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PhD Defence Tanmaya Mishra

modelling of ploughing by by an elliptical asperity through a zinc coated steel sheet - with application to modelling friction in deep-drawing

Tanmaya Mishra is a PhD student in the department of Mechanics of Solids, Surfaces & Systems (MS3). His supervisors are M.B. de Rooij and D.J. Schipper from the Faculty of Engineering Technology.

Modelling of friction in deep-drawing process is critical to the design to the product. Typically, the steel sheets used in deep-drawing are coated with a thin zinc layer by hot dip galvanization. The zinc coated steel sheets are further lubricated and provided with the required surface texture, amongst other things, to optimize the frictional stresses in a deep-drawing process. The friction in deep-drawing during loading and sliding of the tool against the sheet, in boundary lubrication regime, results from shearing of the interfacial layers, but also from ploughing of the flattened sheet surface by rigid tool asperities. The asperities on the surface of the tool have been mapped with elliptic bases of varying sizes and orientation relative to sliding direction. The current thesis aims to model the ploughing behaviour by an elliptical asperity sliding through a zinc coated steel sheet.

The friction in ploughing results from the plastic deformation of the sheet substrate and the shearing of the interface between the asperity and the substrate. These two factors are also part of a material point method (MPM)-based numerical ploughing model and a simplistic analytical ploughing model. Both the numerical and the analytical models have been extended to calculate the friction in ploughing of uncoated and zinc coated steel sheets by elliptical and spherical asperities of varying sizes, ellipticity ratios and orientation relative to the sliding direction. The analytical ploughing model has been developed for rigid-plastic material behaviour of the substrate and a constant interfacial frictional shear strength. In contrast, experimentally characterized material strength models, yield functions and interfacial friction models have been implemented in the MPM-based ploughing model.

An experimental characterization technique to measure the interfacial shear strength has been developed for unlubricated and lubricated, uncoated and zinc coated steel sheets at varying loads and sliding velocities using line contacts in linear sliding experiments. Also an experimental characterization technique to determine the yield criteria for the (anisotropic) temper rolled zinc coating on steel sheet has been developed using Knoop indentations. The method has also been applied on cold rolled steel sheet and validated using standard yield criteria. The experimentally characterized parameters for the interfacial friction model, the yield function and the yield criteria for the steel sheet and the zinc coating on steel sheet have been implemented in the MPM model to perform simulations of ploughing asperities with properties close to the reality.

Further ploughing experiments are performed using indenters with spherical tips of varying sizes and indenters with ellipsoidal tips with varying size and orientation relative to sliding direction. Further, experiments have been performed with varying ploughing direction on unlubricated and lubricated steel sheets, lubricated zinc block and lubricated, temper rolled and unrolled zinc coated steel sheets under a range of applied loads. The developed MPM-based ploughing model is validated using experimental results such as the measured friction force and measured ploughing depth. The measured results are found to be in very good agreement with calculations. The MPM-based ploughing model results are also compared and shown to agree well with the analytical model results for simpler rigid-plastic material behaviour of the substrate.  

The developed MPM-based ploughing model and the analytical models can therefore be used as robust tools in computing friction in single asperity ploughing. The models can be utilized to accurately model friction due to ploughing for tool – sheet contacts in a deep-drawing processes. In this way, the models describing friction in deep-drawing processes can be improved.