Shaw.Din        shaw@teclab.cn       TECLAB

Summary:The modulus value of materials is one of the important physical parameters for characterizing the mechanical properties of engineering materials. Static stretching method is currently the mainstream technical means. This method has a large load and slow loading due to stretching, resulting in relaxation strain. The size and loading speed of the load will affect the measurement accuracy. The conventional suspension resonance dynamic method forces the sample to vibrate by loading a small alternating stress, measures the natural frequency, calculates the modulus, and improves accuracy and measurement speed. The new resonance iterative calculation method introduced in this article calculates the theoretical resonance frequency through finite element analysis after obtaining the natural frequency, and obtains the elastic constant value closest to the true value through iterative algorithm. This method is not only easy to operate, but also provides more accurate measurement results.

key word:Material mechanical properties, modulus measurement, suspension resonance, elastic constant

introduce

The traditional tensile test measures the modulus of the specimen by applying external force to the testing machine and measuring the elongation of the specimen. The Young's modulus is obtained by calculating the stress-strain ratio. The excitation resonance analysis technique introduced in this article measures the resonance frequency by tapping the sample and then using an accelerometer. Further analyze the modulus through finite element analysis and iterative inversion algorithms.

Taking a uniform rectangular rod as an example, when the sample undergoes bending vibration under its own conditions at both ends, its elastic modulus and natural frequency, sample size, and mass satisfy the following relationship:

Unit Pa

In the formula, m is the mass g of the sample, L is the length mm of the sample, B is the width mm of the sample (in the vertical vibration direction), H is the thickness of the sample, f is the natural frequency Hz of the sample, and K is the correction factor.
For orthotropic materials, prepare a test template and two test beams (one longitudinally cut and one transversely cut). Measure the first three natural frequencies of the test sample and the first natural frequency of the two beams. When the aspect ratio of the test board satisfies a specific relationship, the three natural frequencies will respond very well to the orthogonal anisotropic elastic constants.

Sample production (two beams and one plate)

Finite Element Analysis of Bending Vibration Modes of Beam Samples

Finite element analysis of three vibration modes (respiratory mode, saddle mode, torsional mode) of the test plate (Poisson plate)

The modulus measurement and analysis of this method are carried out according to the following steps:

1. Measure the length and natural frequency of the beam sample

2. Determine the aspect ratio L1/L2 of the Poisson plate (tested material plate) and make such a tested plate

3. Measure the first three natural frequencies of the Poisson plate

4. Determine the four orthotropic elastic engineering constants of the material based on finite element analysis of two beams and Poisson's plate

5. Analyze and calculate the elastic constants of materials through inversion method

Inversion calculation

Modulus inversion calculation calculates the natural frequency of the template by changing the elastic engineering constants in the Poisson's plate finite element model to match the experimentally measured natural frequency, so that the two natural frequency values are as close as possible (eigenvalue solution). Therefore, it is necessary to iteratively update the natural frequency values obtained from experiments and those calculated from finite element models using algorithms. The iterative update algorithm reduces the difference between the two. The process is shown in the following figure:

Application Cases

1. Modulus measurement of isotropic thermoplastic polyvinyl chloride (PVC) sheets

2. Measurement of modulus of orthotropic composite wood panels

3. Resonance frequency measurement and mechanical performance evaluation of objects of arbitrary shapes

summary

The inversion iterative algorithm based on external excitation resonance is used to analyze the elastic modulus testing method of materials, which is simple, convenient, cost-effective, and highly accurate. This method avoids the disadvantages of long time consumption, low measurement accuracy, and expensive equipment in static tensile testing; At the same time, it avoids the problem of significant errors and even inability to obtain results in directly calculating modulus by measuring resonance frequency using conventional suspension resonance method. The inversion iterative algorithm ensures the accuracy of the experimental resonance frequency and improves the accuracy of the final material modulus value. Further research is needed to increase the finite element analysis and inversion iteration algorithms for complex anisotropic materials. For limited size material samples, the external excitation method is replaced with ultrasonic scanning excitation to increase the resonance frequency range.

reference:

Tom Lauwagiea,*, Hugo Solb, Gert Roebbenc, Ward Heylena, Yinming Shib, Omer Van der Biestc，Mixed numerical–experimental identification of elastic properties of orthotropic metal plates，NDT&E International 36 (2003) 487–495，