CN108732029B - Creep induction period prediction method containing residual stress under elastic condition - Google Patents

Abstract

The invention discloses a creep induction period prediction method containing residual stress under an elastic condition. And (3) calculating a creep induction period considering the residual stress by introducing an elastic following factor Z by utilizing a reference legislation. The method has the advantages that a corrected creep induction period prediction model under the elastic condition is provided, and compared with the existing model, the original prediction model can be expanded into the model containing the residual stress by the design method.

Description

Prediction method of creep incubation period with residual stress under elastic conditions

technical field

The invention relates to the engineering critical evaluation of the creep incubation period of a high temperature structure with residual stress under elastic conditions, that is, a method for evaluating the creep crack initiation life of the high temperature structure when surface cracks exist in the structure and under elastic stress conditions .

Background technique

The coal-based energy structure is one of the main causes of smog weather in my country, and coal-fired power generation is currently the most important power generation method in my country, and this trend will exist for a long time. Therefore, in addition to changing the energy structure, the development of efficient and clean ultra-supercritical (USC) units is one of the important ways to save energy and reduce emissions. However, the improvement of parameters such as steam temperature and pressure leads to a very harsh service environment for the key high-temperature pipelines of the unit. In particular, there are various defects such as cracks, incomplete penetration, welding pores and slag inclusions in the pipelines, which seriously threaten the safe operation of the unit. Scientifically accurate lifespan assessment.

For decades, for cracked components at high temperature, a variety of evaluation specifications and methods for high temperature creep life have been developed abroad. The creep incubation period is the longest stage in the creep process, and the accurate prediction of the incubation period is of great significance for the creep life prediction of high-temperature structures; the incubation period prediction model proposed by Davies et al. The integrity of the stress change during the creep process, but the influence of the residual stress of the structure on the incubation period has not been studied; the residual stress widely exists in the high-temperature components manufactured, and has a significant impact on the service life of the components. A large number of studies on residual stress (residual stress) under high temperature creep conditions are also widely carried out. Therefore, a creep incubation period prediction model considering residual stress can be established, which can more accurately and completely evaluate the creep incubation period of composite loaded structures.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for predicting the creep incubation period with residual stress under elastic conditions, aiming at the technical defects existing in the prior art. By using the reference law, the elastic following factor Z is introduced to calculate the creep considering the residual stress. gestation period. Creep experiments were performed using compact tensile specimens (CTs) by pre-compression to generate residual stresses and applying principal loads.

The technical scheme adopted for realizing the purpose of the present invention is:

The creep inoculation period prediction model of the high-temperature structure with residual stress under elastic conditions of the present invention includes a CT sample body, the upper and lower ends of the CT sample body are respectively provided with an upper round pin and a lower round pin. The CT sample body There is a groove at the front end of the middle part, a notch at the back of the groove, and a prefabricated crack at the rear of the notch. The groove, the notch and the prefabricated crack are on the same plane. The main load pin hole, the upper main load pin hole and the lower main load pin hole are arranged symmetrically up and down, and are respectively arranged at the upper and lower ends of the groove.

The method for predicting the creep incubation period with residual stress under elastic conditions of the present invention comprises the following steps:

S1: Build a model: the model includes a CT sample body, a middle front end of the CT sample body is provided with a groove, a rear part of the groove is provided with a notch, and the CT sample body is also provided with an upper main load pin hole, a lower The main load pin hole, the upper main load pin hole and the lower main load pin hole are correspondingly arranged up and down, and are respectively arranged at the upper and lower ends of the slot;

S2: First, use the upper and lower round pins to compress the upper and lower ends of the CT sample body with a predetermined size, and then release the upper and lower round pins, which will generate residual stress distribution near the notch of the CT sample body ;

S3: insert prefabricated cracks at the notch containing residual stress for creep test;

S4: Use a pin to apply the main load to the upper main load pin hole and the lower main load pin hole to conduct a high temperature creep test;

S5: The necessary parameters needed to calculate the incubation period of CT specimens with residual stress can be obtained through creep finite element simulation; under elastic conditions, the calculation of the incubation period mainly includes the following steps:

(1) First, calculate the stress intensity factor under composite loading, and its calculation formula is:

In (I):

是主载荷应力强度因子，单位为MPa·(m^1/2)；P是主载荷，单位为N；B是试样厚度，单位为mm，B_n是试样净厚度，单位为mm；a/W是预制裂纹长度比率，a是预制裂纹长度，采用上主载荷销孔圆心到预制裂纹后端的水平直线距离，单位为mm；W是名义试样宽度，采用上主载荷销孔圆心到CT试样本体后端的水平直线距离，单位为mm；f(a/W)是CT试样几何系数，只与a/W有关；V是无量纲的塑性相关项，计算如下：in: is the stress intensity factor calculated by simulation only with residual stress, and the unit is MPa·(m ^1/2 );

is the main load stress intensity factor, in MPa·(m ^1/2 ); P is the main load, in N; B is the thickness of the sample, in mm, B _n is the net thickness of the sample, in mm; a /W is the length ratio of prefabricated cracks, a is the length of prefabricated cracks, the horizontal straight line distance from the center of the upper main load pin hole to the rear end of the prefabricated crack, in mm; W is the nominal sample width, using the center of the upper main load pin hole to CT The horizontal straight-line distance from the rear end of the specimen body, in mm; f(a/W) is the geometric coefficient of the CT specimen, which is only related to a/W; V is a dimensionless plastic correlation term, calculated as follows:

In (II): V ₀ is a dimensionless parameter,

是模拟计算的只含有残余应力下的应力强度因子，单位为MPa·(m^1/2)，

利用J_S计算，J_S是残余应力场下断裂参量，单位为MPa·m： is the plastic residual stress intensity factor, in MPa·(m ^1/2 );

is the stress intensity factor calculated by simulation only with residual stress, the unit is MPa·(m ^1/2 ),

Calculated using J _S , J _S is the fracture parameter under the residual stress field, in MPa m:

和J_S都利用有限元模拟结果提取；Where: E' is the effective elastic modulus: E'=E/(1-ν ² ), E is the elastic modulus, ν is the Poisson's ratio, E, ν refer to the literature: (Zhao L, Jing H, Xu L, Han Y, Xiu J. Evaluation of constraint effects on creepcrack growth by experimental investigation and numerical simulation. Engng Fract Mech 2012;96:251–66.),

and J _S are both extracted using finite element simulation results;

In (II): L _r is a dimensionless parameter describing the main load amplitude:

Among them: σ _y is the yield strength, which is related to the material properties, the unit is MPa, see literature: ₍ Zhao L, Jing H, XuL, Han Y, Xiu J.Evaluation of constraint effects on creep crack growth by experimental investigation and numerical simulation.Engng Fract Mech 2012;96:251–66.); is the main load reference stress, in MPa, calculated with the following formula:

Among them: n _L is the dimensionless crack aspect ratio parameter, which is calculated by the following formula:

constant

In (II):

是主载荷应力强度因子，

是塑性主载荷应力强度因子，单位为MPa·(m^1/2)；利用有限元模拟结果计算：

is the principal load stress intensity factor,

is the plastic principal load stress intensity factor, in MPa·(m ^1/2 ); Using the finite element simulation results to calculate:

In (II): β describes the magnitude of residual stress and is a dimensionless parameter;

is the secondary load reference stress, calculated by finite element simulation:

与等效弹性应变增量

的比值：In (II): Z is a dimensionless elastic following factor, the stress-strain relationship is extracted from the finite element simulation results, and the equivalent creep strain increment is taken.

with the equivalent elastic strain increment

The ratio of:

(2) Then calculate the incubation time t _i ^K under the linear elastic stress field, and its calculation formula is:

是蠕变应变变化率，单位为h^-1，与材料高温蠕变属性有关，ε_crit和

见文献：(Zhao L,Jing H,Xu L,Han Y,XiuJ.Evaluation of constraint effects on creep crack growth by experimentalinvestigation and numerical simulation.Engng Fract Mech 2012；96:251–66.)。

是与裂纹尖端角度θ和泊松比ν有关的无量纲函数，可查表获得(Webster,G.A.,1994.Fracture mechanics in the creep range.Journal of Strain Analysis forEngineering Design 29,215–223.)；n为无量纲的蠕变应力硬化指数，见文献(Shih,C.F..1983.Tables of Hutchinson-Rice-Rosengren Singular Field Quantities.BrownUniversity Technical Report,MRL E-147)d是判定蠕变萌生发生时裂尖前蠕变损伤达到1所延伸的距离，即蠕变萌生发生的临界距离，单位为mm；In (III): ε _crit is the uniaxial creep toughness, the unit is 1, which is related to the material properties,

is the rate of change of creep strain, in h ^-1 , which is related to the high temperature creep properties of the material, ε _crit and

See literature: (Zhao L, Jing H, Xu L, Han Y, Xiu J. Evaluation of constraint effects on creep crack growth by experimental investigation and numerical simulation. Engng Fract Mech 2012;96:251–66.).

is a dimensionless function related to the crack tip angle θ and Poisson’s ratio ν, which can be obtained by looking up the table (Webster, GA, 1994. Fracture mechanics in the creep range. Journal of Strain Analysis for Engineering Design 29, 215–223.); n is dimensionless The creep stress hardening index, see literature (Shih, CF. 1983. Tables of Hutchinson-Rice-Rosengren Singular Field Quantities. Brown University Technical Report, MRL E-147) d is to determine the creep damage before the crack tip when creep initiation occurs The distance to reach 1, that is, the critical distance for creep initiation to occur, in mm;

In (III): MSF _K is the multiaxial stress factor under elastic conditions, calculated according to the relationship of Cocks and Ashby:

Where: n is the dimensionless creep stress hardening exponent, sinh is the hyperbolic sine function, h _k is the elastic stress triaxiality, in the elastic stress state:

where: θ is the crack tip angle and ν is the Poisson's ratio.

Preferably, d is taken as the grain size of the studied material.

Preferably, B _n =B.

Z的提取过程包括以下步骤：Preferably, the finite element simulation is completed by using abaqus, _JS ,

The extraction process of Z includes the following steps:

(1) First, according to the size, the finite element model of the CT specimen loaded by pre-compression is established. Elastoplastic parameters are set in the material properties module. Set the compression load and restraint conditions in the load module, the restraint conditions include symmetry conditions and fixed conditions, set the rigid contact between the compression round pin and the upper and lower surfaces of the sample in the contact module, and set the output parameters in the analysis step module : stress value, meshed in the mesh module;

(2) Submit the task calculation in the operation module to obtain the calculation result of residual stress. In the results file, the secondary load reference stress can be extracted directly from the field variables

(3) Establish a sample model of the same size and carry out the main load tensile test, as shown in Figure 2. Set the elastic-plastic creep parameters at high temperature in the material property module, divide the mesh in the mesh module, set the rigid contact between the tensile pin and the pin hole in the contact module, and insert prefabricated cracks in the model, in the analysis step Set the output parameters in the module: stress value, stress intensity factor K value, fracture parameter J integral value, set tensile load in the load module, and restraint conditions: including symmetry conditions and fixed conditions, import in the preload stress field Step calculated residual stress;

以及残余应力断裂参量J_S，在施加拉伸载荷的初始时刻，可以获取塑性主载荷强度因子从历史变量中可以获取等效应力随总应变增量的变化曲线，从曲线中得到等效蠕变应变增量，

等效弹性应变增量

进而得到弹性追随因子Z计算方法。(4) Submit the task calculation in the operation module, and obtain the calculation result of the creep tensile experiment with residual stress. In the result file, when the tensile load is not applied after the crack is inserted, the simulation calculation can be obtained from the historical variables. Stress intensity factor under residual stress

and the residual stress fracture parameter J _S , at the initial moment of applying the tensile load, the plastic principal load intensity factor can be obtained The change curve of equivalent stress with total strain increment can be obtained from the historical variables, and the equivalent creep strain increment can be obtained from the curve,

Equivalent elastic strain increment

Then the calculation method of elastic following factor Z is obtained.

Compared with the prior art, the beneficial effects of the present invention are:

Compared with the existing model, the present design method can extend the original prediction model to the model containing residual stress, so as to propose a simplified elastic condition Therefore, the creep incubation period under elastic conditions can be predicted concisely and effectively in the structure.

Description of drawings

FIG. 1 is a schematic structural diagram of the creep incubation period prediction model of the high temperature structure with residual stress under elastic conditions according to the present invention.

Among them: 1-upper round pin, 2-CT specimen body, 3-upper main load pin hole, 4-slot, 5-notch, 6-prefabricated crack, 7-lower main load pin hole, 8-lower round pin.

Figure 2 is a schematic diagram of the critical conditions for creep crack initiation.

Figure 3 is a stress-strain relationship curve.

Detailed ways

The technical solutions of the present invention are further described below in conjunction with specific examples.

In this example, P92 high temperature heat-resistant steel is selected, the CT specimen with B=20mm, W=40mm, a=10mm, a/W=0.5 is used as the research object, and the preload is 12000N and the main load P=12000N is used as the research load . Its main material properties are shown in the following table:

Among them: E-16 is 10 to the -16th power.

The method for predicting the creep incubation period with residual stress under elastic conditions of the present invention comprises the following steps:

S1: Build a model as shown in Figure 1: the model includes a CT sample body 2, a groove 4 is provided at the front end of the middle part of the CT sample body 2, a gap 5 is provided at the rear of the groove 4, and the CT sample body 1 is also provided with an upper main load pin hole 3 and a lower main load pin hole 7, the upper main load pin hole 3 and the lower main load pin hole 7 are correspondingly arranged up and down, and are respectively arranged at the upper and lower ends of the groove 4;

S2: First, use the upper round pin 1 and the lower round pin 8 to compress and load the CT sample body 2 with a predetermined size, and then release the upper round pin 1 and the lower round pin 8, which will generate near the gap 5 of the CT sample body 2 A certain residual stress distribution;

S3: insert the prefabricated crack 6 at the notch containing residual stress, and the groove 4, the notch 5, and the prefabricated crack 6 are on the same plane to carry out the creep test;

S4: use a pin to apply a main load to the upper main load pin hole 3 and the lower main load pin hole 7 to carry out a high temperature creep test;

S5: The necessary parameters needed to calculate the incubation period of CT specimens with residual stress can be obtained through creep finite element simulation; under elastic conditions, the calculation of the incubation period mainly includes the following steps:

(1) First calculate each parameter:

(a) Elastic principal load intensity factor:

The following data are extracted from the finite element results:

i) First, according to the size, the finite element model of the CT specimen loaded by pre-compression is established. Elastoplastic parameters are set in the material properties module. Set the compression load and restraint conditions in the load module, the restraint conditions include symmetry conditions and fixed conditions, set the rigid contact between the compression round pin and the upper and lower surfaces of the sample in the contact module, and set the output parameters in the analysis step module : stress value, meshed in the mesh module;

ii) Submit the task calculation in the operation module to obtain the calculation result of residual stress. In the results file, the secondary load reference stress can be extracted directly from the field variables

iii) Establish a sample model of the same size, and perform the main load tensile test, see Figure 1. Set the elastic-plastic creep parameters at high temperature in the material property module, divide the mesh in the mesh module, set the rigid contact between the tensile pin and the pin hole in the contact module, and insert prefabricated cracks in the model, in the analysis step Set the output parameters in the module: stress value, stress intensity factor K value, fracture parameter J integral value, set tensile load in the load module, and restraint conditions: including symmetry conditions and fixed conditions, import in the preload stress field Step calculated residual stress;

从历史变量中可以获取等效应力随总应变增量的变化曲线，如图3所示，从曲线中得到等效蠕变应变增量

等效弹性应变增量

进而得到弹性追随因子Z计算方法。iv) Submit the task calculation in the operation module to obtain the calculation results of the creep tensile test with residual stress. In the result file, when the tensile load is not applied after the crack is inserted, the elastic residual stress intensity factor can be obtained from the historical variables. And the residual stress fracture parameter J _S =0.013MPa m, the plastic residual stress intensity factor can be calculated: At the initial moment of applying the tensile load, the plastic principal load intensity factor can be obtained

The change curve of equivalent stress with total strain increment can be obtained from the historical variables, as shown in Figure 3, and the equivalent creep strain increment can be obtained from the curve

Equivalent elastic strain increment

Then the calculation method of elastic following factor Z is obtained.

(b) Main load reference stress:

in:

(c) Main load amplitude:

(d) Residual stress reference stress:

Amplitude of residual stress:

由图3可读出：(e) Through step (4) in the above abaqus finite element simulation steps, the equivalent creep strain increment can be obtained from the historical variables, and Fig. 3 is obtained, Equivalent elastic strain increment

It can be read from Figure 3:

(f) Plastic related terms:

(2) Therefore, the stress intensity factor under composite loading

(3) Then calculate the initiation under the linear elastic stress field:

P92钢的材料参数n＝5.23，ε_crit＝0.2；(a) Look up the table to obtain:

Material parameters of P92 steel n = 5.23, ε _crit = 0.2;

Stress triaxiality:

Multiaxial stress factor:

The gestation period under elastic conditions:

Among them: As shown in Figure 2, d is the distance that the creep damage reaches 1 before the crack tip when creep initiation occurs, that is, the critical distance for creep initiation to occur, and d is defined as the grain size of the studied material, d =0.05mm.

The above are only the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. These improvements and Retouching should also be regarded as the protection scope of the present invention.

Claims (4)

1. The creep incubation period prediction method containing residual stress under elastic conditions is characterized in that: comprising the following steps: S1: Build a model: the model includes a CT sample body, a middle front end of the CT sample body is provided with a groove, a rear part of the groove is provided with a notch, and the CT sample body is also provided with an upper main load pin hole, a lower The main load pin hole, the upper main load pin hole and the lower main load pin hole are correspondingly arranged up and down, and are respectively arranged at the upper and lower ends of the slot; S2: First, use the upper and lower round pins to compress the upper and lower ends of the CT sample body with a predetermined size, and then release the upper and lower round pins, which will generate residual stress distribution near the notch of the CT sample body ; S3: Insert prefabricated cracks at the notch containing residual stress for creep test; S4: Use a pin to apply the main load to the upper main load pin hole and the lower main load pin hole to conduct a high temperature creep test; S5: The necessary parameters needed to calculate the incubation period of CT specimens with residual stress can be obtained through creep finite element simulation; under elastic conditions, the calculation of the incubation period mainly includes the following steps: (1) First, calculate the stress intensity factor under composite loading, and its calculation formula is:

In (I):

in:

is the stress intensity factor calculated by simulation only with residual stress, and the unit is MPa·(m ^1/2 );

is the main load stress intensity factor, in MPa·(m ^1/2 ); P is the main load, in N; B is the thickness of the sample, in mm, B _n is the net thickness of the sample, in mm; a /W is the length ratio of prefabricated cracks, a is the length of prefabricated cracks, the horizontal straight line distance from the center of the upper main load pin hole to the rear end of the prefabricated crack, in mm; W is the nominal sample width, using the center of the upper main load pin hole to CT The horizontal straight-line distance from the rear end of the specimen body, in mm; f(a/W) is the geometric coefficient of the CT specimen, which is only related to a/W; V is a dimensionless plastic correlation term, calculated as follows:

In (II): V ₀ is a dimensionless parameter, in:

is the plastic residual stress intensity factor, in MPa·(m ^1/2 );

is the stress intensity factor calculated by simulation only with residual stress, the unit is MPa·(m ^1/2 ), Using J _S to calculate, J _S is the fracture parameter under the residual stress field, the unit is MPa m;

Where: E' is the effective elastic modulus: E'=E/(1-ν ² ), E is the elastic modulus, and ν is the Poisson's ratio;

and J _S are both extracted using finite element simulation results; In (II): L _r is a dimensionless parameter describing the main load amplitude:

Where: σ _y is the yield strength, in MPa;

is the main load reference stress, in MPa, calculated with the following formula:

Among them: n _L is the dimensionless crack aspect ratio parameter, which is calculated by the following formula:

constant In (II): in: is the principal load stress intensity factor,

is the plastic principal load stress intensity factor, in MPa·(m ^{1 /2} ); Using the finite element simulation results to calculate: In (II): β describes the magnitude of residual stress and is a dimensionless parameter;

in:

is the secondary load reference stress, calculated by finite element simulation: In (II): Z is a dimensionless elastic following factor, the stress-strain relationship is extracted from the finite element simulation results, and the equivalent creep strain increment is taken.

with the equivalent elastic strain increment

The ratio of:

(2) Then calculate the incubation time t _i ^K under the linear elastic stress field, and its calculation formula is:

In (III): ε _crit is the uniaxial creep toughness, which is related to the material properties;

is the creep strain rate of change, in h ^-1 , and is related to the high temperature creep properties of the material;

is a dimensionless function related to the crack tip angle θ and Poisson’s ratio ν, d is the distance that the creep damage before the crack tip reaches 1 when the creep initiation occurs, that is, the critical distance for creep initiation, the unit is mm; In (III): MSF _K is the multiaxial stress factor under elastic conditions, calculated according to the Cocks and Ashby relation:

Where: n is the dimensionless creep stress hardening exponent, sinh is the hyperbolic sine function, h _k is the elastic stress triaxiality, in the elastic stress state:

where: θ is the crack tip angle and ν is the Poisson's ratio. 2 . The method for predicting the creep incubation period with residual stress under elastic conditions according to claim 1 , wherein d is the grain size of the studied material. 3 . 3 . The method for predicting the creep incubation period with residual stress under elastic conditions according to claim 1 , wherein: B _n =B. 4 . 4. The method for predicting the creep incubation period with residual stress under elastic conditions according to claim 1, wherein the finite element simulation is completed by using abaqus,

_JS ,

The extraction process of Z includes the following steps: (1) First, establish the finite element model of the pre-compressed CT specimen according to the size, set the elastic-plastic parameters in the material property module, set the compressive load in the load module, and restraint conditions, the restraint conditions include symmetry conditions and Fixed conditions, set the rigid contact between the compression round pin and the upper and lower surfaces of the sample in the contact module, set the output parameter: stress value in the analysis step module, and divide the mesh in the mesh module; (2) Submit the task calculation in the operation module to obtain the calculation result of the residual stress. In the result file, the secondary load reference stress can be directly extracted from the field variables

(3) Establish a sample model of the same size, carry out the main load tensile test, set the elastic-plastic creep parameters at high temperature in the material property module, divide the mesh in the mesh module, and set the tensile pin in the contact module Rigid contact with the pin hole, and insert a prefabricated crack in the model, set the output parameters in the analysis step module: stress value, stress intensity factor K value, fracture parameter J integral value, set tensile load in the load module, and Constraint conditions: including symmetry conditions and fixed conditions, import the residual stress calculated in the previous step into the preload stress field; (4) Submit the task calculation in the operation module, and obtain the calculation result of the creep tensile experiment with residual stress. In the result file, when the tensile load is not applied after the crack is inserted, the simulation calculation can be obtained from the historical variables. Stress intensity factor under residual stress

and the residual stress fracture parameter J _S , at the initial moment of applying the tensile load, the plastic principal load stress intensity factor can be obtained

The change curve of equivalent stress with total strain increment can be obtained from the historical variables, and the equivalent creep strain increment can be obtained from the curve,

Equivalent elastic strain increment

Then the elastic following factor Z is obtained.

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