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Journal ArticleDOI

Identification of constitutive parameters for thin-walled aluminium tubes using a hybrid strategy

TL;DR: In this paper, a hybrid strategy to determine constitutive parameters for thin-walled tubes based on experimental responses from hydraulic bulge tests is presented, where initial guesses of material parameters are generated quickly by a theoretical method, then they are input to an inverse framework integrating Gauss-Newton algorithm and finite element method.
Abstract: The paper presents a hybrid strategy to determine constitutive parameters for thin-walled tubes based on experimental responses from hydraulic bulge tests. This developed procedure integrates the analytical model, finite element analysis and gradient-based optimization algorithm, where initial guesses of material parameters are generated quickly by a theoretical method, then they are input to an inverse framework integrating Gauss-Newton algorithm and finite element method. The solving for this inverse problem leads to a more accurate identification of material parameters by reducing the discrepancies between simulated results and experimental data. To evaluate its feasibility and performance, hydraulic bulge tests with different end-conditions for annealed 6060 and 5049 aluminium tubes are carried out. The strength coefficient and hardening exponent are determined using the hybrid strategy based on the collected measurements in the experiment. These material parameters are used to compare with those obtained by a single analytical model and inverse model. The comparison validates that the proposed hybrid strategy is not sensitive to starting points and can improve the calculation efficiency and determine more accurate constitutive parameters.
Citations
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Journal ArticleDOI
TL;DR: In this article , a hybrid strategy for the identification of material parameters of constitutive models is presented, which employs an artificial neural network that is trained with data obtained from the material model, more precisely speaking, from different solutions of the direct problem for homogeneous states of deformation.
Abstract: A hybrid strategy for the identification of material parameters of constitutive models is presented. One main challenge in the context of classic optimisation-based parameter identification schemes is the generation of adequate starting values for the multi-objective optimisation procedure. We address this issue by employing an artificial neural network that is trained with data obtained from the material model, more precisely speaking, from different solutions of the direct problem for homogeneous states of deformation. As a result, a solution of the inverse problem of parameter identification can be approximated with the help of a neural network processing experimental data. This approximate solution is used as a starting value for a subsequent, classic optimisation-based parameter identification approach. One key advantage of this strategy is that a network only has to be trained once per material model and can subsequently be applied for different materials. A rather sophisticated material model, incorporating gradient-enhanced damage coupled to plasticity in a geometrically non-linear setting, is used to demonstrate the capabilities of this approach. Two different strategies for the generation of training data are investigated and compared, and the neural network’s hyperparameters are optimised for improved prediction capabilities. In view of the calibration of material parameters related to the non-locality of the model, the obtained set of parameters is again considered as a starting value for a final optimisation step, where we consider inhomogeneous states of deformation and digital image correlation data. • Comprehensive hybrid multi-stage optimisation framework for parameter identification combining the strengths of machine learning techniques and classic optimisation algorithms. • Neural network-based prediction of high-quality sets of constitutive parameters, automatically refined by subsequent application of error square minimisation algorithms. • Proposed neural network framework allows for the consideration of any number of experimental loading path sequences such as modes of deformation, modes of loading/unloading, temperature levels, etc. • Rigorous analysis of the neural network’s predictive qualities. • Application examples include a finite strain plasticity model including gradient-enhanced damage in a fully coupled manner. • Final optimisation step based on inhomogeneous states of deformation combining FEM and DIC due to the non-locality of some of the model parameters.

6 citations

01 Jan 2006
TL;DR: In this paper, the authors proposed a general applicable optimisation strategy that makes use of FEM simulations of metal forming processes, which can be applied to a hydroforming process in general and more specific to a specific metal forming problem.
Abstract: Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of finite element (FEM) simulations for processes has contributed to these goals in a major way. More recently, coupling FEM simulations to mathematical optimisation techniques has shown the potential to make a further giant contribution to product improvement and cost reduction. Much research on the optimisation of metal forming processes has been published during the last couple of years. Although the results are impressive, the optimisation techniques are generally only applicable to specific optimisation problems for specific products and specific metal forming processes. As a consequence, applying optimisation techniques to other metal forming problems requires a lot of optimisation expertise, which forms a barrier for more general industrial application of these techniques. In this paper, we overcome this barrier by proposing a generally applicable optimisation strategy that makes use of FEM simulations of metal forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming. Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design variables. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is generally applicable in a sense that it is not constrained to a certain type of metal forming problem, product or process. Also, any FEM code may be included in the strategy. Furthermore, the structured approach for modelling and solving optimisation problems should enable non-optimisation specialists to apply optimisation techniques to improve their products and processes. The optimisation strategy has been successfully applied to a hydroforming process, which demonstrates the potential of the optimisation of metal forming processes in general and more specific the proposed optimisation strategy.

1 citations

TL;DR: In this article , an inverse identification method of the constitutive parameters of S32760 duplex stainless steel were reversely modified using an equal shear zone model and an orthogonal cutting experiment.
Abstract: : The mechanical properties of S32760 duplex stainless steel under dynamic loading conditions at high strain rates are significantly different from those under quasi-static conditions. As a result of large strain, high strain rate, and high temperature, the analysis of the cutting process needs to factor in the influence of the viscous behavior of the material on the plastic deformation process. Based on the viscous effect of the two phases and the mixing rule, a mechanical threshold stress (MTS) constitutive model of S32760 duplex stainless steel considering the viscous effect is established to analyze the effect of strain rate on flow stress. An inverse identification method of the constitutive parameters based on Oxley’s theory is proposed. The constitutive parameters of S32760 duplex stainless steel were reversely modified using an equal shear zone model and an orthogonal cutting experiment. The results show that the viscosity of the austenite phase was greater than that of the ferrite phase, and the strain rate had the greatest influence on the viscosity effect in the constitutive model. The prediction error of the constitutive model constructed in this manuscript was less than 4%, which had high accuracy.
Journal ArticleDOI
TL;DR: In this article , a multi-objective optimization approach is proposed to identify hardening and damage parameters based on tensile and compression tests featuring the effects of tensiledominant and compressive-dominant stress states.
Abstract: This work addresses a modeling framework for identification of material parameters based on multi-objective optimization aiming at multiple mechanical tests or experimental data sets. The multi-objective problem is described within the Pareto theory, from which a strategy based on the global method solved in a normalized feasible objective space is proposed. The method maps the objective space onto a new normalized space where the optimal solution is found by minimizing a global error function. The strategy is illustrated by identification of hardening and damage parameters based on tensile and compression tests featuring the effects of tensile-dominant and compressive-dominant stress states.
Journal ArticleDOI
TL;DR: In this paper , an inverse identification method of the constitutive parameters of S32760 duplex stainless steel were reversely modified using an equal shear zone model and an orthogonal cutting experiment.
Abstract: The mechanical properties of S32760 duplex stainless steel under dynamic loading conditions at high strain rates are significantly different from those under quasi-static conditions. As a result of large strain, high strain rate, and high temperature, the analysis of the cutting process needs to factor in the influence of the viscous behavior of the material on the plastic deformation process. Based on the viscous effect of the two phases and the mixing rule, a mechanical threshold stress (MTS) constitutive model of S32760 duplex stainless steel considering the viscous effect is established to analyze the effect of strain rate on flow stress. An inverse identification method of the constitutive parameters based on Oxley's theory is proposed. The constitutive parameters of S32760 duplex stainless steel were reversely modified using an equal shear zone model and an orthogonal cutting experiment. The results show that the viscosity of the austenite phase was greater than that of the ferrite phase, and the strain rate had the greatest influence on the viscosity effect in the constitutive model. The prediction error of the constitutive model constructed in this manuscript was less than 4%, which had high accuracy.
References
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Book
25 Nov 2010
TL;DR: In this article, the convergence theory for inverse line search is used for line search and convergence theory of Inexact Line Search Exercises is used to define convergence conditions for unconstrained line search.
Abstract: Preface 1 Introduction 11 Introduction 12 Mathematics Foundations 121 Norm 122 Inverse and Generalized Inverse of a Matrix 123 Properties of Eigenvalues 124 Rank-One Update 125 Function and Differential 13 Convex Sets and Convex Functions 131 Convex Sets 132 Convex Functions 133 Separation and Support of Convex Sets 14 Optimality Conditions for Unconstrained Case 15 Structure of Optimization Methods Exercises 2 Line Search 21 Introduction 22 Convergence Theory for Exact Line Search 23 Section Methods 231 The Golden Section Method 232 The Fibonacci Method 24 Interpolation Method 241 Quadratic Interpolation Methods 242 Cubic Interpolation Method 25 Inexact Line Search Techniques 251 Armijo and Goldstein Rule 252 Wolfe-Powell Rule 253 Goldstein Algorithm and Wolfe-Powell Algorithm 254 Backtracking Line Search 255 Convergence Theorems of Inexact Line Search Exercises 3 Newton's Methods 31 The Steepest Descent Method 311 The Steepest Descent Method 312 Convergence of the Steepest Descent Method 313 Barzilai and Borwein Gradient Method 314 Appendix: Kantorovich Inequality 32 Newton's Method 33 Modified Newton's Method 34 Finite-Difference Newton's Method 35 Negative Curvature Direction Method 351 Gill-Murray Stable Newton's Method 352 Fiacco-McCormick Method 353 Fletcher-Freeman Method 354 Second-Order Step Rules 36 Inexact Newton's Method Exercises 4 Conjugate Gradient Method 41 Conjugate Direction Methods 42 Conjugate Gradient Method 421 Conjugate Gradient Method 422 Beale's Three-Term Conjugate Gradient Method 423 Preconditioned Conjugate Gradient Method 43 Convergence of Conjugate Gradient Methods 431 Global Convergence of Conjugate Gradient Methods 432 Convergence Rate of Conjugate Gradient Methods Exercises 5 Quasi-Newton Methods 51 Quasi-Newton Methods 511 Quasi-Newton Equation 512 Symmetric Rank-One (SR1) Update 513 DFP Update 514 BFGS Update and PSB Update 515 The Least Change Secant Update 52 The Broyden Class 53 Global Convergence of Quasi-Newton Methods 531 Global Convergence under Exact Line Search 532 Global Convergence under Inexact Line Search 54 Local Convergence of Quasi-Newton Methods 541 Superlinear Convergence of General Quasi-Newton Methods 542 Linear Convergence of General Quasi-Newton Methods 543 Local Convergence of Broyden's Rank-One Update 544 Local and Linear Convergence of DFP Method 545 Superlinear Convergence of BFGS Method 546 Superlinear Convergence of DFP Method 547 Local Convergence of Broyden's Class Methods 55 Self-Scaling Variable Metric (SSVM) Methods 551 Motivation to SSVM Method 552 Self-Scaling Variable Metric (SSVM) Method 553 Choices of the Scaling Factor 56 Sparse Quasi-Newton Methods 57 Limited Memory BFGS Method Exercises 6 Trust-Region and Conic Model Methods 61 Trust-Region Methods 611 Trust-Region Methods 612 Convergence of Trust-Region Methods 613 Solving A Trust-Region Subproblem 62 Conic Model and Collinear Scaling Algorithm 621 Conic Model 622 Generalized Quasi-Newton Equation 623 Updates that Preserve Past Information 624 Collinear Scaling BFGS Algorithm 63 Tensor Methods 631 Tensor Method for Nonlinear Equations 632 Tensor Methods for Unconstrained Optimization Exercises

837 citations

Journal ArticleDOI
TL;DR: In this paper, a hybrid algorithm was proposed to improve the performance of the gradient-based algorithm, which is strongly dependent on the initial set of results, in order to analyse the effectiveness of this optimization procedure, numerical and experimental results for an EN AW-5754 aluminium alloy are compared.

192 citations

Journal ArticleDOI
TL;DR: In this article, the authors present the results of an experimental study involving stainless steel specimens with diameter-to-thickness ratios between 23 and 52, where 15 specimens were designed and machined to achieve uniform loading conditions in the test section.

175 citations

Journal ArticleDOI
TL;DR: In this article, the characterization and specification of tubular material properties under hydroforming conditions is the main concern of this paper, and analytical improvements and their comparison with experimental findings on measurement of material properties of tubes under hydraulic bulging conditions are explained.
Abstract: Increasing acceptance and use of hydroforming technology within the automotive industry demands a comprehensive understanding of related issues such as material characteristics, tribology, part and tooling design. Among these issues, characterization and specification of tubular material properties under hydroforming conditions is the main concern of this paper. Analytical improvements and their comparison with experimental findings on measurement of material properties of tubes under hydraulic bulging conditions are explained. With these improvements, ‘on-line’ and continuous measurement of flow stress for tubular materials become possible, and are proven to be in good agreement with previous ‘off-line’ measurements presented by the authors.

110 citations

Journal ArticleDOI
TL;DR: In this article, an overall review of tube hydroforming studies is presented so that other researchers at different parts of the world can use it for further investigations in this area, and a guideline for employing finite element modeling (FEM) in the process analysis is proposed.

97 citations