J.M.C. Rodrigues

Fracture predicting in bulk metal forming

Abstract An important concern in forming is whether the desired deformation can be accomplished without failure of the work material. This paper describes the utilization of ductile fracture criteria in conjunction with the finite element method for predicting failures in cold bulk metal forming. Four previously published ductile fracture criteria are selected, and their relative accuracy for predicting and quantifying fracture initiation sites is investigated. Experiments with ring, cylindrical, tapered and flanged upset samples are performed to investigate the validity of the workability criteria under conditions of stress and strain similar to those usually found in bulk metal forming processes. The implementation of ductile fracture criteria into a rigid—plastic finite element computer program is presented. Local stress and strain distributions throughout the deformation are computed and compared with experimental measurements. A general good agreement is found. However, only two of these workability criteria have successfully predicted the location at which fracture initiates for all the upset tests performed in this work. The paper concludes with a discussion of the importance of the critical damage at fracture to remain independent from the technological processes.

Ductile fracture in metalworking: experimental and theoretical research

Abstract An important concern in metalworking is whether the desired deformation can be accomplished without failure of the material. This paper describes the utilisation of ductile fracture criteria in conjunction with the finite element method for predicting surface and internal failures in cold metalworking processes. Four previously published ductile fracture criteria are selected, and their relative accuracy for predicting and quantifying fracture initiation sites is investigated. Ring, cylindrical, tapered and flanged upset test samples are utilised for providing the experimental values of the critical damage at fracture under several different loading conditions. Two of the ductile fracture criteria are then utilised to predict the initiation site and the level of deformation at which surface or internal cracking will occur during finite element simulation of three types of metalworking processes, namely, radial extrusion, open-die forging and blanking. The analysis is made in conjunction with metal experiments, good agreement being found to occur.

On the utilisation of ductile fracture criteria in cold forging

In most cold forging operations, formability is limited by ductile fracture. This paper describes the utilisation of ductile fracture criteria in conjunction with the finite element method to predict when and where material is likely to fracture during cold forging. Several previously published ductile fracture criteria are selected, and their values of critical damage at the levels of deformation at which fracture starts are obtained through a series of experimental upset tests comprising cylindrical, tapered and flanged geometries. The experiments are also used to investigate the validity and the relative accuracy of each criterion under loading conditions of stress and strain similar to those usually found in cold forging.

Simulation of three-dimensional bulk forming processes by finite element flow formulation

This paper focuses from the fundamentals of finite element flow formulation to the main aspects of computer implementation and modelling of three-dimensional bulk forming processes. Fundamental research and development is based on a comprehensive analysis of a wide range of theoretical and computational subjects such as selection of elements, solution procedures, contact algorithms, and meshing and remeshing procedures. We also focus on elastic analysis of tooling and a simple algorithm is proposed for transferring the load across the die–workpiece contact interface. The overall study is supported by several specially designed, cold forming experimental parts that were manufactured under laboratory-controlled conditions. Comparisons between theoretical predictions and experimental results comprise a wide range of topics such as material flow, geometry, forming load and strain distribution.

Three-dimensional modelling of forging processes by the finite element flow formulation

Abstract This paper draws from the fundamentals of the finite element flow formulation to obtain aspects of computer implementation and modelling of industrial forging processes. Emphasis is given to a wide range of theoretical and numerical subjects such as selection of elements, solution procedures, contact algorithms, elastic analysis of tooling and interaction between two- and three-dimensional finite element models. New algorithms are proposed for the elastic analysis of tooling and for transferring history-dependent scalar and tensorial quantities from axisymmetric into full three-dimensional mesh system. The overall presentation is illustrated with the numerical modelling of two cold forging operations. Theoretical predictions obtained from the closed-die forging of a spider part (with predominantly complex three-dimensional material flow) are validated against experimental measurements obtained from laboratory-controlled manufacturing conditions. Assessment is provided in terms of material flow, geometrical profile, effective strain distribution and forging load. The latter is employed for illustrating the proposed methodology for performing the elastic analysis of tooling. The usefulness and efficiency of the algorithm for combining two- and three-dimensional finite element models is demonstrated by the numerical modelling of a typical multistage forging sequence utilized in the production of a Phillips-head screw.

Cold forging of gears : experimental and theoretical investigation

This paper draws from fundamental research on precision forging for the development of a flexible tool system for producing gear parts. The overall investigation makes use of conventional spur gears. Fundamental research is undertaken by using virtual prototyping modeling techniques based on the finite element method. The utilization of such techniques provides a better insight into the deformation mechanics during the forging process, by giving an accurate description of the material flow, filling conditions and corresponding geometrical profiles. The finite element method also enables the prediction of stresses and forces exerted on tools as well as the distribution of the major field variables in the forged parts. The application of tool design expertise in conjunction with the virtual prototyping modeling techniques made possible the development of a tool system for performing the experiments. The experimental work is mainly utilized for supporting and validating the theoretical investigation but a later stage can be further developed in order to put the proposed forging concept on an industrial basis.

Finite-element modelling of cold forward extrusion

Abstract Simulating metal forming processes using an updated Lagrangian finite-element formulation is not ideal when steady-state material flow conditions prevail. Firstly, repeated calculations of large non-linear finite element systems are needed for continuously updating the mesh, and secondly, remeshing operations must be undertaken to avoid excessive mesh distortion and to introduce localised refinements in regions where large gradients are likely to occur. The combined Eulerian–Lagrangian formulation overcomes these difficulties by using a temporary incremental mesh to calculate the strain and stress fields, coupled with a mathematical scheme to interpolate the updated mechanical state into a spatially fixed mesh. In this paper the cold forward extrusion of rods is analysed using both the updated Lagrangian and the combined Eulerian–Lagrangian finite-element formulations. The theoretical background for both formulations is reviewed, and the numerical results obtained with the two formulations are compared with experimental extrusion data. Excellent agreement is found for the flow pattern and for the distribution of strain within the plastically deformed region. In what concerns the extrusion load curve, the results demonstrate that the latter can be predicted more accurately using a combined Eulerian–Lagrangian finite-element formulation.

On the utilization of the reproducing kernel particle method for the numerical simulation of plane strain rolling

This paper draws from fundamental research on the reproducing kernel particle method (RKPM) to the development of an innovative numerical approach for analyzing rolling under plane strain conditions. The approach is based on the flow formulation for slightly compressible rigid-plastic materials and a detailed description of the method and its numerical implementation is presented with the objective of making clear the fundamental differences to the well-established finite element method for slightly compressible rigid-plastic materials. Special emphasis is placed on the construction of shape functions and their derivatives, enforcement of the essential boundary conditions and treatment of frictional effects, along the contact interface between the workpiece and the roll. The effectiveness of the proposed approach is discussed by comparing theoretical predictions with experimental data found in the literature.

Finite element remeshing in metal forming using hexahedral elements

Abstract Many finite element programs currently utilised in the three-dimensional simulation of bulk metal forming processes make use exclusively of tetrahedral shaped elements because of the advantages of such elements in meshing and remeshing operations. This paper addresses the problem of utilising hexahedral elements and discusses the relative performance between structured meshes of hexahedral elements, with initially perfect aspect ratios, and unstructured meshes of hexahedral elements obtained from decomposition of tetrahedral elements. The presentation is oriented to remeshing operations and its application to the numerical simulation of metal forming processes, therefore some supporting techniques related to this issue such as: recovery techniques, mesh quality assessment and data transfer, are also included. A metal forming example obtained from the three-dimensional numerical simulation of a fullering operation, utilised to reduce the cross-section of a bar and increase its length, is included with the objective of illustrating some of the algorithms and supporting the overall presentation.

Three-dimensional modelling of the vertical-horizontal rolling process

This paper discusses the utilisation of the slightly compressible finite element formulation to the numerical analysis of the vertical-horizontal rolling process. The first part of the paper details the basis of the plasticity theory for slightly compressible materials and presents an overview of its numerical implementation. Of particular interest in vertical-horizontal rolling are topics related to the prediction of the dog-bone shape when using a Eulerian formulation, the treatment of the frictional boundary conditions along the three-dimensional roll-workpiece contact interfaces and the modelling of the material streamlines within the plastically deforming region.The second part of the paper presents a comparison between theoretical predictions obtained by means of a special purpose computer program developed under the proposed approach and experimental results taken from the literature. Assessment is made in terms of the cross-sectional shapes, roll separating force and torque.