**1. Introduction**

Mechanical characteristics of lithium-ion battery cells are of major importance when designing applications with maximized energy density and lifetime [1,2]. With the inherent volume variations during the use of lithium-ion batteries, the integration of cells into modules, packs, and systems needs to account for geometric variations and the induced mechanical stresses changing with state-of-charge and state-of-health [3,4]. In this context, an inappropriate design will lead to premature ageing of components on all levels. In extreme cases, a mismatch of volume requirements and device integration can lead to catastrophic failure [5].

In the past, chemical and electrochemical ageing e ffects of lithium-ion batteries have been the major focus in the international research community. Topics such as side reactions, the solid electrolyte interphase (SEI) growth, loss of lithium inventory, and separator clogging have been investigated in grea<sup>t</sup> detail [6–9]. The influence of mechanical ageing has often been ignored and is now attracting attention with the aim of the highest energy densities and the introduction of alloying materials with high volume variations during charging and discharging [3]. Moreover, complex system integration in electric vehicles requires detailed understanding and quantitative prediction of geometric variations as a function of state-of-charge and state-of-health.

Mechanical ageing might be one of the reasons for early and unexpected cell death, especially considering that graphite can expand up to 7–12% [3,10,11], Lithium Nickel Cobalt Aluminium Oxide (NCA) up to 5% [3], Nickel Manganese Cobalt (NMC) 1–2% [3,12,13], and silicon up to 280% [14] within the given voltage limits. Thus, the question to be clarified is how serious is the influence of mechanics on cell ageing in commercially relevant cells with respect to its used case?

The volume change can have various causes: The first is lithium migration, in which electrode materials change in volume as a result of lithium intercalation and deintercalation into their crystal structures [14–18]. In addition, the gas formation can occur due to side reactions [6,19,20]. Furthermore, it is known that thick layers of electrolyte decomposition products are formed as an almost impermeable covering layer [6,21,22]. Alternatively, lithium plating can also occur, resulting in swelling behavior [6,23,24].

It has already been shown by other measurement methods, such as thickness gauge [3,25–27], pressure [3], digital image correlation, [28] and multi-scale investigation [11], that a volume change takes place, which is strongly material dependent and measures between 3 and 10% for a full cell [3,11,25–28] between charge and discharge.

For our study, we investigated an ageing matrix consisting of 51 Samsung 35E battery cells. Twelve di fferent ageing conditions were applied and a minimum of three batteries per ageing point were tested. At three ageing points, the C-rate was additionally varied with two batteries each. Before the data of all batteries can be evaluated in detail, the measuring method must be verified in a first step. Because long time frames of the study, in combination with expected e ffects in the lower micrometer range, it desires a careful evaluation of the method. In this context, the current study evaluates the application of strain gauges as a valuable tool to monitor geometric changes in cylindrical cells with high precision. Firstly, the validity of the strain gauge is evaluated by investigating the signal drifts as a function of temperature and time. Secondly, the results from one battery are presented as an illustrative example. Finally, a post-mortem investigation was performed. The data of the strain gauge, in combination with electrochemical characterization, gives information regarding the lithium-ion battery and their degradation as well as parameters for battery system designs.

#### **2. Materials and Methods**

#### *2.1. Investigated Lithium-Ion Battery*

A commercially available lithium-ion battery, Samsung SDI INR18650 35E, was selected as the test object to check the functionality of the strain gauge. Verification measurements and ageing measurements were carried out on this lithium-ion battery.

The battery's specifications are given in Table 1. The investigated battery was a high-energy lithium-ion battery with a usable voltage range of 2.65–4.20 V according to the datasheet of the producer [29].


**Table 1.** Specification of the investigated lithium-ion battery [29].

Computer tomography (CT) measurements were performed in order to obtain more information about the geometry and construction details of the investigated battery cell. A Werth TomoScope HV Compact (Werth Messtechnik GmbH, Gießen, Germany) was used with a microfocus transmission tube with up to 225 kV. All shown images have a resolution of 38 μm/voxel. The visualization software myVGL 3.2.5 (Volume Graphics GmbH, Heidelberg, Germany) was used for analyzing the data.

One Samsung 35E lithium-ion battery was opened under an argon atmosphere. A remaining voltage of 2.60 V was measured directly before opening. Spatially distributed discs of the double-coated electrodes, with a diameter of 20 mm, were taken. As preparation, each sample was washed with Dimethylcarbonat (Dimethylcarbonat Msynth®plus, Merck KGaA, Darmstadt, Germany) before it was dissolved in aqua regia. The solution was filled with distilled water until a 100 ml solution was obtained. Induced coupled plasma-optical emission spectrometer (ICP-OES) was conducted on this solution. The electrode compositions of anode and cathode were measured with Varian 725 induced coupled plasma-optical emission spectrometer (Agilent, Santa Clare, USA). The electrodes and the separator were evaluated by their surface morphology and color using a Keyence VK-9710 laser microscope (KEYENCE DEUTSCHLAND GmbH, Neu-Isenburg, Germany).
