3.1. Cell Characterization
A common way to measure battery performance indicators is to perform a HPPC test [
13]. This involves pulsing current at differing SOCs and analyzing the voltage response to find characteristic resistances and capacitances from a determined equivalent circuit model. While many models are developed for this function, the most common are 1 RC and 2 RC thevenin equivalent models as shown in
Figure 2. Fitting models to 1 RC circuits is simple as the characteristic equation is a single exponential function, however the behaviors represented by this model do not match with experimental responses observed by the batteries. 2 RC models do better at simulating this behavior, with the compromise of being more difficult to accurately fit. These models also better line up with other experimental techniques that are more robust, such as electro-impedance spectroscopy, where equivalent order models can describe film growth and charge transfer resistances. These models often replace a capacitance element with a constant phase element to describe frequency domain phenomenon. HPPC cannot reliably obtain these values as it is a time domain measurement, but their behavior can be correlated with pulse measurements.
The voltage profile in these models is described as
where
OCV (open circuit voltage) is the true potential difference of the electrodes without any dynamic losses,
I is the current of the pulses,
is the internal resistance of the entire battery, and
,
,
, and
are equivalent resistances and relaxation constants that simulate dynamic reaction kinetics such as film growth and charge transfer. The time constants
can further be described as
where an additional capacitance element
is added. For 1 RC the resistance
is set to 0 in the model, removing the secondary element and simplifying the equation. In both cases of 1 and 2 RC, the internal ohmic resistance can be described as voltage change at the point of current change
The ohmic resistance often holds the greatest electric resistance of the battery. Additionally, this resistance is typically used as the primary indicator for capacity fade as its change can describe bulk changes in both electrochemical dynamics and usable active material that occur as a byproduct of cycling. The remaining voltages better describe the dynamics that occur during polarization, where the migration of ions affects local electrochemistry at the interfaces and interphases. Given the greater accuracy of a 2 RC circuit to describe the polarization voltage, the remainder of this work only considers this model when measuring equivalent components.
As fitting can resolve in arbitrary placement of the resistances and capacitances of the RC elements, this work applies the convention of ordering them from greatest to least in magnitude. The fitting was performed with a Levenberg-Marquardt algorithm using MATLAB R2023a. Capacity of the cells was additionally measured using cycler data to obtain
for a capacity of Q and over the entire discharge time for each cycle. This measurement was recorded for both capacity and life cycles.
To measure early trends in capacity and performance change from cycling, HPPC and capacity cycles were performed at the beginning of life and after 15 life cycles.
Figure 3 shows the impact of these cycles from a select cell over a discharge profile.
HPPC measurements from fresh cells saw resistance increase as SOC decreased. Measured values of charge and discharge pulses show little variation, with sight deviations near 0.4 SOC and at the end of discharge. The first variation may be due to cathode a phase change near that point, with excessive pulsing changing the distribution of ions at the surface of the electrodes. Near the end of discharge the increase in resistance from over discharging is related to the rapid potential increase from the anode. As cycling continues and active material is lost from the anode, resistance increases from discharge pulses at these low SOCs measures an accelerated resistance growth as the electrode surface becomes more dramatically lithiated.
Resistances were collected at the first cycle and last cycle prior to impact. In all cells a resistance decrease of 5 m
was noted. This corresponds with a small capacity increase which is common for nickel rich cathodes as the ceramic structure stabilizes inactive lithium sites which are important for the cathode stability [
14]. This phenomenon is apparent for the early cycles of the cells, with later SEI growth and other side reactions becoming dominant. Additional resistance increase is noted at the end of capacity for discharge vs charge cycles. This is due to the coulombic inefficiencies from discharge resulting in a slightly lower capacity during discharge vs charge despite the same time and current magnitude being used for both profiles.
3.2. Mechanical Response
The drop weight mechanical results from the cells are shown in
Figure 4. All impact energies saw a similar development of initial linear compression, followed by a short softening region and then a nonlinear plastic damage region. This nonlinearity can be explained by a combination of factors, most notably porous fluid flow and buckling of electrode sheets away from the jellyroll construction. Force plotted against time shows a slight increase in force as impact velocity increases with time, whereas the displacement response follows the same linear trajectory with only the region of yielding migrating. The similarity of initial slopes for force displacement profiles at differing impact energies across all cells shows a dynamically consistent elastic modulus. Traditional dynamic impacts on saturated porous bodies, such as battery electrode and separator, can lead to an increase in stiffening from incompressible fluid flow. Since the batteries which survived impact also did so in a region where the elastic modulus was nominally independent of impact velocity, porous saturation considerations in the damaging of the electrode can reasonably be ignored. As the highest impact energy cells still observed this relationship while all failing in voltage retention, substantial tearing of the separator appears to be present before fluid stiffening becomes a dominant material consideration. The final loads for all impact energies were within a confidence interval of the mean for every loading energy demonstrating minimal effect of defects on final yielding of the samples.
All materials saw the existence of a transition region, referred to as the plateau. This is defined as a region of lowered force loading rate with increasing displacement located inside regions of higher force loading rates. With higher impact energies the value of the onset load of these regions increases however the displacement of these regions remains consistent at 0.5 mm. SOC seemed to have minimal effect on the profile of these plateaus, with all SOCs maintaining a range of onset loads for the plateau at each impact energy. Additionally the slope of the plateau region also showed variation in each impact energy, however all began and ended within a consistent force range with the plateau remaining consistent throughout. These variations may be from experimental variations in battery placement as a 1 mm offset from center is may be large enough for the cell size to affect the force displacement response. The 7J cells saw a change in this trend, with no apparent upper limit on the initiation of the plateau region. Most 7J cells exhibited plateaus starting at 5 N with additional cells initiating plateaus at loads near the maximal force.
The format of the jellyroll also has an impact in the nonlinear force response of the batteries. The layered structure of the jellyroll alongside the flexible nature of the casing allows for the cells to behave in a bistable manner under mechanical load, with the layers deforming relative to each other to achieve a preferable final structure. During impact the whole cell becomes concave centered at the impact site until a critical response time is reached, after which the regions far from the mechanical load settle into a more mechanically stable final orientation. The time where this occurs would absorb some mechanical energy away from the impact leading to a slowing force increase during this process. All cells saw this occur from 0.7–0.95 s after impact, where the inciting force when this occurred was dependent on impact energy from 3–5.5 kN. The similar onset times can be seen as a natural material response time to the deflection which causes the bistable transition, where the force would also increase more rapidly during this response time depending on impact energies as more energy is imparted onto the structure immediately underneath.
Figure 5 demonstrates the voltage vs force response window from impacts of a 7J cell. The voltage measurements from the experiment showed little live voltage drop during testing. The 3J and 5J impact groups saw no immediate voltage change from measurement, while several 7J cells saw shorts. Not all shorts were immediately demonstrative of complete voltage loss, however all shorts were irreversible and saw no recovery in the testing window. Further monitoring of the cells saw continual voltage drop from cells which had not survived. A short circuit is a reliable indicator of a mechanical event but not all mechanical events show a measurable voltage drop during impact. Nascent shorts not detected during the observation window will cause continual parasitic capacity loss throughout cycling and may lead to side reactions where excess electrolyte decomposition will dramatically affect ionic transport and charge transfer mechanisms. This shows that live voltage measurements may not be sufficient to determine all levels of mechanical impact on cells.
Higher impact energies saw lower survival rates after the week resting period, with all 3J impacted cells surviving at every SOC, half of the 5J cells surviving and none of the 15 7J cells surviving. The specific survival rates for the 5J cells are all 5 SOC = 20 cells survived while 4 SOC = 0 cells and 2 SOC = 40 cells failed after a week. The lack of survivability from the 7J impacted cells shows that for cells in this experimental configuration saw complete failure when loading reached above 6 kN. Dynamics likely have minimal effect on this threshold as stiffening was not noticed, however as the separator is known to be viscoelastic the failure loading may not necessarily be entirely strain rate independent for the measured cells. While all 5J cells survived from immediate ISC and only 3 of the 7J cells saw an ISC from oscilloscope measurements, small tears in the separator were still present creating a slower parasitic current draw. As each dataset contains too small of a sample size to statistically isolate the clear SOC dependence for 5J impacts, the effect of SOC on survival rate of both 5J and 7J energies was inconclusive. The distribution in survivability for varying SOC in 5J impact cases suggests any mechanical stiffening electrodes due to phase changes may dissipate enough energy to restrict destructive shorting, however the degree to how strong the effect is cannot be determined using present data. As the cells were manufactured in a large batch and there were some experimental variances, the exact relationship between SOC and survivability during the procedure cannot be deduced, however as cell survival was still prevalent it can be inferred that the 5J impact energy exists near the point of completed failure during mechanical impact of the measured cells under the experimental setup.
3.3. Cycling Performance
Figure 6 shows average capacity fade trajectories vs impact conditions compared against control cells for every discharge cycle with the shaded regions showing the range of cycled cells. The control cells saw a consistent decay profile following a parabolic profile. This is indicative of both film growth on the anode surface and cathode decomposition from the byproducts of electrolyte decay. This matches well with literature from similar cells. After each capacity/hppc cycle the following cycles also saw a short increase in capacity likely due to better coulombic efficiency from shorter discharge.
All impacted cells showed a similar capacity fade profile compared to control cells, with additional decrease in capacity fade rate. Most cells saw an initial capacity decrease after resting for 1 week and a slight initial change in rate of capacity fade compared to control cells. Throughout cycling this rate of capacity fade increased, or the difference in capacity between control and damaged cells grew. For 3J cells there appears to be no discrete relationship between SOC at impact and the degree of acceleration of capacity fade. 5J saw higher variation between SOC at impact however the reduced survivability of cells after impact obscures the clarity of the relationship SOC and rate of capacity fade. Cells charged to SOC 20 had high survivability, but once cycling began some cells saw rapid capacity fade after 50 cycles, similar to a knee event seen in highly aged cells. These cells later appeared to reduce their rate of capacity fade which demonstrates the instability of some cells after 5J of impact. All cells similarly saw reduction in capacity for their capacity cycles demonstrating the structural changes from impact reduce true capacity retention in addition to dynamic effects seen during the faster charge rates. The small recovery peaks after capacity cycles seen in control cells are also present in damaged cells, with damage having no correlation to larger peaks. This shows little relationship to reduced coulombic inefficiency from structural changes due to impact.
3.4. Resistance Change
The surviving cells saw additional resistance change from impact. For the ohmic resistance
, control cells saw minimal change in resistance except towards the lower SOCs, in which resistance rose up to 6 m
for SOC = 0.1, as shown in
Figure 7.
This behavior is likely influenced by progressive capacity fade during aging, where discharge by a fixed absolute capacity may correspond to slightly different relative SOC conditions as cycling proceeds. Consequently, the terminal HPPC measurements may probe differing electrode lithiation states due to cumulative degradation processes including LLI and LAM. A similar phenomenon is noted in impacted cells for
with later lower SOC ohmic resistances rising. These rises for impacted cells are paired with a general increase in resistance, and are far more pronounced than undamaged cells. The heightened shift may be attributed to larger capacity losses seen in the damaged cells leading to larger discrepancies in ideal compared to real SOCs. For the control cells minimal global resistance growth is measured, suggesting the capacity loss attributed to internal changes to cyclable lithium is minimal. For damaged cells the global ohmic resistance increased which suggests aging mechanisms are accelerated as they are cycled under the same conditions as the control cells. The larger resistance increases observed in the impacted cells are consistent with accelerated electrochemical degradation following mechanical damage. However, because HPPC-derived resistance parameters represent global cell responses, the present measurements cannot uniquely distinguish among contributing mechanisms such as SEI growth, LLI, LAM, evolving charge-transfer kinetics, separator deformation, or localized micro-short formation. The observed resistance evolution should therefore be interpreted as evidence of increased overall electrochemical heterogeneity and degradation rather than definitive identification of a single dominant mechanism. A similar trend in ohmic resistance
, first equivalent resistance
and second equivalent resistance
for lower SOCs is also seen in
Figure 8.
The ohmic resistance is a byproduct of all phenomenon affect electron migration which couples induced shorts, SEI thickness and any balancing changes that occur as the cell becomes more discharged. Internal shorts growth is likely to be limited as the change in electrode contact required to affect the resistance is the byproduct of dendrite growth from lithium plating. SEI growth is continual as more current is applied to electrode over charge cycles, however the short thickness of the films may have minimal affects compared to changes in bulk performance. The dramatic increase in for 5J compared to 3J and control cells demonstrates the 5J impact induced a change that smaller 3J impact did not perpetuate. The existence of a short would likely not see exceptional growth under the present cycling conditions during cycling signifying the primary reason for this growth is due to coupled electrochemical changes due to nonuniform stress distributions.
The changes in and describe additional changes in underlying ionic transfer dynamics, where the growth shows trends in primary dynamic modes and shows changes in secondary. The increase in 5J primary modes show there is more localized current density exposed to the electrode surfaces which creates more energy for additional to develop. The 3J cells saw a smaller increase compared to the 5 J cells while also being greater than control, demonstrating a relationship between mechanical impact load and future electrochemical change exists from nonuniform stress distributions. The secondary mode showed relationship at SOC = 0.1 where all batches showed an increase in resistance. The magnitude was greater with 5J and 3J cells where the 5J cells saw a predominant change in SOC = 0.2 whereas 3J only saw an increase in SOC = 0.1. Overall, the results demonstrate that mechanical impact severity measurably influences the long-term electrochemical evolution of the cells during subsequent cycling, with the 5J condition consistently exhibiting the largest resistance growth across all fitted resistance components.