Predicting failure distribution for varying load histories applied to paper materials

Abstract: Paper materials are renewable and recyclable and are often used for packaging applications, e.g., as in corrugated fiberboard boxes. From an engineering perspective, paper materials can be used to construct packaging with low weight but with high relative strength. However, compared to other packaging materials, it can be a challenge to design paper-based packaging for distribution chains with demanding conditions. Boxes made from paper can be sensitive to exposure of moisture, duration of load, and dynamic forces. Along the distribution chain, boxes can be exposed to forces that could potentially cause failure before the boxes intended service life is fulfilled. Therefore, it is important to know how to predict the failure distribution for a specific combination of packaging and distribution chain so that materials with the right properties can be chosen for a given purpose and the risk of failures can be minimized. In this project, we have investigated a statistical material model developed by Bernard D. Coleman. It is based on three material parameters that describe the cumulative distribution function (CDF) of a fiber-breaking behavior for an arbitrary load history. The model has been shown to work for fiber network systems subjected to constant load and constant load rate (CLR). Our purpose was to investigate if it is applicable for fiber network systems of higher structural hierarchy and for more complex load histories. To investigate this, we have performed compression tests with CLR on four different types of corrugated fiberboard and determined the material parameters. Afterward, we performed compression tests for a more complex load history. A periodic, triangular-shaped, load curve was chosen for cyclic testing. Finally, we used the material parameters from the CLR tests to determine the CDF for the periodic load cases. We compared the result with an empirical CDF. The CDFs showed to be in relatively good agreement, but there were some differences. We found that our measurements turned out to produce load history data that deviated from the intended load history. The material parameters were also shown to be less accurate than expected. Due to these deviations, we could not expect a perfect agreement between the CDFs. Therefore, we can not with certainty state that Coleman’s theory is applicable for varying load histories. However, despite the difficulties to experimentally achieve the intended load history, the results showed good agreement in several cases, and the deviations from the theory could possibly be explained by the load history deviations. To be certain, more accurate measurements with higher accuracy need to be done.