Luís Marcelo Tavares

Modeling of particle fracture by repeated impacts using continuum damage mechanics

Damage mechanics is a field in the mechanics of solids that has evolved significantly in the past few decades, particularly given its ability of describing situations where traditional fracture mechanics becomes either too complex or is unavailable. This paper exploits the link between damage accumulation that takes place during a single impact and the progressive weakening that occurs after repeated impact, ultimately resulting in a broken particle. It associates the increase in internal crack-like damage in the particle to the degradation of the material stiffness. The model has been validated using experimental data from repeated-impact tests on single particles in the ultrafast load cell (UFLC).

Energy absorbed in breakage of single particles in drop weight testing

Drop weight tests are a useful tool to determine energy-size reduction relationships for breakage of particulate materials. Their use in modeling and simulation of size reduction operations has increased significantly in recent years. The main limitation of the classical drop weight test lies in the fact that it does not allow the direct measurement of the fraction of the input energy that is used in particle breakage (called comminution energy). A procedure that overcomes this limitation through the calculation of the comminution energy and the coefficient of restitution in drop weight tests is proposed in the present study. It uses force-time histories of the entire event measured in a modified drop weight apparatus, the Ultrafast Load Cell, along with assumptions of conservation of energy and momentum during impact. Calculations using the procedure have been compared to measurements of the coefficient of restitution using high-speed video, and the agreement is excellent. Experimental results show that the fraction of the input energy that is actually used in particle breakage increases with an increase in relative impact energy and decreases for more elastic and crystalline materials.

Modeling classification in small-diameter hydrocyclones under variable rheological conditions

Although several mathematical models describing hydrocyclone performance exist in the literature, only a few suitably describe classification of non-Newtonian slurries in small-diameter hydrocyclones (smaller than 75 mm of diameter). In order to develop a mathematical model accounting for the effects of slurry rheology on classification, experiments have been conducted with phosphate ore slurries of variable solids concentration and chemical environment, covering a wide range of rheological conditions, both Newtonian and non-Newtonian. Semi-empirical models for estimating the hydrocyclone capacity and corrected cut size and an empirical model of water split have been proposed and/or modified from the literature in order to describe classification under such extreme rheological conditions. Of particular interest is the application of a model developed by the authors and based on the residence time theory, that is used to predict the corrected cutpoint. Experimental results demonstrated that, under the conditions studied, hydrocyclone capacity and sharpness of separation were not affected by slurry rheology. It was also found that the plastic viscosity is the most significant parameter for modeling the corrected cut size in 50 and 25 mm diameter hydrocyclones.

Chapter 1 Breakage of Single Particles: Quasi-Static

Publisher Summary This chapter focuses on the process related to the breakage of single particles. Particle breakage in comminution and degradation processes is the result of a number of poorly understood microprocesses. The single-particle fracture process does not terminate after first failure at a flaw because kinetic energy may still be available either from the tools that apply the stresses or from the flying fragments of the particles. This remaining energy must be dissipated during the second stage of the process, which results in secondary fracture of the initial progeny and possibly several further stages of sequential fracture as well. Material characteristics relevant to particle breakage are the fracture strength and the deformation behavior. Fracture strength can be defined in terms of the energy required to cause fracture (or critical tensile stress). A variety of testing methods have been used to measure the breakage characteristics of single particles subject to compression, each of which allowing investigation over a restricted range of deformation rates. These tests can be classified according to the mode of application of stresses and the number of contact points in (1) single impact, (2) double impact, and (3) slow compression.

Dynamic Modeling of Comminution Using a General Microscale Breakage Model

Abstract The traditional population balance model has been successfully used in the past to describe size reduction in industrial crushers and grinding mills, but presented limitations in scale-up from information obtained in the laboratory. The paper presents a general model that describes comminution of multi-component feeds in full-scale machines using a combination of information from breakage mechanisms, fundamental material characteristics, and the mechanical environment, allowing to overcome the limitations of traditional population balance model formulations. Since it is based on a detailed description of each stressing event, this model can be used to describe particle size reduction in different types of crushers and mills using the same fundamental material characteristics. In order to demonstrate its potential, the model has been applied to describe grinding in a ball mill, where the mechanical environment was predicted using the Discrete Element Method and breakage of particles was described using a model based on continuum damage mechanics. A good agreement was observed between measured and predicted results from a batch grinding test for a single-component feed. Simulations of the dynamics of grinding in a continuous mill demonstrated the effect of change in feed composition in both product size and fracture strength of particles discharged from the mill.

Extending breakage characterisation to fine sizes by impact on particle beds

Abstract Mathematical models used to describe size reduction processes have been undergoing significant advances in recent years, demanding progressively more detailed information characterising ore response to the mechanical environment. In most crushers and grinding mills, the stressing rate is moderate to high, so it is relevant to understand the response of particles to impact loading. Single particle breakage has been a very useful tool to characterise material response for mathematical modelling and simulation of comminution machines. However, finer sizes, which represent a significant proportion of the material contained in most grinding mills, are not generally characterised by breaking single particles given the tediousness involved in conducting the test. In the present work, a standard breakage test that aims at overcoming this limitation has been proposed. It is based on carefully conducted bed breakage experiments and a fitting routine, which allows predicting breakage of particles down to ∼100 μm in size as a function of stressing energy. The model has been calibrated with selected materials and demonstrated to be capable of providing a reasonably good fit to experimental data, as well as to predict breakage at finer particle sizes.

Célula de carga de impacto na caracterização de materiais para a cominuição. Parte 1: calibração

In recent decades there has been a major growth in the application of fundamental particle fracture data to modeling and simulation of industrial comminution processes. Among the devices used in assessing the mechanical response of particles is the impact load cell. It is a hybrid between the drop weight apparatus and the split Hopkinson pressure bar, which allows measurement of the force-deformation response from the impact of single particles and particle beds. Impact load cells with different diameters have been designed and installed at COPPE/UFRJ, so that it is now possible to measure fracture characteristics of particles within a wide range of sizes and input energies. This first part of the paper describes the operation and calibration of the device, carried out from principles of the longitudinal wave propagation theory and the Hertz theory of contacts.

HPGR simulation from piston-die tests with an itabirite ore

The Minas Rio project, owned by Anglo American, has HPGRs in open circuit operated as a tertiary/quaternary crushing stage. Currently this type of equipment is designed from HPGR tests on laboratory scale and pilot scale tests. This paper presents a methodology for simulating HPGR from piston-die tests on laboratory scale and a mathematical model developed in Hacettepe University in Turkey. The parameters determined from the results of the piston-die tests were used to validate the HPGR testing on pilot scale. Finally, the model was used to predict the particle size distribution in the HPGR product on industrial scale.

Simulation-aided UT weld inspection for improving integrity during pipe manufacture

Computational simulations and reliability analysis were used to optimize an automated ultrasonic system used in pipe inspections in a manufacture plant in operation. Through the application of these tools the quality of the final product could be improved from more efficiency inspections. The main purpose was to establish the influence of each variable involved in the capacity of the ultrasonic system in detecting flaws. Tests were conducted considering a calibration API X65 steel pipe in which fitted reflectors were inserted artificially according to the DNV-OS-F101 standard. Experimental variables such as index, probe angle and gate position showed an important effect on the efficiency of the system and statistical analyses proved to be a powerful tool to validate the simulated and experimental results.

Influência de variáveis operacionais no desempenho de classificador aerodinâmico

Dynamic air classification occupies a central position in the grinding circuits of cement and several other industrial minerals. An important recent application of this device is in the reduction of the proportion of fine (< 75 µm) material contained in fine aggregate for construction that is produced by crushing. The present paper analyzes the influence of a number of variables on the performance of a pilot-scale Sturtevant classifier, aiming at providing data for mathematical modeling. It is demonstrated that the performance of the classifier is significantly influenced by feed moisture content, rotor frequency and the position of the rejection elements, being just marginally influenced by particle shape and the feed rate, within the range of the studied conditions.