P. A. Prates

Inverse Strategies for Identifying the Parameters of Constitutive Laws of Metal Sheets

This article is a review regarding recently developed inverse strategies coupled with finite element simulations for the identification of the parameters of constitutive laws that describe the plastic behaviour of metal sheets. It highlights that the identification procedure is dictated by the loading conditions, the geometry of the sample, the type of experimental results selected for the analysis, the cost function, and optimization algorithm used. Also, the type of constitutive law (isotropic and/or kinematic hardening laws and/or anisotropic yield criterion), whose parameters are intended to be identified, affects the whole identification procedure.

On the identification of kinematic hardening with reverse shear test

Abstract An inverse analysis methodology for determining the parameters of the kinematic law of sheet metals is proposed. The sensitivity of the load versus displacement curves, obtained by reverse shear tests of rectangular and notched specimens, to the kinematic law parameters are studied following a forward analysis, based on finite element simulations. Afterwards, an inverse analysis methodology using a gradient-based Levenberg–Marquardt method is established, by evaluating the relative difference between numerical and experimental results of the shear test, i.e. the load evolution in function of the displacements of the grips. The use of a notched specimen is proposed in order to allow an easy and suitable numerical representation of the boundary conditions of the shear experimental test. This methodology has proven to be appropriate for determining the parameters of the kinematic hardening law.

How to Combine the Parameters of the Yield Criteria and the Hardening Law

The numerical simulation of sheet metal forming processes needs the accurate identification of the material parameters, for a given constitutive model. This identification can follow different methodologies and different sets of experimental data can be used, which lead to distinct sets of material parameters. In order to accurately compare the results of several methodologies, it is necessary to guarantee uniformity of their presentation. In this work, the correspondence between sets of parameters of the Hill’48 criterion is explored. The meaning of the “isotropic values” of the parameters associated with the out-of-plane stresses components is discussed and a required condition is proposed, in order to properly compare numerical simulation results obtained by using different input sets of constitutive parameters, identified by different procedures. Finite element simulations of complex shaped forming process, involving strain-path changes, are carried out in order to support the analysis.

Model Prediction of Defects in Sheet Metal Forming Processes

Predicting defects is a challenge in many processing steps during manufacturing because there is a great number of variables involved in the process. In this paper, we take a machine learning perspective to choose the best model for defects prediction of sheet metal forming processes. An empirical study is presented with the objective to choose the best machine learning algorithm that will be able to perform accurately this task. For building the model, three distinct datasets were created using numerical simulation for three mild steel materials: mild steel, DH600, HSLA340. The numerical simulation was performed on the basis of sixteen input features representing characteristics of the materials. Moreover, two kinds of defects, springback and maximum thinning, each one is binary with 1 (defects) and 0 (non-defects) were considered in the simulator. The experimental setup consists of running MLP, CART, NB, RF and SVM algorithms using cross-validation for correctly choosing model parameters. The results were averaged in 30 runs and the standard deviations recorded. The initial conclusion is that the learning algorithm scores differently depending on the type of defect and conditions of the experiment. Although the preliminary results show good performance of the algorithms in simulated environment, a further study with real data will be addressed in future work.

Effect of numerical parameters on plastic CTOD

Fatigue crack growth (FCG) is associated with irreversible and non-linear processes happening at the crack tip. This explains different problems observed in the use of da/dN-?K curves, namely the inability to explain stress ratio and load history effects. The replacement of ?K by nonlinear crack tip parameters, namely the crack tip opening displacement (CTOD) is an interesting alternative. However, the determination of CTOD, using the finite element method, depends on different numerical parameters, not sufficiently studied so far. The objective here is to study the effect of these parameters on plastic CTOD, and therefore on da/dN-?CTODp curves. A transient behaviour was found at the beginning of numerical crack propagation which is linked to the formation of residual plastic wake. Therefore, a minimum number of crack increments is required to obtain stabilized values. On the other hand, the predicted ?CTODp decreases with the distance to crack tip. Close to the crack tip, sensitivity to the measured values is much higher, but it also exists at remote positions. In addition, the mesh has a relatively low influence on ?CTODp. Finally, the effect of the number of load cycles between crack increments greatly depends on material properties.

Numerical Determination of Fatigue Threshold from CTOD

The experimental procedure to obtain valid and comparable values of ΔKth is laborious and time consuming. The objective of this work is to determine ΔKth using a numerical approach. The CTOD is plotted versus load, and the fatigue threshold corresponds to the onset of plastic deformation. A parametric study was developed in order to understand the effect of material parameters on ΔKth.

Inverse analysis methodology on metal sheets for constitutive parameters identification

This work proposes an inverse analysis methodology for determining the constitutive models parameters, used to describe the plastic behaviour of metal sheets, from results of a single experimental biaxial tensile test on a flat cruciform sample. The proposed methodology is based on a direct analysis of finite element simulation results carried out for different combinations of material plastic properties. The biaxial test sensitivity to the in-plane r-value distribution was evaluated. An inverse analysis methodology was thus established, enabling the determination of the yield criterion parameters by evaluating the relative error between numerical and experimental results of the biaxial tensile test, namely the load evolution with the displacement and the equivalent strain distribution along the symmetry axes. Finally, the proposed methodology was numerically validated throughout the identification of Hill’48 yield criterion parameters for a material with a plastic behaviour well described by this criteri...