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WO2018171315A1 - 一种材料多轴蠕变失效应变预测方法 - Google Patents

一种材料多轴蠕变失效应变预测方法 Download PDF

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Publication number
WO2018171315A1
WO2018171315A1 PCT/CN2018/072896 CN2018072896W WO2018171315A1 WO 2018171315 A1 WO2018171315 A1 WO 2018171315A1 CN 2018072896 W CN2018072896 W CN 2018072896W WO 2018171315 A1 WO2018171315 A1 WO 2018171315A1
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creep
multiaxial
failure strain
strain
stress
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PCT/CN2018/072896
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English (en)
French (fr)
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张玉财
蒋文春
王传龙
涂善东
王宁
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中国石油大学(华东)
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Publication of WO2018171315A1 publication Critical patent/WO2018171315A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

Definitions

  • a multi-axial creep failure strain prediction method for materials belongs to the field of strain prediction technology.
  • strain-based continuous damage mechanics models have received increasing attention.
  • the model based on strain damage is also called the ductility exhaustion model.
  • the conversion relationship between classical uniaxial and multiaxial creep failure strain is the conversion relationship proposed by Cocks-Ashby.
  • the empirical multiaxial creep ductility factor (MCDF) obtained from the conversion relationship is widely used for creep damage and creep life prediction.
  • the multiaxial creep ductility factor can be easily used to simulate creep crack propagation and give acceptable predictions, it lacks the physical meaning and, in some cases, Cocks-Ashby MCDF The prediction of the axial creep failure strain is not reasonable and therefore needs to be improved.
  • the technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a multi-axial creep failure strain prediction method for material failure prediction which can more accurately predict the multi-axis creep of a material under high temperature conditions.
  • the technical solution adopted by the present invention to solve the technical problem thereof is: the multi-axis creep failure strain prediction method of the material, characterized in that the method comprises the following steps:
  • Step (1) based on the strain damage criterion, obtain a relationship between the material creep rate and the strain rate according to the microscopic hole growth mechanism;
  • Step (2) controlling the hole growth theory by power law creep, obtaining uniaxial and multiaxial stress state parameters
  • Step (3) integrating the microscopic holes to obtain the failure time under the constant load of the material, thereby indicating the creep failure strain under the uniaxial and multiaxial stress, and obtaining the multiaxial creep ductility factor;
  • Step (4) the multi-axis creep ductility factor is fitted to the parameters, and the multi-axial creep failure strain fitting parameters under different stress states are obtained, thereby obtaining a multi-axis creep ductility factor prediction equation;
  • step (5) the finite element software is used to predict the creep failure strain and life of the material under multiaxial stress state.
  • the microscopic pore growth mechanism described in the step (1) is a mechanism for the viscoplastic pore length in the crack tip region.
  • the relationship between the creep rate and the strain rate of the material described in the step (1) is:
  • the axial strain rate of a cylinder containing a hole The radial strain rate of a cylinder containing a hole, The steady-state creep rate when the cylinder does not contain holes.
  • the uniaxial and multiaxial stress state parameters described in step (2) utilize the energy principle and are obtained by the New-Raphson method.
  • the calculation formula of the uniaxial and multiaxial stress state parameters described in the step (2) is:
  • ⁇ is a multiaxial stress state parameter
  • ⁇ 0 is a uniaxial stress state parameter
  • a and b 0 are material-dependent constants
  • n is a determined material constant
  • ⁇ m / ⁇ eq is a stress triaxiality
  • the formula for calculating the multiaxial creep ductility factor described in the step (3) is as follows:
  • ⁇ f is the creep failure strain under uniaxial stress
  • a and b are material-dependent constants
  • n is the determined material constant
  • ⁇ m / ⁇ eq is the stress triaxiality
  • the creep failure strain fitting parameters a and b under different stress states are obtained by the notch creep test, and the multiaxial creep ductility factor prediction equation described in the step (4) is obtained.
  • the multi-axis creep ductility factor prediction equation described in the step (4) is combined with the creep-damage constitutive equation and embedded into the finite element software by the Fortran language.
  • the present invention has the following beneficial effects:
  • the multiaxial creep failure strain prediction method of the material can define the multiaxial creep ductility factor through the creep failure strain calculation method of the material under multiaxial stress state, and obtain the multiaxial creep ductility factor calculation equation, and then obtain The multiaxial creep failure strain of the material is based on the established multiaxial creep damage constitutive equation.
  • the finite element software is used to predict the creep failure strain of the material under multiaxial stress state, which can more accurately predict the material under high temperature conditions. Failure strain of multiaxial creep.
  • the invention defines the multiaxial creep ductility factor by using the energy principle, and gives corresponding physical meaning to the multiaxial creep ductility factor, and obtains a new multiaxial creep ductility factor prediction.
  • the subroutine is programmed and embedded in the finite element software, so as to more accurately predict the failure strain of the multiaxial creep of the material under high temperature conditions.
  • Figure 1 is a flow chart of a multi-axial creep failure strain prediction method for materials.
  • Fig. 2 is a model diagram of a crack-containing sample subjected to a tensile load.
  • Fig. 3 is a model diagram of a crack tip region of a crack-containing sample.
  • Figure 4 is a diagram of the ideal grain model under multiaxial loading.
  • Figure 5 is an enlarged schematic view of a cylinder containing a hole.
  • Figure 6 is a comparison of the multiaxial creep failure strain and experimental values obtained by different conversion models of 9Cr-1Mo alloy at 600 °C.
  • Figure 7 is a geometrical view of a cylindrical notched tensile specimen.
  • a material multi-axis creep failure strain prediction method is characterized in that the method comprises the following steps:
  • Step (1) based on the strain damage criterion, obtain a relationship between the material creep rate and the strain rate according to the microscopic hole growth mechanism;
  • the microscopic pore growth mechanism considers that the pores are mainly nucleated and grown at the crystal interface (especially at the crystal interface perpendicular to the tensile stress), and the fully grown pores will be polymerized to form micro-cracks of grain size (porous crystals). interface). Finally, the combination of microcracks leads to the expansion of macroscopic creep cracks.
  • the volume change rate of the cylinder is related to f h as follows:
  • V represents the volume of the cylinder
  • V is the steady-state creep rate when there is no hole.
  • the volume change of a cylinder can also be defined by the creep rate:
  • the axial strain rate of a cylinder containing a hole The radial strain rate of a cylinder containing a hole.
  • Step (2) using the energy principle, controlling the hole growth theory by power law creep, and obtaining the uniaxial and multiaxial stress state parameters by the New-Raphson method;
  • the multiaxial stress state parameter ⁇ is defined as:
  • ⁇ 0 is a uniaxial stress state parameter
  • Step (3) integrating the microscopic holes to obtain the failure time under the constant load of the material, thereby indicating the creep failure strain under the uniaxial and multiaxial stress, and obtaining the multiaxial creep ductility factor;
  • f i is the initial hole area fraction
  • f c is the area fraction at which the hole combination occurs
  • t c is the time required from the initial to the hole combination in the multiaxial stress state.
  • Creep failure strain under multiaxial stress Can be obtained by:
  • t c0 is the time required for the merging from the initial to the hole in the uniaxial stress state.
  • a new multiaxial creep ductility factor MCDF can be defined:
  • Equation (15) can be simplified to the following formula:
  • Step (4) the multi-axis creep ductility factor is fitted to the parameters, and the multi-axial creep failure strain fitting parameters under different stress states are obtained, thereby obtaining a multi-axis creep ductility factor prediction equation;
  • a and b are material-dependent constants, and the creep failure strain at different stress triaxial degrees ⁇ m / ⁇ eq can be obtained by the notch creep test, and then fitted by formula (16). Obtain the parameters a and b to obtain a multi-axis creep ductility factor prediction equation.
  • Step (5) using finite element software to predict the creep failure strain and life of the material under multiaxial stress state
  • the Fortran language is used to compile the subroutine and embed into the finite element software ABAQUS to realize the multiaxial stress state of the material. Prediction of creep failure strain and life.
  • Table 3 Contrast data table of different creep damage constitutive models and tensile stresses compared with the creep life prediction values and test values of the specimens under tensile load
  • the multiaxial creep failure strain of 9Cr-1Mo alloy at 600 °C is predicted.
  • Figure 6 shows the comparison of the multi-axial creep failure strain and the experimental values predicted by different models under different stress triaxial degrees.
  • the parameters in the model proposed in the present invention were obtained by fitting experimental data.
  • the conversion model proposed in the present invention effectively avoids the occurrence of stress triaxiality ⁇ m / ⁇ eq >3 in the material. The ratio is too small.
  • Table 1 shows the multi-axis creep failure strain and the experimental value error analysis obtained by using the Cocks and Ashby (CA) model, the Wen and Tu (WT) model, and the transformation model proposed in the present invention.
  • CA Cocks and Ashby
  • WT Wen and Tu
  • Table 1 shows the multi-axis creep failure strain and the experimental value error analysis obtained by using the Cocks and Ashby (CA) model, the Wen and Tu (WT) model, and the transformation model proposed in the present invention.
  • CA Cocks and Ashby
  • WT Wen and Tu
  • the geometry of the notched creep specimen is shown in Fig. 7, and the data of the sensitivity ratio is shown in Table 2.
  • the KR creep damage constitutive model and the WT creep damage constitutive model were used respectively. Under different tensile loads, different notch sensitivity was simulated and predicted than the creep life of the specimen.
  • the comparative data of the test value and the simulated value are shown in Table 3. It can be seen from the table that compared with the experimental creep life, the error of the fitting correction model proposed by the present invention is the smallest, and then the KR creep damage model, and the Wen-Tu creep damage model has the largest error. In addition to the individual data, the error of the proposed model prediction is controlled within the range of 50%.
  • the notch sensitivity ratio of the cylindrical notched tensile specimen was changed.
  • the finite element software ABAQUS was used to simulate the creep life of the cylindrical notched tensile specimen under the tensile load of 130 MPa, 150 MPa, 170 MPa and 210 MPa.
  • the geometry of the notched creep specimen is shown in Fig. 7, and the data of the sensitivity ratio is shown in Table 2.
  • the K-R creep damage constitutive model and the W-T creep damage constitutive model were used respectively. Under different tensile loads, different notch sensitivity was simulated and predicted than the creep life of the specimen.
  • the comparative data of the test value and the simulated value are shown in Table 3.
  • the error of the fitting correction model proposed by the present invention is the smallest, and then the K-R creep damage model, and the Wen-Tu creep damage model has the largest error.
  • the error of the proposed model prediction is controlled within the range of 50%. It is reflected from the results of Tables 1 and 3 that the creep constitutive model proposed by the present invention can reasonably predict the creep and failure behavior of high temperature materials. Therefore, the creep failure strain prediction method proposed by the present invention can accurately calculate the material. Multiaxial creep failure strain and structural life.

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Abstract

一种材料多轴蠕变失效应变预测方法，属于应变预测技术领域。其特征在于：包括如下步骤：步骤(1)，获得材料蠕变速率和应变速率之间的关系；步骤(2)，由幂律蠕变控制孔洞长大理论，获得单轴及多轴应力状态参数；步骤(3)，表示单轴及多轴应力作用下的蠕变失效应变，并获得多轴蠕变延性因子；步骤(4)，获得不同应力状态下的多轴蠕变失效应变拟合参数，从而得到多轴蠕变延性因子预测方程；步骤(5)，利用有限元软件预测材料在多轴应力状态下的蠕变失效应变及其寿命。本材料多轴蠕变失效应变预测方法能够通过材料在多轴应力状态下的蠕变失效应变计算方法，更准确地预测材料在高温状态下的多轴蠕变的失效应变。

Description

一种材料多轴蠕变失效应变预测方法 技术领域
一种材料多轴蠕变失效应变预测方法，属于应变预测技术领域。
背景技术
在核电、石油化工和航空航天等领域中，许多结构部件如换热器等长期在高温高压下工作，整个结构处于复杂的多轴应力状态，蠕变及其引起的损伤是结构的主要失效方式之一。多轴应力状态下的蠕变-损伤失效研究是结构完整性评定中最为重要的环节之一，因此对多轴应力状态下材料的蠕变-损伤进行研究，对高温高压工作条件下部件的寿命预测具有积极的意义。
针对模型参数繁冗的问题，基于应变的连续损伤力学模型日渐得到人们的重视。基于应变损伤的模型又称延性耗竭模型，认为局部蠕变应变累积达到蠕变延性(蠕变失效应变)值时，材料将完全损伤，出现裂纹直至失效。多轴蠕变失效应变的测试较为困难，成本也较高，其值通常利用单轴蠕变失效应变转换而来。经典的单轴与多轴蠕变失效应变的转化关系是Cocks-Ashby提出的转换关系。根据转换关系获得的经验多轴蠕变延性因子(MCDF)被广泛的应用于蠕变损伤和蠕变寿命的预测。虽然多轴蠕变延性因子可以很容易地被用来模拟蠕变裂纹扩展并给出可接受的预测结果，但它缺乏应有的物理意义，并且在某些情况下，Cocks-Ashby MCDF对多轴蠕变失效应变的预测并不合理，因而亟需改进。
发明内容
本发明要解决的技术问题是：克服现有技术的不足，提供一种能更准确的预测材料在高温状态下的多轴蠕变的失效应变的材料多轴蠕变失效应变预测方法。
本发明解决其技术问题所采用的技术方案是：该材料多轴蠕变失效应变预测方法，其特征在于：包括如下步骤：
步骤(1)，基于应变损伤准则，根据微观孔洞长大机制，获得材料蠕变速率和应变速率之间的关系；
步骤(2)，由幂律蠕变控制孔洞长大理论，获得单轴及多轴应力状态参数；
步骤(3)，对微观孔洞进行积分获得材料恒载下的失效时间，进而表示单轴及多轴应力作用下的蠕变失效应变，并获得多轴蠕变延性因子；
步骤(4)，对多轴蠕变延性因子进行参数拟合，获得不同应力状态下的多轴蠕变失效应变拟合参数，从而得到多轴蠕变延性因子预测方程；
步骤(5)，利用有限元软件预测材料在多轴应力状态下的蠕变失效应变及其寿命。
优选的，步骤(1)中所述的微观孔洞长大机制在裂尖区域为粘塑性孔洞长的机制。
优选的，步骤(1)中所述的材料蠕变速率和应变速率之间的关系为：
Figure PCTCN2018072896-appb-000001
其中，
Figure PCTCN2018072896-appb-000002
为包含一个孔洞的圆柱体的轴向应变速率，
Figure PCTCN2018072896-appb-000003
为包含一个孔洞的圆柱体的径向应变速率，
Figure PCTCN2018072896-appb-000004
为圆柱体不包含孔洞时的稳态蠕变速率。
优选的，步骤(2)中所述的单轴及多轴应力状态参数利用能量原理，并通过New-Raphson方法获得。
优选的，步骤(2)中所述的单轴及多轴应力状态参数的计算公式为：
Figure PCTCN2018072896-appb-000005
Figure PCTCN2018072896-appb-000006
其中，α为多轴应力状态参数，α 0为单轴应力状态参数，a与b 0为与材料相关的常数，n为确定的材料常数，σ m/σ eq为应力三轴度。
优选的，步骤(3)中所述的多轴蠕变延性因子的计算公式如下：
Figure PCTCN2018072896-appb-000007
其中，ε f为单轴应力作用下的蠕变失效应变，
Figure PCTCN2018072896-appb-000008
为多轴应力作用下的蠕变失效应变，a和b均为与材料相关的常数，n为确定的材料常数，σ m/σ eq为应力三轴度。
优选的，利用缺口蠕变试验获得不同应力状态下的蠕变失效应变拟合参数a和b，进而得到步骤(4)中所述的多轴蠕变延性因子预测方程。
优选的，步骤(4)中所述的多轴蠕变延性因子预测方程结合蠕变-损伤本构方程，并通过Fortran语言嵌入到有限元软件中。
与现有技术相比，本发明所具有的有益效果是：
1、本材料多轴蠕变失效应变预测方法能够通过材料在多轴应力状态下的蠕变失效应变计算方法，定义多轴蠕变延性因子，获得多轴蠕变延性因子计算方程，进而可获得材料的多轴蠕变失效应变，根据建立的多轴蠕变损伤本构方程，利用有限元软件预测材料在多轴应力状态下的蠕变失效应变，能更准确地预测材料在高温状态下的多轴蠕变的失效应变。
2、本发明根据幂率蠕变控制孔洞长大理论，利用能量原理，定义多轴蠕变延性因子，为多轴蠕变延性因子赋予相应的物理意义，获得新的多轴蠕变延性因子预测公式，并利用Fortran语言，根据建立的多轴蠕变损伤本构方程编制子程序并嵌入到有限元软件中，从而能更准确地预测材料在高温状态下的多轴蠕变的失效应变。
附图说明
图1为材料多轴蠕变失效应变预测方法的流程图。
图2为受拉伸载荷作用的含裂纹试样模型图。
图3为含裂纹试样裂尖区域模型图。
图4为多轴载荷作用下的理想晶粒模型图。
图5为包含一个孔洞的圆柱体的放大示意图。
图6为600℃下，9Cr-1Mo合金不同转化模型获得的多轴蠕变失效应变与试验值比较图。
图7为圆柱缺口拉伸试样的几何尺寸图。
具体实施方式
图1～7是本发明的最佳实施例，下面结合附图1～7对本发明做进一步说明。
如图1所示，一种材料多轴蠕变失效应变预测方法，其特征在于：包括如下步骤：
步骤(1)，基于应变损伤准则，根据微观孔洞长大机制，获得材料蠕变速率和应变速率之间的关系；
微观孔洞长大机制认为孔洞主要在晶界面上(尤其是与拉应力垂直的晶界面上)形核和长大，充分长大的孔洞将聚合进而形成晶粒尺寸大小的微裂纹(孔化晶界面)。最后，微裂纹合并导致宏观蠕变裂纹的扩展。
尽管空位凝聚，晶界滑移及位错堆积通常被认为是空洞形核的可能驱动力，但孔洞形核背后的真正机制还不清晰。所以本实施例中将主要考虑晶界上孔洞长大与合并的过程。
孔洞长大的机制也有许多种。其中，粘塑性孔洞长大，扩散控制孔洞长大和受约束扩散孔洞长大是三种被广泛接受的孔洞长大模型。而具体哪一种机制起关键作用则取决于材料性能、温度和应力水平等。例如，在高应变速率和高应力下，孔洞的长大更倾向于受周边晶粒的蠕变或塑性变形控制；而在低应力水平下，晶界上的空位扩散则可能是主要原因。如图2～3所示，在裂尖附近的区域，由于宏观裂纹的存在，局部应力和应变总体上保持在一个很高的水平。因此，粘塑性孔洞长大机制将在裂尖区域起到主导作用。
如图4所示：在多轴载荷作用下的理想晶粒模型的晶界上一系列孔洞。若以下假设成立，孔洞的长大可以通过包含孔洞的板层的体积变化来度量：
(i)蠕变变形中材料不可压缩，且其总体积保持不变；
(ii)球形孔洞只改变体积而不改变形状；
(iii)包含孔洞的板层的宽度要远大于其厚度；
(iv)晶界滑移使得两边的晶粒刚性位移和板层体积变化相适应；
(v)静水压力对于无孔洞时的蠕变变形没有影响；
(vi)晶界孔洞长大仅受幂律蠕变控制。
图5所示：包含一个孔洞的圆柱体的d为晶粒尺寸，r h为孔洞的半径，2h为孔洞间的距离，w是进入边界计算的距离，σ a是轴向应力，T是附加的三轴应力。那么，晶界上孔洞的面积分数可表示为：
Figure PCTCN2018072896-appb-000009
单轴应力作用下，圆柱体的体积变化率与f h的关联如下：
Figure PCTCN2018072896-appb-000010
其中，V代表圆柱体的体积，
Figure PCTCN2018072896-appb-000011
是不含孔洞时的稳态蠕变速率。另一方面，圆柱体的体积变化还可以由蠕变速率来定义：
Figure PCTCN2018072896-appb-000012
其中，
Figure PCTCN2018072896-appb-000013
为包含一个孔洞的圆柱体的轴向应变速率，
Figure PCTCN2018072896-appb-000014
为包含一个孔洞的圆柱体的径向应变速率。
步骤(2)，利用能量原理，由幂律蠕变控制孔洞长大理论，通过New-Raphson方法，获得单轴及多轴应力状态参数；
利用能量原理，Cocks和Ashby给出了多轴应力状态下
Figure PCTCN2018072896-appb-000015
的上边界具有如下形式：
Figure PCTCN2018072896-appb-000016
式中G的定义为：
Figure PCTCN2018072896-appb-000017
其中，f w＝r 2/w 2，T/σ a＝σ m/σ eq-1/3，且σ m/σ eq为应力三轴度，n为确定的材料常数。
合并式(2)、式(3)和式(4)，可以得到描述幂律蠕变控制孔洞长大速率的复杂数学表达式：
Figure PCTCN2018072896-appb-000018
应当注意的是，从式(6)中无法直接获得孔洞长大速率df h/dt和应力三轴度σ m/σ eq之间的关系，为了使结果更方便实用，Cocks和Ashby给出了一个拟合的半经验公式，如下所示：
Figure PCTCN2018072896-appb-000019
其中，多轴应力状态参数α定义为：
Figure PCTCN2018072896-appb-000020
然而，公式(8)在材料处于压缩状态，即应力三轴度σ m/σ eq≤0时，多轴应力状态参数α为负值或出现数值奇异现象，这显然与实际情况不符。此外，α随应力三轴度σ m/σ eq的增加而逐渐减小，当σ m/σ eq＞3时，α近乎为0，这与实际观察到的空洞变化理论不相符。为了解决此问题，本发明中提出了另外一种近似公式，如下式所示：
Figure PCTCN2018072896-appb-000021
其中，a与b 0为与材料相关的常数，在简单拉伸的情况下，即σ m/σ eq＝1/3时，a＝1，b 0＝0，式(9)退化为下式：
Figure PCTCN2018072896-appb-000022
其中，α 0为单轴应力状态参数。
步骤(3)，对微观孔洞进行积分获得材料恒载下的失效时间，进而表示单轴及多轴应力作用下的蠕变失效应变，并获得多轴蠕变延性因子；
为了获得多轴加载情况下的蠕变失效应变，将式(7)在如下所示的上下限进行积分：
Figure PCTCN2018072896-appb-000023
其中，f i为初始孔洞面积分数，f c为孔洞合并发生时的面积分数，t c为多轴应力状态下从初始到孔洞合并发生所需的时间。恒载荷下积分所得结果便是失效时间：
Figure PCTCN2018072896-appb-000024
多轴应力作用下的蠕变失效应变
Figure PCTCN2018072896-appb-000025
可通过下式得到：
Figure PCTCN2018072896-appb-000026
用同样的方法可以得到单轴应力状态下的蠕变失效应变ε f：
Figure PCTCN2018072896-appb-000027
其中，t c0为单轴应力状态下从初始到孔洞合并发生所需的时间。
可定义新的多轴蠕变延性因子MCDF：
Figure PCTCN2018072896-appb-000028
对于具体的材料，在某一应力状态下，n为确定的材料常数，因而公式(15)可以简化为下式：
Figure PCTCN2018072896-appb-000029
其中，b为与材料相关的常数。
步骤(4)，对多轴蠕变延性因子进行参数拟合，获得不同应力状态下的多轴蠕变失效应变拟合参数，从而得到多轴蠕变延性因子预测方程；
对公式(16)中的参数进行拟合：
公式(16)中，a和b均为与材料有关的常数，可通过缺口蠕变试验获得不同应力三轴度σ m/σ eq下的蠕变失效应变，然后利用公式(16)进行拟合，获得参数a和b，从而得到多轴蠕变延性因子预测方程。
步骤(5)，利用有限元软件预测材料在多轴应力状态下的蠕变失效应变及其寿命；
根据步骤(4)中建立的多轴蠕变延性因子预测方程，结合蠕变-损伤本构方程，利用Fortran语言，编制子程序并嵌入到有限元软件ABAQUS中，从而实现材料在多轴应力状态下的蠕变失效应变及寿命的预测。
表1 不同转化模型获得的多轴蠕变失效应变与试验值误差分析
Figure PCTCN2018072896-appb-000030
表2 圆柱缺口拉伸试样缺口敏度比的数据变化表
Figure PCTCN2018072896-appb-000031
表3 不同蠕变损伤本构模型及拉伸载荷下，各缺口敏度比试样的蠕变寿命预测值及试验值的对比数据表
Figure PCTCN2018072896-appb-000032
预测9Cr-1Mo合金在600℃下的多轴蠕变失效应变。图6所示为在不同的应力三轴度下不同模型预测的多轴蠕变失效应变与试验值的比较曲线。本发明中所提的模型中的参数通过试验数据拟合获得，拟合过程中蠕变指数n＝8.55，单轴蠕变失效应变ε f＝0.24，获得的材料常数a＝0.9574，b＝0.0426。从图3中可以看出，本发明中提出的转化模型有效的避 免了因材料中应力三轴度σ m/σ eq＞3时出现的
Figure PCTCN2018072896-appb-000033
比值过小的问题。表1所示为利用Cocks and Ashby(C-A)模型、Wen and Tu(W-T)模型以及本发明中提出的转化模型获得的多轴蠕变失效应变与试验值得误差分析。从表1中可以看出，本发明中提出的模型获得多轴蠕变失效应变的误差最小。从图6及表1中的数据表明了本发明中提出的计算多轴蠕变失效应变的合理性和可靠性。改变圆柱缺口拉伸试样的缺口敏度比，利用有限元软件ABAQUS模拟预测在拉伸载荷为130MPa、150MPa、170MPa、210MPa四种情况下，圆柱缺口拉伸试样的蠕变寿命。缺口蠕变试样的几何形状如图7所示，敏度比的数据变化如表2所示。计算过程中分别采用K-R蠕变损伤本构模型、W-T蠕变损伤本构模型，对不同拉伸载荷下，不同缺口敏度比试样的蠕变寿命进行模拟预测。试验值及模拟值的对比数据如表3所示。从表中可以看出，与试验蠕变寿命对比，本发明提出的拟合修正模型估计的误差是最小的，然后是K-R蠕变损伤模型，Wen-Tu蠕变损伤模型计算结果误差最大。除了个别数据外，所提出的模型预测的误差控制在50％的范围内。从表1和表3的结果反映，本发明所提出的蠕变本构模型可以合理地预测高温材料的蠕变和失效行为，因此，本发明提出的蠕变失效应变预测方法可以准确计算材料的多轴蠕变失效应变及结构的寿命。
改变圆柱缺口拉伸试样的缺口敏度比，利用有限元软件ABAQUS模拟预测在拉伸载荷为130MPa、150MPa、170MPa、210MPa四种情况下，圆柱缺口拉伸试样的蠕变寿命。缺口蠕变试样的几何形状如图7所示，敏度比的数据变化如表2所示。计算过程中分别采用K-R蠕变损伤本构模型、W-T蠕变损伤本构模型，对不同拉伸载荷下，不同缺口敏度比试样的蠕变寿命进行模拟预测。试验值及模拟值的对比数据如表3所示。从表中可以看出，与试验蠕变寿命对比，本发明提出的拟合修正模型估计的误差是最小的，然后是K-R蠕变损伤模型，Wen-Tu蠕变损伤模型计算结果误差最大。除了个别数据外，所提出的模型预测的误差控制在50％的范围内。从表1和表3的结果反映，本发明所提出的蠕变本构模型可以合理地预测高温材料的蠕变和失效行为，因此，本发明提出的蠕变失效应变预测方法可以准确计算材料的 多轴蠕变失效应变及结构的寿命。
以上所述，仅是本发明的较佳实施例而已，并非是对本发明作其它形式的限制，任何熟悉本专业的技术人员可能利用上述揭示的技术内容加以变更或改型为等同变化的等效实施例。但是凡是未脱离本发明技术方案内容，依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化与改型，仍属于本发明技术方案的保护范围。

Claims (8)

  1. 一种材料多轴蠕变失效应变预测方法，其特征在于：包括如下步骤：
    步骤(1)，基于应变损伤准则，根据微观孔洞长大机制，获得材料蠕变速率和应变速率之间的关系；
    步骤(2)，由幂律蠕变控制孔洞长大理论，获得单轴及多轴应力状态参数；
    步骤(3)，对微观孔洞进行积分获得材料恒载下的失效时间，进而表示单轴及多轴应力作用下的蠕变失效应变，并获得多轴蠕变延性因子；
    步骤(4)，对多轴蠕变延性因子进行参数拟合，获得不同应力状态下的多轴蠕变失效应变拟合参数，从而得到多轴蠕变延性因子预测方程；
    步骤(5)，利用有限元软件预测材料在多轴应力状态下的蠕变失效应变及其寿命。
  2. 根据权利要求1所述的材料多轴蠕变失效应变预测方法，其特征在于：步骤(1)中所述的微观孔洞长大机制在裂尖区域为粘塑性孔洞长的机制。
  3. 根据权利要求1所述的材料多轴蠕变失效应变预测方法，其特征在于：步骤(1)中所述的材料蠕变速率和应变速率之间的关系为：
    Figure PCTCN2018072896-appb-100001
    其中，
    Figure PCTCN2018072896-appb-100002
    为包含一个孔洞的圆柱体的轴向应变速率，
    Figure PCTCN2018072896-appb-100003
    为包含一个孔洞的圆柱体的径向应变速率，
    Figure PCTCN2018072896-appb-100004
    为圆柱体不包含孔洞时的稳态蠕变速率。
  4. 根据权利要求1所述的材料多轴蠕变失效应变预测方法，其特征在于：步骤(2)中所述的单轴及多轴应力状态参数利用能量原理，并通过New-Raphson方法获得。
  5. 根据权利要求1所述的材料多轴蠕变失效应变预测方法，其特征在于：步骤(2)中所述的单轴及多轴应力状态参数的计算公式为：
    Figure PCTCN2018072896-appb-100005
    Figure PCTCN2018072896-appb-100006
    其中，α为多轴应力状态参数，α 0为单轴应力状态参数，a与b 0为与材料相关的常数，n为确定的材料常数，σ m/σ eq为应力三轴度。
  6. 根据权利要求1所述的材料多轴蠕变失效应变预测方法，其特征在于：步骤(3)中所述的多轴蠕变延性因子的计算公式如下：
    Figure PCTCN2018072896-appb-100007
    其中，ε f为单轴应力作用下的蠕变失效应变，
    Figure PCTCN2018072896-appb-100008
    为多轴应力作用下的蠕变失效应变，a和b均为与材料相关的常数，n为确定的材料常数，σ m/σ eq为应力三轴度。
  7. 根据权利要求6所述的材料多轴蠕变失效应变预测方法，其特征在于：利用缺口蠕变试验获得不同应力状态下的蠕变失效应变拟合参数a和b，进而得到步骤(4)中所述的多轴蠕变延性因子预测方程。
  8. 根据权利要求1所述的材料多轴蠕变失效应变预测方法，其特征在于：步骤(4)中所述的多轴蠕变延性因子预测方程结合蠕变-损伤本构方程，并通过Fortran语言嵌入到有限元软件中。
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