Improved criteria for evaluating impact targets in regulative drop tests of dangerous goods packagings

For dangerous goods packagings, drop testing onto an essential unyielding target can be used to assess the mechanical resistance to impact loads. Adopted regulations like Agreement concerning the International Carriage of Dangerous Goods by Road (ADR)/Regulation concerning the International Carriage of Dangerous Goods by Rail (RID) require that the impact surface provided shall be integral with a mass at least 50 times than that of the heaviest package to be tested. The problem is that many manufacturers do not possess impact targets that satisfy the required 50 times mass ratio for regulative drop tests during series production. The objective of this work is to verify existing and define improved criteria for impact target structures based on systematic investigations. Previous evidence highlights the relevance of other parameters in addition to the mass ratio. Therefore, in this research, a variation of drop test parameters was carried out experimentally. Furthermore, numerical vibration analysis was applied to investigate the deformability of the impact surface. The results conclude that the mass ratio of 1:50 cannot be defined as a decisive criterion. In order to determine the influence of further drop test parameters, the research findings were used to validate a parametric model that assesses impact target deflection. An approximation quality of over 90% was achieved. As a result, new evaluation criteria are proposed. First, a method for identifying critical impact target designs is provided. Second, a new comprehensive formula compares the approximated maximum deflection of a real impact target to the respective theoretical threshold derived from a worst‐case assumption. In practice, this leads to great advantages in the evaluation of already installed impact targets for dangerous goods packagings.

manufacturers do not possess impact targets that satisfy the required 50 times mass ratio for regulative drop tests during series production. The objective of this work is to verify existing and define improved criteria for impact target structures based on systematic investigations. Previous evidence highlights the relevance of other parameters in addition to the mass ratio. Therefore, in this research, a variation of drop test parameters was carried out experimentally. Furthermore, numerical vibration analysis was applied to investigate the deformability of the impact surface. The results conclude that the mass ratio of 1:50 cannot be defined as a decisive criterion. In order to determine the influence of further drop test parameters, the research findings were used to validate a parametric model that assesses impact target deflection. An approximation quality of over 90% was achieved. As a result, new evaluation criteria are proposed. First, a method for identifying critical impact target designs is provided.
Second, a new comprehensive formula compares the approximated maximum deflection of a real impact target to the respective theoretical threshold derived from a worst-case assumption. In practice, this leads to great advantages in the evaluation of already installed impact targets for dangerous goods packagings. Goods by Road (ADR) 6.1.5, 2 are used for the approval of dangerous goods packagings. One aspect of design type tests concerns mechanical safety. Due to the possibility of vertical or oblique impact loading in the transportation system, the structural integrity of packages needs to be evaluated. Therefore, transport packages are subjected to free fall drop testing to assess their resistance to mechanical damage.
To this end, the impact surface must be considered essentially unyielding. ADR 6.1.5.3 2 refers to ISO 2248, 3 which describes that the impact surface shall be part of an impact target structure with a mass at least 50 times larger than that of the heaviest package to be tested. However, fulfilling this requirement may cause difficulties for many manufacturers of fibreboard packages in Germany since production facilities often do not have appropriately dimensioned impact targets. Thus, regulative drop tests during series production are not possible. Therefore, an investigation of the dependency between impact target characteristics, for example, mass ratio, and the assessment of a packaging's ability to withstand damage is highly relevant for industrial application.
This work aims to provide a detailed analysis of drop test parameters and to improve current criteria for impact target structures comparable to a typical impact pad. 4 Experimental data of recent research 5 indicates that parameters other than the generalized requirement of a mass ratio of 1:50 could have significant influence on the behaviour of the impact surface. For instance, the energy amount in target motion during impact and the mechanical response of the packaging should be considered. Thus, based on systematic investigations and numerical analyses, new criteria for evaluating impact targets are developed. This allows to describe the complex interactions of packaging and target properties during impact. Hence, a framework is established for evaluating the suitability of already installed impact targets in practice. This holds great benefits for manufacturers that would otherwise not be able to conduct regulative drop tests in their own facility.

| Drop test setup
Steel plates of different thicknesses have been used as model impact target to achieve mass ratios of 1:15, 1:30, and 1:50 to packages weighing approx. 18 kg. Their anchoring is simulated using a mounting of five high strength spring elements to control and minimize forces that get transmitted outwards from the system during impact. The model target properties are given in Table 1. 5 A schematic representation of the model impact target structure is shown in Figure 1.
Each model impact target has been examined and validated in accordance with requirements of regulations 2,3 as well as with previous work. 5 This allows in the investigation to examine the mass ratio as an independent input parameter in the investigations. The experimental setup is depicted in Figure 2 by means of the model impact target consisting of the 280-kg steel plate.
The mechanical response of the impact surface is captured by uniaxial piezoelectric accelerometers. Those sensors feature an amplitude range of ±50 g and a frequency range up to 10 000 Hz. The expanded measurement uncertainty lies within a range of were determined by spectral analysis of preliminary drop tests as well as by numerical vibration analysis. 5 As illustrated in Figure  The packages are filled with substitute filling substances that exhibit good flow properties (large damage effect on impact) and achieve a gross mass of 18 kg whilst satisfying the minimum filling degree of 95% (ADR 6.1.5.2.1 2 ). Specifically, glass beads are used for the 1A2 packaging and a polymethylmethacrylate (PMMA) granulate for the 4G packaging, as shown in Figure 4.
The specifications for the 1A2 and 4G packagings as well as the corresponding filling substances are described in a previous work. 5 Regarding drop test parameters, the point of impact should be chosen to cause the most severe damage for each type of packaging. Thus, the drop positions are defined according to ISO 2206. 6 The steel drum The  Furthermore, assuming normal distribution, it is possible to calculate the standard deviation for each test series according to Equation (2).
F I G U R E 4 1A2 and 4G packaging type designs with their respective filling substances.

F I G U R E 5 Drop positions for steel drum and fibreboard box.
F I G U R E 6 Experimental verification of drop position for steel drum and fibreboard box using DIC.

| Parametric model based on maximum rigid body deflection
The maximum deflection is evaluated regarding the rigid body motion of impact pads with characteristics of sinusoidal underdamped vibrations. The rigid body deflection as a function of time d t ð Þ is described Equation (3) represents the solution for the differential equation of motion of an underdamped vibration corresponding to an impact pad resting on a spring-dashpot system with one degree of freedom. 8 This is an accurate representation of the impact response for an impact target structure if vertical rigid body motion is dominant and elastic deformation of the impact surface is negligible. 5 A schematic representation of impact dynamics is illustrated in Figure 8. respectively. 8,9 Thereby, Equation (3) is valid (underdamped vibration), only if the damping ratio ζ is greater than or equal to 0 (harmonic oscillation) and less than 1 (critical damping). In practice, this is the case for the damp-  Velocities v 1 and v 2 are initial velocities of packaging and impact target, respectively. Since the impact target is stationary at Thus, the total momentum p is given by the product of packaging mass m 1 and packaging velocity v 1 . The packaging velocity v 1 is derived directly from the potential energy so where g is gravitational acceleration and h is drop height. Furthermore, velocities V 1 at time t 1 and U 1 at time t 2 are the relative rigid body velocities between packaging and impact surface.
Velocities V 2 at time t 1 and U 2 at time t 2 are the rigid body velocities of the impact target. The impact target assumes the first maximum velocity value at time t 1 ; thus, In addition, maximum impact target deflection at time t 2 means that U 2 ¼ _ d t 2 ð Þ¼0. Lastly, the terms J Dt 1 , J Dt 2 , and ΔJ D relate to the impulse of deformation 11,12 caused by the impact force F impact in the time periods Δt 10 ¼ t 1 À t 0 , , , with Thus, velocity V 2 consists of two parts. One part is a velocity term that relates to ideally plastic collision. It is multiplied by the second part, denoted by parameter α, which depends on packaging deformation, given by the ratio of impulse of deformation to total momentum ΔJ D =p, and elastic recoil, given by the coefficient of restitution e. 13 Parameter α is a dimensionless parameter that takes values greater than 0 (no collision) and less than 1 (ideally plastic collision).
In addition, substituting the mass ratio MR ¼ m 1 =m 2 in Equation (9), a parametric model for the maximum rigid body deflection d 0 is given in Equation (10).
This model reinforces the argument of the importance of further drop test parameters other than the mass ratio between package and impact target. For example, the contact to the ground (stiffness, damping properties) are crucial and should not be neglected. This is also evident in Equation (11) (given by substituting the mass ratio MR in Equation 4), which relates eigenfrequency f 0 to stiffness k, mass ratio MR, and mass of packaging m 1 .
The stiffness coefficient k in Equation (11) can be interpreted as the contact stiffness 14,15 between impact target and ground in the case of already installed impact target structures (e.g., reinforced concrete foundation with solidly anchored steel plate). [16][17][18] To investigate such effects, the proposed model impact targets shall be used.
Thereby, the mounting of high-strength spring elements is designed to simulate the contact stiffness of a real structure.

| Determination of critical impact target designs
Only impact target structures comparable to the impact pad are described according to Equation (10). Thus, a criterion is necessary to evaluate if vertical rigid body motion is the dominant mode of vibration, that is, if the impact surface can be considered essentially unyielding. It is common to assume that modes of elastic deformation are negligible if their contribution to the total vibration of a body is less than 1%. [19][20][21][22] Numerical eigenvalue analysis is used as a tool to extract modes of vibration. Mode participation in the vibration is determined by examining the effective masses compared to the total mass of the system. 20,21 This method can be applied to derive critical impact target designs. In this work, the observed impact target structures are cuboids. Hence, two parameters are defined. Parameter λ 1 is defined to express the impact surface A impact in relation to the target's thickness z (see Equation 12). Parameter λ 2 is defined as the ratio of the length L to the width W of the impact target (with L ≥ W). Thereby, significant bending modes of vibration are identified for critical designs of impact target structures.
The results of the sensitivity analysis are illustrated in Figure 11.
The ratio of the sum of effective masses of elastic deformation modes The accessible plot provided in Figure 12 can be used (e.g., by manufacturers) to decide if the surface of a real installed foundation structure can be considered unyielding for the purpose of drop testing of dangerous goods packagings. Results in association with drop test presets are illustrated in Table 3.

| RESULTS AND DISCUSSION
In Figure 13 Figure 13B). This means that less impact energy is needed for a 1A2 packaging to fail the drop test than for a 4G packaging. This result is plausible due to the significant difference of mechanical response between steel and fibreboard materials. Compared to the steel drum, the fibreboard box can absorb considerably higher amounts of energy in form of deformation before reaching failure; thus, the 50% failure drop height is much larger corresponding to larger potential energy at the moment of impact (t ¼ t 0 ).
Steel drums exhibit lower variance in 50% failure drop height than fibreboard boxes, as shown in Figure 13. F I G U R E 1 2 Identification of critical impact target designs. failure drop height results. Therefore, the Bruceton method is not a suitable procedure to investigate the influence of the mass ratio on the failure behaviour of the tested packaging types.  F I G U R E 1 4 Bar charts of 50% failure drop height including standard deviation. Figure 9) was performed to derive the damping ratio ζ of each impact target structure. It was determined to be ζ ¼ 0:1 AE 0:02 across all model impact targets. In addition, parameter α was derived for 1A2

| Validation of parametric model based on maximum rigid body deflection
and 4G packaging types according to Equation (14). 23 α ¼ Thereby, the x vector is composed of parameter values specific to each drop test (drop height, mass ratio, eigenfrequency, and damping ratio according to Equation 10) and the d vector contains the measured maximum deflection values at time t ¼ t 2 . The detailed expression for calculating α is given in Equation (15).
The approximation quality regarding each packaging type was evaluated by means of the coefficient of determination R 2 , as described in Equation (16). 23 The parameters b d 0i and d 0i represent the predicted deflection value and the measured deflection value for the i-th drop test, and d 0 is the mean deflection value of the total amount n of observed drop tests. A good approximation quality is given for values of R 2 close to 1. In Table 4, the results for parameter α as well as for the respective coefficient of determination R 2 are given. A very good approximation quality was achieved. Hence, the approximation of the maximum rigid body deflection of impact target structures comparable to the impact pad according to Equation (10) Figure 15 as well.
It is evident that the mass ratio is important but not the only deciding factor for the evaluation of impact target structures. Packaging characteristics such as material properties and drop position are very important as well. Furthermore, the stiffness of the impact target's connection to the ground is essential and should not be neglected considering Equations (10) and (11), that is, significantly higher stiffness of the connection to the ground results in significantly lower deflection values. Consequently, a mass ratio of 1:50 on its own is not a necessary criterion.

| IMPROVED CRITERIA FOR EVALUATING IMPACT TARGETS
Based on the validated results of this work, two new evaluation criteria are proposed that can be used instead of the generalized 1:50 mass ratio between impact target and heaviest package to be tested.
First, the ratio of impact target length to impact target width must correspond to a ratio of the square root of target surface area to target thickness, which lies below the defined threshold (see Figure 12).
This guarantees negligible elastic deformation of the impact surface.
Second, a threshold of maximum admissible rigid body deflection d 0,LIMIT is defined based on the impact energy percentage that gets transmitted to the impact target structure. An analytical threshold δ LIMIT ¼ 1:96% regarding this energy percentage was calculated in Lengas et al. 5 ; that is, the energy amount absorbed by the test package must be greater than 98.04%. Here, the parameter δ LIMIT is given by the energy ratio between time t ¼ t 0 (moment of impact) and t ¼ t 2 (maximum potential energy of impact target), as described in Equation (17).
A transposition of Equation (17) into Equation (18) A value of f greater than 1 signifies that the actual deflection value surpasses the defined threshold; that is, the respective impact target would not be suitable to use in regulative drop tests.

| Example of application in practice
An example of a hypothetical impact target with properties in line with those of a typical already installed impact target structure 4 is considered, as shown in Figure 16. The impact target consists of an installed concrete slab with an anchored impact plate made of mild steel.
Results of drop test series with parameter variation.
F I G U R E 1 6 Schematic representation of typical installed impact target structure.
To illustrate the practical application of the new evaluation criteria, following drop test parameters are chosen and listed in Table 5.
Both new criteria need to be fulfilled for the impact target in Table 5 to be suitable for assessing the respective packaging's resistance to mechanical damage in regulative drop tests.
2. However, the deflection ratio function f α, MR, ζ ð Þyields a value of f ¼ 1:3 according to Equation (11); the second criterion is not satisfied.
The impact target is therefore not admissible for use in regulative drop tests with respect to the observed packaging. They represent an amount of potential energy that exceeds the analytically defined limit of approx. 2%. If both new criteria are satisfied, then the respective impact target structure is suitable for regulative drop testing. This evaluation method encompassing both new criteria can substitute the current regulation requirement of mass ratio of 1:50 between impact target and package. The results of this work can make a substantial contribution to improve the transferability of experimental and analytical data into practice, that is, in quality control during series production of dangerous goods packagings. Furthermore, this research forms the basis for introducing a standard practice, its technical implementation, and the development of templates for coordination at European and UN level, particularly for proposing changes to ISO 2248.

| CONCLUSION
T A B L E 5 Impact target and packaging properties in drop test.