Determination of plastic properties of weld metals using an optimal regression of tensile and hardness test data

https://doi.org/10.1016/j.ijmecsci.2020.106196Get rights and content

Highlights

  • A new optimal regression process for acquiring the weld material properties is proposed by using tensile and hardness test data.

  • The regression function for the hardness distribution with local softening of weld zone is proposed.

  • The change in material properties resulting from the change in hardness showed a similar tendency in the two materials used in this study.

  • The weld material properties of two different pipes were estimated, and showed great accuracy compared to the finite element results and tensile test in terms of load-displacement curve.

Abstract

A new method is proposed to obtain the coefficients of plastic constitutive laws of weld metal via tensile test and hardness test. In this method, a general expression between hardness ratio and flow stress model coefficients is established. The predicted flow stresses for the differential areas are integrated over the entire section of tensile specimen to predict the tensile load. The optimal regression coefficients that minimize the difference between the predicted and experimental loads are derived using the Nelder-Mead simplex direction search algorithm. The constraint for the diffuse necking strain is applied in the convergence procedure to avoid the ‘mystical’ material property shown as non-unique solution. The material constants obtained from the proposed method are independent of the width of tensile specimen. The difference of tensile loads between finite element analysis results using the determined material constants and the experiment was less than 8 %. As the derived material constants were shown to be consistent and reliable, the methodology can be applied to general line welded parts.

Introduction

In the joining of two sheet metals, the welding process (e.g., laser welding and high-frequency welding) is used for weight and process cost reduction [1], [2], [3], [4], [5]. The material properties of the weld zone (WZ) are inhomogeneous due to the hardening or softening of the base material (BM) by heat generated during the welding process [6], [7], [8], [9]. Since these inhomogeneous zones may cause failures during the forming process [10], [11], [12], numerical analysis of the forming process of weld parts is required with an accurate plastic constitutive model defining the stress-strain relationship of material.

Indentation techniques are normally adopted to identify the material properties of local area [13], [14], [15], [16]. Yang et al. (2005) [17] used the indentation method to obtain the yield and tensile strengths of the WZ; however, the overall stress-strain relationship could not be acquired. Lee et al. (2005) [18] and Evdokimov et al. (2018) [19] proposed a methodology for material property evaluation using the spherical indentation technique. Since acquiring the load-displacement curve is quite difficult because of the frame compliance effect [20,21], the effect of frame compliance on the load - depth curve should be calibrated before the test. Also, as the material property estimation using indentation techniques requires a complex regression function consisting of FEA solutions for various material properties, if the plastic constant model is changed, the regression function must be reestablished [18,22].

On the other hand, the tensile test method has the advantage of obtain the accurate stress - strain relationship directly without the calibration of load frame compliance effect. Kim et al. (2004) [23] obtained the material properties of weld zone using a tensile specimen comprising of a weld zone only. However, it is difficult to fabricate the tensile specimen when the width of weld zone is too narrow. Cheng et al.(2007) [24] proposed an experimental method for acquiring the material properties of the weld zone of tailor-welded blanks. They used a real-time microscopic video recording system to capture the deformation of tensile specimen during tensile test. However, their methods still require additional equipment. Abdullah et al. (2011) [25] proposed the rule of mixtures: a method of predicting the material properties of a fusion zone (FZ) with tensile tests. Abdullah's method, however, assumes the entire weld zone as FZ, thus, preventing the precise acquisition of material properties. Zhan et al. [26] predicted the stress distribution of the FZ and heat-affected zone (HAZ) by modifying the rule of mixtures with hardness testing and dividing the WZ into several sections. The material properties derived by the proposed method, however, depend on the size of tensile specimen, requiring the measurement of the WZ area. In addition, the continuous distribution of stresses in the WZ cannot be obtained.

The method of dividing the WZ into several sections is often used to apply the discrete material properties of the WZ into the FEA model [27], [28], [29]. Lee et al. (2005) [30] used this method to apply the WZ properties, using a FEA model for predicting the overload failure of spot-welded specimens. On the other hand, Ren et al. (2012) [31] divided the WZ of electric resistance welded (ERW) tube into four sections and analyzed the tube bending process using the WZ properties obtained from the rule of mixtures. In this case, since averaged material properties are applied to each section of the WZ, the accurate material properties cannot be applied to the FEA model. Furthermore, applying discrete weld material properties may result in discontinuous stress distribution, degrading the reliability of the FEA solution.

A mapping method has been used to apply continuously distributed material properties into FEA models [32,33]. Ficquet et al. (2015) [33] investigated the size influence of flaws on residual stress by measuring the residual stress of a butt-welded tube and mapping it onto an FEA model. Compared to the section discretization method, the mapping method can be numerically implemented in an easier manner and has advantages when applying complex distributions of material properties. However, the continuous distribution of material properties is needed.

This study proposes a method for the acquisition of coefficients of the WZ plastic constitutive model using the tensile and hardness tests. Tensile and hardness tests are performed to obtain the tensile load-displacement (P - δ ) curve and hardness distribution of the WZ. Consequently, a general equation describing the relationship between hardness and material properties is established. The differential load acting on a local area of the WZ is calculated from material properties estimated with the proposed equation. The predicted tensile load is obtained from integration of differential load over the entire cross-section of weld specimen. Then, the regression coefficients of general equation that minimizes the difference between the predicted load and test load are determined according to the convergence procedure. For verification of the method, the process is applied to an electrical resistance welded (ERW) tube to derive the material constants of WZ. The derived relation between hardness ratio and material properties is used to apply the continuously changing material properties of WZ onto an FEA model for tensile test. P - δ  curves are then verified with experimental results.

Section snippets

Modified rule of mixtures

This section describes the methodology for estimating the coefficients of the flow stress model of WZ. Fig. 1 shows the overall process of the proposed method. Each step is as follows: (i) the tensile and hardness test specimens are fabricated from welded parts; (ii) the hardness distribution function and tensile load-gauge displacement (P - δ ) curve are acquired from the hardness test and tensile test for the WZ and base material (BM); (iii) the tensile load-gauge displacement curves are

Materials

Specifications and mechanical properties of the ERW tubes used in this study are presented in Table 2. σ ο,ΒΜ and σ TS,ΒΜ are the yield and tensile strengths of the base material, respectively; do and t are the outer diameter and thickness of the tube. The elastic modulus E was assumed to be E = 190 GPa based on the typical value of the elastic modulus of steel (E = 180 ~ 210 GPa). STKM15C tube was manufactured in accordance with the Korean Industrial Standard (KS) D3517, and SPFC780DP in

Finite element analysis for verification

Tensile FE analysis was performed using the commercial FEM software Abaqus 6.14 ver. [46] to validate the material properties of the WZ predicted using the proposed method. Fig. 7 shows the FE model for 1 / 4 of the tensile specimen and boundary conditions. The dimensions of the tensile specimen are same as listed in Table 4. A tensile speed of vy = 0.1 mm / s identical to the actual tensile test and symmetry conditions are assigned to each surface. Here, the size of the WZ element was set to

Microhardness test and tensile test results

The Vickers hardness distributions obtained from the micro hardness tests for the two tubes are shown in Fig. 8. Local softening is not observed in the STKM15C tube, and the width of the WZ is approximately 2.5 mm. At the WZ, an estimated increase of 55 % in hardness from the BM hardness of 207.5 HV is observed. Compared to STKM15C, SPFC780DP exhibited approximately 20 % local softening relative to the hardness of BM. The indentation imprints of SPFC780DP are compared in Fig. 9, where a

Conclusions

A new combined method, considering the use of rule of mixture to predict the continuous material properties of weld metal, was proposed. Here, a general expression of the relation between the coefficients of the flow stress model and the hardness ratio of base material / weld zone was established. Data from the hardness and tensile tests conducted on the weld zone were used to predict the material properties of weld zone. Furthermore, an FE modeling approach was proposed, which is distinct from

Author statement

Giyeol Han: Conceptualization, Methodology, Finite element analysis, Writing – Review & Editing.

João Henrique Fonseca: Experiments, Data curation.

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).

References (53)

  • M Kim et al.

    Spherical indentation method to evaluate material properties of high-strength materials

    Int J Mech Sci

    (2016)
  • Y Yang et al.

    The Measurement of Mechanical Properties of Pipe Steels in Service through Continuous Ball Indentation Test

    Procedia Eng

    (2015)
  • H Lee et al.

    A numerical approach to spherical indentation techniques for material property evaluation

    J Mech Phys Solids

    (2005)
  • A Evdokimov et al.

    Mechanical properties of dissimilar steel-aluminum welds

    Mater Sci Eng A

    (2018)
  • C Ullner et al.

    Effect and measurement of the machine compliance in the macro range of instrumented indentation test

    Meas J Int Meas Confed

    (2010)
  • A Nayebi et al.

    New procedure to determine steel mechanical parameters from the spherical indentation technique

    Mech Mater

    (2002)
  • J Kim et al.

    Finite element analysis for bursting failure prediction in bulge forming of a seamed tube

    Finite Elem Anal Des

    (2004)
  • CH Cheng et al.

    True stress-strain analysis on weldment of heterogeneous tailor-welded blanks-a novel approach for forming simulation

    Int J Mech Sci

    (2007)
  • K Abdullah et al.

    Tensile testing for weld deformation properties in similar gage tailor welded blanks using the rule of mixtures

    J Mater Process Technol

    (2001)
  • M Zhan et al.

    A method for establishing the plastic constitutive relationship of the weld bead and heat-affected zone of welded tubes based on the rule of mixtures and a microhardness test

    Mater Sci Eng A

    (2010)
  • J Chen et al.

    Multi-scale mechanical modeling of Al-steel resistance spot welds

    Mater Sci Eng A

    (2018)
  • J Lee et al.

    Modeling of failure mode of laser welds in lap-shear specimens of HSLA steel sheets

    Eng Fract Mech

    (2011)
  • K Paveebunvipak et al.

    Microstructure based modeling of deformation and failure of spot-welded advanced high strength steels sheets

    Mater Des

    (2018)
  • H Lee et al.

    Overload failure curve and fatigue behavior of spot-welded specimens

    Eng Fract Mech

    (2005)
  • N Ren et al.

    Constraining effects of weld and heat-affected zone on deformation behaviors of welded tubes in numerical control bending process

    J Mater Process Technol

    (2012)
  • J Lee et al.

    Change of the yield stress in roll formed ERW pipes considering the Bauschinger effect

    J Mater Process Technol

    (2017)
  • Cited by (7)

    • Integrative measurement method for tensile test based on DIC using modified second-order shape function

      2024, Measurement: Journal of the International Measurement Confederation
    • Physically-based constitutive models for hot gas pressure forming of laser-welded titanium alloy blank

      2022, Journal of Manufacturing Processes
      Citation Excerpt :

      Based on the assumption of the constant ratio of the microhardness to flow stress, continuous constitutive models for welded metals could be developed by building the relationships among the microhardness, flow stress and the weld shape [11]. More similar studies were also reported in references [12,13]. However, most of the constitutive models developed for welded metals are developed for deformation at room temperature.

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

      2021, International Journal of Mechanical Sciences
      Citation Excerpt :

      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.

    View all citing articles on Scopus
    View full text