WO2018171315A1

WO2018171315A1 - Predicting method for multiaxial creep failure strain of material

Info

Publication number: WO2018171315A1
Application number: PCT/CN2018/072896
Authority: WO
Inventors: 张玉财; 蒋文春; 王传龙; 涂善东; 王宁
Original assignee: 中国石油大学(华东)
Priority date: 2017-03-21
Filing date: 2018-01-16
Publication date: 2018-09-27
Also published as: CN106934168A; CN106934168B

Abstract

A predicting method for the multiaxial creep failure strain of a material, relating to the technical field of strain prediction. The method is characterized by comprising the following steps: step (1), acquiring the relation between the creep rate and strain rate of a material; step (2), obtaining uniaxial and multiaxial stress state parameters according to the theory of controlling void growth by power-law creep; step (3), indicating a creep failure strain under the actions of uniaxial and multiaxial stresses and obtaining a multiaxial creep ductility factor; step (4), obtaining multiaxial creep failure strain fitting parameters under different stress states so as to obtain a multiaxial creep ductility factor prediction equation; and step (5), predicting the creep failure strain and the life of the material under a multiaxial stress state by using a finite element software. The predicting method for the multiaxial creep failure strain of a material can more accurately predict the multiaxial creep failure strain of the material under a high temperature state by using a creep failure strain calculation method of the material under the multiaxial stress state.

Description

Multiaxial creep failure strain prediction method for materials

Technical field

A multi-axial creep failure strain prediction method for materials belongs to the field of strain prediction technology.

Background technique

In the fields of nuclear power, petrochemicals and aerospace, many structural components such as heat exchangers work under high temperature and high pressure for a long time, and the whole structure is in a complex multiaxial stress state. Creep and damage caused by it are the main failure modes of the structure. one. The study of creep-damage failure under multiaxial stress is one of the most important aspects in structural integrity assessment. Therefore, the creep-damage of materials under multiaxial stress state is studied, and the life of components under high temperature and high pressure working conditions is studied. Forecasting has a positive meaning.

For the problem of cumbersome model parameters, strain-based continuous damage mechanics models have received increasing attention. The model based on strain damage is also called the ductility exhaustion model. When the local creep strain accumulation reaches the creep ductility (creep failure strain) value, the material will be completely damaged, and cracks will appear until failure. Multi-axis creep failure strain testing is more difficult and costly, and its value is usually converted by uniaxial creep failure strain. 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. Although 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.

Summary of the invention

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;

In step (5), the finite element software is used to predict the creep failure strain and life of the material under multiaxial stress state.

Preferably, the microscopic pore growth mechanism described in the step (1) is a mechanism for the viscoplastic pore length in the crack tip region.

Preferably, the relationship between the creep rate and the strain rate of the material described in the step (1) is:

among them,

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.

Preferably, the uniaxial and multiaxial stress state parameters described in step (2) utilize the energy principle and are obtained by the New-Raphson method.

Preferably, the calculation formula of the uniaxial and multiaxial stress state parameters described in the step (2) is:

Where α is a multiaxial stress state parameter, α ₀ is a uniaxial stress state parameter, a and b ₀ are material-dependent constants, n is a determined material constant, and σ _m /σ _eq is a stress triaxiality.

Preferably, the formula for calculating the multiaxial creep ductility factor described in the step (3) is as follows:

Where ε _f is the creep failure strain under uniaxial stress,

For creep failure strain under multiaxial stress, both a and b are material-dependent constants, n is the determined material constant, and σ _m /σ _eq is the stress triaxiality.

Preferably, 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.

Preferably, 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.

Compared with the prior art, the present invention has the following beneficial effects:

1. 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.

2. According to the theory of power rate creep control hole growth, 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. Formula, and using Fortran language, according to the established multi-axis creep damage constitutive equation, 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.

DRAWINGS

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.

detailed description

1 to 7 are preferred embodiments of the present invention, and the present invention will be further described below with reference to Figs.

As shown in FIG. 1 , a material multi-axis creep failure strain prediction method is characterized in that the method comprises the following steps:

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.

Despite the vacancy condensation, grain boundary slip and dislocation accumulation are generally considered to be possible driving forces for void nucleation, but the real mechanism behind the pore nucleation is still unclear. Therefore, in this embodiment, the process of growing and merging the holes on the grain boundaries will be mainly considered.

There are also many kinds of mechanisms for the growth of holes. Among them, the growth of viscoplastic pores, the diffusion control pore growth and the constrained diffusion pore growth are three widely accepted pore growth models. Which specific mechanism plays a key role depends on material properties, temperature and stress levels. For example, at high strain rates and high stresses, the growth of pores is more inclined to be controlled by creep or plastic deformation of surrounding grains; at low stress levels, vacancy diffusion at grain boundaries may be the main reason. As shown in Figures 2 to 3, in the vicinity of the crack tip, the local stress and strain are generally maintained at a high level due to the presence of macroscopic cracks. Therefore, the viscoplastic pore growth mechanism will play a leading role in the crack tip region.

As shown in Figure 4: a series of holes in the grain boundary of an ideal grain model under multiaxial loading. If the following assumptions hold, the growth of the hole can be measured by the volume change of the ply containing the hole:

(i) the material in the creep deformation is incompressible and its total volume remains the same;

(ii) the spherical hole only changes volume without changing shape;

(iii) the width of the ply containing the holes is much larger than its thickness;

(iv) grain boundary slip so that the grain stiffness displacement on both sides and the plate volume change are adapted;

(v) Hydrostatic pressure has no effect on creep deformation in the absence of holes;

(vi) Grain boundary pore growth is only controlled by power law creep.

Figure 5: The cylinder of a hole containing a hole is the grain size, r _h is the radius of the hole, 2h is the distance between the holes, w is the distance calculated into the boundary, σ _a is the axial stress, and T is the additional Triaxial stress. Then, the area fraction of the hole in the grain boundary can be expressed as:

Under the uniaxial stress, the volume change rate of the cylinder is related to f _h as follows:

Where V represents the volume of the cylinder,

It is the steady-state creep rate when there is no hole. On the other hand, the volume change of a cylinder can also be defined by the creep rate:

among them,

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;

Using the energy principle, Cocks and Ashby give the multiaxial stress state.

The upper boundary has the following form:

The definition of G is:

Where f _w =r ² /w ² , T/σ _a =σ _m /σ _eq -1/3, and σ _m /σ _eq is the stress triaxiality, and n is the determined material constant.

By combining equations (2), (3), and (4), a complex mathematical expression describing the rate of growth of power-law creep control holes can be obtained:

It should be noted that the relationship between the hole growth rate df _h /dt and the stress triaxiality σ _m /σ _eq cannot be directly obtained from the equation (6). In order to make the result more convenient and practical, Cocks and Ashby give A fitted semi-empirical formula, as follows:

Among them, the multiaxial stress state parameter α is defined as:

However, in the formula (8), when the material is in a compressed state, that is, the stress triaxiality σ _m /σ _eq ≤ 0, the multiaxial stress state parameter α is a negative value or a numerical singular phenomenon occurs, which is obviously inconsistent with the actual situation. In addition, α decreases with increasing stress triaxiality σ _m /σ _eq . When σ _m /σ _eq >3, α is almost 0, which is inconsistent with the actual observed cavity variation theory. In order to solve this problem, another approximate formula is proposed in the present invention, as shown in the following formula:

Where a and b ₀ are material-dependent constants. In the case of simple stretching, ie σ _m /σ _eq =1/3, a=1, b ₀ =0, and equation (9) degenerates into the following formula :

Where α ₀ is a uniaxial stress state parameter.

In order to obtain the creep failure strain under multiaxial loading, the equation (7) is integrated at the upper and lower limits shown below:

Where f _i is the initial hole area fraction, f _c is the area fraction at which the hole combination occurs, and t _c is the time required from the initial to the hole combination in the multiaxial stress state. The result of the integral under constant load is the expiration time:

Creep failure strain under multiaxial stress

Can be obtained by:

In the same way, the creep failure strain ε _f under uniaxial stress can be obtained:

Where 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:

For a specific material, n is a certain material constant under a certain stress state, and thus equation (15) can be simplified to the following formula:

Where b is a constant associated with the material.

Fit the parameters in equation (16):

In formula (16), a and b are material-dependent constants, and the creep failure strain at different stress triaxial degrees σ _m /σ _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;

According to the multi-axis creep ductility factor prediction equation established in step (4), combined with the creep-damage constitutive equation, 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 1 Error analysis of multi-axial creep failure strain and test value obtained by different transformation models

Table 2 Data change table of notch sensitivity ratio of cylindrical notched tensile specimen

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 creep index n=8.55 during the fitting process, the uniaxial creep failure strain ε _f =0.24, and the obtained material constant a=0.9574, b=0.0426 . As can be seen from FIG. 3, the conversion model proposed in the present invention effectively avoids the occurrence of stress triaxiality σ _m /σ _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. As can be seen from Table 1, the model proposed in the present invention minimizes the error of multiaxial creep failure strain. The data from Fig. 6 and Table 1 demonstrate the rationality and reliability of calculating the multiaxial creep failure strain proposed in the present invention. 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. In the calculation process, 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%. 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.

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. In the calculation process, 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. 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 K-R 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%. 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.

The above is only the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any person skilled in the art may use the above-disclosed technical contents to change or modify the equivalent equivalent. Example. However, any simple modifications, equivalent changes and modifications made to the above embodiments in accordance with the technical spirit of the present invention are still within the scope of protection of the technical solutions of the present invention.

Claims

A multi-axis creep failure strain prediction method for a material, comprising: 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;

In step (5), the finite element software is used to predict the creep failure strain and life of the material under multiaxial stress state.
The multiaxial creep failure strain prediction method according to claim 1, wherein the microscopic hole growth mechanism described in the step (1) is a mechanism of a viscoplastic pore length in the crack tip region.
The multiaxial creep failure strain prediction method according to claim 1, wherein the relationship between the material creep rate and the strain rate in the step (1) is:

among them,
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 multiaxial creep failure strain prediction method according to claim 1, wherein the uniaxial and multiaxial stress state parameters described in the step (2) are obtained by using the energy principle and by the New-Raphson method.
The multiaxial creep failure strain prediction method according to claim 1, wherein the calculation formula of the uniaxial and multiaxial stress state parameters in the step (2) is:

Where α is a multiaxial stress state parameter, α 0 is a uniaxial stress state parameter, a and b 0 are material-dependent constants, n is a determined material constant, and σ m /σ eq is a stress triaxiality.
The multiaxial creep failure strain prediction method according to claim 1, wherein the calculation formula of the multiaxial creep ductility factor in the step (3) is as follows:

Where ε f is the creep failure strain under uniaxial stress,
For creep failure strain under multiaxial stress, both a and b are material-dependent constants, n is the determined material constant, and σ m /σ eq is the stress triaxiality.
The multi-axis creep failure strain prediction method according to claim 6, wherein the creep failure strain fitting parameters a and b under different stress states are obtained by using a notch creep test, and then the step (4) is obtained. The multiaxial creep ductility factor prediction equation.
The multiaxial creep failure strain prediction method according to claim 1, wherein the multiaxial creep ductility factor prediction equation described in the step (4) is combined with the creep-damage constitutive equation and passed the Fortran language. Embedded in finite element software.