CN113252465B - M-H method-based creep life prediction method for heat-resistant steel - Google Patents
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Abstract
本发明公开了基于M‑H法的耐热钢蠕变寿命预测方法，包括：S1，对蠕变试样进行蠕变试验，获取蠕变试验温度下耐热钢的蠕变性能数据；S2，根据的述蠕变性能数据计算出该温度下不同试验应力σ对应的PM‑H值；S3，对PM‑H值进行参数法曲线拟合，得到该温度下改进M‑H法的拟合参数主曲线；S4，根据得到的拟合参数主曲线得出该温度下不同低应力值对应的PM‑H值，进而求出该温度下不同低应力对应的蠕变寿命；S5，重复步骤S1‑S4，得到其它温度下、不同低应力对应的蠕变断裂寿命。该方法解决了过度预测了材料低应力区的蠕变寿命的缺点，对工程上维修及更换材料提供了可靠的依据，其适用范围广、预测精度高、可靠性高。
The invention discloses a method for predicting the creep life of heat-resistant steel based on the M-H method. According to the above-mentioned creep performance data, the P M-H values corresponding to different test stresses σ at this temperature are calculated; S3, the parameter method curve fitting is performed on the P M-H values, and the simulation results of the improved M-H method at this temperature are obtained. The main curve of fitting parameters is obtained; S4, according to the obtained main curve of fitting parameters, the PM-H values corresponding to different low stress values at the temperature are obtained, and then the creep life corresponding to different low stresses at the temperature is obtained; S5, repeat In steps S1-S4, the creep rupture life corresponding to different low stresses at other temperatures is obtained. The method solves the shortcoming of over-predicting the creep life of the material in the low stress region, and provides a reliable basis for the maintenance and replacement of materials in engineering. It has a wide range of applications, high prediction accuracy and high reliability.
Description
技术领域technical field
本发明涉及高温材料与结构强度领域，特别是涉及一种基于M-H法的耐热钢蠕变寿命预测方法。The invention relates to the field of high-temperature materials and structural strength, in particular to a method for predicting the creep life of heat-resistant steel based on the M-H method.
背景技术Background technique
准确预测火电、核电高温材料服役寿命是保障工程材料与结构安全服役的前提。高铬耐热钢，尤其是铬含量在9％～12％的耐热钢，由于其突出的抗蠕变性能、良好的抗腐蚀和高温抗氧化能力而成为热电厂主要部件的主选或更新换代材料。其高温蠕变断裂对火电厂的安全和正常生产有很大的影响。目前，工程上通过高应力短程蠕变试验获得蠕变断裂寿命，进而外推获得实际服役低应力下的蠕变断裂寿命，但此方法过度预测了材料低应力区的蠕变寿命。Accurately predicting the service life of thermal power and nuclear power high-temperature materials is the premise to ensure the safe service of engineering materials and structures. High-chromium heat-resistant steel, especially heat-resistant steel with a chromium content of 9% to 12%, has become the main choice or replacement for the main components of thermal power plants due to its outstanding creep resistance, good corrosion resistance and high temperature oxidation resistance. Material. Its high temperature creep rupture has a great influence on the safety and normal production of thermal power plants. At present, in engineering, the creep rupture life is obtained through the high-stress short-range creep test, and then the creep rupture life under low stress in actual service is obtained by extrapolation. However, this method overly predicts the creep life of the material in the low stress region.
随着工作温度的升高，现代工业中的高温设备和高温机构发生蠕变失效的可能性以及由于蠕变失效引发事故的严重性也都有所增加。因此，无论从经济性和安全性考虑，正确预测材料的蠕变寿命都具有非常重要的现实意义。As the operating temperature increases, the possibility of creep failure of high-temperature equipment and high-temperature mechanisms in modern industry and the severity of accidents caused by creep failure also increase. Therefore, it is of great practical significance to correctly predict the creep life of materials in terms of economy and safety.
目前，应用最广泛的蠕变寿命预测方法是以Larson-Miller法为代表的时间-温度参数法。该方法通过Larson-Miller参数将蠕变温度、应力、时间联系在一起构成Larson-Miller参数方程：At present, the most widely used creep life prediction method is the time-temperature parameter method represented by the Larson-Miller method. The method combines the creep temperature, stress and time through the Larson-Miller parameter to form the Larson-Miller parameter equation:
PL-M＝T(CL-N+lgtr) (1)P LM =T(C LN +lgt r ) (1)
其中，PL-M为Larson-Miller参数；T为蠕变试验温度，单位为K(Kelvins)；C0、C1、C2、C3、C4为材料常数；σ为蠕变试验应力；CL-M为常数，对于高铬马氏体耐热钢，CL-M＝20或33，对于铁素体钢，CL-M＝17或31，对于奥氏体钢和Ni-Cr-Fe铸造高合金，CL-M＝15或36。Among them, P LM is the Larson-Miller parameter; T is the creep test temperature, in K (Kelvins); C 0 , C 1 , C 2 , C 3 , and C 4 are the material constants; σ is the creep test stress; C LM is a constant, for high chromium martensitic heat-resistant steel, C LM = 20 or 33, for ferritic steel, C LM = 17 or 31, for austenitic steel and Ni-Cr-Fe cast high alloy, C LM LM = 15 or 36.
该方程具有很好的综合性，但公式(2)参数多，结构复杂，预测精度不高，而且过度预测了材料低应力区的蠕变寿命，应用时需要较多的试验数据，该方法适用于不超过3倍于试验蠕变寿命范围内的预测。This equation has a good comprehensiveness, but the formula (2) has many parameters, complex structure, low prediction accuracy, and over-predicts the creep life of the material in the low stress region, so more test data is required for application, and this method is suitable Predicted within a range of not more than 3 times the experimental creep life.
上世纪80年代新发展的θ法虽能较好地描述常应力条件下试验所得蠕变曲线，但若载荷发生变化就不能适用，而且对温度均匀性要求甚高，不能用于精确的长时寿命外推。近年来人们建立了各种形式的修正θ方程，在表达蠕变曲线方面取得了较好的效果，但θ方程参数对蠕变的变形过程非常敏感，与应力以及温度的关系比较分散，因此，用θ影射法预测蠕变寿命同样需要大量的试验数据。Although the θ method newly developed in the 1980s can better describe the creep curve obtained from the test under constant stress conditions, it cannot be applied if the load changes, and the temperature uniformity is very demanding, so it cannot be used for accurate long-term Extrapolation of life. In recent years, various forms of modified θ equations have been established, which have achieved good results in expressing the creep curve. However, the parameters of the θ equation are very sensitive to the deformation process of creep, and the relationship with stress and temperature is relatively scattered. Therefore, Predicting creep life by theta projection method also requires a large amount of experimental data.
M-H参数法(Manson-Haferd)将蠕变温度、应力、时间联系在一起构成M-H参数方程：The M-H parameter method (Manson-Haferd) links the creep temperature, stress and time together to form the M-H parameter equation:
其中，PM-H为M-H参数；T为蠕变试验，温度单位为K(Kelvins)；a0、a1、a2、a3、a4为材料常数；σ为蠕变试验应力；lgta、Ta为常数。该方程具有很好的综合性，但公式(4)参数多，预测精度不高，而且过度预测了材料低应力区的蠕变寿命，且适用于不超过3倍于试验蠕变寿命范围内的预测。Among them, P MH is the MH parameter; T is the creep test, and the temperature unit is K (Kelvins); a 0 , a 1 , a 2 , a 3 , and a 4 are the material constants; σ is the creep test stress; T a is a constant. This equation has a good comprehensiveness, but formula (4) has many parameters, the prediction accuracy is not high, and the creep life in the low stress region of the material is over-predicted, and it is suitable for the creep life within the range of no more than 3 times the experimental creep life. predict.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于改进现有蠕变寿命预测技术存在的问题和不足，提供一种能够在常规的蠕变强度试验基础上，更加精确、有效预测耐热合金蠕变寿命，尤其是低应力下耐热合金蠕变寿命的方法。The purpose of the present invention is to improve the existing problems and deficiencies of the existing creep life prediction technology, and to provide a method that can more accurately and effectively predict the creep life of heat-resistant alloys on the basis of conventional creep strength tests, especially under low stress. Methods for creep life of heat-resistant alloys.
为此，本发明采用以下技术方案：For this reason, the present invention adopts the following technical solutions:
一种基于M-H法的耐热钢蠕变寿命预测方法，包括以下步骤：A method for predicting the creep life of heat-resistant steel based on the M-H method, comprising the following steps:
S1，依据蠕变试验规范对蠕变试样进行蠕变试验，获取蠕变试验温度为T时耐热钢的蠕变性能数据，蠕变断裂时间；S1, perform a creep test on the creep sample according to the creep test specification, and obtain the creep performance data of the heat-resistant steel when the creep test temperature is T, and the creep rupture time;
S2，根据步骤S1得到的蠕变性能数据计算出该温度下不同试验应力σ对应的PM-H值，计算公式如下：S2, according to the creep performance data obtained in step S1, calculate the PMH values corresponding to different test stresses σ at the temperature, and the calculation formula is as follows:
其中：in:
PM-H：M-H参数；P MH : MH parameter;
tr为蠕变断裂时间，单位为h；t r is the creep rupture time, the unit is h;
T为蠕变试验温度，单位为K；T is the creep test temperature, in K;
lgta和Ta为常数；lgt a and T a are constants;
S3，对所述PM-H值进行参数法曲线拟合，得到该温度下改进的M-H法的拟合参数主曲线，数学表达式为：S3, carry out parametric method curve fitting to described PMH value, obtain the fitting parameter main curve of the improved MH method under this temperature, mathematical expression is:
其中：in:
σ为试验应力，单位为MPa；σ is the test stress, the unit is MPa;
a、b、c为待定系数；a, b, c are undetermined coefficients;
S4，根据步骤S3得到的拟合参数主曲线，得出该温度下不同低应力值对应的PM-H值，代入公式(1)，求出该温度下不同低应力对应的蠕变寿命；S4, according to the main curve of the fitting parameters obtained in step S3, obtain the PMH values corresponding to different low stress values at the temperature, and substitute them into formula (1) to obtain the creep life corresponding to different low stresses at the temperature;
S5，重复步骤S1-S4，得到其它温度下、不同低应力对应的蠕变断裂寿命。S5, repeating steps S1-S4 to obtain the creep rupture life corresponding to different low stresses at other temperatures.
其中，所述试验应力σ的范围为80-220MPa。Wherein, the range of the test stress σ is 80-220MPa.
所述耐热钢为高铬耐热钢时，公式(1)中的lgta＝15，Ta＝450；；所述耐热钢为铁素体钢时，公式(1)中的lgta＝31；Ta＝190；所述耐热钢为奥氏体钢或Ni-Cr-Fe铸造高合金时，公式(1)中的lgta＝18，Ta＝520。When the heat-resistant steel is high-chromium heat-resistant steel, lgt a =15 and Ta = 450 in formula (1); when the heat-resistant steel is ferritic steel, lgt a in formula (1) =31; Ta = 190; when the heat-resistant steel is austenitic steel or Ni-Cr-Fe cast high alloy, Igt a =18 and Ta = 520 in formula (1).
步骤S2中，利用数学分析软件，按最小二乘法回归，将试验数据lgtr和常数lgta、Ta、以及温度T一组一组输入软件中求出该温度下不同应力下的参数PM-H。In step S2, using mathematical analysis software, according to least squares regression, the test data lgt r and constants lgt a , T a , and temperature T are input into the software group by group to obtain the parameter P MH under different stress at the temperature. .
步骤S3中，运用数学分析软件，对定温不同应力下的参数PM-H进行数据分析及拟合，求得各待定系数a、b、c，将待定系数代入表达式
本发明的预测方法首先在M-H参数法关于蠕变寿命与温度的关系方程的基础上，考虑高温强度对蠕变性能的有益作用以及应力对材料的蠕变机制的影响，建立应力与M-H参数PM-H的关系的拟合方程，即拟合主曲线；通过该模型采用最小二乘法对定温不同应力下的蠕变寿命数据进行拟合，确定模型参数值，得到应力与参数PM-H的关系式；通过该关系式求出低应力下的预测蠕变寿命。The prediction method of the present invention firstly establishes the relationship between the stress and the MH parameter P by considering the beneficial effect of high temperature strength on the creep performance and the influence of stress on the creep mechanism of the material on the basis of the relationship equation between the creep life and temperature of the MH parameter method. The fitting equation of the relationship between MH , that is, the fitting main curve; the least squares method is used to fit the creep life data at constant temperature and different stresses, the model parameter values are determined, and the relationship between the stress and the parameter P MH is obtained; The predicted creep life under low stress is obtained from this relational expression.
与现有技术相比，本发明的预测方法具有以下有益效果：Compared with the prior art, the prediction method of the present invention has the following beneficial effects:
1.本发明提供了一种改进的M-H法回归曲线的主曲线方程：
2.本发明的方法能够准确预测材料低应力区的蠕变寿命，能够预测不同材料的耐热钢在不同温度、不同应力下的蠕变寿命，解决了过度预测材料低应力区的蠕变寿命的缺点，为工程上维修及更换材料提供了可靠的依据；2. The method of the present invention can accurately predict the creep life of the low stress region of the material, can predict the creep life of the heat-resistant steel of different materials at different temperatures and different stresses, and solves the problem of over-predicting the creep life of the low stress region of the material. It provides a reliable basis for the maintenance and replacement of materials in the project;
3.本发明的预测方法简便、高效，在一定范围内只需通过多组高应力蠕变试验数据即可实现有效的蠕变寿命预测，具有很好的实用性；3. The prediction method of the present invention is simple and efficient, and within a certain range, effective creep life prediction can be achieved only through multiple sets of high-stress creep test data, which has good practicability;
4.本发明的方法适合用于各种耐热钢、耐热合金、高温合金等金属材料蠕变寿命的预测，适用范围广，可靠性高。4. The method of the present invention is suitable for predicting the creep life of various heat-resistant steels, heat-resistant alloys, high-temperature alloys and other metal materials, with wide application range and high reliability.
5.利用本发明的方法能够对耐高温金属的服役时间进行有效估计，减小了危害，降低了成本。5. The method of the present invention can effectively estimate the service time of the high-temperature-resistant metal, thereby reducing the harm and the cost.
附图说明Description of drawings
图1为ASME级P92钢在650℃下应力与蠕变断裂寿命数据；Figure 1 shows the stress and creep rupture life data of ASME grade P92 steel at 650℃;
图2为P92钢在650℃下基于M-H法模型下拟合主曲线与实际参数值PM-H的对比图；Figure 2 is a comparison diagram of the fitted master curve and the actual parameter value P MH of P92 steel at 650°C based on the MH method model;
图3为P92钢在650℃下基于江冯-赵杰课题组法模型下拟合主曲线与实际参数值PM-H的对比图；Figure 3 is a comparison diagram of the fitted master curve and the actual parameter value P MH of P92 steel at 650°C based on the Jiang Feng-Zhao Jie research group method model;
图4为P92钢在650℃下基于本发明的改进M-H法模型下拟合主曲线与实际参数值PM-H的对比图；Figure 4 is a comparison diagram of the fitted master curve and the actual parameter value PMH of P92 steel at 650°C based on the improved MH method model of the present invention;
图5为ASME级P92钢在650℃下基于M-H法、江冯-赵杰课题组法、改进M-H法、L-M法的蠕变寿命外推曲线；Figure 5 is the extrapolation curve of creep life of ASME grade P92 steel at 650℃ based on M-H method, Jiang Feng-Zhao Jie research group method, improved M-H method and L-M method;
图6为ASME级P92钢在650℃下基于M-H法、江冯-赵杰课题组法、改进M-H法、L-M法预测得到的蠕变断裂时间与实际蠕变断裂时间的比较图。Figure 6 shows the comparison between the creep rupture time predicted by the M-H method, the Jiang Feng-Zhao Jie research group method, the improved M-H method, and the L-M method for ASME grade P92 steel at 650 °C and the actual creep rupture time.
具体实施方式Detailed ways
下面结合附图及实施例对本发明的预测方法进行详细说明。The prediction method of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.
实施例一Example 1
本实施例选取ASME(American Society of Mechanical Engineers)级的高铬耐热钢P92作为研究对象，蠕变试样的取样方向为板内短横向(垂直于挤压板的挤压方向)，试样尺寸参照《GB/T 2039-1997金属拉伸蠕变及持久试验方法》。In this example, ASME (American Society of Mechanical Engineers) grade high-chromium heat-resistant steel P92 is selected as the research object, and the sampling direction of the creep sample is the short transverse direction (perpendicular to the extrusion direction of the extruded plate), Dimensions refer to "GB/T 2039-1997 Metal Tensile Creep and Endurance Test Methods".
本实施例的基于M-H法的耐热钢蠕变寿命预测方法包括以下步骤：The method for predicting the creep life of heat-resistant steel based on the M-H method of this embodiment includes the following steps:
S1，获取蠕变性能数据：在蠕变试验温度T＝650℃、试验应力范围为220～80MPa条件下，依据蠕变试验规范的规定对蠕变试样进行蠕变试验，获得不同应力σ下的68个有效蠕变数据，数据分布图如图1所示。S1, obtain creep performance data: under the conditions of creep test temperature T=650℃ and test stress range of 220-80MPa, perform creep test on creep samples according to the provisions of creep test specification, and obtain different stress σ The 68 valid creep data of , the data distribution diagram is shown in Figure 1.
S2，用上述效蠕变数据按下式计算出650℃时不同试验应力σ下相对应的PM-H值(M-H参数)：S2, use the above effective creep data to calculate the corresponding P MH values (MH parameters) under different test stresses σ at 650 °C as follows:
式中：where:
tr为蠕变断裂时间，单位为h；t r is the creep rupture time, the unit is h;
T为蠕变试验温度，单位为K；T is the creep test temperature, in K;
在此试验温度下，根据日本金属材料研究所公开的这些材料的M-H常数(lgta、Ta)值，取lgta＝450，Ta＝15；At this test temperature, according to the MH constant (lgt a , T a ) values of these materials disclosed by the Japan Institute of Metal Materials, take lgt a =450, T a =15;
利用数学分析软件，按最小二乘法回归，将试验数据lgtr和常数lgta、Ta、以及温度T一组一组输入软件中，即可求出该温度下不同应力下的参数PM-H。Using mathematical analysis software, according to least squares regression, the test data lgt r and constants lgt a , Ta , and temperature T are input into the software group by group, and the parameters P MH under different stress at the temperature can be obtained.
S3，运用数学分析软件，对所得到的同一温度、不同应力下的PM-H值进行拟合，求得各待定系数a、b、c，将待定系数代入下式：S3, use the mathematical analysis software to fit the obtained PMH values under the same temperature and different stress, obtain the undetermined coefficients a, b, and c, and substitute the undetermined coefficients into the following formula:
其中：in:
σ为试验应力，单位为MPa；σ is the test stress, the unit is MPa;
a、b、c为待定系数；a, b, c are undetermined coefficients;
得到改进的M-H法回归的拟合主曲线：The fitted master curve of the improved M-H method regression is obtained:
σ＝219.0934-5506.5105*exp(162.8230*PM-H)σ=219.0934-5506.5105*exp(162.8230*P MH )
S4，根据步骤S3得到的拟合参数主曲线，得出该温度下不同低应力值对应的PM-H值，代入公式(1)，或按下式：S4, according to the main curve of the fitting parameters obtained in step S3, obtain the PMH values corresponding to different low stress values at the temperature, and substitute them into formula (1), or as follows:
求出650℃下，不同低应力对应的蠕变寿命。Calculate the creep life corresponding to different low stress at 650℃.
S5，重复步骤S1-S4，得到其它温度下、不同低应力对应的蠕变断裂寿命。S5, repeating steps S1-S4 to obtain the creep rupture life corresponding to different low stresses at other temperatures.
在650℃下，采用本发明的预测方法和传统的几种方法对ASME级P92耐热钢在220-20MPa应力下的蠕变寿命进行预测，相应的实际参数值PM-H与应力之间的拟合关系表达式如表1所示，其对应模型下拟合主曲线与实际参数值的对比图如图2-4所示；各方法的蠕变寿命外推曲线如图5所示；各方法预测得到的蠕变断裂时间与实际蠕变断裂时间的比较图如图6所示。At 650℃, the prediction method of the present invention and several traditional methods are used to predict the creep life of ASME grade P92 heat-resistant steel under the stress of 220-20MPa . The expression of the fitting relationship is shown in Table 1, and the comparison between the fitted main curve and the actual parameter value under the corresponding model is shown in Figure 2-4; the creep life extrapolation curve of each method is shown in Figure 5; A comparison of the predicted creep rupture time with the actual creep rupture time is shown in Figure 6.
表1Table 1
其中：σ为试验应力，单位为MPa。Among them: σ is the test stress, the unit is MPa.
由上表可知，传统的L-M法和M-H法拟合主曲线的相关性系数都较本发明的改进的M-H法的拟合主曲线的相关性系数低，虽然江冯-赵杰课题组法的拟合主曲线的相关性系数最高，但由图5可知，其蠕变寿命外推曲线高于实际蠕变寿命。It can be seen from the above table that the correlation coefficient of the traditional L-M method and the M-H method for fitting the main curve is lower than that of the improved M-H method of the present invention. The correlation coefficient of the fitted main curve is the highest, but as can be seen from Figure 5, the extrapolation curve of its creep life is higher than the actual creep life.
由图5和图6可知，传统的M-H法、江冯-赵杰课题组法、传统的L-M法都过度预测了材料低应力区的蠕变寿命，而本发明的改进的M-H法预测的低应力区结果较好，且预测误差在2倍误差之内。It can be seen from Fig. 5 and Fig. 6 that the traditional M-H method, the Jiang Feng-Zhao Jie research group method, and the traditional L-M method all overly predict the creep life of the material in the low stress region, while the improved M-H method of the present invention predicts the low creep life. The stress region results are good, and the prediction error is within 2 times the error.
由图6可知，用本发明的方法预测的数据点大部分在tp＝tr的右侧，而不在tp＝tr右侧的点也基本在tp＝tr线附近，说明本发明的方法在低应力下预测的蠕变断裂寿命均低于已有的低应力实际蠕变断裂寿命，具有良好的预测效果，也有巨大的工程意义。It can be seen from FIG. 6 that most of the data points predicted by the method of the present invention are on the right side of t p =tr, and the points not on the right side of t p = tr are basically near the line t p = tr , which illustrates the present invention The creep rupture life predicted by the method under low stress is lower than the existing low stress actual creep rupture life, which has a good prediction effect and great engineering significance.
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