CN115204013A - A life prediction method for materials under multiaxial stress state - Google Patents

A life prediction method for materials under multiaxial stress state Download PDF

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CN115204013A
CN115204013A CN202210809588.XA CN202210809588A CN115204013A CN 115204013 A CN115204013 A CN 115204013A CN 202210809588 A CN202210809588 A CN 202210809588A CN 115204013 A CN115204013 A CN 115204013A
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张冬旭
吕盟辉
郭晓钥
李晓闻
罗壮
宋智超
李夏霜
李海涛
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Shaanxi University of Science and Technology
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Abstract

The invention discloses a method for predicting the service life of a material in a multiaxial stress state, and belongs to the field of material service life prediction. The method specifically comprises the following steps: the method comprises the following steps: obtaining relevant material parameters in the continuous damage mechanical model through a uniaxial creep experiment; step two: defining a material creep-damage constitutive model based on a continuous damage mechanical model in finite element software; step three: obtaining node positions corresponding to different gaps through a node position curve; step four: calculating the maximum main stress at each node on the cross section of the related notch according to finite element
Figure DDA0003740121390000011
Stress of von Mises
Figure DDA0003740121390000012
Step five: obtained based on step four
Figure DDA0003740121390000013
And with
Figure DDA0003740121390000014
And calculating the service life of the material by using a node stress method and a service life calculation formula. The method for predicting the creep-fracture life of the material in the multi-axis stress state can more efficiently, conveniently and accurately predict the creep life of the material in the multi-axis stress state.

Description

一种多轴应力状态下的材料的寿命预测方法A life prediction method for materials under multiaxial stress state

技术领域technical field

本发明属于材料寿命预测领域，具体涉及一种多轴应力状态下的材料的寿命预测方法。The invention belongs to the field of material life prediction, and in particular relates to a life prediction method of a material under a multiaxial stress state.

背景技术Background technique

在航空航天、核电领域中，有许多重要部件在运行过程中受到高温、高压、高速载荷的影响，例如航空发动机与燃气轮机的涡轮盘，其中大部分断裂失效发生在槽连接结构中。作为这些高载荷的热端构件，影响槽连接结构寿命的因素很多，包括高温长时间运行下的蠕变变形和断裂、工作条件反复变化引起的低周疲劳、振动引起的高周疲劳、高温气体腐蚀、氧化等等。一般来说，蠕变断裂和低周疲劳起决定性作用，而且通常这些部件都处于复杂的多轴应力场中。而对这些材料蠕变行为与多轴蠕变寿命预测的研究是有着重大意义的。In the fields of aerospace and nuclear power, many important components are affected by high temperature, high pressure, and high-speed loads during operation, such as the turbine disks of aero-engines and gas turbines. Most of the fracture failures occur in the groove connection structure. As these high-load hot-end components, there are many factors that affect the life of the groove connection structure, including creep deformation and fracture under long-term operation at high temperature, low-cycle fatigue caused by repeated changes in working conditions, high-cycle fatigue caused by vibration, high temperature gas corrosion, oxidation, etc. In general, creep rupture and low cycle fatigue play a decisive role, and often these components are exposed to complex multiaxial stress fields. The research on the creep behavior and multiaxial creep life prediction of these materials is of great significance.

在目前工程领域设计中大多采用单轴应力状态下的材料数据，缺乏符合多轴应力下结构可靠性的设计方法与评估手段。近年来在学术领域，国内外研究人员对多轴应力状态下的蠕变断裂行为展开了大量的研究，并提出了大量基于商用有限元软件的蠕变-损伤计算模型，诸如晶体塑性模型、连续损伤力学模型和通过唯像本构模型描述蠕变行为。其中，晶体塑性模型能够准确的描述蠕变过程中微观层面的应力应变行为，适用于基础科学研究，但难以在工程中用于宏观性能评估；连续损伤力学模型可以准确反映材料多轴应力状态下的蠕变行为，也是目前在相关研究中应用最广泛的计算模型，但目前相关的寿命预测方法大多本构复杂且过程繁琐，难以有效应用于工程领域；而大量的非统一的唯像本构模型对于蠕变过程进行定性研究尚可，但并不适用于多轴应力下蠕变断裂的寿命预测。各种预测方法或繁琐或不精确全面，因此，目前在工程领域中缺乏行之有效的多轴蠕变寿命预测的方法。In the current engineering design, the material data under uniaxial stress state is mostly used, and there is a lack of design methods and evaluation methods that conform to the structural reliability under multiaxial stress. In recent years, in the academic field, domestic and foreign researchers have carried out a lot of research on the creep rupture behavior under multiaxial stress state, and proposed a large number of creep-damage calculation models based on commercial finite element software, such as crystal plasticity model, continuous Damage mechanics model and creep behavior described by phenomenological constitutive model. Among them, the crystal plasticity model can accurately describe the stress-strain behavior at the microscopic level during the creep process, which is suitable for basic scientific research, but difficult to be used for macroscopic performance evaluation in engineering; the continuous damage mechanics model can accurately reflect the multiaxial stress state of the material. The creep behavior is also the most widely used computational model in related research. However, most of the current life prediction methods are constitutively complex and cumbersome, so they are difficult to be effectively applied to the engineering field; and a large number of non-uniform phenomenological The model is acceptable for qualitative study of creep process, but it is not suitable for life prediction of creep rupture under multiaxial stress. Various prediction methods are either cumbersome or imprecise and comprehensive. Therefore, there is currently a lack of effective multi-axial creep life prediction methods in the engineering field.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于克服上述不足，提供一种简单、便捷、高效和准确的多轴应力状态下蠕变寿命的预测方法，以此更小成本、更高效的实现热端高温部件的剩余寿命预测、性能评估与设计优化。The purpose of the present invention is to overcome the above deficiencies, and provide a simple, convenient, efficient and accurate method for predicting the creep life under multi-axial stress state, so as to realize the prediction of the remaining life of the hot-end high temperature components at a lower cost and more efficiently. , performance evaluation and design optimization.

为了达到上述目的，本发明采用的技术方案如下：In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

一种多轴应力状态下的材料的寿命预测方法，包括以下步骤：A life prediction method for a material under a multiaxial stress state, comprising the following steps:

步骤一：进行材料单轴蠕变断裂实验，分别获取材料在多个单轴应力加载下的蠕变曲线，基于多条单轴蠕变曲线，获得连续损伤力学模型中的材料参数；Step 1: Carry out a uniaxial creep rupture experiment of the material, obtain the creep curves of the material under multiple uniaxial stress loadings, and obtain the material parameters in the continuous damage mechanics model based on the multiple uniaxial creep curves;

步骤二：在ABAQUS中建立有限元模型，使用用户子程序UMAT定义基于连续损伤力学模型的材料蠕变-损伤本构模型；Step 2: Establish a finite element model in ABAQUS, and use the user subprogram UMAT to define the material creep-damage constitutive model based on the continuous damage mechanics model;

步骤三：通过节点位置曲线获得不同缺口对应的节点位置；Step 3: Obtain the node positions corresponding to different gaps through the node position curve;

步骤四：基于有限元软件ABAQUS中的creep模块计算得出相关截面应力加载时对应缺口截面上各节点处的最大主应力

Figure BDA0003740121370000021
与Mises应力
Figure BDA0003740121370000022
Step 4: Calculate the maximum principal stress at each node on the corresponding notch section when the relevant section stress is loaded based on the creep module in the finite element software ABAQUS
Figure BDA0003740121370000021
Stress with Mises
Figure BDA0003740121370000022

步骤五：基于步骤四中获得的

Figure BDA0003740121370000023
与
Figure BDA0003740121370000024
利用节点应力法与寿命计算公式进行相应多轴应力状态下的蠕变-损伤寿命计算。Step 5: Based on the results obtained in Step 4
Figure BDA0003740121370000023
and
Figure BDA0003740121370000024
The creep-damage life calculation under the corresponding multiaxial stress state is carried out by using the nodal stress method and the life calculation formula.

步骤一中所述材料参数包括A、B、M、n、m、n0、χ和φ，A、B、M、n、m、n0、χ和φ是连续损伤力学模型中与温度相关的材料常数，由单轴蠕变试验曲线拟合计算得出。The material parameters described in step 1 include A, B, M, n, m, n 0 , χ and φ. A, B, M, n, m, n 0 , χ and φ are related to temperature in the continuous damage mechanics model. The material constants are calculated from curve fitting of uniaxial creep tests.

单轴蠕变曲线拟合方法如下所示：The uniaxial creep curve fitting method is as follows:

Figure BDA0003740121370000025
Figure BDA0003740121370000025

其中，A和n是Norton方程

Figure BDA0003740121370000026
中的材料参数，需要至少同种温度下不同应力的至少两条单轴蠕变曲线进行确定，
Figure BDA0003740121370000027
为最小蠕变应变速率，其独立于施加应力与温度；where A and n are the Norton equations
Figure BDA0003740121370000026
The material parameters in , require at least two uniaxial creep curves with different stresses at the same temperature to determine,
Figure BDA0003740121370000027
is the minimum creep strain rate independent of applied stress and temperature;

Figure BDA0003740121370000028
Figure BDA0003740121370000028

其中tf为单轴蠕变寿命，σ为单轴截面应力；where t f is the uniaxial creep life, and σ is the uniaxial section stress;

基于公式

Figure BDA0003740121370000029
利用不同应力对应的蠕变寿命拟合得到M、χ和φ。formula based
Figure BDA0003740121370000029
M, χ and φ are obtained by fitting the creep life corresponding to different stresses.

步骤二中所述基于连续损伤力学模型的材料蠕变-损伤本构模型如下所示：The material creep-damage constitutive model based on the continuous damage mechanics model described in step 2 is as follows:

Figure BDA00037401213700000210
Figure BDA00037401213700000210

Figure BDA00037401213700000211
Figure BDA00037401213700000211

σrep＝ασ1+(1-α)σe σ rep = ασ 1 +(1-α)σ e

其中

Figure BDA00037401213700000212
为蠕变速率，ω数值大小由0到1表示蠕变损伤，σ1为最大主应力，σe是等效应力，σrep是代表应力，α是与材料蠕变失效机理相关的参数，数值大小由0到1。in
Figure BDA00037401213700000212
is the creep rate, the value of ω is from 0 to 1 to represent the creep damage, σ 1 is the maximum principal stress, σ e is the equivalent stress, σ rep is the representative stress, α is a parameter related to the creep failure mechanism of the material, the numerical value The size ranges from 0 to 1.

步骤三中通过节点位置曲线获得不同缺口对应的节点位置的过程为：首先统计不同缺口形貌参数对应的节点位置，然后进行拟合得出曲线方程，即节点位置曲线，基于该曲线，在实际问题中可以直接通过缺口形貌计算节点位置，具体如下：In step 3, the process of obtaining the node positions corresponding to different gaps through the node position curve is as follows: first, the node positions corresponding to different gap topography parameters are counted, and then a curve equation, namely the node position curve, is obtained by fitting. In the problem, the node position can be calculated directly through the notch shape, as follows:

给定蠕变率

Figure BDA00037401213700000213
和载荷，选取诺顿模型常数n，通过公式
Figure BDA00037401213700000214
计算出相应的A值，对不同的n值以及对应的A值，输入基于诺顿模型的用户子程序UMAT中，在ABAQUS中进行蠕变模拟，当达到蠕变第二阶段时，绘制缺口截面处的Mises应力沿缺口截面的分布曲线，多条曲线的交点处就是节点位置。given creep rate
Figure BDA00037401213700000213
and load, choose the Norton model constant n, by formula
Figure BDA00037401213700000214
Calculate the corresponding A value, input different n values and corresponding A values into the user subroutine UMAT based on the Norton model, and perform creep simulation in ABAQUS. When the second stage of creep is reached, draw the notch section. The distribution curve of Mises stress along the notch section, the intersection of multiple curves is the node position.

绘制节点位置曲线的参数过程及曲线方程如下所示：The parametric process and curve equation for drawing the node position curve are as follows:

采用2r/(D-d)表示缺口锐度，(D-d)/D表示缺口深度，2r*/(D-d)表示归一化节点位置。其中D为光滑试样缺口截面直径，d为缺口截面处的直径，r为缺口半径，r*为节点位置距离缺口根部的距离，(D-d)/2为实际缺口深度，且当缺口度≥1时缺口为C-型缺口，当缺口度＜1时缺口为U-型缺口；We use 2r/(Dd) to represent the notch sharpness, (Dd)/D to represent the notch depth, and 2r*/(Dd) to represent the normalized node position. Where D is the diameter of the notch section of the smooth sample, d is the diameter of the notch section, r is the notch radius, r * is the distance between the node position and the notch root, (Dd)/2 is the actual notch depth, and when the notch degree ≥ 1 When the notch is a C-type notch, when the notch degree is less than 1, the notch is a U-type notch;

由缺口锐度与对应归一化节点位置绘制缺口位置曲线，曲线方程如公式如下：The notch position curve is drawn from the notch sharpness and the corresponding normalized node position. The curve equation is as follows:

y＝0.7410x0.5483 y=0.7410x 0.5483

其中，x＝2r/(D-d)表示为缺口锐度，y＝2r*/(D-d)表示为归一化节点位置。Among them, x=2r/(Dd) represents the notch sharpness, and y=2r * /(Dd) represents the normalized node position.

步骤五中所述的多轴应力状态下的蠕变-损伤寿命计算过程如下所示：The calculation process of the creep-damage life under the multiaxial stress state described in step 5 is as follows:

Figure BDA0003740121370000031
Figure BDA0003740121370000031

Figure BDA0003740121370000032
Figure BDA0003740121370000032

其中tf为多轴应力下的蠕变寿命，σrep为多轴应力状态下的参考应力，

Figure BDA0003740121370000033
为节点处的最大主应力，
Figure BDA0003740121370000034
为节点处的Mises应力，σnet为截面应力，α为应力修正参数；where t f is the creep life under multiaxial stress, σ rep is the reference stress under multiaxial stress state,
Figure BDA0003740121370000033
is the maximum principal stress at the node,
Figure BDA0003740121370000034
is the Mises stress at the node, σ net is the section stress, and α is the stress correction parameter;

其中当σrep/σnet>1时，该缺口对试样有减弱作用，当σrep/σnet<1时，该缺口对试样有强化作用；并且，

Figure BDA0003740121370000035
When σ rep /σ net >1, the notch has a weakening effect on the sample, and when σ rep /σ net <1, the notch has a strengthening effect on the sample; and,
Figure BDA0003740121370000035

应力修正参数α的获取方法如下所示：The method of obtaining the stress correction parameter α is as follows:

选取α数值，由公式

Figure BDA0003740121370000036
计算获得对应的σrep，进而由公式
Figure BDA0003740121370000037
计算蠕变寿命，以α的值为横坐标，蠕变寿命为纵坐标，根据已知的蠕变寿命在纵坐标处作平行于横坐标的横线，此时会发现横线与寿命曲线的交点相连是垂直于坐标的直线，最后交于横坐标，此时与横坐标交点的α值便为精确的α值。Select the value of α, by the formula
Figure BDA0003740121370000036
Calculate to obtain the corresponding σ rep , and then by the formula
Figure BDA0003740121370000037
Calculate the creep life, take the value of α as the abscissa, and the creep life as the ordinate. According to the known creep life, draw a horizontal line parallel to the abscissa at the ordinate. At this time, you will find the difference between the horizontal line and the life curve. The intersection point is connected by a straight line perpendicular to the coordinates, and finally intersects the abscissa. At this time, the α value of the intersection with the abscissa is the exact α value.

与现有技术相比，本发明所具有的有益效果如下：Compared with the prior art, the beneficial effects that the present invention has are as follows:

本发明的多轴应力状态下的材料的寿命预测方法适用于各种金属材料以及各个温度状态下的蠕变寿命预测，只需要改变连续损伤力学模型中的相关材料参数，适用范围广，该蠕变寿命预测方法操作简单便捷，以此更小成本、更高效的实现热端高温部件的设计优化、性能评估与剩余寿命预测。便于推广使用。其次，本方法通过进行材料单轴蠕变断裂实验，分别获取材料在多个单轴应力加载下的蠕变曲线，基于多条单轴蠕变曲线，获得连续损伤力学模型中的材料参数，材料参数精准可靠，提高了实验结果的准确性。另外，本发明在缺口形貌参数描述上区别于其他研究，提出了创新性的参数描述，更加科学、合理、准确的进行缺口形貌描述，进一步提高了实验结果的准确性。The life prediction method for materials under multiaxial stress state of the present invention is suitable for creep life prediction of various metal materials and various temperature states, only needs to change the relevant material parameters in the continuous damage mechanics model, and has a wide range of applications. The variable life prediction method is simple and convenient to operate, so as to achieve design optimization, performance evaluation and remaining life prediction of hot-end high-temperature components at a lower cost and more efficiently. Easy to promote and use. Secondly, this method obtains the creep curves of the material under multiple uniaxial stress loading by performing the material uniaxial creep rupture experiment, and obtains the material parameters in the continuous damage mechanics model based on the multiple uniaxial creep curves. The parameters are accurate and reliable, which improves the accuracy of the experimental results. In addition, the present invention is different from other studies in the description of the notch shape parameters, and proposes an innovative parameter description, which can describe the notch shape more scientifically, reasonably and accurately, and further improves the accuracy of the experimental results.

进一步的，本发明所述的基于节点应力法材料在c-型缺口结构下的蠕变-损伤寿命预测方法包含具有普适性的节点位置曲线，在工程实际中可以直接由缺口形貌计算节点位置，大大减小寻找节点的工作量。Further, the creep-damage life prediction method for materials based on the nodal stress method under the c-type notch structure according to the present invention includes a universal node position curve, and in engineering practice, the node can be directly calculated from the notch topography. location, greatly reducing the workload of finding nodes.

附图说明Description of drawings

图1为本发明的实施方式流程图；1 is a flow chart of an embodiment of the present invention;

图2为本发明在一种实施方式下的缺口圆柱试样结构图；2 is a structural diagram of a notched cylindrical sample under an embodiment of the present invention;

图3为650℃下GH4169镍基单晶高温合金在不同单轴应力载荷下的蠕变曲线；Figure 3 shows the creep curves of GH4169 nickel-based single crystal superalloy under different uniaxial stress loads at 650℃;

图4为本发明所述数值模拟在ABAQUS中建立的简化后的有限元模型；Fig. 4 is the simplified finite element model established in ABAQUS by the numerical simulation of the present invention;

图5为缺口半径为1mm的试验样件的节点位置；Figure 5 shows the node position of the test sample with a notch radius of 1mm;

图6为相同缺口结构，不同截面直径下节点的位置对比图；Fig. 6 is the same notch structure, the position comparison diagram of the node under different section diameters;

图7为本发明材料节点位置曲线；Fig. 7 is the material node position curve of the present invention;

图8为计算节点位置与相关研究中节点位置误差对比图；Figure 8 is a comparison diagram of the node position error in the calculation node position and related research;

图9为本发明材料参数α的精确测定，两条水平虚线分别为η＝0.2和η＝0.4处的蠕变试验寿命；Fig. 9 is the accurate measurement of the material parameter α of the present invention, and the two horizontal dotted lines are respectively the creep test life at η=0.2 and η=0.4;

图10为预估寿命与实验寿命误差对比图；Figure 10 is a comparison chart of the estimated life and experimental life errors;

图11(a)为缺口锐度为0.2时缺口截面上随蠕变时间的损伤演化0.001tf；Figure 11(a) shows the damage evolution 0.001tf on the notch section with creep time when the notch sharpness is 0.2;

图11(b)为缺口锐度为0.2时缺口截面上随蠕变时间的损伤演化tf；Figure 11(b) shows the damage evolution tf on the notch section with creep time when the notch sharpness is 0.2;

图12(a)为缺口锐度为1.6时缺口截面上随蠕变时间的损伤演化0.001tf；Figure 12(a) shows the damage evolution 0.001tf on the notch section with creep time when the notch sharpness is 1.6;

图12(b)为缺口锐度为1.6时缺口截面上随蠕变时间的损伤演化tf。Figure 12(b) shows the damage evolution tf on the notch section with creep time when the notch sharpness is 1.6.

具体实施方式Detailed ways

下面结合附图1-12对本发明做进一步说明。The present invention will be further described below in conjunction with accompanying drawings 1-12.

如图1所示，一种多轴应力状态下的材料的寿命预测方法，包括以下步骤：As shown in Figure 1, a method for predicting the life of a material under a multiaxial stress state includes the following steps:

步骤一：进行材料单轴蠕变断裂实验，分别获取材料在多个单轴应力加载下的蠕变曲线，基于多条单轴蠕变曲线，获得连续损伤力学模型中的材料参数；Step 1: Carry out a uniaxial creep rupture experiment of the material, obtain the creep curves of the material under multiple uniaxial stress loadings, and obtain the material parameters in the continuous damage mechanics model based on the multiple uniaxial creep curves;

步骤二：在ABAQUS中建立有限元模型，使用用户子程序UMAT定义基于连续损伤力学模型的材料蠕变-损伤本构模型；Step 2: Establish a finite element model in ABAQUS, and use the user subprogram UMAT to define the material creep-damage constitutive model based on the continuous damage mechanics model;

步骤三：通过节点位置曲线获得不同缺口对应的节点位置；Step 3: Obtain the node positions corresponding to different gaps through the node position curve;

步骤四：基于有限元软件ABAQUS中的creep模块计算得出相关截面应力加载时对应缺口截面上各节点处的最大主应力

Figure BDA0003740121370000051
与Mises应力
Figure BDA0003740121370000052
Step 4: Calculate the maximum principal stress at each node on the corresponding notch section when the relevant section stress is loaded based on the creep module in the finite element software ABAQUS
Figure BDA0003740121370000051
Stress with Mises
Figure BDA0003740121370000052

步骤五：基于步骤四中获得的

Figure BDA0003740121370000053
与
Figure BDA0003740121370000054
利用节点应力法与寿命计算公式进行相应多轴应力状态下的蠕变-损伤寿命计算。Step 5: Based on the results obtained in Step 4
Figure BDA0003740121370000053
and
Figure BDA0003740121370000054
The creep-damage life calculation under the corresponding multiaxial stress state is carried out by using the nodal stress method and the life calculation formula.

进一步的，步骤一中所述材料参数包括A、B、M、n、m、n0、χ和φ，A、B、M、n、m、n0、χ和φ是连续损伤力学模型中与温度相关的材料常数，由单轴蠕变试验曲线拟合计算得出。Further, the material parameters described in step 1 include A, B, M, n, m, n 0 , χ and φ, A, B, M, n, m, n 0 , χ and φ are in the continuous damage mechanics model. Temperature-dependent material constants, calculated from curve fitting of uniaxial creep tests.

单轴蠕变曲线拟合方法如下所示：The uniaxial creep curve fitting method is as follows:

Figure BDA0003740121370000055
Figure BDA0003740121370000055

其中，A和n是Norton方程

Figure BDA0003740121370000056
中的材料参数，需要至少同种温度下不同应力的至少两条单轴蠕变曲线进行确定，
Figure BDA0003740121370000057
为最小蠕变应变速率，其独立于施加应力与温度；where A and n are the Norton equations
Figure BDA0003740121370000056
The material parameters in , require at least two uniaxial creep curves with different stresses at the same temperature to determine,
Figure BDA0003740121370000057
is the minimum creep strain rate independent of applied stress and temperature;

Figure BDA0003740121370000058
Figure BDA0003740121370000058

其中tf为单轴蠕变寿命，σ为单轴截面应力；where t f is the uniaxial creep life, and σ is the uniaxial section stress;

基于公式

Figure BDA0003740121370000059
利用不同应力对应的蠕变寿命拟合得到M、χ和φ。formula based
Figure BDA0003740121370000059
M, χ and φ are obtained by fitting the creep life corresponding to different stresses.

进一步的，步骤二中所述基于连续损伤力学模型的材料蠕变-损伤本构模型如下所示：Further, the material creep-damage constitutive model based on the continuous damage mechanics model described in step 2 is as follows:

Figure BDA00037401213700000510
Figure BDA00037401213700000510

Figure BDA00037401213700000511
Figure BDA00037401213700000511

σrep＝ασ1+(1-α)σe σ rep = ασ 1 +(1-α)σ e

其中

Figure BDA00037401213700000512
为蠕变速率，ω数值大小由0到1表示蠕变损伤，σ1为最大主应力，σe是等效应力，σrep是代表应力，α是与材料蠕变失效机理相关的参数，数值大小由0到1。in
Figure BDA00037401213700000512
is the creep rate, the value of ω is from 0 to 1 to represent the creep damage, σ 1 is the maximum principal stress, σ e is the equivalent stress, σ rep is the representative stress, α is a parameter related to the creep failure mechanism of the material, the numerical value The size ranges from 0 to 1.

进一步的，步骤二中所述的蠕变-损伤本构模型通过FORTRAN语言嵌入ABAQUS。研究对象圆柱棒料的C-型缺口有限元模型建立如下所示：Further, the creep-damage constitutive model described in step 2 is embedded in ABAQUS through FORTRAN language. The C-shaped notch finite element model of the cylindrical bar of the research object is established as follows:

在ABAQUS/CAE建立带C-型缺口圆柱棒料的简化二维模型，如图2所示，设置材料属性并且划分网格，建立蠕变分析步，定义相关所需输出变量至ODB文件。Create a simplified two-dimensional model of cylindrical bar with C-shaped notch in ABAQUS/CAE, as shown in Figure 2, set the material properties and divide the mesh, establish a creep analysis step, and define the relevant required output variables to the ODB file.

进一步的，步骤三中通过节点位置曲线获得不同缺口对应的节点位置的过程为：首先统计不同缺口形貌参数对应的节点位置，然后进行拟合得出曲线方程，即节点位置曲线，基于该曲线，在实际问题中可以直接通过缺口形貌计算节点位置，具体如下：Further, in step 3, the process of obtaining the node positions corresponding to different gaps through the node position curve is as follows: first, the node positions corresponding to different gap topography parameters are counted, and then a curve equation is obtained by fitting, that is, the node position curve, based on the curve. , in the actual problem, the node position can be calculated directly through the notch shape, as follows:

给定蠕变率

Figure BDA00037401213700000513
载荷为200MPa，取诺顿模型常数n＝1、3、5、7或10，通过公式
Figure BDA00037401213700000514
计算出相应的A值，对五组不同n值以及对应的A值，输入基于诺顿模型的用户子程序UMAT中，在ABAQUS中进行蠕变模拟，当达到蠕变第二阶段时，绘制缺口截面处的Mises应力沿缺口截面的分布曲线，多条曲线的交点处就是节点位置。given creep rate
Figure BDA00037401213700000513
The load is 200MPa, take the Norton model constant n = 1, 3, 5, 7 or 10, through the formula
Figure BDA00037401213700000514
Calculate the corresponding A value, input the five groups of different n values and the corresponding A value into the user subroutine UMAT based on the Norton model, carry out the creep simulation in ABAQUS, and draw the notch section when the second stage of creep is reached. The distribution curve of Mises stress along the notch section, and the intersection of multiple curves is the node position.

优选的，节点应力法又称骨点应力法，其表示构件在多轴应力状态下，随着蠕变过程中时间的变化，有一点处的应力值始终近似不变。此外，当材料的应力指数n不同时，该点处的应力值也保持近似恒定。这个点被称为节点或者骨点。Preferably, the nodal stress method is also called the bone point stress method, which indicates that the stress value at one point remains approximately unchanged with the time change in the creep process of the member under the multiaxial stress state. Furthermore, when the stress exponent n of the materials is different, the stress value at this point also remains approximately constant. This point is called a node or bone point.

进一步的，绘制节点位置曲线的参数过程及曲线方程如下所示：Further, the parameter process and curve equation for drawing the node position curve are as follows:

采用2r/(D-d)表示缺口锐度，(D-d)/D表示缺口深度，2r*/(D-d)表示归一化节点位置。其中D为光滑试样缺口截面直径，d为缺口截面处的直径，r为缺口半径，r*为节点位置距离缺口根部的距离，(D-d)/2为实际缺口深度，且当缺口度≥1时缺口为C-型缺口，当缺口度＜1时缺口为U-型缺口，发现缺口深度对归一化缺口位置无影响，缺口锐度与归一化节点位置有着函数关系。We use 2r/(Dd) to represent the notch sharpness, (Dd)/D to represent the notch depth, and 2r*/(Dd) to represent the normalized node position. Where D is the diameter of the notch section of the smooth sample, d is the diameter of the notch section, r is the notch radius, r * is the distance between the node position and the notch root, (Dd)/2 is the actual notch depth, and when the notch degree ≥ 1 When the gap is C-shaped, when the gap degree is less than 1, the gap is U-shaped. It is found that the gap depth has no effect on the normalized gap position, and the gap sharpness has a functional relationship with the normalized node position.

由缺口锐度与对应归一化节点位置绘制缺口位置曲线，该曲线在工程实际中可以适用于所有同类型缺口的问题，曲线方程如公式如下：The notch position curve is drawn from the notch sharpness and the corresponding normalized node position. The curve can be applied to all the same type of notch problems in engineering practice. The curve equation is as follows:

y＝0.7410x0.5483 y=0.7410x 0.5483

其中，x＝2r/(D-d)表示为缺口锐度，y＝2r*/(D-d)表示为归一化节点位置。Among them, x=2r/(Dd) represents the notch sharpness, and y=2r * /(Dd) represents the normalized node position.

进一步的，步骤五中所述的多轴应力状态下的蠕变-损伤寿命计算过程如下所示：Further, the calculation process of the creep-damage life under the multiaxial stress state described in step 5 is as follows:

在步骤三和步骤四中得到相关应力后，基于公式

Figure BDA0003740121370000061
和公式
Figure BDA0003740121370000062
Figure BDA0003740121370000063
进行寿命计算。After obtaining the relevant stresses in steps 3 and 4, based on the formula
Figure BDA0003740121370000061
and formula
Figure BDA0003740121370000062
Figure BDA0003740121370000063
Do life calculations.

其中tf为多轴应力下的蠕变寿命，σrep为多轴应力状态下的参考应力，

Figure BDA0003740121370000064
为节点处的最大主应力，
Figure BDA0003740121370000065
为节点处的Mises应力，σnet为截面应力，α为应力修正参数；where t f is the creep life under multiaxial stress, σ rep is the reference stress under multiaxial stress state,
Figure BDA0003740121370000064
is the maximum principal stress at the node,
Figure BDA0003740121370000065
is the Mises stress at the node, σ net is the section stress, and α is the stress correction parameter;

其中当σrep/σnet>1时，该缺口对试样有减弱作用，当σrep/σnet<1时，该缺口对试样有强化作用；并且，

Figure BDA0003740121370000066
When σ rep /σ net >1, the notch has a weakening effect on the sample, and when σ rep /σ net <1, the notch has a strengthening effect on the sample; and,
Figure BDA0003740121370000066

应力修正参数α的获取方法如下所示：The method of obtaining the stress correction parameter α is as follows:

取α＝0、0.2、0.4、0.6、0.8或1，由公式

Figure BDA0003740121370000067
计算获得对应的σrep，进而由公式
Figure BDA0003740121370000068
计算蠕变寿命，如图9所示，以α的值为横坐标，蠕变寿命为纵坐标，根据已知的蠕变寿命在纵坐标处作平行于横坐标的横线，此时会发现横线与寿命曲线的交点相连是垂直于坐标的直线，最后交于横坐标，此时与横坐标交点的α值便为精确的α值。Take α = 0, 0.2, 0.4, 0.6, 0.8 or 1, by the formula
Figure BDA0003740121370000067
Calculate to obtain the corresponding σ rep , and then by the formula
Figure BDA0003740121370000068
Calculate the creep life, as shown in Figure 9, take the value of α as the abscissa, and the creep life as the ordinate. According to the known creep life, draw a horizontal line parallel to the abscissa at the ordinate. At this time, it will be found that The intersection of the horizontal line and the life curve is a straight line perpendicular to the coordinates, and finally intersects the abscissa. At this time, the α value of the intersection with the abscissa is the exact α value.

优选的，以下为第二代镍基单晶高温合金GH4169材料在图2所示C-型缺口多轴应力下的蠕变-损伤寿命预测。Preferably, the following is the creep-damage life prediction of the second-generation nickel-based single crystal superalloy GH4169 material under the C-notch multiaxial stress shown in FIG. 2 .

表1为第二代镍基单晶高温合金GH4169的材料成分(wt％)。Table 1 shows the material composition (wt%) of the second generation nickel-based single crystal superalloy GH4169.

Figure BDA0003740121370000071
Figure BDA0003740121370000071

表2为图2中各组缺口结构的尺寸。Table 2 shows the dimensions of each group of notch structures in FIG. 2 .

Figure BDA0003740121370000072
Figure BDA0003740121370000072

通过650℃下单轴蠕变断裂实验获得GH4169高温合金在750MPa和700MPa加载应力下的蠕变-应变曲线。基于多条单轴蠕变曲线，进行相关计算，获得连续损伤力学模型中的材料参数。其中连续损伤力学模型如下The creep-strain curves of GH4169 superalloy under loading stress of 750MPa and 700MPa were obtained by uniaxial creep rupture experiment at 650℃. Based on multiple uniaxial creep curves, relevant calculations are performed to obtain material parameters in the continuous damage mechanics model. The continuous damage mechanics model is as follows

Figure BDA0003740121370000073
Figure BDA0003740121370000073

Figure BDA0003740121370000074
Figure BDA0003740121370000074

σrep＝ασ1+(1-α)σe (3)σ rep = ασ 1 +(1-α)σ e (3)

其中

Figure BDA0003740121370000075
为蠕变速率，ω数值大小由0到1表示蠕变损伤，σ1为最大主应力，σe是等效应力，σrep是代表应力，α是与材料蠕变失效机理相关的参数，数值大小由0到1。A、B、M、n、m、n0、χ和φ是连续损伤力学模型中与温度相关的材料常数，由单轴蠕变试验曲线拟合计算得出。所述650℃下GH4169高温合金材料参数拟合过程如下所示：in
Figure BDA0003740121370000075
is the creep rate, the value of ω is from 0 to 1 to represent the creep damage, σ 1 is the maximum principal stress, σ e is the equivalent stress, σ rep is the representative stress, α is a parameter related to the creep failure mechanism of the material, the numerical value The size ranges from 0 to 1. A, B, M, n, m, n 0 , χ and φ are the temperature-dependent material constants in the continuous damage mechanics model, calculated from uniaxial creep test curve fitting. The parameter fitting process of the GH4169 superalloy material at 650°C is as follows:

图3是650℃下GH4169镍基单晶高温合金在不同单轴应力载荷下的蠕变曲线。由图3的2条蠕变曲线通过Norton方程(4)计算材料参数A和n。Figure 3 shows the creep curves of GH4169 nickel-based single crystal superalloy under different uniaxial stress loads at 650°C. The material parameters A and n are calculated from the 2 creep curves of Fig. 3 by Norton's equation (4).

Figure BDA0003740121370000076
Figure BDA0003740121370000076

其中

Figure BDA0003740121370000077
为最小蠕变应变速率，其独立于施加应力与温度。in
Figure BDA0003740121370000077
is the minimum creep strain rate, which is independent of applied stress and temperature.

基于公式(5)，利用图3所示不同应力对应的蠕变寿命计算得到χ和M(1+φ)。Based on formula (5), χ and M(1+φ) are obtained by calculating the creep life corresponding to different stresses shown in Fig. 3.

Figure BDA0003740121370000078
Figure BDA0003740121370000078

其中tf为单轴蠕变寿命，σ为单轴截面应力。where t f is the uniaxial creep life and σ is the uniaxial section stress.

再将M代入

Figure BDA0003740121370000079
中，利用数据处理软件进行曲线拟合得到φ。Substitute M into
Figure BDA0003740121370000079
, use data processing software to perform curve fitting to obtain φ.

表3为650℃下，截面载荷为750MPa下GH4169镍基单晶高温合金在多轴应力下不同缺口尺寸对应的蠕变寿命与蠕变应变。具体如下：Table 3 shows the creep life and creep strain corresponding to different notch sizes of GH4169 nickel-based single crystal superalloy under multiaxial stress at 650 °C and a cross-sectional load of 750 MPa. details as follows:

Figure BDA0003740121370000081
Figure BDA0003740121370000081

表4为650℃下GH4169高温合金材料参数。Table 4 shows the material parameters of GH4169 superalloy at 650°C.

Figure BDA0003740121370000082
Figure BDA0003740121370000082

通过步骤二中所述方法，将蠕变-损伤本构模型通过FORTRAN语言嵌入ABAQUS。图4为在ABAQUS/CAE建立的带C-型缺口圆柱棒料的简化二维模型。The creep-damage constitutive model is embedded in ABAQUS through FORTRAN language by the method described in step 2. Figure 4 is a simplified two-dimensional model of a cylindrical bar with C-shaped notches established in ABAQUS/CAE.

如步骤三所述需要获得仅与缺口结构形貌有对应关系的节点位置曲线。则给定蠕变率

Figure BDA0003740121370000083
载荷为200MPa，取诺顿模型常数n＝1、3、5、7或10，通过公式(4)计算出相应的A值。对五组不同n值以及对应的A值，输入基于诺顿模型的用户子程序UMAT中，在ABAQUS中进行蠕变模拟。当达到蠕变第二阶段时，绘制缺口截面处的Mises应力沿缺口截面的分布曲线，多条曲线的交点处就是节点位置。图5即为缺口半径为1mm的试验样件的节点位置，节点距缺口根部的距离大约为1.125mm。As described in step 3, it is necessary to obtain a node position curve that only has a corresponding relationship with the morphology of the notch structure. Then given the creep rate
Figure BDA0003740121370000083
The load is 200MPa, taking the Norton model constant n=1, 3, 5, 7 or 10, and calculating the corresponding A value by formula (4). Five groups of different n values and corresponding A values are input into the user subroutine UMAT based on the Norton model, and the creep simulation is performed in ABAQUS. When the second stage of creep is reached, the distribution curve of Mises stress at the notch section along the notch section is drawn, and the intersection of multiple curves is the node position. Figure 5 shows the node position of the test sample with a notch radius of 1mm, and the distance between the node and the root of the notch is about 1.125mm.

在参考文献1和2中为了更好地定义缺口形貌尺寸，都采用缺口度d/r来描述缺口尺寸。图6的(a)(b)分别表示D＝10,d＝6,r＝2和D＝20,d＝16,r＝2在n＝1、3、5、7或10时的缺口试样缺口截面的mises应力分布，发现节点位置大约都在距缺口根部1.5mm处。这说明在D与d的差值不发生改变的情况下，同时增大或缩小D与d的值，不改变缺口半径时，节点到缺口根部的的距离始终不发生改变。也就是说D-d不改变的前提下，d的大小与节点的位置无关。所以为了更加准确的表示影响节点位置的缺口尺寸参数，本发明中采用2r/(D-d)表示缺口锐度，(D-d)/D表示相对缺口深度，2r*/(D-d)表示节点相对位置。其中(D-d)/2为实际缺口深度距离，并且当缺口锐度≥1时缺口描述为C-型，当缺口锐度＜1时缺口可描述为为U-型缺口。In order to better define the size of the notch in References 1 and 2, the notch degree d/r is used to describe the size of the notch. (a) and (b) of Fig. 6 represent the notch tests of D=10, d=6, r=2 and D=20, d=16, r=2 when n=1, 3, 5, 7 or 10, respectively The mises stress distribution of the sample notch section shows that the node positions are about 1.5mm away from the root of the notch. This shows that when the difference between D and d does not change, increase or decrease the values of D and d at the same time, and when the gap radius does not change, the distance from the node to the root of the gap does not change. That is to say, under the premise that D-d does not change, the size of d has nothing to do with the position of the node. Therefore, in order to more accurately represent the notch size parameter that affects the position of the node, 2r/(D-d) is used in the present invention to represent the sharpness of the gap, (D-d)/D to represent the relative gap depth, and 2r*/(D-d) to represent the relative position of the node. Where (D-d)/2 is the actual notch depth distance, and when the notch sharpness ≥ 1, the notch is described as a C-shaped notch, and when the notch sharpness is less than 1, the notch can be described as a U-shaped notch.

参考文献references

[1]S.Goyal,K.Laha,Creep life prediction of 9Cr–1Mo steel undermultiaxial state of stress,Materials Science and Engineering:A.615(2014)348–360.https://doi.org/10.1016/j.msea.2014.07.096.[1]S.Goyal,K.Laha,Creep life prediction of 9Cr–1Mo steel undermultiaxial state of stress,Materials Science and Engineering:A.615(2014)348–360.https://doi.org/10.1016/j .msea.2014.07.096.

[2]Y.Chang,H.Xu,Y.Ni,X.Lan,H.Li,The effect of multiaxial stress stateon creep behavior and fracture mechanism of P92 steel,Materials Science andEngineering:A.636(2015)70–76.https://doi.org/10.1016/j.msea.2015.03.056.[2] Y.Chang,H.Xu,Y.Ni,X.Lan,H.Li,The effect of multiaxial stress stateon creep behavior and fracture mechanism of P92 steel,Materials Science and Engineering:A.636(2015)70– 76. https://doi.org/10.1016/j.msea.2015.03.056.

表5为有限元模拟出不同缺口尺寸样件节点到缺口根部距离Table 5 shows the distance from the node to the root of the notch of the sample with different notch sizes simulated by finite element

Figure BDA0003740121370000091
Figure BDA0003740121370000091

Figure BDA0003740121370000101
Figure BDA0003740121370000101

通过这些节点的位置分析拟合得到了图7中的节点位置曲线，拟合公式为式(6)。图8是该曲线预测节点位置与参考文献1和2中所述节点位置的相对误差。其相对误差在两倍误差带以内。则可由式(6)在工程实际中直接计算节点位置。Through the position analysis and fitting of these nodes, the node position curve in Fig. 7 is obtained, and the fitting formula is formula (6). Figure 8 is the relative error of the predicted node positions of this curve and the node positions described in References 1 and 2. The relative error is within twice the error band. Then, the node position can be directly calculated by formula (6) in engineering practice.

步骤四通过有限元模拟确定GH4169镍基单晶高温合金在缺口截面上节点处的最大主应力

Figure BDA0003740121370000102
与Mises应力
Figure BDA0003740121370000103
Step 4 Determine the maximum principal stress at the node on the notch section of GH4169 nickel-based single crystal superalloy by finite element simulation
Figure BDA0003740121370000102
Stress with Mises
Figure BDA0003740121370000103

步骤五，在步骤三和步骤四中得到相关应力后，基于公式(7)和公式(8)进行多轴应力状态下的蠕变-损伤寿命计算。In step 5, after the relevant stress is obtained in step 3 and step 4, based on formula (7) and formula (8), the creep-damage life calculation under the multiaxial stress state is performed.

Figure BDA0003740121370000104
Figure BDA0003740121370000104

Figure BDA0003740121370000105
Figure BDA0003740121370000105

其中tf为多轴应力下的蠕变寿命，σrep为多轴应力状态下的参考应力，

Figure BDA0003740121370000106
为节点处的最大主应力，
Figure BDA0003740121370000107
为节点处的Mises应力，σnet为截面应力。α为应力修正参数。where t f is the creep life under multiaxial stress, σ rep is the reference stress under multiaxial stress state,
Figure BDA0003740121370000106
is the maximum principal stress at the node,
Figure BDA0003740121370000107
is the Mises stress at the node, and σnet is the section stress. α is the stress correction parameter.

当σrep/σnet>1时，该缺口对试样有减弱作用，当σrep/σnet<1时，该缺口对试样有强化作用。此外，

Figure BDA0003740121370000108
的关系始终存在。When σ rep /σ net >1, the notch has a weakening effect on the sample, and when σ rep /σ net <1, the notch has a strengthening effect on the sample. also,
Figure BDA0003740121370000108
relationship always exists.

进一步的，应力修正参数α的获取方法如下所示：Further, the method for obtaining the stress correction parameter α is as follows:

取α＝0、0.2、0.4、0.6、0.8或1，由公式(8)计算获得对应的σrep，进而由公式(7)计算蠕变寿命。如图9所示，以α的值为横坐标，蠕变寿命为纵坐标，根据已知的蠕变寿命在纵坐标处作平行于横坐标的横线，此时会发现横线与寿命曲线的交点相连是垂直于坐标的直线，最后交于横坐标，此时与横坐标交点的α值便为精确的α值。计算得到650℃下GH4169镍基单晶高温合金的应力修正参数α＝0.51。Taking α=0, 0.2, 0.4, 0.6, 0.8 or 1, the corresponding σ rep is obtained by calculation from formula (8), and then the creep life is calculated by formula (7). As shown in Figure 9, the value of α is taken as the abscissa, and the creep life is the ordinate. According to the known creep life, a horizontal line parallel to the abscissa is drawn at the ordinate. At this time, the horizontal line and the life curve will be found. The intersection points of , are connected by a straight line perpendicular to the coordinates, and finally intersect with the abscissa. At this time, the α value of the intersection with the abscissa is the exact α value. The stress correction parameter α=0.51 of GH4169 nickel-based single crystal superalloy at 650℃ was calculated.

基于求得材料应力修正参数α，可由公式(7)和公式(8)计算缺口试样的蠕变损伤寿命。图10为计算寿命与实验寿命的对比图，发现其误差在13.02％以内，故而本发明在工程实际中实用便捷有效。Based on the obtained material stress correction parameter α, the creep damage life of the notched specimen can be calculated from formula (7) and formula (8). Figure 10 is a comparison diagram of the calculated life and the experimental life, and it is found that the error is within 13.02%, so the present invention is practical, convenient and effective in engineering practice.

此外，图11和图12分别为缺口锐度为0.2时和缺口锐度为1.6时缺口截面上随蠕变时间的损伤演化，图11(a)和图12(a)为0.001tf,图11(b)和图12(b)为tf。In addition, Fig. 11 and Fig. 12 show the damage evolution of the notch section with creep time when the notch sharpness is 0.2 and 1.6 respectively, Fig. 11(a) and Fig. 12(a) are 0.001tf, Fig. 11 (b) and Figure 12(b) are tf.

综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (8)

1.A method for predicting the service life of a material in a multiaxial stress state is characterized by comprising the following steps:
the method comprises the following steps: performing a material uniaxial creep rupture experiment, respectively obtaining creep curves of the material under a plurality of uniaxial stress loads, and obtaining material parameters in the continuous damage mechanical model based on the plurality of uniaxial creep curves;
step two: establishing a finite element model in ABAQUS, and defining a material creep-damage constitutive model based on a continuous damage mechanical model by using a user subprogram UMAT;
step three: obtaining node positions corresponding to different gaps through a node position curve;
step four: calculating to obtain the maximum main stress at each node on the corresponding notch section when the stress of the relevant section is loaded based on a crop module in finite element software ABAQUS
Figure FDA0003740121360000011
And Mises stress
Figure FDA0003740121360000012
Step five: obtained based on step four
Figure FDA0003740121360000013
And
Figure FDA0003740121360000014
and calculating the creep-damage life under the corresponding multi-axis stress state by using a node stress method and a life calculation formula.
2. A method of predicting the lifetime of a material under multiaxial stress conditions as recited in claim 1, characterized in that the material parameters in the first step comprise A,B、M、n、m、n 0 Chi and phi, A, B, M, n, M, n 0 And chi and phi are material constants related to temperature in a continuous damage mechanics model and are calculated by fitting a uniaxial creep test curve.
3. The method of claim 2, wherein the uniaxial creep curve fitting method is as follows:
Figure FDA0003740121360000015
wherein A and n are Norton's equations
Figure FDA0003740121360000016
The material parameters in (2) need to be determined by at least two uniaxial creep curves of different stresses at least the same temperature,
Figure FDA0003740121360000017
is a minimum creep strain rate, which is independent of applied stress and temperature;
Figure FDA0003740121360000018
wherein t is f For uniaxial creep life, σ is uniaxial section stress;
based on the formula
Figure FDA0003740121360000019
And obtaining M, chi and phi by using creep life fitting corresponding to different stresses.
4. The method for predicting the service life of the material under the multiaxial stress state as recited in claim 1, wherein the material creep-damage constitutive model based on the continuous damage mechanical model in the second step is as follows:
Figure FDA00037401213600000110
Figure FDA00037401213600000111
σ rep ＝ασ 1 +(1-α)σ e
wherein
Figure FDA00037401213600000112
For creep rate, the magnitude of ω is 0 to 1 representing creep damage, σ 1 Is the maximum principal stress, σ e Is the equivalent stress, σ rep Is representative of stress, alpha is a parameter related to the material creep failure mechanism, and the numerical value is from 0 to 1.
5. The method for predicting the service life of the material in the multiaxial stress state as claimed in claim 1, wherein the process of obtaining the node positions corresponding to different notches through the node position curve in the third step is as follows: firstly, counting node positions corresponding to different notch morphology parameters, then fitting to obtain a curve equation, namely a node position curve, and based on the curve, directly calculating the node positions through the notch morphology in an actual problem, wherein the method specifically comprises the following steps:
given creep rate
Figure FDA0003740121360000021
And load, selecting a Nuon model constant n, and obtaining the load through a formula
Figure FDA0003740121360000022
Calculating corresponding A values, inputting different n values and corresponding A values into a user subprogram UMAT based on a Nonton model, carrying out creep simulation in ABAQUS, and drawing a distribution curve of Mises stress at the notch section along the notch section when reaching a second stage of creep,the intersection of the curves is the node position.
6. The method for predicting the service life of the material under the multiaxial stress state as recited in claim 5, wherein a parametric process and a curve equation for drawing a node position curve are as follows:
using 2 r/(D-D) to represent the notch sharpness, (D-D)/D to represent the notch depth, and 2 r/(D-D) to represent the normalized nodal position, wherein D is the smooth specimen notch cross-section diameter, D is the diameter at the notch cross-section, r is the notch radius * The distance between the node position and the root of the notch is (D-D)/2, the actual notch depth is, when the notch degree is more than or equal to 1, the notch is a C-shaped notch, and when the notch degree is less than 1, the notch is a U-shaped notch;
drawing a notch position curve by the notch acutance and the corresponding normalized node position, wherein the curve equation is as follows:
y＝0.7410x 0.5483
where x =2 r/(D-D) is expressed as notch sharpness, y =2r * and/D-D is expressed as normalized node position.
7. The method for predicting the service life of the material under the multiaxial stress state as claimed in claim 1, wherein the calculation process of the creep-damage service life under the multiaxial stress state in the step five is as follows:
Figure FDA0003740121360000023
Figure FDA0003740121360000024
wherein t is f For creep life under multiaxial stress, σ rep For the reference stress in the multi-axial stress state,
Figure FDA0003740121360000025
is the most at the nodeThe high principal stress is a function of the stress,
Figure FDA0003740121360000026
is the Mises stress at the node, σ net Is section stress, alpha is a stress correction parameter;
wherein when σ rep /σ net >1, the notch has a weakening effect on the sample, when σ rep /σ net <1, the notch has a reinforcing effect on the sample, and,
Figure FDA0003740121360000027
8. the method for predicting the service life of the material under the multiaxial stress state as recited in claim 7, wherein the stress correction parameter α is obtained as follows:
selecting alpha value, from formula
Figure FDA0003740121360000028
Calculating to obtain corresponding sigma rep And then by the formula
Figure FDA0003740121360000031
Calculating the creep life, taking the value of alpha as an abscissa and the creep life as an ordinate, and making a transverse line parallel to the abscissa at the ordinate according to the known creep life, wherein the intersection point of the transverse line and the life curve is a straight line perpendicular to the coordinate and is finally intersected with the abscissa, and the value of alpha at the intersection point of the transverse line and the abscissa is the accurate value of alpha.
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