Modelling of wet grinding in tumbling mills is an interesting challenge. A key factor is that the pulp fluid and its simultaneous interactions with both the charge and the mill structure have to be handled in a computationally efficient way. In this work, the pulp fluid is modelled with a Lagrange based method based on the particle finite element method (PFEM) that gives the opportunity to model free surface flow. This method gives robustness and stability to the fluid model and is efficient as it gives possibility to use larger time steps. The PFEM solver can be coupled to other solvers as in this case both the finite element method (FEM) solver for the mill structure and the DEM solver for the ball charge. The combined PFEM-DEM-FEM model presented here can predict charge motion and responses from the mill structure, as well as the pulp liquid flow and pressure. All cases presented here are numerically modelled and validated against experimentally measured driving torque signatures from an instrumented small-scale batch ball mill equipped with a torque meter and charge movements captured from high-speed video. Numerical results are in good agreement with experimental torque measurements and the PFEM solver also improves on efficiency and robustness for solving charge movements in wet tumbling mill systems.

Wet grinding of minerals in tumbling mills is a highly important process in the mining industry. During grinding in tumbling mills, lifters submerge into the charge and create motions in the ball charge, the lifters is exposed for impacts and shear loads that will wear down the lifters. Increased loading can accelerate the wear and the lining has to be replaced. Replacing the lining is an expensive and time consuming operation that is preferred to be done within planned maintenance stops. Prediction of the charge motion and wear rate for different grinding operations and linings are therefore desirable to predict the lining life.

Modelling of wet grinding in tumbling mills that include pulp fluid and its interaction with both the grinding balls and the mill structure is an interesting challenge and some different approaches have been suggested, see [1-2]. For an effective and successful prediction, the numerical model has to be able to handle the pulp fluid and its simultaneous interactions with both the ball charge and the mill structure, in a computationally efficient approach. In this work, the pulp fluids are modelled with a Lagrange based method called incompressible computational fluid dynamics, (ICFD), which gives the opportunity to model free surface flow. This method gives robustness and stability to the fluid model and is efficient as it gives possibility to use larger time steps than the conventional CFD. The ICFD solver can be coupled to other solvers as in this case the finite element method, (FEM) solver for the mill structure and the discrete element method (DEM) solver for the ball charge. The combined ICFD-DEM-FEM model can predict both charge motion and responses from the mill structure, as well as the pulp liquid flow and pressure. The numerical grinding case presented here is validated against experimentally measured driving torque signatures from an instrumented small-scale batch ball mill, see [3]. This approach opens up the possible to predict the volume of the high-energy zone and optimise lifter design and operating conditions. The ICFD solver improve efficiency and robustness for studying wet grinding in tumbling mill systems and can predict the charge dynamics and the wear distribution in such systems.

References

[1]   Jonsén, P. et al., (2018). Preliminary validation of a new way to model physical interactions between pulp, charge and mill structure in tumbling mills. Minerals Enginering. Accepted for publication

[2]   Jonsén, P., Stener, J.F., Pålsson, B.I. and Häggblad, H.-Å., (2015). Validation of a model for physical interactions between pulp, charge and mill structure in tumbling mills. Minerals Engineering, Vol. 73, 77–84.

[3]   Jonsén, P. Stener, J. F. Pålsson, B. I. and Häggblad, H.-Å., (2013). Validation of tumbling mill charge induced torque as predicted by simulations. Minerals and Metallurgical Processing, vol. 30, No. 4, 220-225.

To efficiently model wet grinding in tumbling mills is a difficult task. Because of the complex behaviour of the pulp with free surfaces and large deformations, the difficulty is usually that the method to represent and reproduce its movements is demanding and time consuming. In this work, an investigation of the possibility to efficiently model and simulate the whole mill body, including the pulp and the charge, and its simultaneous interactions with both the charge and the mill structure is presented. This is done by the ICFD method, which is a Lagrange based method that gives the opportunity to efficiently model the pulp free surface flow, and its interaction with grinding balls and mill structure. Validation is done against experimentally measured driving torque signatures from an instrumented small-scale batch ball mill equipped with an accurate torque meter, and charge movements captured from high-speed video. Numerical results are in good agreement with experimental torque measurements.  

A method for characterisation of materials subjected to large strains beyond the levels when plastic instability occurs in standard tension tests is presented. Thin sheets of two types of hot-rolled steel are subjected to tension loading until fracture occurs. The deformation process is captured with a digital camera and by digital speckle photography (DSP) in-plane pointwise displacement fields are obtained. By numerical differentiation and assuming plastic incompressibility the equivalent plastic strain is determined. The characterisation performed in this paper consists of estimating material parameters in two constitutive models. These models are a piecewise linear plasticity model and a parabolic hardening model. By using inverse modelling including finite element analyses (FEA) of the tension tests the material parameters are adjusted to achieve a minimum in a so-called objective function. The objective function is basically a least-square functional based on the difference between the experimental and FE-calculated displacement and strain fields. Due to the large deformations an adaptive meshing technique is used in order to avoid highly distorted elements. The DSP- technique provided measurements, where the uncertainty of the equivalent plastic strain varied between 0.0015 and 0.0056. The maximum obtained strain was approximately 0.8. The true stress-strain curves based on the estimated parameters are validated in the low strain region by comparison with curves from standard tension tests

Tools for numerical analysis is a prerequisite in product development. Variations of the finite element method is widely used for simulation of metal manufacturing processes, for example sheet metal forming and hot stamping. However accurate the models are, there is still the issue of parameter estimation for the constitutive models used in the simulations.The increased use of high-strength steel in metal manufacturing processes necessitates forming at elevated temperatures. Formblowing and hardening (FH), where an austenitized profile blank is formed in a closed tool by injection of pressurised gas followed by rapid water cooling, is a recent development.The objectives are to increase knowledge regarding: characterisation methods for parameter estimation in constitutive models; numerical simulations of metal forming processes at elevated temperatures.Experimental material characterisation tests have been performed for deformation levels beyond plastic instability in standard tests. Methods for field measurements of deformation have been applied. Measurements were combined with inverse modelling for parameter estimation. Thermomechanical simulation models of the FH process have been developed. Complete process simulations were performed and compared with experiments. A pre-bursting failure criteria were implemented and compared with experimental burst tests.

The rapid development of computing technology has made powerful tools, such as finite element codes, available for more and more companies. The use of simulation tools, predictive engineering, is a prerequisite today in product development. To describe the material deformation a variety of constitutive models, based both on physical foundations and empirical considerations, are available. Common for all models is that they contain material parameters, which have to be estimated by utilising experimental methods. Despite the advanced numerical tools, the most common method to characterise materials in industry today is to use standard tensile tests. Those tests have a major drawback. When the loading is no longer homogenous, and plastic instability has initiated, the stress-strain relationship is no longer valid. The aim for this work is to investigate methods for parameter estimation in material models. The test material used is hot-rolled cold-forming steel. A further aim is to yield stress-strain curves more appropriate for large deformations compared to a standard tensile test. The main features are the use of experiments, finite element analysis (FEA) and inverse modelling combined. The parameter estimation is formulated as an inverse problem and an objective function, describing the residual error between experimental data and data from a FEA of the experiment, is formulated as a least-square functional. The objective function is minimised by an optimisation algorithm yielding a vector of best fit, or estimated, material parameters. Two approaches are investigated. One global, where experimental data from a forming experiment is used. Data is in the form of tool force and displacement, hence global data. This is in contrast with a local approach where in-plane full-field measurements of displacements on a flat specimen (hence, local data), subjected to a tensile test, are collected through the whole deformation history until fracture. The measurements are made with digital speckle photography (DSP). Parameters are estimated for a total of three different material models, assuming isotropic material properties and yield surface according to von Mises. Results from the global approach show significant difference in the stress-strain curves and a force response with optimised models compared to an extrapolated tensile test curve. In the local approach the DSP-technique provided measurements, where the maximum equivalent plastic strain in a specimen was approximately 0.8. The true stress-strain curves based on the estimated parameters are validated in the low strain region by comparison with curves from standard tension tests.

This study is concerned with plasticity and ductile fracture modelling aspects of press hardened steels, where multiple phases of different yield strength, work hardening and ductility are present. Macroscopic constitutive properties are determined using a semi-analytical approach termed Mean Field Homogenization (MFH), based on the properties of individual phases and micro-topology. This is combined with a phenomenological ductile fracture initiation criterion formulated in stress space at the microscopic scale. Localization enhanced kinematics are introduced at the macro-scale when instability is signaled by a local bifurcation analysis of the homogenized material. Discontinuities in the strain field are introduced into a quadrilateral shell based on the weak discontinuity approach. Fracture properties and flow curves up to large strains are determined from single phase tensile experiments using digital image correlation. The predictions of the integrated MFH and fracture model is compared with experimental results on steel sheets with different thermal histories, in terms of fracture prediction and and overall mechanical properties

The process studied in this work is high temperature formblowing and hardening (HTFH). Bursting failure is an irrecoverable failure mode present in the HTFH process. The main objective was to determine if a ductile fracture criterion would be possible to use as pre-bursting failure indicator in finite element (FE) simulations of the forming process. The failure criterion was implemented in the utilised FE code. Calibration was performed by the use of analytical forming limit curves (FLC:s). The FLC:s were derived from experimentally obtained stress-strain curves for different temperatures using theory for localised necking. Experiments with the HTFH process in the form of burst tests were performed. Experimental data and output from thermomechanical FE simula-tions of the process were compared. Results indicated that the implemented numerical criterion predicted failure prior to irrecoverable experimental failure. It is concluded that the implemented fracture criterion can be used as a failure indicator in FE simulations of the HTFH process.

Numerical modelling, for example FE-analysis, of powder processes requires detailed material data from physical experiments. This work intends to show possibilities to retrieve such data by TV-holography. A small disc of pressed metal powder is subjected to diametral loading. In-plane displacement field information is measured by the change in interference pattern of two laser beams diffusively reflected on the powder disc surface. Strain fields can be obtained by numerical differentiation. Findings show that non-linear elastic behaviour in the material can be detected.

In metal forming operations the stress and strain levels can locally reach much higher magnitudes than those measurable in a standardised uniaxial tension test. Additionally, the stress and strain states are in many cases multi-axial. In this paper an inverse method to obtain material data is proposed. The aim is to yield more accurate data for a wider range of strain compared to a standard uniaxial tensile test. The outline of the work is that a forming experiment is designed to reproduce tensile strains present in a full-scale cold forming process. The blanks used are made of relatively thick high strength hot-rolled steel. Process data from experiments, i.e. punch force and punch displacement, are used as input to an in-house optimisation software package. The direct problem solved in the inverse modelling and optimisation scheme is a finite element analysis (FEA) of the experiment. The goal is to find parameters in a constitutive model of the material that minimises the difference between experimental and FE-calculated data. The experiments are modelled in a commercial FE software. Four different isotropic hardening laws are used in the FE-model. One of the optimised models is applied in a forming simulation and geometric optimisation of a demonstrator part.

With the press hardening technology it is possible to produce components with tailor- made material properties. The present work is based on a comprehensive thermo-mechanical material model for simulation of press hardening and similar processes. The model accounts for and predicts time dependent and timeindependent phase transformations, mechanical and thermal properties as well as transformation plasticity during the complete cooling and deformation process from 900 °C to room temperature. The model predicts the microstructure evolution during the complete process as well as the final fractions. The thermal contact properties and the thermal properties in the tools have influence on the final material state. Solutions for tool heating and cooling for manufacturing of components with soft zones are studied. Based on the results from the press hardening simulations, thermal properties of special tool materials are taken into account in order to optimise the manufacturing thermal cycle.

With the press hardening technology, it is possible to produce automotive structural components with a tailor-made material property distribution. The properties can range from a soft ferrite dominated micro-structure to ultra-high strength martensitic structure. Tailor-made material prop-erty distribution is especially useful in components subjected to crash deformation. With this tech-nique it is possible to account for structural integrity and in the same time maximize the energy absorption in the structure. The present work is based on a comprehensive thermo-mechanical material model for simulation of press hardening and similar processes. The model accounts for and predicts time dependent and time-independent phase transformations, mechanical and thermal properties as well as transformation plasticity during the complete cooling and deformation proc-ess from 900 oC to room temperature. The model predicts the microstructure evolution during the complete process and the final fractions of martensite, bainite, perlite and ferrite. The thermal properties in the contact between the blank and the tools as well as the thermal properties in the tools have influence on the processes for tailor-made material properties. In this work, solutions for tool heating and cooling in the design of tools for manufacturing of components with soft zones are studied. Based on the results from the press hardening simulations, thermal properties of special tool materials are taken into account in order to optimise the manufacturing thermal cycle.