A digital testing method for the tensile properties of foamed silicone rubber

Abstract

This invention relates to the field of digital testing technology for the tensile properties of foamed silicone rubber, and discloses a digital testing method for the tensile properties of foamed silicone rubber. First, the material is cut into standard discs and ultrasonic transducers are arranged on them. Propagation delays are collected before and after stretching, and effective features are extracted. A clamp is used to load and maintain a stable deformation state. Then, the ultrasonic propagation path is segmented by region, the proportion of propagation length in each region is calculated, a linear relationship model between time delay change and regional strain is constructed, and a numerical algorithm is used to solve the model, outputting a regionalized average axial strain table. This method solves the problem of traditional techniques being unable to achieve non-destructive testing of internal strain in soft materials. It has advantages such as high resolution, non-contact, and full-field sensing, significantly improving measurement accuracy, automation level, and engineering adaptability. It is suitable for the precision strain testing needs in intelligent manufacturing and material quality assessment.

Description

Technical Field

[0001] This invention relates to the field of digital testing technology for the tensile properties of foamed silicone rubber, specifically to a digital testing method for the tensile properties of foamed silicone rubber. Background Technology

[0002] In existing technologies, the tensile properties testing of foamed silicone rubber materials generally adopts a combination of conventional mechanical tensile testing and optical strain measurement. The common practice is to first cut the foamed silicone rubber specimen to standard size, then apply a constant rate of tensile load using a universal tensile testing machine, hold the specimen with a fixture and record the load-displacement data, and then use digital image correlation (DIC) or traditional strain gauges to calibrate the surface deformation of the specimen.

[0003] On the one hand, mechanical tensile testing often requires a strict testing environment and complex clamping procedures, which is time-consuming. Furthermore, in materials like foamed silicone rubber, where internal pore distribution is complex and surface micro-slippage or warping is prone to occur, optical measurement errors are significant, making it difficult to accurately capture the full-field micro-strain. On the other hand, optical methods such as digital image correlation have stringent requirements for speckle preparation and camera calibration. If the speckle pattern is inhomogeneous or imaging lighting conditions change, measurement stability is low, and it is difficult to obtain complete three-dimensional deformation information when the specimen thickness is insufficient. In addition, these methods typically only perform two-dimensional strain detection on the specimen surface, failing to directly probe the internal foamed layers, resulting in a "strain blind zone" and making it difficult to reflect the strain gradient distribution at different depths of the material. To compensate for the limitations of optical methods, recent studies have also employed ultrasound as a detection method. By propagating ultrasonic guided waves in solid materials and measuring their propagation delay, the internal strain state of the material can be inferred. For homogeneous or layered structures, the ultrasonic guided wave method has advantages over traditional methods, including greater penetration depth and higher sensitivity to internal micro-defects or strain. However, existing ultrasonic testing methods are mainly applied to underloaded environments of metals, ceramics, composite materials, or saturated water-containing elastomers. For foamed silicone rubber with uneven pore height and easy interface scattering, directly applying existing ultrasonic time-delay methods results in difficulties in obtaining accurate propagation path distribution and refraction / reflection compensation. Furthermore, common techniques use disk-shaped or strip-shaped specimens as the measurement object, only calculating the overall ultrasonic group velocity change with strain, which is simple to compare but has low strain spatial resolution. In actual measurements, ultrasonic sensors are often fixedly distributed, without considering subdividing the specimen cross-section into multiple concentric or grid regions, making it easy to overlook large strain differences within each region. Additionally, most existing solutions use pre-calibrated velocity-strain relationships or are based on finite element simulation predictions, lacking real-time performance and self-correction capabilities. Moreover, without considering the dynamic coupling effects of the material itself, it is difficult to accurately distinguish the influence of surface friction, interface reflection, and internal stress gradients on time-delay measurements. This means that if the measured ultrasonic propagation time delay increment is simply multiplied by a constant for linear mapping, local nonlinearity and path coupling errors may occur due to the random distribution of bubbles and the pore morphology as they deform under tension, ultimately affecting the accuracy of the strain values.

[0004] Therefore, this study aims to propose a digital testing method for the tensile properties of foamed silicone rubber. Based on ultrasonic transducer arrays and wave velocity delay analysis, a multi-path propagation model is constructed, and the 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 marking, surface feature extraction, and high-resolution imaging. Instead, it relies on ultrasonic waves that can penetrate the material's interior, combined with matrix modeling and numerical solution algorithms, to accurately extract 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] This invention provides a digital testing method for the tensile properties of foamed silicone rubber, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a digital testing method for the tensile properties of foamed silicone rubber, comprising:

[0007] Select foamed silicone rubber material, cut it into disc specimens of standard geometric dimensions, and arrange ultrasonic transducers;

[0008] The ultrasonic propagation delay of the specimen under unstressed state was measured using a transducer, and the received signal waveform was recorded and the effective delay characteristics were extracted.

[0009] An axial tensile load is applied to the specimen using a fixture, and a stable tensile state is maintained.

[0010] The ultrasonic propagation delay under tensile conditions was measured using a transducer, and the received signal waveform was recorded and the effective delay characteristics were extracted.

[0011] The propagation trajectory of the measurement path in the specimen is segmented by region, and its length percentage in each region is calculated.

[0012] 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.

[0013] The linear equations are solved using a numerical algorithm to extract the average axial strain value within the region.

[0014] The obtained strain vectors are output in the form of a data table.

[0015] Optionally, the step of selecting foamed silicone rubber material, cutting it into disc specimens of standard geometric dimensions, and arranging ultrasonic transducers specifically includes:

[0016] Take foamed silicone rubber material and cut it into pieces with a radius of [missing information]. Circular specimen;

[0017] The specimen was placed in the center of the planar fixture and the ultrasonic coupling agent was evenly coated on its side.

[0018] Arranged at equal intervals on the circumference of the specimen There are 10 ultrasonic transducers, numbered sequentially as follows: ;

[0019] Set up an ultrasonic transducer The polar coordinate angle is ;

[0020] The test area disk specimen is divided into equal parts. The first concentric ring domain, the... The inner and outer radii of the ring are respectively:

[0021] , , ;in, For the first Inner radius of the ring; For the first Outer radius of the ring.

[0022] Optionally, the measurement of ultrasonic propagation delay of the specimen under unstressed state using a transducer, recording the received signal waveform, and extracting effective delay features specifically includes:

[0023] S1. Let the total number of measurements be... For each measurement pair index The corresponding transducer pair is denoted as ,and ;in, For the first The transducer number of the measurement pair; For the first The receiving transducer number of the measurement pair;

[0024] By transducer Emits a single-cycle ultrasonic pulse and records the transducer. The received time-domain signal waveform is denoted as , ;in, It is a time variable; This is the maximum sampling time;

[0025] S2, Calculation first derivative ;

[0026] calculate The second derivative ;

[0027] S3. Determine the receiving time. ;in, This is the minimum value operator, which finds the minimum value at any given time point that meets the condition. For logical AND operator;

[0028] S4. Record baseline arrival delay ;

[0029] Repeat steps S1 to S4 until all Baseline arrival delay of the group of measurement pairs All were recorded.

[0030] Optionally, applying an axial tensile load to the specimen using a clamp and maintaining a stable tensile state specifically includes:

[0031] Fix both ends of the specimen to the movable and fixed clamps respectively;

[0032] Slowly stretch the moving clamp until the displacement gauge reading reaches the specified axial displacement. ;

[0033] Lock the clamp immediately after stretching to maintain displacement. constant.

[0034] Optionally, the measurement of ultrasonic propagation time delay of the specimen under tensile conditions using a transducer, recording the received signal waveform, and extracting effective time delay features specifically includes:

[0035] Repeat steps S1 to S4 to obtain the determined receiving time for each measurement pair after stretching. Delay of arrival with recorded baseline .

[0036] Optionally, the step of segmenting the propagation trajectory of the measurement path in the specimen by region and calculating its length proportion in each region specifically includes:

[0037] For each measurement pair Calculate the transducer angle difference ;in, For the first The polar angle of each transducer; For the first The polar angle of each transducer;

[0038] Calculate the first The perpendicular distance from the measurement path to the center of the circle ;

[0039] For each ring domain Perform the following steps:

[0040] S5, if ,but ;

[0041] S6, if ,but ;

[0042] S7, if ,but ;

[0043] in, For the first Group measurement path in the first chord length within the annular region;

[0044] Calculate the first Total length of the group measurement path ;

[0045] Calculate the first Group measurement path in the first The proportion of length within the ring domain .

[0046] Optionally, the establishment of a linear model describing the relationship between strain distribution and time delay response based on the relationship between the time delay variation of the propagation path and regional division specifically includes:

[0047] Calculate the time delay change ratio ;

[0048] Let the first The average axial strain of each annular region is ;

[0049] Establish a time delay variation model for ;

[0050] All The linear equations for the set of measurement pairs are organized in matrix form, as follows:

[0051] Construct the segmented proportion matrix: , ;in, For segmented proportion matrix Element;

[0052] Construct a column vector of time delay variation ratios: ;

[0053] Construct the column vector of unknown strain in the annular domain: ;

[0054] linear system .

[0055] Optionally, the step of using a numerical algorithm to solve the linear equation system and extract the average axial strain value within the region specifically includes:

[0056] Construct the normal equation: , ;in, For matrix transpose;

[0057] in, ,for Dimensional matrix; ; For matrix No. Line 1 Column elements equal to matrix The Line 1 Column and number Line 1 The product of column elements over all Summation, satisfying ; ,for dimensional vector; ; For vectors The The component is equal to the first component in all measurement pairs. The sum of the products of the column coefficients and their corresponding delay increments;

[0058] At this point, the normal equation is ;

[0059] right Perform the following steps:

[0060] S801, Row Exchange:

[0061] Select from the first Arrive at the In the line, the first The row index with the largest absolute value in the column is Specifically:

[0062] ;

[0063] like Then the exchange matrix The Line and number Rows, while swapping vectors The Element and the The elements are specifically:

[0064] like : ;in, For matrix The All columns in the row; For matrix The All columns in the row;

[0065] S802, Forward Elimination:

[0066] For each row to be eliminated Perform the following operations:

[0067] Calculate elimination factors ;

[0068] For matrix Perform row transformations: ;in, The matrix after elimination The Line 1 Column elements; For the first element used for elimination Line 1 Column elements; To update the operation, the original Replace with the new value;

[0069] For vectors Make the corresponding updates: ;in, For vectors After elimination, the first One element;

[0070] After completing forward elimination, the matrix Solve in reverse order, starting from the last row:

[0071] Seek the first Strain unknowns in each annular region ;in, For matrix The Line 1 Column elements; The currently updated vector The One element;

[0072] right Calculate sequentially:

[0073] ;in, For matrix The Line 1 Column elements; For the first Strain in the annular region;

[0074] Finally, the strain vector is obtained. .

[0075] Optionally, outputting the obtained strain vector in the form of a data table specifically includes:

[0076] The calculated discrete strain vector Export in tabular form, with the first column being the annular region number and the second column being the strain value. .

[0077] The present invention has the following beneficial effects:

[0078] 1. The material geometry was standardized, and the choice of a disk structure facilitated 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 improves spatial sampling density and measurement direction diversity, resulting in stronger data redundancy and directional coverage. By dividing the disk into several concentric ring domains and combining angle mapping and path partitioning methods, a data structure foundation was laid for spatial discretization in subsequent linear modeling, improving model solvability and the ability to resolve local strain.

[0079] 2. A strategy combining first and second derivatives for main peak identification of the received signal is proposed. By utilizing the zero intersections and extreme points of the derivatives, the arrival delay is accurately extracted, achieving high-precision calibration of the main wave packet arrival time and significantly reducing errors caused by manual intervention and window setting. Compared to traditional peak detection or empirical threshold methods, this algorithm exhibits higher robustness to waveform distortion and noise interference. Furthermore, this step establishes a systematic baseline time delay database as a reference standard for subsequent relative time delay variation and strain field inversion.

[0080] 3. The combined use of a displacement gauge and a locking device was emphasized to ensure the accuracy and stability of the loading. In particular, locking the tensile state during the measurement cycle prevents strain fluctuations in the specimen due to material springback, environmental interference, and other factors during testing, thereby ensuring the static consistency between the tensile state and the ultrasonic measurement.

[0081] 4. Resampling the ultrasonic waveform under tension allows each measurement pair to have a dual-state data channel ("before tension" and "after tension"), facilitating the subsequent construction of a time delay increment model. This dual-state data structure improves the measurement system's response sensitivity to minute deformations, enabling the detection of micrometer-level tensile behavior. Simultaneously, by unifying the sampling structure, system complexity is reduced, and the accuracy of time delay difference calculation is enhanced.

[0082] 5. This method innovatively employs polar angle difference and perpendicular distance calculations to determine the path, and combines segmented geometric conditions (crossing / partially crossing / not crossing) to segment each measurement path into ring domains. This achieves a precise correspondence between the propagation path and the physical region, avoiding modeling errors caused by path length ambiguity. Simultaneously, by introducing length proportions as weighting coefficients into the model, geometric information and measurement data are integrated, effectively improving the sensitivity of the solution model to local strain.

[0083] 6. The core of this scheme is the construction of a "path-region" mapping matrix and a time delay variation vector, which are then systematically organized into a system of linear equations. By encoding the length proportions of each path traversing each annular region as matrix elements and using the time delay variation ratio as a constant term on the right side, an efficient physical-mathematical conversion model is formed. In particular, by using the region-average strain as an unknown quantity, the continuous mechanical field is transformed into a solvable finite parameter problem, greatly reducing the computational complexity and laying the foundation for subsequent iterative solutions.

[0084] 7. The introduction of normal equation construction and row exchange strategies in Gaussian elimination enhances the stability and convergence of the matrix solution. It avoids solution deviation problems caused by singular and ill-conditioned matrices during numerical processing, making it suitable for complex systems with measurement errors or path redundancy. Through stepwise inversion and elimination calculations, the system obtains high-precision strain field inversion results, particularly suitable for situations involving strain decoupling in annular domains.

[0085] 8. By outputting ring domain numbers and strain values ​​in a tabular format, the solution presents complex matrix results intuitively, facilitating quick understanding and visualization or further processing by engineers. 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. Attached Figure Description

[0086] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] Example, refer to Figure 1 A digital testing method for the tensile properties of foamed silicone rubber, comprising:

[0089] Select foamed silicone rubber material, cut it into disc specimens of standard geometric dimensions, and arrange ultrasonic transducers;

[0090] The ultrasonic propagation delay of the specimen under unstressed state was measured using a transducer, and the received signal waveform was recorded and the effective delay characteristics were extracted.

[0091] An axial tensile load is applied to the specimen using a fixture, and a stable tensile state is maintained.

[0092] The ultrasonic propagation delay under tensile conditions was measured using a transducer, and the received signal waveform was recorded and the effective delay characteristics were extracted.

[0093] The propagation trajectory of the measurement path in the specimen is segmented by region, and its length percentage in each region is calculated.

[0094] 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.

[0095] The linear equations are solved using a numerical algorithm to extract the average axial strain value within the region.

[0096] The obtained strain vectors are output in the form of a data table.

[0097] This paper systematically proposes a general workflow for testing the tensile properties of foamed silicone rubber, covering key steps such as sample preparation, ultrasonic measurement, data modeling, and strain inversion. Specifically, standardized cutting of the specimen and sensor placement establish a structured foundation for subsequent data acquisition; ultrasonic time delay measurements before and after stretching form a data framework of "comparison reference - state difference"; path segmentation and proportion calculation map the time delay changes to different regions; and linear equation modeling and solving ultimately output regionalized strain values. This workflow solves the problem of traditional methods being unable to non-destructively detect the internal tensile distribution of soft materials, achieving a high-resolution, non-contact, and full-field visible strain detection mode, improving the automation level and adaptability of the detection, and providing a powerful tool foundation for intelligent manufacturing and material quality assessment.

[0098] The process of selecting foamed silicone rubber material, cutting it into disc specimens of standard geometric dimensions, and arranging ultrasonic transducers specifically includes:

[0099] Take foamed silicone rubber material and cut it into pieces with a radius of [missing information]. The disc specimen; to obtain the standard geometry (disc) of the sample to be tested, and to establish a unified reference for ultrasonic testing;

[0100] The specimen is placed in the center of the planar fixture, and an ultrasonic coupling agent is uniformly coated on its side to improve the acoustic energy coupling efficiency between the transducer and the specimen surface, and reduce signal reflection and attenuation.

[0101] Arranged at equal intervals on the circumference of the specimen There are 10 ultrasonic transducers, numbered sequentially as follows: Establish a ring-shaped sensor array to ensure that guided wave delay can be measured in multiple paths and directions;

[0102] Set up an ultrasonic transducer The polar coordinate angle is The remainder-to-integer mapping converts the numbering into precise, equally spaced angles, ensuring uniform distribution of transducers; providing accurate parameters for subsequent calculations of the geometric position and angle of the measurement path;

[0103] The test area disk specimen is divided into equal parts. The first concentric ring domain, the... The inner and outer radii of the ring are respectively:

[0104] , , ;in, For the first Inner radius of the ring; For the first Outer radius of the ring; the disk cross section is subdivided into several concentric regions for subsequent path segmentation and strain discretization modeling.

[0105] By cutting foamed silicone rubber material into standard geometric dimensions (such as disks) and setting up a ring-shaped array of equally spaced transducers, the problems of inconsistent data and difficulty in controlling the propagation path caused by inconsistent sample shapes and random layout in traditional detection methods are solved. Specifically, the disk sample provides a structurally sound foundation with good symmetry, which is beneficial for building mathematical models and simplifying geometric calculations; the polar coordinate numbering and equally spaced arrangement of the transducers ensure that the propagation path covers the entire area and is evenly distributed, giving the subsequently acquired ultrasonic propagation data directional diversity and redundancy; in addition, by dividing the disk area into several concentric ring domains to form fine regional units, a high-precision spatial analysis foundation is laid for subsequent path segmentation and strain discretization modeling. This scheme significantly improves the geometric controllability, measurement accuracy, and model matching degree of the detection system.

[0106] The measurement of ultrasonic propagation time delay of the specimen under unstressed state using a transducer, recording the received signal waveform, and extracting effective time delay features specifically includes:

[0107] S1. Let the total number of measurements be... For each measurement pair index The corresponding transducer pair is denoted as ,and ;in, For the first The transducer number of the measurement pair; For the first Number the receiving transducers of the measurement pairs; establish a measurement pair mapping table to select them one by one for subsequent cyclic measurements;

[0108] By transducer Emits a single-cycle ultrasonic pulse and records the transducer. The received time-domain signal waveform is denoted as , ;in, It is a time variable; This is the maximum sampling time; It is the original signal of voltage or amplitude changing over time, which is used to extract the arrival time; to obtain complete waveform data in the frequency domain or time domain, in order to prepare for subsequent location of the main peak;

[0109] S2, Calculation first derivative The first derivative is used to detect the rising or falling inflection points of a waveform and identify the location of potential main peaks; it lays the foundation for detecting the extreme points of a signal.

[0110] calculate The second derivative The second derivative determines whether a value is a local maximum or a local minimum when the first derivative is zero; at points where the first derivative is zero, a negative second derivative indicates a major peak.

[0111] S3. Determine the receiving time. ;in, This is the minimum value operator, which finds the minimum value at any given time point that meets the condition. The logical AND operator is used; the earliest time point is taken under the condition that the first derivative is zero and the second derivative is less than zero, and the main peak of the signal is located.

[0112] S4. Record baseline arrival delay The collected arrival times are used as baseline reference values ​​for subsequent calculations of relative time delay changes.

[0113] Repeat steps S1 to S4 until all Baseline arrival delay of the group of measurement pairs All data were recorded to ensure the integrity of the baseline time delay data and to provide an accurate reference for subsequent strain calculation.

[0114] By establishing detailed steps S1 to S4, ultrasonic propagation delay acquisition under unstressed material conditions serves as the "zero reference line" for subsequent strain analysis. This process combines the first and second derivatives of the signal waveform for peak identification, avoiding the instability issues of traditional threshold methods. Especially when dealing with poor signal quality conditions such as absorption by foamed materials and waveform blurring, the derivative method provides stronger stability and accuracy. By comprehensively measuring the propagation delay of each transducer pair, a complete baseline database is established, enabling high-contrast quantification of the state during subsequent tensile testing, resolving the error accumulation problems caused by system offset and material heterogeneity. Ultimately, this ensures accurate comparability of the subsequent inversion model in relative quantity calculations, providing reliable input for strain mapping.

[0115] The process of applying an axial tensile load to the specimen using a clamp and maintaining a stable tensile state specifically includes:

[0116] Fix both ends of the specimen to the moving and fixed clamps respectively; ensure that the specimen position is controlled and the force is uniform when the axial tensile load is applied to the specimen through the clamps and a stable tensile state is maintained;

[0117] Slowly stretch the moving clamp until the displacement gauge reading reaches the specified axial displacement. By precisely applying a known axial deformation through controlled displacement, a clear strain input is provided for subsequent measurements.

[0118] Lock the clamp immediately after stretching to maintain displacement. The tensile strength of the specimen remains constant during the measurement process to avoid dynamic errors.

[0119] By fixing the specimen between a moving fixture and a fixed fixture, and using a displacement measuring device to monitor the tensile load in real time, and then maintaining constant tensile load through fixture locking, this scheme achieves full controllability and repeatability of the tensile load process. Common problems in traditional tensile tests include uneven loading, fixture slippage, or inaccurate loading, leading to unstable strain states and large testing errors. This scheme, through precise control and position locking, avoids secondary deformation or springback of the specimen during measurement, ensuring a stable strain field under tensile conditions. This facilitates highly reliable data acquisition and creates clear boundary conditions for digital modeling, significantly improving the repeatability and effectiveness of the testing system.

[0120] The method of measuring the ultrasonic propagation time delay of the specimen under tensile conditions using a transducer, recording the received signal waveform, and extracting the effective time delay features specifically includes:

[0121] Repeat steps S1 to S4 to obtain the determined receiving time for each measurement pair after stretching. Delay of arrival with recorded baseline Accurately locate the time point corresponding to the main wave peak under tensile conditions to provide data for calculating time delay changes; save the time delay data under tensile conditions for comparison with the baseline time delay to obtain the relative increment; ensure complete acquisition of tensile time delay across the entire path and multiple pairs of transducers to improve data redundancy and robustness.

[0122] By repeating steps S1-S4 of the sampling process on the specimen under tension, the quantitative capture of "state change" was achieved. The core of this step is the "comparative analysis" mechanism, which derives the internal mechanical response of the material by 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 scheme uses a repeated measurement mechanism to collect dual-state data, forming a comparative benchmark under the same transducer path, which significantly improves the resolution and sensitivity of strain estimation, while ensuring the consistency and integrity of the data path, providing stable data support for linear mapping modeling.

[0123] The step of segmenting the propagation trajectory of the measurement path in the specimen by region and calculating its length proportion in each region specifically includes:

[0124] For each measurement pair Calculate the transducer angle difference ;in, For the first The polar angle of each transducer; For the first The polar angles of the transducers are determined; the angle between the line connecting the two transducers and the line connecting the centers of the circles is determined for subsequent geometric calculations.

[0125] Calculate the first The perpendicular distance from the measurement path to the center of the circle ; Obtain the minimum distance from the path to the center of the circle, in order to determine whether the path passes through each concentric ring region;

[0126] For each ring domain Perform the following steps:

[0127] S5, if ,but The path is obtained at the . The specific length of the passage within the ring;

[0128] S6, if ,but ; Calculate the value of the path when it lies between the inner and outer radii, at the th... The specific length of the passage within the ring;

[0129] S7, if ,but The path is clearly not within the loop, so its length does not need to be included in the calculation.

[0130] in, For the first Group measurement path in the first chord length within the annular region;

[0131] Calculate the first Total length of the group measurement path ; obtained the first The actual total length of the group measurement path is used for subsequent percentage calculations;

[0132] Calculate the first Group measurement path in the first The proportion of length within the ring domain ; Quantization path in the first The proportion of the length within the loop to the total path length is used to assign weights to the linear model.

[0133] By calculating the polar angle difference and vertical distance between the center and the propagation path, the actual traversal of the path in each concentric annular region 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 approach 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 make region assignment errors, leading to misjudgments. 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.

[0134] The linear model describing the relationship between strain distribution and time delay response, based on the relationship between propagation path time delay variation and regional division, specifically includes:

[0135] Calculate the time delay change ratio ; Measures the relative change in time delay caused by strain along the path, and is used as a constant term on the right-hand side of the linear equation;

[0136] Let the first The average axial strain of each annular region is Discretize the continuous strain domain into The equivalent approximation of concentric rings reduces the number of unknowns;

[0137] Establish a time delay variation model for A linear mapping is established between the measured time delay increment and the unknown strain, providing a model basis for the solution.

[0138] All The linear equations for the set of measurement pairs are organized in matrix form, as follows:

[0139] Construct the segmented proportion matrix: , ;in, For segmented proportion matrix Element;

[0140] Construct a column vector of time delay variation ratios: ;

[0141] Construct the column vector of unknown strain in the annular domain: ;

[0142] linear system ;

[0143] All The linear relationships corresponding to the group of measurements are arranged in a set, forming a set of regular, solvable matrix equations.

[0144] By constructing a linear relationship between the time delay variation ratio and the average strain in each region, and organizing it into a matrix structure, the transformation from a "physical phenomenon" to a "mathematical model" is achieved. This technical solution addresses the problem of how to discretize, quantify, and model spatial strain information, which is the theoretical core of the entire method. Compared with traditional empirical models or black-box machine learning models, this method has advantages such as clear physical background, strong interpretability, and high verifiability. Furthermore, the matrix organization structure facilitates efficient solution using 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.

[0145] The step of solving the linear equation system using a numerical algorithm and extracting the average axial strain value within the region specifically includes:

[0146] Construct the normal equation: , ;in, For matrix transpose;

[0147] in, ,for Dimensional matrix; ; For matrix No. Line 1 Column elements equal to matrix The Line 1 Column and number Line 1 The product of column elements over all Summation, satisfying ; ,for dimensional vector; ; For vectors The The component is equal to the first component in all measurement pairs. The sum of the products of the column coefficients and their corresponding delay increments;

[0148] At this point, the normal equation is The original problem is transformed into a system of symmetric positive definite equations, which facilitates numerical solutions.

[0149] right Perform the following steps:

[0150] S801, Row Exchange:

[0151] Select from the first Arrive at the In the line, the first The row index with the largest absolute value in the column is Specifically:

[0152] ; The function iterates through the index set and outputs the position where the absolute value is maximized.

[0153] like Then the exchange matrix The Line and number Rows, while swapping vectors The Element and the The elements are specifically:

[0154] like : ;in, For matrix The All columns in the row; For matrix The All columns; by swapping rows, the main diagonal element is placed in the row with the largest absolute value to enhance numerical stability; ensuring the main diagonal element is in the correct position during elimination. It is the element with the largest absolute value in its column, reducing rounding errors;

[0155] S802, Forward Elimination:

[0156] For each row to be eliminated Perform the following operations:

[0157] Calculate elimination factors ; Determine the main line number column multiplied by Later and the Subtracting rows from rows can make the first row... Line 1 The column element is zero;

[0158] For matrix Perform row transformations: ;in, The matrix after elimination The Line 1 Column elements; For the first element used for elimination Line 1 Column elements; To update the operation, the original Replace with the new value; change the first Subtract the first row element proportionally Okay, eliminate Partially, this makes the matrix form an upper triangle;

[0159] For vectors Make the corresponding updates: ;in, For vectors After elimination, the first Each element; maintain the consistency of the linear equation, and synchronize the constant term on the right-hand side with the matrix changes;

[0160] After completing forward elimination, the matrix Solve in reverse order, starting from the last row:

[0161] Seek the first Strain unknowns in each annular region ;in, For matrix The Line 1 Column elements; The currently updated vector The One element; directly using the last row of the upper triangular matrix, only one element remains. One solution is possible;

[0162] right Calculate sequentially:

[0163] ;in, For matrix The Line 1 Column elements; For the first Strain in the annular domain; progressively working backwards to determine each unknown until all are obtained. ;

[0164] Finally, the strain vector is obtained. .

[0165] By constructing normal equations and performing Gaussian elimination steps (including row swapping and forward / backward substitution), stable and accurate solutions to linear systems are achieved. Especially in ultra-large-scale, multi-path measurement systems, traditional solution methods may fail due to matrix singularities or non-convergence. This scheme significantly improves numerical stability and result reliability by enhancing the stability of diagonal principal components and eliminating computational errors. Finally, the average axial strain values ​​of each annular domain can be extracted, achieving a complete conversion from data to mechanical parameters. This method is applicable to parameter inversion needs in various engineering applications and has good versatility and scalability.

[0166] The step of outputting the obtained strain vector in the form of a data table specifically includes:

[0167] The calculated discrete strain vector Export in tabular form, with the first column being the annular region number and the second column being the strain value. .

[0168] By organizing the calculated strain results into standardized data tables, a bridge is established between model solution results and user-accessible data. This output format is concise, clear, and highly compatible, easily integrating with various post-processing tools, visualization platforms, and quality assessment systems, thus enhancing the method's engineering applicability. Especially in real-world testing environments, users often focus on the spatial distribution and specific values ​​of structural strain; the structured table output avoids the subjectivity of image interpretation, improving data interpretation efficiency and decision-making reference value.

[0169] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0170] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A digital method for the detection of the tensile properties of foamed silicone rubbers, characterized in that, Comprise: Selecting foamed silicone rubber material cutting into standard geometric size disc test piece, and arranging ultrasonic transducer; The selecting foamed silicone rubber material cutting into standard geometric size disc test piece, and arranging ultrasonic transducer, specifically includes: A foamed silicone rubber material is taken and cut into disc test pieces of radius of 50 mm. Place the test piece in the center of the plane clamp, and evenly coat the ultrasonic coupling agent on the side surface of the test piece; Arranged at equal intervals on the circumference of the specimen There are 10 ultrasonic transducers, numbered sequentially as follows: ; An ultrasonic transducer The polar angle of the transducer ; The detection domain disc test piece is equally divided into concentric ring domains, the first The inner and outer radii of the first ring are respectively , , ; wherein, is the radius of the first ring; is the radius of the second ring; Measure the ultrasonic propagation time delay of the test piece under the unstressed state by using the transducer, record the received signal waveform and extract the effective time delay characteristics; The measuring the ultrasonic propagation time delay of the test piece under the unstressed state by using the transducer, recording the received signal waveform and extracting the effective time delay characteristics, specifically includes: S1, set total measurement log , for each measurement pair index , the corresponding transducer pair is denoted as , and ; wherein, is the transmitting transducer number of the th measurement pair; is the receiving transducer number of the th measurement pair; By the transducer emitting a single-cycle ultrasound pulse, recording the transducer The time-domain signal waveform received is denoted , ; wherein, is a time variable; is the maximum sampling time; S2, compute first derivative ; Calculations of the second derivative ; S3, determining the reception time ; wherein is a minimum operator that finds the minimum of the time points that satisfy the condition; is a logical and operator; S4, record baseline arrival latency ; Steps S1 to S4 are repeated until all Baseline reach latency for each group measurement pair are recorded; Apply axial tensile load to the test piece through the clamp, and maintain stable tensile state; The applying axial tensile load to the test piece through the clamp, and maintaining stable tensile state, specifically includes: Fix the two ends of the test piece to the moving and fixed clamps respectively; Slowly stretch the moving clamp until the displacement meter indicates the specified axial displacement ; Lock the clamps immediately after stretching, hold the displacement unchanged; Measure the ultrasonic propagation time delay of the test piece under the tensile state by using the transducer, record the received signal waveform and extract the effective time delay characteristics; The measuring the ultrasonic propagation time delay of the test piece under the tensile state by using the transducer, recording the received signal waveform and extracting the effective time delay characteristics, specifically includes: Repeating steps S1 to S4, obtaining the determined receiving time of each measurement pair after stretching with the recorded baseline arrival time delay ; Segment the propagation trajectory of the measurement path in the test piece according to regions, and calculate the length proportion in each region; The segmenting the propagation trajectory of the measurement path in the test piece according to regions, and calculating the length proportion in each region, specifically includes: for each measurement pair , calculate the transducer angle difference ; wherein, is the polar angle of the th transducer; is the polar angle of the th transducer; Computing the first The vertical distance of the measurement path to the circle center ; for each ring domain the following steps are performed: S5, if then ; S6、if then ; S7, if then ; wherein is the group of measurement paths in the chord length within the annulus; calculating the first total length of the group of measurement paths ; The computer calculates the The group measurement path occupies a length proportion in the ring domain The length proportion of the ring domain ; Based on the relationship between the time delay change of the propagation path and the region division, a linear model describing the relationship between the strain distribution and the time delay response is established; The linear model describing the relationship between the strain distribution and the time delay response is established based on the relationship between the time delay change of the propagation path and the region division, specifically includes: Computing a latency variation ratio ; Set the average axial strain of the first ring domain to ; The delay change model is established as ; All The system of linear equations of the set of measurement pairs is organized in matrix form as follows: Constructing the segment share matrix: , ; wherein is an element of the segment share matrix . Constructing the delay variation ratio vector: ; Construct the annulus strain unknown column vector: ; Linear system ; Solving the linear equation set by using numerical algorithm, and extracting the average axial strain value in the region; The solving the linear equation set by using numerical algorithm, and extracting the average axial strain value in the region, specifically includes: Construct normal equations: , ; where, is the transpose of matrix ; in, ,for Dimensional matrix; ; For matrix No. Line number Column elements equal to matrix The Line number Column and number Line number The product of column elements over all Summation, satisfying ; ,for dimensional vector; ; For vectors The The component is equal to the first component in all measurement pairs. The sum of the products of the column coefficients and their corresponding delay increments; At this time, the normal equation is ; To The following steps are performed: S801, row exchange: Select the row index of the maximum absolute value in the column from the first row to the last row, the first column, which is , specifically: ； If , then exchange the first row of the matrix with the first row, while exchanging the first element of the vector with the first element. Specifically, If : ; wherein, is the matrix of all columns of the row of the matrix ; is the matrix of all columns of the row of the matrix S802, forward elimination: For each row to be annihilated the following is performed: Computing the elimination factor ; On the matrix Perform row transformation: ; where, is the element in the th row and th column of the matrix after elimination; is the element in the th row and th column used for elimination; is the update operation that replaces the original with the new value; vector corresponding updates are made: ; where, is a vector the element at the th element after elimination; After the forward elimination is completed, the matrix Solve backward from the last row: the strain unknown of the nth ring domain ; wherein, is the element of matrix in the nth row and the mth column; is the element of matrix in the nth row and the mth column; is the element of matrix in the nth row and the mth column; is the element of matrix in the nth row and the mth column; are calculated in sequence:​ ;in, For matrix The Line number Column elements; For the first Strain in the annular region; Final strain vector ; Output the obtained strain vector in the form of data table.

2. A digital method for detecting the tensile properties of foamed silicone rubber according to claim 1, characterized in that, The outputting the obtained strain vector in the form of data table, specifically includes: The calculated discrete strain vectors are exported in a table form, the first column of the table being the ring domain number and the second column being the strain value .

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