Eliminating Forging Defects Using Genetic Algorithms

In this article, an optimization method for metal forging process designs using finite element-based simulation is presented. Using as entry parameters the specifications of the final product the so-called inverse techniques developed for optimization problems allows the calculation of the optimal solution, the design parameters that produce the required product. An evolutionary genetic algorithm is proposed to calculate optimal shape geometry and temperature. An example demonstrating the efficiency of the developed method is presented considering a two-stage hot forging process. It considers optimization of the process parameters to reduce the difference between the realized and the prescribed final forged shape under minimal energy consumption, restricting the maximum temperature.     

On the Objective Function Evaluation in Parameter Identification of Material Constitutive Models - Single-point or FE Analysis

This work deals with the identification of constitutive parameters by inverse methodology. Two different approaches are presented and analysed: the single-point and FE analysis. The use of these two different methodologies for the evaluation of objective functions in the identification process is still an open question and the interest in this field has been increasing among the metal forming community. To discuss this issue, two different constitutive models suitable for metals were used, i.e. an elastoplastic hardening model and an elastoplastic model with isotropic and kinematic hardening. The determined material parameters for the two models, the respective objective function values and the CPU time required to perform the simulations are presented and discussed.     

An inverse analysis approach to determine fatigue performance of bituminous mixes

In pavement engineering, fatigue resistance is evaluated using different tests protocols and different specimen geometries. The dependency of the specimen shape geometry on fatigue performance does not allow the evolution of intrinsic material properties. This paper deals with the calibration of intrinsic fatigue damage parameters for bituminous materials. A fatigue damage model is implemented. The decrease of stiffness of the specimen during fatigue tests for different laboratory testing conditions is calculated from finite element computations. An inverse optimization technique is used in order to adjust the fatigue damage parameters on bending fatigue tests. A Levenberg-Marquardt algorithm is implemented to fit the finite element specimen global response on experimental results. An application on bending laboratory fatigue tests is presented to illustrate the applicability of the method for pavement engineering.     

Shape optimization of the initial blank in the sheet metal forming process using equivalent static loads

In the sheet metal forming process, forming the final desired shape is difficult to obtain due to wrinkling, tearing, failure of material, etc. Various conditions of the forming process should be controlled for the desired shape. These conditions are the velocity of the punch, the friction factor, the blank holding force, the initial shape of the blank and others. Many researchers have conducted studies to predetermine the initial blank shape. The structural optimization technique is one of them. Non‐linear response structural optimization is required because non‐linearities are involved in the analysis of the metal forming process. When the conventional method is utilized, the cost is extremely high due to repeated non‐linear analysis for function and sensitivity calculation. In this paper, the equivalent static loads (ESLs) method is used to determine the blank shape which leads to the final desired shape and reduced wrinkling. The ESLs method is a structural optimization method where non‐linear dynamic loads are transformed into ESLs, and these ESLs are utilized as external loads in linear response optimization. The design is updated in linear response optimization. Non‐linear analysis is performed with the updated design and the process proceeds in a cyclic manner. An optimization formulation is defined for the examples, the formulated problems are solved to verify the proposed method and the results are discussed. Non‐linear analysis is performed using the commercial software LS‐DYNA, NASTRAN is used for calculating the ESLs and linear response optimization, and an interface program for LS‐DYNA and NASTRAN is developed. Copyright © 2010 John Wiley & Sons, Ltd.     

Design of heterogeneous mechanical tests: Numerical methodology and experimental validation

Standard material parameters identification strategies for constitutive equations generally use an extensive number of classical tests for collecting the required experimental data. Recently, new specimen geometries for heterogeneous tests were designed to enhance the richness of the strain field and capture supplementary strain states using full‐field measurement techniques. The butterfly specimen is an example of such a geometry, designed through a numerical optimization procedure where an indicator capable of evaluating the heterogeneity and the richness of strain information is used. The aim of this work is to experimentally validate the heterogeneous butterfly mechanical test in the parameter identification framework. Blanks of mild steel DC04 are cut with the butterfly geometry, and specific grips are designed. Tests are performed with Digital Image Correlation technique, and a Finite Element Model Update inverse strategy is used for the parameter identification, as well as the calculation of the indicator. The identification strategy is accomplished with the data obtained from the experimental tests, and the results are compared with quasi‐homogeneous tests.     

A hybrid experimental/numerical technique to extract cohesive fracture properties for mode-I fracture of quasi-brittle materials

We propose a hybrid technique to extract cohesive fracture properties of a quasi-brittle (not exhibiting bulk plasticity) material using an inverse numerical analysis and experimentation based on the optical technique of digital image correlation (DIC). Two options for the inverse analysis were used—a shape optimization approach, and a parameter optimization for a potential-based cohesive constitutive model, the so-called PPR (Park-Paulino-Roesler) model. The unconstrained, derivative free Nelder-Mead algorithm was used for optimization in the inverse analysis. The two proposed schemes were verified for realistic cases of varying initial guesses, and different synthetic and noisy displacement field data. As proof of concept, both schemes were applied to a Polymethyl-methacrylate (PMMA) quasi-static crack growth experiment where the near tip displacement field was obtained experimentally by DIC and was used as input to the optimization schemes. The technique was successful in predicting the applied load-displacement response of a four point bend edge cracked fracture specimen.     

Inverse methodology as applied to reconstruct local textile features from measured pressure field

One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior.In such cases the initial geometry is known,and all operators mapping the deformation are defined on the reference domain.However,there are situations in which the final configuration of a deformation might be known but not the initial.The inverse formulation allows one to determine the initial geometry of a domain,given its final deformation state,the material behavior law and a set of boundary conditions.In the present work we propose a method to reconstruct the mesoscale geometry of a textile based on its mechanical response during compaction.To do so,stress boundary conditions are acquired by means of a pressuresensitive film.By adopting an appropriate material law,the thickness and width information of the yarns are deduced from the pressure field experienced by the compacted textile.Unlike 3D scanning techniques such asβ-CT,the proposed method can be applied on any domain size,allowing long-range variability to be captured.To the best of the authors' knowledge,there are no previous works that use a pressure-sensitive film on a large domain to capture the input data for a shape reconstruction.This example application serves as a demonstration of a methodology which could be applied to other classes of materials.     

Identification of Elasto-Plastic Constitutive Parameters by Self-Optimizing Inverse Method: Experimental Verifications

In this paper, the Self-Optimizing Inverse Method (Self-OPTIM) has been experimentally verified by identifying constitutive parameters solely based on prescribed boundary loadings without full-field displacements. Recently the Self-OPTIM methodology was developed as a computational inverse analysis tool that can identify parameters of nonlinear material constitutive models. However, the methodology was demonstrated only by numerically simulated testing with full-field displacement fields and prescribed boundary loadings. The Self-OPTIM is capable of identifying parameters of the chosen class of material constitutive models through minimization of an implicit objective function defined as a function of full-field stress and strain fields in the optimization process. The unique advantages of the Self-OPTIM includes: 1) model independency that is expected to open up a wide range of applications for various engineering simulations; 2) capabilities of parameter identification based solely on global measurements of boundary forces and displacements. In this paper, the Self-OPTIM inverse method is experimentally verified by using two different shapes of specimens made of AISI 1095 steel: 1) dog-bone and 2) notched specimens under a loading and unloading course. Parameters of a cyclic plasticity model with nonlinear kinematic hardening rule and associated flow theory are identified by the Self-OPTIM. Multiple tests and the inverse simulations are conducted to ensure consistent performance of the Self-OPTIM. The identified parameters are successively used to reconstruct the material response.     

General design of the forming collar of the vertical form,fill and seal packaging machine using the finite element method

The basic part of the vertical form, fill and seal packaging machine is the forming collar. The forming collar provides the shape over which packaging film is smoothly formed at high speed into a cylindrical shape. Describing the forming collar geometry and hence its design is, however, remarkably difficult. This paper presents, for the first time, a flexible methodology for calculating the complete geometry of the film rather than the usually non‐complete collar over which the film is formed. That is, a methodology to calculate the film geometry over the collar including the seam along which the film is longitudinally sealed. The film geometry is calculated such that it has minimum deformation energy. Advantages of the proposed methodology include its great flexibility to generate collars with different configurations for different needs. Among the collar generation methods reviewed, the proposed methodology is the first that can systematically consider all collar configuration parameters such as the seam configuration, general package cross‐section, flat or straight part of the collar, collar back angle, etc. A means for obtaining the exact collar geometry is also demonstrated. This enables right‐first‐time and repeatable collar production and reduces the time and cost for producing next generation packaging machines. Copyright © 2010 John Wiley & Sons, Ltd.     

A Dirichlet–Neumann cost functional approach for the Bernoulli problem

The Bernoulli problem is rephrased into a shape optimization problem. In particular, the cost function, which turns out to be a constitutive law gap functional, is borrowed from inverse problem formulations. The shape derivative of the cost functional is explicitly determined. The gradient information is combined with the level set method in a steepest descent algorithm to solve the shape optimization problem. The efficiency of this approach is illustrated by numerical results for both interior and exterior Bernoulli problems.     

Analytical prediction of formed geometry in multi-stage single point incremental forming

Single Point Incremental Forming (SPIF) is a die-less forming process that can be economically used for low volume production of sheet metal components. One of the limitations of SPIF is the maximum wall angle that can be formed in a single stage. To overcome this limitation, Multi-stage Single Point Incremental Forming (MSPIF) is used to form components with large wall angles. When the tool is moved from out-to-in during any stage, material present ahead of it (towards the centre of the component) moves down rigidly. If this rigid body displacement is not considered during tool path generation for MSPIF, it leads to stepped/unwanted features. Predicting the component geometry after each stage helps in monitoring the shape being developed and in turn is useful in designing intermediate stages to form required final geometry with desired accuracy. In the present work, a simple methodology is proposed to predict rigid body displacement based on tool path and process parameters (tool diameter, incremental depth, sheet thickness) used. Tool and sheet deflections due to forming force are also considered to predict final geometry of the component. Proposed methodology is validated by comparing predicted profiles with experimentally measured profiles of high wall angle axisymmetric components formed using different materials and sheet thicknesses. Predicted profiles are in good agreement with experimental results.     

Solution of identification inverse problems in elastodynamics using semi-analytical sensitivity computation

The purpose of this work is to study a class of inverse problems that arises in solid mechanics areas such as quantitative non-destructive testing (QNDT) or shape optimization. The technique is based on the boundary integral equations (BIEs) used in the classical boundary element method (BEM), which are differentiated semi-analytically with respect to variations of the boundary geometry and used in an iterative search algorithm. The extension of this strategy is presented here for the case of elasticity in dynamics using the displacement or singular BIE, which allows to apply this strategy to QNDT problems based on vibrations or ultrasonics.The central point is the evaluation of the capability of solving numerically a QNDT problem such as the location and characterization of cavity and inclusion-type defects by measuring the dynamic response at an accessible boundary of the specimen. To test this capability, comprehensive convergence tests are made for the badness of the initial guess, the amount of supplied measurements, and simulated errors on measurements, geometry, elastic constants and frequency.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

A Methodology for the Design of Effective Cooling System in Injection Moulding

In this work, the forming behaviour of a commercial sheet of AZ31B magnesium alloy at elevated temperatures is investigated and reported. The experimental activity is performed in two phases. The first phase consists in free bulging test and the second one in analysing the ability of the sheet in filling a closed die. Different pressure and temperature levels are applied. In free bulging tests, the specimen dome height is used as characterizing parameter; in the same test, the strain rate sensitivity index is calculated using an analytical approach. Thus, appropriate forming parameters, such as temperature and pressure, are individuated and used for subsequent forming tests. In the second phase, forming tests in closed die with a prismatic shape cavity are performed. The influence of relevant process parameters concerning forming results in terms of cavity filling, fillet radii on the final specimen profile are analysed. Closed die forming tests put in evidence how the examined commercial magnesium sheet can successfully be formed in complicated geometries if process parameters are adequately chosen.     

MICROSTRUCTURAL MODELING AND NUMERICAL ANALYSIS FOR THE SUPERPLASTIC FORMING PROCESS

Superplastic forming is a manufacturing process during which a sheet is blow formed into a die to produce lightweight and strong components. In this paper, the microstructural mechanism of grain growth during superplastic deformation is studied. A new model, which considers grain growth, is proposed and applied to conventional superplastic materials. The relationships among the strain, strain rate, test temperature, initial grain size, and grain growth in superplastic materials are discussed. According to the proposed model, theoretical predictions for superplastic forming processes are presented, and comparison with experimental data is given. The new constitutive equation of superplasticity is introduced into a finite element method program to study superplastic blow forming. The effects of the geometric shape parameters of the die on the superplastic blow forming process are investigated, and the inhomogeneity in the thickness distribution of the specimen is analyzed.     

RC members strengthened with externally bonded FRP plates: A FE-based limit analysis approach

Fiber-reinforced-polymer (FRP) strengthening systems have been increasingly studied and used as an effective strategy to rehabilitate existing reinforced concrete (RC) structures. The present paper addresses the problem of predicting the load-carrying capacity of these strengthened structural elements. To this aim, in the framework of limit analysis a numerical methodology is presented which employs iterative finite element (FE) analyses with adaptive elastic parameters and a multi-yield-criteria formulation. The latter is adopted to appropriately describe the constitutive behaviour of the three main constituent materials, namely: concrete, steel reinforcement bars (re-bars) and strengthening FRP-laminates. The effectiveness of the promoted methodology is verified by comparison between numerical results and experimental findings regarding FRP-plated RC elements. Despite being based on a simplified approach which is affected by the underlying assumptions of limit analysis theory, the numerical procedure may be useful for the assessment of the load-carrying capacity in large RC structures repaired or retrofitted by FRP plates. Potentialities and limitations of the proposed methodology are discussed carefully.     

Stochastic optimization using a sparse grid collocation scheme

In computational sciences, optimization problems are frequently encountered in solving inverse problems for computing system parameters based on data measurements at specific sensor locations, or to perform design of system parameters. This task becomes increasingly complicated in the presence of uncertainties in boundary conditions or material properties. The task of computing the optimal probability density function (PDF) of parameters based on measurements of physical fields of interest in the form of a PDF, is posed as a stochastic optimization problem. This stochastic optimization problem is solved by dividing it into two problems—an auxiliary optimization problem to construct stochastic space representations from the PDF of measurement data, and a stochastic optimization problem to compute the PDF of problem parameters. The auxiliary optimization problem is solved using a downhill simplex method, whilst a gradient based approach is employed for solving the stochastic optimization problem. The gradients required for stochastic optimization are defined, using appropriate stochastic sensitivity problems. A computationally efficient sparse grid collocation scheme is utilized to compute the solution of these stochastic sensitivity problems. The implementation discussed, requires minimum intrusion into existing deterministic solvers, and it is thus applicable to a variety of problems. Numerical examples involving stochastic inverse heat conduction problems, contamination source identification problems and large deformation robust design problems are discussed.     

Wirkmedienbasierte Herstellung hybrider Metall‐Kunststoff‐Verbundbauteile mit Kunststoffschmelzen als Druckmedium

Working media based manufacturing of hybrid metal‐plastic‐compounds by using thermoplastic melt as pressurized media This paper presents an alternative manufacturing process for metal plastic hybrid parts. The focus is placed on the integration of injection moulding technology with hydroforming technology. The forming of bulging geometry and cup geometry from Aluminium and Steel sheets was examined. Particularly, the process parameters involved in forming such geometries including Injection pressure, volume flow rate, were measured, and their influence on the final shape of product as well on the strain distribution was analyzed.     

Finite element modelling and experimental investigation of single point incremental forming process of aluminum sheets: influence of process parameters on punch force monitoring and on mechanical and geometrical quality of parts

New trends in sheet metal forming are rapidly developing and several new forming processes have been proposed to accomplish the goals of flexibility and cost reduction. Among them, Incremental CNC sheet forming operations (ISF) are a relatively new sheet metal forming processes for small batch production and prototyping. In single point incremental forming (SPIF), the final shape of the component is obtained by the CNC relative movements of a simple and small punch which deform a clamped blank into the desired shape and which appear quite promising. No other dies are required than the ones used in any conventional sheet metal forming processes. As it is well known, the design of a mechanical component requires some decisions about the mechanical resistance and geometrical quality of the parts and the product has to be manufactured with a careful definition of the process set up. The use of computers in manufacturing has enabled the development of several new sheet metal forming processes, which are based upon older technologies. Although standard sheet metal forming processes are strongly controlled, new processes like single point incremental sheet forming can be improved. The SPIF concept allows to increase flexibility and to reduce set up costs. Such a process has a negative effect on the shape accuracy by initiating undesired rigid movement and sheet thinning. In the paper, the applicability of the numerical technique and the experimental test program to incremental forming of sheet metal is examined. Concerning the numerical simulation, a static implicit finite element code ABAQUS/Standard is used. These two techniques emphasize the necessity to control some process parameters to improve the final product quality. The reported approaches were mainly focused on the influence of four process parameters on the punch force trends generated in this forming process, the thickness and the equivalent plastic deformation distribution within the whole volume of the workpiece: the initial sheet thickness, the wall angle, the workpiece geometry and the nature of tool path contours controlled through CNC programming. The tool forces required to deform plastically the sheet around the contact area are discussed. The effect of the blank thickness and the tool path on the punch load and the deformation behaviour is also examined with respect to several tool paths. Furthermore, the force acting on the traveling tool is also evaluated. Similar to the sheet thickness, the effect of wall angle and part geometry on the load evolution, the distribution of calculated equivalent plastic strain and the variation of sheet thickness strain are also discussed. Experimental and numerical results obtained allow having a better knowledge of mechanical and geometrical responses from different parts manufactured by SPIF with the aim to improve their accuracy. It is also concluded that the numerical simulation might be exploited for optimization of the incremental forming process of sheet metal.     

Analysis of the formability magnesium alloys using a new ductile fracture criterion

An innovative methodology for the determination of forming limits is proposed, based on the strain energy density criterion. In the first section of this paper a modification of the strain energy density criterion, that has mainly been applied for crack propagation in fracture mechanics, is performed, in order to become applicable in metal forming processes. In the second section, experimental methods and Finite Element (FE) analysis for the case of deep drawing forming process are used for the verification of the methodology. Based on the simulation methodology, the forming limits and some process parameters namely, forming temperature, punch radius, punch profile radius and strain rate sensitivity of magnesium alloys AZ31 and WE43 are determined. The optimization results for the studied case show that magnesium alloys have limited formability especially at room temperature; however the formability can be improved by forming at higher temperatures. Finally, formability is improved as the punch and punch profile radii increase up to an optimum value.