Appl. Sci. 2023 , 13 , 1389
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Figure 17 summarizes the diagrams of changes in the period of the sinusoidal function approximating the shape of the test sample as a function of displacement of the movable handle of the testing machine. Estimating the period until buckling occurs is not justified, since the shape of the edge of the sample does not resemble a sinusoid. From the moment the maximum force is reached, the value of the period stabilizes at a level comparable to the length of the fastening.
Figure 17. Dependence of the period of the sine wave modelling the shape of the sample on the displacement of the movable handle at the lengths of fastening: ( a ) 3mm, ( b ) 4mm, ( c ) 5mm. 5. Conclusions A measurement technique was developed, based on the simultaneous measurement of the dependence of the compressive force on the displacement of the movable handle of a universal testing machine and the recording of a series of images of a compressed sample of the tested material. This technique has a number of advantages over the traditional approach of recording only jaw movement and the force curve during the test. It enables non-contact measurement of the value of the deflection arrow of the sample during the test and gives the opportunity to observe its shape. This allows the shape of the tested paper samples to be modelled with different curves, e.g., a sinusoidal function. Thanks to this, it becomes possible to determine the relationship between the deflection arrow and other variables, e.g., force, displacement of the handle of the testing machine or work carried out on the sample. Visualization of changes in the shape of the sample in subsequent phases of the test together with the quantities measured using a universal testing machine facilitates the prediction of the model of destruction under given conditions and gives the possibility of its quantitative verification by determining the modelling error of the shape itself or the parameters determined on its basis. As an example of such a possibility, the effects of approximating the shape of the sample using the sinusoidal function and the error graph of this approximation allowing to estimate the limits of applicability of the proposed model are shown. The development of a model of paper destruction during compression is of great importance for predicting the strength properties of corrugated board and cardboard packaging produced from it. This will allow for savings in terms of packaging products in transport and reducing the consumption of paper raw materials for the production of cardboard. In order for the developed measurement technique to be fully useful in testing the strength properties of paper, the process of registration and pre-processing of sample images must be optimized. In particular, the procedure used to detect the optical edge of the sample does not allow for its correct detection in the vicinity of the attachment to
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