Prediction of fracture in press bend forming of aluminum alloy high-stiffener integral panels

https://doi.org/10.1016/j.commatsci.2011.02.034Get rights and content

Abstract

Aluminum alloy high-stiffener integral panels are widely used on modern aircrafts to meet the demand of light weight and high stiffness. Press bend forming is an important method of producing this structure, of which fracture on stiffeners is a severe forming defect. In this study, a series of ductile fracture criteria that have been successfully applied in the metal forming field are adopted, the constants of which are obtained by tensile tests of different specimens and their corresponded FEM simulations. Then all the criteria are implemented into ABAQUS with user subroutine. A set of press bending dies is designed, with which bend to fracture experiments of single stiffener and multi-stiffener specimens are carried out. By comparative analysis of the experiments and the FEM simulations including many ductile fracture criteria, the most suitable ductile fracture criteria for predicting the fractures in this forming process are determined. The reasons of the usability are also explained based on the mechanics of the fracture.

Highlights

► The constants of a series of fracture criteria are obtained. ► All the criteria are implemented into FE software and several fracture experiments are carried out. ► The most suitable ductile fracture criteria for predicting the fractures are determined. ► The reasons of the usability of the fracture criteria are also explained.

Introduction

Because of the light weight, high stiffness, and high structural efficiency, Aluminum alloy high-stiffener integral panels are widely used on modern aircrafts. Press bend forming is an important way of manufacturing integral panels, which has many advantages, such as low tooling cost, short cycle time and adaptability to different contours. Fracture is a severe forming defect in this forming process, and its occurrence may lead to great loss. Research on the fracture mechanisms and the prediction of the fracture appearance moment and position is very important to improve the production quality and efficiency.

Numerous attempts have been made to study the mechanisms of fracture [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], and many ductile fracture criteria have been proposed, most of which are based on the damage theory [1]. These ductile fracture criteria are related to the macroscopic variables associated with the process. In 1950, Freudenthal [2] derived a generalized plastic work criterion based on Von Mises stress and strain. In 1968, Cockcroft and Latham [3] proposed a fracture criterion based on the total plastic work per unit volume. In 1968, McClintock [4] developed a ductile fracture criterion by studying cylindrical holes under a prescribed history of applied principal components of stress and strain. In 1969, Rice and Tracey [5] introduced a stress triaxiality function to describe the growth of a spherical void in a general remote field. In 1972, Brozzo et al. [6] made a modification to the Cockroft–Latham criterion based on experiments which includes the influences of the maximum main stress and hydrostatic stress. In 1978, Norris [7] proposed a fracture criterion based on some tensile experiments and finite difference method analysis. In 1979, Oh et al. [8] modified the Cockcroft–Latham criterion by normalizing the maximum principal tensile stress by the equivalent stress. In 1980, Oyane and Sato [9] proposed a criterion which is derived from plasticity theory for porous materials. In 1981, Atkins [10] modified the Norris criterion [7] to accommodate sheet metal behavior. In 1981, Le Roy et al. [11] proposed a ductile fracture model by examining void growth and accumulation of damage during tensile loading. In 2003, Toribio and Ayaso [12] studied the fracture performance of axisymmetric notched samples taken from pearlitic steels with different levels of cold drawing. They proposed a materials science approach to the phenomenon so that the strongly anisotropic fracture behavior of the steels with high level of strain hardening is rationalized on the basis of the markedly oriented pearlitic microstructure of the drawn steels which influences the operative micromechanism of fracture in this case. In 2007, Huang et al. [13] established a practical 3D-FE model for the investigation and understanding of the splitting spinning process. They introduced the shear failure model predict whether to fracture in the radial direction. In 2009, Zhan et al. [14] built finite element models for predicting rupture failure in the shear spin-forming, splitting spin-forming and tube-bending processes by embedding the Lemaitre and Cockcroft–Latham (C&L) criteria into ABAQUS FE software. Their results show that the Lemaitre criterion is better than the C&L criterion at accurately predicting the position at which damage will occur and its distribution for both spin-forming and tube bending.

The ductile fracture criteria predict the fractures based on the changes of the stress, strain and plastic deformation energy of the forming process, which can be extracted from the FEM simulation results. Therefore, the ductile fracture criteria can be used together with the FEM simulations to predict the fractures [15]. Numerous researchers [16], [17], [18], [19], [20], [21], [22] have worked on this issue, and fractures in different forming processes have been predicted correctly using suitable criteria. Takuda et al. [16], [17], [18] used the embedded Oyane criterion predicted the fractures in bore expanding, deep drawing of magnesium alloy, and forming limit experiments successfully. Goijaerts et al. [19] used many criteria to predict the material failure in the blanking process. Shim et al. [20] found that the Cockcroft–Latham criterion gives the best prediction in the blanking process by comparative study. Bao and Wierzbicki [22] performed many experiments including upsetting and tensile tests on the 2024-T351 alloy to evaluate the validity of different ductile fracture criteria.

But the existing ductile fracture criteria are only successful when they are both characterized and applied under similar loading conditions [23]. Because of the complexity of the mechanics of fractures, no one criterion is universally suitable. The critical values of each criterion for the same material under different stress states are different. Therefore, selecting the suitable criterion and the critical values according to the specific problem is the key to predict the fractures. Because the stiffener shapes and their connection structures are various, the stress states of the stiffeners in the press bending process are very complicated, and the stress states of the fracture position may also be different. Therefore, 10 widely used ductile fracture criteria are adopted in this study to predict the stiffener fractures. Then the comparisons between the experiments and the simulation results are performed and the most suitable criteria are chosen. In order to predict the fractures in the press bend forming of integral panels, the stress and strain history of the press bend forming process should be analyzed carefully to select a proper criterion, and the proper experiments need to be performed to obtain the constants of the criterion.

The first objective of this research is to calculate the critical value and constants of various ductile fracture criteria by the numerical method analysis of tensile experiments and corresponding FEM simulations. The second objective is to implement these criteria into the FEM simulation of press bend forming and identify the most suitable criteria based on the mechanics of fractures by comparative study of bend to fracture experiments and FEM simulations. This study introduces the ductile fracture criteria into the prediction of fractures in press bend forming of integral panels for the first time, and it will be of great importance to the process optimization in the future.

Section snippets

Expressions of ductile fracture criteria

Ductile fracture criteria contain the influences of the history of strain and stress, which can be expressed in a general form as0ε¯ff(σ)dε¯=Cwhere f(σ) is a certain function of the actual stress state, and when the integral value reaches the critical value C, the ductile fracture is supposed to happen. Different variables that affect the fracture are included in different criteria, such as hydrostatic stress, stress triaxiality (σmσ¯), and plastic strain. C is often considered as the material

Establishment of the press bending experimental system

Two single stiffener specimens including I-stiffener and T-stiffener specimens and two multi-stiffener specimens including parallely stiffened and crossedly stiffened specimens are designed with reference to typical structures of airplane integral panels. The dimensions of the cross sections are shown in Fig. 6. The lengths of the single stiffener specimen and multi-stiffener specimen are 500 mm and 300 mm, respectively. The material is aluminum 7B04-T7451, which is widely used on the

Conclusions

  • (1)

    Combined the experimental results of the tensile tests of two types of specimens with the corresponding FEM results, and calculated the constants of different ductile fracture criteria with the strain and stress data at the fracture position obtained from simulation results.

  • (2)

    Implemented the ductile fracture criteria into FEM simulations using user subroutine UVARM. By comparative study of the bend to fracture experiments and the simulation results, the applicability of different fracture

Acknowledgements

The authors would like to thank the National Natural Science Foundation of China (No. 51005010), the Specialized Research Fund for the Doctoral Program of High Education of China (No. 20091102110021) and the China Postdoctoral Science Foundation (No. 20100470186) for the supports given to this research.

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