P.A.F. Martins

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.

Single‐point incremental forming and formability—failure diagrams

In recent work, the present authors constructed a closed‐form analytical model that is capable of dealing with the fundamentals of single‐point incremental forming (SPIF) and explaining the experimental and numerical results published in the literature over the past couple of years. The model is based on membrane analysis with in‐plane contact frictional forces but is limited to plane strain, rotationally symmetric conditions. The aim of the present paper is twofold: first, to extend the previous closed‐form analytical model into a theoretical framework that can easily be applied to the different modes of deformation that are commonly found in general single‐point incremental forming processes and, second, to investigate the formability limits of SPIF in terms of ductile damage mechanics and the question of whether necking does, or does not, precede fracture. Experimentation by the present authors, together with data retrieved from the literature, confirms that the proposed theoretical framework is capable of successfully addressing the influence of the major parameters of the SPIF process. It is demonstrated that neck formation is suppressed in SPIF, so that traditional forming limit diagrams are inapplicable to describe failure. Instead fracture forming limit diagrams should be employed.

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.

Friction in bulk metal forming: a general friction model vs. the law of constant friction

Abstract Commercially available finite-element programs for the simulation of bulk metal-forming processes usually model the frictional restraint acting at the interface between the workpiece and the tools according to the law of constant friction. Such description is often inadequate and does not represent the state-of-the-art in tribology. In the present paper it is shown that the application of the general friction model, developed by Wanheim and Bay, involves a major improvement in the ability to simulate processes where low tool-workpiece interface stresses may prevail. This is confirmed by experimental and numerical investigations into the upsetting of a semi-tapered specimen between parallel dies. Additionally, it has led to the proposal of a new ring-compression test geometry intended to complement the conventional ring test for the calibration of friction models under conditions where the normal stresses over considerable parts of the tool-workpiece interface may be lower than the yield stress of the material.

Strategies and limits in multi-stage single-point incremental forming

Multi-stage single-point incremental forming (SPIF) is a state-of-the-art manufacturing process that allows small-quantity production of complex sheet metal parts with vertical walls. This paper is focused on the application of multi-stage SPIF with the objective of producing cylindrical cups with vertical walls. The strategy consists of forming a conical cup with a taper angle in the first stage, followed by three subsequent stages that progressively move the conical shape towards the desired cylindrical geometry. The investigation includes material characterization, determination of forming-limit curves and fracture forming-limit curves (FFLCs), numerical simulation, and experimentation, namely the evaluation of strain paths and fracture strains in actual multi-stage parts. Assessment of numerical simulation with experimentation shows good agreement between computed and measured strain and strain paths. The results also reveal that the sequence of multi-stage forming has a large effect on the location of strain points in the principal strain space. Strain paths are linear in the first stage and highly non-linear in the subsequent forming stages. The overall results show that the experimentally determined FFLCs can successfully be employed to establish the forming limits of multi-stage SPIF.

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.

FINITE ELEMENT REMESHING: A METAL FORMING APPROACH FOR QUADRILATERAL MESH GENERATION AND REFINEMENT

The paper presents an automatic finite element remeshing system for quadrilateral elements consisting of modules for mesh generation, densification, smoothing and interpolation of field variables. The mesh generator takes into account the contour of the old mesh, eventual interference with dies and the plastic deformation of the material. An initial coarse mesh is created by utilizing a grid-based approach for creating well-shaped internal elements, in conjunction with a nodal connection approach based on constrained Delaunay triangulation, for linking with the boundary. Subsequent local mesh refinement is performed according to parameters depending on past, present and predicted future deformation related field variables; being, respectively, the strain gradient and strain rate distribution in relation with the velocity field, element size and quality. Smoothing is accomplished using an iterative Laplacian repositioning method. As illustrated in the presented examples this overall strategy ensures a robust and efficient remeshing scheme for finite element simulation of bulk metal-forming processes.

Accuracy, reliability and validity of finite element analysis in metal forming: a user's perspective

Purpose – The purpose of this paper is to provide industrial, education and academic users of computer programs a basic overview of finite elements in metal forming that will enable them to recognize the pitfalls of the existing formulations, identify the possible sources of errors and understand the routes for validating their numerical results.Design/methodology/approach – The methodology draws from the fundamentals of the finite elements, plasticity and material science to aspects of computer implementation, modelling, accuracy, reliability and validation. The approach is illustrated and enriched with selected examples obtained from research and industrial metal forming applications.Findings – The presentation is a step towards diminishing the gap being formed between developers of the finite element computer programs and the users having the know‐how on the metal forming technology. It is shown that there are easy and efficient ways of refreshing and upgrading the knowledge and skills of the users wit...

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.

An alternative ring-test geometry for the evaluation of friction under low normal pressure

Abstract Quantitative evaluation of the tribological conditions at the tool–workpiece interface in metal forming is usually accomplished by the ring-compression test. The popularity of the test can be attributed to its practical convenience including the fact that friction can be judged from deformation alone. Due to the geometrical design of the conventional ring-test, the interface stresses will, however, always be greater than the flow stress of the material, thereby impeding quantification of friction, and evaluation of the behaviour of lubricants, for processes where interface stresses below the flow stress of the material occur. This paper presents a new complementary ring-test geometry, which allows the characterisation of friction under low pressure conditions. Finite-element analysis in conjunction with metal experiments applying both the conventional and the modified geometry for different lubricants provides the validation for the general feasibility of the proposed test geometry.