Experimental Study and Reliability Analysis of Compressive Strength of Corrugated Boxes (I)

Abstract : The 0201 C three-layer corrugated carton is taken as the test object, and the statistical characteristics of each design variable are analyzed through the test data. The carton bears its ultimate compressive strength as the main failure mode, and the reliability analysis of the corrugated carton compressive strength is established. Methods: Through sensitivity analysis, the influence of various design variables on the compressive capacity of corrugated boxes was quantitatively evaluated: The range of variation of random safety factors was calculated, and it was pointed out that the current strength design method was somewhat safe. The results of this study can provide some necessary theoretical guidance and reference opinions for the design, production and inspection departments of corrugated boxes.

Keywords: corrugated box; compressive strength; reliability: safety factor

introduction

Among the many paper packaging materials, corrugated boxes are recognized as the most economical, practical and most widely used. In order to ensure that the packaged goods are not damaged during storage and transportation, the compressive capability of the corrugated box is a key factor. For a long time, the strength design of corrugated boxes has mainly depended on experience and sample tests. It lacks the necessary theoretical basis. Its safety standards are mainly based on adopting deterministic thinking methods, which makes the design results with great experience and roughness. In fact, the compressive strength of corrugated boxes is affected by many factors such as the properties of the base paper, corrugated type, carton structure, manufacturing process, and circulation conditions. Essentially, most of these influencing factors have characteristics of random changes and contain large amounts of Subjective and objective uncertainty. Because the theory and method of structural reliability can reflect objectively and accurately the influence of the characteristics of the external load and structural performance on the design structure, it is very appropriate to introduce the concept of reliability to study the strength design problem of corrugated boxes that is affected by a large number of uncertainties. necessary. This article attempts to do some exploration and tentative work in the field of compressive strength reliability of corrugated boxes. Due to the diversity and complexity of raw materials, carton structures, and manufacturing processes, it is difficult to obtain a large number of samples. In order to facilitate the study, a 0201-type C-three-layer corrugated cardboard box produced by a Wuhan company was selected as the test object. Through the test, the statistical data of the main factors affecting the compressive strength of such cartons were collected, and the statistical characteristics of each design variable were analyzed; The carton bears its ultimate compressive resistance as a failure mode and establishes a reliability calculation model for the compressive strength of the corrugated carton.

1, corrugated box compressive strength test test

1.1 Test object

The selected test object was a 0201-type C-layer three-layer corrugated cardboard box produced by Mie’s milk from a Wuhan company. The geometric dimensions of the box were: 3170×300×152 mm. Each box was filled with 20 bottles of 500 ml of milk.

1.2 Test Environment

Temperature: 23 degrees Celsius; Humidity: 89%.

1.3 Test data

The base paper made of milk cartons was selected and subjected to ring crush strength test. The geometric dimensions of the test standard were: (152 ± 5) × (12.7 ± 0.1) mm; and the compression test of the formed empty box was carried out to determine the carton's Compression strength. The test data is as follows: (Unit: N)
Surface paper ring pressure strength: [192,193,194,195,196,197,198,200,200,205,206,206,207,207,208]
In the paper ring pressure strength: [142,144,147,148,152,153,154,155,155,156,160,161,162,163,164]
Core paper ring pressure strength: [198,198,199,200,20l,204. ,206,207,207,207,208,216,217,218,218
Carton compressive strength: [2051.5,2118.2,2279.3,2356.6.2500.6,2604.4,2744.0,2833.72833.7.2967.1,3140.6,3366.7,3453.8,3528.6,3592.6]

2. Calculation of compressive strength of corrugated boxes

There are many formulas for calculating the compressive strength of a carton based on the ring pressure strength of the base paper, but the more concise and practical formula is the Keli Carter formula. It is suitable for estimating the compressive strength of the 0201 carton. The Kerry Carter formula under the metric system is:
R=Rx(4aXz/Z)2/3·Z·J (1)
Where: aXz - corrugation constant, J - carton constant, Z-carton perimeter length (cm); R-corrugated box compressive strength (N); Rx - unit length corrugated board base paper composite ring pressure strength (N/cm ).
For three-layer corrugated paperboard, the formula for calculating the composite ring crush strength of the base paper is:
Rx=(R1+R2+Rm×C)/15.2 (2)
In the formula: R1-sheet paper ring pressure strength measurement (N); R2-in paper ring pressure strength measurement (N); Rm-core paper ring pressure strength measurement (N); C-core paper stretching coefficient.
According to the Keli Carter formula, for a specific carton, the linear relationship between the compressive strength of the carton and the integrated ring crush strength of the base paper is consistent with the test results, but the theoretical calculation results of the test data and the Keli Carter formula There is a large error between them (see Figure 1).

Figure 1 shows that the linear relationship between the compressive strength of the test object and the integrated paper crush strength of the base paper is inconsistent with the formula of the Keli Carter. In this paper, a linear regression analysis is performed according to the test data to obtain the linear relationship between the two:
R=338Rx-11849 (3)
Substituting equation (2) into (3) and combining the constants, the formula for calculating the compressive strength of the test carton is:
R=22.24(R1+R2)+32.84Rm-11849 (4)
In reliability analysis, the intensity distribution model of structural materials or components is usually selected as a normal distribution or Weibull distribution model. In this paper, it is assumed that the ring pressure strengths of face paper, inner paper, and core paper are all normally distributed, and their statistical eigenvalues ​​can be calculated from the test data (see Table 1).