JPH06288884A - Measuring method of deformation resistance of material - Google Patents
Measuring method of deformation resistance of materialInfo
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- JPH06288884A JPH06288884A JP22219292A JP22219292A JPH06288884A JP H06288884 A JPH06288884 A JP H06288884A JP 22219292 A JP22219292 A JP 22219292A JP 22219292 A JP22219292 A JP 22219292A JP H06288884 A JPH06288884 A JP H06288884A
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- Prior art keywords
- deformation resistance
- deformation
- value
- finite element
- unknown
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- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
Description
【０００１】[0001]
【産業上の利用分野】圧延、鍛造、押出し、深絞り、張
出し、などの塑性加工プロセスを使って金属をはじめと
する各種の材料に変形加工を与えて所望の形状を得る方
法において、その加工に必要な加工力を見積ったり、材
料の変形の挙動を予測したり、加工工程や金型の設計を
したりする上で、被加工材料の変形抵抗（応力ひずみ曲
線、加工硬化曲線、とも呼ばれている）は基本的なデー
タとして不可欠である。本発明はその変形抵抗を測定す
る方法に関するものである。[Industrial application] In the method of deforming various materials including metal using plastic working processes such as rolling, forging, extruding, deep drawing, bulging to obtain the desired shape Deformation stress (stress strain curve, work hardening curve, etc.) of the material to be processed in estimating the processing force required for the process, predicting the deformation behavior of the material, and designing the processing process and mold. Are included as basic data. The present invention relates to a method for measuring the deformation resistance.
【０００２】[0002]
【従来の技術】一般的には、材料の変形抵抗は試験片の
加工や試験方法が簡単な単軸の引張り試験によって測定
されることが多い。引張り試験における一様変形の範囲
内での引張り荷重と変位との関係から材料の変形抵抗を
求めるものである。又、例えば円柱状の試験片を平行平
板工具間で圧縮変形し、その時の圧縮荷重との変位との
関係を測定してその材料の変形抵抗を決定する方法も広
く行われている。2. Description of the Related Art Generally, the deformation resistance of a material is often measured by a uniaxial tensile test in which a test piece is processed and the test method is simple. The deformation resistance of the material is obtained from the relationship between the tensile load and the displacement within the uniform deformation range in the tensile test. Further, for example, a method in which a cylindrical test piece is compressed and deformed between parallel plate tools, and the deformation resistance of the material is determined by measuring the relationship between the compression load and the displacement at that time is widely used.
【０００３】[0003]
【発明が解決しようとする課題】しかしながら引張り試
験による変形抵抗測定法の最大の難点は、その試験片の
引張り加工における一様変形限界までのデータしか採取
できない点にある。冷間における鋼系の材料を例にとれ
ば、対数ひずみ（以下単に「ひずみ」）でせいぜい０．
４（約５０％の単軸引張り変形）程度までのひずみ範囲
のデータしか得られない。ところが、圧延、鍛造、深絞
りなどの金属材料の塑性加工において、特に圧縮変形が
支配的である場合には、到達するひずみのレベルが２．
０（単軸圧縮なら８６％、単軸引張りなら６３９％）程
度であることは日常的である。したがって、引張り試験
のデータをこのような大ひずみの領域に適用するために
は大きく外挿をしなければならず、全く不正確なもので
あるといわざるを得ない。However, the greatest difficulty of the deformation resistance measuring method by the tensile test is that only data up to the uniform deformation limit in the tensile working of the test piece can be collected. Taking cold steel materials as an example, logarithmic strain (hereinafter simply “strain”) is at most 0.
Only data in the strain range up to about 4 (about 50% uniaxial tensile deformation) can be obtained. However, in plastic working of metal materials such as rolling, forging, and deep drawing, when the compressive deformation is predominant, the level of strain reached is 2.
It is routinely 0 (86% for uniaxial compression, 639% for uniaxial tension). Therefore, in order to apply the data of the tensile test to the region of such a large strain, extrapolation must be largely performed, and it must be said that it is completely inaccurate.
【０００４】また、円柱状試験片の平行平板工具間での
圧縮変形を利用する変形抵抗測定法においては、圧縮用
の工具と材料との間に摩擦力が作用するため、材料に一
様な変形を付与するのは困難である。摩擦係数をできる
だけ０に近付けるために種々の工夫がなされてはいる
が、注意深い実験をしても大変形領域になると摩擦の影
響が顕著になって、円柱状の試験片が樽型に不均一変形
することは避けられず、その平均断面積や平均ひずみか
ら変形抵抗を計算することになるので、得られる変形抵
抗の精度は悪い。Further, in a deformation resistance measuring method utilizing compression deformation between parallel plate tools of a cylindrical test piece, a frictional force acts between the compression tool and the material, so that the material is uniform. It is difficult to give deformation. Although various measures have been taken to bring the friction coefficient as close to 0 as possible, the effect of friction becomes noticeable in the large deformation region even with careful experimentation, and the cylindrical test piece is uneven in barrel shape. Deformation is inevitable, and the deformation resistance is calculated from the average cross-sectional area and average strain, so the accuracy of the obtained deformation resistance is poor.
【０００５】このような圧縮試験の欠点を克服しよう
と、円柱状の試験片の端面を拘束して圧縮し、その加工
荷重と、あらかじめ有限要素法を使用して解析的に求め
た被加工材料全体の平均ひずみとを結び付けて変形抵抗
を決定する方法（参照文献：加藤、品川、「塑性と加
工」、３０巻３４２号（１９８９年７月）、１０３０ペ
ージ）や、その方法をリング圧縮試験と組み合わせた方
法（参照文献：小坂田、白石、村木、徳岡、「日本機械
学会論文集（Ｃ編）」５５巻５１６号（１９８９年８
月）、２２１３ページ）が提案されている。しかしなが
ら、これらの方法で求まるのは被加工材全体の平均変形
抵抗であり、その物理的意味は不明確で、複雑なひずみ
分布を呈する実際の鍛造加工や板の成形加工に適用でき
るのかどうかの点が不明確である。本発明は、上記の従
来の変形抵抗測定法の持っている問題点を解決しようと
するもので、本発明の目的は、実際の加工に現れるよう
な大ひずみ領域までの変形抵抗を実加工の形態に応じた
任意の試験形態で、容易に精度よく測定できる、といっ
た利点をもっている新しい変形抵抗測定法を提供するこ
とにある。In order to overcome such a drawback of the compression test, the end surface of a cylindrical test piece is constrained and compressed, the processing load and the material to be processed which is analytically obtained in advance by using the finite element method. A method for determining deformation resistance by linking with the overall average strain (reference document: Kato, Shinagawa, "Plasticity and Machining", Vol. 30, No. 342 (July 1989), p. 1030), and the ring compression test. (Reference: Kosakada, Shiraishi, Muraki, Tokuoka, "Journal of the Japan Society of Mechanical Engineers (C)", Volume 55, 516 (1989, 1989).
Mon), page 2213). However, what is obtained by these methods is the average deformation resistance of the entire work material, its physical meaning is unclear, and whether it can be applied to the actual forging process or plate forming process that exhibits a complicated strain distribution. The points are unclear. The present invention is intended to solve the problems of the above-mentioned conventional deformation resistance measuring method, and an object of the present invention is to obtain the deformation resistance up to a large strain region which appears in actual processing in actual processing. An object of the present invention is to provide a new deformation resistance measuring method which has an advantage that it can be easily and accurately measured in an arbitrary test form depending on the form.
【０００６】[0006]
【課題を解決するための手段】本発明にかかる変形抵抗
の測定方法は、任意の形態の塑性変形試験を実施して測
定される荷重と変位の関係と、その変形の有限要素法シ
ミュレーションから得られる情報とを組合せて、対象と
した材料の変形抵抗式を決定するものである。この方法
の特徴は、次の（ａ）項から（ｄ）項までの手順をとる
点にある。A method for measuring deformation resistance according to the present invention is obtained by performing a plastic deformation test of an arbitrary form and measuring the relationship between load and displacement and finite element method simulation of the deformation. This is combined with the information provided to determine the deformation resistance formula of the target material. The feature of this method is that steps (a) to (d) below are taken.
【０００７】（ａ）材料に塑性変形を与え、その変形に
要した外力とその外力の荷重点の変位との関係を測定し
て外力のなした単位時間当りの仕事（以下において「実
仕事率」という）の推移を求める。 （ｂ）当該材料の変形抵抗を、１つのまたは複数の未知
定数を含む適当な関数形を設定して、ひずみなどの関数
として表現する。 （ｃ）上記の未知定数に適当な推定値を与えることによ
って当該材料の変形抵抗式を仮定し、有限要素法を用い
て（ａ）項の塑性変形を計算機シミュレーションし、外
力のなす単位時間当りの仕事（以下において「計算仕事
率」という）の推移を求める。 （ｄ）実仕事率と計算仕事率との誤差が許容できる範囲
以下になるまで未知定数の値を変えて（ｃ）項を繰り返
し、許容範囲以下になったらその時の未知定数の値を使
用して当該材料の変形抵抗を決定する。(A) The material is plastically deformed, and the relationship between the external force required for the deformation and the displacement of the load point of the external force is measured to measure the work per unit time (hereinafter referred to as "actual work rate"). )) Transition. (B) The deformation resistance of the material is expressed as a function such as strain by setting an appropriate function form including one or more unknown constants. (C) The deformation resistance equation of the material is assumed by giving an appropriate estimated value to the above unknown constant, and the plastic deformation of the term (a) is computer-simulated using the finite element method, and per unit time made by external force. The transition of the job (hereinafter referred to as "calculation work rate") is calculated. (D) The value of the unknown constant is changed until the error between the actual work rate and the calculated work rate falls within the allowable range, and (c) is repeated. When the error falls below the allowable range, the value of the unknown constant at that time is used. Determines the deformation resistance of the material.
【０００８】有限要素法を使用して塑性変形をシミュレ
ーションすると材料内部のひずみや応力の分布の時間推
移が容易に求まるので、材料の塑性変形の仕事率及び材
料と工具の接触面の摩擦の仕事率を計算することができ
る。その両仕事率の和（以下において「内部仕事率」と
いう）は計算仕事率に等しいので、内部仕事率を応力や
ひずみの関数として数式で表現しておけば、上記の
（ｄ）項に述べた繰り返しは、例えば、次の手順とな
る。即ち、実仕事率と内部仕事率との差の自乗を全変形
過程にわたって時間積分し、その積分値が最小になるよ
うに未知定数の値を決める。具体的には、積分値最小の
条件から導かれる未知定数に関する連立方程式を解けば
良い。この連立方程式は当該積分値を表現する式を未知
定数で偏微分することによって得られる。連立方程式の
係数行列や右辺ベクトルの値は有限要素法解析から得ら
れる材料内部の応力やひずみの値から計算することがで
きる。こうして決められた未知定数を上記（ｃ）項の推
定値に代えて新たな変形抵抗式を仮定し、実仕事率と計
算仕事率の誤差があらかじめ決めた収束条件を満足する
まで（ｃ）項を繰り返す。しかしながら、この繰り返し
の手順は本発明の実施の一態様であって、繰り返しの際
に使用すべき未知定数を求める方法はこの手順に限定さ
れるものではない。また、収束を判定する条件として
は、例えば、外力仕事率と計算仕事率をそれぞれ時間積
分して得られる仕事の差が一定程度より小さくなるとの
条件を設定する。これも本発明の実施の一態様であっ
て、収束判定条件がこれに限定されるものではない。本
発明は、実際の材料の塑性変形の際の荷重と変位との測
定値を利用するものであり、また、外力のなす仕事は材
料内部の変形の仕事に等しいといったエネルギー保存則
を利用しており、有限要素法による塑性変形の解析その
ものもポテンシャル最小の原理または仮想仕事の原理を
利用するものであるので、自然法則を利用したものであ
る。When the plastic deformation is simulated by using the finite element method, the time transition of strain and stress distribution inside the material can be easily obtained. Therefore, the work rate of the plastic deformation of the material and the work of friction between the contact surface of the material and the tool are calculated. The rate can be calculated. Since the sum of both powers (hereinafter referred to as “internal power”) is equal to the calculated power, if the internal power is expressed as a function of stress or strain by mathematical expression, it is mentioned in the above item (d). The repetition is performed as follows, for example. That is, the square of the difference between the actual work rate and the internal work rate is time-integrated over the entire deformation process, and the value of the unknown constant is determined so that the integrated value becomes the minimum. Specifically, the simultaneous equations regarding the unknown constant derived from the condition of the minimum integral value may be solved. This simultaneous equation is obtained by partially differentiating the expression expressing the integral value with an unknown constant. The coefficient matrix and right-hand side vector values of the simultaneous equations can be calculated from the stress and strain values inside the material obtained from the finite element method analysis. The unknown constant determined in this way is replaced with the estimated value of the above item (c), and a new deformation resistance equation is assumed, until the error between the actual work rate and the calculated work rate satisfies the predetermined convergence condition. repeat. However, this iterative procedure is one embodiment of the present invention, and the method of obtaining the unknown constant to be used in the iterative procedure is not limited to this procedure. Further, as the condition for determining the convergence, for example, a condition is set such that the difference between the work obtained by time integration of the external power work and the calculated work power is smaller than a certain level. This is also one embodiment of the present invention, and the convergence determination condition is not limited to this. The present invention utilizes the measured values of the load and the displacement during the actual plastic deformation of the material, and uses the energy conservation law such that the work of the external force is equal to the work of the internal deformation of the material. However, since the analysis of plastic deformation by the finite element method itself uses the principle of minimum potential or the principle of virtual work, it is based on the law of nature.
【０００９】[0009]
【作用】本発明の作用を示すために実際に変形抵抗を決
定する手順とその原理とを式を用いて詳述すれば、以下
のとおりである。 度Ｔの関数として（ｉ）式のように表される。関数の形
を設定してやれば、変形 ことができる。そこでまず、変形抵抗を測定したい材料
の関数の形を設定して、未知定数に初期値を与えて変形
抵抗曲線を仮定する。ただし、この関数の形は未知定数
で２回微分可能なものとする。In order to show the operation of the present invention, the procedure for actually determining the deformation resistance and the principle thereof will be described in detail using formulas as follows. It is expressed as a function of the degree T as shown in equation (i). Transform if you set the shape of the function be able to. Therefore, first, the shape of the function of the material whose deformation resistance is to be measured is set, and an initial value is given to the unknown constant to assume a deformation resistance curve. However, the form of this function can be differentiated twice with an unknown constant.
【００１０】[0010]
【数１】 [Equation 1]
【００１１】工具と材料との接触面における摩擦力τは
剪断摩擦則に従うとして、（ｉｉ）式で示される。ここ
に、ｍは剪断摩擦定数、τ0 は剪断変形抵抗である。The frictional force τ at the contact surface between the tool and the material is expressed by the equation (ii) assuming that the shear friction law is obeyed. Here, m is a shear friction constant, and τ 0 is a shear deformation resistance.
【００１２】[0012]
【数２】 [Equation 2]
【００１３】当該材料に関するある塑性変形を考え、先
に仮定した変形抵抗を使用してその塑性変形を有限要素
法を利用して解析すると、変形形状、応力、ひずみ、の
分布の時間推移が得られる。従って、内部仕事率ｅは、
△ｕを工具と材料との接触面における接線方向の相対す
べり速度、ｖを体積、ｓを面積とすれば、（ｉｉｉ）式
によって求めることができる。ただし、∫v は材料の全
体積において、∫s は全接触表面で積分することを表
す。When a certain plastic deformation of the material is considered and the plastic deformation is analyzed using the finite element method using the deformation resistance assumed above, the time transition of the distribution of the deformed shape, stress and strain is obtained. To be Therefore, the internal work rate e is
If Δu is the relative slip velocity in the tangential direction on the contact surface between the tool and the material, v is the volume, and s is the area, then it can be determined by the equation (iii). However, ∫ v is the integral of the total volume of the material, and ∫ s is the integral of all contact surfaces.
【００１４】[0014]
【数３】 [Equation 3]
【００１５】一方、当該材料に対して実際にその塑性変
形を付与してその時の荷重ｐと変位δとの関係を測定す
れば、実仕事率ｗは、速度をｕ，時間をｔとして、（ｉ
ｖ）式で示される。On the other hand, when the plastic deformation is actually applied to the material and the relationship between the load p and the displacement δ at that time is measured, the actual work rate w is u for speed and t for time. i
v) It is shown by a formula.
【００１６】[0016]
【数４】 [Equation 4]
【００１７】ここで、実際の材料の変形抵抗を表すよう
に未知定数が与えられていればｅとｗとは等しくなるは
ずであるが、（ｉ）式で与えた定数は初期推定値である
からｗとｅとの間に差が生ずる。その偏差の自乗を当該
塑性変形工程にわたって時間積分（∫t ）して求めた値
を（ｖ）式で示されるようにρとする時、ρが最小に ことになる。即ち、（ｖｉ）式で表されるｋ個の式から
なる連立方程式を解けば Here, if an unknown constant is given to represent the actual deformation resistance of the material, e and w should be equal, but the constant given by the equation (i) is an initial estimated value. There is a difference between w and e. When the value obtained by time integration (∫ t ) of the square of the deviation over the plastic deformation process is ρ as shown in equation (v), ρ is minimized. It will be. That is, if a simultaneous equation consisting of k equations represented by equation (vi) is solved,
【００１８】[0018]
【数５】 [Equation 5]
【００１９】（ｖｉ）式は、後で述べるように（ｉ）式
の関数形が未知定数に関して線形でない限り、一般には
非線形連立方程式となるので、初期推定値から出発し
て、加 式で未知定数を入れ換えて収束判定をし、収束していな
ければこの過程を繰り返すといった方法で解く。ここに
（ｒ）の記号は第ｒ回目の収束計算を表し、（ｖｉｉ）
式の行列及びベクトルの要素は（ｖ）式を偏微分して
（ｉｘ）及び（ｘ）式のように得られる。また、（ｉ
ｘ）、（ｘ）式中のｅの偏微分は（ｉｉｉ）式から（ｘ
ｉ）及び（ｘｉｉ）式のように得られ、いずれも（ｉ）
式を未知定数によって偏微分して得られる式と有限要素
法解析の結果とから計算できる。As will be described later, the equation (vi) is generally a non-linear simultaneous equation unless the functional form of the equation (i) is linear with respect to the unknown constant. The unknown constants are replaced in the formula to make a convergence judgment, and if not converged, this process is repeated to solve. Here, the symbol (r) represents the r-th convergence calculation, and (vii)
The matrix and vector elements of the equation are obtained by partially differentiating the equation (v) as in the equations (ix) and (x). Also, (i
x), the partial differential of e in the expressions (x) can be calculated from the expression (iii) as (x
i) and (xii), both of which are (i)
It can be calculated from the expression obtained by partially differentiating the expression by an unknown constant and the result of the finite element method analysis.
【００２０】[0020]
【数６】 [Equation 6]
【００２１】 である。このようにして当該材料の変形抵抗が実際の塑
性変形の荷重と変位の関係の測定値と有限要素法解析と
から定式化され、本発明の方法によって変形抵抗が測定
される。[0021] Is. In this way, the deformation resistance of the material is formulated from the measured value of the relationship between the actual plastic deformation load and displacement and the finite element method analysis, and the deformation resistance is measured by the method of the present invention.
【００２２】[0022]
【実施例】以下に本発明の実施例をもって、本発明にか
かる方法が材料の変形抵抗を測定する方法として有効で
あることを示す。図１は本実施例に使用した材料の変形
抵抗を示す曲線である。この曲線はＪＩＳ規格のＳＵＳ
３０４ステンレス鋼の２０℃における変形抵抗の測定値
で、中実丸棒の軸方向圧縮試験において、潤滑に十分に
注意を払って摩擦が無視できる程度の一様変形の状態で
測定したものである。この変形抵抗を既知変形抵抗と
し、以下に、本発明にかかる変形抵抗測定法をもって、
本実施例においてこの既知変形抵抗と許容できる誤差の
範囲で同一の値をもつ変形抵抗を求めることができたこ
とを示す。EXAMPLES The following examples show that the method according to the present invention is effective as a method for measuring the deformation resistance of a material. FIG. 1 is a curve showing the deformation resistance of the material used in this example. This curve is JIS standard SUS
This is the measured value of the deformation resistance of 304 stainless steel at 20 ° C., which was measured in the axial compression test of a solid round bar in the state of uniform deformation in which friction was negligible while paying sufficient attention to lubrication. . This deformation resistance is a known deformation resistance, and with the deformation resistance measuring method according to the present invention,
In the present embodiment, it is shown that the deformation resistance having the same value as this known deformation resistance can be obtained within the allowable error range.
【００２３】まず、上記ＳＵＳ３０４ステンレス鋼から
図２に示されている外径３０ｍｍ、内径１５ｍｍ、高さ
１０ｍｍのリング状の試験片を採取し、２０℃の雰囲気
下においてその試験片を剛体とみなせる平行平板工具の
間で無潤滑で軸方向に６ｍｍ（６０％）圧縮した。得ら
れたリングの変形形状の測定によって、この試験におけ
る剪断摩擦定数ｍの値は、０．４１であることが知られ
た。圧縮にはアムスラー型万能試験機を使用し、圧縮過
程中の圧縮に要した荷重と工具の圧縮変位を時間ととも
に測定記録した。図３はその測定の結果で、圧縮荷重と
圧縮変位の関係を示したものである。この関係から（ｉ
ｖ）式による実仕事率ｗの推移を求めた。この圧縮変形
に必要であった実仕事Ｗは図３の曲線の下の面積であ
り、容易に計算できて、３５９ｋｇ・ｍであった。ここ
で、後述の有限要素法の解析の繰り返しにおいて、計算
仕事率の時間積分値として求められる計算仕事Ｅと実仕
事Ｗの差の実仕事Ｗに対する割合（以下において「仕事
誤差率」という）が５％以下であるとの条件が満足され
たら収束したとみなすこととする。即ちFirst, a ring-shaped test piece having an outer diameter of 30 mm, an inner diameter of 15 mm, and a height of 10 mm shown in FIG. 2 was taken from the SUS304 stainless steel, and the test piece can be regarded as a rigid body in an atmosphere of 20 ° C. It was compressed 6 mm (60%) in the axial direction without lubrication between the parallel plate tools. By measuring the deformed shape of the obtained ring, the value of the shear friction constant m in this test was found to be 0.41. An Amsler type universal testing machine was used for compression, and the load required for compression during the compression process and the compression displacement of the tool were measured and recorded over time. FIG. 3 shows the result of the measurement and shows the relationship between the compressive load and the compressive displacement. From this relationship (i
The transition of the actual work rate w was calculated by the equation v). The actual work W required for this compressive deformation is the area under the curve in FIG. 3, which can be easily calculated and was 359 kg · m. Here, in repeated analysis of the finite element method described later, the ratio of the difference between the calculated work E and the actual work W, which is obtained as the time integral value of the calculated work ratio, to the actual work W (hereinafter referred to as “work error rate”) is If the condition of 5% or less is satisfied, it is considered to have converged. I.e.
【００２４】[0024]
【数７】 [Equation 7]
【００２５】次に、上記のリングの圧縮変形を有限要素
法を使用して解析した。使用したプログラムは市販の汎
用非線形有限要素法解析プログラムである。その際、変
形抵抗は（ｘｉｖ）式に示されているように、５個の未
知定数を含むひずみの４次多項式で表されるものとし
て、その未知定数ｃ1 の初期値として２５ｋｇ／ｍｍ2
の値を与え、ｃ2 からｃ5 までの未知定数は初期値を０
とした。即ち、完全弾塑性体の変形抵抗式を初期値とし
たものである。Next, the compressive deformation of the above ring was analyzed using the finite element method. The program used is a commercially available general-purpose nonlinear finite element method analysis program. At that time, the deformation resistance is represented by a fourth-order polynomial of strain including five unknown constants as shown in the equation (xiv), and 25 kg / mm 2 is set as an initial value of the unknown constant c 1.
, And the unknown constants from c 2 to c 5 have an initial value of 0.
And That is, the deformation resistance equation of the perfect elasto-plastic body is used as the initial value.
【００２６】[0026]
【数８】 [Equation 8]
【００２７】有限要素法解析には４節点４辺形１次アイ
ソパラメトリック要素を使用した。図２に示したよう
に、試験片に対称性があるので、軸を含む断面形状の１
／４を解析の対象とし、軸方向を１０等分割、半径方向
を１５等分割して全体で１５０要素のメッシュとした。
また材料のヤング率、ポアソン比、降伏点は、それぞ
れ、１９７００ｋｇ／ｍｍ2 、０．３、２５．０ｋｇ／
ｍｍ2 とした。境界条件としては、対称性を維持するた
めの条件の他、リング端面には軸方向に０．０５ｍｍ／
ｓの一定速度の変位を与えた。工具との間の剪断摩擦定
数は、上記の実測に基づいて０．４１とした。未知定数
初期値を使用したこの有限要素法解析によって、たとえ
ば図４及び図５のような解析結果が得られた。図４は６
０％圧縮した時の各要素の形状を初期の形状と比較して
示したものである。図５は同じ時点での相当塑性ひずみ
分布を等高線で表したものである。この例で示したよう
に、有限要素法解析によれば、任意の時点における材料
内の任意の位置の変位、応力、ひずみ、ひずみ速度など
が求まる。For the finite element method analysis, a 4-node quadrilateral primary isoparametric element was used. As shown in FIG. 2, since the test piece has symmetry, the cross-sectional shape including the axis 1
/ 4 was set as an analysis target, and the axial direction was divided into 10 equal parts and the radial direction was divided into 15 equal parts to form a mesh of 150 elements as a whole.
The Young's modulus, Poisson's ratio, and yield point of the material are 19700 kg / mm 2 , 0.3, and 25.0 kg /, respectively.
It was set to mm 2 . As the boundary condition, in addition to the condition for maintaining symmetry, the ring end surface has an axial direction of 0.05 mm /
A constant velocity displacement of s was given. The shear friction constant with the tool was set to 0.41 based on the above actual measurement. By the finite element method analysis using the unknown constant initial value, the analysis results as shown in FIGS. 4 and 5, for example, were obtained. 6 in FIG.
The shape of each element when compressed by 0% is shown in comparison with the initial shape. FIG. 5 shows contour lines of the equivalent plastic strain distribution at the same time point. As shown in this example, according to the finite element method analysis, displacement, stress, strain, strain rate, etc. at any position in the material at any time can be obtained.
【００２８】この解析結果と先に測定で求めた実仕事率
ｗを使用して、（ｖｉ）式の５元連立方程式（この場
合、（ｘｉｖ）式の変形抵抗が未知定数に関して線形で
あるので、この連立方程式も線形となる）の係数行列と
右辺ベクトルの値を計算し、当該連立方程式を解いた。
こうして得られｃ1 からｃ5 までの未知定数を（ｘｉ
ｖ）式に代入して、再び上記と同様に有限要素法を使用
して解析をした。有限要素法解析を３回繰り返すと（ｘ
ｉｉｉ）式の収束条件が満足されたので解析を終了し
た。各回における仕事誤差率の値は次の通りである。 有限要素法解析回数 仕事誤差率 第１回目 ７８．４％ 第２回目 ５．９％ 第３回目 ４．１％Using this analysis result and the actual work rate w previously obtained by the measurement, the simultaneous equation of five elements of the formula (vi) (in this case, the deformation resistance of the formula (xiv) is linear with respect to the unknown constant, , This simultaneous equation is also linear) and calculated the coefficient matrix and the value of the right-hand side vector, and solved the simultaneous equation.
The unknown constants c 1 to c 5 obtained in this way are given by (xi
Substituting in v) formula, it analyzed again using the finite element method like the above. When the finite element method analysis is repeated three times, (x
Since the convergence condition of the equation iii) was satisfied, the analysis was ended. The value of the work error rate at each time is as follows. Number of finite element method analyzes Work error rate 1st time 78.4% 2nd time 5.9% 3rd time 4.1%
【００２９】また、図６は各回の有限要素法解析による
荷重と変位の関係曲線を、図３の実測の曲線と共に示し
たものである。上記仕事誤差率からも分かるように、第
１回目解析では実測と大幅に差異があるが、第２回目解
析ではすでにほとんど実測と一致している。収束が得ら
れた第３回目の解析結果から求めた未知定数の値は次の
通りである（単位はｋｇ／ｍｍ2 ）。 Ｃ1 ＝ ２１．３２ Ｃ2 ＝ ２７９．３ Ｃ3 ＝−１５７．０ Ｃ4 ＝ ８．２９２ Ｃ5 ＝ ３５．３０Further, FIG. 6 shows a relation curve of load and displacement by the finite element method analysis of each time together with the actually measured curve of FIG. As can be seen from the work error rate, the first analysis has a large difference from the actual measurement, but the second analysis already almost agrees with the actual measurement. The values of the unknown constants obtained from the results of the third analysis at which convergence was obtained are as follows (unit: kg / mm 2 ). C 1 = 21.32 C 2 = 279.3 C 3 = -157.0 C 4 = 8.292 C 5 = 35.30
【００３０】図７は各回の解析によって求めた未知定数
の値を（ｘｉｖ）式に与えて得られた変形抵抗を、初期
推定値及び図１の実測の変形抵抗と共に示したものであ
る。第３回目解析ではほとんど実測と一致しており、そ
の差は最大でも５．４ｋｇ／ｍｍ2 （実測値の３．４
％）である。以上、本発明にかかる変形抵抗測定法をも
ってＳＵＳ３０４ステンレス鋼の変形抵抗を求められた
ことが実施例によって示された。FIG. 7 shows the deformation resistance obtained by giving the value of the unknown constant obtained by each analysis to the equation (xiv) together with the initial estimated value and the actually measured deformation resistance of FIG. In the third analysis, it almost agrees with the actual measurement, and the difference is at most 5.4 kg / mm 2 (3.4 of the actual measurement value).
%). As described above, the examples show that the deformation resistance of SUS304 stainless steel was obtained by the deformation resistance measuring method according to the present invention.
【００３１】参考までに、収束の得られた第３回目の解
析による変形の形状と相当塑性ひずみの分布を図８及び
図９に示す。いずれも６０％圧縮した時のものである。
これらを図４及び図５と比較してみれば、与えた変形抵
抗式が異なるので形状やひずみ分布の著しい相違がある
ことがわかる。For reference, the shape of the deformation and the distribution of the equivalent plastic strain by the third analysis in which the convergence is obtained are shown in FIGS. 8 and 9. Both are when compressed by 60%.
Comparing these with FIG. 4 and FIG. 5, it can be seen that there is a significant difference in shape and strain distribution because the applied deformation resistance formulas are different.
【００３２】[0032]
【発明の効果】本発明によって従来の変形抵抗測定法の
持っている問題点が解決され、次のような効果が得られ
る。即ち、実際の加工で現れるような大ひずみ領域まで
の変形抵抗を測定できること、採取できる試験片の形状
に応じて、または対象とする加工の形態に応じて、任意
の試験形態で変形抵抗を求められること、小さい試験片
で簡単に変形抵抗を測定できるシテスムを構成すること
が可能であること、試験において摩擦に特に注意を払う
必要がないこと、供試材全体の平均変形抵抗や平均ひず
みといった概念を用いないので、得られる変形抵抗はそ
の定義に基づくものそのものであること、などである。
従って、本発明にかかる変形抵抗測定方法によれば、工
業的に塑性加工プロセスを適用する製造工程を設計する
にあたって、加工に必要な加工力の見積り、材料の変形
挙動の予測、加工工程や金型の設計、などに有用データ
を提供する。According to the present invention, the problems of the conventional deformation resistance measuring method are solved, and the following effects are obtained. That is, it is possible to measure the deformation resistance up to a large strain region that appears in the actual processing, depending on the shape of the test piece that can be collected, or according to the shape of the target processing, obtain the deformation resistance in any test form. That it is possible to construct a system that can easily measure deformation resistance with a small test piece, that it is not necessary to pay particular attention to friction in the test, average deformation resistance and average strain of the entire test material, etc. Since the concept is not used, the deformation resistance obtained is based on the definition itself, and so on.
Therefore, according to the deformation resistance measuring method according to the present invention, when designing a manufacturing process in which a plastic working process is industrially applied, the working force required for working is estimated, the deformation behavior of the material is predicted, the working process and the money are processed. Provide useful data for type design, etc.
【図１】実施例において使用したＳＵＳ３０４鋼の２０
℃における実測変形抵抗を示す図である。1 of 20 of SUS304 steel used in the examples
It is a figure which shows the measured deformation resistance in ° C.
【図２】実施例において使用したリング形状試験片の断
面形状と、その有限要素法解析の対象とした部分の要素
分割状況を示す図である。FIG. 2 is a diagram showing a cross-sectional shape of a ring-shaped test piece used in Examples and a state of element division of a portion subjected to the finite element method analysis.
【図３】実施例において実測された圧縮荷重と変位の関
係曲線を示す図である。FIG. 3 is a diagram showing a relational curve of the compressive load and the displacement actually measured in the example.
【図４】実施例において、未知定数に初期推定値を与え
て有限要素法解析を実施した結果得られた、６０％圧縮
時の変形形状と圧縮前の形状を示す図である。FIG. 4 is a diagram showing a deformed shape at the time of 60% compression and a shape before the compression, which are obtained as a result of performing the finite element method analysis by giving an initial estimated value to an unknown constant in the example.
【図５】実施例において、未知定数に初期推定値を与え
て有限要素法解析を実施した結果得られた、６０％圧縮
時の相当塑性ひずみの分布を示す図である。FIG. 5 is a diagram showing a distribution of equivalent plastic strain at 60% compression, which is obtained as a result of performing a finite element method analysis by giving an initial estimated value to an unknown constant in an example.
【図６】実施例における各回の有限要素法解析によって
得られた圧縮荷重と変位の関係曲線と、図３の実測曲線
を示す図である。FIG. 6 is a diagram showing a relationship curve of a compressive load and a displacement obtained by each finite element method analysis in an example, and an actual measurement curve of FIG.
【図７】実施例における各回の有限要素法解析を通じて
得られた未知定数による変形抵抗と、図１の実測変形抵
抗を示す図である。FIG. 7 is a diagram showing a deformation resistance according to an unknown constant obtained through a finite element method analysis each time and an actually measured deformation resistance in FIG.
【図８】実施例において、第３回目有限要素法解析の結
果得られた６０％圧縮時の変形形状と圧縮前の形状を示
す図である。FIG. 8 is a diagram showing a deformed shape at the time of 60% compression and a shape before the compression obtained as a result of the third finite element method analysis in the example.
【図９】実施例において、第３回目有限要素法解析の結
果得られた６０％圧縮時の相当塑性ひずみの分布を示す
図である。FIG. 9 is a diagram showing a distribution of equivalent plastic strain at 60% compression obtained as a result of the third finite element method analysis in an example.
１ 変形抵抗の測定値 ２ 解析の対象範囲 ３ 圧縮荷重の測定値 ４ 圧縮前の形状 ５ ６０％圧縮後の形状 ６ 圧縮荷重の第１回目計算値 ７ 圧縮荷重の第２回目計算値 ８ 圧縮荷重の第３回目計算値 ９ 変形抵抗の初期推定値 １０ 変形抵抗の第１回目計算値 １１ 変形抵抗の第２回目計算値 １２ 変形抵抗の第３回目計算値 1 Deformation resistance measurement value 2 Analysis target range 3 Compression load measurement value 4 Shape before compression 5 Shape after 60% compression 6 First calculation value of compression load 7 Second calculation value of compression load 8 Compression load 3rd calculation value of 9 9 Initial estimation value of deformation resistance 10 1st calculation value of deformation resistance 11 2nd calculation value of deformation resistance 12 3rd calculation value of deformation resistance
Claims (1)
た外力とその外力の荷重点の変位との関係を測定して外
力のなした単位時間当りの仕事（以下において「実仕事
率」という）の推移を求め、一方において、当該材料の
変形抵抗を一つの又は複数の未知定数を含む適当な関数
形を設定してひずみなどの関数として表現し、上記の未
知定数に適当な推定値を与えることによって当該材料の
変形抵抗式を仮定し、有限要素法を用いて前記塑性変形
を計算機シミュレーションし外力のなす単位時間当りの
仕事（以下において「計算仕事率」という）の推移を求
め、実仕事率と計算仕事率との誤差が許容できる範囲以
下になるまで未知定数の値を変えて有限要素法解析を繰
り返し、許容範囲以下になったらその時の未知定数の値
を使用して当該材料の変形抵抗を決定することを特徴と
する材料の変形抵抗測定方法。1. A work per unit time (hereinafter referred to as "actual work rate") made by an external force by subjecting a material to plastic deformation and measuring the relationship between the external force required for the deformation and the displacement of the load point of the external force. On the other hand, the deformation resistance of the material is expressed as a function such as strain by setting an appropriate function form containing one or more unknown constants, and an appropriate estimated value for the above unknown constants. Assuming the deformation resistance equation of the material by giving, the transition of the work per unit time (hereinafter referred to as "calculation work rate") made by the external force is calculated by computer simulation of the plastic deformation using the finite element method, Repeat the finite element method analysis by changing the value of the unknown constant until the error between the actual work rate and the calculated work rate falls within the allowable range, and if the error falls below the allowable range, use the unknown constant value at that time and use the material. A method for measuring deformation resistance of a material, characterized in that the deformation resistance of the material is determined.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP4222192A JPH0816644B2 (en) | 1992-07-30 | 1992-07-30 | Material deformation resistance measurement method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP4222192A JPH0816644B2 (en) | 1992-07-30 | 1992-07-30 | Material deformation resistance measurement method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH06288884A true JPH06288884A (en) | 1994-10-18 |
| JPH0816644B2 JPH0816644B2 (en) | 1996-02-21 |
Family
ID=16778597
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP4222192A Expired - Fee Related JPH0816644B2 (en) | 1992-07-30 | 1992-07-30 | Material deformation resistance measurement method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH0816644B2 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2018077179A (en) * | 2016-11-11 | 2018-05-17 | 株式会社ニチリン | Method for rubber compression test |
| WO2018169013A1 (en) * | 2017-03-16 | 2018-09-20 | 新日鐵住金株式会社 | Method for estimating hardness of cold worked part, and method for acquiring hardness/equivalent plastic strain curve of steel material |
| JP2021053678A (en) * | 2019-09-30 | 2021-04-08 | 名北工業株式会社 | Index measuring apparatus of plastic workability of wire material or wire for cold heading and index measuring method of plastic workability of wire material or wire for cold heading |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US10352836B2 (en) | 2014-05-08 | 2019-07-16 | Nippon Steel & Sumitomo Metal Corporation | Evaluation method of plastic material and evaluation method of deformation processing of plastic material |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH04155240A (en) * | 1990-10-18 | 1992-05-28 | Sumitomo Light Metal Ind Ltd | Calculation of material constant for honeycomb core |
-
1992
- 1992-07-30 JP JP4222192A patent/JPH0816644B2/en not_active Expired - Fee Related
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH04155240A (en) * | 1990-10-18 | 1992-05-28 | Sumitomo Light Metal Ind Ltd | Calculation of material constant for honeycomb core |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2018077179A (en) * | 2016-11-11 | 2018-05-17 | 株式会社ニチリン | Method for rubber compression test |
| WO2018169013A1 (en) * | 2017-03-16 | 2018-09-20 | 新日鐵住金株式会社 | Method for estimating hardness of cold worked part, and method for acquiring hardness/equivalent plastic strain curve of steel material |
| JP6399269B1 (en) * | 2017-03-16 | 2018-10-03 | 新日鐵住金株式会社 | Hardness estimation method for cold-worked parts and hardness-equivalent plastic strain curve acquisition method for steel |
| KR20190126376A (en) * | 2017-03-16 | 2019-11-11 | 닛폰세이테츠 가부시키가이샤 | Method for estimating hardness of cold worked parts and acquiring hardness-equivalent plastic deformation curve of steel |
| US11131612B2 (en) | 2017-03-16 | 2021-09-28 | Nippon Steel Corporation | Method for estimating hardness of cold worked component and method for acquiring hardness-equivalent plastic strain curve of steel material |
| JP2021053678A (en) * | 2019-09-30 | 2021-04-08 | 名北工業株式会社 | Index measuring apparatus of plastic workability of wire material or wire for cold heading and index measuring method of plastic workability of wire material or wire for cold heading |
Also Published As
| Publication number | Publication date |
|---|---|
| JPH0816644B2 (en) | 1996-02-21 |
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