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Mohammad Reza Vaziri

Grade:  Ph.D.


Ph.D. Thesis:

Evaluation of Material Constitutive Models and Development of Damage Model in Orthogonal Machining Process (Co-supervised by Dr. Salimi).


Year: Sept. 2006- Feb. 2010.




Finite element method is a commonly-used method in simulation of machining processes. Usually, researchers in this field establish their elements based on displacements of nodes and gradients of these displacements with respect to a reference configuration as nodal variables. Recently, new formulation, Absolute Nodal Coordinate Formulation (ANCF), has been developed. In this formulation, the gradients of the global position vector are used as nodal coordinates and no rotations are interpolated over the finite element. In this study, the application, efficiency and domain of application of these two formulations have been studied by some numerical examples. These examples showed that high nonlinearity and very large computation time and extra wrinkling in the predicted deformed shape are some disadvantages of ANCF models in comparison to the classical FEM models. Therefore the application of FE methods based on displacements as nodal variables is preferred in simulation of large deformation processes such as machining.

Several leading commercial codes offer a number of different and sophisticated fracture options. At the same time no guidance is given for the users to identify the suitable fracture criterion for a particular application and how to determine the fracture parameters for different materials. This study presents some insight to this subject by systematic evaluation of the relative performance of six fracture models to identify the most suitable fracture criterion for chip separation. Three of these models are cumulative-damage fracture models including the Wilkins, the Johnson–Cook (J-C) and the modified Cockcroft–Latham (C-L). The other three models are stress and strain-based failure criteria including the maximum shear stress (Tresca), the constant failure strain and the critical strain-to-fracture models. A new algorithm is developed to calculate constants of the damage models in the range of very high strain, strain rate, temperature and pressure that occur in the machining processes and in the presence of combination of the two different failure mechanisms; void growth and shear decohesion. Few Arbitrary Lagrangian-Eulerian (ALE) models are utilized to study the accumulation of damage. The experimental data of Assessment of Machining Models (AMM) effort for continuous-chip orthogonal cutting of AISI 1045 steel is used as a source to verify the models. A code was developed to find the optimized set of fracture constants based on the nonlinear least-squares method. As a result a new set of fracture constants for the J-C damage model is presented for AISI 1045 steel. It is demonstrated that due to different failure mechanism a unique fracture model cannot be the representative of crack generation in all machining zone. Therefore, the desired damage model was implemented as the chip separation criterion in an update Lagrangian (UL) simulation, where crack propagates in front of the tool through failure of elements in sacrificial layer as a result of meeting the damage failure criteria. Consequently, the calibrated J–C damage model presents acceptable predictions for the cutting forces. Comparison of the predicted resistance of workpiece material to cutting with the failure data collected from “Incremental Compression” test certified realistic prediction for the chip separation phenomenon. Moreover, the developed algorithm is applicable to study the accumulation of damage in any metal cutting and metal forming processes. 

This study appraises two major chip formation techniques in finite element (FE) simulation of machining. The first one considers chip formation as a wedge indentation process, while the second one considers chip separation due to ductile fracture. The first technique has been implemented in an Arbitrary Lagrangian-Eulerian (ALE) simulation of machining and the chip formation is assumed to be due to plastic flow. Therefore, the chip is formed by continuous remeshing of workpiece. In updated Lagrangian (UL) simulation as an implementation of the second technique, the Johnson-Cook (J-C) damage criterion is used where elements in the sacrificial layer are deleted, when the accumulated damage in such elements exceeds the predefined critical value. The experimental data of the Assessment on Machining Models (AMM) effort for orthogonal cutting is used as a source to verify the models. It is found that ALE approach predictions for strains and temperatures within the deformation zones are not satisfactory and the predicted resistance of workpiece material to cutting is unrealistically high. Instead, the UL approach results are shown to be more reasonable with less computational cost and less possibility of software crash. However, in the case of calculating field variables the major differences are located in the material separation affected zones; the two thin boundary layers on the cut surface and on the underside of the chip.

Among the effects of strain hardening, strain-rate hardening, and temperature softening, it has been long argued about which effect is predominant in governing the material flow stress in machining. In addition, there is a belief that neither temperature nor strain-rate affects the resistance of workpiece material in cutting. If this is the case in metal cutting material flow stress, there will be no need to consider temperature and strain-rate related terms in mathematical form of material constitutive law and similar to many other forming processes, the flow stress will be the function of strain only; while, the magnitudes of strain-rates, and temperatures involved in machining are several orders higher than those generated in other forming processes. This study discusses these issues. As a result the first predominant factor governing the material flow stress is strain hardening. It is demonstrated that strain-rate and temperature do not counterbalance the effects of each other in all machining zone. Therefore implemented material model in metal cutting should include their effects separately. It is demonstrated that friction is an independent heat source to plastic dissipated energy; therefore its contribution should be considered by implementing temperature in mathematical equation of material model.

Mechanical and thermal properties significantly affect many aspects of machining, such as chip formation, cutting forces, cutting temperatures, and surface integrity of machined products. One of the most important mechanical properties is the material flow stress, which is governed by field variables including strain, strain-rate, and temperature. Due to the presence of high values of field variables in machining, it is extremely important to evaluate the performance of different material models, typically developed at much lower strains, strain-rates and temperatures. In addition, this study discuses the importance of history dependency in material flow stress and compares the performance of three commonly-employed material constitutive models including Johnson-Cook's (J-C), Oxley's, and Maekawa et al.'s history dependent models. It is demonstrated that for b.c.c. metals, due to very short period of time available for a microvolume of workpiece material to pass through the deformation zone, loading path (history) plays no significant role in changing the flow stress. In addition, in simulation of machining, extrapolation of these material model equations is possible.

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