CN106407544A - Method for establishing stiffness prediction model of IC10 directional solidification material - Google Patents

Abstract

The invention discloses a method for establishing a stiffness model of an IC10 directional solidification material considering the effects of grain boundaries and loading directions. 2) Monotonic tensile test of IC10 directionally solidified alloy along different loading directions at room temperature; 3) Scanning electron microscope and transmission electron microscope observation of IC10 directionally solidified alloy; 4) Establishment of IC10 directionally solidified alloy based on single crystal properties Stiffness prediction model, the model parameters are calculated by software; 5) After the model is established, the Young's modulus of IC10 directionally solidified alloy along different loading directions is verified. The invention can accurately predict the Young's modulus of the IC10 directionally solidified material loaded in different directions, provide accurate elastic material parameters for further research on the strength and fatigue of the material, and is of great significance to the engineering design of the material.

Description

A Method for Establishing Stiffness Prediction Model of IC10 Directional Solidification Material

technical field

The invention relates to the field of aviation materials, in particular to a method for establishing a stiffness model of a directionally solidified superalloy material for a turbine disk.

Background technique

Directional solidification superalloy is one of the new superalloys developed to meet the increasing gas temperature before the turbine of aero-engines. The so-called directional solidification means that when the superalloy melt solidifies in the mold, columnar crystals almost parallel to each other are generated by controlling the growth direction of the grains. The direction of grain growth of directionally solidified alloys is parallel to the direction of the largest principal axis of the material, and its mechanical properties are generally better than those of polycrystalline materials with general grain boundaries. At present, the acquisition of elastic constants of directionally solidified alloys is based on experiments or approximately replaced by single crystal elastic constants. The first method requires a large number of experiments and is expensive. The second method has low prediction accuracy and cannot meet engineering requirements in most cases. Accuracy requirements.

At present, the easiest way to predict the elastic constants of polycrystals is the average method of Voigt and Reuss. Based on the constant strain assumption, Voigt gives the upper limit of the true solution of the effective modulus of polycrystals. Reuss gives the effective modulus of polycrystals based on the assumption of equal stress. The lower limit of the real solution. Although this method is good for predicting the elastic constants of general polycrystals, it is not suitable for directly predicting directionally solidified alloys because it does not consider the influence of directionally solidified alloy grain boundaries. Some researchers have established a prediction method for the elastic constant of directionally solidified alloys using the self-consistency theory, but the implementation process is complex and requires repeated iterations, and its engineering application has certain limitations.

Contents of the invention

Purpose of the invention: Aiming at the above-mentioned prior art, a method for establishing a stiffness model of IC10 directional solidification material is proposed, which can accurately predict the Young's modulus of directional solidification alloy under different loading directions.

Technical solution: A method for establishing a stiffness model of an IC10 directional solidification material, comprising the following steps:

1) Carry out monotonic tensile tests on the IC10 single crystal alloy along the [001], [010] and [011] directions, and obtain its single crystal elastic material constants D ₁₁ , D ₁₂ , and D ₄₄ in the three directions, respectively;

2) Carry out monotonic tensile tests on the IC10 directionally solidified alloy along the [001] and [010] directions, obtain its elastic modulus along the [001] and [010] directions, and combine the matlab nonlinear fitting module to determine the stiffness model Grain boundary influence parameters f(T) and n; among them, f(T) represents the limit degree of grain boundary to the deformation perpendicular to the grain boundary, which is a model coefficient related to temperature, and n is a coefficient representing the size of the grain boundary influence area ;

3), using a scanning electron microscope and a transmission electron microscope to obtain the microstructure observation map of the IC10 directionally solidified alloy, and obtain the diameter D and grain boundary width d of each grain in the IC10 directionally solidified alloy;

4), based on the elastic properties of IC10 single crystal alloy, considering the influence of loading direction and grain boundary, the stiffness model of IC10 directionally solidified alloy is established, including the following steps:

4-1), establish the stiffness model inside the grain:

In the formula, E ₁ is the Young's modulus inside a single grain, D ₁₁ , D ₁₂ , and D ₄₄ are the single crystal elastic material constants obtained in step 1), α ₁ , β ₁ , and γ ₁ are the angles related to the loading direction Coefficients, defined as follows:

α ₁ =-sin(ψ)

β ₁ ＝-cos(ψ)sin(θ)

γ ₁ =cos(ψ)cos(θ)

where ψ and θ are Euler angles;

4-2), according to the Young's modulus and grain boundary influence parameters inside a single grain, the stiffness model in the grain boundary influence zone is established:

In the formula, _E2 is the Young's modulus in the zone affected by the grain boundary;

4-3), assuming that the width d' of the grain boundary influence zone is

d'=nd

In the formula, n is a coefficient representing the size of the grain boundary influence area, and d is the width of the grain boundary;

According to the average method of Voigt and Reuss, combined with the stiffness model inside the grain and the stiffness model in the grain boundary influence zone, the

In the formula, E _voigt and E _Reuss represent the upper and lower limits of Young's modulus of directionally solidified alloys, f _v1 represents the volume fraction of a single grain, f _v2 represents the volume fraction of the grain boundary affected area; f _v1 and f _v2 are the grain Function of diameter D and grain boundary width d:

f _v2 ＝1-f _v1

Young's modulus of directionally solidified alloy for:

Beneficial effects: The experimental research shows that the grain boundary has a certain influence on the performance of the material. The single crystal material does not contain the grain boundary, but the directionally solidified material contains the grain boundary. Therefore, when establishing the stiffness prediction model of the directionally solidified material The effect of grain boundaries must be considered. The properties of single crystal material and directionally solidified material are both anisotropic. Experimental research shows that the stiffness of single crystal is different under different loading directions, and the stiffness of single crystal material and directionally solidified material are also different. Therefore, it is necessary to establish IC10 directionally solidified alloy For the stiffness model along different loading directions, the effects of loading directions and grain boundaries on stiffness must be fully considered. On the basis of the original single crystal stiffness model, the method of the present invention quantitatively considers the restrictive effect of the grain boundary on the deformation of its nearby particles during the deformation process, and truly reflects the elastic deformation behavior of the directionally solidified alloy. The stiffness model of the present invention has a good prediction effect, It can accurately predict the Young's modulus of IC10 directionally solidified materials loaded in different directions, and provide accurate elastic material parameters for further strength and fatigue research of materials, which is of great significance for further engineering design of materials.

Description of drawings

Fig. 1 is the flowchart of the inventive method;

Fig. 2 is a diagram of Young's modulus test results and prediction results of IC10 directionally solidified alloy along different loading directions.

detailed description

The present invention will be further explained below in conjunction with the accompanying drawings.

As shown in Figure 1, a method for establishing a stiffness model of an IC10 directional solidification material includes the following steps:

1), in order to obtain the elastic constant of IC10 single crystal alloy at room temperature, the material was taken from the master batch of IC10 single crystal alloy, and processed into a standard tensile specimen of φ5mm along the three directions of [001], [010] and [011] Static monotonic tensile tests were carried out to obtain the single crystal elastic material constants D ₁₁ , D ₁₂ , and D ₄₄ in the three directions respectively. See Table 1 for the test conditions.

2) Carry out monotonic tensile tests along the [001] and [010] directions of the IC10 directionally solidified alloy at room temperature, obtain its elastic modulus along the [001] and [010] directions, and combine the matlab nonlinear fitting module to determine The grain boundary influence parameters f(T) and n in the stiffness model; among them, f(T) represents the restriction degree of the grain boundary to the deformation perpendicular to the grain boundary, which is a model coefficient related to temperature, and n represents the influence area of the grain boundary The coefficient of the size, n characterizes the size of the grain boundary influence area. And carry out the monotonic tensile test along the [025], [011] and [025] directions, and the elastic modulus obtained in these directions is used for the model verification of the model of the present invention. See Table 1 for test conditions.

Table 1

Test conditions IC10 Single Crystal Tensile Test IC10 Directional Solidification Alloy Tensile Test Sample size φ5mm φ5mm Strain rate 10 ^-3 /s 10 ^-3 /s loading direction [001], [010], [011] [001], [025], [011], [052], [010] temperature room temperature room temperature Strain range Stretch until the specimen breaks Stretch until the specimen breaks test equipment SDS-50 Electro-hydraulic Servo Dynamic and Static Testing Machine SDS-50 Electro-hydraulic Servo Dynamic and Static Testing Machine

3), cut out 1.5mm thick metal flakes on the sample of untested IC10 directionally solidified alloy, respectively, process the scanning electron microscope and transmission electron microscope samples available for observation according to the production specifications of the scanning electron microscope and transmission electron microscope samples, The microstructure observation map of IC10 directionally solidified alloy was obtained by scanning electron microscope and transmission electron microscope, and the diameter D and grain boundary width d of each grain in IC10 directionally solidified alloy were obtained.

4), based on the elastic properties of IC10 single crystal alloy, considering the influence of loading direction and grain boundary, the stiffness model of IC10 directionally solidified alloy is established, including the following steps:

4-1), establish the stiffness model inside the grain:

In the formula, E ₁ is the Young's modulus inside a single grain, D ₁₁ , D ₁₂ , and D ₄₄ are the single crystal elastic material constants obtained in step 1), α ₁ , β ₁ , and γ ₁ are the angles related to the loading direction Coefficients, defined as follows:

α ₁ =-sin(ψ)

β ₁ ＝-cos(ψ)sin(θ)

γ ₁ =cos(ψ)cos(θ)

where ψ and θ are Euler angles.

4-2), according to the Young's modulus and grain boundary influence parameters inside a single grain, the stiffness model in the grain boundary influence zone is established:

In the formula, E ₂ is the Young's modulus in the zone affected by the grain boundary; f(T) is obtained by step 2).

4-3), assuming that the width d' of the grain boundary influence zone is

d'=nd

In the formula, n is a coefficient representing the size of the grain boundary influence area, and d is the width of the grain boundary;

According to the average method of Voigt and Reuss, combined with the stiffness model inside the grain and the stiffness model in the grain boundary influence zone, the

In the formula, E _voigt and E _Reuss represent the upper and lower limits of Young's modulus of directionally solidified alloys, f _v1 represents the volume fraction of a single grain, f _v2 represents the volume fraction of the grain boundary affected area; f _v1 and f _v2 are the grain Function of diameter D and grain boundary width d:

f _v2 ＝1-f _v1

Young's modulus of directionally solidified alloy for:

In this embodiment, each parameter in the model is as shown in table 2:

Table 2

Model parameters D ₁₁ /GPa D ₁₂ /GPa D ₄₄ /GPa D/mm d/mm f no value 290.92 188.76 133.62 400 4.4 0.35 7

On the basis of the original single crystal stiffness model, the present invention quantitatively considers the restrictive effect of the grain boundary on the deformation of its nearby particles during the deformation process, and truly reflects the elastic deformation behavior of the directionally solidified alloy, so the new stiffness model developed has a better prediction effect . After the stiffness model of the IC10 directionally solidified alloy is established, the Young's model measured by the monotonic tensile test loaded with IC10 in different directions is used for verification, and the predicted Young's modulus is compared with the test results, as shown in Figure 2. It is found that the predicted results are in good agreement with the experimental results, which verifies the reliability of the model.

The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (1)

1. a stiffness model building method of IC10 directional solidification material, is characterized in that, comprises the steps: 1) Carry out monotonic tensile tests on the IC10 single crystal alloy along the [001], [010] and [011] directions, and obtain its single crystal elastic material constants D ₁₁ , D ₁₂ , and D ₄₄ in the three directions, respectively; 2) Carry out monotonic tensile tests on the IC10 directionally solidified alloy along the [001] and [010] directions, obtain its elastic modulus along the [001] and [010] directions, and combine the matlab nonlinear fitting module to determine the stiffness model Grain boundary influence parameters f(T) and n; among them, f(T) represents the restriction degree of grain boundary to the deformation perpendicular to the grain boundary, which is a model coefficient related to temperature, and n is a coefficient representing the size of the grain boundary influence area ; 3), using a scanning electron microscope and a transmission electron microscope to obtain the microstructure observation map of the IC10 directionally solidified alloy, and obtain the diameter D and grain boundary width d of each grain in the IC10 directionally solidified alloy; 4), based on the elastic properties of IC10 single crystal alloy, considering the influence of loading direction and grain boundary, the stiffness model of IC10 directionally solidified alloy is established, including the following steps: 4-1), establish the stiffness model inside the grain: ${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$ In the formula, E ₁ is the Young's modulus inside a single grain, D ₁₁ , D ₁₂ , and D ₄₄ are the single crystal elastic material constants obtained in step 1), α ₁ , β ₁ , and γ ₁ are the angles related to the loading direction Coefficients, defined as follows: α ₁ =-sin(ψ) β ₁ ＝-cos(ψ)sin(θ) γ ₁ =cos(ψ)cos(θ) where ψ and θ are Euler angles; 4-2), according to the Young's modulus and grain boundary influence parameters inside a single grain, the stiffness model in the grain boundary influence zone is established: ${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ In the formula, _E2 is the Young's modulus in the zone affected by the grain boundary; 4-3), assuming that the width d' of the grain boundary influence zone is d'=nd In the formula, n is a coefficient representing the size of the grain boundary influence area, and d is the width of the grain boundary; According to the average method of Voigt and Reuss, combined with the stiffness model inside the grain and the stiffness model in the grain boundary influence zone, the $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; Re</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right.$ In the formula, E _voigt and E _Reuss represent the upper and lower limits of Young's modulus of directionally solidified alloys, f _v1 represents the volume fraction of a single grain, f _v2 represents the volume fraction of the grain boundary affected area; f _v1 and f _v2 are the grain Function of diameter D and grain boundary width d: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; Dd</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ f _v2 ＝1-f _v1 Young's modulus of directionally solidified alloy for: $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; Re</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>$