Full-Field Measurements in the Edge Crush Test of a Corrugated Board—Analytical and Numerical Predictive Models

Abstract

This article focuses on the derivation of simplified predictive models for the identification of the overall compressive stiffness and strength of corrugated cardboards. As a representative example an unsymmetrical 5-ply sample (with E and B flute) was used in this study. In order to exclude unreliable displacement measurement in the standard edge crush test, virtual strain gauges were used. Video extensometry was employed to collect measurements from the outer surfaces of the sample on both sides. Additional data allowed real force-displacement curves to be obtained, which were used in the validation procedure. To emulate the experimental results, besides a simple analytical model, a 3D numerical model fully reflecting the geometry of the corrugated board, based on the finite elements method was also built. In both cases good agreement between the experimental results and the analytical and numerical calculations was observed. This proved that the proposed analytical model can be successfully used to determine the overall stiffness and compressive strength of corrugated board, provided that the geometry and properties of all the layers of the board are known. The simple model presented in this work enables quick and reliable design and prototyping of new assemblies without the need to manufacture them.

New Edge Crush Test Configuration Enhanced with Full-Field Strain Measurements

“…The results summarized in Table 3 clearly show that the use of the displacements obtained from the machine crosshead introduces an error in the estimation of the stiffness index, underestimating this value almost 3 times. The same observation can also be found in the recent work of Garbowski et al [ 15 ]. The compressive strength given in Table 3 (shown in column 4) is consistent with the value provided by the manufacturer of the corrugated board, namely 7.6 N/mm %.…”

“…On the other hand, the video extensometry main procedures utilized in this study, were as follows: Use a speckle pattern compatible with DIC (pen marks would work equally well, per [ 15 ]). Only perpendicular cameras were used (front = Cam1, back = Cam2).…”

“…Numerous approaches to sandwich element strength determination, including for corrugated cardboard, can be found in the literature. Analytical methods, starting already in the 1950s, were presented, e.g., in [ 1 , 2 , 3 , 4 , 5 ], whereas numerical methods can be found in [ 6 , 7 , 8 , 9 , 10 , 11 ], and analytical-numerical techniques in [ 12 , 13 , 14 , 15 , 16 ]. Analytical calculations of the edge crush resistance of cellular paperboard, both in MD and CD, based on the paperboard’s geometric parameters and the mechanical properties of the materials used for its production, was discussed by Kmita-Fudalej et al [ 17 ].…”

“…To assemble the measurements from the outer surfaces of the specimen during the examination, video extensometry can be employed. Such a procedure is based on the measurement of the relative distances between pairs of points traced across images captured at different load values [ 15 ]. This is a method comparable to, yet simpler than digital image correlation (DIC) which, as full-field non-contact optical measurement method, is gaining more popularity in the field of experimental mechanics since it ensures very high accuracy of data acquisition.…”

Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

“…The reduction in individual stiffnesses depends not only on the type of perforation, but also on the orientation of the perforation and the orientation of the fluting, but does not depend on the location of the perforation along the wavelength. Further development of the launched research is planned related to the validation of the proposed model with experimental models while engaging the non-contact displacement measurements [ 46 ].…”