Electrical Tests

For examination and ageing of the lithium-ion battery, the cell test system Digatron MCFT 20-05-50ME with the precision of the current measurement of 0.2% (Digatron Power Electronics GmbH, Aachen, Germany) was used. The temperature sensor Dallas Semiconductor DS18B20 (Maxim Integrated, San Jose, USA) with a precision of ±1 ◦C was located on the lithium-ion battery case close to the strain gauge.

The lithium-ion battery test was conducted in a temperature chamber Binder MK 720 (BINDER GmbH, Tuttlingen, Germany) with a temperature precision of ±2 ◦C. The experiment was conducted at a constant ambient temperature of 25 ◦C. However, the lithium-ion battery temperature may have changed due to self-heating depending on the current.

The battery was electrically aged by charge-discharge cycling. The ageing cycles were performed at 25 ◦C and a mean state of charge (SOC) of 50%. A cycle depth of 50% was chosen. The lithium-ion battery was charged with 0.5 C to the upper charging voltage limit and discharged Ah-based to avoid voltage drift.

In order to determine the ageing of the lithium-ion battery, check-ups were performed at 25 ◦C. Check-ups were done every 50th equivalent full cycle and included capacity determination, pulse resistance, and quasi-open-circuit voltage (quasi-OCV) characteristics. During the check-up, the lithium-ion battery was first discharged down to 2.65 V, followed by a pause of 10 min. Then the battery was charged with 0.5 C (1.7 A) up to 4.20 V, followed by constant-voltage charging up to

I < 0.02C (maximum 180 min). Afterwards, the lithium-ion battery was kept at rest for 30 min before the capacity was determined with a discharge of 0.5C until the voltage of 2.65 V was reached, followed by a pause of 10 min. Next, the lithium-ion battery was charged, followed by a pause of 30 min.

The quasi-OCV was measured with a current of 0.1C. For this, the lithium-ion battery was discharged down to 2.65 V and charged up to 4.20 V with a current of 0.1C, followed by a pause of 30 min.

## *2.2. Strain Gauges*

The strain gauge 1-LY11-6/120A from HBM Germany (Hottinger Baldwin Messtechnik GmbH, Darmstadt, Germany) was attached to the lithium-ion battery housing with superglue Z70 (Hottinger Baldwin Messtechnik GmbH, Darmstadt, Germany) according to the enclosed manufacturer's instructions. It was assumed that the height (z-direction) of the battery does not change, as there is enough buffer in the housing in this direction. Therefore, it was assumed that only the diameter will change. In order to measure the change in diameter without the influence of edge effects, the strain gauge was placed in the middle of the housing height in the circumferential direction.

The area and the measuring grid area of the strain gauge were 6 × 13 mm<sup>2</sup> and 6 × 2.7 mm2, respectively. The resistance of the strain gauge was the electrical resistance between the two connecting cables. The change in volume of the measuring body caused a strain of the measuring grid. Due to the strain of the measuring grid, the resistance of the measuring grid changed [30]. This resistance change induced a signal which was amplified by a measuring amplifier Q.bloxx A116 120/350 and converted into a strain ε in μm/m by Gantner Q.station 101DT (Gantner Instruments Test & Measurement GmbH, Darmstadt, Germany) according to Equation (1).

$$
\varepsilon = \frac{\text{signal}}{k} \times \frac{4}{F} \times 1000 \,\text{\AA} \tag{1}
$$

The signal is the measured signal of the strain gauge. The *k* factor is the characteristic value of a strain gauge. The value here is *k* = 2.04. The bridge factor *F* indicates how many active strain gauges are present in the Wheatstone bridge. For a quarter bridge, the manufacturer indicated a value of one.

The resulting diameter change of the cylindrical lithium-ion battery is calculated as follows: It is assumed that the elongation of the lithium-ion battery in the circumferential direction is constant over the height of the casing. The change in diameter can be inferred from the elongation of the circumference using Equation (2).

$$
\Delta d = \frac{lI\_0 + lI\_0 \times (\varepsilon - \varepsilon(1))}{\pi} - d\_{0\prime} \tag{2}
$$

Δ*d* is the diameter change of the lithium-ion battery. *U*0 in mm represents the circumference at the start of the test. *U*0 is calculated using Equation (3). ε is the measured strain in μm/m and *d*0 is the diameter at the start of the test. In our case, this corresponds to 18.5 mm.

$$dlo = \pi \times do\_{\prime} \tag{3}$$
