P.M. Dixit

Thermal stresses due to electrical discharge machining

The high temperature gradients generated at the gap during electrical discharge machining (EDM) result in large localized thermal stresses in a small heat-affected zone. These thermal stresses can lead to micro-cracks, decrease in strength and fatigue life and possibly catastrophic failure. A finite element model has been developed to estimate the temperature field and thermal stresses due to Gaussian distributed heat flux of a spark during EDM. First, the developed code calculates the temperature in the workpiece and then the thermal stress field is estimated using this temperature field. The effects of various process variables (current and duty cycle) on temperature distribution and thermal stress distribution have been reported. The results of the analysis show high temperature gradient zones and the regions of large stresses where, sometimes, they exceed the material yield strength.

Modeling of material removal and surface roughness in abrasive flow machining process

Abrasive flow machining process provides a high level of surface finish and close tolerances with an economically acceptable rate of surface generation for a wide range of industrial components. This paper deals with the theoretical investigations into the mechanism of abrasive flow machining (AFM) process. A finite element model is developed for the flow of media during AFM and the same is used to evaluate the stresses and forces developed during the process. Theoretical analysis to estimate the material removal and surface roughness obtained during AFM is also proposed. The theoretical results are compared with the experimental data available in the literature, and they are found to agree well.

On the analysis of the electrochemical spark machining process

The electrochemical spark machining (ECSM) process has been proved as a potential process for machining of low machinability high-strength electrically non-conducting materials, but the mechanism of material removal during the process, by and large, is not yet understood. In the present work, the electrochemical discharge is modelled as a phenomenon similar to that which occurs in arc discharge valves. This phenomenon is used to explain various experimental results, on the basis of circuit and arc discharge valve characteristics. The spark energy and the approximate order of hydrogen gas bubble diameter are computed by the proposed valve theory. Material removal rate is evaluated by modelling the problem as a 3-D unsteady state heat conduction problem. The problem is solved by the finite element method to compute the temperature distribution which is post-processed for estimating material removal per spark, overcut obtained in the machined cavity, and attainable maximum penetration depth. The conclusion drawn is that the application of valve theory to the ECSM process seems to be realistic. Estimated material removal rate, overcut and maximum penetration depth show a good agreement with experimental findings.

A continuum damage mechanics model for ductile fracture

Abstract Continuum damage mechanics theory together with large deformation elastic–plastic finite element analysis has been used to predict crack growth initiation in ductile materials. The damage growth law is based on experimental observations reported in the literature. A local crack growth initiation criterion is proposed. The criterion makes use of the critical damage as the continuum parameter and the average austenite grain size as the characteristic length. To test the validity of this criterion, experiments have been conducted on standard specimens and have also been simulated numerically. The proposed criterion has been used to predict the values of the critical load at crack growth initiation and the fracture toughness. The numerically predicted values compare favourably with the experimental values.

An analysis of the steady-state wire drawing of strain-hardening materials

Abstract A comprehensive investigation of the steady-state wire drawing process has been done to study the effects of various process variables on important drawing parameters and deformation, the process variables considered being the reduction ratio, the die semi-angle, the coefficient of friction and the back tension, whilst the drawing parameters studied are the die-pressure, the drawing stress and the separation force. The deformation is represented by contours of equivalent strain and of equivalent strain-rate. The quantitative effects of strain hardening on the drawing parameters and qualitative effects on the deformation are studied also. A comparison of the drawing parameters is made for three materials (copper, aluminium and steel).

Die design for axisymmetric extrusion

Abstract Determination of total extrusion power and die pressure distribution is very important for die design. In this work, an upper-bound model with strain hardening is proposed, the prediction of the extrusion power of which is as accurate as that determined by the finite-element method (FEM) and is in excellent agreement with published experimental results. The upper-bound model, when combined with the slab method, also predicts the die pressure distribution, which again is in reasonable agreement with FEM results. Further, the computational time taken by the combined upper-bound/slab method is significantly less than that for FEM. The proposed combined upper-bound/slab method is applied to compare eight different die shapes, namely, stream-lined (third and fourth-order polynomial, cosine and modified Blazynskis CRHS), elliptical, hyperbolic, conical and Blazynskis CRHS. Based on the consideration of total extrusion power (under optimal conditions), it is concluded that third- and fourth-order polynomial dies and the cosine die are the best amongst the profiles considered. Parametric study is carried out for the third-order polynomial die to study the effects of reduction ratio, friction factor and strain-hardening on the optimal die length and die pressure distribution.

Modeling and Simulation of Surface Roughness in Magnetic Abrasive Finishing Using Non-Uniform Surface Profiles

Surface roughness plays an important role in product quality, particularly in situations such as precision fits and high-strength applications. Magnetic abrasive finishing (MAF) is an advanced finishing process in which the cutting force is controlled by magnetic field. This process is capable of giving nanometer-scale surface finish. This paper describes modeling, simulation and analysis of the profiles of the surface obtained after MAF. The real-life surface profile is so complicated that a single parameter can not give a full description of surface quality. However, in the present work, the height of the surface profile distribution before MAF is considered to be Gaussian. The surface roughness model is developed which computes center-line average (R a ) surface roughness. The validity of this model is checked by comparison with the experimental results. A series of numerical experiments are performed using finite-element methods and surface roughness models of the process, to study the effect of flux density, height of working gap, size of magnetic abrasive particles and rotational speed of magnetic pole on the surface quality. Based upon the results, we concluded that R a values of the finished workpiece surface decrease with increase in magnetic flux density, size of magnetic abrasive particles and rotational speed of flexible magnetic abrasive brush. On the other hand, the surface roughness values increase with increase in the working gap.

Ductile fracture criteria and its prediction in axisymmetric drawing

Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. The ductile fracture criteria (P.F. Thomason, Ductile Fracture of Metals, Pergamon, 1990; S. Dhar et al., A continuum damage mechanics model for void growth and micro-crack initiation, Engineering Fracture Mechanics 53 (1996) 917) developed based on the microscopic phenomena of void nucleation, growth and coalescence along with a simple criterion (N.V. Reddy et al., Central bursting and optimal die profile for axisymmetric extrusion, ASME Journal of Manufacturing Science and Engineering 118 (1996) 579) based on the concept of the hydrostatic stress component at a point in the deformation zone falling to zero and compressive elsewhere are used to predict the fracture initiation in drawing (i.e. central bursting). Even though the first two criteria are based on microscopic description, the material parameters required are available for a few steels only and their determination involves difficult metallurgical experimentation. The above criteria used along with the results of Eulerian Rigid-Plastic and Elasto-Plastic formulations are presented in this paper. Finite element formulations for obtaining the generalized strain distribution and for obtaining the damage distribution by using the critical damage criteria are also presented. The present study shows that predictions based on the simple criterion are in good agreement with the experimental as well as numerical results published earlier and are, in general, conservative. Further, comparison of the predictions of the three criteria shows that the hydrostatic stress criterion is highly conservative and hence safe for die design.

A CONTINUUM DAMAGE MECHANICS MODEL FOR VOID GROWTH AND MICRO CRACK INITIATION

A damage mechanics model is proposed to study the void growth and crack initiation. J2 incremental flow theory along with a damage variable is used to model the material behaviour in elasto-plastic regime. Large deformation (large rotation and finite strain) finite element analysis is carried out for five different cases. In all the cases it is observed that the triaxiality and the plastic strain play an important role in void growth and crack initiation in ductile material. A failure curve is obtained for the material AISI-1090 spheroidised steel. Finally, it is concluded that the critical value of the damage variable can be taken as a crack initiation parameter.

A finite element analysis of flat rolling and application of fuzzy set theory

In this work, a model for steady-state plane strain cold rolling of a strain hardening material is proposed. The mixed pressure and velocity formulation is used and front and back tensions are included in the model. Roll deformation is taken into account by Hitchcocks formula and the friction model of Wanheim and Bay is used. Comparisons with the experimental results found in the literature are made to evaluate the accuracy of the present model. In the rolling process, material properties and friction coefficients are not known precisely and hence they can be treated as fuzzy numbers. Analysis with the fuzzy parameters is carried out to highlight the usefulness of such an analysis. A method to assess the reliability of a design is also proposed.