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 by considering influence of a grain boundary and a loading direction. The method comprises the following steps of: (1), performing a monotonic tensile test of an IC10 mono-crystal at room temperature along the directions [001], [010] and [011]; (2), performing a monotonic tensile test of an IC10 directional solidification alloy at room temperature along different loading directions; (3), observing the IC10 directional solidification alloy by using a scanning electron microscope and a transmission electron microscope; (4), on the basis of the mono-crystal performance, establishing a stiffness prediction model of the IC10 directional solidification alloy, and obtaining model parameters through software calculation; and (5), after completing model establishing, verifying Young modulus of the IC10 directional solidification alloy along different loading directions. By means of the method disclosed by the invention, the Young modulus loaded by the IC10 directional solidification material along different loading directions can be accurately predicted; accurate elastic material parameters can be provided for further strength and fatigue research of the material; and thus, the method has a great significance for engineering design of the material.

Description

A kind of method for building up of IC10 unidirectional solidification material Stiffness prediction models

Technical field

The present invention relates to aeronautical material field is and in particular to turbine disk directionally solidified superalloy, DS superalloy material stiffness model Method for building up.

Background technology

Directionally solidified superalloy, DS superalloy is in order to meet the turbine entrance temperature temperature of aero-engine continuous improvement and to develop One of novel high-temperature alloy coming.So-called directional solidification it is simply that when high temperature alloy melt solidifies in casting mold, by controlling crystal grain The direction of growth, generate the column crystal that is almost parallel to each other.The grain growth direction of directional solidificating alloy and the maximum master of material Direction of principal axis is parallel, and its mechanical property is generally better than the polycrystalline material with general crystal boundary.At present, directional solidificating alloy elastic constant Acquisition be approximately replaced based on test or with the elastic constant of monocrystalline, first method needs lot of experiments, relatively costly, Second method precision of prediction is not high, in most cases cannot meet requirement of engineering precision.

At present, the prediction simplest method of polycrystalline elastic constant is exactly Voigt the and Reuss method of average, and Voigt is based on often should Become it is assumed that giving the upper limit of the true solution of polycrystal effective modulus, Reuss is based on iso-stress and assumes to give polycrystal effective mould The lower limit of the true solution of amount, though this method predicts that typically multicrystal elastic constant effect is good, because it does not consider that orientation is solidifying Gu the impact of alloy crystal boundary, it is less suitable for direct use in prediction directional solidificating alloy.Researcher is had to be established with self-consistency theory The Forecasting Methodology of directional solidificating alloy elastic constant, but its to realize process complex, need to iterate, engineering application has one Foregone conclusion is sex-limited.

Content of the invention

Goal of the invention：For above-mentioned prior art, a kind of rigidity model method for building up of IC10 unidirectional solidification material is proposed, Can Accurate Prediction directional solidificating alloy difference loading direction under Young's modulus.

Technical scheme：A kind of rigidity model method for building up of IC10 unidirectional solidification material, comprises the steps：

1), along [001], [010] and [011] direction, monotonic tension test is carried out to IC10 single crystal alloy, obtain it respectively Monocrystalline elastomeric material constant D in this three directions₁₁、D₁₂、D₄₄；

2), along [001] and [010] direction, monotonic tension test is carried out to IC10 directional solidificating alloy, obtain its edge [001] [010] elastic modelling quantity in direction, determines crystal boundary affecting parameters f (T) in rigidity model in conjunction with matlab nonlinear fitting module And n；Wherein, f (T) represents that crystal boundary, to the limited degree perpendicular to crystal boundary Direction distortion, is a model system related to temperature Number, n is the coefficient representing GB affected zone size；

3), see with the microstructure that SEM and transmission electron microscope obtain IC10 directional solidificating alloy Mapping, obtains the diameter D and grain boundary width d of each crystal grain IC10 directional solidificating alloy Nei；

4), the elastic performance based on IC10 single crystal alloy, it is considered to the impact of loading direction and crystal boundary, sets up IC10 orientation solidifying Gu the rigidity model of alloy, comprise the steps：

4-1), set up the rigidity model of intra-die：

In formula, E₁It is the Young's modulus of single intra-die, D₁₁、D₁₂、D₄₄For step 1) obtain monocrystalline elastomeric material normal Number, α₁、β₁、γ₁It is the coefficient of angularity related to loading direction, be defined as follows：

α₁=-sin (ψ)

β₁=-cos (ψ) sin (θ)

γ₁=cos (ψ) cos (θ)

In formula, ψ and θ is Eulerian angles；

4-2), the Young's modulus according to single intra-die and crystal boundary affecting parameters, set up the rigidity in GB affected zone Model：

In formula, E₂It is the Young's modulus in GB affected zone；

4-3) it is assumed that the width d' of GB affected zone is

D'=nd

In formula, n is the coefficient representing GB affected zone size, and d is grain boundary width；

According to Voigt and Reuss averaging method, in conjunction with the rigidity mould in the rigidity model and GB affected zone of intra-die Type obtains

In formula, E_voigtAnd E_ReussRepresent the bound of directional solidificating alloy Young's modulus, f respectively_v1Represent single crystal grain Volume fraction, f_v2Represent the volume fraction of GB affected zone；f_v1And f_v2It is crystal grain diameter D and the function of grain boundary width d：

f_v2=1-f_v1

The then Young's modulus of directional solidificating alloyFor：

Beneficial effect：Shown by experimental study, crystal boundary has a certain impact to the performance tool of material, in monocrystal material not Containing crystal boundary, and in unidirectional solidification material, contain crystal boundary, therefore, be necessary for when setting up the Stiffness prediction models of unidirectional solidification material Consider the impact of crystal boundary.The performance of monocrystal material and unidirectional solidification material is anisotropy, and experimental study shows, different loadings Under direction, the rigidity of monocrystalline is different, and the rigidity of monocrystal material and unidirectional solidification material is also different, so IC10 to be set up The rigidity model of the different loading directions in directional solidificating alloy edge is it is necessary to take into full account the impact to rigidity of loading direction and crystal boundary. The inventive method is quantitative on the basis of original monocrystalline rigidity model to consider crystal boundary particle change nearby for it in deformation process The restriction effect of shape, the actual response elastic deformation behavior of directional solidificating alloy, the rigidity model prediction effect of the present invention is relatively Good, the Young's modulus that IC10 unidirectional solidification material loads along different directions can be predicted exactly, be the further intensity of material There is provided accurate elastomeric material parameter with fatigue study, significant to the further engineering design of material.

Brief description

Fig. 1 is the flow chart of the inventive method；

Fig. 2 is the Young's modulus result of the test of the different loading directions in IC10 directional solidificating alloy edge and the figure that predicts the outcome.

Specific embodiment

Below in conjunction with the accompanying drawings the present invention is done and further explain.

As shown in figure 1, a kind of rigidity model method for building up of IC10 unidirectional solidification material, comprise the steps：

1), in order to obtain IC10 single crystal alloy elastic constant at room temperature, draw materials from IC10 single crystal alloy masterbatch, edge [001], the standard tensile specimen that φ 5mm is processed in [010] and [011] three direction carries out static(al) monotonic tension test, respectively Obtain its monocrystalline elastomeric material constant D in this three directions₁₁、D₁₂、D₄₄, experimental condition is shown in Table 1.

2), along [001] and [010] direction, monotonic tension test is carried out at room temperature to IC10 directional solidificating alloy, obtain It, along the elastic modelling quantity in [001] and [010] direction, determines crystal boundary impact in rigidity model in conjunction with matlab nonlinear fitting module Parameter f (T) and n；Wherein, f (T) represent crystal boundary to the limited degree perpendicular to crystal boundary Direction distortion, be one related to temperature Model coefficient, n is the coefficient representing GB affected zone size, and n characterizes the size of GB affected zone.And edge [025], [011] and [025] direction carry out monotonic tension test, these directions obtain elastic modelling quantity set up model in order to the present invention Model is verified.Experimental condition is shown in Table 1.

Table 1

Experimental condition	IC10 monocrystalline tension test	IC10 directional solidificating alloy tension test
			Specimen 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
			Range of strain	Stretching is up to sample fracture	Stretching is up to sample fracture
Testing equipment	SDS-50 electro-hydraulic servo static and dynamic test machine	SDS-50 electro-hydraulic servo static and dynamic test machine

3), the sample of not test (N.T.) IC10 directional solidificating alloy cuts out respectively the thick sheet metal of 1.5mm, respectively according to sweeping Retouch Electronic Speculum and the making specification of transmission electron microscope sample, process the ESEM being available for observing and transmission electron microscope sample, use and sweep Retouch electron microscope and transmission electron microscope obtains the microstructure observation figure of IC10 directional solidificating alloy, obtain IC10 orientation The diameter D and grain boundary width d of each crystal grain in solidified superalloy.

4), the elastic performance based on IC10 single crystal alloy, it is considered to the impact of loading direction and crystal boundary, sets up IC10 orientation solidifying Gu the rigidity model of alloy, comprise the steps：

4-1), set up the rigidity model of intra-die：

In formula, E₁It is the Young's modulus of single intra-die, D₁₁、D₁₂、D₄₄For step 1) obtain monocrystalline elastomeric material normal Number, α₁、β₁、γ₁It is the coefficient of angularity related to loading direction, be defined as follows：

α₁=-sin (ψ)

β₁=-cos (ψ) sin (θ)

γ₁=cos (ψ) cos (θ)

In formula, ψ and θ is Eulerian angles.

4-2), the Young's modulus according to single intra-die and crystal boundary affecting parameters, set up the rigidity in GB affected zone Model：

In formula, E₂It is the Young's modulus in GB affected zone；F (T) passes through step 2) obtain.

4-3) it is assumed that the width d' of GB affected zone is

D'=nd

In formula, n is the coefficient representing GB affected zone size, and d is grain boundary width；

According to Voigt and Reuss averaging method, in conjunction with the rigidity mould in the rigidity model and GB affected zone of intra-die Type obtains

In formula, E_voigtAnd E_ReussRepresent the bound of directional solidificating alloy Young's modulus, f respectively_v1Represent single crystal grain Volume fraction, f_v2Represent the volume fraction of GB affected zone；f_v1And f_v2It is crystal grain diameter D and the function of grain boundary width d：

f_v2=1-f_v1

The then Young's modulus of directional solidificating alloyFor：

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

Table 2

Model parameter	D11/GPa	D12/GPa	D44/GPa	D/mm	d/mm	f	n
								Numerical value	290.92	188.76	133.62	400	4.4	0.35	7

The present invention on the basis of original monocrystalline rigidity model quantitative consider in deformation process crystal boundary for it near matter The restriction effect of point deformation, the actual response elastic deformation behavior of directional solidificating alloy, so the new rigidity model of exploitation Prediction effect is preferable.After the completion of the rigidity model to IC10 directional solidificating alloy is set up, loaded along different directions with IC10 The Young's model that monotonic tension test records is verified, the Young's modulus of prediction and result of the test is contrasted, sees Fig. 2, It is good that discovery predicts the outcome and result of the test is coincide, and demonstrates the reliability of model.

The above is only the preferred embodiment of the present invention it is noted that ordinary skill people for the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (1)

1. a kind of rigidity model method for building up of IC10 unidirectional solidification material is it is characterised in that comprise the steps：

1), along [001], [010] and [011] direction, monotonic tension test is carried out to IC10 single crystal alloy, obtain it respectively at this The monocrystalline elastomeric material constant D in three directions₁₁、D₁₂、D₄₄；

2), to IC10 directional solidificating alloy along [001] and [010] direction carry out monotonic tension test, obtain its edge [001] and [010] elastic modelling quantity in direction, in conjunction with matlab nonlinear fitting module determine in rigidity model crystal boundary affecting parameters f (T) and n；Wherein, f (T) represents that crystal boundary, to the limited degree perpendicular to crystal boundary Direction distortion, is a model coefficient related to temperature, N is the coefficient representing GB affected zone size；

3) the microstructure observation of IC10 directional solidificating alloy, is obtained with SEM and transmission electron microscope Figure, obtains the diameter D and grain boundary width d of each crystal grain IC10 directional solidificating alloy Nei；

4), the elastic performance based on IC10 single crystal alloy, it is considered to the impact of loading direction and crystal boundary, is set up IC10 directional solidification and is closed The rigidity model of gold, comprises the steps：

4-1), set up the rigidity model of intra-die：

$E_1=\[\frac{D_{11}+D_{12}}{(D_{11}+2D_{12})(D_{11}-D_{12})}+(\frac{1}{D_{44}}-\frac{2}{(D_{11}-D_{12})})\]({\mathrm{\α}}_1^2{\mathrm{\β}}_1^2+{\mathrm{\α}}_1^2{\mathrm{\γ}}_1^2+{\mathrm{\α}}_1^2{\mathrm{\β}}_1^2)$

In formula, E₁It is the Young's modulus of single intra-die, D₁₁、D₁₂、D₄₄For step 1) obtain monocrystalline elastomeric material constant, α₁、 β₁、γ₁It is the coefficient of angularity related to loading direction, be defined as follows：

α₁=-sin (ψ)

β₁=-cos (ψ) sin (θ)

γ₁=cos (ψ) cos (θ)

In formula, ψ and θ is Eulerian angles；

4-2), the Young's modulus according to single intra-die and crystal boundary affecting parameters, set up the rigidity model in GB affected zone：

$E_2=\frac{E_1}{cos{\left(\mathrm{\θ}\right)}^2+f\left(T\right)sin{\left(\mathrm{\θ}\right)}^2}$

In formula, E₂It is the Young's modulus in GB affected zone；

4-3) it is assumed that the width d' of GB affected zone is

D'=nd

In formula, n is the coefficient representing GB affected zone size, and d is grain boundary width；

According to Voigt and Reuss averaging method, obtain in conjunction with the rigidity model in the rigidity model and GB affected zone of intra-die Arrive

$\left\{\begin{array}{c}{E}_{voigt}=f_{v1}{E}_1+f_{v2}{E}_2\\ \frac{1}{E_{\mathrm{Re}uss}}=\frac{f_{v1}}{E_1}+\frac{f_{v2}}{E_2}\end{array}\right.$

In formula, E_voigtAnd E_ReussRepresent the bound of directional solidificating alloy Young's modulus, f respectively_v1Represent the volume of single crystal grain Fraction, f_v2Represent the volume fraction of GB affected zone；f_v1And f_v2It is crystal grain diameter D and the function of grain boundary width d：

$f_{v1}=\frac{2{\mathrm{Dd}}^{\′}-d^{\′2}}{D^2}$

f_v2=1-f_v1

The then Young's modulus of directional solidificating alloyFor：

$\stackrel{\‾}{E}=\frac{E_{voigt}+E_{\mathrm{Re}uss}}{2}.$