Method and system for constructing and applying tensile constitutive model of electric porcelain material

Abstract

The invention provides an electric porcelain material tensile constitutive model construction and application method and system, and the method comprises the steps: introducing a damage variable item and a strain rate effect item based on Weibull distribution; determining the relationship between the dynamic elastic modulus and the strain rate of the electroceramic material and the relationship between the shape parameters of the Weibull distribution and the strain rate by combining a constitutive relationship test curve under the medium-high strain rate, and constructing a tensile constitutive model of the electroceramic material; according to the method and the system, a damage variable item and a strain rate effect item are introduced, a constitutive relation test curve under the medium-high strain rate is combined to construct a tensile constitutive model of the electroceramic material, the influence of the strain rate is considered, and the dynamic tensile constitutive relation of the electroceramic material under the medium-high strain rate is obtained; parameters in the model construction process depend on test results, and the precision is high; the high-precision tensile constitutive model of the electroceramic material is used for carrying out tensile analysis on the electroceramic material, so that an anti-seismic calculation analysis result which is subsequently carried out by utilizing a tensile analysis result is more accurate.

Description

Technical Field

[0001] This invention belongs to the technical field of mechanical property research on power facility materials under extreme conditions, specifically involving a method and system for constructing and applying a tensile constitutive model of electrical porcelain materials. Background Technology

[0002] The area between the Circum-Pacific Seismic Belt and the Eurasian Seismic Belt is prone to earthquakes, which severely damage electrical equipment, especially porcelain-insulated equipment in substations. This damage affects the safe and stable operation of the power grid and causes huge economic losses. Porcelain-insulated electrical equipment, such as surge arresters, current transformers, voltage transformers, circuit breakers, and disconnect switches, are highly susceptible to fracture at the base of the porcelain bushing during earthquakes.

[0003] Porcelain support structures are made by sintering various powders and are characterized by high brittleness. Dynamic analyses, such as those analyzing seismic response, do not consider the impact of varying strain rates on the mechanical parameters of the porcelain sleeve under dynamic loads. In reality, many materials, especially those with medium to high strain rates (10⁻⁶), exhibit significant brittleness under dynamic loads. 2 s -1 -10 4 s -1 Under these conditions, the mechanical properties of materials exhibit strong rate-dependent characteristics. Specifically, the stress-strain relationship curve obtained at a certain strain rate shows that, as the strain rate changes, the peak strength, elastic modulus, and other mechanical parameters all change accordingly. For example, for a considerable number of materials, the strength increases with increasing strain rate, which is reflected in the constitutive relationship curve as a corresponding "upward shift".

[0004] Existing constitutive models for the tensile strength of ceramic materials do not consider strain rate effects, resulting in low accuracy in subsequent seismic analysis of equipment and hindering the improvement of seismic design for ceramic support structures. Therefore, it is necessary to conduct research on the constitutive relationship of ceramic bushings that considers strain rate effects, establishing a more accurate tensile constitutive relationship for ceramic bushings to provide guidance for subsequent seismic calculations and analyses. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention proposes a method for constructing a tensile constitutive model of electrical porcelain materials, comprising:

[0006] Based on the Weibull distribution, an initial tensile constitutive model for electrical porcelain materials is constructed, incorporating damage variable terms and strain rate effect terms; the damage variable in the damage variable term follows a Weibull distribution.

[0007] The stress and strain of the electrical porcelain material specimen under medium and high strain rates are obtained, and the constitutive relationship test curves of the electrical porcelain material specimen under various strain rates in the medium and high strain rate range are constructed.

[0008] Based on the constitutive relationship test curves at various strain rates within the medium-high strain rate range, the relationship between the dynamic elastic modulus of the electrical porcelain material and the strain rate is determined, as well as the relationship between the shape parameters of the Weibull distribution and the strain rate is determined.

[0009] Based on the initial tensile constitutive model, and combining the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material and the relationship between the shape parameters and strain rate of the Weibull distribution, a constructed tensile constitutive model of the electrical porcelain material is obtained.

[0010] Preferably, the initial tensile constitutive model of the electrical porcelain material based on the Weibull distribution, which incorporates damage and strain rate effect terms, includes:

[0011] Based on the Weibull distribution, damage variables that follow a Weibull distribution are determined, and the damage variable terms are obtained.

[0012] The strain rate effect term is determined based on the ratio of the applied strain rate to the reference strain rate;

[0013] By incorporating the damage variable term and the strain rate effect term into the linear elastic constitutive relation formula, the initial tensile constitutive model is obtained.

[0014] Preferably, the damage variable is represented as:

[0015]

[0016] Where D is the damage variable, E is the dynamic elastic modulus of the ceramic material, ε is the strain of the ceramic material, Y is the yield strength of the ceramic material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant.

[0017] Preferably, the initial tensile constitutive model is expressed as:

[0018]

[0019] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. This refers to the strain rate effect term.

[0020] Preferably, determining the relationship between the dynamic elastic modulus of the electrical porcelain material and the strain rate based on the constitutive relation test curves at various strain rates within the medium-high strain rate range includes:

[0021] Based on the constitutive relationship test curves at various strain rates within the medium-high strain rate range, the dynamic elastic modulus of the electrical porcelain material specimen at various strain rates within the medium-high strain rate range is determined.

[0022] Using the logarithmic strain rate corresponding to the strain rate as the independent variable and the dynamic elastic modulus as the dependent variable, a linear fit is performed on the logarithmic strain rate and the dynamic elastic modulus to obtain the relationship between the dynamic elastic modulus and the strain rate of the electrical porcelain material.

[0023] The relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material is expressed as follows:

[0024]

[0025] Where E is the dynamic elastic modulus of the electrical porcelain material, E s Let f be the reference elastic modulus and the linear fitting coefficient. To apply strain rate, The reference strain rate is used.

[0026] Preferably, determining the relationship between the shape parameters of the Weibull distribution and the strain rate includes:

[0027] Based on each strain rate in the medium-high strain rate range, and based on the dynamic elastic modulus and yield strength of the electrical porcelain material specimen, the fitting degree of the tensile constitutive model of the electrical porcelain material with the constitutive relation test curve corresponding to the strain rate under different adjustment values ​​of the shape parameter is determined, and the adjustment value with the best fitting degree is selected as the value of the shape parameter corresponding to the strain rate.

[0028] Using the logarithmic strain rate corresponding to the strain rate as the independent variable and the shape parameter as the dependent variable, a curve fitting is performed on the logarithmic strain rate and the shape parameter to obtain the relationship between the shape parameter and the strain rate of the Weibull distribution.

[0029] The relationship between the shape parameter of the Weibull distribution and the strain rate is expressed as follows:

[0030]

[0031] Where n is the shape parameter of the Weibull distribution. To apply strain rate, The reference strain rate is 10.837, 5.91, and 5.05, which are curve fitting coefficients obtained from curve fitting.

[0032] Preferably, the constructed tensile constitutive model of the electrical porcelain material is represented as follows:

[0033]

[0034] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. The strain rate effect term is given; Y is the yield strength of the electrical porcelain material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant; E s The reference elastic modulus is f, and the linear fitting coefficient is f.

[0035] Based on the same inventive concept, this invention also provides a system for constructing a tensile constitutive model of electrical porcelain materials, comprising:

[0036] An initial construction module is used to construct an initial tensile constitutive model of an electrical porcelain material based on a Weibull distribution, incorporating a damage variable term and a strain rate effect term; the damage variable in the damage variable term follows a Weibull distribution.

[0037] The data acquisition module is used to acquire the stress and strain of the electrical porcelain material specimen under medium and high strain rates, and to construct the constitutive relationship test curves of the electrical porcelain material specimen at various strain rates in the medium and high strain rate range.

[0038] The calculation module is used to determine the relationship between the dynamic elastic modulus of the electrical porcelain material and the strain rate, and to determine the relationship between the shape parameters of the Weibull distribution and the strain rate, based on the constitutive relation test curves at various strain rates in the medium-high strain rate range.

[0039] The model building module is used to obtain the constructed tensile constitutive model of the electric porcelain material based on the initial tensile constitutive model, combined with the relationship between the dynamic elastic modulus and strain rate of the electric porcelain material and the relationship between the shape parameters and strain rate of the Weibull distribution.

[0040] Preferably, the initial construction module is specifically used for:

[0041] Based on the Weibull distribution, damage variables that follow a Weibull distribution are determined, and the damage variable terms are obtained.

[0042] The strain rate effect term is determined based on the ratio of the applied strain rate to the reference strain rate;

[0043] By incorporating the damage variable term and the strain rate effect term into the linear elastic constitutive relation formula, the initial tensile constitutive model is obtained.

[0044] Preferably, the damage variable is represented as:

[0045]

[0046] Where D is the damage variable, E is the dynamic elastic modulus of the ceramic material, ε is the strain of the ceramic material, Y is the yield strength of the ceramic material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant.

[0047] Preferably, the initial tensile constitutive model is expressed as:

[0048]

[0049] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. This refers to the strain rate effect term.

[0050] Preferably, the calculation module is specifically used for:

[0051] Based on the constitutive relationship test curves at various strain rates within the medium-high strain rate range, the dynamic elastic modulus of the electrical porcelain material specimen at various strain rates within the medium-high strain rate range is determined.

[0052] Using the logarithmic strain rate corresponding to the strain rate as the independent variable and the dynamic elastic modulus as the dependent variable, a linear fit is performed on the logarithmic strain rate and the dynamic elastic modulus to obtain the relationship between the dynamic elastic modulus and the strain rate of the electrical porcelain material.

[0053] The relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material is expressed as follows:

[0054]

[0055] Where E is the dynamic elastic modulus of the electrical porcelain material, E s Let f be the reference elastic modulus and the linear fitting coefficient. To apply strain rate, The reference strain rate is used.

[0056] Preferably, the calculation module is specifically used for:

[0057] Based on each strain rate in the medium-high strain rate range, and based on the dynamic elastic modulus and yield strength of the electrical porcelain material specimen, the fitting degree of the tensile constitutive model of the electrical porcelain material with the constitutive relation test curve corresponding to the strain rate under different adjustment values ​​of the shape parameter is determined, and the adjustment value with the best fitting degree is selected as the value of the shape parameter corresponding to the strain rate.

[0058] Using the logarithmic strain rate corresponding to the strain rate as the independent variable and the shape parameter as the dependent variable, a curve fitting is performed on the logarithmic strain rate and the shape parameter to obtain the relationship between the shape parameter and the strain rate of the Weibull distribution.

[0059] The relationship between the shape parameter of the Weibull distribution and the strain rate is expressed as follows:

[0060]

[0061] Where n is the shape parameter of the Weibull distribution. To apply strain rate, The reference strain rate is 10.837, 5.91, and 5.05, which are curve fitting coefficients obtained from curve fitting.

[0062] Preferably, the constructed tensile constitutive model of the electrical porcelain material is represented as follows:

[0063]

[0064] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. The strain rate effect term is given; Y is the yield strength of the electrical porcelain material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant; E s The reference elastic modulus is f, and the linear fitting coefficient is f.

[0065] Based on the same inventive concept, this invention also provides a method for applying a tensile constitutive model of electrical porcelain materials, including:

[0066] Impact tests were conducted on the electrical porcelain material to be analyzed under medium-high strain rate loading conditions to obtain the dynamic loading force time history curve of the impact test.

[0067] Using the dynamic loading force time history curve of the impact test as input, the tensile constitutive model of the electrical porcelain material is adopted to obtain the stress and strain of the electrical porcelain material under medium and high strain rates.

[0068] The tensile constitutive model of the electrical porcelain material adopts the tensile constitutive model of the electrical porcelain material as described above.

[0069] Based on the same inventive concept, this invention also provides an application system for a tensile constitutive model of electrical porcelain materials, comprising:

[0070] The test module is used to conduct impact tests on the electrical porcelain material to be analyzed under loading conditions of medium to high strain rates, and to obtain the dynamic loading force time history curve of the impact test.

[0071] The application module is used to obtain the stress and strain of the electrical porcelain material under medium and high strain rates by taking the dynamic loading force time history curve of the impact test as input and using the tensile constitutive model of the electrical porcelain material.

[0072] The tensile constitutive model of the electrical porcelain material adopts the tensile constitutive model of the electrical porcelain material as described above.

[0073] Based on the same inventive concept, the present invention also provides a computer device, comprising: one or more processors;

[0074] Memory, used to store one or more programs;

[0075] When the one or more programs are executed by the one or more processors, a method for constructing a tensile constitutive model of an electrical porcelain material or a method for applying a tensile constitutive model of an electrical porcelain material as described above is implemented.

[0076] Based on the same inventive concept, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed, it implements a method for constructing a tensile constitutive model of an electric porcelain material or a method for applying a tensile constitutive model of an electric porcelain material as described above.

[0077] Compared with the closest existing technology, the present invention has the following beneficial effects:

[0078] This invention provides a method and system for constructing a tensile constitutive model of electrical porcelain materials, including: constructing an initial tensile constitutive model of the electrical porcelain material based on a Weibull distribution, incorporating a damage variable term and a strain rate effect term; the damage variable in the damage variable term follows a Weibull distribution; obtaining the stress and strain of the electrical porcelain material specimen under medium-high strain rates, and constructing constitutive relation test curves of the electrical porcelain material specimen at various strain rates within the medium-high strain rate range; determining the relationship between the dynamic elastic modulus of the electrical porcelain material and the strain rate, and determining the relationship between the shape parameter of the Weibull distribution and the strain rate, based on the constitutive relation test curves at various strain rates within the medium-high strain rate range; and based on... The initial tensile constitutive model, combined with the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material and the relationship between the shape parameter of the Weibull distribution and strain rate, yields a constructed tensile constitutive model of the electrical porcelain material. This method and system introduce damage variable terms and strain rate effect terms, and, by combining constitutive relation test curves under medium-high strain rates, determine the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material and the relationship between the shape parameter of the Weibull distribution and strain rate, constructing a tensile constitutive model of the electrical porcelain material. This model considers the influence of strain rate and obtains the dynamic tensile constitutive relation of the electrical porcelain material under medium-high strain rates. The parameters in the model construction process rely on experimental results, resulting in high accuracy.

[0079] This invention also provides a method and system for applying a tensile constitutive model of electrical porcelain materials, including conducting impact tests on the electrical porcelain material to be analyzed under loading conditions of medium to high strain rates to obtain the dynamic loading force time history curve of the impact test; using the dynamic loading force time history curve of the impact test as input, and employing a tensile constitutive model of electrical porcelain materials to obtain the stress and strain of the electrical porcelain material to be analyzed under medium to high strain rates; this method and system use a high-precision tensile constitutive model of electrical porcelain materials to perform tensile analysis on the electrical porcelain material, making the subsequent seismic calculation analysis results based on the tensile analysis results more accurate. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of a method for constructing a tensile constitutive model of an electrical porcelain material provided by the present invention;

[0081] Figure 2 This is a schematic diagram of the structure of the electrical porcelain material specimen provided by the present invention;

[0082] Figure 3 This is a schematic diagram of the three-wave method testing principle provided by the present invention;

[0083] Figure 4 A schematic diagram showing the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material provided by the present invention.

[0084] Figure 5 A schematic diagram showing the relationship between the shape parameters and strain rate of the Weibull distribution provided by the present invention;

[0085] Figure 6 A schematic diagram comparing the fitting degree between the tensile constitutive model of the electrical porcelain material provided by this invention and the experimental curve of the constitutive relation. Figure 1 ;

[0086] Figure 7 A schematic diagram comparing the fitting degree between the tensile constitutive model of the electrical porcelain material provided by this invention and the experimental curve of the constitutive relation. Figure 2 ;

[0087] Figure 8 A schematic diagram comparing the fitting degree between the tensile constitutive model of the electrical porcelain material provided by this invention and the experimental curve of the constitutive relation. Figure 3 ;

[0088] Figure 9 A schematic diagram of a tensile constitutive model construction system for electrical porcelain materials provided by the present invention;

[0089] Figure 10 This is a schematic diagram of the application method of the tensile constitutive model of electrical porcelain material provided by the present invention;

[0090] Figure 11 This invention provides a schematic diagram of the application system of a tensile constitutive model for electrical porcelain materials.

[0091] Figure 12 This is a schematic diagram of an electronic device structure provided by the present invention. Detailed Implementation

[0092] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0093] Example 1:

[0094] This invention provides a method for constructing a tensile constitutive model of electrical porcelain materials, such as... Figure 1 As shown, it includes:

[0095] S1. Based on the Weibull distribution, an initial tensile constitutive model for electrical porcelain materials is constructed, incorporating damage variable terms and strain rate effect terms; the damage variable in the damage variable term follows a Weibull distribution.

[0096] S2. Obtain the stress and strain of the electrical porcelain material specimen under medium and high strain rates, and construct the constitutive relationship test curves of the electrical porcelain material specimen under various strain rates in the medium and high strain rate range;

[0097] S3. Based on the constitutive relation test curves at various strain rates in the medium-high strain rate range, determine the relationship between the dynamic elastic modulus of the electrical porcelain material and the strain rate, and determine the relationship between the shape parameters of the Weibull distribution and the strain rate.

[0098] S4. Based on the initial tensile constitutive model, and combining the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material and the relationship between the shape parameter and strain rate of the Weibull distribution, a well-constructed tensile constitutive model of the electrical porcelain material is obtained.

[0099] To gain a deeper understanding of the mechanical behavior of electrical porcelain materials, improve their constitutive relations, and thus enhance the accuracy of seismic analysis and design of porcelain-supported equipment, this invention introduces damage and strain rate variables and combines constitutive relation test curves under medium-to-high strain rates to determine the relationship between the dynamic elastic modulus and strain rate of electrical porcelain materials and the relationship between the shape parameter of the Weibull distribution and strain rate. This constructs a tensile constitutive model for electrical porcelain materials, taking into account the influence of strain rate, and obtains the dynamic tensile constitutive relation of electrical porcelain materials under medium-to-high strain rates. The parameters in the model construction process rely on experimental results, resulting in high accuracy.

[0100] Previous studies on seismic resistance assessment methods for ceramic support-type electrical equipment did not consider the influence of strain rate on material strength and other mechanical parameters. Consequently, the same mechanical parameters were used for ceramic supports under different loading rates in actual seismic analyses, leading to poor accuracy. Therefore, in S1 above, a tensile constitutive relation for ceramic materials based on damage mechanics and considering strain rate effects is established, laying the foundation for future development of more accurate seismic analysis simulation models for ceramic equipment.

[0101] In this embodiment, S1 may include:

[0102] Based on the Weibull distribution, damage variables that follow a Weibull distribution are identified, and damage variable terms are obtained;

[0103] The strain rate effect term is determined based on the ratio of the applied strain rate to the reference strain rate.

[0104] By incorporating the damage variable term and strain rate effect term into the linear elastic constitutive relation formula, the initial tensile constitutive model is obtained.

[0105] Specifically, considering the complex damage modes of electrical porcelain materials under impact loads, a term containing a damage variable is first introduced into the linear elastic constitutive relation formula to obtain a damage mechanics constitutive model. This model assumes that the formation and development of micro-damage within the electrical porcelain material are mainly described by the damage variable D, expressed as:

[0106] σ=Eε(1-D);

[0107] Assuming the damage variable D follows a Weibull distribution, the damage variable is represented as:

[0108]

[0109] Where D is the damage variable, E is the dynamic elastic modulus of the ceramic material, ε is the strain of the ceramic material, Y is the yield strength of the ceramic material, n is the shape parameter of the Weibull distribution, i.e. the influence parameter of the curve shape, and e is the natural logarithm constant.

[0110] Subsequently, in order to describe the strain rate effect of electrical porcelain materials under dynamic tensile conditions, a term considering the strain rate effect was introduced on the basis of the damage mechanics constitutive model to obtain the initial tensile constitutive model.

[0111] In this embodiment, the initial tensile constitutive model is expressed as:

[0112]

[0113] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. This is the strain rate effect term.

[0114] Considering that the constitutive relationship test curves of ceramic sleeve materials (i.e., electrical porcelain materials) differ under different strain rate conditions, a reasonable mathematical model is adopted and derived based on the constitutive relationship test curves to obtain an expression for ceramic sleeve materials considering the strain rate effect under medium and high strain rate conditions. According to this expression, the constitutive relationship of materials under other strain rate conditions can be predicted.

[0115] Specifically, the constitutive relationship test curve of the electrical porcelain material is constructed based on the stress and strain of the electrical porcelain material specimen. In this embodiment, when obtaining the stress and strain of the electrical porcelain material specimen under medium to high strain rates, S2 may include:

[0116] Tensile tests are used to obtain the stress and strain of electrical porcelain material specimens under medium to high strain rates. The principle of tensile tests under medium and high strain rates is as follows: Figure 2 and Figure 3 As shown. The experimental apparatus mainly consists of an incident rod 1, a transmission rod 2, and an impact rod 3 (i.e., a bullet). The incident rod 1 is a circular steel rod with a diameter of 16 mm and a length of 2400 mm. The transmission rod 2 has a diameter of 16 mm and a length of 1500 mm. Both the incident rod 1 and the transmission rod 2 are made of steel with an elastic modulus of 210 GPa and a wave velocity of 5500 m / s. The air pressure range is 0.1 MPa-0.4 MPa, and the bullet velocity range is 5 m / s-25 m / s.

[0117] The preparation process of the electrical porcelain material specimen, namely specimen 5, is as follows: The electrical porcelain raw materials are processed through batching, ball milling, sieving to remove iron, mixing into a slurry, pressing, molding, drying, and firing to produce a specimen that meets the test requirements. According to standards GB / T 8411.2-2008 "Ceramic and Glass Insulating Materials - Part 2: Test Methods" and IEC 60672 "Ceramic and Glass Insulating Materials", the diameter of specimen 5 is set to 10 mm. Specimen 5 is made from a specimen with a diameter of 10 mm (… Figure 2 The rod (denoted as M10×1) is cut and ground into an electrical porcelain material specimen that meets the test conditions, with the structure as follows: Figure 2 As shown.

[0118] In the experiment, the two ends of the specimen 5 were connected to the incident rod 1 and the transmission rod 2, respectively, with the flange 4 at the end of the incident rod 1 serving as a fixed support. High-pressure air was released from the high-pressure chamber to accelerate the impact rod 3, i.e., the bullet. The bullet impacted the mass block connected to the end of the incident rod 1, generating a tensile wave that propagated to the left along the incident rod 1. Upon reaching the interface between the incident rod 1 and the specimen 5, the specimen 5 was subjected to tensile loading. During this process, the strain gauge 6 on the transmission rod recorded the signal transmitted through the specimen 5, and the strain gauge 7 on the incident rod recorded the incident and reflected wave signals. In the experiment, the impact velocity Vo of the bullet was controlled by changing the air pressure, ranging from 5 m / s to 25 m / s.

[0119] The incident wave signal ε is acquired on the incident rod 1 using the incident rod strain gauge 7. I (t) and reflected wave signal ε R (t), the transmitted wave signal ε is acquired on the transmission rod 2 through the strain gauge 6 of the transmission rod. T (t). Based on the "three-wave method", the experimental parameters, including the stress and strain of the electrical porcelain material specimens under medium and high strain rates, were obtained and calculated as follows:

[0120] strain rate curve

[0121] Strain curve ε(t):

[0122] Stress curve σ(t):

[0123] In the formula: t is time; A is the cross-sectional area of ​​the rod; A s C is the cross-sectional area of ​​sample 5; C0 is the elastic wave velocity in the rod; E G For the elastic modulus of the rod, l s The original length of sample 5 along the axial direction of incident rod 1;

[0124] Based on the stress and strain of the electrical porcelain material specimens under medium to high strain rates, constitutive relationship test curves of the electrical porcelain material specimens at various strain rates in the medium to high strain rate range are constructed.

[0125] By fitting the stress-strain curve (i.e., the linear segment of the constitutive relation test curve) of the electrical porcelain material specimen, the dynamic elastic modulus of the specimen at different strain rates can be calculated. Subsequently, a system is constructed as follows... Figure 4 The curve shown represents the relationship between the experimental value of the dynamic elastic modulus and the logarithmic strain rate. The reference strain rate in the curve is taken as 350 s. -1 , Figure 4 The ordinate of the graph represents the dynamic elastic modulus as measured by experiments, and COD is the coefficient of determination for different strain rates. dBy obtaining the values, we can obtain the experimental values ​​and fitting curves of the dynamic elastic modulus under different strain rates. The linear relationship between the two can be seen from the fitting curve. A linear relationship equation between the experimental values ​​of the dynamic elastic modulus and the logarithmic strain rate can be constructed, expressed as:

[0126]

[0127] In the formula: E d E represents the experimental values ​​of the dynamic elastic modulus at different strain rates. s is the reference elastic modulus; f is the undetermined linear fitting coefficient; To apply strain rate, For reference strain rate;

[0128] In this embodiment, S3, when determining the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material, may include:

[0129] Based on the constitutive relationship test curves at various strain rates in the medium-high strain rate range, the dynamic elastic modulus of the electrical porcelain material specimens at various strain rates in the medium-high strain rate range was determined.

[0130] For example, the medium to high strain rate range is 10. 2 s -1 -10 4 s -1 ;

[0131] Using the logarithmic strain rate corresponding to the strain rate as the independent variable and the dynamic elastic modulus as the dependent variable, a linear fit is performed on the logarithmic strain rate and the dynamic elastic modulus. After the linear fit is completed, the actual value of the linear fit coefficient f can be obtained. This value is then applied to the relationship between the dynamic elastic modulus and the strain rate in S3 above to obtain the relationship between the dynamic elastic modulus and the strain rate of the electrical porcelain material.

[0132] The relationship between the dynamic elastic modulus and strain rate of electrical porcelain materials is expressed as follows:

[0133]

[0134] Where E is the dynamic elastic modulus of the electrical porcelain material, E s Let f be the reference elastic modulus and the linear fitting coefficient. To apply strain rate, The reference strain rate is used.

[0135] In this embodiment, S3, when determining the relationship between the shape parameters of the Weibull distribution and the strain rate, may include:

[0136] Based on each strain rate in the medium-high strain rate range, and based on the dynamic elastic modulus and yield strength of the electrical porcelain material specimen, the fitting degree of the tensile constitutive model of the electrical porcelain material with the constitutive relationship test curve corresponding to the strain rate under different adjustment values ​​of the shape parameter is determined, and the adjustment value with the best fitting degree is selected as the value of the shape parameter corresponding to the strain rate.

[0137] Specifically, given the dynamic elastic modulus E d Based on the yield strength Y (see Table 1), adjust the size of the shape parameter n, such as Figures 6 to 8 As shown, this makes the theoretical model, namely the tensile constitutive model of electrical porcelain material (in... Figures 6 to 8 The fitted line (represented in the text) can best fit the experimental data, i.e., the constitutive relation experimental curve, and thus determine the value of n under different strain rates. Then, the parameter n is fitted with the logarithmic strain rate.

[0138] Table 1 Yield strength at different strain rates

[0139] <![CDATA[Strain rate / s -1 > Strength at strain softening (yield strength Y) / MPa 350 96.24 500 105.5 715 116.89

[0140] Using the logarithmic strain rate corresponding to the strain rate as the independent variable and the shape parameter as the dependent variable, a curve fitting was performed on the logarithmic strain rate and the shape parameter to obtain... Figure 5 The curve shown illustrates the relationship between the shape parameters of the Weibull distribution and the strain rate, obtained from the curve fitting coefficients.

[0141] The relationship between the shape parameter of the Weibull distribution and the strain rate is expressed as:

[0142]

[0143] Where n is the shape parameter of the Weibull distribution. To apply strain rate, The reference strain rate is 10.837, 5.91, and 5.05, which are curve fitting coefficients obtained from curve fitting.

[0144] In this embodiment, the tensile constitutive model of the electrical porcelain material constructed in S4 above is represented as follows:

[0145]

[0146] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. The strain rate effect term; Y is the yield strength of the electrical porcelain material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant; Es The reference elastic modulus is f, and the linear fitting coefficient is f.

[0147] Example 2:

[0148] Based on the same inventive concept, this invention also provides a system for constructing a tensile constitutive model of electrical porcelain materials, such as... Figure 9 As shown, it includes:

[0149] The initial building block is used to construct an initial tensile constitutive model of the electrical porcelain material based on the Weibull distribution, incorporating damage variable terms and strain rate effect terms; the damage variable in the damage variable term follows a Weibull distribution;

[0150] The data acquisition module is used to acquire the stress and strain of the electrical porcelain material specimens under medium and high strain rates, and to construct the constitutive relationship test curves of the electrical porcelain material specimens at various strain rates in the medium and high strain rate range.

[0151] The calculation module is used to determine the relationship between the dynamic elastic modulus of the electrical porcelain material and the strain rate, as well as the relationship between the shape parameters of the Weibull distribution and the strain rate, based on the constitutive relation test curves at various strain rates in the medium-high strain rate range.

[0152] The model building module is used to obtain a constructed tensile constitutive model of the electrical porcelain material based on the initial tensile constitutive model, combined with the relationship between the dynamic elastic modulus and strain rate of the electrical porcelain material and the relationship between the shape parameters and strain rate of the Weibull distribution.

[0153] In this embodiment, the initial construction module is specifically used for:

[0154] Based on the Weibull distribution, damage variables that follow a Weibull distribution are identified, and damage variable terms are obtained;

[0155] The strain rate effect term is determined based on the ratio of the applied strain rate to the reference strain rate.

[0156] By incorporating the damage variable term and strain rate effect term into the linear elastic constitutive relation formula, the initial tensile constitutive model is obtained.

[0157] In this embodiment, the damage variable is represented as:

[0158]

[0159] Where D is the damage variable, E is the dynamic elastic modulus of the ceramic material, ε is the strain of the ceramic material, Y is the yield strength of the ceramic material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant.

[0160] In this embodiment, the initial tensile constitutive model is expressed as:

[0161]

[0162] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. This is the strain rate effect term.

[0163] In this embodiment, the calculation module is specifically used for:

[0164] Based on the constitutive relationship test curves at various strain rates in the medium-high strain rate range, the dynamic elastic modulus of the electrical porcelain material specimens at various strain rates in the medium-high strain rate range was determined.

[0165] By using the logarithmic strain rate corresponding to the strain rate as the independent variable and the dynamic elastic modulus as the dependent variable, a linear fit was performed on the logarithmic strain rate and the dynamic elastic modulus to obtain the relationship between the dynamic elastic modulus and the strain rate of the electrical porcelain material.

[0166] The relationship between the dynamic elastic modulus and strain rate of electrical porcelain materials is expressed as follows:

[0167]

[0168] Where E is the dynamic elastic modulus of the electrical porcelain material, E s Let f be the reference elastic modulus and the linear fitting coefficient. To apply strain rate, The reference strain rate is used.

[0169] In this embodiment, the calculation module is specifically used for:

[0170] Based on each strain rate in the medium-high strain rate range, and based on the dynamic elastic modulus and yield strength of the electrical porcelain material specimen, the fitting degree of the tensile constitutive model of the electrical porcelain material with the constitutive relationship test curve corresponding to the strain rate under different adjustment values ​​of the shape parameter is determined, and the adjustment value with the best fitting degree is selected as the value of the shape parameter corresponding to the strain rate.

[0171] By using the logarithmic strain rate corresponding to the strain rate as the independent variable and the shape parameter as the dependent variable, curve fitting is performed on the logarithmic strain rate and the shape parameter to obtain the relationship between the shape parameter and the strain rate of the Weibull distribution.

[0172] The relationship between the shape parameter of the Weibull distribution and the strain rate is expressed as:

[0173]

[0174] Where n is the shape parameter of the Weibull distribution. To apply strain rate, The reference strain rate is 10.837, 5.91, and 5.05, which are curve fitting coefficients obtained from curve fitting.

[0175] In this embodiment, the constructed tensile constitutive model of the electrical porcelain material is represented as follows:

[0176]

[0177] Where σ is the stress of the electrical porcelain material, E is the dynamic elastic modulus of the electrical porcelain material, ε is the strain of the electrical porcelain material, D is the damage variable, and (1-D) is the damage variable term. To apply strain rate, The reference strain rate is denoted by m, and the strain rate coefficient is denoted by m. For strain rate effect term, Y is the logarithmic strain rate; n is the yield strength of the electrical porcelain material; e is the shape parameter of the Weibull distribution; and E is the natural logarithmic constant. s The reference elastic modulus is f, and the linear fitting coefficient is f.

[0178] Example 3:

[0179] Based on the same inventive concept, this invention also provides a method for applying a tensile constitutive model of electrical porcelain materials, such as... Figure 10 As shown, it includes:

[0180] A1. Based on the loading conditions of medium to high strain rate, impact tests were conducted on the electrical porcelain material to be analyzed to obtain the dynamic loading force time history curve of the impact test.

[0181] A2. Using the dynamic loading force time history curve of the impact test as input, the tensile constitutive model of the electrical porcelain material is adopted to obtain the stress and strain of the electrical porcelain material to be analyzed under medium and high strain rates; based on the stress and strain, other mechanical properties, such as displacement, are obtained through software.

[0182] The tensile constitutive model of the electrical porcelain material adopts the tensile constitutive model of the electrical porcelain material in the above embodiments.

[0183] Specifically, based on the tensile constitutive model of the electrical porcelain material obtained in the above embodiments, the tensile constitutive model of the electrical porcelain material can be further developed in the finite element analysis software and embedded into the simulation software. During the finite element simulation calculation, the tensile constitutive model of the electrical porcelain material can be directly called to realize the tensile analysis of the electrical porcelain material under medium and high strain rates, and obtain the stress, strain and other mechanical properties of the electrical porcelain material. The seismic calculation analysis performed using the results of the tensile analysis makes the seismic analysis results more accurate.

[0184] Example 4:

[0185] Based on the same inventive concept, this invention also provides an application system for the tensile constitutive model of electrical porcelain materials, such as... Figure 11 As shown, it includes:

[0186] The test module is used to conduct impact tests on the electrical porcelain material to be analyzed under loading conditions of medium to high strain rates, and to obtain the dynamic loading force time history curve of the impact test.

[0187] The application module is used to obtain the stress and strain of the electrical porcelain material under medium and high strain rates by taking the dynamic loading force time history curve of the impact test as input and using the tensile constitutive model of the electrical porcelain material.

[0188] The tensile constitutive model of the electrical porcelain material adopts the same tensile constitutive model as before.

[0189] Example 5

[0190] like Figure 12 As shown, the present invention also provides an electronic device, which may be a computer device, a microcontroller device, a smart mobile device, etc. The electronic device in this embodiment may include a processor, a memory, a transceiver component, etc. The memory, processor, and transceiver component are connected via a bus; the memory can be used to store executable programs, and an exemplary executable program may include instructions; the processor is used to execute the instructions stored in the memory. The memory can also be used to store data, which can be accessed and / or modified when instructions are executed.

[0191] The processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, and it is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions in the storage medium to realize the corresponding method flow or corresponding function, so as to realize the steps of the method for constructing a tensile constitutive model of an electric porcelain material or the method for applying a tensile constitutive model of an electric porcelain material in the above embodiments.

[0192] Example 6

[0193] Based on the same inventive concept, this invention also provides a readable storage medium, specifically an electronic device readable storage medium (Memory). This readable storage medium is a memory device within an electronic device used to store programs and data. It is understood that the storage medium here can include both built-in storage media within the electronic device and extended storage media supported by the electronic device. The storage medium provides storage space, which stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more executable programs (including program code). It should be noted that the storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. Loading and executing one or more instructions stored in the storage medium by the processor can implement the steps of the method for constructing a tensile constitutive model of an electrical porcelain material or the method for applying a tensile constitutive model of an electrical porcelain material as described in the above embodiments.

[0194] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0195] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0196] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0197] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the application, but these changes, modifications or equivalent substitutions are all within the scope of protection of the claims of the present invention.

Claims

1. A method for constructing a tensile constitutive model of an electric porcelain material, characterized in that, The method comprises the steps of: constructing an initial tensile constitutive model of the electric porcelain material based on Weibull distribution, the initial tensile constitutive model introducing a damage variable term and a strain rate effect term; the damage variable in the damage variable term is subject to Weibull distribution; obtaining stress and strain of the electric porcelain material specimen under medium-high strain rates, and constructing a constitutive relationship test curve of the electric porcelain material specimen under each strain rate in the medium-high strain rate range; determining a relationship between dynamic elastic modulus of the electric porcelain material and strain rate, and a relationship between a shape parameter of Weibull distribution and strain rate according to the constitutive relationship test curve of the electric porcelain material specimen under each strain rate in the medium-high strain rate range; obtaining a constructed tensile constitutive model of the electric porcelain material based on the initial tensile constitutive model, the relationship between dynamic elastic modulus of the electric porcelain material and strain rate, and the relationship between the shape parameter of Weibull distribution and strain rate.

2. The method of claim 1, wherein, The method of constructing an initial tensile constitutive model of the electric porcelain material based on Weibull distribution, the initial tensile constitutive model introducing a damage variable term and a strain rate effect term, comprises the steps of: determining a damage variable subject to Weibull distribution based on Weibull distribution, to obtain the damage variable term; determining the strain rate effect term according to a ratio of a loading strain rate to a reference strain rate; introducing the damage variable term and the strain rate effect term into a linear elastic constitutive relationship formula to obtain the initial tensile constitutive model.

3. The method of claim 2, wherein, The damage variable is expressed as: wherein D is the damage variable, E is dynamic elastic modulus of the electric porcelain material, ε is strain of the electric porcelain material, Y is yield strength of the electric porcelain material, n is the shape parameter of Weibull distribution, and e is a natural logarithm constant.

4. The method of claim 2, wherein, The initial tensile constitutive model is expressed as: wherein σ is a stress of the electric porcelain material, E is a dynamic modulus of elasticity of the electric porcelain material, ε is a strain of the electric porcelain material, D is a damage variable, (1-D) is the damage variable term, is a loading strain rate, is a reference strain rate, and m is a strain rate coefficient; is the strain rate effect term.

5. The method of claim 1, wherein, The method of determining a relationship between dynamic elastic modulus of the electric porcelain material and strain rate according to the constitutive relationship test curve of the electric porcelain material specimen under each strain rate in the medium-high strain rate range comprises the steps of: determining dynamic elastic modulus of the electric porcelain material specimen under each strain rate in the medium-high strain rate range according to the constitutive relationship test curve of the electric porcelain material specimen under each strain rate in the medium-high strain rate range; performing linear fitting on the logarithmic strain rate corresponding to the strain rate as an independent variable and the dynamic elastic modulus as a dependent variable to obtain the relationship between dynamic elastic modulus of the electric porcelain material and strain rate; The relationship between dynamic elastic modulus of the electric porcelain material and strain rate is expressed as: where E is the dynamic modulus of elasticity of the electric porcelain material, E s is the reference modulus of elasticity, f is the linear fitting coefficient, is the loading strain rate, is the reference strain rate.

6. The method of claim 5, wherein, The method of determining a relationship between a shape parameter of Weibull distribution and strain rate comprises the steps of: determining a fitting degree of the tensile constitutive model of the electric porcelain material and a constitutive relationship test curve corresponding to the strain rate of the electric porcelain material under each strain rate in the medium-high strain rate range based on the dynamic elastic modulus and the yield strength of the electric porcelain material specimen, and selecting a best fitting degree as a value of the shape parameter corresponding to the strain rate; performing curve fitting on the logarithmic strain rate corresponding to the strain rate as an independent variable and the shape parameter as a dependent variable to obtain the relationship between the shape parameter of Weibull distribution and strain rate; The relationship between the shape parameter of Weibull distribution and strain rate is expressed as: where n is a shape parameter of the Weibull distribution, is a loading strain rate, is a reference strain rate, and 10.837, 5.91, 5.05 are curve fitting coefficients obtained by curve fitting.

7. The method of claim 1, wherein, The constructed tensile constitutive model of the electric porcelain material is expressed as: wherein σ is the stress of the electric porcelain material, E is the dynamic elastic modulus of the electric porcelain material, ε is the strain of the electric porcelain material, D is a damage variable, (1-D) is the damage variable term, is the loading strain rate, is the reference strain rate, and m is the strain rate coefficient; is the strain rate effect term; Y is the yield strength of the electric porcelain material, n is the shape parameter of the Weibull distribution, and e is the natural logarithm constant; E s is the reference elastic modulus, and f is the linear fitting coefficient.

8. A tensile constitutive model construction system for an electric porcelain material, characterized by, The method comprises the steps of: An initial construction module is configured to construct an initial tensile constitutive model of the electric porcelain material by introducing a damage variable term and a strain rate effect term based on a Weibull distribution; The damage variable in the damage variable term is subject to a Weibull distribution; A data acquisition module is configured to acquire stress and strain of the electric porcelain material specimen under a medium-high strain rate, and to construct a constitutive relationship test curve of the electric porcelain material specimen under each strain rate in a medium-high strain rate range; A calculation module is configured to determine a relationship between dynamic elastic modulus and strain rate of the electric porcelain material, and a relationship between a shape parameter of the Weibull distribution and strain rate according to the constitutive relationship test curve under each strain rate in the medium-high strain rate range; A model construction module is configured to obtain a constructed tensile constitutive model of the electric porcelain material based on the initial tensile constitutive model, the relationship between dynamic elastic modulus and strain rate of the electric porcelain material, and the relationship between the shape parameter of the Weibull distribution and strain rate.

9. A method for applying an electrical porcelain material tensile constitutive model, characterized in that, It comprises: Performing an impact test on the electric porcelain material to be analyzed based on a loading condition of a medium-high strain rate, and acquiring a dynamic loading force time history curve of the impact test; Using the electric porcelain material tensile constitutive model to obtain stress and strain of the electric porcelain material to be analyzed under a medium-high strain rate by taking the dynamic loading force time history curve of the impact test as input; The electric porcelain material tensile constitutive model adopts the electric porcelain material tensile constitutive model according to any one of claims 1-7.

10. An electric porcelain material tensile constitutive model application system, characterized in that, It comprises: A test module is configured to perform an impact test on the electric porcelain material to be analyzed based on a loading condition of a medium-high strain rate, and to acquire a dynamic loading force time history curve of the impact test; An application module is configured to use the electric porcelain material tensile constitutive model to obtain stress and strain of the electric porcelain material to be analyzed under a medium-high strain rate by taking the dynamic loading force time history curve of the impact test as input; The electric porcelain material tensile constitutive model adopts the electric porcelain material tensile constitutive model according to any one of claims 1-7.

Images