One of the characteristic features of sintered steels is the porosity in their microstructure resulting from the compaction and sintering process. This porosity strongly influences the mechanical properties. To enhance the understanding for the structure–property relationship of sintered Astaloy®85Mo with 0.4 wt.%C, a micromechanical modelling approach based on face-centred cubic (fcc) representative volume elements (RVE) is proposed. The fcc-like periodic arrangement of the sintered particles in the RVE enables the consideration of a realistic non-spherical pore morphology. To compare the predictions with experimental results, accompanying uniaxial tensile tests are considered at different pore volume fractions after initial microstructure characterisation. In addition to the effect of pore volume fraction, the influence of sinter necks on the predicted overall strength is also systematically investigated. Despite the fairly simple nature of the underlying fcc structure, the RVE simulations are perfectly capable of reproducing the experimental trend, showing that the elasto-plastic properties decrease with increasing porosity. This is in contrast to analytical predictions, which underestimate the decrease in properties due to spherical pore assumptions. Moreover, the finite element-based simulations reveal a less pronounced influence of the sinter neck shape on the macroscopic behaviour, even though substantial differences in plastic strain localisation are discernible at the microscopic scale.

The effects of electrochemical aging on the mechanical properties of electrodes in lithium-ion batteries are challenging to measure and are largely unknown. Mechanochemical degradation processes occur at different scales within an electrode and understanding the correlation between the degradation of mechanical properties, electrochemical aging, and morphological changes is crucial for mitigating battery performance degradation. This paper explores the evolution of mechanical and electrochemical properties at the layer level in a Ni-rich positive electrode during the initial stages of electrochemical cycling. The investigation involves complementary cross-section analyses aimed at unraveling the connection between observed changes on both macroscopic and microscopic scales. The macroscopic constitutive properties were assessed using a U-shaped bending test method that had been previously developed. The compressive modulus exhibited substantial dependency on both the porous structure and binder properties. It experienced a notable reduction with electrolyte wetting but demonstrated an increase with cycling and aging. During the initial stages of aging, electrochemical impedance spectra revealed increased local resistance near the particle–electrolyte interface. This is likely attributable to factors such as secondary particle grain separation and the redistribution of carbon black. The swelling of particles, compression of the binder phase, and enhanced particle contact were identified as probable factors adding to the elevation of the elastic modulus within the porous layer as a result of cycling.

In this study, we developed a robust methodology for extracting the mechanical properties of individual components in complex systems such as Li-ion battery electrodes and provided quantitative values that can be used as input for modelling and lifetime estimation of Li-ion batteries. We employed micromechanical testing techniques, including micropillar compression, microcantilever bending, and nanoindentation, to measure the mechanical properties of the PVdF binder phase in the active layer. We discovered that nanoindentation tends to overestimate the modulus due to uncertainty associated with the test volume and initial large compression strains, while the micropillar compression technique provides more accurate modulus data with a narrower spread. Additionally, the yield stress of the binder phase can be evaluated using micropillar compression. Our obtained modulus values were in the range of 2.5–4.4 GPa, and the yield stress was in the range of 162–270 MPa. By microcantilever bending tests, we determined that the binder–particle interface often fails before the binder itself, suggesting that the interface significantly influences the failure mechanics. Overall, our results indicate that the microcantilever bending tests provide moduli estimates that agree with those obtained from micropillar compression tests. We also qualitatively examined the binder-particle and binder-current collector interfaces, further emphasising the significance of our methodology and the obtained quantitative values.

Battery packs in electric vehicles consist of several battery modules, each containing several battery cells with numerous layers (electrodes, separators and current collector layers. A finite element model that can capture the stresses on the layer level would be extremely large in order to resolve the details. In the present paper, a novel homogenization method is presented which is based on three-dimensional laminate theory. The number of finite elements for the simulation of stresses in batteries can in this way be drastically reduced. Based on a homogenized solution, layer-level stresses can then be determined in a post-processing step. The present formulation is adaptive and fast, eliminating the need to model individual layers. It allows for non-linear elastic behavior of active layers that undergo swelling and separator layers as well as elastic-plastic behavior of current collectors. Three realistic battery structures subjected to swelling in electrode layers have been simulated: 1. free jellyroll, 2. jellyroll enclosed by a stiff enclosure, and 3. battery module consisting of 10 cells. The presented homogenized method allows for the inclusion of battery cells as parts of larger models representing vehicle structures and facilitates studying the interaction between batteries and surrounding structures.

A statistical representative volume element for a cathodic NMC active porous materials is developed as a periodic face-centered-cubic structure. Finite element analyses (FEA) are conducted to calculate effective elastic properties and contact force distributions for various numbers of particle–particle and binder-particle contacts. The statistics for the RVE is attained through simulations of stochastic distributions of contact conditions. The variations of effective properties with changing particle–particle and binder-particle contacts are compared to experimental results in the literature. The stiffening behavior at compressive loading is correlated with increasing interparticle connections in the RVE. The average values and the statistical distribution of particle–particle and binder-particle contact forces that result from particle swelling are as well investigated. The significance of contact force distributions, for both particle–particle and binder-particle contacts, on potential particle cracking and binder debonding is addressed. It is noted that particle–particle contact forces appear that are 4–5 times larger than their corresponding average values. Conclusions drawn from differences in average contact forces between particle–particle and particle-binder contacts as well as normalized standard deviations of contact forces are utilized to improve a previously developed analytical model for effective stiffness properties and contact forces. Excellent agreements are found in comparisons to the numerical simulations.

The influence on macroscopic work hardening of small, spherical, elastic particles dispersedwithin a matrix is studied using an isotropic strain gradient plasticity framework. An analyticalsolution for strain hardening, i.e. the flow stress as a function of plastic strain, based ona recently developed model for initial yield strength is proposed. The model accounts forrandom variations in particle size and elastic properties, and is numerically validated againstFE solutions in 2D/3D unit cell models. Excellent agreement is found as long as the typicalparticle radius is much smaller than the material length scale, given that the particle volumefraction is not too large (< 10%) and that the particle/matrix elastic mismatch is within arealistic range. Finally, the model is augmented to account for strengthening contribution from shearable particles using classic line tension models and successfully calibrated againstexperimental tensile data on an 𝐴𝑙 − 2.8𝑤𝑡%𝑀𝑔 − 0.16𝑤𝑡%𝑆𝑐 alloy.

An analytical flow stress model, based on isotropic strain gradient plasticity theory, for precipitation hardened materials, is proposed and evaluated against tensile data on a 15 wt% Cr - 5 wt% Ni (15-5) PH stainless steel. The 15-5 PH material was aged at 500 °C for 1 h, 2 h, 5 h and 50 h to obtain a wide range of precipitate sizes. Detailed characterisation of precipitates was obtained using atom probe tomography (APT). A second material, a 15-5 stainless steel without added Cu was heat treated to obtain a similar matrix microstructure as in the 15-5 PH, but without Cu precipitates. Tensile testing revealed that the heat treated 15-5 PH material covered the full range from under- to overaged conditions. The analytical model, which accounts for stress reducing effects of plastic relaxation around particles, manages to capture the experimental data in a very satisfying manner using only a total of three tunable parameters. It is believed that the proposed model can offer an alternative to the much more commonly used work hardening models based on the internal variable approach.

The stress-strain relationship of a dry lithium-ion graphite anode coating has been characterized by a bending test method. The method is based on U-shaped bending of single-side coated electrodes, which enables separate measurements of tensile and compressive properties of the electrode coating. The experiments reveal that the elastic modulus of the anode coating in compression is higher than the elastic modulus in tension and that the compressive stiffness increases with strain level. Contrary, the tensile modulus is approximately independent of strain. The quantitative results for compressive modulus, and in particular the stiffening effect with increasing strain, are believed to be new to the battery research community. The measured stiffness of the anode coating is compared to previously reported results for a cathode coating. It is found that the anode coating is stiffer in compression compared to the cathode coating despite a much larger particle stiffness of the cathode material in comparison to the anode. It is concluded that differences in porosity are the main reason for the observed behavior. The method also successfully captures the hysteresis effects, both in tension and compression, that are present due to the polymeric binder and the evolution of microstructural contacts. Relaxation experiments are as well conducted to characterize the time-dependent properties of the anode coating, and the response is modeled by a Prony series.

Astaloy™ 85 Mo is a pre-alloyed, water-atomized 0.85% Mo steel powder. The aim of the present investigation is to study the influence of porosity, controlled by both mechanical and thermal processing, on the mechanical properties in a bainitic microstructure of a pressed and sintered steel. To achieve this, uniaxial tensile and compression testing is performed, together with Vickers macro- and microhardness experiments. Microhardness testing is carried out in order to determine the behavior of the matrix material at a scale where porosity influence is minimized. Both the influence from size and shape of the pores is investigated and compared with relevant mechanical analyses for porous solids. Such mechanical analyses are pertinent to both elastic and plastic properties, where in the latter case the well-known Gurson-Tvergaard model for solids with spherical pores is relied upon. It is shown that assuming a spherical pore shape is not sufficient in order to achieve good agreement between predictions and experimental results and will be further investigated in future studies.

An analytical model, based on an isotropic strain gradient plasticity theory, describing work hardening during cyclic straining in a metal reinforced by a dispersion of non shearable particles is presented. The yield criterion is expressed in terms of isotropic and kinematic hardening contributions and the model is validated against full field finite element (FE) solutions on a 2D axi-symmetric unit cell model. Excellent agreement between analytical and FE results is obtained. The theory presented includes mixed energetic/dissipative contributions from higher order stresses in both bulk and at particle/matrix interfaces. In particular, the influence of a quadratic interface free energy that transitions into a linear form at some threshold value of plastic strain is investigated. It is shown that such an energy is capable of capturing the experimentally observed phenomenon of inflections in the reverse stress-strain curve. It is argued, based on the well known phenomenon where particles are shielded by Orowan dislocation loops during reverse strain, that an energetic interface contribution could be physically relevant for low plastic strains.