CN111506992B - Method for obtaining relaxation parameters of glass material structure - Google Patents

Method for obtaining relaxation parameters of glass material structure Download PDF

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CN111506992B
CN111506992B CN202010272909.8A CN202010272909A CN111506992B CN 111506992 B CN111506992 B CN 111506992B CN 202010272909 A CN202010272909 A CN 202010272909A CN 111506992 B CN111506992 B CN 111506992B
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李建伟
王小蕾
刘超
李庆定
吴立新
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Abstract

The invention provides a method for obtaining a structural relaxation parameter of a glass material, which comprises the steps of processing and calculating a cooling specific heat curve measured in an experiment to obtain a dimensionless experiment dimensionless specific heat, obtaining a theoretical dimensionless specific heat through a TNM (trinitrotoluene) model, and performing least square fitting on the experiment dimensionless specific heat and the theoretical dimensionless specific heat to obtain the optimal solution of all required parameters so as to obtain the structural relaxation parameter of the glass material. The invention uses a common differential scanning calorimeter, saves time-consuming and labor-consuming high-temperature viscosity test and expensive high-temperature viscosity test equipment, greatly improves the convenience and reliability of obtaining the structure relaxation parameters, and can conveniently repeat the method to obtain the structure relaxation parameters for different glass materials.

Description

Method for obtaining relaxation parameters of glass material structure
The technical field is as follows:
the invention relates to the field of material performance parameter testing, in particular to a method for obtaining a relaxation parameter of a glass material structure.
The background art comprises the following steps:
automotive glass molding is a process in which a glass sheet is heated in a heating furnace to a softened state at a temperature higher than the glass transition temperature, and then molded by various processes, such as dead weight, BT, GT, and the like. The glass belongs to a viscoelastic body in a softening state, accurate representation of the mechanical property of the material of the glass is related to development of key technologies such as a molded surface, a process and a mold for glass molding, the development is the research basis of the glass product molding technology, and the most common viscoelastic constitutive structure is used at present. Two types of relaxation, stress relaxation and structural relaxation, are involved in the viscoelastic constitutive model. Methods for obtaining stress relaxation and stress relaxation parameters are relatively mature. However, few experimental approaches have been investigated for structural relaxation and acquisition of its parameters. Structural relaxation is a process in which a material such as glass is in a glass state in a glass transition region, and is in a thermodynamically nonequilibrium state, and a structure is spontaneously relaxed toward an equilibrium state. For the forming mode with tempering, because the glass is quenched by rapid cooling and contains a large amount of structural relaxation during forming, obvious resilience and tempering stress can be caused, and therefore the influence of the structural relaxation on the forming needs to be considered.
The relaxation of the glass structure is usually described by a Tool-Narayanawamy-Moynihan (TNM) model, which includes four parameters, namely, a pre-factor tau 0 Ratio of structure relaxation activation energy to ideal gas constant- Δ H * a/R, a non-linearity parameter x, and a non-exponential degree β. TNM model parameters can be obtained by two experimental methods, one is a specific heat test method based on a DSC differential scanning calorimeter, and the other is an expansion coefficient test mode based on a DIL thermal expansion instrument.
The parameter acquisition method adopted by the invention is a specific heat test method based on DSC, and the difference from DSC test of studying optical glass material structure relaxation by other scholars is mainly shown in acquiring parameter-delta H * on/R, the parameter is not specific to a certain relaxation unit, but the activation enthalpy which a plurality of relaxation units must have in cooperative motion is-Delta H which cannot be obtained by directly utilizing a single specific heat curve * Per (the values obtained in this way are smaller), other scholars usually use the high-temperature viscosity test of the material to calculate- Δ H by the Vogel-Fulcher-Tammann model * the/R is time-consuming and labor-consuming, and the equipment is expensive. The invention makes a great deal of improvement on the structure relaxation parameter acquisition method by utilizing the relation between the limit hypothetical temperature and the cooling rate provided by Moynihan.
Although the scholars in studying the structure relaxation behavior of pharmaceutical freeze-drying materials (e.g. glycerol) mention that the Moynihan relationship can be used to determine- Δ H * R, but the patent proposes- Δ H * The parameter/R is fixed, and then the optimal solution of the other three parameters is found by the least square method, thereby being initiated. The research on the structural relaxation parameter of the freeze-drying material of the medicine belongs to the low-temperature performance of the material, while the structural relaxation of the automobile glass, which is aimed at by the patent, belongs to the high-temperature performance of the materialThe difference of performance and research objects causes obvious difference of research methods, used instruments and the like.
The invention provides a method for obtaining the relaxation parameters of the glass material structure on the basis of integrating the advantages of the optical glass research and the freeze-drying material research.
The invention content is as follows:
aiming at the technical problems in the prior art, the invention provides the method for obtaining the structure relaxation parameters of the glass material, so that the time-consuming and labor-consuming high-temperature viscosity test and the expensive high-temperature viscosity test equipment are saved, and the convenience and the reliability for obtaining the structure relaxation parameters are greatly improved.
The technical scheme adopted by the invention is as follows:
a method for obtaining a structural relaxation parameter of a glass material, characterized by comprising the steps of:
step 1, obtaining cooling specific heat curves at least two different cooling rates by using a differential scanning calorimeter, and obtaining a limit fictive temperature T 'at each cooling rate through conversion of the cooling specific heat curves' f ；
And 2, according to a relational expression between the limit hypothetical temperature and the cooling rate:
Figure BDA0002443751560000021
calculated to obtain-Delta H * R, wherein q is cooling rate, T' f Is a limit fictive temperature, - Δ H * the/R is the ratio of the structure relaxation activation energy to the ideal gas constant;
step 3, carrying out dimensionless treatment on the cooling specific heat curve obtained in the step 1 to obtain experimental dimensionless specific heat
Figure BDA0002443751560000031
Step 4, obtaining theoretical dimensionless specific heat based on TNM model
Figure BDA0002443751560000032
The theoretical dimensionless specific heat comprises a presymptor factor tau 0 Knot ofRatio of structure relaxation activation energy to ideal gas constant-delta H * a/R, a non-linearity parameter x and a non-exponential degree β;
step 5, converting the-delta H obtained in the step 1 * substituting/R into the theoretical dimensionless specific heat in the step 4, carrying out nonlinear least square fitting on the experimental dimensionless specific heat by using the theoretical dimensionless specific heat, and calculating and searching tau by an optimization method 0 Optimal solutions of x, beta;
step 6, reacting the-delta H obtained in the step * R and tau 0 And substituting the optimal solution of x and beta into computer software to calculate and obtain the structural relaxation parameters.
In a possible implementation mode, each cooling specific heat curve in the step 1 comprises a glass section specific heat curve and a liquid section specific heat curve which are positioned at two ends of the cooling specific heat curve, and the cooling specific heat curves are integrated to obtain an enthalpy curve.
In one possible embodiment, the enthalpy curves include a glass segment enthalpy curve and a liquid segment enthalpy curve corresponding to the glass segment specific heat curve and the liquid segment specific heat curve, respectively, the glass segment enthalpy curve and the liquid segment enthalpy curve are extended, and the temperature corresponding to the intersection point of the two is the limit hypothetical temperature T' f 。
In one possible embodiment, the glass segment specific heat curve and the liquid segment specific heat curve are linearly fitted in step 3 by the formula
Figure BDA0002443751560000033
Obtaining the experimental non-dimensional specific heat by non-dimensional treatment
Figure BDA0002443751560000034
In the formula C pg (T) and C pl (T) respectively represents a straight line after the specific heat curve of the glass section and the specific heat curve of the liquid section are fitted, C p (T) is the experimentally determined specific heat value.
In a possible implementation mode, the formula used for fitting the dimensionless specific heat of the experiment to the dimensionless specific heat expression in the step 5 to obtain the optimal solution of the TNM model is as follows
Figure BDA0002443751560000041
N and N respectively represent the number of cooling specific heat curves and the discrete points on each cooling specific heat curve, w i And representing weights for balancing the contribution of each cooling specific heat curve in the optimization process.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
the method for obtaining the structure relaxation parameters of the glass materials uses a common differential scanning calorimeter, saves time-consuming and labor-consuming high-temperature viscosity tests and expensive high-temperature viscosity test equipment, greatly improves the convenience and reliability of obtaining the structure relaxation parameters, and can conveniently repeat the method for obtaining the structure relaxation parameters for different glass materials.
Description of the drawings:
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic view of a temperature-decreasing specific heat curve and an enthalpy curve obtained by integrating the temperature-decreasing specific heat curve in the present invention.
Description of reference numerals:
1. a glass section specific heat curve, a liquid section specific heat curve, a glass section enthalpy curve and a liquid section enthalpy curve, wherein the glass section specific heat curve is 2, and the liquid section enthalpy curve is 3.
The specific implementation mode is as follows:
to explain technical contents, achieved objects and effects of the present invention in detail, the present invention will be further described with reference to the accompanying drawings and embodiments, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments.
As shown in fig. 1, a method for obtaining a structural relaxation parameter of a glass material according to the present invention comprises the following steps:
step 1, selecting proper detection equipment, wherein the glass transition temperature of the glass is higher, the maximum temperature of common DSC equipment can only reach 650 ℃, and the liquid phase of the automobile glass is usually above 650 ℃, so that a high-temperature DSC differential scanning calorimeter, such as DSC404F or Setaram 96line, needs to be selected, and the DSC differential scanning calorimeter is debugged and calibrated to facilitateObtaining cooling specific heat curves at least two different cooling rates by using a differential scanning calorimeter, and obtaining a limit fictive temperature T 'at each cooling rate through conversion of the cooling specific heat curves' f ；
Step 2, according to a relation between the limit hypothetical temperature and the cooling rate:
Figure BDA0002443751560000051
calculated by the formula (1) to obtain-Delta H * [ R ] in the formula, q is cooling rate, T' f For the limit fictive temperature, - Δ H * the/R is the ratio of the structure relaxation activation energy to the ideal gas constant, due to- Δ H * R and cooling rates q and T' f The more tests are carried out, the more cooling specific heat curves under different cooling rates can be known, and the-delta H obtained in the experiment * The more accurate the/R value is;
because the automobile glass has a high toughening speed, the temperature reduction rate selected in the experiment is as large as possible, and the range is wide, the preferable specific experiment condition of the invention is that the automobile glass is heated to 800 ℃ at the same temperature rise rate of 10 ℃/min, and then the automobile glass is cooled from 800 ℃ to 300 ℃ at the temperature reduction rates of 20, 50, 100, 150 and 200 ℃/min respectively (the glass transition temperature of the automobile glass is about 610 ℃).
Step 3, carrying out dimensionless treatment on the cooling specific heat curve obtained in the step 1 to obtain experimental dimensionless specific heat
Figure BDA0002443751560000052
The dimensionless treatment is normalization treatment, so that a temperature-reducing specific heat curve is converted into a curve with the maximum value of 1;
step 4, obtaining theoretical dimensionless specific heat based on TNM model
Figure BDA0002443751560000053
The theoretical dimensionless specific heat comprises a presymptor factor tau 0 Ratio of structure relaxation activation energy to ideal gas constant- Δ H * R, non-linearity parameter x and non-index degree beta, TNM modeThe model, namely, the Tool-Narayanawamy-Moynihan model is the prior art, and a theoretical-calculated dimensionless specific heat value is obtained through a TNM model, wherein the obtained theoretical dimensionless specific heat is related to-delta H * R and τ 0 X, beta;
step 5, converting the-delta H obtained in the step 1 * substituting/R into the theoretical dimensionless specific heat in the step 4, carrying out nonlinear least square fitting on the experimental dimensionless specific heat by using the theoretical dimensionless specific heat, and calculating and searching tau by an optimization method 0 X, beta, fix- Δ H * The value of/R thus gives the values of the other parameters;
step 6, reacting the-delta H obtained in the step * R and τ 0 And substituting the optimal solution of x and beta into computer software to calculate and obtain the structural relaxation parameters, wherein the computer calculation simulation software such as Abaqus and the like has mature modeling and calculation functions, the four parameters are required for obtaining the structural relaxation parameters of the glass material, and the four parameters obtained through the steps are input into the software to obtain the required structural relaxation parameters of the glass material.
Usually, four parameters-delta H required for calculating the structural relaxation parameters of the glass material can be directly obtained by a DSC differential scanning calorimeter * R and tau 0 X, beta, but in practice it has been found that the structural relaxation parameters of the glass material thus obtained vary from the actual ones. Compared with other testing methods, the method saves time-consuming and labor-consuming high-temperature viscosity test and expensive high-temperature viscosity testing equipment, greatly improves the convenience and reliability of obtaining the structural relaxation parameters, and can conveniently repeat the method to obtain the structural relaxation parameters for different glass materials.
FIG. 2 shows a cooling specific heat curve obtained by a differential scanning calorimeter and an enthalpy curve obtained by integrating the cooling specific heat curve, in which the abscissa is temperature T and the ordinate is specific heat CValue C p (T); the ordinate in the enthalpy curve becomes enthalpy H.
Wherein, every cooling specific heat curve in step 1 includes glass section specific heat curve 1 and liquid section specific heat curve 2 that are located cooling specific heat curve both ends, will cooling specific heat curve integral obtains the enthalpy curve. The obtained enthalpy curve comprises a glass section enthalpy curve 3 and a liquid section enthalpy curve 4 which correspond to a glass section specific heat curve 1 and a liquid section specific heat curve 2 at two ends of the cooling specific heat curve. When the temperature is in the glass section, the glass is in a solid glass state; and when the temperature is in the liquid phase section, the glass is in a molten liquid state. The glass segment enthalpy curve 3 and the liquid segment enthalpy curve 4 are approximately in a straight line, the two are extended, and the temperature corresponding to the intersection point is the limit fictive temperature T' f Subsequently, in step 2, -. DELTA.H is calculated using the value obtained in step 1 * /R。
In step 3, the specific heat curve 1 of the glass section and the specific heat curve 2 of the liquid section are subjected to linear fitting through a formula
Figure BDA0002443751560000071
Carrying out dimensionless treatment on the specific heat measured in the test to obtain the dimensionless specific heat of the test
Figure BDA0002443751560000072
In the formula C pg (T) and C pl (T) represents the straight line after the glass segment specific heat curve 1 and the liquid segment specific heat curve 2 are fitted respectively, and is a fitted straight line obtained by cutting the positions of the starting point and the ending point of the curve, C p (T) is the specific heat value recorded by the experimental equipment.
Wherein, the expression of theoretical dimensionless specific heat is obtained by a TNM model in the step 4
Figure BDA0002443751560000073
Wherein
Figure BDA0002443751560000074
Figure BDA0002443751560000075
The TNM model is the combination of formulas (3), (4) and (5) and is used for expressing and calculating theoretical dimensionless specific heat
Figure BDA0002443751560000076
The theoretical dimensionless specific heat capacity comprises four structural relaxation model parameter pre-exponential factors tau 0 Ratio of structural relaxation activation energy to ideal gas constant- Δ H * a/R, a non-linearity parameter x, and a non-exponential degree β, where- Δ H * the/R is substituted by the numerical value calculated in the step 2; in addition, Δ T i For the temperature step, 1K is generally taken; i. j and k represent discrete points of numerical integration; q is the ramp rate used for the experiment.
In step 5, a formula used for obtaining an optimal solution of the TNM model by fitting the dimensionless specific heat of the experiment is as follows:
Figure BDA0002443751560000077
formula (6) is a calculation formula for fitting experimental dimensionless specific heat and theoretical dimensionless specific heat by using a least square method, wherein N and N respectively represent the number of cooling specific heat curves and the number of discrete points on each cooling specific heat curve, w i And representing weights for balancing the contribution of each cooling specific heat curve in the optimization process. The three parameters are led into computer simulation calculation software for optimization and adjustment, and are fixed, so that three parameters tau are obtained 0 X, beta.
In the last step, the four parameters obtained in the above process are input into computer simulation calculation software such as Abaqus, so as to obtain the required glass material structure relaxation parameters.
The above description is intended to provide preferred embodiments of the present invention, and not to limit the present invention, and the present invention is not limited to the above examples, and variations, modifications, additions and substitutions which can be made by those skilled in the art within the spirit and scope of the present invention are also within the scope of the present invention.

Claims (5)

1. A method for obtaining a structural relaxation parameter of a glass material, characterized by comprising the steps of:
step 1, obtaining cooling specific heat curves of glass with a liquid section at least two different cooling rates of 650 ℃ by using a high-temperature DSC differential scanning calorimeter, and obtaining a limit fictive temperature T 'at each cooling rate through conversion of the cooling specific heat curves' f ；
And 2, according to a relational expression between the limit hypothetical temperature and the cooling rate:
Figure FDA0004005045520000011
calculated to obtain-Delta H * [ R ] in the formula, q is cooling rate, T' f For the limit fictive temperature, - Δ H * the/R is the ratio of the structure relaxation activation energy to the ideal gas constant;
step 3, carrying out dimensionless treatment on the cooling specific heat curve obtained in the step 1 to obtain experimental dimensionless specific heat
Figure FDA0004005045520000012
Step 4, obtaining theoretical dimensionless specific heat based on TNM model
Figure FDA0004005045520000013
Including a pre-exponential factor τ in the theoretical dimensionless specific heat 0 Ratio of structure relaxation activation energy to ideal gas constant- Δ H * a/R, a non-linearity parameter x and a non-exponential degree beta;
step 5, converting the-delta H obtained in the step 2 * substituting/R into the theoretical dimensionless specific heat in the step 4, carrying out nonlinear least square fitting on the experimental dimensionless specific heat by using an expression of the theoretical dimensionless specific heat, and calculating and searching tau by a least square method 0 Optimal solutions of x, beta;
step 6, the-delta H obtained in the step is treated * R and τ 0 And substituting the optimal solution of x and beta into computer software to calculate and obtain the structural relaxation parameters.
2. The method for obtaining the structural relaxation parameters of the glass material as claimed in claim 1, wherein each temperature-reducing specific heat curve in the step 1 comprises a glass section specific heat curve and a liquid section specific heat curve which are positioned at two ends of the temperature-reducing specific heat curve, and the temperature-reducing specific heat curves are integrated to obtain an enthalpy curve.
3. The method for obtaining the structural relaxation parameters of glass materials as claimed in claim 2, wherein the enthalpy curves include a glass segment enthalpy curve and a liquid segment enthalpy curve corresponding to the glass segment specific heat curve and the liquid segment specific heat curve, respectively, the glass segment enthalpy curve and the liquid segment enthalpy curve are extended, and the temperature corresponding to the intersection point of the two is the limit fictive temperature T' f 。
4. The method for obtaining the structural relaxation parameters of glass material as claimed in claim 2, wherein the specific heat curve of glass segment and the specific heat curve of liquid segment are linearly fitted in step 3 by the formula
Figure FDA0004005045520000021
Obtaining the experimental non-dimensional specific heat by non-dimensional treatment
Figure FDA0004005045520000022
In the formula C pg (T) and C pl (T) respectively represents a straight line after the specific heat curve of the glass section and the specific heat curve of the liquid section are fitted, C p (T) is the experimentally determined specific heat value.
5. The method for obtaining the structural relaxation parameters of glass material as claimed in claim 1, wherein the said step 5 is to fit the said dimensionless specific heat to the expression of theoretical dimensionless specific heat to obtain the most suitable TNM modelThe optimal solution uses the formula of
Figure FDA0004005045520000023
N and N respectively represent the number of cooling specific heat curves and the discrete points on each cooling specific heat curve, w i And representing weights for balancing the contribution of each cooling specific heat curve in the optimization process.
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