JP2020046184A - Stress-strain relationship estimation method - Google Patents
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本発明は、応力−ひずみ関係推定方法に関し、特に、金属材料の均一伸び以降の高ひずみ域における応力とひずみの関係を精度良く推定することができる応力−ひずみ関係推定方法に関する。 The present invention relates to a stress-strain relationship estimation method, and more particularly, to a stress-strain relationship estimation method capable of accurately estimating the relationship between stress and strain in a high strain region after uniform elongation of a metal material.
従来、自動車などに用いられる部材は、所定の強度を有する金属板をプレス成形して製造されている。また、近年、特に自動車産業においては環境問題に起因した車体の軽量化が進められており、車体の設計にコンピュータ支援工学による解析（以下、「ＣＡＥ解析」という）は欠かせない技術となっている。
自動車の軽量化と衝突安全性能を両立させるため、自動車の車体の構造部材として、高強度鋼板の適用が増加している。高強度鋼板は、冷間でプレス成形するとスプリングバックが発生しやすく、寸法精度の向上も課題となっている。
これらプレス成形解析、衝突解析、スプリングバック解析などにおいては、金属材料の塑性加工シミュレーションが実施されている。
2. Description of the Related Art Conventionally, members used for automobiles and the like are manufactured by press-forming a metal plate having a predetermined strength. In recent years, particularly in the automobile industry, weight reduction of a vehicle body due to environmental problems has been promoted, and analysis by computer-aided engineering (hereinafter, referred to as “CAE analysis”) has become an indispensable technique in vehicle body design. I have.
In order to achieve both light weight and collision safety performance of automobiles, high-strength steel sheets are increasingly used as structural members of automobile bodies. When a high-strength steel sheet is cold-pressed, springback is likely to occur, and improvement in dimensional accuracy has also been a problem.
In these press forming analysis, collision analysis, springback analysis, and the like, a plastic working simulation of a metal material is performed.
金属材料の塑性加工シミュレーションにおいては、当該金属材料の応力−ひずみ関係が必要不可欠である。特に、プレス成形や鍛造成形では金属材料は大きな変形を受けるため、高ひずみ域での応力−ひずみ関係がシミュレーションにおける解析精度に大きな影響を及ぼす。 In the plastic working simulation of a metal material, the stress-strain relationship of the metal material is indispensable. In particular, since the metal material undergoes large deformation in press forming and forging, the stress-strain relationship in a high strain region has a great influence on the analysis accuracy in the simulation.
金属材料の応力−ひずみ関係を測定する最も一般的な方法として引張試験がある。引張試験においては、図１５に示すような平行部３を有する引張試験片（以下、「第１引張試験片１」という。）に引張変形を与え、評点間の伸びと引張荷重から応力−ひずみ関係を算出する。図１６に、第１引張試験片１を用いた引張試験で得られる応力−ひずみ関係の一例を示す。金属材料の応力が降伏応力（図１６中の点Ａ）に達すると塑性変形が開始され、ひずみの進展に伴い応力は上昇して金属材料は加工硬化を起こす。そして、点Ｂで荷重は最大となり、その後、第１引張試験片１にくびれが生じて引張荷重は低下し、破断に至る（図１６中の点Ｃ）。図１６中の点Ｂでのひずみを均一伸びといい、均一伸びに達するまでは安定した単軸引張変形とみなされ、この領域（図１６中の点０（ゼロ）から点Ｂ）における応力−ひずみ曲線が有限要素法（FEM）等の塑性加工シミュレーションに用いられる。 The most common method for measuring the stress-strain relationship of a metal material is a tensile test. In the tensile test, a tensile test piece having a parallel portion 3 as shown in FIG. 15 (hereinafter referred to as “first tensile test piece 1”) is subjected to tensile deformation, and the stress-strain is calculated from the elongation between the evaluation points and the tensile load. Calculate the relationship. FIG. 16 shows an example of a stress-strain relationship obtained in a tensile test using the first tensile test piece 1. When the stress of the metal material reaches the yield stress (point A in FIG. 16), plastic deformation starts, and as the strain progresses, the stress increases and the metal material undergoes work hardening. Then, the load becomes maximum at the point B, and thereafter, the first tensile test piece 1 is constricted, the tensile load is reduced, and the first tensile test piece 1 is broken (point C in FIG. 16). The strain at point B in FIG. 16 is called uniform elongation. Until the uniform elongation is reached, it is regarded as a stable uniaxial tensile deformation, and the stress in this region (from point 0 (zero) to point B in FIG. 16) − The strain curve is used for plastic working simulation such as finite element method (FEM).
引張試験により得られる均一伸びは、一般加工鋼で0.20〜0.3、アルミニウム合金で0.15〜0.25である。一方、近年、自動車の骨格部品への適用が進んでいる高張力鋼板は、材料強度が高くなると延性は低下し、590MPa級鋼板では0.14〜0.17程度、980MPa級鋼板では0.07〜0.1程度である。
しかしながら、実際の加工、特にプレス成形において金属材料が受けるひずみを考慮すると、上記の引張試験で得られる均一ひずみの範囲は十分でない。とりわけプレス成形シミュレーションにおける割れ予測においては、金属材料は割れ直前に大きなひずみを受けるため、均一伸び以降の応力−ひずみ関係（硬化特性）が割れ発生の予測精度に大きな影響を及ぼす。
FEMによるプレス成形シミュレーションでは、均一伸び以降の高ひずみ域の応力−ひずみ関係を硬化則（材料の硬化挙動を規定する数式モデル）で外挿する手法が一般的である。しかしながら、これは実測値に基づくものではなく、硬化則の種類や材料定数に依存して大きく変化し得るという問題がある。
The uniform elongation obtained by the tensile test is 0.20 to 0.3 for general work steel and 0.15 to 0.25 for aluminum alloy. On the other hand, in recent years, ductility of high-strength steel sheets, which have been increasingly applied to frame parts of automobiles, decreases as the material strength increases.
However, the range of uniform strain obtained by the above-described tensile test is not sufficient in consideration of the strain applied to the metal material in actual processing, particularly in press forming. Particularly in crack prediction in press forming simulation, since a metal material receives a large strain immediately before cracking, the stress-strain relationship (hardening characteristics) after uniform elongation greatly affects the prediction accuracy of crack generation.
In press molding simulation by FEM, a method of extrapolating a stress-strain relationship in a high strain region after uniform elongation by a hardening rule (a mathematical model that defines the hardening behavior of a material) is generally used. However, this is not based on actually measured values, but has a problem that it can vary greatly depending on the type of hardening rule and the material constant.
そのため、均一伸び以降の応力−ひずみ関係を得るための試験として、過去に様々な方法が提案されている。例えば、せん断試験（特許文献１）や、液圧バルジ試験（非特許文献１）や圧縮試験（非特許文献２）がある。これらの試験によれば、引張変形で生じるくびれのような不安定な変形が生じずに試験片に大きな変形を与えることができる。 Therefore, various methods have been proposed in the past as tests for obtaining a stress-strain relationship after uniform elongation. For example, there are a shear test (Patent Document 1), a hydraulic bulge test (Non-Patent Document 1), and a compression test (Non-Patent Document 2). According to these tests, a large deformation can be given to the test piece without causing unstable deformation such as necking caused by tensile deformation.
上記の先行文献に開示されている方法により得られる結果は、特許文献１ではせん断状態での応力−ひずみ関係、非特許文献１では等二軸状態（面内に等方的に負荷される状態）の応力−ひずみ関係、非特許文献２では圧縮状態の応力−ひずみ関係である。したがって、これらの方法で得られた応力−ひずみ関係をFEMによるプレス成形シミュレーションで用いるためには、単軸引張状態での応力−ひずみ関係に変換する必要がある。しかしながら、この変換の際に誤差が生じる可能性があり、変換により得られる応力−ひずみ関係は十分な精度とはいえなかった。また、上記方法の実施には特殊な試験機が必要になるため、汎用性という面で実用的ではなかった。 The results obtained by the methods disclosed in the above-mentioned prior art documents are as follows: a stress-strain relationship in a shearing state in Patent Document 1, an equi-biaxial state in Non-Patent Document 1 (state in which isotropic load is applied in a plane). ), And in Non-Patent Document 2, the stress-strain relationship in a compressed state. Therefore, in order to use the stress-strain relationship obtained by these methods in a press-forming simulation by FEM, it is necessary to convert the relationship into a stress-strain relationship in a uniaxial tension state. However, errors may occur during this conversion, and the stress-strain relationship obtained by the conversion was not sufficiently accurate. Further, the above method requires a special test machine, which is not practical in terms of versatility.
本発明は、かかる課題を解決するためになされたものであり、特殊な試験機を用いることなく、金属材料の高ひずみ域における応力−ひずみ関係を高精度に推定することができる応力−ひずみ関係推定方法を提供することを目的とする。 The present invention has been made in order to solve such a problem, and a stress-strain relationship capable of accurately estimating a stress-strain relationship in a high strain region of a metal material without using a special tester. It is intended to provide an estimation method.
（１）本発明に係る応力−ひずみ関係推定方法は、金属材料の応力とひずみの関係を推定するものであって、平行部を有する第１引張試験片に引張荷重を作用させて、均一伸びまでの応力とひずみの関係を取得する応力−ひずみ関係取得ステップと、応力とひずみの関係を与える２種類の硬化則を選択し、該２種類の硬化則それぞれの材料定数を、前記応力−ひずみ関係取得ステップで取得した応力−ひずみ関係に基づいて同定する材料定数同定ステップと、引張方向の所定位置における引張直角方向の直線上に単数又は複数の穴形状及び／又は切り欠き形状を形成した第２引張試験片に引張荷重を作用させて、該引張荷重と前記引張直角方向の直線上におけるひずみの分布との関係を取得する引張荷重−ひずみ分布取得ステップと、該取得したひずみの分布と、前記２種類の硬化則を仮の重み係数を用いて足し合わせた混合則により求められる応力とを用いて、前記第２引張試験片に作用する引張荷重を推算する引張荷重推算ステップと、該引張荷重推算ステップにおいて推算した引張荷重と前記引張荷重−ひずみ分布取得ステップにおいて取得した引張荷重とが一致するように、前記混合則の重み係数の値を決定する重み係数決定ステップと、を備え、前記引張荷重推算ステップは、前記第２引張試験片について、前記引張直角方向に沿って複数の微小領域に分割し、前記取得したひずみの分布に基づいて、各前記微小領域に前記引張方向及び前記引張直角方向のひずみを設定し、各前記微小領域に設定した前記引張方向及び前記引張直角方向のひずみと前記混合則により求められる応力とを用いて各微小領域の引張方向の応力を算出し、各前記微小領域に設定した前記引張方向及び前記引張直角方向のひずみに基づいて、各前記微小領域の板厚を算出し、各前記微小領域について算出した前記引張方向の応力と前記板厚とから各前記微小領域に作用する引張荷重を算出し、該算出した各前記微小領域に作用する引張荷重を足し合わせて前記第２引張試験片に作用する引張荷重を算出する、ことを特徴とするものである。 (1) The method for estimating the stress-strain relationship according to the present invention is for estimating the relationship between the stress and the strain of a metal material, and applies a tensile load to a first tensile test piece having a parallel portion to achieve uniform elongation. A stress-strain relationship acquisition step of acquiring a stress-strain relationship up to, and selecting two types of hardening rules that give a stress-strain relationship, and calculating the material constant of each of the two types of hardening rules by the stress-strain A material constant identification step for identifying based on the stress-strain relationship acquired in the relationship acquisition step, and a step of forming one or more hole shapes and / or notch shapes on a straight line in a tensile perpendicular direction at a predetermined position in a tensile direction. (2) a tensile load-strain distribution obtaining step of applying a tensile load to a tensile test piece to obtain a relationship between the tensile load and a strain distribution on a straight line in a direction perpendicular to the tensile direction; The tensile load for estimating the tensile load acting on the second tensile test piece using the strain distribution obtained and the stress obtained by the mixing rule obtained by adding the two types of hardening rules using a temporary weighting coefficient. An estimation step, and a weight coefficient determining step of determining a value of a weight coefficient of the mixing rule so that the tensile load estimated in the tensile load estimation step matches the tensile load obtained in the tensile load-strain distribution obtaining step. Wherein the tensile load estimating step comprises: dividing the second tensile test piece into a plurality of minute regions along the direction perpendicular to the tensile direction, and dividing each of the minute regions based on the acquired strain distribution. The strain in the tensile direction and the strain in the perpendicular direction to the tensile direction is set, and the strain in the tensile direction and the strain in the perpendicular direction to the tensile direction set in each of the micro regions are determined by the mixing rule. Calculate the stress in the tensile direction of each minute region using the stress to be applied, based on the strain in the tensile direction and the direction perpendicular to the tension set in each minute region, calculate the plate thickness of each of the minute regions, A tensile load acting on each of the minute regions is calculated from the stress in the tensile direction and the plate thickness calculated for each of the minute regions, and the calculated tensile load acting on each of the minute regions is added to the second load. Calculating a tensile load acting on the tensile test piece.
（２）上記（１）に記載のものにおいて、前記引張荷重推算ステップにおける各前記微小領域の前記引張方向の応力は、以下の手順（ａ）〜（ｃ）に従って算出することを特徴とするものである。
（ａ）各前記微小領域に設定した引張方向及び引張直角方向のひずみから、ひずみ増分を算出する。
（ｂ）該算出したひずみ増分比から各前記微小領域における引張方向及び引張直角方向の応力比を算出する。
（ｃ）各前記微小領域に設定したひずみから算出した前記相当ひずみ及び前記応力比と、前記混合則により算出した相当応力とに基づいて、各前記微小領域の前記引張方向の応力を算出する。
(2) The method according to (1), wherein the stress in the tensile direction of each of the micro regions in the tensile load estimating step is calculated according to the following procedures (a) to (c). It is.
(A) Calculating the strain increment from the strain in the tensile direction and the direction perpendicular to the tensile direction set in each of the minute regions.
(B) calculating the stress ratio in the tensile direction and the tensile perpendicular direction in each of the micro regions from the calculated strain increment ratio.
(C) calculating the stress in the tensile direction of each of the minute regions based on the equivalent strain and the stress ratio calculated from the strain set in each of the minute regions and the equivalent stress calculated by the mixing rule.
本発明によれば、金属材料の均一伸び以降の高ひずみ域における応力とひずみの関係を精度良く推定することができる。 According to the present invention, the relationship between stress and strain in a high strain region after uniform elongation of a metal material can be accurately estimated.
本発明の実施の形態に係る応力−ひずみ関係推定方法は、金属材料の応力とひずみの関係を推定するものであって、図１に示すように、応力−ひずみ関係取得ステップＳ１と、材料定数同定ステップＳ３と、引張荷重−ひずみ分布取得ステップＳ５と、引張荷重推算ステップＳ７と、重み係数決定ステップＳ９と、を備えたものである。以下、上記各ステップについて説明する。 The stress-strain relationship estimation method according to the embodiment of the present invention estimates a relationship between stress and strain of a metal material. As shown in FIG. 1, a stress-strain relationship acquisition step S1 and a material constant It includes an identification step S3, a tensile load-strain distribution obtaining step S5, a tensile load estimating step S7, and a weight coefficient determining step S9. Hereinafter, each of the above steps will be described.
＜応力−ひずみ関係取得ステップ＞
応力−ひずみ関係取得ステップＳ１は、図１５に示すような引張荷重を作用させる引張方向に平行な平行部３を有する短冊状の第１引張試験片１に引張荷重を作用させて、均一伸び（図１６に示すＢ点）までの応力とひずみの関係を取得するステップである。
前述のとおり、第１引張試験片１に引張荷重を作用させると、均一伸びに達するまでは平行部３が一様に変形するため、安定して応力−ひずみ関係を取得することができる。
なお、平行部３を有する第１引張試験片１としては、例えば、JIS5号を使用することができる。
<Step of acquiring stress-strain relationship>
The stress-strain relationship acquiring step S1 is to apply a tensile load to the strip-shaped first tensile test piece 1 having the parallel portion 3 parallel to the tensile direction for applying the tensile load as shown in FIG. This is the step of acquiring the relationship between stress and strain up to point B shown in FIG.
As described above, when a tensile load is applied to the first tensile test piece 1, the parallel portion 3 is uniformly deformed until uniform elongation is reached, so that a stress-strain relationship can be stably acquired.
In addition, as the first tensile test piece 1 having the parallel portion 3, for example, JIS No. 5 can be used.
＜材料定数同定ステップ＞
材料定数同定ステップＳ３は、応力とひずみの関係を与える２種類の硬化則を選択し、該２種類の硬化則それぞれの材料定数を、応力−ひずみ関係取得ステップＳ１で取得した応力−ひずみ関係に基づいて同定するステップである。
<Material constant identification step>
The material constant identification step S3 selects two types of hardening rules giving the relationship between stress and strain, and converts the material constants of the two types of hardening rules into the stress-strain relationship obtained in the stress-strain relationship obtaining step S1. This is the step of identifying based on the information.
硬化則としては、以下に示すn乗硬化則（式（１））、Ludwik則（式（２））、Swift則（式（３））及びVoce則（式（４））等が知られており、これらのうちいずれか２種類の硬化則を選択すればよい。 As the hardening rule, the following n-th power hardening rule (Equation (1)), Ludwik rule (Equation (2)), Swift rule (Equation (3)), Voce rule (Equation (4)) and the like are known. Therefore, any two of these curing rules may be selected.
硬化則の選択においては、以下の点を考慮する。
まず、２種類の硬化則を、次式（５）に示すように、重み係数αを用いて足し合わせた混合則を考える。
In selecting a hardening rule, the following points are considered.
First, a mixing rule in which two types of hardening rules are added using a weight coefficient α as shown in the following equation (5) is considered.
式（５）において、σeq,HRは混合則により与えられる相当応力、σeq,A及びσeq,Bは２種類の硬化則それぞれにより表される相当応力である。また、重み係数αは任意の定数であり、αが1のときσeq,HR＝σeq,Aとなり、αが0のときσeq,HR＝σeq,Bとなる。 In Equation (5), σ eq, HR is the equivalent stress given by the mixing rule, and σ eq, A and σ eq, B are the equivalent stresses represented by the two types of hardening rules, respectively. The weighting coefficient α is an arbitrary constant. When α is 1, σ eq, HR = σ eq, A , and when α is 0, σ eq, HR = σ eq, B.
材料定数同定ステップＳ３において選択する２種類の硬化則は、重み係数αの値によって相当応力σeq,HRの値が大きく変わることが望ましい。そのためには、ひずみに対する応力の挙動が大きく異なる2種類の硬化則を選択するとよく、例えば、Swift則（式（３））及びVoce則（式（４））を選択することが好ましい。そして、Swift則及びVoce則を選択した場合には、上記の式（３）中の材料定数ε0、C及びnと、式（４）中のY、Q及びbを本ステップでそれぞれ同定する。 In the two types of hardening rules selected in the material constant identification step S3, it is desirable that the value of the equivalent stress σ eq, HR greatly changes depending on the value of the weight coefficient α. For this purpose, it is preferable to select two types of hardening rules having greatly different stress behaviors with respect to strain. For example, it is preferable to select the Swift rule (formula (3)) and the Voce rule (formula (4)). When the Swift rule and the Voce rule are selected, the material constants ε 0 , C and n in the above equation (3) and Y, Q and b in the above equation (4) are identified in this step, respectively. .
＜引張荷重−ひずみ分布取得ステップ＞
引張荷重−ひずみ分布取得ステップＳ５は、図２に示すような引張方向の所定位置における引張直角方向の直線上に穴形状１３が形成された第２引張試験片１１に引張荷重を作用させて、第２引張試験片１１に作用する引張荷重と前記引張直角方向の直線上におけるひずみの分布との関係を取得するステップであり、前述した硬化則（式（５））の重み係数αを決定するための引張試験である。
<Tension load-strain distribution acquisition step>
The tensile load-strain distribution acquiring step S5 is to apply a tensile load to the second tensile test piece 11 in which the hole shape 13 is formed on a straight line in the direction perpendicular to the tensile direction at a predetermined position in the tensile direction as shown in FIG. This is a step of acquiring the relationship between the tensile load acting on the second tensile test piece 11 and the strain distribution on the straight line in the direction perpendicular to the tensile direction, and determines the weight coefficient α of the above-described hardening rule (Equation (5)). This is a tensile test for
ここで、引張荷重−ひずみ分布取得ステップＳ５で取得するひずみの分布は、引張方向及び引張直角方向の２方向のひずみの引張直角方向における分布であり、第２引張試験片１１に作用する引張荷重とひずみの引張直角方向における分布との関係を、引張試験開始から所定の時間ステップで取得するものとする。 Here, the strain distribution acquired in the tensile load-strain distribution acquiring step S5 is a distribution of strain in two directions, a tensile direction and a perpendicular direction to the tensile direction, in a direction perpendicular to the tensile direction, and a tensile load acting on the second tensile test piece 11. The relationship between the strain and the distribution of strain in the direction perpendicular to the tensile direction is obtained at a predetermined time step from the start of the tensile test.
また、引張荷重−ひずみ分布取得ステップＳ５で用いる第２引張試験片１１は、第２引張試験片１１の引張方向中央における引張直角方向の直線（図２中の点線）に対して線対称となるように該直線上に穴形状１３が形成されたものである。 Further, the second tensile test piece 11 used in the tensile load-strain distribution obtaining step S5 is symmetric with respect to a straight line (dotted line in FIG. 2) in the tensile direction center of the second tensile test piece 11 in the tensile direction. Thus, the hole shape 13 is formed on the straight line.
もっとも、引張荷重−ひずみ分布取得ステップＳ５においては、図３に示すような、切り欠き形状２３が形成された第２引張試験片２１を用いてもよい。第２引張試験片２１は、引張方向中央における引張直角方向の直線（図３中の点線）に対して線対称となるように該直線上に2つの切り欠き形状２３が形成されたものである。 However, in the tensile load-strain distribution obtaining step S5, the second tensile test piece 21 having the cutout shape 23 as shown in FIG. 3 may be used. The second tensile test piece 21 has two notches 23 formed on a straight line (dotted line in FIG. 3) perpendicular to the tensile direction at the center in the tensile direction so as to be symmetrical with the straight line. .
図４及び図５に、第２引張試験片の形状の具体例を示す。
穴形状１３は、真円（図４（ｂ））、楕円（図４（ａ）、（ｃ））のいずれでもよく、また、切り欠き形状２３についても同様に、半円（図４（ｅ））又は半楕円（図４（ｄ）、（ｆ））のいずれでもよい。
4 and 5 show specific examples of the shape of the second tensile test piece.
The hole shape 13 may be any of a perfect circle (FIG. 4 (b)) or an ellipse (FIGS. 4 (a) and 4 (c)). )) Or a semi-ellipse (FIGS. 4D and 4F).
切り欠き形状２３は第２引張試験片２５の片側のみでもよい（図５（ａ））。さらには、単数の穴形状１３や切り欠き形状２３が形成されたものに限らず、複数の穴形状１３が形成された第２引張試験片２７（図５（ｂ））や、穴形状１３と切り欠き形状２３の両方が形成された第２引張試験片２９（図５（ｃ））であってもよい。この場合、複数の穴形状１３及び／又は切り欠き形状２３は、引張方向の所定位置における引張直角方向の直線に対して線対称となるように当該直線上に形成されているものとする。 The notch shape 23 may be on only one side of the second tensile test piece 25 (FIG. 5A). Further, the present invention is not limited to the one in which the single hole shape 13 or the notch shape 23 is formed, but also the second tensile test piece 27 (FIG. 5B) in which the plurality of hole shapes 13 are formed, and the hole shape 13. The second tensile test piece 29 (FIG. 5C) in which both of the notch shapes 23 are formed may be used. In this case, it is assumed that the plurality of hole shapes 13 and / or notch shapes 23 are formed on a straight line in a tension perpendicular direction at a predetermined position in the tension direction so as to be line-symmetric.
図２〜図５に示すような第２引張試験片の引張方向の両端部をクランプして引張試験を行うと、後述するように、引張直角方向の端部側となる直線部に比べて穴形状の淵又は切り欠き形状の淵に変形が集中し、大きなひずみとなる。さらに、破断前の淵１３ａ（図２参照）又は淵２３ａ（図６照）のひずみは、第１引張試験片１を用いた単軸引張試験結果から想定される変形限界よりも大きなひずみとなる。これは、ひずみ勾配による材料の保持効果が要因と考えられ、本発明は、この効果を利用して均一伸び以降の応力−ひずみ関係を推定するものである。 When a tensile test is performed by clamping both ends in the tensile direction of the second tensile test piece as shown in FIGS. 2 to 5, as described later, the hole is smaller than the straight part on the end side in the direction perpendicular to the tensile direction. Deformation concentrates on the edge of the shape or the edge of the notch, resulting in large distortion. Further, the strain of the edge 13a (see FIG. 2) or the edge 23a (see FIG. 6) before the fracture is larger than the deformation limit assumed from the result of the uniaxial tensile test using the first tensile test piece 1. . This is considered to be due to the effect of retaining the material due to the strain gradient, and the present invention estimates the stress-strain relationship after uniform elongation using this effect.
なお、図２〜図５に示すような第２引張試験片の形状の違いにより、引張荷重−ひずみ分布取得ステップＳ５で取得することができるひずみの値の範囲は変わるが、取得する引張荷重とひずみ分布との関係には影響を及ぼさない。 Although the range of the value of the strain that can be obtained in the tensile load-strain distribution obtaining step S5 changes depending on the difference in the shape of the second tensile test piece as shown in FIGS. It does not affect the relationship with the strain distribution.
引張荷重−ひずみ分布取得ステップＳ５においては、通常の引張試験機を用いて第２引張試験片に引張荷重を作用させることができる。そして、引張変形中に第２引張試験片に作用する引張荷重は引張試験機に組み込まれているロードセルを用いて測定し、引張変形中の第２引張試験片の表面の引張方向ひずみと引張直角方向ひずみ、それぞれの引張直角方向分布は、例えば、画像相関法（DIC）によるカメラシステムを用いて測定すればよい。 In the tensile load-strain distribution acquisition step S5, a tensile load can be applied to the second tensile test piece using a normal tensile tester. The tensile load acting on the second tensile test piece during the tensile deformation is measured using a load cell built in the tensile tester, and the strain in the tensile direction on the surface of the second tensile test piece during the tensile deformation and the tensile perpendicularity are measured. The directional strain and the respective distributions in the perpendicular direction to tension may be measured, for example, using a camera system based on an image correlation method (DIC).
＜引張荷重推算ステップ＞
引張荷重推算ステップＳ７は、引張荷重−ひずみ分布取得ステップＳ５において取得したひずみの分布と、材料定数同定ステップＳ３で選択した２種類の硬化則を足し合わせた混合則に仮の重み係数の値を与えて算出した応力とを用いて、引張荷重−ひずみ分布取得ステップＳ５において第２引張試験片に作用した引張荷重を推算するステップである。
<Tension load estimation step>
The tensile load estimating step S7 calculates a temporary weighting factor value to a mixing rule obtained by adding the strain distribution acquired in the tensile load-strain distribution acquiring step S5 and the two types of hardening rules selected in the material constant identifying step S3. This is a step of estimating the tensile load applied to the second tensile test piece in the tensile load-strain distribution obtaining step S5 using the stress calculated and given.
以下、切り欠き形状２３が片側に付与された第２引張試験片２５（図６参照）の引張荷重を推算する場合について説明する。 Hereinafter, a case will be described in which the tensile load of the second tensile test piece 25 (see FIG. 6) in which the notch shape 23 is provided on one side is estimated.
第２引張試験片２５に単軸引張荷重を作用させると不均一変形となるため、ひずみは場所によって異なり、図６に示すように、引張方向中央における引張方向のひずみεxは、切り欠き形状２３の淵２３ａで最も大きくなり、引張直角方向における反対側の直線部２５ａで最も小さくなるような分布を示す。 Since the exert a uniaxial tensile load to the second tensile test specimen 25 becomes non-uniform deformation, distortion depends on the location, as shown in FIG. 6, the strain epsilon x direction tensile in a tensile direction center, notched shape The distribution is such that it becomes the largest at the edge 23a of 23 and the smallest at the straight portion 25a on the opposite side in the direction perpendicular to the tension.
そこで、引張荷重推算ステップＳ７では、第２引張試験片２５の中央断面において複数の微小領域を設定し、各微小領域に働く引張荷重を離散的に求め、全ての微小領域で推算される引張荷重を足し合わせることで、断面全体の引張荷重を推算するものとする。図７に引張荷重を推算する具体的な手順の流れ（Ｓ１１〜Ｓ２５）を示す。 Therefore, in the tensile load estimating step S7, a plurality of minute regions are set in the central cross section of the second tensile test piece 25, the tensile loads acting on each minute region are obtained discretely, and the tensile loads estimated in all the minute regions are determined. , The tensile load of the entire cross section is estimated. FIG. 7 shows the flow of the specific procedure for estimating the tensile load (S11 to S25).
なお、本実施の形態では、引張方向中央における引張直角方向の直線に対して線対称な形状である第２引張試験片２５の中心断面におけるひずみと応力を評価するものであるため、当該中心断面が受けるひずみ及び応力は引張方向（x方向）と引張直角方向（y方向）のみであり、引張荷重の推算においては、せん断成分（xy成分）は考慮しないものとする。以下、Ｓ１１〜Ｓ２５の各手順について説明する。 Note that, in the present embodiment, the strain and the stress in the center section of the second tensile test piece 25, which is line-symmetric with respect to the straight line in the tensile perpendicular direction at the center in the tensile direction, are evaluated. Are subjected only to the tensile direction (x direction) and the direction perpendicular to the tensile direction (y direction), and the estimation of the tensile load does not consider the shear component (xy component). Hereinafter, each procedure of S11 to S25 will be described.
≪微小領域の分割≫
まず、図８に示すように、第２引張試験片２５の中央断面において引張直角方向に沿って複数の微小領域３１に分割する（Ｓ１１）。
微小領域３１の分割数は、ひずみ分布−引張荷重取得ステップＳ５におけるひずみ測定の分解能に依存するが、微小領域３１の分割幅dyを小さく設定することが望ましい。
≫Division of minute area≫
First, as shown in FIG. 8, the second tensile test piece 25 is divided into a plurality of minute regions 31 along the direction perpendicular to the tensile direction in the central cross section (S11).
Although the number of divisions of the minute region 31 depends on the resolution of the strain measurement in the strain distribution-tensile load acquisition step S5, it is desirable to set the division width dy of the minute region 31 small.
≪各微小領域のひずみの設定≫
次に、引張荷重−ひずみ分布取得ステップＳ５において取得した所定の時間ステップにおけるひずみの分布に基づいて、各微小領域に引張方向のひずみεx及び引張直角方向のひずみεyを設定する（Ｓ１３）。
設定するひずみεx及びεyは全ひずみ（対数ひずみ）とし、次式（６）に示すように、弾性ひずみεi eと塑性ひずみεi pの和とする。
ひ ず み Setting of strain for each minute area≫
Next, based on the strain distribution at the predetermined time step acquired in the tensile load-strain distribution acquiring step S5, a strain ε x in a tensile direction and a strain ε y in a direction perpendicular to the tensile direction are set in each minute region (S13). .
Set to strain epsilon x and epsilon y is the total strain (logarithmic strain), as shown in the following equation (6), the sum of the elastic strain epsilon i e and plastic strain epsilon i p.
≪ひずみ増分比の算出≫
続いて、各微小領域３１に設定した引張方向及び引張直角方向のひずみから、ひずみ増分比を算出する。（Ｓ１５、特許請求の範囲の手順（ａ）に対応）。
具体的には、引張荷重を推算する時間ステップをnとすると、次式（７）に示すように、前後の時間ステップにおけるひずみからひずみ増分dεx及びdεyを求める。
≫Calculation of strain increment ratio≫
Subsequently, a strain increment ratio is calculated from the strain in the tensile direction and the direction perpendicular to the tensile direction set in each micro region 31. (S15, corresponding to step (a) in the claims).
Specifically, assuming that the time step for estimating the tensile load is n, the strain increments dε x and dε y are obtained from the strains at the preceding and following time steps as shown in the following equation (7).
式（７）において、nは引張荷重を推算する時間ステップ、n+c及びn-cは前後の時間ステップであり、cはひずみ増分を求める時間ステップの間隔を設定するパラメータ（1以上の整数）である。 In the equation (7), n is a time step for estimating a tensile load, n + c and nc are time steps before and after, and c is a parameter (an integer of 1 or more) for setting an interval between time steps for obtaining a strain increment. is there.
そして、引張方向x及び引張直角方向yそれぞれのひずみ増分の比をaとすると、次式（８）のように表せる。 When the ratio of the strain increment in each of the tensile direction x and the tensile perpendicular direction y is a, it can be expressed as the following equation (8).
ここで、dεi（i＝x、y）は全ひずみ増分であるが、大変形している場合は弾性ひずみの成分が相対的に微小となり無視できるため、εi≒εi pとなり、下式（９）のように近似できる。 Here, dε i (i = x, y) is the total incremental strain, because if you are large deformation negligible component of elastic strain becomes relatively small, ε i ≒ ε i p, and the lower Equation (9) can be approximated.
式（９）により近似された塑性ひずみ増分dεi pについて、関連流動則（参考文献：吉田総仁、弾塑性変形の基礎、pp.164−165、共立出版、1997）を仮定する。
関連流動則とは、塑性ひずみ増分と応力状態との関係を表した関係式であり、弾塑性有限要素解析等では、この仮定に従って応力−ひずみ計算を行っている。
関連流動則を仮定した場合、引張方向（x方向）と引張直角方向（y方向）それぞれの塑性ひずみ増分dεx p及びdεy pは、次のように表せる。
As for the plastic strain increment dε i p approximated by the equation (9), a related flow rule (reference: Sojin Yoshida, Basics of elasto-plastic deformation, pp. 164-165, Kyoritsu Shuppan, 1997) is assumed.
The related flow law is a relational expression expressing the relationship between the plastic strain increment and the stress state. In the elasto-plastic finite element analysis or the like, the stress-strain calculation is performed according to this assumption.
Related If flow law assuming a tensile direction (x direction) and the tensile direction perpendicular (y direction) of the respective plastic strain increment d? X p and d? Y p can be expressed as follows.
ここで、fは降伏関数であり、x及びy方向の応力σx及びσyの関数である。
降伏関数fは、例えば等方性を仮定したMisesの降伏関数の場合、次式（１２）のように与えられる。
Here, f is a yield function, which is a function of the stresses σ x and σ y in the x and y directions.
The yield function f is given by the following equation (12), for example, in the case of a Mises yield function assuming isotropic properties.
ここで、σeqは相当応力（多軸応力を単軸応力に変換した場合の相当値）である。この場合、塑性ひずみ増分は、以下の式（１３）及び式（１４）のように表せる。 Here, σ eq is an equivalent stress (an equivalent value when multiaxial stress is converted to uniaxial stress). In this case, the plastic strain increment can be expressed as in the following Expressions (13) and (14).
式（１３）及び式（１４）において、dλは正のスカラー値である。
よって、ひずみ増分比は式（１５）で表せる。
In Expressions (13) and (14), dλ is a positive scalar value.
Therefore, the strain increment ratio can be expressed by equation (15).
また、降伏関数fは、Hill’48の異方性降伏関数の場合、次式（１６）のように与えられる。 The yield function f is given by the following equation (16) in the case of the Hill'48 anisotropic yield function.
これより、x方向及びy方向のひずみ増分はそれぞれ、以下の式（１７）及び式（１８）で表せる。 Thus, the strain increments in the x and y directions can be expressed by the following equations (17) and (18), respectively.
よって、ひずみ増分比aは、次式（１９）と表せる。 Therefore, the strain increment ratio a can be expressed by the following equation (19).
上記の説明は、降伏関数として、Misesの降伏関数及びHill’48の異方性降伏関数を用いた場合のものであったが、降伏関数は他に、Yld2000−2d降伏関数、Yoshida降伏関数等があり、本発明ではいずれの降伏関数を用いてもよい。もっとも、異方性のある材料には、その異方性を忠実に再現する降伏関数を用いることが望ましい。 In the above description, as the yield function, the Mises yield function and the Hill'48 anisotropic yield function were used, but other yield functions include the Yld2000-2d yield function, the Yoshida yield function, and the like. In the present invention, any yield function may be used. However, for a material having anisotropy, it is desirable to use a yield function that faithfully reproduces the anisotropy.
≪応力比の算出≫
算出したひずみ増分比aから、各微小領域３１における引張方向の応力σxと引張直角方向の応力σyの比を算出する（Ｓ１７、特許請求の範囲の手順（ｂ）に対応）。具体的には、以下のように算出する。
まず、応力比bは、次式（２０）で表せる。
≫Calculation of stress ratio≫
From the calculated strain increment ratio a, the ratio between the stress σ x in the tensile direction and the stress σ y in the direction perpendicular to the tension in each micro-region 31 is calculated (S17, corresponding to step (b) in the claims). Specifically, it is calculated as follows.
First, the stress ratio b can be expressed by the following equation (20).
降伏関数fとしてMisesの降伏関数を用いた場合、式（１５）より次式（２１）が得られる。 When the Mises yield function is used as the yield function f, the following equation (21) is obtained from the equation (15).
よって、応力比bは、次式（２０）となる。 Therefore, the stress ratio b is given by the following equation (20).
ここでは、ひずみ増分比の算出Ｓ１５においてひずみの測定値から求めたひずみ増分比aを式（２０）に代入することで、応力比bが求まる。 Here, the stress ratio b is obtained by substituting the strain increment ratio a obtained from the measured value of the strain in the calculation of the strain increment ratio S15 into the equation (20).
また、降伏関数fとして、Hill’48の異方性降伏関数を用いた場合、式（１９）より次式（２３）が得られる。 When the Hill'48 anisotropic yield function is used as the yield function f, the following equation (23) is obtained from the equation (19).
よって、応力比bは、次式（２４）と表せられ、既知のひずみ増分比aを用いて応力比bを求めることができる。 Therefore, the stress ratio b is expressed by the following equation (24), and the stress ratio b can be obtained using the known strain increment ratio a.
≪引張方向応力の算出≫
続いて、各微小領域３１について算出した応力比bと、混合則により算出される相当応力σeq,HRとに基づいて、各微小領域３１における引張方向の応力σxを算出する（Ｓ１９、特許請求の範囲の手順（ｃ）に対応）。
≫Calculation of tensile stress≪
Subsequently, based on the stress ratio b calculated for each of the minute regions 31 and the equivalent stress σ eq, HR calculated by the mixing rule, the tensile stress σ x in each of the minute regions 31 is calculated (S19, Patent (Corresponds to step (c) in the claims).
前述のとおり、各微小領域３１の応力比bの算出においては、各微小領域３１に設定した引張方向及び引張直角方向のひずみεx及びεyを用いている。そのため、本実施の形態では、各微小領域３１に設定した引張方向及び引張直角方向のひずみと混合則により求められる応力（相当応力σeq,HR）とを用いて、各微小領域３１の引張方向の応力σxを算出するわけである。 As described above, in the calculation of the stress ratio b of each minute region 31, the strains ε x and ε y in the tensile direction and the direction perpendicular to the tension set in each minute region 31 are used. For this reason, in the present embodiment, the tensile direction of each micro-region 31 is determined using the strain set in each micro-region 31 in the tensile direction and the direction perpendicular to the tensile direction and the stress (equivalent stress σ eq, HR ) obtained by the mixing rule. it is not to calculate the stress σ x.
混合則により算出される相当応力σeq,HRは、前述の式（５）に示すように、材料定数同定ステップＳ３で材料定数を同定した２種類の硬化則それぞれにより相当応力σeq,A及びσeq,Bを重み係数αを用いて足し合わせたものとする。 The equivalent stress σ eq, HR calculated by the mixing rule is, as shown in the above equation (5), the equivalent stress σ eq, A and the equivalent stress σ eq, A by the two types of hardening rules whose material constants were identified in the material constant identification step S3. It is assumed that σ eq, B is added using the weight coefficient α.
式（５）中の２種類の硬化則により与えられる相当応力σeq,A及びσeq,Bは、いずれも相当塑性ひずみεeqの関数である。そして、相当塑性ひずみεeqは、引張方向（x方向）及び引張直角方向（y方向）の塑性ひずみεx及びεyを用いて、次式（２５）で表せる。 The equivalent stresses σ eq, A and σ eq, B given by the two types of hardening rules in equation (5) are all functions of the equivalent plastic strain ε eq . The equivalent plastic strain ε eq can be expressed by the following equation (25) using the plastic strains ε x and ε y in the tensile direction (x direction) and the direction perpendicular to the tensile direction (y direction).
式（２５）より求めた相当ひずみεeqを各硬化則に代入することで相当応力σeq,A及びσeq,Bが求まり、重み係数αの値を与えることで式（１）により混合則の相当応力σeq,HRが求まる。 The equivalent stresses σ eq, A and σ eq, B are obtained by substituting the equivalent strain ε eq obtained from the equation (25) into each hardening rule, and by giving the value of the weight coefficient α, the mixing rule is obtained by the equation (1). The equivalent stress σ eq, HR of is obtained.
一方、降伏関数fを用いても相当応力σeqを求めることができる（例えば、式（１２）や式（１６））。ここで、降伏関数fから求められる相当応力をσeq,YFとする。そして、降伏関数fを与える式に、σy＝bσxの関係（式（２０）参照）を代入すれば、σeq,YFは、引張方向の応力σxと相当応力σeq,YFの関数になる。そして、混合則から求めた相当応力σeq,HRと降伏関数から求めた相当応力σeq,YFは等しいため、σeq,HR＝σeq,YFとなるような引張方向の応力σxを算出する。 On the other hand, the equivalent stress σ eq can be obtained by using the yield function f (for example, equation (12) or equation (16)). Here, the equivalent stress obtained from the yield function f is σ eq, YF . Then, by substituting the relationship of σ y = bσ x (see equation (20)) into the equation that gives the yield function f, σ eq, YF becomes a function of the stress σ x in the tensile direction and the equivalent stress σ eq, YF become. Then, since the equivalent stress σ eq, HR determined from the mixing rule and the equivalent stress σ eq, YF determined from the yield function are equal, the tensile stress σ x is calculated such that σ eq, HR = σ eq, YF I do.
≪板厚の算出≫
前述のとおり、第２引張試験片２５においては、引張直角方向に変形量が異なるため、各微小領域３１での板厚tを考慮する必要がある。そして、板厚tは、初期板厚t0と板厚方向ひずみεzより求まり、板厚方向ひずみεzは体積一定条件より面内の２方向のひずみ測定値εx及びεyより計算できる。そこで、次式（２６）に示すように、各微小領域３１に設定した引張方向及び引張直角方向のひずみに基づいて、各微小領域３１の板厚tを算出する（Ｓ２１）。
≫Calculation of plate thickness≫
As described above, in the second tensile test piece 25, since the deformation amount differs in the direction perpendicular to the tensile direction, it is necessary to consider the plate thickness t in each minute region 31. Then, the thickness t is obtained from the initial thickness t 0 and the strain ε z in the thickness direction, and the strain ε z in the thickness direction can be calculated from the measured in-plane strains ε x and ε y under the constant volume condition. . Therefore, as shown in the following equation (26), the plate thickness t of each minute region 31 is calculated based on the strain in the tensile direction and the direction perpendicular to the tension set in each minute region 31 (S21).
≪微小領域引張荷重の算出≫
各微小領域３１について算出した引張方向の応力σxと板厚tを用いて、次式（２７）に示すように、各微小領域３１に作用する引張荷重を求める（Ｓ２３）。
≫Calculation of micro area tensile load 領域
Using the stress σ x in the tensile direction and the plate thickness t calculated for each minute region 31, a tensile load acting on each minute region 31 is obtained as shown in the following equation (27) (S 23).
式（２７）において、ΔTは微小領域引張荷重、dyは微小領域の幅である（図８（ｂ）参照）。 In Expression (27), ΔT is a minute region tensile load, and dy is a width of the minute region (see FIG. 8B).
≪引張荷重の推算≫
次式（２８）に示すように、各微小領域３１について求めた微小領域引張荷重ΔTを足し合わせて、第２引張試験片２５の引張直角方向の断面全体に作用する引張荷重Tを求める（Ｓ２５）。
≪Estimation of tensile load≫
As shown in the following expression (28), the tensile load T acting on the entire cross section of the second tensile test piece 25 in the direction perpendicular to the tensile direction is calculated by adding the microscopic area tensile loads ΔT obtained for the respective microscopic areas 31 (S25). ).
このように、引張荷重推算ステップＳ７においては、Ｓ１１〜Ｓ２５の手順により引張荷重Tを推算することができる。 Thus, in the tensile load estimating step S7, the tensile load T can be estimated by the procedures of S11 to S25.
＜重み係数決定ステップ＞
重み係数決定ステップＳ９は、引張荷重推算ステップＳ７において推算した引張荷重と引張荷重−ひずみ分布取得ステップＳ５において取得した引張荷重とが一致するように、前記混合則の重み係数αの値を決定するステップである。
<Weight coefficient determination step>
The weight coefficient determining step S9 determines the value of the weight coefficient α of the mixing rule so that the tensile load estimated in the tensile load estimating step S7 matches the tensile load acquired in the tensile load-strain distribution acquiring step S5. Step.
重み係数αの値を決定する具体的な手順として、引張荷重推算ステップＳ７において、仮の重み係数αを与えて引張荷重を推算し、該推算した引張荷重の値に基づいて重み係数αの値を変更し、引張荷重の推算値と取得した値とが一致するまで、図７に示すＳ１９〜Ｓ２５を繰り返す。これにより、式（５）に示す混合則の重み係数αの値を決定する。 As a specific procedure for determining the value of the weight coefficient α, in a tensile load estimation step S7, a temporary weight coefficient α is given to estimate a tensile load, and the value of the weight coefficient α is calculated based on the estimated tensile load value. Is changed, and S19 to S25 shown in FIG. 7 are repeated until the estimated value of the tensile load matches the acquired value. Thereby, the value of the weighting coefficient α of the mixing rule shown in Expression (5) is determined.
以上、本発明の実施の形態に係る応力−ひずみ関係推定方法によれば、従来の引張試験では得られない均一伸び以降の高ひずみ域における応力とひずみの関係を精度良く推定することができる。さらに、本発明に係る応力−ひずみ関係推定方法を金属薄板のプレス成形シミュレーションに適用することで、プレス成形で生じる割れやしわ、あるいはスプリングバックといった成形不良を高精度の予測することができる。そして、プレス成形シミュレーションの予測結果に基づいた金型設計や部品設計により、高品質なプレス成形品を得ることが可能となる。 As described above, according to the stress-strain relationship estimation method according to the embodiment of the present invention, the relationship between stress and strain in a high strain region after uniform elongation, which cannot be obtained by a conventional tensile test, can be accurately estimated. Furthermore, by applying the stress-strain relationship estimation method according to the present invention to a press forming simulation of a thin metal plate, it is possible to predict a forming defect such as a crack, a wrinkle, or a springback caused by press forming with high accuracy. Then, high-quality press-formed products can be obtained by die design and component design based on the prediction results of the press-forming simulation.
また、本発明によれば、既存の単軸引張試験装置を用いることができるため、特殊な試験機を用いることを要するものではなく、汎用性という面で実用性に優れている。 Further, according to the present invention, since an existing uniaxial tensile tester can be used, it is not necessary to use a special tester, and it is excellent in practicality in terms of versatility.
本発明に係る応力−ひずみ関係推定方法の作用効果について確認するための検証を行ったので、以下、これについて説明する。 Verification for confirming the operation and effect of the stress-strain relationship estimation method according to the present invention has been performed, and will be described below.
実施例では、まず、金属材料として板厚1.2mmの590MPa級鋼板の応力−ひずみ関係の推定を行った。 In the examples, first, a stress-strain relationship of a 590 MPa class steel sheet having a thickness of 1.2 mm as a metal material was estimated.
まず、図１５に示す形状の第１引張試験片１（JIS5号）を用いて引張試験を行い、均一伸びまでの応力−ひずみ関係を取得した。 First, a tensile test was performed using a first tensile test piece 1 (JIS No. 5) having the shape shown in FIG. 15 to obtain a stress-strain relationship up to uniform elongation.
そして、２種類の硬化則としてSwift則及びVoce則を選択し、均一伸びまでの応力−ひずみ関係に基づいて、Swift則及びVoce則それぞれの材料定数（式（３）及び式（４）参照）を同定した。表１に、同定した材料定数を示す。 Then, the Swift rule and the Voce rule are selected as two types of hardening rules, and based on the stress-strain relationship up to uniform elongation, the material constants of the Swift rule and the Voce rule (see equations (3) and (4)) Was identified. Table 1 shows the identified material constants.
均一伸び以降の相当応力σeqは、次式（２９）に示すように、Swift則の相当応力σeq,SwiftとVoce則の相当応力σeq,Voceの混合則で表す。 The equivalent stress σ eq after uniform elongation is expressed by a mixture rule of the equivalent stress σ eq, Swift of the Swift rule and the equivalent stress σ eq, Voce of the Voce rule, as shown in the following equation (29).
続いて、図９に示すように、機械加工で真円の穴形状１３を形成した第２引張試験片１１を用いて引張試験を行い、該引張試験中における引張荷重と第２引張試験片の表面におけるひずみ分布を取得した。
そして、穴形状１３の淵１３ａにおけるひずみが0.3、0.4、0.5及び0.6となった時間ステップにおいて、図７に示す手順Ｓ１１〜Ｓ２５により第２引張試験片１１に作用する引張荷重を推算した。
Subsequently, as shown in FIG. 9, a tensile test was performed using the second tensile test piece 11 in which a perfect circular hole shape 13 was formed by machining, and the tensile load during the tensile test and the tensile test of the second tensile test piece were performed. The strain distribution on the surface was obtained.
Then, in the time steps in which the strain at the edge 13a of the hole shape 13 was 0.3, 0.4, 0.5 and 0.6, the tensile load acting on the second tensile test piece 11 was estimated by steps S11 to S25 shown in FIG.
図１０に、第２引張試験片１１を用いた引張試験により取得した引張荷重と、当該引張試験で取得したひずみ分布の値を用いて推算した引張荷重を示す。
図１０において、横軸は、引張試験開始から経過した時間、縦軸は各時間における引張荷重の値であり、実線は、第２引張試験片１１を用いて取得した引張荷重の測定値、プロットは、Swift則、Voce則、及び混合則（式（５））の重み係数の値をα＝0.8として推算した引張荷重である。
FIG. 10 shows the tensile load obtained by the tensile test using the second tensile test piece 11 and the tensile load estimated by using the value of the strain distribution obtained by the tensile test.
In FIG. 10, the horizontal axis represents the time elapsed from the start of the tensile test, the vertical axis represents the value of the tensile load at each time, and the solid line represents the measured value of the tensile load obtained using the second tensile test piece 11. Is a tensile load estimated assuming that the value of the weight coefficient of the Swift rule, the Voce rule, and the mixing rule (Equation (5)) is α = 0.8.
Swift則、すなわち、混合則において重み係数α＝1として推算した引張荷重は、引張荷重の測定値より大きくなり、Voce則、すなわち、混合則において重み係数α＝0として推算した引張荷重の測定値よりも小さくなった。 The tensile load estimated by the Swift rule, that is, the weighting factor α = 1 in the mixing rule, is larger than the measured value of the tensile load. Smaller than.
これに対し、重み係数α＝0.8を与えた混合則により推算した引張荷重は、穴形状１３の淵１３ａにおけるひずみがいずれの値の場合においても、第２引張試験片１１を用いた引張試験における引張荷重の値と一致する結果となった。 On the other hand, the tensile load estimated by the mixing rule giving the weight coefficient α = 0.8 is the same in the tensile test using the second tensile test piece 11 regardless of the value of the strain at the edge 13 a of the hole shape 13. The result was consistent with the value of the tensile load.
この結果から、混合則の重み係数がα＝0.8と決定され、図１１に示すように、混合則により均一伸び以降の応力−ひずみ関係を推定できることが示された。 From this result, the weighting factor of the mixing rule was determined to be α = 0.8, and as shown in FIG. 11, it was shown that the stress-strain relationship after uniform elongation could be estimated by the mixing rule.
続いて、金属材料として板厚1.2mmの1180MPa級鋼板についても、上記と同様に応力−ひずみ関係の推定を行った。 Subsequently, a stress-strain relationship was also estimated for a 1180 MPa class steel sheet having a thickness of 1.2 mm as a metal material in the same manner as described above.
まず、図１５に示す形状のJIS5号の第１引張試験片１を用いて引張試験を行い、均一伸びまでの応力−ひずみ関係を取得した。そして、取得した応力−ひずみ関係から、Swift則（式（３））及びVoce則（式（４））それぞれの材料定数を同定した。同定した材料定数の値を表２に示す。 First, a tensile test was performed using the first tensile test piece 1 of JIS No. 5 having the shape shown in FIG. 15 to obtain a stress-strain relationship up to uniform elongation. Then, from the obtained stress-strain relationship, the material constants of the Swift law (Equation (3)) and the Voce law (Equation (4)) were identified. Table 2 shows the values of the identified material constants.
均一伸び以降の相当応力σeqは、前述の式（２９）に示すように、Swift則の相当応力σeq,SwiftとVoce則の相当応力σeq,Voceの混合則で表す。 The equivalent stress σ eq after the uniform elongation is expressed by a mixture rule of the equivalent stress σ eq, Swift of the Swift rule and the equivalent stress σ eq, Voce of the Voce rule, as shown in the above equation (29).
続いて、図１２に示すように、幅方向の両端に機械加工で真円の切り欠き形状２３を形成した第２引張試験片１１を用いて引張試験を行い、引張荷重とひずみ分布を取得した。
そして、切り欠き形状２３の淵２３ａにおけるひずみが0.2、0.3、0.35となった時間ステップにおけるひずみ分布の値から、図７に示す手順Ｓ１１〜Ｓ２５により第２引張試験片２１に作用する引張荷重を推算した。
Subsequently, as shown in FIG. 12, a tensile test was performed using a second tensile test piece 11 in which a perfect circular cutout shape 23 was formed at both ends in the width direction by machining to obtain a tensile load and a strain distribution. .
Then, from the values of the strain distribution at the time steps at which the strain at the edge 23a of the notch shape 23 becomes 0.2, 0.3, and 0.35, the tensile load acting on the second tensile test piece 21 in steps S11 to S25 shown in FIG. Estimated.
図１３に、第２引張試験片２１を用いた引張試験により取得した引張荷重と、当該引張試験で取得したひずみ分布の値を用いて推算した引張荷重を示す。
図１３において、横軸は、引張試験開始からの経過時間、縦軸は各時間における引張荷重の値であり、実線は、第２引張試験片１１を用いて取得した引張荷重の測定値、プロットは、Swift則、Voce則、及び混合則（式（５））の重み係数の値をα＝0.55として推算した引張荷重である。
FIG. 13 shows the tensile load obtained by the tensile test using the second tensile test piece 21 and the tensile load estimated using the value of the strain distribution obtained by the tensile test.
In FIG. 13, the horizontal axis represents the elapsed time from the start of the tensile test, the vertical axis represents the value of the tensile load at each time, and the solid line represents the measured value of the tensile load obtained using the second tensile test piece 11, plotted. Is the tensile load estimated by setting the value of the weighting coefficient of the Swift rule, the Voce rule, and the mixing rule (Equation (5)) to α = 0.55.
Swift則、すなわち、混合則において重み係数α＝1として推算した引張荷重は、引張荷重の測定値より大きくなり、Voce則、すなわち、混合則において重み係数α＝0として推算した引張荷重の測定値よりも小さくなった。 The tensile load estimated by the Swift rule, that is, the weighting factor α = 1 in the mixing rule, is larger than the measured value of the tensile load. Smaller than.
これに対し、重み係数α＝0.55を与えた混合則により推算した引張荷重は、切り欠き形状２３の淵２３ａにおけるひずみがいずれの値の場合においても、第２引張試験片２１を用いた引張試験におえる引張荷重の値と一致する結果となった。 On the other hand, the tensile load estimated by the mixing rule giving the weighting coefficient α = 0.55 indicates that the tensile test using the second tensile test piece 21 is performed regardless of the value of the strain at the edge 23 a of the notch 23. The result was in agreement with the value of the tensile load in Table 1.
この結果から、混合則の重み係数がα＝0.55と決定され、図１４に示すように、混合則により均一伸び以降の応力−ひずみ関係を推定できることが示された。 From this result, the weighting factor of the mixing rule was determined to be α = 0.55, and as shown in FIG. 14, it was shown that the stress-strain relationship after uniform elongation could be estimated by the mixing rule.
１ 第１引張試験片
３ 平行部
１１ 第２引張試験片
１３ 穴形状（真円）
１３ａ 淵
２１ 第２引張試験片
２３ 切り欠き形状（半円）
２３ａ 淵
２５ 第２引張試験片
２７ 第２引張試験片
２９ 第２引張試験片
３１ 微小領域
DESCRIPTION OF SYMBOLS 1 1st tensile test piece 3 Parallel part 11 2nd tensile test piece 13 Hole shape (true circle)
13a Fuchi 21 Second tensile test piece 23 Notch shape (semicircle)
23a edge 25 second tensile test piece 27 second tensile test piece 29 second tensile test piece 31 minute area
Claims (2)
平行部を有する第１引張試験片に引張荷重を作用させて、均一伸びまでの応力とひずみの関係を取得する応力−ひずみ関係取得ステップと、
応力とひずみの関係を与える２種類の硬化則を選択し、該２種類の硬化則それぞれの材料定数を、前記応力−ひずみ関係取得ステップで取得した応力−ひずみ関係に基づいて同定する材料定数同定ステップと、
引張方向の所定位置における引張直角方向の直線上に単数又は複数の穴形状及び／又は切り欠き形状を形成した第２引張試験片に引張荷重を作用させて、該引張荷重と前記引張直角方向の直線上におけるひずみの分布との関係を取得する引張荷重−ひずみ分布取得ステップと、
該取得したひずみの分布と、前記２種類の硬化則を仮の重み係数を用いて足し合わせた混合則により求められる応力とを用いて、前記第２引張試験片に作用する引張荷重を推算する引張荷重推算ステップと、
該引張荷重推算ステップにおいて推算した引張荷重と前記引張荷重−ひずみ分布取得ステップにおいて取得した引張荷重とが一致するように、前記混合則の重み係数の値を決定する重み係数決定ステップと、を備え、
前記引張荷重推算ステップは、
前記第２引張試験片について、前記引張直角方向に沿って複数の微小領域に分割し、
前記取得したひずみの分布に基づいて、各前記微小領域に前記引張方向及び前記引張直角方向のひずみを設定し、
各前記微小領域に設定した前記引張方向及び前記引張直角方向のひずみと前記混合則により求められる応力とを用いて各微小領域の引張方向の応力を算出し、
各前記微小領域に設定した前記引張方向及び前記引張直角方向のひずみに基づいて、各前記微小領域の板厚を算出し、
各前記微小領域について算出した前記引張方向の応力と前記板厚とから各前記微小領域に作用する引張荷重を算出し、
該算出した各前記微小領域に作用する引張荷重を足し合わせて前記第２引張試験片に作用する引張荷重を算出する、ことを特徴とする応力−ひずみ関係推定方法。 A stress-strain relationship estimation method for estimating the relationship between stress and strain of a metal material,
A stress-strain relationship obtaining step of applying a tensile load to a first tensile test piece having a parallel portion to obtain a relationship between stress and strain up to uniform elongation,
Material constant identification for selecting two types of hardening rules giving the relationship between stress and strain, and identifying the material constants of the two types of hardening rules based on the stress-strain relationship obtained in the stress-strain relationship obtaining step. Steps and
A tensile load is applied to a second tensile test piece having one or more hole shapes and / or notched shapes formed on a straight line in a tensile perpendicular direction at a predetermined position in a tensile direction, and the tensile load and the tensile perpendicular direction are applied. Tensile load-strain distribution acquisition step of acquiring the relationship with the distribution of strain on a straight line,
The tensile load acting on the second tensile test piece is estimated using the obtained strain distribution and the stress obtained by the mixing rule obtained by adding the two types of hardening rules using a temporary weighting coefficient. Tensile load estimation step,
A weighting factor determining step of determining a value of a weighting factor of the mixing rule, such that the tensile load estimated in the tensile load estimating step and the tensile load obtained in the tensile load-strain distribution obtaining step match. ,
The tensile load estimating step,
The second tensile test piece is divided into a plurality of minute regions along the direction perpendicular to the tensile direction,
Based on the obtained distribution of strain, set the strain in the tensile direction and the tensile perpendicular direction to each of the micro regions,
Using the strain in the tensile direction and the direction perpendicular to the tension set in each of the micro regions and the stress determined by the mixing rule, calculate the stress in the tensile direction of each of the micro regions,
Based on the strain in the tensile direction and the tensile perpendicular direction set in each of the micro regions, calculate the thickness of each of the micro regions,
Calculate a tensile load acting on each of the micro regions from the tensile direction stress and the plate thickness calculated for each of the micro regions,
A method for estimating a stress-strain relationship, comprising: calculating a tensile load acting on the second tensile test piece by adding the calculated tensile loads acting on each of the minute regions.
（ａ）各前記微小領域に設定した引張方向及び引張直角方向のひずみから、ひずみ増分を算出する。
（ｂ）該算出したひずみ増分比から各前記微小領域における引張方向及び引張直角方向の応力比を算出する。
（ｃ）各前記微小領域に設定したひずみから算出した前記相当ひずみ及び前記応力比と、前記混合則により算出した相当応力とに基づいて、各前記微小領域の前記引張方向の応力を算出する。 The stress-strain relationship estimating method according to claim 1, wherein the stress in the tensile direction of each of the micro regions in the tensile load estimating step is calculated according to the following procedures (a) to (c).
(A) Calculating the strain increment from the strain in the tensile direction and the direction perpendicular to the tensile direction set in each of the minute regions.
(B) calculating the stress ratio in the tensile direction and the tensile perpendicular direction in each of the micro regions from the calculated strain increment ratio.
(C) calculating the stress in the tensile direction of each of the minute regions based on the equivalent strain and the stress ratio calculated from the strain set in each of the minute regions and the equivalent stress calculated by the mixing rule.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111812023A (en) * | 2020-06-24 | 2020-10-23 | 河钢股份有限公司邯郸分公司 | Sheet material wrinkling performance testing method based on perforated sample unidirectional stretching |
| CN111948041A (en) * | 2020-07-13 | 2020-11-17 | 首钢集团有限公司 | Method for determining elastic-plastic transition boundary line of high-speed tensile plate-shaped sample |
| WO2021205693A1 (en) * | 2020-04-07 | 2021-10-14 | Ｊｆｅスチール株式会社 | Method for identifying constriction limit strain of metal plate |
| CN113865954A (en) * | 2021-08-26 | 2021-12-31 | 唐山钢铁集团有限责任公司 | Construction method of non-contact forming limit diagram |
| CN114112685A (en) * | 2021-12-29 | 2022-03-01 | 国网新源控股有限公司 | Method for determining early-stage consolidation stress of on-site compacted soil-rock mixture |
| WO2022185883A1 (en) * | 2021-03-03 | 2022-09-09 | 株式会社クラレ | Breakage prediction program and breakage prediction method |
| KR20230052148A (en) * | 2021-10-12 | 2023-04-19 | 경상국립대학교산학협력단 | Method of analyzing and evaluating flow stress or metal forming process using instability index |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2007232714A (en) * | 2006-02-01 | 2007-09-13 | Nippon Steel Corp | Method and apparatus for acquiring breaking limit, program and recording medium |
| JP2007285832A (en) * | 2006-04-14 | 2007-11-01 | Nippon Steel Corp | System and method for acquiring breaking point, system and method for estimating break, programs and recording media of these method |
| JP2011022125A (en) * | 2009-06-18 | 2011-02-03 | Polyplastics Co | Method of measuring local stress, method of deriving stress-strain curve in resin material, and method of predicting lifetime of resin molding |
| JP2012104042A (en) * | 2010-11-12 | 2012-05-31 | Kobe Steel Ltd | Prediction method of uniform extension and prediction program for uniform extension |
| JP2014077700A (en) * | 2012-10-10 | 2014-05-01 | Mazda Motor Corp | Method and device for calculating dynamic physical quantity |
| JP2014178168A (en) * | 2013-03-14 | 2014-09-25 | Jfe Steel Corp | Stress-distortion relation simulating method, spring-back extent predicting method, and spring-back analyzing apparatus |
| WO2014181491A1 (en) * | 2013-05-10 | 2014-11-13 | 新日鐵住金株式会社 | Deformation analysis device, deformation analysis method, and program |
-
2018
- 2018-09-14 JP JP2018172102A patent/JP6958521B2/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2007232714A (en) * | 2006-02-01 | 2007-09-13 | Nippon Steel Corp | Method and apparatus for acquiring breaking limit, program and recording medium |
| JP2007285832A (en) * | 2006-04-14 | 2007-11-01 | Nippon Steel Corp | System and method for acquiring breaking point, system and method for estimating break, programs and recording media of these method |
| JP2011022125A (en) * | 2009-06-18 | 2011-02-03 | Polyplastics Co | Method of measuring local stress, method of deriving stress-strain curve in resin material, and method of predicting lifetime of resin molding |
| JP2012104042A (en) * | 2010-11-12 | 2012-05-31 | Kobe Steel Ltd | Prediction method of uniform extension and prediction program for uniform extension |
| JP2014077700A (en) * | 2012-10-10 | 2014-05-01 | Mazda Motor Corp | Method and device for calculating dynamic physical quantity |
| JP2014178168A (en) * | 2013-03-14 | 2014-09-25 | Jfe Steel Corp | Stress-distortion relation simulating method, spring-back extent predicting method, and spring-back analyzing apparatus |
| WO2014181491A1 (en) * | 2013-05-10 | 2014-11-13 | 新日鐵住金株式会社 | Deformation analysis device, deformation analysis method, and program |
Non-Patent Citations (2)
| Title |
|---|
| CAPILLA, GUSTAVO ET AL.: "Determination of uniaxial large-strain workhardening of high-strength steel sheets from in-plane str", JOURNAL OF MATERIALS PROCESSING TECHNOLOGY [ONLINE], vol. 243, JPN6019050802, 8 December 2016 (2016-12-08), pages 152 - 169, XP029913610, ISSN: 0004468591, DOI: 10.1016/j.jmatprotec.2016.12.002 * |
| 神原 大輔 ほか: "金属材料の大ひずみ域における応力-ひずみ曲線の決定", 中国四国支部総会・講演会 講演論文集, vol. 第52巻, セッションID 101, JPN6019050799, 2014, pages 1 - 2, ISSN: 0004468590 * |
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2021205693A1 (en) * | 2020-04-07 | 2021-10-14 | Ｊｆｅスチール株式会社 | Method for identifying constriction limit strain of metal plate |
| JP2021164933A (en) * | 2020-04-07 | 2021-10-14 | Ｊｆｅスチール株式会社 | Method for identifying constriction limit strain of metal plate |
| EP4134183A4 (en) * | 2020-04-07 | 2023-09-27 | JFE Steel Corporation | Method for identifying constriction limit strain of metal plate |
| CN111812023A (en) * | 2020-06-24 | 2020-10-23 | 河钢股份有限公司邯郸分公司 | Sheet material wrinkling performance testing method based on perforated sample unidirectional stretching |
| CN111948041A (en) * | 2020-07-13 | 2020-11-17 | 首钢集团有限公司 | Method for determining elastic-plastic transition boundary line of high-speed tensile plate-shaped sample |
| CN111948041B (en) * | 2020-07-13 | 2023-03-17 | 首钢集团有限公司 | Method for determining elastic-plastic transition boundary line of high-speed tensile plate-shaped sample |
| WO2022185883A1 (en) * | 2021-03-03 | 2022-09-09 | 株式会社クラレ | Breakage prediction program and breakage prediction method |
| CN113865954A (en) * | 2021-08-26 | 2021-12-31 | 唐山钢铁集团有限责任公司 | Construction method of non-contact forming limit diagram |
| KR20230052148A (en) * | 2021-10-12 | 2023-04-19 | 경상국립대학교산학협력단 | Method of analyzing and evaluating flow stress or metal forming process using instability index |
| KR102548622B1 (en) | 2021-10-12 | 2023-06-29 | 경상국립대학교산학협력단 | Method of analyzing and evaluating flow stress or metal forming process using instability index |
| CN114112685A (en) * | 2021-12-29 | 2022-03-01 | 国网新源控股有限公司 | Method for determining early-stage consolidation stress of on-site compacted soil-rock mixture |
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