Digital detection method for tensile property of foamed silicone rubber

Abstract

The invention relates to the technical field of digital detection of tensile properties of foamed silicone rubber, and discloses a digital detection method for tensile properties of foamed silicone rubber. Firstly, a material is cut into a standard disc, an ultrasonic transducer is arranged, propagation time delay is collected before and after stretching, effective characteristics are extracted, loading is conducted through a clamp, and a stable deformation state is maintained. And then, segmenting an ultrasonic propagation path according to regions, calculating the propagation length ratio of each region, constructing a linear relation model of time delay change and region strain, solving by adopting a numerical algorithm, and outputting a regionalized average axial strain table. According to the method, the problem that nondestructive testing of the internal strain of the soft material is difficult to realize in the prior art is solved, the method has the advantages of high resolution, non-contact, full-field sensing and the like, the measurement precision, the automation level and the engineering adaptability are remarkably improved, and the method is suitable for precision strain detection requirements in intelligent manufacturing and material quality evaluation.

Description

Technical Field

[0001] The invention relates to the technical field of digital detection of the tensile properties of foamed silicone rubber, in particular to a digital detection method for the tensile properties of foamed silicone rubber. Background Art

[0002] Prior art testing of the tensile properties of foamed silicone rubber typically involves combining conventional mechanical tensile testing with optical strain measurement. This typically involves cutting the foamed silicone rubber specimen into standard dimensions, applying a constant rate of tensile load using a universal tensile testing machine, clamping the specimen with a fixture, and recording load-displacement data. Surface deformation is then calibrated using digital image correlation (DIC) or traditional strain gauges.

[0003] On the one hand, mechanical tensile testing often requires a rigorous testing environment and complex clamping procedures, which are time-consuming. Furthermore, optical measurement errors are significant on materials like foamed silicone rubber, which have complex internal pore distributions and are prone to microscopic surface slippage and warping, making it difficult to accurately capture full-field microscopic strain. On the other hand, optical methods such as digital image correlation (DIC) place stringent requirements on speckle pattern preparation and camera calibration. Measurement stability is low if the speckle pattern is non-uniform or imaging lighting conditions vary, and complete three-dimensional deformation information cannot be obtained when the specimen thickness is insufficient. Furthermore, these methods typically only measure two-dimensional strain on the specimen surface and cannot directly detect the internal foaming layer, resulting in a "strain blind zone" that makes it difficult to interpret the strain gradient distribution at various depths. To address the limitations of optical methods, recent research has also utilized ultrasonic detection. By propagating ultrasonic guided waves through solid materials and measuring their propagation delay, the internal strain state of the material can be inferred. For homogeneous or layered structures, ultrasonic guided wave methods offer the advantages of greater penetration depth and greater sensitivity to internal microscopic defects or strain compared to traditional methods. However, existing ultrasonic testing is mainly used in underload environments for metals, ceramics, composite materials or saturated water-containing elastomers. For foamed silicone rubber with highly uneven pores and easy interface scattering, directly using the existing ultrasonic time delay method has the problem of difficulty in obtaining accurate propagation path distribution and refraction and reflection compensation. In addition, common technologies use disk or strip specimens as measurement objects and only calculate the change of the overall ultrasonic group velocity with strain, which is simple to compare and has low strain spatial resolution. In actual measurements, ultrasonic sensors mostly adopt a fixed distribution and do not consider subdividing the specimen cross section into multiple concentric or grid areas. When the strain differences within each area are large, they are easily ignored. In addition, the strain inversion models involved in most existing solutions use pre-calibrated velocity-strain relationships or are based on finite element simulation estimation results. They lack real-time and self-correction capabilities. Without combining the dynamic coupling effect of the material itself, it is difficult to accurately distinguish the effects of surface friction, interface reflection and internal stress gradient on time delay measurement. This means that if a linear mapping is simply performed by multiplying the measured ultrasonic propagation delay increment by a constant, it is likely that local nonlinearity and path coupling errors will occur due to the random distribution of bubbles and the pore morphology with tensile deformation, which will ultimately affect the accuracy of the corresponding strain value.

[0004] To this end, this project aims to propose a digital testing method for the tensile properties of foamed silicone rubber. Based on an ultrasonic transducer array and wave velocity delay analysis, a multipath propagation model is constructed, and spatial reconstruction of the strain field is achieved through path segmentation and linear modeling. This approach overcomes the limitations of traditional material tensile testing, which relies on optical markers, surface feature extraction, and high-resolution imaging. Instead, it relies on ultrasonic waves that can penetrate the interior of the material. Combined with matrix modeling and numerical solution algorithms, it accurately extracts the average axial strain in each region, achieving digital, non-destructive, and high-resolution characterization of the internal mechanical behavior of complex soft materials. Summary of the Invention

[0005] The present invention provides a digital detection method for the tensile properties of foamed silicone rubber, which helps solve the problems mentioned in the above background technology.

[0006] The present invention provides the following technical solution: a digital detection method for the tensile properties of foamed silicone rubber, comprising: Select foamed silicone rubber material and cut it into disc specimens of standard geometric dimensions, and arrange ultrasonic transducers; The ultrasonic propagation delay of the specimen under no-stress condition is measured using a transducer, the received signal waveform is recorded, and the effective delay characteristics are extracted. Apply axial tensile load to the specimen through the fixture and maintain a stable tensile state; The ultrasonic propagation delay of the specimen under tension is measured using a transducer, the received signal waveform is recorded, and the effective delay characteristics are extracted. The propagation trajectory of the measurement path in the specimen is segmented by region, and its length proportion in each region is calculated; Based on the relationship between the time delay variation of the propagation path and the regional division, a linear model describing the relationship between strain distribution and time delay response is established; A numerical algorithm is used to solve the linear equations and extract the average axial strain value in the region; The strain vector obtained by solution is output in the form of a data table.

[0007] Optionally, the step of cutting the foamed silicone rubber material into disc specimens of standard geometric dimensions and arranging ultrasonic transducers specifically includes: Take the foamed silicone rubber material and cut it into pieces with a radius of Disc specimen; Place the specimen in the center of the plane fixture and evenly apply ultrasonic coupling agent on its sides; Arranged at equal intervals around the circumference of the specimen Ultrasonic transducers are numbered ; Ultrasonic transducer The polar coordinate angle is ; The disc specimen in the test area is divided into concentric rings, The inner and outer radii of the ring are: , , ;in, For the Inner radius of the ring; For the The outer radius of the ring.

[0008] Optionally, measuring the ultrasonic propagation delay of the specimen in an unstressed state using a transducer, recording the received signal waveform and extracting effective delay characteristics specifically includes: S1, set the total number of measured pairs , for each measurement pair index , the corresponding transducer pair is denoted as ,and ;in, For the The transmitting transducer number of the group measurement pair; For the The receiving transducer number of the group measurement pair; By transducer Transmit a single-cycle ultrasonic pulse and record the transducer The received time domain signal waveform is recorded as , ;in, is the time variable; is the maximum sampling time; S2. Calculation The first derivative of ; calculate The second derivative of ; S3. Determine the receiving time ;in, It is the minimum operator, which finds the minimum value at the time point that meets the conditions; is the logical AND operator; S4. Record baseline arrival delay ; Repeat steps S1 to S4 until all Baseline arrival delay of the group measurement pair All are recorded.

[0009] Optionally, applying an axial tensile load to the specimen by a fixture and maintaining a stable tensile state specifically includes: Fix the two ends of the specimen to the movable and fixed fixtures respectively; Slowly stretch and move the fixture until the displacement meter reading reaches the specified axial displacement ; Lock the clamp immediately after stretching to maintain displacement constant.

[0010] Optionally, measuring the ultrasonic propagation delay of the specimen in a stretched state using a transducer, recording the received signal waveform and extracting effective delay characteristics specifically includes: Repeat steps S1 to S4 to obtain the determined reception time of each measurement pair after stretching Arrival delay with recorded baseline .

[0011] Optionally, segmenting the propagation trajectory of the measurement path in the specimen by region and calculating the length ratio of the measurement path in each region specifically includes: For each measurement pair , calculate the transducer angle difference ;in, For the The polar angle of each transducer; For the The polar angle of each transducer; Calculate the The perpendicular distance from the measuring path to the center of the circle ; For each ring domain , perform the following steps: S5, if ,but ; S6, if ,but ; S7, if ,but ; in, For the The measurement path of the group chord length within the ring domain; Calculate the Total length of the group measurement path ; Calculate the The measurement path of the group The length ratio of the ring .

[0012] Optionally, establishing a linear model describing the relationship between strain distribution and delay response based on the relationship between the delay change of the propagation path and the regional division specifically includes: Calculating the delay variation ratio ; Set up the first The average axial strain of the annular domain is ; The delay variation model is established as ; All The linear equations for the measurement pairs are organized in matrix form as follows: Construct the segment proportion matrix: , ;in, is the segment proportion matrix Elements of Construct the delay variation ratio column vector: ; Construct the unknown column vector of the annular domain strain: ; Get linear system .

[0013] Optionally, the step of solving the linear equations using a numerical algorithm to extract the average axial strain value within the region specifically includes: Construct the normal equations: , ;in, is a matrix The transpose of in, ,for dimensional square matrix; ; is a matrix No. Rank Column elements, equal to the matrix No. Rank Column and Rank The product of the column elements is Seek peace and satisfy ; ,for dimensional vector; ; is a vector No. component, equal to the The sum of the products of the column coefficients and the corresponding delay increments; At this time, the normal equation is ; right Perform the following steps: S801, row exchange: Select from Go to In the row, The row index with the largest absolute value of the column is , specifically: ; like , then the exchange matrix No. Row and Rows, swapping vectors No. Elements and The elements are: like : ;in, is a matrix No. Row all columns; is a matrix No. Row all columns; S802, forward elimination: For each row to be eliminated , do the following: Calculate the elimination factor ; Pair Matrix Perform row transformation: ;in, is the matrix after elimination No. Rank Column elements; is used for elimination Rank Column elements; For update operation, the original Replace with new value; Pair Vector Make corresponding updates: ;in, is a vector After elimination elements; After forward elimination, the matrix Start from the last line and solve in reverse order: Seeking the first The strain unknowns of the ring domain ;in, is a matrix No. Rank Column elements; is the currently updated vector No. elements; right Calculate in sequence: ;in, is a matrix No. Rank Column elements; For the strain in the ring domain; Finally, the strain vector .

[0014] Optionally, outputting the obtained strain vector in a data table format may include: The calculated discrete strain vector Export in table form, the first column of the table is the ring domain number, the second column is the strain value .

[0015] The present invention has the following beneficial effects: 1. The material geometry was standardized. The choice of a circular disk structure facilitates the establishment of a symmetrical and standardized ultrasonic propagation model. A "polar coordinate array transducer arrangement" method was proposed, enabling multi-directional, multi-path ultrasonic guided wave acquisition. Compared to traditional linear arrays or single-point scanning, this arrangement significantly increases spatial sampling density and measurement direction diversity, resulting in greater data redundancy and directional coverage. By dividing the disk into several concentric rings and combining angle mapping and path partitioning methods, the data structure foundation is established for spatial discretization in subsequent linear modeling, improving model solvability and the ability to resolve local strains.

[0016] 2. A strategy combining first- and second-order derivatives to identify the main peak of the received signal is proposed. The zero-crossing and extreme value points of the derivatives are used to accurately extract the arrival delay, achieving high-precision calibration of the main wave packet arrival time and significantly reducing manual intervention and window setting errors. Compared with traditional peak detection or empirical thresholding methods, this algorithm is more robust to waveform distortion and noise interference. Furthermore, this step establishes a systematic baseline delay database, which serves as a reference for subsequent relative delay changes and strain field inversion.

[0017] 3. Emphasize the combined use of a displacement meter and a locking device to ensure accurate and stable loading. In particular, locking the tensile state during the measurement cycle prevents strain fluctuations in the specimen due to factors such as material rebound and environmental interference during testing, thereby ensuring static consistency between the tensile state and ultrasonic measurement.

[0018] 4. The ultrasonic waveform under tension is resampled, resulting in each measurement pair having a dual-state data channel: "before and after stretching," facilitating the subsequent construction of a time-delay increment model. This dual-state data structure improves the measurement system's sensitivity to minute deformations, enabling detection of micron-level stretching behavior. Furthermore, a unified sampling structure reduces system complexity and enhances the accuracy of delay difference calculations.

[0019] 5. Path determination is innovatively performed using polar angle difference and perpendicular distance from the center of a circle. Each measurement path is then segmented into rings and domains, combining segmented geometric conditions (crossing / partially crossing / not crossing). This method achieves a precise correspondence between the propagation path and the physical area, avoiding modeling errors caused by path length ambiguity. Furthermore, the length fraction is introduced as a weighting factor into the model, integrating geometric information with measurement data, effectively increasing the solution model's sensitivity to local strain.

[0020] 6. The mathematical core of this approach lies in constructing a "path-region" mapping matrix and a time-delay variation vector, systematically organizing them into a system of linear equations. By encoding the length ratios of each path traversing each annular region as matrix elements and using the time-delay variation ratio as a constant term on the right-hand side, an efficient physics-to-mathematics conversion model is formed. In particular, by using the regional average strain as an unknown quantity, the continuous mechanical field is transformed into a solvable finite parameter problem, significantly reducing the solution complexity and laying the foundation for subsequent iterative solutions.

[0021] 7. The introduction of normal equation construction and row-interchange strategies in Gaussian elimination during the solution process enhances the stability and convergence of the matrix solution. The numerical processing avoids solution deviations caused by singular and ill-conditioned matrices, making it suitable for complex systems with measurement errors or path redundancy. Through step-by-step back-substitution and elimination, the system achieves highly accurate strain field inversion results, particularly suitable for annular strain decoupling scenarios.

[0022] 8. By tabulating the output of ring domain numbers and strain values, the solution intuitively presents complex matrix results, enabling engineers to quickly understand, visualize, and further process the results. This structured output provides an interface standard for various subsequent data processing methods (such as graphical display, database access, and quality assessment), enhancing the solution's versatility and engineering compatibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0024] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0025] Example, see Figure 1 , a digital detection method for tensile properties of foamed silicone rubber, comprising: Select foamed silicone rubber material and cut it into disc specimens of standard geometric dimensions, and arrange ultrasonic transducers; The ultrasonic propagation delay of the specimen under no-stress condition is measured using a transducer, the received signal waveform is recorded, and the effective delay characteristics are extracted. Apply axial tensile load to the specimen through the fixture and maintain a stable tensile state; The ultrasonic propagation delay of the specimen under tension is measured using a transducer, the received signal waveform is recorded, and the effective delay characteristics are extracted. The propagation trajectory of the measurement path in the specimen is segmented by region, and its length proportion in each region is calculated; Based on the relationship between the time delay variation of the propagation path and the regional division, a linear model describing the relationship between strain distribution and time delay response is established; A numerical algorithm is used to solve the linear equations and extract the average axial strain value in the region; The strain vector obtained by solution is output in the form of a data table.

[0026] The overall process of the tensile property testing method of foamed silicone rubber is systematically proposed, covering key steps such as specimen preparation, ultrasonic measurement, data modeling and strain inversion. Among them, by pre-standardizing the cutting of the specimen and laying out the sensors, a structured foundation is established for subsequent data acquisition; by measuring the ultrasonic time delay before and after stretching, a "comparison reference-state difference" data framework is formed; then, through path segmentation and proportion calculation, the time delay changes are mapped to different regions; and finally, through linear equation modeling and solution, the regionalized strain value is output. This process solves the problem that traditional methods are difficult to non-destructively detect the internal tensile distribution of soft materials, realizes a high-resolution, non-contact, full-field visual strain detection mode, improves the automation level and adaptability of detection, and provides a powerful tool foundation for intelligent manufacturing and material quality assessment.

[0027] The method of cutting the foamed silicone rubber material into a disc specimen of standard geometric size and arranging an ultrasonic transducer specifically includes: Take the foamed silicone rubber material and cut it into pieces with a radius of The disc specimen is obtained to obtain the standard geometry of the sample to be tested (disc) and establish a unified reference for ultrasonic testing; Place the specimen in the center of the plane fixture and evenly apply ultrasonic coupling agent on its sides; improve the acoustic energy coupling efficiency between the ultrasonic transducer and the specimen surface and reduce signal reflection and attenuation; Arranged at equal intervals around the circumference of the specimen Ultrasonic transducers are numbered ; Establish a ring sensor array to ensure multi-path and multi-directional measurement of guided wave delay; Ultrasonic transducer The polar coordinate angle is The remainder and integer mapping converts the number into a precise, equally spaced angle to ensure uniform distribution of the transducers; providing precise parameters for subsequent calculation of the geometric position and angle of the measurement path; The disc specimen in the test area is divided into concentric rings, The inner and outer radii of the ring are: , , ;in, For the Inner radius of the ring; For the The outer radius of the ring; subdivides the disk cross section into several concentric regions for subsequent path segmentation and strain discretization modeling.

[0028] By cutting the foamed silicone rubber material into standard geometric dimensions (such as a disk) and setting up a circular array of equally spaced transducers, the problems of inconsistent data and difficult-to-control propagation paths caused by inconsistent sample shapes and random layouts in traditional testing are solved. Specifically, the disk sample provides a well-symmetrical structural foundation, which is conducive to building mathematical models and simplifying geometric calculations; the polar coordinate numbering and equally spaced layout of the transducers ensure that the propagation path covers the entire globe and is evenly distributed, so that the subsequently collected ultrasonic propagation data has directional diversity and redundancy; in addition, by dividing the disk area into several concentric ring domains, fine regional units are formed, laying a high-precision spatial analysis foundation for subsequent path segmentation and strain discrete modeling. This solution significantly improves the geometric controllability, measurement accuracy, and model matching of the detection system.

[0029] The method of measuring the ultrasonic propagation delay of the specimen in an unstressed state by using a transducer, recording the received signal waveform and extracting the effective delay feature specifically includes: S1, set the total number of measured pairs , for each measurement pair index , the corresponding transducer pair is denoted as ,and ;in, For the The transmitting transducer number of the group measurement pair; For the The receiving transducer number of the group measurement pair; establish a measurement pair mapping table and select them one by one for subsequent cyclic measurement; By transducer Transmit a single-cycle ultrasonic pulse and record the transducer The received time domain signal waveform is recorded as , ;in, is the time variable; is the maximum sampling time; It is the original signal of the sampled voltage or amplitude changing with time, which is used to extract the arrival time; obtain the complete waveform data in the frequency domain or time domain to prepare for the subsequent positioning of the main peak; S2. Calculation The first derivative of The first-order derivative is used to detect the rising or falling inflection point of the waveform and identify the potential main peak position; it lays the foundation for detecting the extreme point of the signal; calculate The second derivative of The second-order derivative determines whether it is a maximum or minimum when the first-order derivative is zero; at the point where the first-order derivative is zero, a negative second-order derivative indicates a major peak; S3. Determine the receiving time ;in, It is the minimum operator, which finds the minimum value at the time point that meets the conditions; It is a logical AND operator; under the condition that the first-order derivative is zero and the second-order derivative is less than zero, the earliest time is taken to locate the main peak of the signal; S4. Record baseline arrival delay The collected arrival time is used as the baseline reference value, which is then used to calculate the relative delay change. Repeat steps S1 to S4 until all Baseline arrival delay of the group measurement pair All are recorded to ensure the integrity of the baseline time delay data and provide an accurate reference for subsequent strain calculations.

[0030] By formulating detailed steps S1 to S4, the ultrasonic propagation delay acquisition performed when the material is unstressed becomes the "zero reference line" for subsequent strain analysis. This process combines the first-order and second-order derivatives of the signal waveform for peak identification, avoiding the problem of unstable identification by the traditional threshold method; especially in the face of poor signal quality such as foam material absorption and waveform ambiguity, the derivative method provides greater stability and accuracy. By comprehensively measuring the propagation delay of each pair of transducer combinations, a complete baseline database is established, which can be used to quantify the state during subsequent stretching with high contrast, solving the problem of error accumulation caused by system offset and material heterogeneity. Ultimately, it ensures that the subsequent inversion model is accurately comparable in relative quantity calculations, providing reliable input for strain mapping.

[0031] The method of applying an axial tensile load to the specimen by a fixture and maintaining a stable tensile state specifically includes: Fix the two ends of the specimen to the movable and fixed fixtures respectively; ensure that the axial tensile load is applied to the specimen through the fixture, and the position of the specimen is controlled and the force is evenly distributed when maintaining a stable tensile state; Slowly stretch and move the fixture until the displacement meter reading reaches the specified axial displacement ; Accurately apply known axial deformation by controlling displacement, providing clear strain input for subsequent measurements; Lock the clamp immediately after stretching to maintain displacement Unchanged; ensure that the tensile strength of the specimen does not change during the measurement process to avoid dynamic errors.

[0032] By fixing the specimen between a mobile fixture and a fixed fixture, combining a displacement meter to monitor the stretching amount in real time, and then maintaining a constant stretching amount through a fixture locking operation, this solution achieves controllable and repeatable stretching loading throughout the entire process. Common problems in traditional tensile tests are uneven loading, fixture slippage, or inaccurate loading, which lead to unstable strain states and large test errors. This solution uses precise control and position locking to avoid secondary deformation or rebound of the specimen during the measurement process, making the strain field under tension a stable state, which is conducive to high-reliability data acquisition and creates clear boundary conditions for digital modeling, significantly improving the repeatability and effectiveness of the detection system.

[0033] The method of measuring the ultrasonic propagation delay of the specimen under tension by using a transducer, recording the received signal waveform and extracting the effective delay feature specifically includes: Repeat steps S1 to S4 to obtain the determined reception time of each measurement pair after stretching Arrival delay with recorded baseline Accurately find the time point corresponding to the main peak in the stretched state to provide data for calculating the delay change; save the delay data in the stretched state for comparison with the baseline delay to obtain the relative increment; ensure the complete acquisition of the stretch delay of the entire path and multiple pairs of transducers to improve data redundancy and robustness.

[0034] By repeating the sampling process of steps S1-S4 while the specimen is in tension, the quantitative capture of "state changes" is achieved. The core of this step is the "comparative analysis" mechanism, which is to deduce the mechanical response inside the material by comparing the difference in ultrasonic propagation between the two states. Traditional strain detection methods often use static one-time measurements, ignoring the dynamic changes in the material response process. This solution uses a repeated measurement mechanism to collect dual-state data, forming a comparison benchmark under the same transducer path, significantly improving the resolution and sensitivity of strain estimation, while ensuring the path consistency and integrity of the data, providing stable data support for linear mapping modeling.

[0035] The propagation trajectory of the measurement path in the specimen is segmented by region, and its length proportion in each region is calculated, specifically including: For each measurement pair , calculate the transducer angle difference ;in, For the The polar angle of each transducer; For the The polar angle of each transducer is determined; the angle between the line connecting the two transducers and the line connecting the centers of the circle is determined for subsequent geometric calculations; Calculate the The perpendicular distance from the measuring path to the center of the circle ; Get the minimum distance between the path and the center of the circle to determine whether the path passes through the concentric rings; For each ring domain , perform the following steps: S5, if ,but ; Get the path in The specific traversing length within the loop; S6, if ,but ; Calculate when the path is between the inner radius and the outer radius, The specific traversing length within the loop; S7, if ,but ; Clearly the path is not within the loop and does not need to be counted in the length; in, For the The measurement path of the group chord length within the ring domain; Calculate the Total length of the group measurement path ; get the first The actual total length of the group measurement path, which is used for subsequent ratio calculation; Calculate the The measurement path of the group The length ratio of the ring ; The quantitative path is in the The ratio of the length inside the loop to the total path length gives weight to the linear model.

[0036] By calculating the polar angle difference and perpendicular distance of the propagation path, the actual crossing situation of the propagation path in each concentric ring domain is determined, and the proportion of the path in each region is further calculated, forming a quantitative mapping relationship between the path and the region. This processing method solves the problem of inconsistency between path geometry and regional strain mapping in traditional modeling. Especially in multi-path propagation scenarios, if the actual distribution of the path is not considered, the model will have regional assignment errors, resulting in misjudgment. This path segmentation mechanism ensures the physical rationality and mathematical rigor of the strain contribution weight reflected by each path in the linear model, providing an accurate and authoritative geometric foundation for the subsequent construction and solution of matrix equations.

[0037] The linear model describing the relationship between strain distribution and delay response is established based on the relationship between the delay change of the propagation path and the regional division, specifically including: Calculating the delay variation ratio ; Measures the relative change in path delay caused by strain and is used as the constant term on the right side of the linear equation; Set up the first The average axial strain of the annular domain is ; Discretize the continuous strain domain into The equivalent approximation of concentric rings reduces the number of unknowns; The delay variation model is established as ; Establish a linear mapping between the measured delay increment and the unknown strain to provide a model basis for the solution; All The linear equations for the measurement pairs are organized in matrix form as follows: Construct the segment proportion matrix: , ;in, is the segment proportion matrix Elements of Construct the delay variation ratio column vector: ; Construct the unknown column vector of the annular domain strain: ; Get linear system ; All The linear relationships corresponding to the group measurements are arranged together to form a set of regular, solvable matrix equations.

[0038] By constructing a linear relationship between the time delay change ratio and the average strain of each region and organizing it into a matrix structure, the transformation from "physical phenomenon" to "mathematical model" is completed. This claim solves the problem of how to discretize, quantify and model spatial strain information, and is the theoretical core of the entire method. Compared with traditional empirical models or black-box machine learning models, this method has the advantages of clear physical background, strong interpretability, and high verifiability. At the same time, the matrix organization structure facilitates efficient solution by subsequent standard numerical methods. The establishment of this model not only improves the engineering level of the detection method, but also expands its adaptability in multi-material and complex structural environments.

[0039] The method of using a numerical algorithm to solve the linear equations to extract the average axial strain value in the region specifically includes: Construct the normal equations: , ;in, is a matrix The transpose of in, ,for dimensional square matrix; ; is a matrix No. Rank Column elements, equal to the matrix No. Rank Column and Rank The product of the column elements is Seek peace and satisfy ; ,for dimensional vector; ; is a vector No. component, equal to the The sum of the products of the column coefficients and the corresponding delay increments; At this time, the normal equation is ;Convert the original problem into a symmetric positive definite system of equations to facilitate numerical solution; right Perform the following steps: S801, row exchange: Select from Go to In the row, The row index with the largest absolute value of the column is , specifically: ; The function traverses the index set and outputs the position where the absolute value reaches the maximum; like , then the exchange matrix No. Row and Rows, swapping vectors No. Elements and The elements are: like : ;in, is a matrix No. Row all columns; is a matrix No. All columns of the row; by exchanging rows, the main diagonal elements are placed in the row with the largest absolute value to enhance numerical stability; ensure that the main diagonal elements in the process of elimination It is the element with the largest absolute value in the column, reducing rounding errors; S802, forward elimination: For each row to be eliminated , do the following: Calculate the elimination factor ; Make sure to put the main row first Multiply columns by After and Subtracting the rows can make the Rank The column elements are zero; Pair Matrix Perform row transformation: ;in, is the matrix after elimination No. Rank Column elements; is used for elimination Rank Column elements; For update operation, the original Replace with new value; The row elements are proportionally reduced by the OK, eliminate part, making the matrix upper triangular; Pair Vector Make corresponding updates: ;in, is a vector After elimination elements; maintain the consistency of the linear equation and synchronize the constant term on the right side with the matrix change; After forward elimination, the matrix Start from the last line and solve in reverse order: Seeking the first The strain unknowns of the ring domain ;in, is a matrix No. Rank Column elements; is the currently updated vector No. elements; directly use the last row of the upper triangular matrix, only One item is solvable; right Calculate in sequence: ;in, is a matrix No. Rank Column elements; For the The strain of the ring domain; gradually reverse each unknown number until all ; Finally, the strain vector .

[0040] By constructing normal equations and performing Gaussian elimination steps (including row permutations and forward / backward elimination), a stable and accurate solution of the linear system is achieved. This approach, particularly for ultra-large-scale, multi-path measurement systems, can fail due to matrix singularities or non-convergence. This approach significantly improves numerical stability and result reliability by enhancing diagonal pivot stability and eliminating computational errors. Ultimately, the average axial strain value for each annular domain can be extracted, achieving a complete conversion from data to mechanical parameters. This method is suitable for parameter inversion in a variety of engineering applications and exhibits excellent versatility and scalability.

[0041] Outputting the obtained strain vector in a data table format specifically includes: The calculated discrete strain vector Export in table form, the first column of the table is the ring domain number, the second column is the strain value .

[0042] By organizing the calculated strain results into standardized data tables, a bridge is established between model solution results and user-accessible data. This concise and clear output format offers high compatibility and facilitates integration with various post-processing tools, visualization platforms, and quality assessment systems, enhancing the method's engineering capabilities. In practical testing environments, users are often more concerned with the spatial distribution and specific values ​​of structural strain. Structured table output avoids subjectivity in image interpretation, improving data interpretation efficiency and decision-making value.

[0043] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0044] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A digital detection method for tensile properties of foamed silicone rubber, characterized in that: include: Select foamed silicone rubber material and cut it into disc specimens of standard geometric dimensions, and arrange ultrasonic transducers; The ultrasonic propagation delay of the specimen under no-stress condition is measured using a transducer, the received signal waveform is recorded, and the effective delay characteristics are extracted. Apply axial tensile load to the specimen through the fixture and maintain a stable tensile state; The ultrasonic propagation delay of the specimen under tension is measured using a transducer, the received signal waveform is recorded, and the effective delay characteristics are extracted. The propagation trajectory of the measurement path in the specimen is segmented by region, and its length proportion in each region is calculated; Based on the relationship between the time delay variation of the propagation path and the regional division, a linear model describing the relationship between strain distribution and time delay response is established; A numerical algorithm is used to solve the linear equations and extract the average axial strain value in the region; The strain vector obtained by solution is output in the form of a data table.

2. A digital detection method for tensile properties of foamed silicone rubber according to claim 1, characterized in that: The method of cutting the foamed silicone rubber material into a disc specimen of standard geometric size and arranging an ultrasonic transducer specifically includes: Take the foamed silicone rubber material and cut it into pieces with a radius of Disc specimen; Place the specimen in the center of the plane fixture and evenly apply ultrasonic coupling agent on its sides; Arranged at equal intervals around the circumference of the specimen Ultrasonic transducers are numbered ; Ultrasonic transducer The polar coordinate angle is ; The disc specimen in the test area is divided into concentric rings, The inner and outer radii of the ring are: , , ;in, For the Inner radius of the ring; For the The outer radius of the ring.

3. A digital detection method for tensile properties of foamed silicone rubber according to claim 2, characterized in that: The method of measuring the ultrasonic propagation delay of the specimen in an unstressed state by using a transducer, recording the received signal waveform and extracting the effective delay feature specifically includes: S1, set the total number of measured pairs , for each measurement pair index , the corresponding transducer pair is denoted as ,and ;in, For the The transmitting transducer number of the group measurement pair; For the The receiving transducer number of the group measurement pair; By transducer Transmit a single-cycle ultrasonic pulse and record the transducer The received time domain signal waveform is recorded as , ;in, is the time variable; is the maximum sampling time; S2. Calculation The first derivative of ; calculate The second derivative of ; S3. Determine the receiving time ;in, It is the minimum operator, which finds the minimum value at the time point that meets the conditions; is the logical AND operator; S4. Record baseline arrival delay ; Repeat steps S1 to S4 until all Baseline arrival delay of the group measurement pair All are recorded.

4. A digital detection method for tensile properties of foamed silicone rubber according to claim 3, characterized in that: The method of applying an axial tensile load to the specimen by a fixture and maintaining a stable tensile state specifically includes: Fix the two ends of the specimen to the movable and fixed fixtures respectively; Slowly stretch and move the fixture until the displacement meter reading reaches the specified axial displacement ; Lock the clamp immediately after stretching to maintain displacement constant.

5. A digital detection method for tensile properties of foamed silicone rubber according to claim 4, characterized in that: The method of measuring the ultrasonic propagation delay of the specimen under tension by using a transducer, recording the received signal waveform and extracting the effective delay feature specifically includes: Repeat steps S1 to S4 to obtain the determined reception time of each measurement pair after stretching Arrival delay with recorded baseline .

6. A digital detection method for tensile properties of foamed silicone rubber according to claim 5, characterized in that: The propagation trajectory of the measurement path in the specimen is segmented by region, and its length proportion in each region is calculated, specifically including: For each measurement pair , calculate the transducer angle difference ;in, For the The polar angle of each transducer; For the The polar angle of each transducer; Calculate the The perpendicular distance from the measuring path to the center of the circle ; For each ring domain , perform the following steps: S5, if ,but ; S6, if ,but ; S7, if ,but ; in, For the The measurement path of the group chord length within the ring domain; Calculate the Total length of the group measurement path ; Calculate the The measurement path of the group The length ratio of the ring .

7. A digital detection method for tensile properties of foamed silicone rubber according to claim 6, characterized in that: The linear model describing the relationship between strain distribution and delay response is established based on the relationship between the delay change of the propagation path and the regional division, specifically including: Calculating the delay variation ratio ; Set up the first The average axial strain of the annular domain is ; The delay variation model is established as ; All The linear equations for the measurement pairs are organized in matrix form as follows: Construct the segment proportion matrix: , ;in, is the segment proportion matrix Elements of Construct the delay variation ratio column vector: ; Construct the unknown column vector of the annular domain strain: ; Get linear system .

8. A digital detection method for tensile properties of foamed silicone rubber according to claim 7, characterized in that: The method of using a numerical algorithm to solve the linear equations to extract the average axial strain value in the region specifically includes: Construct the normal equations: , ;in, is a matrix The transpose of in, ,for dimensional square matrix; ; is a matrix No. Rank Column elements, equal to the matrix No. Rank Column and Rank The product of the column elements is Seek peace and satisfy ; ,for dimensional vector; ; is a vector No. component, equal to the The sum of the products of the column coefficients and the corresponding delay increments; At this time, the normal equation is ; right Perform the following steps: S801, row exchange: Select from Go to In the row, The row index with the largest absolute value of the column is , specifically: ； like , then the exchange matrix No. Row and Rows, swapping vectors No. Elements and The elements are: like : ;in, is a matrix No. Row all columns; is a matrix No. Row all columns; S802, forward elimination: For each row to be eliminated , do the following: Calculate the elimination factor ; Pair Matrix Perform row transformation: ;in, is the matrix after elimination No. Rank Column elements; is used for elimination Rank Column elements; For update operation, the original Replace with new value; Pair Vector Make corresponding updates: ;in, is a vector After elimination elements; After forward elimination, the matrix Start from the last line and solve in reverse order: Seeking the first The strain unknowns of the ring domain ;in, is a matrix No. Rank Column elements; is the currently updated vector No. elements; right Calculate in sequence: ;in, is a matrix No. Rank Column elements; For the strain in the ring domain; Finally, the strain vector .

9. A digital detection method for tensile properties of foamed silicone rubber according to claim 8, characterized in that: Outputting the obtained strain vector in a data table format specifically includes: The calculated discrete strain vector Export in table form, the first column of the table is the ring domain number, the second column is the strain value .

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