Fragmentation processes like crushing and grinding are complex and extensively energy-consuming activities in the mining and mineral processing industry. Numerical analysis of different materials and loading conditions will gain more knowledge and support in the improvement of the efficiency of the fragmentation process. Although, a challenge is the lack of experimental data both for calibration and validation hampering the development of constitutive models. As a case of study, a mechanical characterization of pre-processed MnSiFe-slags was performed. Diametral and axial compressive tests under quasi-static conditions were used to load the mineral material and obtain a strain  field (ε) during increasing and cyclic loading until failure accounting for progressive damage. The evolution of the strain captured by digital image correlation (DIC) techniques exposed a mechanical behavior of composite-like material where random failure of the components caused high variability of the elastic parameters. These were found to be load dependent and they are strongly related to the ability of the material to internal rearrangement during loading. Irreversible damage affects the structure of the material and is perceived as non-linearities in the load-strain curves. It was found a degradation of the material under repetitive loading decreasing of the elastic modulus perceived as a weakening of the matrix and dominant behavior of the inclusions on the mechanical response of the material.

In recent years, slag, a residue from pyrometallurgical processes, has become more attractive in circular economy frameworks to increase the efficient use of resources throughout the life cycle of steel products and help in the reduction of carbon emissions. Its applicability is strongly dependent on the particle size, and therefore, the optimization of breaking processes should be approached by increasing the knowledge of the dynamics of slag to promote fracture. Increasing the knowledge on the mechanical response of manganese slag opens up the potential for the development of cost-effective numerical models, e.g., constitutive models based on inverse engineering calibration frameworks or digital twins. In this study, rate-dependent tests of manganese slag have been performed using a split Hopkinson pressure bar device for testing its dynamic mechanical response. In order to obtain information about the crack initiation and fracture process, 2D ultra-high speed imaging was implemented with a sampling frequency of 663,200 fps for diametrically loaded specimens. Full-field deformation measurements using digital image correlation (DIC) techniques showed a staggered fracture process where failure points on mechanical response curves vary due to the internal events happening in the material. Localized frictional occurrences and inertial effects acting inside the pre-cracked matrix have a strong effect on the global mechanical response, and therefore, a great variability of strengths was obtained.

The growing global demand for minerals and metals, coupled with the need for improved energy and water efficiency in resource extraction, has led to the use of numerical modeling, particularly the discrete element method (DEM), to evaluate and optimize comminution processes that account for a significant portion of the energy consumption in mineral and metal extraction. Despite advancements, a significant challenge remains in balancing the local resolution of fractures at the rock particle level, where physics-based material models using the finite element method (FEM) have excelled, with the resolution of industrial-scale total particle interactions within the machine system. This work explores the high-resolution fracture of rock particles using the KST-DFH material model implemented within FEM as a valuable reference for fractures with a balanced mid-level resolution achieved through a bonded discrete element method applicable to industrial-scale systems. Brazilian tests were performed on granite and limestone to calibrate the models. Single particle breakage (SPB) experiments employing digital image correlation (DIC) were conducted to evaluate the performance of the models. Finally, the DEM model was demonstrated in an industrial-scale cone crusher application. The results show good agreement for the highly resolved FEM approach (requiring only two parameters in the KST-DFH model to be determined, which is particularly advantageous for generating virtual particle breakage data across various rock materials, shapes, and sizes) and reasonable agreement for the DEM fracture response, which is attributed to the much coarser mesh used that does not capture the crumbling mechanism (as revealed by the comparison between the two numerical approaches). Despite these discrepancies, the cone crusher predictions fall within the expected ranges for the system response at the machine level.

Capturing the mechanical behavior of slag is important to optimize crushing processes for liberation of secondary raw materials. Despite advancements in experimental and numerical approaches to optimize crushing, modeling large-scale systems of highly heterogeneous batches of materials, such as slag, in a simple manner remains a significant challenge. In this investigation, a finite element simulation approach was implemented and evaluated to model the fracture process of manganese slag at a macroscale, specifically at a sample scale in which only coarse structures were considered. Critical structural features were identified and evaluated to determine the most efficient method for calibrating finite element models. FEM simulations of Brazilian disc samples under quasi-static and dynamic conditions were validated against experimental results. Results demonstrated  the feasibility of modeling electric ar furnace (EAF) manganese slags were developed from a macroscopic standpoint using an established anisotropic plasticity damage material model to describe the behavior of mineral materials under dynamic conditions. This approach adequately describes the mechanical response of EAF manganese slags by merely accounting for variations in the average failure strength resulting from dynamic effects and structural imperfections, such as inclusions. This methodology presents a simplified approach that generates a realistic cumulative failure probability for a batch of materials at both quasi-static and dynamic conditions.