Method for predicting defect concentration of amorphous alloy through dynamic relaxation analysis

Abstract

The invention belongs to the technical field of amorphous alloy dynamic relaxation behavior modeling, and particularly relates to a method for predicting defect concentration of amorphous alloy through dynamic relaxation analysis. A fractional order viscoelastic model is adopted to simulate the dynamic relaxation behavior of the amorphous alloy, model parameters are few, and the defect concentration evolution of the amorphous alloy in the dynamic relaxation process can be reflected; the established fractional order viscoelastic model can be verified through a dynamic relaxation experiment, and the evolution of defect concentration is obtained by fitting the experiment. According to the method, multiple key parameters such as the high-frequency shear modulus, the low-frequency shear modulus and the relaxation time are comprehensively utilized, and quantitative analysis of the complex interaction between the microstructure and the macroscopic performance of the material is achieved. The verification method not only proves the reliability of the model, but also can quantitatively calculate the evolution of the defect concentration. The application of the technology in alloy design and preparation stages provides a new theoretical guidance and experimental method for prediction and evaluation of amorphous alloy performance.

Description

Technical Field

[0001] The invention belongs to the technical field of dynamic relaxation behavior modeling of amorphous alloys, and in particular relates to a method for predicting defect concentration of amorphous alloys through dynamic relaxation analysis. Background Art

[0002] Amorphous alloys are obtained by rapid cooling of supercooled liquids. They are characterized by long-range structural disorder and short-range structural order. They have the characteristics of both metals and glasses, and exhibit unique mechanical and physical properties, such as high strength, high fracture toughness, large elastic strain limit, superplasticity in the supercooled liquid phase, good corrosion resistance, and excellent soft magnetic properties. These excellent properties make them widely used in microelectronic devices, defense industry, aerospace, biomedicine, sports and leisure, etc.

[0003] Dynamic mechanical relaxation is an important indicator for understanding the mechanical / physical properties of viscoelastic amorphous solids. Due to the heterogeneity of the microstructure, the relaxation behavior of amorphous solids usually shows a strong deviation from the Debye relaxation. Due to the lack of long-range order in amorphous structures, traditional crystal models cannot be directly applied, making it complicated to predict their relaxation behavior under stress. At the same time, the existing technology lacks a model that relates microscopic defects to macroscopic properties, resulting in the prediction of defect concentration relying on experimental data, which is difficult to accurately describe. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for predicting the defect concentration of an amorphous alloy by dynamic relaxation analysis. Specifically, for the dynamic relaxation behavior of an amorphous alloy, a viscoelastic fractional-order model is constructed that is easy to apply, has a clear physical meaning, and can meet the accuracy requirements. The viscoelastic fractional-order model provided by the present invention can better describe the dynamic relaxation master curve and accurately predict the evolution of the defect concentration, verifying the rationality of the model.

[0005] To achieve the above object, the technical solution adopted by the present invention is a method for predicting the defect concentration of an amorphous alloy by dynamic relaxation analysis, comprising the following steps:

[0006] Step 1: Using a dynamic relaxation analysis method, aiming at the viscoelastic mechanical behavior of the amorphous alloy, a constitutive equation for describing the dynamic relaxation behavior of the amorphous alloy is established, the dynamic relaxation behavior of the amorphous alloy is analyzed, and the complex modulus and loss modulus are obtained;

[0007] Step 2: Under fixed temperature conditions, the defect concentration of the amorphous alloy is predicted by using the complex modulus and loss modulus obtained in the analysis of step 1.

[0008] Furthermore, the dynamic relaxation analysis method described in step 1 includes:

[0009] Step 1: Use the Riemann-Liouville type fractional derivative operator to define the constitutive equation of the fractional viscoelastic unit, as shown in formula (1):

[0010]

[0011] Where σ is stress, c is the material viscoelastic coefficient, α is the derivative order, ε is strain, and t is time; when α = 0, σ = cε, and the fractional viscoelastic unit corresponds to the Hooke spring unit; when α = 1, The fractional viscoelastic element corresponds to the Newtonian viscoelastic element;

[0012] Step 2: According to the constitutive equation of the fractional viscoelastic unit obtained in the first step, the spring in the Maxwell unit is replaced by a fractional viscoelastic unit, and a spring is connected in series outside the entire model to describe the asymmetric loss modulus peak of the amorphous alloy;

[0013] The control equation is obtained through the relationship between each unit, as shown in formula (2):

[0014]

[0015] Among them, E1, E2, η1 are the spring coefficients and viscosity of the sticky pot in the corresponding unit respectively;

[0016] Step 3: Based on the control equation obtained in the second step, the combination rule of fractional calculus and Fourier integral are applied to obtain the complex modulus, as shown in formula (3):

[0017]

[0018] The parameters in the formula are as shown in formula (4):

[0019]

[0020] Parameters G0 and G ∞ Corresponding to the low-frequency modulus and high-frequency modulus, τ MF is the characteristic relaxation time of the model, κ is the digital factor, and ω is the angular frequency;

[0021] Step 4: Based on the complex modulus relationship obtained in step 3, the loss modulus expression is further obtained as shown in formula (5):

[0022]

[0023] The parameter A is as shown in formula (6),

[0024]

[0025] The above constitutive equations are established for the viscoelastic mechanical behavior of amorphous alloys, and the dynamic relaxation behavior of amorphous alloys is described. The dynamic relaxation behavior of amorphous alloys is analyzed using the constitutive equations in order to predict the defect concentration.

[0026] The method of predicting the defect concentration of the amorphous alloy includes:

[0027] (1) According to the complex modulus and loss modulus obtained in the dynamic relaxation analysis, the expression of internal friction tanδ is obtained as shown in formula (7):

[0028]

[0029] (2) When ωτ MF When it is large enough, that is, at low temperature or high frequency measurement, ωτ MF >>1, as in formula (8):

[0030] tanδ~(ω τM F) -α (8)

[0031] (3) According to the approximate relationship in formula (8), taking into account According to formula (9):

[0032]

[0033] Where K is the Boltzmann constant and N is a constant;

[0034] According to the formula (9) given above, at a fixed temperature, after dynamic relaxation analysis of the amorphous alloy, the slope x of ln(tanδ) and ln(ω) is used as the correlation factor of the defect concentration of the amorphous alloy, thus completing the prediction of the defect concentration of the amorphous alloy.

[0035] The beneficial effects of the present invention are as follows: the present invention provides a method for predicting the defect concentration of an amorphous alloy by dynamic relaxation analysis, adopts a fractional-order viscoelastic model to simulate the dynamic relaxation behavior of an amorphous alloy, has fewer model parameters, and can reflect the evolution of the defect concentration of an amorphous alloy during the dynamic relaxation process; the established fractional-order viscoelastic model can be verified by a dynamic relaxation experiment, and the evolution of the defect concentration can be obtained by fitting the experiment. This verification method not only proves the reliability of the model, but also can quantitatively calculate the evolution of the defect concentration. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the present invention;

[0037] Figure 2 is a schematic diagram of a fractional viscoelastic model in an embodiment of the present invention;

[0038] Figure 3 Cu at different temperatures in the embodiments of the present invention 46 Zr 35 Hf 12 Experimental graph of normalized loss modulus and normalized storage modulus of Al7 amorphous alloy evolving with frequency;

[0039] Figure 4 The master curve obtained by the time-temperature equivalence principle and the curve fitted by the MF model in the embodiment of the present invention;

[0040] Figure 5 The double logarithmic variation of the loss factor tanδ with the driving frequency and the evolution law of the defect concentration with temperature at different temperatures in the examples of the present invention are shown. DETAILED DESCRIPTION

[0041] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0042] like Figure 1 As shown, the method for predicting the defect concentration of an amorphous alloy by dynamic relaxation analysis according to the present invention comprises the following steps:

[0043] Firstly, dynamic relaxation analysis is performed on the model alloy.

[0044] Step 1: Use the Riemann-Liouville type fractional derivative operator to define the constitutive equation of the fractional viscoelastic unit, as shown in formula (1):

[0045]

[0046] Where σ is stress, c is the material viscoelastic coefficient, α is the derivative order, ε is strain, and t is time; when α = 0, σ = cε, and the fractional viscoelastic unit corresponds to the Hooke spring unit; when α = 1, The fractional viscoelastic element corresponds to the Newtonian viscoelastic element;

[0047] Step 2: According to the constitutive equation of the fractional viscoelastic unit obtained in the first step, the spring in the Maxwell unit is replaced by a fractional viscoelastic unit, and a spring is connected in series outside the entire model to describe the asymmetric loss modulus peak of the amorphous alloy;

[0048] The control equation is obtained through the relationship between each unit, as shown in formula (2):

[0049]

[0050] Among them, E1, E2, η1 are the spring coefficients and viscosity of the corresponding unit, respectively, such as Figure 2.

[0051] Step 3: Based on the control equation obtained in the second step, the combination rule of fractional calculus and Fourier integral are applied to obtain the complex modulus, as shown in formula (3):

[0052]

[0053] The parameters in the formula are as shown in formula (4):

[0054]

[0055] Parameters G0 and G ∞ Corresponding to the low-frequency modulus and high-frequency modulus, τ MF is the characteristic relaxation time of the model, κ is the digital factor, and ω is the angular frequency;

[0056] Step 4: Based on the complex modulus relationship obtained in step 3, the loss modulus expression is further obtained as shown in formula (5):

[0057]

[0058] The parameter A is as shown in formula (6),

[0059]

[0060] like Figure 2 As shown, in order to verify the feasibility and effectiveness of the present invention, Cu 46 Zr 35 Hf 12 Al7 amorphous alloy was used as the model alloy; the Cu 46 Zr 35 Hf 12 Dynamic relaxation experiments were carried out on Al7 amorphous alloy to obtain the dynamic modulus evolution curves at different temperatures. The experimental results of the changes of normalized storage modulus and loss modulus with driving frequency are shown in Figure 3 shown.

[0061] Figure 3 (a) is the curve of normalized storage modulus changing with frequency, the temperature interval is 5K, Figure 3 (b) is the curve of the change of normalized loss modulus with frequency, and the temperature interval is 5 K. Based on the time-temperature equivalence principle, the master curve of the loss modulus at the reference temperature of 700 K is obtained, as shown in Figure 3 shown.

[0062] The master curve is fitted using formula (5), as follows: Figure 4 The fractional-order viscoelastic model fits well with the data points in the entire observed frequency range and can describe Cu in a wide frequency range. 46 Zr35 Hf 12 The viscoelastic behavior of Al7 amorphous alloy completes the dynamic relaxation analysis of the model alloy.

[0063] The following Cu 46 Zr 35 Hf 12 Defect concentration prediction of Al7 amorphous alloy.

[0064] Step 5: Based on the complex modulus and loss modulus obtained in steps 4 and 3, the internal friction tanδ expression can be obtained as shown in formula (7):

[0065]

[0066] Step 6: When ωτ MF When it is large enough, that is, at low temperature or high frequency measurement, ωτ MF >>1, as in equation (8),

[0067] tanδ~(ωτ MF ) -α (8)

[0068] Step 7: Based on the approximate relationship in step 6, taking into account According to formula (9),

[0069]

[0070] Where K is the Boltzmann constant and N is a constant.

[0071] The present invention uses an inverted torsion pendulum internal friction instrument to perform a loss factor tanδ measurement experiment on a model alloy, and obtains a double logarithmic change of the loss factor tanδ with the driving frequency at different temperatures. The experimental results are shown in Figure 5 (a). Using formula (9) Figure 5 The experimental results in (a) are fitted, and finally the evolution of defect concentration correlation factor χ with temperature is obtained, as shown in Figure 5 (b) as shown.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting defect concentration of an amorphous alloy by dynamic relaxation analysis, characterized in that: The following steps are involved: Step 1: Using a dynamic relaxation analysis method, aiming at the viscoelastic mechanical behavior of the amorphous alloy, a constitutive equation for describing the dynamic relaxation behavior of the amorphous alloy is established, the dynamic relaxation behavior of the amorphous alloy is analyzed, and the complex modulus and loss modulus are obtained; Step 2: Under fixed temperature conditions, the defect concentration of the amorphous alloy is predicted by using the complex modulus and loss modulus obtained in the analysis of step 1.

2. The method for predicting defect concentration of an amorphous alloy by dynamic relaxation analysis according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1: Use the Riemann-Liouville type fractional derivative operator to define the constitutive equation of the fractional viscoelastic unit, as shown in formula (1): In the formula, σ is stress, c is the material viscoelastic coefficient, α is the derivative order, ε is strain, and t is time; When α=0, σ=cε, and the fractional viscoelastic unit corresponds to the Hookean spring unit; when α=1, The fractional viscoelastic element corresponds to the Newtonian viscoelastic element; Step 2: According to the constitutive equation of the fractional viscoelastic unit obtained in the first step, the spring in the Maxwell unit is replaced by a fractional viscoelastic unit, and a spring is connected in series outside the entire model to describe the asymmetric loss modulus peak of the amorphous alloy; The control equation is obtained through the relationship between each unit, as shown in formula (2): Among them, E1, E2, η1 are the spring coefficients and viscosity of the sticky pot in the corresponding unit respectively; Step 3: Based on the control equation obtained in the second step, the combination rule of fractional calculus and Fourier integral are applied to obtain the complex modulus, as shown in formula (3): The parameters in the formula are as shown in formula (4): The parameters G0 and G∞ correspond to the low-frequency modulus and high-frequency modulus, respectively. MF is the characteristic relaxation time of the model, k is the numerical factor, and ω is the angular frequency; Step 4: Based on the complex modulus relationship obtained in step 3, the loss modulus expression is further obtained as shown in formula (5): The parameter A in the formula is as shown in formula (6): The constitutive equation for the viscoelastic mechanical behavior of amorphous alloys is established above, the dynamic relaxation behavior of amorphous alloys is described, and the dynamic relaxation behavior of amorphous alloys is analyzed using the constitutive equation in order to predict the defect concentration.

3. The method for predicting defect concentration of an amorphous alloy by dynamic relaxation analysis according to claim 1, characterized in that: The step 2 is specifically as follows: (1) According to the complex modulus and loss modulus obtained in the dynamic relaxation analysis, the expression of internal friction tanδ is obtained as shown in formula (7): (2) When ωτ MF When it is large enough, that is, at low temperature or high frequency measurement, ωτ MF >>1, as in equation (8): tanδ~(ωτ MF ) -α (8) (3) According to the approximate relationship in formula (8), taking into account According to formula (9): Where K is the Boltzmann constant and N is a constant; According to the formula (9) given above, at a fixed temperature, after dynamic relaxation analysis of the amorphous alloy, the slope χ of ln(tanδ) and ln(ω) is used as the correlation factor of the defect concentration of the amorphous alloy, thus completing the prediction of the defect concentration of the amorphous alloy.

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