1 Introduction

This study focused on characterizing the strength of ultrasonic welds made in the six polyolefin films. Welds similar to these can be used to seal film of various materials creating bags used for packaging. These seals create a barrier protecting products from air, water, and chemical infiltration. Bags of this type are used for packaging foods, such as potato chips, as well as other applications.

Ultrasonic welding systems are typically controlled by factors such as horn and anvil size and shape, frequency, amount of energy delivered, weld time, joint type, and weld force (the normal force applied to the part [1]). For manufacturing, it is critical to identify a suitable combination of weld parameters in order to meet the design requirements for the product specification (joint performance). One of the most critical requirements is weld strength. Weld strength can be determined in a number of ways and this study, three approaches were examined: peel strength, shear strength, and tearing force.

Several welding parameters were varied during preliminary welding trials at Branson Ultrasonics Corporation (BUC) (Danbury, CT) in order to identify the boundaries of an experimental design space that could be investigated in more detail. These parameters included several discrete energy levels, ranging from 200 to 400 J, three discrete amplitudes from 0.025 to 0.032 mm, and three discrete weld forces, from 412 to 620 N.

Welds created using these initial parameters were inspected visually and findings were documented. Evidence of excessive welding, known as over weld, is shown in Fig. 1. An example of a weld not fully sealed for the length of the horn and anvil, also known as under weld, is shown in Fig. 2. Welds were also inspected for contamination.

Fig. 1
figure 1

Excessive over weld condition

Fig. 2
figure 2

A complete weld (left) and example of under weld (right)

The final experimental design space and various settings that were studied are detailed in Table 1 and it was found that while nearly all of the parameters had an effect on weld quality, energy and amplitude were the most significant. Screening experiments were conducted to determine the design space and were defined by under welding where welds were incomplete and over welding, where weld damage was visibly evident. The weld energy was the energy dissipated by the welding process and was measured by the power supply by integrating the dissipated power as a function of time. It is important to note that in this mode, weld time is allowed to vary to accommodate the preselected energy level. Trigger force, the force threshold at which ultrasonic energy is activated [1], was not varied independently and was set to 95 % of weld force. All other processing factors such as frequency and joint type, horn and anvil design, were held constant. There were 45 total process parameter combinations in the full factorial experimental design and five weld specimens of each of the six materials were made during each treatment. All welds were analyzed for three response variables: peel strength, shear strength, and tearing force.

Table 1 Design of experiment factors

It was believed that all three of these variables—weld energy, amplitude, and force—would affect weld strength as these parameters affect heating, squeeze flow, and interfacial healing [2]. The objective of this study was to identify the set of parameters that yields the highest weld strength.

2 Experimental materials

Commonly seen in packaging applications is the combination of up to seven layers of different plastic films. A process known as coextrusion combines layers of film in order to capitalize on a combination of properties that the individual components alone cannot achieve [3]. For example, one layer may provide resistance to ultraviolet light, another provides chemical resistance, and yet another provides puncture resistance. In the two studies detailed in this thesis, six grades of proprietary 200 gage (0.05 mm thick) triple-layer coextruded polyethylene (PE) and polypropylene (PP) film were examined. These materials were not commercially available and had been supplied by an anonymous manufacturer.

Like for all polymers, there are many grades and densities of polyethylene. Information regarding the specific material properties of the polyethylene film used in this study was not provided by the manufacturer. However, linear low density polyethylene is commonly used for film applications because of its good tensile strength as well as puncture, tear, and impact resistance properties. Applications include produce bags, garbage bags, stretch wrap, industrial liners, diaper liners, and shopping bags [4].

Polypropylene differs chemically from PE in that it has a stiffening methyl group attached to every other carbon atom. This results in a higher melting point and tensile strength for PP. Polypropylene film is commonly used for packaging because it has excellent chemical resistance and flexibility [4]. Grewell et al. also rate PP “easiest” for general weldability [2] and according to the American Welding Society, polypropylene can be welded to itself [5].

The anonymous material supplier provided the proprietary films in the form of 450 × 0.343 m rolls. Each coextruded film consisted of a polyethylene layer sandwiched between a metallized oriented polypropylene (OPP) layer and a variable OPP layer. Metallization of the OPP layer occurs during the extrusion process when a gaseous metal is blown over the film. All specimens in both studies were completed with the material folded so the inside metallized OPP layers were at the weld interface, or faying surface. The variable layers were adjacent to the horn and anvil as shown in Fig. 3.

Fig. 3
figure 3

Schematic of film orientation in bench top weld system

The supplier indicated that both OPP layers were heat sealable. The variable layers differed in thickness, stiffness, and coefficient of friction. The variable layers for the F2A, F2B, and F8 materials were slip modified to lower the coefficient of friction resulting in faster, more efficient processing and package manufacturing. It is unknown whether the film was produced by casting or blowing or whether it was oriented in the machine or transverse direction or both. The differences in the OPP layers are summarized in Table 2.

Table 2 Distinguishing characteristics of variable OPP layers

3 Experimental procedure

All welds for this study were created at BUC using a 30 kHz Branson 2000X 1,500 W power supply, single converter, and gold booster with a gain of 1:1.5. The 3:1 gain horn was a Branson rectangular slotted riser back made of uncoated titanium. It was 152.4 mm long with a 12.7 mm wide front face and a 38.1 mm back stock. The anvil was solid hardened steel with a triple solid bar pattern, which is a common configuration for packaging. The Branson 2000X system was set to the energy mode, meaning that the power supply monitors the dissipated power as a function of time and discontinues the weld cycle once a preselected value of energy has been delivered to the part [2].

Specimens were cut to approximately 350 × by 200 mm rectangles and folded in half. The folded end was secured in a clamp. The remainder was stretched over an anvil and secured as shown in Fig. 4, and the welder was actuated. The specimen was labeled and the following data was documented: material ID, cycle number, specimen number, energy, amplitude, weld force, and trigger force. Table 3 shows the typical weld operations and cycle times for each operation.

Fig. 4
figure 4

Photograph of weld configuration

Table 3 Typical ultrasonic welding cycle [2]

The resultant specimens had a cross-section as shown in Fig. 5. The welded seal was 152.4 mm wide and approximately 38 mm from the fold. Three samples were cut from each weld specimen and each was subjected to a different physical performance test: tearing force, peel, and shear strength as shown in Fig. 6.

Fig. 5
figure 5

Diagram of cross-section of welded specimen

Fig. 6
figure 6

Schematic of individual test specimen locations for weld specimen

3.1 Peel strength testing

Peel strength was determined by a procedure based on the ASTM International D882-12 Standard Test Method for Tensile Properties of Thin Plastic Sheeting [6] though the elongation aspects of ASTM D882 were not used. Specimens met the size and shape requirements outlined in ASTM D882. Specimens were cut to 25 mm width using a paper cutter with a sliding metal blade. Specimen length varied from 65 to 150 mm, and specimens of excessive length were trimmed using ceramic scissors.

Peel strength measurements were taken using an Instron (Norwood, MA) Model 4502 load frame with grip distance of 50 mm and crosshead speed of 25 mm/min. Mechanical wedge action grips were used, and the grip surface was covered with 0.5 mm thick Nexcare Absolute Waterproof First Aid Tape to prevent slip and puncture of the specimens because of the sharp diamond serrated finish on the face of the jaw grips.

Both legs of the sample were placed into the grips such that the weld was centered between the grips as shown in Fig. 7. The bottom grip remained stationary and the top grip traveled 20 mm upward or until the weld failed. The measured maximum load was documented.

Fig. 7
figure 7

Diagram of specimen placement for peel strength testing

3.2 Shear strength testing

Shear strength was also determined by a procedure based on ASTM D882 [6]. Again, the elongation specifications of the standard were not used. Specimens were cut to the same dimensions using the same method as for peel strength testing described above. However, the loop in the specimens was cut so the cross-section would resemble an “X”.

Shear strength measurements were made with the Instron Model 4502 load frame, with grip distance of 50 mm and crosshead speed of 25 mm/min. Mechanical wedge action grips were again covered with 0.5 mm thick Nexcare Absolute Waterproof First Aid Tape to prevent slip and puncture of the specimens.

The top right leg of the “X” was placed in the top jaw grip, and the bottom left leg was secured in the bottom jaw grip as shown in Fig. 8. The weld was centered between the grips while maintaining at least 6 mm of film in the grips. The bottom grip remained stationary, and the top grip traveled 75 mm upward or until the weld failed. The measured maximum load was documented and used to calculate the stress endured based on the area of the three bar pattern on the anvil over the width of the test specimen, 3 × (0.6 × 25 mm). The maximum shear stress sustained prior to failure is equivalent to shear strength [7].

Fig. 8
figure 8

Photograph of specimen placement for shear strength testing

3.3 Tear resistance testing

Tear force was measured according to ASTM D1922-09 Standard Test Method for Propagation Tear Resistance of Plastic Film and Thin Sheeting by Pendulum Method [8]. This method measures the energy absorbed by the specimen when a tearing force is applied to a pre-existing slit in the material. Specimens were cut using ceramic scissors in compliance with the template as shown in Fig. 9.

Fig. 9
figure 9

ASTM D 1922 tear propagation template [8]

Measurements were made with an Oakland Instruments Model ME-800 Elmendorf Tear Tester (Minneapolis, MN) outfitted with an 800 g pendulum. Specimens were clamped into the vice with the constant radius section pointing upward. The slit was centered between the twin vise jaws. One jaw was connected to the tester base and kept stationary throughout the test. The other jaw was attached to and thus moved along with the pendulum.

Prior to testing, the pendulum was swung without a specimen in the vice to verify that the pointer reported a zero reading. The orientation in Fig. 10 shows the beginning of the test, when the pendulum was secured at its maximum height and potential energy position. To initiate the test, a release was pressed and the pendulum swung. The pendulum slowed as it tore the film, indicating that some of the kinetic energy from its motion was absorbed by the specimen [9]. After specimen failure, the pendulum was stopped and the test result was read from the indicator on the pendulum.

Fig. 10
figure 10

Specimen prior to tearing force testing

The result was a percentage of maximum potential energy. This result was used to calculate tearing force (in units of force) as shown in Eq. 1. A reading of 100 % indicates that all potential energy of the pendulum was absorbed by tearing the specimen. For example, for a tearing force reading of 5 % the tearing force would be 392 mN as shown in Eq. (1) [8].

$$ 5\times 8\kern0.5em \mathrm{g}\times 9.81\frac{\mathrm{m}}{{\mathrm{s}}^2}=392\kern0.5em \mathrm{mN} $$
(1)

4 Results and discussion

The three objectives of the experiments described in this chapter were to determine the optimum (1) weld force, (2) amplitude, and (3) energy to produce strong welds. It was expected that excessively high energy, amplitude, and weld force would each increase the rate of internal heating at the faying surface, resulting in excessive squeeze flow and reduced weld strength. Results ranged from 1.6 to 31 N for peel strength testing, 0.05 to 5.6 MPa for shear strength, and 78 to 2,600 mN for tearing force.

The response variables were plotted as function of energy for each of the six materials. Spline curve lines were added in all of the graphs and are shown for visualization only. While they approximate the response as a continuous curve across energy levels, response data only exists at discrete energy values. All error bars correspond to one standard deviation with a population of four or five.

These results were then analyzed in JMP statistical software using three-way analysis of variance (ANOVA) with replications to identify statistically significant relationships between the three single terms and four cross terms variables and the three response (dependent) variables (see Table 4). Effects test tables were created to determine the probability values, or p values, for each independent variable. Low p values, below the 0.05 level of significance adjusted for the total number of effects as shown in Eq. (2), indicated that the means of the response variables were dependent on the explanatory variables.

Table 4 Seven main and interaction effects for benchtop welds
$$ \alpha =\frac{0.05}{7}=0.007 $$
(2)

In addition, all results were analyzed in JMP to determine whether statistically significant relationships existed between the three single term and four cross-term explanatory variables and the coefficient of variance, Eq. (3), for each of the response variables. That is to say, statistical tests were conducted to determine if the independent variable affected the repeatability of the dependent variables. Effects tests tables were created to determine the p values for each explanatory variable. p values less than the adjusted level of significance, 0.007, indicate that the C v of the response variable was dependent on the explanatory variables [10].

$$ {C}_{\mathrm{v}}=\frac{\sigma}{\mu} $$
(3)

The test results for the coefficient of variance for peel strength and tear resistance were not found to be statistically significant and are not detailed. A discussion of the significant relationships between coefficient of variance for shear strength and the dependent variables is provided in Section 4.3 in the following section.

4.1 Peel strength results

The p values for peel strength in Table 5 show evidence of a significant effect of amplitude on peel strength for F2A and YH materials, although this relationship is not clear in Figs. 11 and 16. Table 5 also shows an interaction effect of energy and weld force for peel strength for those materials. In more detail, the effects of energy and weld force were dependent on each other [11]. This can be seen by comparing the different slopes of the curves in Figs. 11 and 16. The error bars correspond to one standard deviation of the population for each data point. It is seen that the slope of the lines (peel strength as a function of energy) is higher at higher weld forces. This is likely the result of better coupling of the horn to the part at the higher forces, allowing better heating. In addition, the higher weld forces may have promoted better alignment between the horn and the anvil, in turn promoting more uniform welding. Because this higher energy and high force did not result in lower weld strength, it is suggested that no effects of excessive squeeze flow were seen and the energy and force levels were below the critical value that would promote this adverse effect.

Table 5 p values for peel strength
Fig. 11
figure 11

Peel strength (N) as a function of energy (J) for F2A

The peel strength for materials F2B, F8, and PW were significantly affected by energy and weld force. These were not interaction effects. For these materials, peel strength was generally proportional to weld force and energy. The overall slope of the curves in Figs. 12, 13, 14, and 15 are very similar for each weld force level, unlike the previous plots of interaction effects. This suggests that higher energy and force levels promoted better fusion of the faying surfaces independently. Again, this effect would be limited at higher levels as a result of excessive welding and burn through (Fig. 16).

Fig. 12
figure 12

Peel strength (N) as a function of energy (J) for F2B

Fig. 13
figure 13

Peel strength (N) as a function of energy (J) for F8

Fig. 14
figure 14

Peel strength (N) as a function of energy (J) for CB

Fig. 15
figure 15

Peel strength (N) as a function of energy (J) for PW

Fig. 16
figure 16

Peel strength (N) as a function of energy (J) for YH

For material CB the peel strength was significantly affected by energy, amplitude and the interaction between energy and amplitude. In more detail, Fig. 11, shows that the slope of peel strength as a function of energy appears to be dependent on amplitude (which is statistically supported). For example, in this case, peel strength increased for the 400 J level as amplitude increased. This could be because higher amplitudes promoted more uniform welds (approaching the thickness of the film thickness) and the higher energy promoted better fusion. In more detail, at the high amplitude, the relative standard deviation (experimental error) is 25 %, while at the lower energy and amplitude the relative standard deviation is as high as 50 %. This is in agreement with the fact that higher amplitudes promote more uniform welds as long as the amplitude and energy are not excessive enough to promote burn through and weld or film damage.

4.2 Shear strength results

Table 6 indicates a significant interaction effect between energy and weld force for shear strength for all materials. This is supported by Fig. 17, 18, 19, 20, 21, and 22, where shear strength is generally inversely proportional to energy. In more detail, shear strength is relatively high for all weld forces at lower energy levels and low for forces of 517 and 620 N at the 300 and 400 J energy levels. It is believed that at the higher energy and force settings, the weld experiences burn through (which was visually observed) and excessive welding resulted in a loss in weld strength.

Table 6 p values for shear strength
Fig. 17
figure 17

Shear strength (MPa) as a function of energy (J) for F2A

Fig. 18
figure 18

Shear strength (MPa) as a function of energy (J) for F2B

Fig. 19
figure 19

Shear strength (MPa) as a function of energy (J) for F8

Fig. 20
figure 20

Shear strength (MPa) as a function of energy (J) for CB

Fig. 21
figure 21

Shear strength (MPa) as a function of energy (J) for PW

Fig. 22
figure 22

Shear strength (MPa) as a function of energy (J) for YH

It is important to note that this was not seen in the peel strength test because here, the ultimate force at failure at the highest weld strengths was 26 to 31 N, while in the shear strength tests the ultimate forces were as high as 85 to 253 N. Thus, the effect of over weld was not seen in peel tests. This pattern was consistent across the balance of the materials, with the exception of some high strength values at the mid-energy levels for materials F8 and PW.

Material F2A also exhibited a significant interaction effect between energy and amplitude. This can be seen in Fig. 17, where shear strength is inversely proportional to energy as amplitude increases. Again, the reason for this loss in weld strength is probably related to over welding and the onset of burn through.

Materials F2B, CB, and YH also exhibited a significant relationship between shear strength and amplitude according to the p values in Table 6. However, this is difficult to differentiate from Fig. 18, 20, and 22.

4.3 Coefficient of variance of shear strength results

The p values for the coefficient of variance of shear strength in Table 7 show evidence of a significant effect of energy for materials F2B, CB, and PW. This evidence is seen in Figs. 23, 24 and 25. It is important to note that because these data points are a commutation of the previous data, there are only three data points for each level. Thus, the individual data is presented and not standard deviation because the population size was too small. The figures show that the coefficient of variance is proportional to energy. It is believed that there is a critical energy value of 300 J at which point burn through may start to occur. When burn through is initiated, the effects of excessive heating compound the burn through, resulting in a wide range of weld strengths. In some cases, the burn through did not initiate, and relatively strong welds were produced. These two possible outcomes resulted large experimental error. This compounding effect is most likely caused by excessive heating resulting in a disproportional increase in loss modulus, resulting in thermal “run away” [2].

Table 7 p values for coefficient of variance for shear strength
Fig. 23
figure 23

C v of shear strength as a function of energy (J) for F2B

Fig. 24
figure 24

C v of shear strength as a function of energy (J) for CB

Fig. 25
figure 25

C v of shear strength as a function of energy (J) for PW

Table 7 also indicates significant p values for the effect of weld force and the interaction effect of energy, weld force, and amplitude on the C v of shear strength for material YH. All three explanatory variable effects on C v were dependent on each other. This can be seen in Fig. 26. For example, at low amplitude and low energy, the shear strength C v is low for all weld forces. At higher amplitudes, the C v increases at the higher energies for the lower weld forces. It is seen that the highest weld force, lowest energies, and highest amplitude had the most variance. Again, it is believed that at higher energy and amplitude values, there were critical values, that once exceeded, resulted in possible over welding, and once initiated, the processes would promote excessive over welding. However, it is clear that in all cases higher weld force resulted in higher variance.

Fig. 26
figure 26

C v of shear strength as a function of energy (J) for YH

Excessive squeeze flow and burn through is more likely to occur at high energy and high weld force levels compared to lower energy and weld force levels. Along with burn through, inconsistencies occur in the weld diffusion zone, which lead to more variation in weld strength.

4.4 Tear resistance results

Materials F2A and F2B both exhibited a significant interaction effect between energy and amplitude as seen in Table 8. In more detail, Figs. 27 and 28 show tearing force is generally inversely proportional to energy increases at the lower amplitude setting. However, it is generally proportional to energy at higher amplitude settings. This pattern is slightly more obvious for the F2A material. It is believed that these observations are related to a balance of over welding (burn through) as well as sufficient fusion to produce a relatively strong weld. It is important to note that there is significant experimental error (large error bars), which is typical of tear testing results.

Table 8 p values for tearing force
Fig. 27
figure 27

Tearing force (mN) as a function of energy (J) for F2A

Fig. 28
figure 28

Tearing force (mN) as a function of energy (J) for F2B

Material F2B also showed an interaction effect for weld force and amplitude. Figure 28 shows moderate and flat tearing force across amplitudes for the two low weld forces and increasing tearing force over amplitudes at the highest weld force. This can likely be explained by brittleness caused by burn because of excessive squeeze flow at higher amplitudes and weld forces.

Weld force was also a significant main effect for F2A, F2B, F8, and PW as indicated in Table 8. For the PW material, shown in Fig. 31, low weld force resulted in higher weld strength. This is incongruent with the other five materials, but within the range of being explained by experimental error. Figure 29 shows the tearing force being consistently proportional to high weld force, especially at the 200 to 300 J energy levels. This suggests that at these levels there is likely better coupling of the horn to the part, allowing better heating and better alignment between the horn and the anvil, in turn promoting more uniform welding. Tearing force decreased at the 400 J level which is believed to be an indication of excessive squeeze flow and over weld conditions resulting in lower strength.

Fig. 29
figure 29

Tearing force (mN) as a function of energy (J) for F8

Amplitude was the only significant main effect for material YH indicated by Table 8. Tearing force is slightly higher across all energies and weld forces at the highest amplitude (Fig. 32). This may be explained by the fact that higher amplitudes promoted more uniform welds (approaching the thickness of the film thickness).

There were no significant effects for material CB, as shown in Table 8 and Fig. 30 (Figs. 31 and 32).

Fig. 30
figure 30

Tearing force (mN) as a function of energy (J) for CB

Fig. 31
figure 31

Tearing force (mN) as a function of energy (J) for PW

Fig. 32
figure 32

Tearing force (mN) as a function of energy (J) for YH

5 Conclusions

The aim of this study was to identify the set of parameters that yielded the highest weld strengths. Three explanatory variables (independent)—energy, amplitude, and weld force—were investigated to determine whether any of them had a significant effect on peel strength, shear strength, or tearing force as well as the effect of the independent variables on the experimental error. All three explanatory variables were expected to have an inversely proportional relationship with weld strength.

Results for all six materials were analyzed to determine whether a set of parameters resulted in high peel strength, shear strength, and tear resistance simultaneously. It as was seen that the 0.032 mm amplitude and 620 N weld force resulted in relatively high peel and shear strength as well as tear resistance for the majority of the materials. There was no single energy level that resulted in relatively high weld strengths for all responses. The 400 J level resulted in the highest peel strength welds for all materials, the 300 J setting had high shear strength outputs for half of the materials, and the highest tear resistance was recorded most often at the 200 J level. In general, the optimized weld parameters for all three response variables, would be an amplitude of 0.032 mm, weld force of 620 N, and weld energy of 300 J.

The highest peel strength was found at high weld forces and high energies for all materials, and for select materials, high amplitudes resulted in even higher peel strength. Energy and weld force were significant factors for almost all materials. Because higher energy and high force did not result in lower weld strength, it is suggested that the effects of excessive squeeze flow were not seen and the energy and force levels were below the critical value that would promote this adverse effect despite visual evidence of over weld. It is possible that the displacement of the metallized layer caused an exaggerated appearance of over weld.

All independent variables were significant for different materials with respect to tear resistance. For the F2A, F2B, F8, and CB materials, the highest tear resistance was the result of high force, high amplitude, and mid-range energies, although none of the variables were statistically significant for the CB material. The YH material was strongest at higher amplitudes as well as mid-range force and energy levels. Despite having a statistically significant dependence on energy, results for the PW were largely indistinguishable.

Both energy and weld force had significant effects on shear strength. For most combinations, results for shear strength did reflect the study predictions with the highest levels of shear strength recorded at the low energy and weld force levels. This may be because the shear strength trials had the least dramatic failures of the three analyses. Peel strength test specimens often exhibited signs of the layers pulling apart from each other (delamination), and the material was also known to break at the weld rather than peeling apart. Tear specimens sometimes tore obliquely or broke along the weld. Those volatile failure modes were audibly noisier than when a specimen tore or peeled cleanly. The sound that accompanied a failure was a release of energy, and that sudden release came as a result of being subjected to maximum load. Further analysis could be completed in order to attempt to correlate the categorical failure mode with the explanatory variables and perhaps also the response variable to determine whether there was an additional relationship that had not yet been considered.

In addition, all results were analyzed to determine whether statistically significant relationships existed between the independent variables and the coefficient of variance for each of the response variables. The tests were not found to be statistically significant for peel strength or tear resistance; however, energy, weld force, and an interaction effect between energy, weld force, and amplitude were found to be significant sources of variation for several of the materials. It is believed that some combinations of these parameters resulted in excessive heating. In this instance, over weld occurred and welds were weak. If this did not occur, strong welds were created consistently.

5.1 Recommendations for future research

The anonymous material provider originally wanted welds to be created and studied in all three possible joint configurations, variable OPP to variable OPP, variable OPP to metallized OPP, and metallized OPP to metallized OPP. Only the metallized OPP to metallized OPP arrangement has been studied thus far. The first recommendation is to conduct studies using the other two possible configurations.

A second recommendation is to more thoroughly examine the differences in the variable layer of the six materials to determine how they impacted the results of these studies. For example, the three “F” materials oftentimes had similar results and the other three materials reacted much differently. However, it is known that some of the materials were modified to decrease the coefficient of friction. During welding, it was also casually observed that some materials were noisier. Some fed through the FFS machine with more tension than others, causing bunching around the forming shoulder and wrinkles at the end seals. Some films even caused the polyurethane film advance belts to shed small bits of material. Not enough is known about the materials at the time of publication to make an informed inference to explain any of these differences.