastic material information storage unit 9, and information on the mold 13, that is, the shape of the mold 13, etc. Is stored in the type information storage unit 11.
[0031]
(processing)
First, the appropriate molding pressure calculation unit 4 activates the time counter in step S1 shown in FIG. 2, and then gives a temporary molding pressure to the material (step S2). And this appropriate forming pressure calculation part 4 calculates the internal stress and distortion which arise in the material 14 with this temporary pressure for every element (step S3). In step S4, the internal stress and strain are applied to the stress-strain relationship stored in the stress-strain relationship storage unit 10 to determine the strain rate for each element. In step S5, it is determined whether the maximum strain rate among the strain rates of each element is the optimal strain rate for superplastic deformation.
[0032]
If the strain rate is not optimum, a pressure at which the optimum strain rate can be obtained is calculated in step S6, and the steps S2 to S5 are repeated using this as the molding pressure P, and finally applied to the material. An appropriate pressure is obtained and output to the superplastic forming / forming apparatus 12.
[0033]
Further, strain information of each element obtained in the above process is output to the deformation analysis unit 5 (deformation analysis process).
[0034]
(Calculation of internal stress and strain (step S3))
Incidentally, as shown in FIGS. 3A and 3B, when the material 14 is not in contact with the molding surface 13a of the mold 13, the internal stress and strain are constant throughout. However, as shown in FIG. 3C, when a part of the material 14 comes into contact with the molding surface 13a of the mold 13 and the contact portion 14b is generated, deformation is regulated by friction with the molding surface 13a. The internal stress and strain for each element vary.
[0035]
That is, the non-contact portion 14a is first the assumption of plane strain theory and film theory, as shown in FIG. 4 (a), the circumferential force _{F ij} element in the count time j 14i (14ij) are forming pressure Balance with P. And this circumferential direction force _Fij is represented by following Formula (1) from geometric relationship.
[0036]
[Expression 1]

[0037]
Here, r ₁ is the radius of curvature of the element 14i, and is geometrically determined from the deformation form and the contact shape. That is, FIG. 3 (b), the as shown in FIG. 4 (a), a molded early in all elements of the non-contact state of the material 14, the radius of curvature r _1, the type width b and shaping of the central angle alpha ₁ of the cylindrical surface that is expressed by the following equation.
[0038]
[Expression 2]

[0039]
Further, when the circumferential stress generated in the element 14ij is σ _θij and the plate thickness is t _ij , the circumferential force F _ij is expressed by the following equation.
[0040]
[Equation 3]

[0041]
Here, σ _θij is expressed by the equivalent stress σ _eqij as follows from the definition of plane strain.
[0042]
[Expression 4]

[0043]
The plate thickness t _{ij of the} element 14ij is expressed by time integration of the strain rate v _{εtij in} the plate thickness direction,
[Equation 5]

[0044]
However, the relationship between the equivalent strain rate v _εeqij and the plate thickness direction strain rate v _εtij is as follows:
[Formula 6]

[0045]
And
[0046]
Next, the concept about the contact part 14b is demonstrated with reference to FIG.4 (b).
[0047]
When a contact portion 14b as shown in this figure is generated in a part of the material 14, each element of the contact portion 14b is pressed against the molding surface 13a by the molding pressure P and receives a frictional force. Therefore, from the balance between the contact portion 14b and the non-contact portion 14a, the circumferential force F is expressed as follows.
[0048]
[Expression 7]

[0049]
Here, μ is a friction coefficient. L _ij is a distance from the boundary point between the contact portion 13b and the non-contact portion 13a to the contact element 14i to be analyzed. The contact portion 13b, to come to influence as a factor in the thickness direction stress sigma _tij considerable stress due to the molding pressure P, _{sigma? Ij} is expressed as follows.
[0050]
[Equation 8]

[0051]
However, from the assumption, σ _tij is as follows.
[0052]
[Equation 9]

[0053]
Further, the relationship between strains is the same as in equations (5) and (6).
[0054]
Therefore, the appropriate molding pressure calculation unit 4 performs calculations based on the formulas (1) to (6) until the material 14 contacts the mold 13, and after the contact portion 14 b is generated in a part of the material 14. In consideration of the above formulas (7) to (9), the internal stress and strain of the non-contact part 14a and the contact part 14b are obtained for each element.
[0055]
(Calculation of strain rate (step S4))
Next, calculation of strain rate will be described.
[0056]
First, as described above, the internal stress σ _θij and the strain ε _ij generated in each element 14ij are obtained using the pressure P provisionally given in step S1. And the stress-strain relationship according to the said material 14 is taken out from the said stress-strain relationship storage part 10, The said internal stress and distortion are applied to this, and a strain rate is calculated | required.
[0057]
This stress-strain relationship is obtained as shown in FIGS. 5A and 5B by conducting a tensile test on the material 14 in advance.
[0058]
First, a tensile test of the material 14 is performed, and a stress-strain that provides a strain rate (v _ε = 2 · 10 ⁻⁴ / sec) most suitable for superplastic deformation as indicated by a solid line in FIG. Obtain a diagram. And the intersection G with the horizontal axis which shows the stress 0 is calculated | required by extending the linear part of this diagram. As a result, a reference stress-strain line (slope = v _ε = 2 · 10 ⁻⁴ / sec) as indicated by 16 in FIG. 5B is obtained.
[0059]
Then, different strain rates are obtained using the reference line 16 as a reference.
[0060]
For example, when the internal stress σ _θij and strain ε _ij of a certain element 14 _ij are plotted on the stress-strain diagram shown in FIG. In this case, a straight line 17 connecting the point H and the vertex G is obtained, and the strain rate v _ε indicated by the straight line 17 is obtained from the internal ratio of the inclination of the straight line 17 with respect to the inclination of the reference line 16.
[0061]
By using such a stress-strain relationship, it is possible to obtain the strain rate by giving only one point (for example, point H).
[0062]
When the strain rate obtained in this way is not the optimum strain rate v _ε = 2 · 10 ⁻⁴ / sec, the appropriate molding pressure calculation unit 4 changes the pressure to be applied in steps S5 and S6. The optimum strain rate can be obtained.
[0063]
Next, the appropriate molding pressure calculation unit 4 obtains the strain amount for each element generated during the interval from the strain rate and the elapsed time obtained by the time counter, and outputs it to the deformation analysis unit 5.
[0064]
(Deformation analysis (steps S7 to S10))
Next, deformation analysis in the deformation analysis unit 5 will be described.
[0065]
In step S7, the deformation analysis unit 5 calculates the length of each element after deformation. That is, the length after deformation of each element deformed by the load P is obtained by adding the strain amount received from the appropriate molding pressure calculation unit 4 to the length before deformation of each element. Then, the total length of the deformed material is obtained by integrating the length of each element after the deformation over the entire length of the material 14. Next, in step S8, the deformation analysis unit 5 obtains the deformed shape of the material 14 based on the overall length of the material.
[0066]
Specifically, for example, it is obtained as shown in FIGS. 6 (a) and 6 (b). That is, first, as shown by a dotted line in FIG. 6, the deformed material shape is obtained assuming that the entire material 14 is not in contact with the molding surface 13 a of the mold 13 (non-contact). In this embodiment, since it is assumed that the material 14 is deformed with a certain curvature in the non-contact state, the deformed shape can be obtained if the total length is obtained.
[0067]
If the shape of the material 14 thus obtained does not interfere with the molding surface 13a of the mold 13, it is determined that the shape is still non-contact, and this shape is determined as the deformed material shape.
[0068]
However, as shown in FIG. 6A, when the shape of the material 14 determined to be non-contact with the mold 13 interferes with the molding surface 13a of the mold 13, as shown in FIG. Thus, the shape of the material 14 is corrected. In addition, the non-contact part 14a shall have a fixed curvature radius as mentioned above. Such correction is performed geometrically.
[0069]
In this manner, the deformed shape of the material 14 in consideration of the shape of the mold 13 is obtained in step S8 based on the deformation amount of each element obtained in step S7.
[0070]
In step S <b> 9, the deformation analysis unit 5 identifies contact / non-contact elements 14 a and 14 b among the elements of the material 14 based on the shape. And based on this, it is judged whether shaping | molding was complete | finished in step S10. That is, when all or almost all of the elements of the material 14 are in contact with the mold 13, it is determined that the molding of the material 14 has been completed. Otherwise, it is determined that the molding has not been completed. To do.
[0071]
If molding has not been completed, the proper molding pressure calculation process (S1 to S6) and the deformation analysis process (S7 to S10) are performed again to continue molding. That is, the appropriate molding pressure calculation unit 4 receives contact / non-contact information of each element from the deformation analysis unit 5, and appropriately obtains strain and internal stress using the balance equation (7). Then, the pressure is determined so that the maximum strain rate is an appropriate strain rate (v _ε = 2 · 10 ⁻⁴ / sec).
[0072]
According to such a configuration, by repeating steps S1 to S10, the plasticity is adjusted while considering the contact between the material 14 and the mold 13 and adjusting the molding pressure to an appropriate value so that a desired strain rate can be obtained. Molding can be performed.
[0073]
(The invention's effect)
According to the configuration described above, the following effects can be obtained.
[0074]
First, since an accurate stress-strain relationship can be obtained in consideration of the contact between the mold 13 and the material 14, and an appropriate pressure can be obtained based on this relationship, good superplastic working can be performed.
[0075]
That is, the stress-strain relationship of a superplastic material is generally expressed by the strain rate sensitivity index m

[0076]
It is often used for analysis of deformation. However, in practice, it is known that the m value changes greatly with respect to the magnitude of the strain, and work hardening also proceeds in accordance with the strain. Therefore, only the equation (10) represents an accurate stress-strain relationship. I can't.
[0077]
Therefore, in the present invention, it is assumed that the internal stress σ, strain ε, and strain rate v _{ε are} individually defined for each element with respect to _the stress-strain relationship. That is, the internal stress (deformation resistance) σ _ij at time j of the element 14 i is expressed as a function of the strain ε _ij and the strain rate v _εij .
[Expression 11]

[0078]
And This relationship is shown in the stress-strain diagram shown in FIG.
[0079]
The stress-strain relationship is defined as described above, and an accurate stress-strain relationship is obtained by executing an operation in consideration of the balance between the contact portion 14b and the non-contact portion 14a, and an appropriate molding is performed based on this. Since the pressure can be obtained, good superplastic working can be performed.
[0080]
Secondly, according to the present invention, when the strain rate for each element is obtained, the corresponding strain rate can be calculated only by obtaining a pair of internal stress and strain. As a result, the strain rate can be calculated quickly, and there is an effect that more accurate processing can be performed.
[0081]
In addition, this invention is not limited to the said one Embodiment, A various deformation | transformation is possible in the range which does not change the summary of invention.
[0082]
For example, the stress-strain diagram used in the embodiment is a straight line as shown in FIG. 5B, but may be a curved line. Even if it is a curve, the strain rate may be determined by the same method.
[0083]
In the above-described embodiment, the present invention is configured as a “system”. However, as a program (storage medium storing the program) for causing a general-purpose computer system to perform the same processing as in this embodiment. It is also possible to provide.
[0084]
【The invention's effect】
First, since an accurate stress-strain relationship can be obtained in consideration of the contact between the mold 13 and the material 14, and an appropriate pressure can be obtained based on this relationship, good superplastic working can be performed.
[0085]
Secondly, according to the present invention, when the strain rate for each element is obtained, the corresponding strain rate can be calculated only by obtaining a pair of internal stress and strain. As a result, the strain rate can be calculated quickly, and there is an effect that more accurate processing can be performed.
[Brief description of the drawings]
FIG. 1 is a schematic configuration diagram showing an embodiment of the present invention.
FIG. 2 is a flowchart showing processing steps in the same manner.
FIG. 3 is also an explanatory diagram for showing a relationship between a mold and a material.
FIG. 4 is an explanatory view showing the deformation of the material in an enlarged manner.
FIG. 5 is a chart similarly showing a stress-strain relationship.
FIG. 6 is also an explanatory diagram for explaining a method for calculating a material shape after deformation.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 4 ... Appropriate molding pressure calculation part, 5 ... Deformation analysis part, 9 ... Superplastic material information storage part, 10 ... Stress-strain relation storage part, 11 ... Mold information storage part, 13 ... Mold, 13a ... Molding surface, 14 ... Material, 14a ... non-contact portion, 14b ... contact portion, 16 ... reference line (stress-strain diagram)

Claims (4)

A superplastic forming system for determining a forming pressure of a superplastic material,
Deformation analysis means for obtaining a material shape after deformation based on a material strain history and a shape of a mold for molding the material, and determining a non-contact element and a contact element for the mold among elements constituting the material;
Determine the strain rate of each element based on the balance between the non-contact element and the material component including the contact element, and determine the molding pressure so that the maximum strain rate matches the strain rate suitable for superplastic deformation. A superplastic forming system comprising: a forming pressure calculating means. The superplastic forming system according to claim 1,
The appropriate molding pressure calculating means includes
Having strain rate calculation means for specifying the strain rate of each element based on a reference curve defining a stress-strain relationship for a predetermined strain rate,
The strain rate calculation means obtains the strain rate of each element using the stress-strain relationship of each element obtained based on the balance of the material constituent elements including the non-contact element and the contact element. Plastic forming system. A recording medium storing a superplastic forming analysis program for causing a computer system to determine a forming pressure of a superplastic material,
The program is
Let the computer system determine the material shape after deformation based on the strain history of the material and the shape of the mold for molding this material, and determine non-contact elements and contact elements for the mold among the elements constituting the material Deformation analysis means,
Let the computer system determine the strain rate of each element based on the balance of the material components including the non-contact element and the contact element so that the maximum strain rate matches the strain rate suitable for superplastic deformation. A recording medium storing a superplastic forming analysis program characterized by having an appropriate forming pressure calculation means for determining a forming pressure. In the recording medium storing the superplastic forming program according to claim 3,
The appropriate molding pressure calculating means includes
The computer system has strain rate calculation means for specifying the strain rate of each element based on a reference curve that defines a stress-strain relationship for a predetermined strain rate,
The strain rate calculation means causes the computer system to determine the strain rate of each element using the stress-strain relationship of each element determined based on the balance of the material components including the non-contact element and the contact element. The recording medium which stored the superplastic forming program characterized by the above-mentioned.

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