Evaluation of ductile fracture in welded tubes with tensile, hardness, flaring tests

https://doi.org/10.1016/j.ijmecsci.2021.106745Get rights and content

Highlights

  • The Lemaitre CDM is modified by damage parameter coupled with local hardness ratio.

  • The modified CDM for FZ and HAZ fracture prediction is verified by notch tensile and flaring tests.

  • A constitutive law in the welds is established with the rule of mixture based on local hardness ratio.

  • A regression function of hardness distribution to local hardening or softening in the welds is proposed.

Abstract

A continuum damage model (CDM) based on local hardness in welds is developed to predict fracture of welded tubes. A regression function of hardness distribution in the welds is proposed to establish hardness continuously through hardness mapping method in the finite element model. A constitutive model of the weld zone is determined by the rule of mixture, which estimates the flow stress of the welds from the hardness ratio. Coefficients of the flow stress model in the welds are validated by comparing finite element analysis (FEA) solution and experimental load - displacement data of tensile specimens. Softening after necking is considered by Lemaitre CDM. A damage parameter is newly given as a function of hardness ratio varying with angular position. Coefficients of damage parameter are obtained by the inverse FEA of tensile and flaring tests. The proposed method finely predicts the ductile fracture of welded tubes by considering local plastic properties and damage evolution.

Introduction

In recent years, automotive industry has used high strength steel welded tubes in vehicle suspensions and seat frames to reduce weight and costs [1], [2], [3]. The welded tubes are generally manufactured by electrical resistance welding (ERW) in the roll forming process, and exhibit inhomogeneous microstructures due to diffusion and cooling of weld heat. The welded tubes have a softening zone in the heat affected zone (HAZ) depending on the welding conditions [4], [5], [6], and the softening zone has a low strength, which may cause cracks in the forming process [7], [8], [9]. To predict the ductile fracture of welded tubes, it is necessary to consider the plastic constitutive laws and damage behavior of the weld zone.

Many researchers have studied to predict flow stress of the weld zone. Abdullah et al. [10] proposed a rule of mixture method (ROM) to estimate plastic properties in the weld zone. The plastic properties were determined using tensile test data, and the flow stress coefficients calculated from four different specimens showed consistent values. Zhan et al. [11] suggested a modified ROM using microhardness test data. In their study, the flow stress model coefficients were calculated by the discretization method; they divided the HAZ into several regions and considered average material properties of each division. Both studies above [10,11] required rigorous measurement of weld region for the accurate solution. Han et al. [12] proposed a novel ROM that required no measurement of weld region. Their study well predicted the flow stress of weld metals by using the hardness distribution regression and optimization algorithm. On the other hand, stress relaxation after necking had yet to be investigated.

The ROM is no longer valid after necking. Softening behavior and fracture can be considered using the damage model. Continuum damage models (CDM) have been studied in thermodynamic frameworks by many researchers [13], [14], [15], [16], [17], [18], and the CDM proposed by Lemaitre [13] has been widely used up to date. The Lemaitre CDM obtains damage parameters from the tensile test data and has industrial applications due to simple procedures. Malcher et al. [19] suggested that accuracy of fracture prediction may decrease under complex stress states which involve discrepancy in calibration point where the damage parameter is obtained. In this background, Malcher and Mamiya [20] modified the denominator of Lemaitre damage parameters by introducing an additional calibration point at a low stress triaxiality range. They well predicted fracture displacement than the original Lemaitre CDM in notch tensile test and shear test. Several studies [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] imply that stress triaxiality is not enough to describe ductility, especially at the shear dominant state; both considerations of stress triaxiality and the Lode parameter are required. These studies showed a good prediction of damage evolution at low stress triaxiality than the original damage model. Other works improved the Lemaitre damage model considering specific effects; pre-existing defects [31], strain rate [32], highly ductility [33], elevated temperature [34], and stress corrosion cracking [35]. However, there are few studies of CDM for ductile fracture on welded materials, except for creep [36,37] and fatigue [38,39] fields.

The weld zone has inhomogeneous microstructures and locally-different mechanical properties. In this work, a novel approach to use the relationship of local hardness ratio in the weld zone to base materials is presented for plastic constitutive law and damage evolution. A general regression function of hardness distribution in the welds is proposed, and hardness of the local region is defined in the FE model using the hardness mapping method [40,41]. The hardness ratio between arbitrary location and base materials is utilized for obtaining flow stress and damage parameter in the weld zone. The flow stress model coefficients in the local region of the welds are determined using the rule of mixture suggested by Han et al. [12]. The reliability of results is verified by comparing experimental and numerical load-displacement curves of tensile specimens with different specifications. Based on the Lemaitre damage model, a new damage parameter combined with the hardness ratio is introduced for the difference in damage evolution of the welds. The local damage parameter is reflected continuously in the FE model by the hardness mapping. The damage parameter is obtained by the inverse FEA of tensile and flaring tests. In the numerical implementation, the negative limit of stress triaxiality for damage evolution of Bao and Wierzbicki [42] and the effect of crack closure on compression stress state of Ladeveze and Lemaitre [43] are considered in user subroutine codes. Finally, the proposed method is verified by conducting a flaring test with a different tool angle and a notch tensile test.

Section snippets

Material

This study uses ERW high strength steel tubes, which have a weld width of 5 mm. Table 1 summarizes information on the welded tube. The yield and tensile strengths are σ 0.2% and σ TS, respectively. The outer diameter and thickness of the tube are indicated by do and t. Considering the elastic modulus E = 190 ~210 GPa of typical steel tubes, E = 190 GPa of the tube is assumed. The chemical compositions of the tube are shown in Table 2.

Tensile test

Tensile tests are carried out to determine the plastic

Methodology

Plastic properties and damage evolution in the weld zone depend on locations. Fig. 4 shows numerical procedures for ductile fracture prediction. Section 3.1 proposes a regression function of hardness distribution in the weld zone. Section 3.2 outlines the rule of mixture method to determine the plastic properties in the weld zone. The rule of mixture uses exponential function relationship of the flow stress model coefficients and the hardness ratio. Section 3.3 briefly describes the Lemaitre

Tensile test and fractography

Fig. 8 shows the engineering stress-strain curves of tensile specimens with standard (BM, WZ1) and non-standard (WZ2) specifications. WZ1, WZ2 specimens have the tensile strength 10% higher than BM specimens. For the WZ1, WZ2 specimens, the smaller the width, the lesser elongation, and the higher the tensile strength. The true stress-strain curve of BM tensile test data and the regression curve is represented in Fig. 8. The Swift model well-fits the experimental true stress-strain curves from

Conclusion

A numerical modeling method for predicting ductile fracture of welded tubes was developed. Hardness ratio to the base material in the welds was coupled to both plastic constitutive relationship and damage evolution law, respectively. A general regression function of hardness distribution in welds was developed, and its coefficients were obtained by a graphing calculator and optimization algorithm. Hardness mapping method based on the regression function was applied to FE model, thus continuous

CRediT authorship contribution statement

Yunseok Jang: Conceptualization, Methodology, Finite element analysis, Writing review & editing.

Youngseo Lee: Data curation, Experiment.

Minwoo Song: Investigation.

Dosuck Han: Supervision.

Naksoo Kim: Project administration.

Hyungyil Lee: Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work was supported by the Material Component Technology Development Program (2000 4983) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).

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