Evaluation Study on Iterative Inverse Modeling Procedure for Determining Post-Necking Hardening Behavior of Sheet Metal at Elevated Temperature

Abstract

The identification of the post-necking strain hardening behavior of metal sheet is important for finite element analysis procedures of sheet metal forming process. The inverse modeling method is a practical way to determine the hardening curve to large strains. This study is thus focused on the evaluation of the inverse modeling method using a novel material performance test. In this article, hot uniaxial tensile test of a commercially pure titanium sheet with rectangular section was first conducted. Utilizing the raw data from the tensile test, the post-necking hardening behavior of the material is determined by a FE-based inverse modeling procedure. Then the inverse method is compared with some classical hardening models. In order to further evaluate the applicability of the inverse method, biaxial tensile test at elevated temperatures was performed using a special designed cruciform specimen. The cruciform specimen could guarantee that the maximum equi-biaxial deformation occurs in the center section. By using the inverse modeling procedure, the hardening curves under biaxial stress state are able to be extracted. Finally the stress-strain curves obtained from the two experiments are compared and analysis studies are provided.2 of 15 point. However, many sheet forming processes usually involve large deformation and can generate strains far beyond the necking point, so the stress-strain curve up to the necking point is not sufficient for numerical simulation procedures. Generally, the available pre-necking stress-strain curves are extrapolated to large strains using different hardening models [5]. It is obvious that the predicted post-necking hardening curve greatly depends on the choice of phenomenological constitutive models and one model that is best fitted to a certain material may not suits for another [6].Recently, numerous investigations have been made to acquire the hardening curve beyond diffuse necking by many researchers [7][8][9][10][11]. The initial attempt was made by Bridgman [7], who derived a set of analytical models for the distribution of stress and strain across the diffuse necking region for a round bar. However, the correction and compensation for stress and stress values of Bridgman's method is based on the measurement of evolving geometrical parameters of the necking area, which requires much experimental effort. Ling [8] and Zhang et al. [9] extended the research of Bridgman by proposing new models for determining the post-necking hardening behavior of strip specimen with rectangular section. Other researchers [10,11] further studied the necking problem experimentally based on Bridgman's work in more sophisticated ways. Currently, a new optical-numerical measurement techniques, i.e., the Digital Image Correlation (DIC) method, is used widely for obtaining full-field information for both in-plane displacements and strains of the test specimen and has been applied by many researchers for determining the post-necking hardening curve of uniaxial test [12,13], Scheider et al. [14] investigat...

Failure Mechanisms in Alloys

“…More specifically, the broad category of static overload includes more generic subjects also from the field of manufacturing-related topics, where the effect of deformation and fracture was studied as an important and undetached ingredient of the fabrication process per se (e.g., hot and cold working, machining). Therefore, the mostly "intense area" (Overload/Static) comprises studies concerning general deformation and fracture phenomena, as the result of instant loading/testing conditions [4,9,10,14,15,19] and studies related to manufacturing and production processes [6,7,12,13,16,20,22,25,26]. Testing and modeling procedures addressing the evolution of deformation and fracture during forming [7,13,26], the impact toughness, [4] and certain production process characteristics [25] are also included.…”

“…Therefore, the mostly "intense area" (Overload/Static) comprises studies concerning general deformation and fracture phenomena, as the result of instant loading/testing conditions [4,9,10,14,15,19] and studies related to manufacturing and production processes [6,7,12,13,16,20,22,25,26]. Testing and modeling procedures addressing the evolution of deformation and fracture during forming [7,13,26], the impact toughness, [4] and certain production process characteristics [25] are also included. Nevertheless, shear fracture processes that emerged in machining and chip formation are also part of this broader group of studies, relevant to manufacturing topics (see [12,16,20]).…”

“…(i) Casting and Metal Forming [6,7,11,13,15,19,[24][25][26] (ii) Machining [12,16,20] (iii) Chemical/Petrochemical [3,17,21,23] (iv) Heat Treatment [22] (v) General Plant Machinery [1,9,18,24] b. Fatigue and Cyclic Loading [8,9,18]; c. Corrosion and Environmentally Assisted Cracking [3,5,11,21]; d. Wear and Surface Degradation [1,24,27].…”

Failure Mechanisms in Alloys

“…Combined (experimental, analytical, numerical model, etc.) [3,[6][7][8][12][13][14][15][16][18][19][20]22,25,26] As can be readily observed, the experimental and empirical approach is the dominant methodology of failure investigation. In addition, the emergence of numerical simulation, using finite element modeling (FEM), tends to be very popular in the prediction of material behavior and potential failure prevention.…”

A Novel Approach to Predict Wrinkling of Aluminum Alloy During Warm/Hot Sheet Hydroforming Based on an Improved Yoshida Buckling Test

“…In contrast to the conventional sheet hot stamping process, fluid pressure provides the through-thickness normal stress and assists the sheet formation process during warm/hot sheet hydroforming [12,13]. Therefore, the stress states under the influence of fluid pressure are of great significance for elucidating the forming mechanism of this technique [14][15][16][17] and also play an important role in selection of processing method, parameter optimization, and determination of the rules governing deformation during forming [18,19]. Consequently, it is necessary to analyze how the fluid pressure acts on the sheet during the forming process [20,21].…”