Fracture parameters calibration and validation for the high strength steel based on the mesoscale failure index

https://doi.org/10.1016/j.tafmec.2021.102929Get rights and content

Highlights

  • The mesoscale critical equivalent plastic strain as a failure index is proposed.

  • The failure index at the unit cell level to calibrate the fracture locus is used.

  • The fracture locus of the uncoupled phenomenological model is identified.

  • The ductile fractures parameters for BS, BT, RN and CN are validated.

  • The ductile fracture process of the SFC specimen is successfully simulated.

Abstract

Accurately obtaining the material parameters of the damage model is very important for the ductile fracture simulation of steel structures made of high strength steel (HSS). The combination of micromechanics with the uncoupled phenomenological fracture model can be used to obtain the material parameters of ductile fracture locus only from the uniaxial engineering stress-strain relationship. A micro failure index is generally used to link the material fracture under different multiaxial stress status. It is relatively difficult to describe the irregular micro-void evolution using the microvoid radius, and also difficult to tackle the micro void coalescence of the mesoscale using microvoid volume fraction. The mesoscale critical equivalent plastic strain (MCEPS) is proposed as the failure index at the unit cell level to calibrate the fracture locus of the uncoupled phenomenological model in this paper. The fracture locus of the HSS is calibrated by comparing the FE results with experimental data using the homogenized MCEPS and maximum MCEPS at the microvoid surface, respectively. The identified fracture locus is further validated against five stress status, including butterfly shear specimen, butterfly tension specimen, the tensile specimen with the symmetric round notch, tension specimen with a central hole in the middle, and Sandia fracture challenge specimens in 2014. The comparisons of predictions with the experimental results showed that the proposed MCEPS index can be used to obtain the material parameters of the ductile fracture locus.

Introduction

The high strength steel (HSS) can provide economical solutions for the highly loaded slender members applied in the long-span or high-rise structures [1], [2], [3]. The steel material generally has the option of either deformation or fracture when it reached its strength [4], [5]. The HSS is usually manufactured very stronger by reducing the plastic deformation through reducing grain size, work hardening, etc. but has less deformation ability. In addition to the concerns of fatigue performance [6], [7], [8], [9], the demands for the failure prediction of HSS structures or components are rising in the analysis and design because the HSS is always less ductile than the general mild structural steel. Material parameters identification of fracture models is the first step for the failure prediction of infrastructure made of HSS.

The failure of HSS is a progressive material deterioration due to the nucleation, growth, and coalescence of micro-voids [10]. The microvoids can be nucleated due to either matrix-particle de-cohesion or particle cracking. The microvoids nucleation is affected by the particle strength, size, and shape, as well as the hardening of the matrix material. The matrix-particle de-cohesion nucleation mechanism generally appeared for the soft matrix materials while the particle cracking nucleation mechanism generally occurred for the hard matrix materials. Besides, microvoids are easily appeared at large particles due to higher possibilities of defects and local stress fields generated by matrix plastic deformation. Noted that the nucleated voids are too small to have an obvious influence on the material macroscopic behaviors [11]. After the nucleation, the microvoids will become larger due to the plastic deformation. The micro void radius is proposed by Rice & Tracey in 1969 [12], and the void volume fraction is further adopted by Gurson in 1977 [13] to model the microvoid growth in terms of a perfect plastic matrix. The ductile fracture happened after the voids coalescence with the following two common modes [14], internal necking mode (Fig. 1 a-e), shear localization mode (Fig. 1 f-j).

The fracture models of steels generally consist of physically-based [12], [13], [15], [16], [17], [18], [19], [20] and phenomenological models [21], [22], [23], [24], [25], [26], [27], [28], [29]. The uncoupled phenomenological model [21], [22], [23], [24], [25], [26], [27], [28], [29], which assumed that the evolution of damage does not affect the effective stress-strain response of HSS before a fracture occurs, is generally adopted in engineering applications because the material parameters are more simple to be obtained compared with the physically-based model. The fracture locus of the uncoupled phenomenological damage model is highly related to the microvoid growth and coalescence process, which is dependent on the stress status and microstructures of the materials. Especially for low-stress triaxiality cases, large shape and relatively small volume changes are observed for the ductile fracture [14]. Hence, the critical equivalent plastic strain at the onset of fracture is the function of the stress triaxiality and the Lode (angle) parameter at the macro scale.

Although the parameters of the uncoupled phenomenological models are relatively easy to obtain, a series of experiments are needed to be conducted for each typical component to identify the parameters in the ductile fracture model. However, large civil structures are all different from each other and there is no serial production and the ductile performance of HSS from different steel grades, producers, manufacturing processes (cold-formed, hot rolled, etc.) varies a lot. It is also difficult to conduct all kinds of reliable experiments to generate different stress status through different initial specimen geometries or by applying different load combinations for typical parts in the civil engineering sector, such as welds, the heat-affected zone(HAZ), bolt, headed studs and fillet corners of cold-formed tube. The combination of mesoscale computational homogenization triggered by the physically-based model and uncoupled phenomenological model is promising to predict the ductile fracture of HSS from only the uniaxial stress-strain relationship [30], [31], [32]. The mesoscale computational homogenization method could be used to identify the fracture strain at different stress status for the calibration of the parameters of the uncoupled phenomenological model.

A mesoscale failure index is generally used to predict the material failure under different multiaxial stress status, such as uniaxial tension, uniaxial compression, plane strain tension, plane strain compression, pure shear, combined tension-shear, and biaxial tension. The basic assumption is that the critical value of the mesoscale failure index is kept constant under multi-axial and non-proportional loading. As mentioned earlier, the micro void radius is proposed by Rice & Tracey in 1969 [12] as the mesoscale index. Base on the scanning electron microscope (SEM) in Fig. 2 [33], it is relatively difficult to describe the micro-void evolution by the micro void radius because the microvoid evolution is quite irregular. The void volume fraction is further adopted as the mesoscale failure index by Gurson in 1977 [13] to alleviate the micro-void shape effects. The rising questions will be how to model the micro void coalescence, as shown in Fig. 1. Hence, an attempt is made in this paper to use the other mesoscale failure index to describe the material fracture considering the “robustness” characteristics, namely (1) simple enough for the numerical implementation; and (2) convenient enough for parameters calibration.

In this paper, the mesoscale critical equivalent plastic strain (MCEPS) is proposed as the failure index at the unit cell level to calibrate the fracture locus of the uncoupled phenomenological model. The fracture locus of the HSS is calibrated by comparing the FE results with experimental data using the homogenized MCEPS and maximum MCEPS at the microvoid surface, respectively. The identified fracture locus is further validated against five stress status, including butterfly shear specimen, butterfly tension specimen, the tensile specimen with the symmetric round notch, tension specimen with a central hole in the middle, and Sandia fracture challenge specimens in 2014.

Section snippets

Material parameters identification

To predict the ductile fracture of high strength steels, this paper divided the identification process into two stages:①Identify the relationship between equivalent plastic strain and uniaxial true stress for the isotropic J2 plasticity model;②Identify parameters of fracture strain under multiaxial stress states. Noted that the evolution of damage does not affect the uniaxial true stress-strain response of HSS before a fracture occurs.

Validation of fracture locus

To validate the identified fracture locus, the ductile fractures of butterfly shear (BS)specimen, butterfly tension (BT)specimen, the tensile specimen with the symmetric round notch(RN), tension specimen with a central hole in the middle(CN) are simulated. The results of FE simulation results are compared with experimental results[40], and also FE prediction using the calibrated MMC model based on the test series reported in this section [40]. Noted that the key areas of all specimens were

Sandia fracture challenge specimens in 2014

The ductile fracture process of the Sandia fracture challenge (SFC) specimen in 2014 [34] is also simulated to validate the identified fracture locus based on the proposed MCEPS failure index. The dimensions, finite element model, and boundary conditions of the SFC specimen are shown in Fig. 25 [34]. The force-crack opening displacement (COD) comparison between FE simulation and experimental results is shown in Fig. 26. A general good agreement is observed for both fracture locus. The fracture

Conclusion

An attempt is made to identify the parameters of the ductile fracture model conveniently from the uniaxial stress-strain relationship obtained from common coupon specimens. The following conclusions are drawn:

  • (1)

    It is relatively difficult to describe the irregular micro-void evolution using the microvoid radius, and also difficult to tackle the micro void coalescence in the mesoscale using void volume fraction. The mesoscale critical equivalent plastic strain (MCEPS) is proposed as the failure

Author contribution

Haohui Xin: Execution of the analytical study, Data analysis, Writing. José A.F.O. Correia: Validation. Milan Veljkovic: Validation. Filippo Berto: Writing - review.

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.

Acknowledgments

This research was supported by the National Natural Science Foundation (Grants #51808398) of the People’s Republic of China, project grant (POCI-01-0145-FEDER-030103) FiberBridge - Fatigue strengthening and assessment of railway metallic bridges using fiber-reinforced polymers by FEDER funds through COMPETE2020 (POCI) and by national funds (PIDDAC) through the Portuguese Science Foundation (FCT/MCTES); and, base funding - UIDB/04708/2020 and programmatic funding - UIDP/04708/2020 of the

References (40)

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