Evaluation of the Stress-Energy Methodology to Predict Transmitted Shock through Expanded Foam Cushions

Mechanical stresses experienced by packages in the distribution environment include shock and vibration amongst several others. The destructive effects of these hazards can typically be restricted by using cushioning materials to help protect fragile goods during distribution. ASTM D 1596 is the conventional standard used to determine shock absorbing performance of a cushioning material for a given combination of static loading, thickness, and drop height. This industry-accepted standard, however, requires significant amounts of transmitted shock data and can be expensive with respect to costs associated with testing and materials amongst others. Alternate stress-energy-based methodologies, developed in the past decade, recommending a considerable reduction in the number of drop tests while providing the ability to predict transmitted shock for any drop height, static loading as well as cushion thickness, are evaluated in this study for their stated accuracy. Based upon an in-depth evaluation of dynamic cushion curves for closed cell moldable foams generated using ASTM D1596, this research evaluates the accuracy of the proposed methodology in relation to the prediction of transmitted shock. Results show that the stress-energy methods while saving time in predicting transmitted shock, produce higher degrees of error than the ±5 % previously stated. In addition, they cannot predict behavior of cushions, and transmitted shock at high drop heights and static loadings with thin cushions, where only the measured values are accurate. INTRODUCTION Goods distributed through the supply chain are commonly exposed to mechanical stresses in the form of shock and vibration. Cushioning materials typically tend to provide economical solutions to counteract these forces while ensuring safe passage of the goods through the supply chain. In case of fragile products, such as sensitive electronic products that are particularly susceptible to me­ chanical stresses, cushioning is typically placed inside a shipping container such as a corrugated fiberboard box, encompassing the product within. The cushion absorbs a proportion of the kinetic energy arising from the distribution of related hazards by deforming to levels below those, which can cause damage to the product being carried within. Besides the cushioning function, cushions are also commonly used to immobilize the products inside a shipper. Some of the key criteria used in the selection of cushioning include its effectiveness against shock, vibration, resilience, cost (material and productivity), effect of temperature and humidity, ef­ fect on size of external shipper, disposal, recycling, and environmental issues. In theory, a cushion can be modeled as a spring in a spring-mass model, with the product representing the mass [1]. With respect to vibration, depending upon its thickness, load-bearing area, and the vibration frequency, a cushion may have no influence, or may amplify or isolate the incoming vibration frequency. However, the primary purpose of a cushion is to absorb mechanical stresses resulting from shocks occurring during distribution. The effect of vibration on the response of cushions is not discussed in this paper. A typical dynamic cushion curve is illustrated in Fig. 1. It represents the dynamic performance of a cushioning material for a given combination of thickness and drop height. The horizontal axis represents a range of static loadings that products of different weights might apply to the cushioning material. The vertical axis represents the transmitted shock experienced by the product when it is subjected to an impact on the cushion. These cushion curves are often presented for both the first impact and multiple impact (average of drops 2–5) data. It is common to include data for several cushion thicknesses from a constant drop height on a single plot. If the product fragility (G) is known, the following procedure can be used to determine the amount of functional cushioning material, which would provide adequate protection for the packaged item against shocks. The functional cushioning material is referred to as that portion of the cushion area, which directly supports the load, and absorbs the shock during impact. In order to calculate the cushion area, the following procedure is used: 1. Consider a product that needs to be cushioned using end-caps or corner protectors. Assume the fragility of the product to be 40 G. 2. Using the set of cushion curves (Fig. 1), draw a horizontal line through the transmitted shock level of 40 G. 3. All cushion curves that either intersect or lie below this line are suitable to provide shock levels at or below 40 G. 4. So for example, a cushion designer can select the least available thickness of 1.5 in. 5. The next step is to determine the cushion bearing area. Using the vertical lines dropped from the point of intersections between the 1.5 in. cushion curve and the deceleration of 40 G, an upper and lower bound of static loadings can be selected. The largest static loading of 1.2 psi shown in Fig. 1, allows the designer to use the smallest amount (area) of cushion that will provide the required shock protection. ASTM D1596 (Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material) covers an industry-accepted procedure for obtaining dynamic shock cushioning characteristics of packaging materials achieved from dropping a weighted and guided platen assembly onto a stationary cushion sample [2]. The dynamic cushion curves can be used to determine minimum thickness, static loading, and bearing area, all of which are essential in the design of a cushion. Although extensively adopted by the cushion manufacturers to develop cushion curves, the ASTM D1596 methodology requires extensive resources and time. According to a recent, study, generation of a full set of cushion curves for a range of drop heights and seven cushion thicknesses requires approximately 10 500 sample drops and over 175 h of test time [3]. The need to simplify and reduce the testing required generating cushion curves have been made in several past studies. ASTM D1596 requires a one minute interval between drops on the same cushion. Generally manufacturers of cushioning materials test the transmitted shock levels from 18 to 48 in. in 6 in. increments, and at five different static loadings. As many as five thicknesses from 1 to 6 in. may be presented on a plot for a given height. Therefore, six drop heights, six thicknesses, five static loadings, and five drops at each static loading will result in 900 drops for a single sample test. If five replicate drops are done at each transmitted shock condition, this would result in 4500 drops, requiring approximately 100 h of data collection. However, in most cases, only one sample per data condition is used, thereby requiring much less time and number of impacts than what has been previously cited [3]. A dynamic stress-strain curve method of consolidating all the cushion curves for a particular material into a single relationship was shown to work for resilient closed-cell foams by Burgess [4]. This study verified that for a range of drop heights (12–48 in.) and cushion thicknesses (1–5 in.), the stress-strain method could predict G values with great accuracy. The results from this methodology also provide information on the maximum cushion strain incurred in the impacts, whereas the conventional curves do not. The predicted strain values for closed-cell foam were confirmed by ex­ perimental methods using both double integration of the shock pulse and a high-speed camera. The actual peak strain values for high-end static loadings (nearing 3 psi) were observed to be within ±5 % of the predicted values [4]. A dynamic stress versus energy density methodology proposed by the same researcher, in a later publication, also validated that complete sets of cushion curves could be generated using only 10– 20 drops, and these could predict transmitted peak G results with an accuracy of ±5 % [5]. The dynamic stress versus energy curves were proposed to be deduced directly using information taken off the published cushion curves or by conducting a limited number (10–20) of shock tests. Energy density, a measure of the severity of the drop, was defined as (static stress x drop height)/ (cushion thickness) or sh/t and stress, a measure of the cushions’ response to it as (peak G x static stress) or Gs. The real usefulness of this method was proposed to be the stress versus energy relationship, a property of the material, which could replace all of the cushion curves while allowing for the predictability of the transmitted shock (G’s) for any situation. Both of the approaches discussed above were accepted to have a trade-off between accuracy and effort. Cushion curves generated using the ASTM D1596 procedure, however extensive, were agreed to be more accurate. A recent study provides improvements to the methodologies discussed above [3]. It proposes a simplified method for manipulating and displaying the stress-energy equation using a common spreadsheet data analysis tool. The underlying relationship between the dynamic energy (sh/t) and dynamic stress (Gs) is described as y =ae, where y is the dynamic stress and x is the dynamic energy. The constants, a and b, are dimensionless values that describe the material properties of the cushion [3]. Another study evaluated the possibilities of reducing the sample size needed to develop dynamic cushion characteristics through reductions in the numbers of energy intervals, replicates per energy level and drops performed on each sample [6]. The study concluded that three energy levels produced statistically valid cushion curves as compared to those created using a full set of data with careful consideration recommended when picking the extremes of the energy levels. The study concluded that though the three energy level model predicted lower shock levels as compared to the cushion curve data, they were found to be acceptable within lab-tolaboratory variations. It also concluded that performing five drops on the same sample was not necessary to predict behavior for multiple impacts. This paper studied an in-depth comparison of dynamic cushion curves for closed-cell moldable foam (ProLam Laminated Polyethylene Plank) generated using ASTM D1596 and the various stress-energy methodologies. The data for the stress-energy methodology was computed using the various methodologies identified in previous studies [3–6]. The objective of this study was to measure the accuracy of the various methodologies in relation to predicting of transmitted shock, and to compare to data actually collected using ASTM D1596, and to determine associated errors.