JP2017053807A - Heat treatment simulation method of steel and heat treatment simulation program of steel - Google Patents
Heat treatment simulation method of steel and heat treatment simulation program of steel Download PDFInfo
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Abstract
Description
この発明は、鋼の熱処理時のシミュレーションを行う鋼の熱処理シミュレーション方法および鋼の熱処理シミュレーションプログラムに関するものである。 The present invention relates to a steel heat treatment simulation method and a steel heat treatment simulation program for performing a simulation during heat treatment of steel.
鋼においては、材料に所要の機械的性質を付与するために様々な熱処理（焼ならし、焼入れ、焼戻し）が施される。大型化により熱処理時に生じる応力が増加し、割れや変形などの要因となることが懸念されるため、熱処理により生じる応力を数値解析により把握しておくことは工程設計を行ううえで非常に有用である。
熱処理の冷却中に生じるひずみ及び応力の解析手法に関する研究は古くから数多く行われている。例えば、特許文献１では、直径７５ｍｍ、高さ１８０ｍｍの丸棒を水スプレー焼入れした場合において熱処理によるひずみを精度よく解析することのできる熱処理シミュレーション方法が提案されている。また、特許文献２では、歯車を焼入れした時のひずみを精度よく推定するシミュレーション方法が提案されている。
従来、熱処理中のひずみを精度良く推定するため、弾性ひずみ、塑性ひずみ、熱ひずみに加えて、変態ひずみや変態塑性ひずみを全ひずみに含めることが検討されている。
In steel, various heat treatments (normalizing, quenching, and tempering) are performed to impart the required mechanical properties to the material. It is feared that the stress generated during heat treatment will increase due to the increase in size, which may cause cracks and deformations, so it is very useful for process design to grasp the stress generated by heat treatment by numerical analysis. is there.
Many studies have been conducted on the analysis methods of strain and stress generated during cooling of heat treatment. For example,
Conventionally, in order to accurately estimate strain during heat treatment, it has been studied to include transformation strain and transformation plastic strain in total strain in addition to elastic strain, plastic strain, and thermal strain.
しかし、上述の研究は、比較的小型部材の焼入れ冷却過程を対象としており、大型鍛鋼品を扱った例は見られない。大型鍛鋼品では、加熱・冷却過程が長時間となる特徴があり、特に焼ならし処理では空冷が行われるため、水冷や油冷が行われる焼入れ処理に比較してその冷却速度はさらに遅くなる。この冷却速度の差異により、冷却中に生じる応力の変化や冷却後の残留応力の分布が大きく異なるため、従来のシミュレーション方法では大型鍛鋼品のひずみおよび応力を精度良く求めることができないという課題がある。 However, the above-mentioned research is aimed at the quenching and cooling process of relatively small members, and no examples of handling large forged steel products are found. Large forged steel products are characterized by a long heating / cooling process, especially air cooling during normalizing, and the cooling rate is even slower compared to quenching where water or oil cooling is used. . Due to this difference in the cooling rate, the change in stress generated during cooling and the distribution of residual stress after cooling differ greatly, so there is a problem that the strain and stress of large forged steel products cannot be accurately obtained with the conventional simulation method. .
本発明は上記課題を解決するためになされたもので、大型鍛鋼品の熱処理においてもひずみ及び応力を精度よく解析することのできるシミュレーション方法およびシミュレーションプログラムを提供することを目的としている。 The present invention has been made to solve the above problems, and an object of the present invention is to provide a simulation method and a simulation program capable of accurately analyzing strain and stress even in heat treatment of large forged steel products.
本発明の鋼の熱処理シミュレーション方法のうち、第１の形態の発明は、
鋼の熱処理シミュレーション方法であって、
前記鋼の材料データとして鋼の各相および各温度における物性値を用いて、有限要素モデル中の各節点における温度の時間変化を有限要素法によって計算する熱伝導解析を行い、
前記熱伝導解析で得られた各節点の温度を温度荷重として、前記鋼の材料データとして鋼の物性値を用い、各要素の積分点におけるひずみ量として、少なくとも変態塑性ひずみとクリープひずみとを算出し、これらの和に基づいて、前記鋼の内部応力の変化を計算する弾塑性応力解析を行うことを特徴とする。
Of the heat treatment simulation methods for steel of the present invention, the first aspect of the invention is:
A steel heat treatment simulation method,
Using the physical properties of each phase and temperature of the steel as the material data of the steel, conduct the heat conduction analysis to calculate the time change of the temperature at each node in the finite element model by the finite element method,
Using the temperature of each node obtained in the heat conduction analysis as the temperature load, using the physical property value of the steel as the material data of the steel, and calculating at least the transformation plastic strain and creep strain as the strain amount at the integration point of each element And based on these sums, the elastic-plastic stress analysis which calculates the change of the internal stress of the said steel is performed, It is characterized by the above-mentioned.
第２の形態の鋼の熱処理シミュレーション方法の発明は、前記形態の本発明において、
前記熱伝導解析の材料データの物性値として、鋼の各相および各温度における比熱、密度、熱伝導率と、境界条件として熱処理時の熱伝達率とを用い、
前記弾塑性応力解析の材料データとして、鋼の各相および各温度における弾性係数、ポアソン比、硬化曲線を用い、前記温度荷重、前記弾性係数、前記ポアソン比、前記硬化曲線を用いて、各要素の積分点におけるひずみ量を、弾性ひずみ、塑性ひずみ、熱ひずみ、変態ひずみ、変態塑性ひずみ、クリープひずみとして算出することを特徴とする。
The invention of the heat treatment simulation method of the steel of the second form is the present invention of the above form,
As the physical property values of the material data of the heat conduction analysis, specific heat, density, thermal conductivity at each phase and temperature of steel, and heat transfer coefficient during heat treatment as boundary conditions,
As the material data of the elastoplastic stress analysis, the elastic coefficient, Poisson's ratio, and hardening curve in each phase and temperature of steel are used, and each element using the temperature load, the elastic modulus, the Poisson's ratio, and the hardening curve. The amount of strain at the integration point is calculated as elastic strain, plastic strain, thermal strain, transformation strain, transformation plastic strain, and creep strain.
第３の形態の鋼の熱処理シミュレーション方法の発明は、前記形態の本発明において、前記熱伝導解析における材料データとして、初期の温度分布をさらに用いることを特徴とする。 The invention of the heat treatment simulation method for steel of the third aspect is characterized in that, in the present invention of the above aspect, an initial temperature distribution is further used as material data in the heat conduction analysis.
第４の形態の鋼の熱処理シミュレーション方法の発明は、前記形態の本発明において、前記熱伝導解析において、冷却時の各相および各温度における材料データを予め測定し、該データを用いて各温度における各相の体積分率から線形混合則を適用して熱伝導解析を行うことを特徴とする。 According to the fourth aspect of the invention of the heat treatment simulation method for steel of the present invention, in the present invention of the above aspect, in the heat conduction analysis, material data at each phase and each temperature at the time of cooling is measured in advance, and each temperature is measured using the data. The heat conduction analysis is performed by applying the linear mixing rule from the volume fraction of each phase in.
第５の形態の鋼の熱処理シミュレーション方法の発明は、前記形態の本発明において、前記弾塑性応力解析において、冷却時の各相および各温度における材料データを予め測定し、該データを用いて各温度における各相の体積分率から線形混合則を適用して熱伝導解析を行うことを特徴とする。 In the invention of the heat treatment simulation method for steel of the fifth aspect, in the invention of the above aspect, in the elastic-plastic stress analysis, material data in each phase and each temperature at the time of cooling is measured in advance, and each data is used using the data. The heat conduction analysis is performed by applying a linear mixing rule from the volume fraction of each phase at temperature.
第６の形態の鋼の熱処理シミュレーション方法の発明は、前記形態の本発明において、前記鋼が５００ｍｍ以上の肉厚からなる材料であることを特徴とする。 An invention of a heat treatment simulation method for steel of a sixth aspect is characterized in that, in the present invention of the above aspect, the steel is a material having a thickness of 500 mm or more.
本発明の鋼の熱処理シミュレーションプログラムのうち、第１の形態の発明は、
表示部と、操作入力を受ける操作部と、を有する熱処理シミュレーション解析装置を制御する制御部であって、
熱伝導解析のために、鋼の材料データとして鋼の各相および各温度における物性値を取得する際に、少なくとも一つの測定値を前記操作部を通して取得する熱伝導データ取得ステップと、
前記熱伝導データ取得ステップで得たデータを用いて、有限要素モデル中の各節点における温度の時間変化を有限要素法によって計算し、得られた各節点の温度を温度荷重として取得する熱伝導解析ステップと、
弾塑性応力解析のために、前記鋼の材料データとして鋼の各相および各温度における物性値を取得する際に、少なくとも一つの測定値を前記操作部を通して取得する弾塑性データ取得ステップと、
前記弾塑性データ取得ステップにおける各要素の積分点におけるひずみ量として、少なくとも、変態塑性ひずみとクリープひずみとを算出して、これらの和に基づいて前記鋼の内部応力の変化を計算する弾塑性応力解析ステップと、
前記内部応力の変化に基づいて、ひずみまたは／および応力を、必要に応じて前記表示部に表示する表示ステップと、を有することを特徴とする。
Among the steel heat treatment simulation programs of the present invention, the invention of the first aspect is
A control unit that controls a heat treatment simulation analysis apparatus having a display unit and an operation unit that receives an operation input,
A heat conduction data acquisition step of acquiring at least one measured value through the operation unit when acquiring physical property values at each phase and temperature of steel as material data for steel for heat conduction analysis;
Using the data obtained in the heat conduction data acquisition step, the temperature change at each node in the finite element model is calculated by the finite element method, and the obtained temperature is obtained as a temperature load. Steps,
An elastic-plastic data acquisition step for acquiring at least one measurement value through the operation unit when acquiring physical properties at each phase and temperature of the steel as material data for the elastic-plastic stress analysis;
As the amount of strain at the integration point of each element in the elastoplastic data acquisition step, at least the transformation plastic strain and creep strain are calculated, and the change in internal stress of the steel is calculated based on the sum of these. An analysis step;
A display step of displaying strain or / and stress on the display unit as needed based on the change in the internal stress.
第２の形態の鋼の熱処理シミュレーションプログラムは、前記形態の発明において、熱伝導データ取得ステップで、鋼の材料データの物性値として鋼の各相および各温度における比熱、密度、熱伝導率と、境界条件として熱処理時の熱伝達率の物性値を取得し、
弾塑性データ取得ステップで、前記鋼の材料データの物性値として鋼の各相および各温度における弾性係数、ポアソン比、硬化曲線を取得し、
弾塑性応力解析ステップでは、前記弾塑性データ取得ステップにおける各要素の積分点におけるひずみ量を、弾性ひずみ、塑性ひずみ、熱ひずみ、変態ひずみ、変態塑性ひずみ、クリープひずみを算出し、これらの和に基づいて前記鋼の内部応力の変化を計算することを特徴とする。
The heat treatment simulation program for steel of the second form is the heat conduction data acquisition step in the invention of the above form, and the specific heat, density, and thermal conductivity at each phase and each temperature of the steel as physical property values of the steel material data, Obtain physical properties of heat transfer coefficient during heat treatment as boundary conditions,
In the elasto-plastic data acquisition step, acquire the elastic modulus, Poisson's ratio, hardening curve at each phase and each temperature of the steel as the physical property value of the material data of the steel,
In the elasto-plastic stress analysis step, the elastic strain, plastic strain, thermal strain, transformation strain, transformation plastic strain, and creep strain are calculated as the strain amount at the integration point of each element in the elasto-plastic data acquisition step. Based on this, the change of the internal stress of the steel is calculated.
以上述べたように、本発明により大型鍛鋼品においても熱処理した際のひずみや応力を精度良く推定することができる。 As described above, according to the present invention, it is possible to accurately estimate strain and stress at the time of heat treatment even in a large forged steel product.
本実施形態では、熱伝導解析用の有限要素モデルに、材料データとして鋼の各相・各温度における比熱、密度、熱伝導率を入力し、境界条件として熱伝達率を入力し、有限要素モデル中の各節点における温度の時間変化を計算する熱伝導解析部を有する。
弾塑性応力解析用の有限要素モデルに、熱伝導解析で得られた各節点の温度を温度荷重として入力し、材料データとして鋼の各相・各温度における弾性係数、ポアソン比、硬化曲線を入力し、各要素の積分点におけるひずみ量を弾性ひずみ、塑性ひずみ、熱ひずみに加えて、変態ひずみ、変態塑性ひずみ、クリープひずみの和として求め、鋼の内部応力の変化を計算する弾塑性応力解析部を有する。
熱伝導解析部と弾塑性応力解析部の実現は、ＣＰＵとこれを動作させるプログラムとによって行うことができる。
In this embodiment, specific heat, density, and thermal conductivity at each phase and temperature of steel are input as material data to a finite element model for heat conduction analysis, and heat transfer coefficient is input as boundary conditions. It has a heat conduction analysis part that calculates the time change of temperature at each node.
In the finite element model for elasto-plastic stress analysis, the temperature of each node obtained by heat conduction analysis is input as a temperature load, and the elastic modulus, Poisson's ratio, and hardening curve at each phase and temperature of steel are input as material data. In addition to elastic strain, plastic strain, and thermal strain, the amount of strain at the integration point of each element is obtained as the sum of transformation strain, transformation plastic strain, and creep strain, and elasto-plastic stress analysis that calculates the change in internal stress of steel Part.
Realization of the heat conduction analysis unit and the elasto-plastic stress analysis unit can be performed by a CPU and a program for operating the CPU.
変態挙動
鋼をオーステナイト相（γ相）から冷却すると、フェライト・パーライト、ベイナイト、マルテンサイト等のα相に相変態が生じる。オーステナイト相から所定の冷却速度で冷却した時の鋼の寸法変化を測定することで、冷却条件に応じた変態挙動を算出することができる。
マルテンサイト変態であれば変態挙動は温度のみの関数で表すことができ、式（１）に示すＫｏｉｓｔｉｎｅｎ−Ｍａｒｂｕｒｇｅｒ則が知られている。ベイナイト変態等の拡散型変態では変態挙動は温度と時間の関数で表され、式（２）に示すＪｏｈｎｓｏｎ−Ｍｅｈｌの式が知られている。
Transformation Behavior When steel is cooled from the austenite phase (γ phase), phase transformation occurs in the α phase of ferrite, pearlite, bainite, martensite and the like. By measuring the dimensional change of the steel when cooled from the austenite phase at a predetermined cooling rate, the transformation behavior according to the cooling conditions can be calculated.
If it is a martensitic transformation, the transformation behavior can be expressed by a function of only temperature, and the Koistinen-Marburger rule shown in the equation (1) is known. In diffusion type transformation such as bainite transformation, the transformation behavior is expressed as a function of temperature and time, and the Johnson-Mehl equation shown in equation (2) is known.
ここで、ξは各相の体積率、Ｔは温度、Ｍｓはマルテンサイト変態開始温度、ｔは時間、Ｋは温度の関数、ｎは定数である。 Here, ξ is the volume fraction of each phase, T is the temperature, Ms is the martensitic transformation start temperature, t is time, K is a function of temperature, and n is a constant.
熱伝導解析
物体の熱伝導方程式は、式（３）で表すことができ、材料物性値（比熱、密度、熱伝導率）の他に、初期条件（初期の温度分布）と境界条件（熱伝達率など）を与えることで解くことができる。例えば、一次元半無限体が一様な温度Ｔ０で保持され、表面温度がＴｓとなった場合には、式（３）は、式（４）と簡単に表され、内部の温度分布は式（５）のように求まる。
複雑な形状では有限要素法を用いて解くことができ、汎用ＦＥＭコードとしては、例えば、ＡＢＡＱＵＳ（登録商標）やＡＮＳＹＳ（登録商標）等を用いることができる。
Heat conduction analysis The heat conduction equation of an object can be expressed by equation (3). In addition to the material properties (specific heat, density, thermal conductivity), initial conditions (initial temperature distribution) and boundary conditions (heat transfer) It can be solved by giving a rate). For example, when the one-dimensional semi-infinite body is held at a uniform temperature T0 and the surface temperature becomes Ts, the equation (3) is simply expressed as the equation (4), and the internal temperature distribution is expressed by the equation It is obtained as in (5).
Complex shapes can be solved using the finite element method, and for example, ABAQUS (registered trademark) or ANSYS (registered trademark) can be used as a general-purpose FEM code.
冷却時の材料物性値は温度及び相変態によって変化するが、所定の冷却速度で生じる各相（γ相、α相）の各温度における物性値をあらかじめ測定し、各温度における各相の体積分率から線形混合則を適用して求めることができる。熱伝導解析用の物性値および変態潜熱による比熱の変化量は式（６）に示され、添え字のｉは各相を表している。 The material property value during cooling changes depending on the temperature and phase transformation, but the physical property value at each temperature of each phase (γ phase, α phase) generated at a predetermined cooling rate is measured in advance, and the volume of each phase at each temperature is measured. The linear mixing rule can be applied from the rate. The physical property value for heat conduction analysis and the amount of change in specific heat due to latent heat of transformation are shown in Equation (6), and the subscript i represents each phase.
例えば、密度はアルキメデス法を、比熱は断熱連続法及びレーザーフラッシュ法を、熱伝導率はレーザーフラッシュ法などを用いて測定することができる。また、冷却時の変態潜熱はＤＳＣ法（示差走査熱量測定法）で測定した値を用いることができる。
但し、本発明としては、物性値の測定方法が特定のものに限定されるものではなく、既知の方法を用いることができる。
For example, the density can be measured using the Archimedes method, the specific heat can be measured using the adiabatic continuous method and the laser flash method, and the thermal conductivity can be measured using the laser flash method. Moreover, the value measured by DSC method (differential scanning calorimetry) can be used for the transformation latent heat at the time of cooling.
However, in the present invention, the method for measuring physical properties is not limited to a specific one, and a known method can be used.
ここで、Ｔは温度、ρは密度、ｃは比熱、λは熱伝導率、Ｑは発熱量、ｔは時間、ｘは端部からの距離である。 Here, T is temperature, ρ is density, c is specific heat, λ is thermal conductivity, Q is calorific value, t is time, and x is the distance from the end.
弾塑性応力解析
弾塑性応力解析における支配方程式は、応力とひずみの関係（材料構成則）、変位とひずみの関係、仮想仕事の原理で表され、それぞれ式（７）に示される。式（７）から要素剛性マトリックス及び剛性方程式が導かれ、例えば平面応力状態における三角形要素に外部荷重が作用する場合では式（８）及び式（９）で表される。
Elasto-plastic stress analysis The governing equation in elasto-plastic stress analysis is expressed by the relationship between stress and strain (material constitutive law), the relationship between displacement and strain, and the principle of virtual work, and is expressed by equation (7). The element stiffness matrix and the stiffness equation are derived from the equation (7). For example, when an external load is applied to the triangular element in the plane stress state, it is represented by the equations (8) and (9).
材料の物性値及び外部荷重と境界条件の下で剛性方程式を解いて変位量を求め、変位量からひずみ及び応力を求めることができる。
材料構成則における全ひずみ増分を式（１０）に、構成則における処理方法の模式図を図１に示す。変態塑性ひずみには、式（１０）に示すＤｅｓａｌｏｓの式以外にも、Ａｂｒａｓｓａｒｔの式などを用いることができる。クリープひずみには、式（１０）に示すＮｏｒｔｏｎ則以外にも、Ｂａｉｌｅｙ−Ｎｏｒｔｏｎ則などを用いることができる
The displacement equation can be obtained by solving the stiffness equation under the physical property value of the material and the external load and the boundary condition, and the strain and stress can be obtained from the displacement amount.
The total strain increment in the material constitutive law is shown in Expression (10), and a schematic diagram of the processing method in the constitutive law is shown in FIG. In addition to the Desalos equation shown in Equation (10), the Abrassart equation can be used for the transformation plastic strain. In addition to the Norton rule shown in Equation (10), the Bailey-Norton rule can be used for the creep strain.
図１に示す材料構成速の内容を具体的に説明する。
はじめに、現ステップと次ステップにおける温度の差から熱ひずみ増分が計算される（ステップｓ１）。次いで、変態温度域かの判定がなされる（ステップｓ２）。現ステップにおける温度が変態温度域内の場合（ステップｓ２、Ｙｅｓ）には、相変態の進行によって生じる変態ひずみ増分と変態塑性ひずみ増分が計算される（ステップｓ３）。全ひずみから、非弾性ひずみ（塑性ひずみ、熱ひずみ、変態ひずみ、変態塑性ひずみ、クリープひずみ）を除き（ステップｓ３）、得られたひずみ量を仮想的な弾性ひずみとして弾性計算が行われ（ステップｓ４）、得られた応力（試行弾性応力）を用いて、降伏判定が行われる（ステップｓ５）。
現ステップにおける温度が変態温度域内でない場合（ステップｓ２、Ｎｏ）には、変態ひずみ増分と変態塑性ひずみ増分はゼロとなる。全ひずみから、非弾性ひずみ（塑性ひずみ、熱ひずみ、変態ひずみ、変態塑性ひずみ、クリープひずみ）を除き（ステップｓ３）、得られたひずみ量を仮想的な弾性ひずみとして弾性計算が行われる（ステップｓ４）。
The contents of the material composition speed shown in FIG. 1 will be specifically described.
First, the thermal strain increment is calculated from the temperature difference between the current step and the next step (step s1). Next, it is determined whether the temperature is in the transformation temperature range (step s2). If the temperature in the current step is within the transformation temperature range (step s2, Yes), a transformation strain increment and a transformation plastic strain increment caused by the progress of the phase transformation are calculated (step s3). From the total strain, inelastic strain (plastic strain, thermal strain, transformation strain, transformation plastic strain, creep strain) is removed (step s3), and the elastic strain is calculated with the obtained strain amount as a virtual elastic strain (step). s4) Yield determination is performed using the obtained stress (trial elastic stress) (step s5).
If the temperature at the current step is not within the transformation temperature range (step s2, No), the transformation strain increment and the transformation plastic strain increment are zero. From the total strain, inelastic strain (plastic strain, thermal strain, transformation strain, transformation plastic strain, creep strain) is removed (step s3), and the elastic calculation is performed with the obtained strain amount as a virtual elastic strain (step). s4).
降伏関数にはミーゼスの降伏関数を用い、硬化則はバウシンガー効果を考慮した移動硬
化則を用いることができる。計算機上で降伏状態を実現するためには、図２に示すリターンマッピング法を用いることができる。降伏する場合（ステップｓ５、Ｙｅｓ）には、塑性ひずみ増分とクリープひずみ増分を算出し（ステップｓ６）、降伏しない場合（ステップｓ５、Ｎｏ）は、クリープひずみ増分のみを算出する（ステップｓ７）。いずれの場合でも、現ステップ終点におけるコンシステント接線係数を算出する（ステップｓ８）。コンシスト接線係数は応力増分とひずみ増分の関係を表すものであり、現ステップで生じた各ひずみ増分に応じて算出される。
これらの解析は、汎用ＦＥＭコード（ＡＢＡＱＵＳやＡＮＳＹＳなど）にそのユーザーサブルーチンを用いて独自の材料構成則（応力とひずみの関係）を組み込んで実施できる。
As the yield function, Mises' yield function can be used, and the kinematic hardening law considering the Bauschinger effect can be used as the hardening law. In order to realize the yield state on the computer, the return mapping method shown in FIG. 2 can be used. When yielding (step s5, Yes), the plastic strain increment and creep strain increment are calculated (step s6), and when not yielding (step s5, No), only the creep strain increment is calculated (step s7). In either case, the consistent tangent coefficient at the current step end point is calculated (step s8). The consistent tangent coefficient represents the relationship between the stress increment and the strain increment, and is calculated according to each strain increment generated in the current step.
These analyzes can be performed by incorporating a unique material constitutive law (relationship between stress and strain) into the general-purpose FEM code (ABAQUS, ANSYS, etc.) using its user subroutine.
リターンマッピングは、現ステップでの応力状態σｉと降伏曲面ｆｉに対して、次ステップにおける変形を弾性変形と仮定して、試行弾性応力σｉ ｔｒが計算される。σｉ ｔｒが現ステップの降伏曲面ｆｉを超える場合には、降伏を生じると判断される。その場合、硬化曲線にそって変形が進行し、後退差分（陰解法）であるＮｅｗｔｏｎ−Ｒａｐｈｓｏｎ法を用いた収束計算により、次ステップにおける塑性ひずみが求まり、応力σｉ＋１と降伏曲面ｆｉ＋１が求まる。σｉ ｔｒが現ステップの降伏曲面ｆｉを超えない場合には、降伏曲面は変化せず、σｉ＋１＝σｉ ｔｒとなり、応力が更新される。 In the return mapping, the trial elastic stress σ i tr is calculated by assuming that the deformation in the next step is elastic deformation with respect to the stress state σ i in the current step and the yield surface f i . If σ i tr exceeds the yield surface f i of the current step, it is determined that yielding will occur. In that case, deformation progresses along the curing curve by convergence calculation using the Newton-Raphson method is backward difference (implicit) Motomari is plastic strain in the next step, the stress sigma i + 1 and the yield surface f i + 1 is obtained. If σ i tr does not exceed the yield surface f i of the current step, the yield surface does not change, σ i + 1 = σ i tr , and the stress is updated.
ここで、σは応力、εは全ひずみ、δは変位、Ｄは応力−ひずみマトリックス（コンシステント接線係数）、Ｂはひずみ−変位マトリックス、δ＊は仮想変位、ε＊は仮想ひずみ、Ｐは単位面積当たりの表面力、Ｆは単位体積当たりの体積力、ｆは節点力、Ｋは要素剛性マトリックス、ｔは三角形要素の板厚、Δは三角形要素の面積、Ｅは弾性係数、νはポアソン比である。 Where σ is stress, ε is total strain, δ is displacement, D is stress-strain matrix (consistent tangent coefficient), B is strain-displacement matrix, δ * is virtual displacement, ε * is virtual strain, P is Surface force per unit area, F is volume force per unit volume, f is nodal force, K is element stiffness matrix, t is the thickness of the triangular element, Δ is the area of the triangular element, E is the elastic modulus, ν is Poisson Is the ratio.
ここで、σは応力、εは全ひずみ、Ｄはコンシステント接線係数、εｅは弾性ひずみ、εｐは塑性ひずみ、εｔｈは熱ひずみ、εｍは変態ひずみ、εｔｐは変態塑性ひずみ、εｃはクリープひずみ、αは線膨張係数、βは変態膨張量、Ｋは変態塑性係数、Ｓは有効応力、Ａ，ｎはクリープ定数である。 Where σ is stress, ε is total strain, D is consistent tangent coefficient, ε e is elastic strain, ε p is plastic strain, ε th is thermal strain, ε m is transformation strain, ε tp is transformation plastic strain, ε c is a creep strain, α is a linear expansion coefficient, β is a transformation expansion amount, K is a transformation plasticity coefficient, S is an effective stress, and A and n are creep constants.
冷却時の材料物性値は温度及び相変化によって変化するが、所定の冷却速度で生じる各相（γ相、α相）の各温度における物性値をあらかじめ測定し、各温度における各相の体積分率から線形混合則を適用して求めることができる。各相の弾性係数及びポアソン比は文献値を用いて推定し、線膨張係数はＪＩＳ Ｚ ２２８５「金属材料の線膨張係数の測定方法」に、強度特性はＪＩＳ Ｇ ０５６７「鉄鋼材料及び耐熱合金の高温引張試験方法」に従って測定することができる。得られた強度特性は、式（１１）に示すＲａｍｂｅｒｇ−Ｏｓｇｏｏｄ則を用いて近似することができる。弾塑性応力解析用の物性値は式（１２）に示され、添え字のｉは各相を表している。 Material property values during cooling vary depending on temperature and phase change, but the physical property values at each temperature of each phase (γ phase, α phase) generated at a predetermined cooling rate are measured in advance, and the volume of each phase at each temperature The linear mixing rule can be applied from the rate. The elastic modulus and Poisson's ratio of each phase are estimated using literature values. The linear expansion coefficient is JIS Z 2285 “Method of measuring the linear expansion coefficient of metal materials” and the strength characteristics are JIS G 0567 “Steel materials and heat-resistant alloys. It can be measured according to the “high temperature tensile test method”. The obtained strength characteristics can be approximated using the Ramberg-Osgood rule shown in Equation (11). The physical property values for elasto-plastic stress analysis are shown in Formula (12), and the subscript i represents each phase.
本発明の有効性を調べるため、残留応力の推定精度を実験結果と比較した。実験にはＮｉＣｒＭｏＶ鋼のφ３２５ｍｍ×１５００ｍｍ長さの丸棒試験材及びφ１０８０ｍｍ×１０５０ｍｍ長さと、φ１２８０ｍｍ×１２５０ｍｍ長さの段付き丸棒試験材を用いた。
８５０℃で加熱後に空冷を施し、空冷時の冷却速度を熱電対を用いて測定し、熱伝導解析結果と比較した。また、空冷後に試験材の長さ方向中央位置における外表面の残留応力をひずみゲージを用いたリングコア法により測定し、弾塑性応力解析結果と比較した。
In order to examine the effectiveness of the present invention, the estimation accuracy of the residual stress was compared with the experimental results. In the experiment, a round bar test material having a length of φ325 mm × 1500 mm and a stepped round bar test material having a length of φ1080 mm × 1050 mm and a length of φ1280 mm × 1250 mm of NiCrMoV steel were used.
After heating at 850 ° C., air cooling was performed, and the cooling rate at the time of air cooling was measured using a thermocouple, and compared with the heat conduction analysis result. In addition, after air cooling, the residual stress on the outer surface at the central position in the length direction of the test material was measured by a ring core method using a strain gauge, and compared with the result of elastic-plastic stress analysis.
図３に熱伝導解析結果と測温結果の比較例を示す。解析結果は測温結果に良く一致している。表１に本手法と比較法を用いて推定した残留応力を実測値と比較して示す。比較法では、式（１０）に示す全ひずみの計算において式（１３）を用いた。つまり、比較法１では全ひずみに変態塑性ひずみとクリープひずみを含めない解析方法であり、比較法２は全ひずみの計算においてクリープひずみを含めない解析方法である。
FIG. 3 shows a comparative example of the heat conduction analysis result and the temperature measurement result. The analysis results agree well with the temperature measurement results. Table 1 shows the residual stress estimated by using this method and the comparison method in comparison with the actual measurement value. In the comparison method, Formula (13) was used in the calculation of the total strain shown in Formula (10). That is,
比較法１ではいずれの解析においても解析値は実測値に一致しない。比較法２では、φ３２５ｍｍ試験材では解析値と実測値が概ね一致するものの、φ１０８０ｍｍ、φ１２８０ｍｍ試験材では一致しない。本発明法では、いずれの試験材でも残留応力を精度良く推定できている。
In
次に、開発法の有効範囲を明確にするため、直径Ｄａ（Ｄａ＝３２５〜２０００ｍｍ）、長さ３Ｄａの丸棒を対象に、８５０℃から空冷した時の残留応力を開発法と比較法２で比較した。解析結果を図４に示す。開発法と比較法２の残留応力の差は、胴径の増加に伴って単調に増加する傾向である。このことから、解析対象寸法が大きく、特に直径が５００ｍｍ以上の部材においては残留応力の差は５０ＭＰａを超えて、比較法では解析精度が低下する。 Next, in order to clarify the effective range of the development method, the residual stress when air-cooled from 850 ° C. for a round bar with a diameter Da (Da = 325-2000 mm) and a length of 3 Da is compared with the development method and the comparison method 2. Compared. The analysis results are shown in FIG. The difference in the residual stress between the development method and the comparison method 2 tends to increase monotonously as the body diameter increases. For this reason, the difference in residual stress exceeds 50 MPa in a member having a large analysis object size, particularly a diameter of 500 mm or more, and the analysis accuracy is lowered in the comparative method.
以上の結果から、鋼の空冷時の熱処理解析においては、変態塑性ひずみに加えてクリープひずみも考慮した本解析手法の有効性が確認された。特に直径が５００ｍｍ以上の大型鍛鋼品において格別な効果が認められた。 From the above results, the effectiveness of this analysis method considering creep strain in addition to transformation plastic strain was confirmed in the heat treatment analysis of steel during air cooling. In particular, a special effect was observed in large forged steel products having a diameter of 500 mm or more.
以上、本発明について、前記実施形態および実施例に基づいて説明を行ったが、本発明の範囲を逸脱しない限りは、前記実施形態に対し適宜の変更を行うことができる。 As described above, the present invention has been described based on the above-described embodiments and examples. However, appropriate modifications can be made to the above-described embodiments without departing from the scope of the present invention.
Claims (8)
前記鋼の材料データとして鋼の各相および各温度における物性値を用いて、有限要素モデル中の各節点における温度の時間変化を有限要素法によって計算する熱伝導解析を行い、
前記熱伝導解析で得られた各節点の温度を温度荷重として、前記鋼の材料データとして鋼の物性値を用い、各要素の積分点におけるひずみ量として、少なくとも変態塑性ひずみとクリープひずみとを算出し、これらの和に基づいて、前記鋼の内部応力の変化を計算する弾塑性応力解析を行うことを特徴とする鋼の熱処理シミュレーション方法。 A steel heat treatment simulation method,
Using the physical properties of each phase and temperature of the steel as the material data of the steel, conduct the heat conduction analysis to calculate the time change of the temperature at each node in the finite element model by the finite element method,
Using the temperature of each node obtained in the heat conduction analysis as the temperature load, using the physical property value of the steel as the material data of the steel, and calculating at least the transformation plastic strain and creep strain as the strain amount at the integration point of each element Then, based on these sums, an elastic-plastic stress analysis for calculating a change in internal stress of the steel is performed.
前記弾塑性応力解析の材料データとして、鋼の各相および各温度における弾性係数、ポアソン比、硬化曲線を用い、前記温度荷重、前記弾性係数、前記ポアソン比、前記硬化曲線を用いて、各要素の積分点におけるひずみ量を、弾性ひずみ、塑性ひずみ、熱ひずみ、変態ひずみ、変態塑性ひずみ、クリープひずみとして算出することを特徴とする請求項１記載の鋼の熱処理シミュレーション方法。 As the physical property values of the material data of the heat conduction analysis, specific heat, density, thermal conductivity at each phase and temperature of steel, and heat transfer coefficient during heat treatment as boundary conditions,
As the material data of the elastoplastic stress analysis, the elastic coefficient, Poisson's ratio, and hardening curve in each phase and temperature of steel are used, and each element using the temperature load, the elastic modulus, the Poisson's ratio, and the hardening curve. The steel heat treatment simulation method according to claim 1, wherein the strain amount at the integration point is calculated as elastic strain, plastic strain, thermal strain, transformation strain, transformation plastic strain, and creep strain.
熱伝導解析のために、鋼の材料データとして鋼の各相および各温度における物性値を取得する際に、少なくとも一つの測定値を前記操作部を通して取得する熱伝導データ取得ステップと、
前記熱伝導データ取得ステップで得たデータを用いて、有限要素モデル中の各節点における温度の時間変化を有限要素法によって計算し、得られた各節点の温度を温度荷重として取得する熱伝導解析ステップと、
弾塑性応力解析のために、前記鋼の材料データとして鋼の各相および各温度における物性値を取得する際に、少なくとも一つの測定値を前記操作部を通して取得する弾塑性データ取得ステップと、
前記弾塑性データ取得ステップにおける各要素の積分点におけるひずみ量として、少なくとも、変態塑性ひずみとクリープひずみとを算出して、これらの和に基づいて前記鋼の内部応力の変化を計算する弾塑性応力解析ステップと、
前記内部応力の変化に基づいて、ひずみまたは／および応力を、前記表示部に表示する表示ステップと、を有することを特徴とする鋼の熱処理シミュレーションプログラム。 A control unit that controls a heat treatment simulation analysis apparatus having a display unit and an operation unit that receives an operation input,
A heat conduction data acquisition step of acquiring at least one measured value through the operation unit when acquiring physical property values at each phase and temperature of steel as material data for steel for heat conduction analysis;
Using the data obtained in the heat conduction data acquisition step, the temperature change at each node in the finite element model is calculated by the finite element method, and the obtained temperature is obtained as a temperature load. Steps,
An elastic-plastic data acquisition step for acquiring at least one measurement value through the operation unit when acquiring physical properties at each phase and temperature of the steel as material data for the elastic-plastic stress analysis;
As the amount of strain at the integration point of each element in the elastoplastic data acquisition step, at least the transformation plastic strain and creep strain are calculated, and the change in internal stress of the steel is calculated based on the sum of these. An analysis step;
And a display step of displaying strain or / and stress on the display unit based on the change of the internal stress.
弾塑性データ取得ステップで、前記鋼の材料データの物性値として鋼の各相および各温度における弾性係数、ポアソン比、硬化曲線を取得し、
弾塑性応力解析ステップでは、前記弾塑性データ取得ステップにおける各要素の積分点におけるひずみ量を、弾性ひずみ、塑性ひずみ、熱ひずみ、変態ひずみ、変態塑性ひずみ、クリープひずみを算出し、これらの和に基づいて前記鋼の内部応力の変化を計算することを特徴とする請求項７記載の鋼の熱処理シミュレーションプログラム。 In the heat conduction data acquisition step, the physical property values of the steel material data are obtained as the specific heat, density, and thermal conductivity at each phase and temperature of the steel, and the physical property values of the heat transfer coefficient during heat treatment as boundary conditions,
In the elasto-plastic data acquisition step, acquire the elastic modulus, Poisson's ratio, hardening curve at each phase and each temperature of the steel as the physical property value of the material data of the steel,
In the elasto-plastic stress analysis step, the elastic strain, plastic strain, thermal strain, transformation strain, transformation plastic strain, and creep strain are calculated as the strain amount at the integration point of each element in the elasto-plastic data acquisition step. 8. The heat treatment simulation program for steel according to claim 7, wherein a change in internal stress of the steel is calculated based on the calculation.
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