Effect of MnS inclusions on plastic deformation and fracture behavior of the steel matrix at high temperature

Vacuum 174 (2020) 109209

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Effect of MnS inclusions on plastic deformation and fracture behavior of the steel matrix at high temperature Can Wang a, Xin-gang Liu a, *, Jiang-tao Gui a, Ze-long Du a, Zhe-feng Xu b, Bao-feng Guo a a b

College of Mechanical Engineering (Yanshan University), Qinhuangdao, 066004, Hebei, China State Key Laboratory of Metastable Materials Science and Technology (Yanshan University), Qinhuangdao, 066004, Hebei, China

A R T I C L E I N F O

A B S T R A C T

Keywords: High temperature Inclusion Response surface method (RSM) Gurson–tvergaard–needleman Dynamic recrystallization (DRX) Deformation behavior Fracture

The effect of MnS inclusions on the plastic deformation and fracture behavior of a steel matrix at high tem­ perature was studied. The macroscopic mechanical properties of the material were analyzed using hightemperature uniaxial tensile testing. Numerical simulations were performed by combining the response sur­ face method and finite element simulations. The Gurson–Tvergaard–Needleman damage parameters and the void growth accelerating factor (k) were obtained at different temperatures. Through the fracture analysis and microstructure analysis of the samples at different temperatures, the reasons that affect the macro mechanical properties of the materials are obtained. At 900 � C–1200 � C, there was a large difference in strength and toughness between steels with and without MnS inclusions. The strength of the materials was determined by both the stress intensification caused by the MnS inclusions and stress softening due to dynamic recrystallization (DRX). The plasticity of the materials was jointly determined by the MnS inclusions promoting void initiation and growth, and the DRX inhibiting void growth and coalescence. Moreover, the accelerating factor of void growth (k) reflected the comprehensive effect of MnS and temperature on the evolution of voids in the matrix.

1. Introduction MnS is a typical non-metallic plastic inclusion commonly found in steel. These inclusions degrade the continuity and uniformity of the steel, which can result in the formation of cracks during hightemperature forging, which greatly degrade the mechanical properties of the material (e.g., plasticity and strength) and affect its application. Therefore, it is of great significance to study the influence of MnS in­ clusions on high-temperature plastic deformation and fracture behavior of the steel matrix. Andr�e [1] reviewed the source and control of non-metallic inclusions in steel and concluded that current steel-making processes inevitably result in a large amount of inclusions in the molten steel. Hence, many scholars have conducted extensive research on the effects of inclusions on the properties of the matrix under different conditions. Ghosh et al. [2] conducted Charpy impact tests to investigate the effect of inclusions on the impact properties of low-carbon high-strength low-alloy steels subjected to different heat-treatment processes. The experimental re­ sults showed that the presence of MnS inclusions had a detrimental ef­ fect on the upper shelf energy of the steel. Li et al. [3] performed low-rate tensile tests to investigate precharged low-alloy steel. The

tensile properties and fracture behavior at different tempering temper­ atures indicated that hydrogen-assisted microcracks were initiated at the lath boundaries and the interface between inclusions and matrix. In addition, cracks in the hydrogen-free samples grew via interfacial debonding. Cracks in the hydrogen-containing samples extended into the steel matrix along the direction of the vertical tensile stress. In addition, researchers have studied the influence of the shape, size, quantity, type, and distribution of inclusions. Wu et al. [4] investigated the influence of MnS inclusion morphology on local ductility, and per­ formed tensile experiments on samples with different orientations. The MnS inclusions transitioned from spindle shaped, to elongated, to ag­ gregates of tiny MnS particles, where the reduction of area obviously decreased and the area of ribbon-like fractures where most local deformation occurred also decreased during this transition. Shi et al. [5] proposed a special casting method that using Al and Ti compound to obtain high number densities of in situ endogenous nanoparticles of Ti3O5 and Al2O3 in order to control MnS inclusions’ shape and size. After that, the influence of MnS inclusions on the matrix properties will be decreased. Ghosh et al. [6] noted that inclusions and crystal textures in the microstructure of hot-rolled low-carbon steel sheets with different sulfur contents affected the anisotropy of the Charpy impact toughness. Coarse and elongated MnS inclusions were primarily responsible for the

* Corresponding author. E-mail address: [email protected] (X.-g. Liu). https://doi.org/10.1016/j.vacuum.2020.109209 Received 4 December 2019; Received in revised form 17 January 2020; Accepted 19 January 2020 Available online 22 January 2020 0042-207X/© 2020 Elsevier Ltd. All rights reserved.

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distribution of inclusions leads to inhomogeneous stress and strain dis­ tributions during deformation, which changes the fracture mechanism in the material; a higher degree of inhomogeneity in the distribution of inclusions resulted in lower strength and plasticity of the material. The GTN damage model has been used to theoretically study the high-temperature plastic deformation and fracture behavior of steel containing inclusions. Liu et al. [13] used the GTN damage model to simulate the crack initiation and propagation in 304 stainless steel containing MnS inclusions, and compared the predictions with experi­ mental results from uniaxially stretching the material at 900 � C. The results showed that MnS inclusions increased the number of induced voids at high temperatures and accelerated failure of coalescence to break. Determination of the GTN damage parameters is important to accurately describe the evolution behavior of materials during defor­ mation. Therefore, it is extremely important to obtain relevant param­ eters by appropriate methods. Wcislik [14] quantitatively calibrated the fF damage parameter using information determined from scanning electron microscopy (SEM) analyses, and then performed numerical simulation of static tensile tests with the obtained fF. The simulation results agreed well with the experimental data. Abbasi et al. [15] used the GTN damage model to investigate the ductile failure behavior of steel to predict the forming limit diagram (FLD) of an interstitial-free steel; they proposed a new method for reversing the parameters of the GTN damage model using the response surface method (RSM). The final test results agreed well with the predicted FLD. Ying et al. [16] opti­ mized GTN damage parameters based on RSM and a genetic algorithm, and proved that the GTN damage model is a suitable tool for evaluating sheet formability. Wang et al. [17] determined the four parameters of the GTN damage model using RSM and the least-squares method, which were applied to a FEM simulation. They found that the temperature has a significant effect on the void volume fraction, where f0, fc, and fF decreased with increasing temperature, and fN increased with increasing temperature. The FEM simulation results were consistent with those obtained from SEM analyses, which showed that RSM is a better method for determining the parameters than the GTN damage model. To date, many researcher have made great progress in exploring the influence of inclusions on the matrix at room temperature; however, detailed analyses of the influence of inclusions on the matrix at high temperature is lacking. This study aimed to investigate the effects of MnS inclusions on the plastic deformation and fracture behavior of the matrix at elevated temperatures. The macroscopic mechanical proper­ ties of the material were obtained using high-temperature tensile testing. The effects of inclusions on the fracture behavior of the matrix at different temperatures were investigated using SEM images of the fracture surface and the electron backscattered diffraction (EBSD) near the fracture. Based on the GTN damage model and the RSM, the effects of MnS inclusions on the mechanical damage evolution during defor­ mation of the matrix were investigated via numerical simulations.

Nomenclature macroscopic Von Mises stress equivalent stress hydrostatic stress Sij stress deviator q1, q2, q3 constitutive parameters f* modified damage parameter initial void volume fraction f0 fc the critical void volume fraction at which the void polymerization begins to occur k accelerating factor of void growth fF critical void volume fraction at the moment of failure dεp macroscopic plastic strain increment dεpl cumulative equivalent plastic strain increment m I second-order unit tensor M1, M2 relevant parameters affecting void nucleation A cavity nucleation coefficient controlled by strain fN volume fraction of inclusions standard deviation of void nucleation strain SN εN average strain during void nucleation

σeq σm σh

anisotropy in the pressure ductility and impact toughness of rolled plates. Mayer et al. [7]investigate the influence of refractory inclusions on the tensile strength of metal melt with the use of the molecular dy­ namics simulations. It is found that the strength of melt with a low volume fraction of inclusions is close to the strength of pure melt, while the increase of volume fraction provokes the higher system strength. With the rapid development of computer hardware and software, and numerical simulation technology, it is now possible to apply finite element method (FEM) simulations to the material damage evolution process. Guan et al. [8] analyzed crack propagation in bearing steel with non-metallic inclusions using the Voronoi cell FEM. The relationship between crack propagation, and the elastic modulus, and size and depth of the inclusions was obtained, which indicated that the cracks more easily propagated when the inclusions were softer, smaller, and shal­ lower. Gao et al. [9] use the finite element method to solve the crack–inclusion problem. Numerical results show that the stress in­ tensity factors at crack tip are always larger with an elastic inclusion than for a rigid inclusion. The crack propagation is easier near an elastic inclusion and the rigid inclusion is helpful for crack arrest. The meso-toughness fracture model, which is now widely used and developed, was proposed by Gurson in 1975, and then modified by Tvergaard and Needleman [10] to obtain the current Gurson–Tver­ gaard–Needleman (GTN) model. This model is applied to the study of ductile damage and fracture behavior of ductile porous materials. Cha et al. [11] determined the GTN parameters by tensile testing and established a FEM based on the elastoplastic material model. The ob­ tained simulation results were compared with those from forming ex­ periments, which showed that the GTN damage model could reliably quantify the amount of microcracks in the steel. Wang et al. [12] used to GTN damage model to study the effects of inclusions on the matrix deformation and fracture behavior considering the number and distri­ bution of inclusions. As the number of inclusions increases, the number and rate of void initiations increases, leading to early damage and fracture of the specimen, and a resulting decrease in strength. An uneven

2. Material and experimental methods 2.1. Material In this study, 304 steel containing MnS was produced by adding FeS powder and electrolytic manganese sheet to forged 304 steel raw ma­ terial, followed by vacuum smelting. The raw material was cut into appropriately sized round rods and placed in a vacuum smelting furnace. The rods were heated to 1600 � C and kept at this temperature for 10 min.

Table 1 The chemical compositions of Casting A and Casting B (wt.%). Element

C

Mn

Si

P

S

Cr

Ni

O

N

H

Casting A Casting B

0.061 0.061

2.70 0.86

0.55 0.55

0.029 0.029

0.30 0.018

18.06 18.06

8.05 8.05

0.0080 0.013

0.032 0.030

0.00047 0.00043

2

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Fig. 1. Microstructure and energy spectrum of Casting A and B: (a1), (b1) Photographs of Casting A, B microstructure; (a2), (b2) Elemental distributions of SEM of Casting A, B.

Fig. 2. Tensile specimen diagram.

Then, 182 g of FeS powder (85% purity) and 368 g of electrolytic manganese flakes were added to the melt in the vacuum furnace at 1400 � C. This sample is henceforth referred to as Casting A. The smelting process of Casting B was the same, but FeS powder and manganese sheet were not added to the raw material (i.e., the control sample) [13]. ICP-OES analysis, SEM observations, and energy dispersive spectroscopy (EDS) analyses were performed to determine the chemical composition, microstructure, and inclusions in the experimental samples [18]. See Table 1 and Fig. 1 for details. Fig. 1(a1) shows an image of the metallographic microstructure of Casting A. The inclusions were well dispersed in the matrix with an average size of about 2–8 μm. Fig. 1(a2) shows the results of SEM and EDS analyses. The EDS map shows that Mn and S elements were distributed at the same sites throughout the matrix. Considering the chemical elements and smelting process, it was concluded that these areas are MnS inclusions, which were quite spherical or spindle shaped. In Casting B (Fig. 1 (b1)), the material contained only a few inclusions. Fig. 1 (b2) shows that these impurities mainly contained Mn and Si; hence, they may be SiO2 and MnS inclusions.

deformation were observed using field-emission SEM (Zeiss Sigma 500). First, SEM observation was performed on the fracture surfaces of the two sample types subjected to different deformation temperatures using an accelerating voltage of 15 kV. Then, a wire cutting machine was used to make a cut along the axis of the fractured samples, which were embedded in resin phenolic. After mechanical grinding, the sample was placed on the sample stage of the microscope and tilted to 70� . The sample was analyzed at a voltage of 20 kV to obtain EBSD images near the fracture. 3. Numerical simulations The collection and analysis of the experimental data gives only the final fracture information and stress–strain curve of the tensile spec­ imen. However, these data cannot describe how the MnS inclusions affect the matrix during the entire deformation process. This is a com­ mon problem faced by scholars in the field. Therefore, we used the GTN damage model to investigate the effect of MnS inclusions on the toughness of the matrix during deformation. The fracture of metal ma­ terials is analyzed from the micro level, and the final fracture is mostly caused by micro pores. The meso damage model can reflect the gradual deterioration of the macro mechanical properties of metal materials due to the accumulation of internal damage with the increase of plastic deformation. GTN model is a typical meso damage model, which is very ideal for simulating the damage behavior and has a general applica­ bility. At the same time, the influence of inclusions on micro damage is also considered in GTN model.

2.2. High-temperature uniaxial tensile tests To clarify the influence of MnS inclusions on the matrix strength and plasticity at high temperature, a series of uniaxial tensile tests were performed on the two sample types using a Thermecamastor-z thermal simulator. The tests were performed at different temperatures, from 900 � C to 1200 � C, but at the same tensile rate (10 mm/s). The dimensions of the standard specimens for tensile testing were Φ 10 mm � 90 mm, while those of the intermediate standard interval segment were Φ 8 mm � 12 mm (Fig. 2). During the experiments, the temperature of the gauge length of the tensile specimens was first increased to 1200 � C at a heating rate of 5 � C/s, and kept at this temperature for 5 min to obtain a uniform original microstructure. The temperature was then lowered to a deformation temperature at 5 � C/s. After a heat preservation time of 5 min, the specimen was tested at a tensile rate of 10 mm/s, and then cooled rapidly to room temperature. To clarify the influence of MnS inclusions on the fracture behavior of the matrix, the microstructure of the tensile samples before and after

3.1. GTN damage model Gurson [19] proposed a microscopic damage constitutive model (i.e., Gurson model) that is suitable for ductile porous materials, and de­ scribes the softening and cracking of macroscopic materials via the initiation, growth, and coalescence of microscopic voids. The void vol­ ume fraction is introduced into the plastic yield criterion to describe the evolution of damage during plastic deformation, which is an ideal mathematical model to describe the ductile fracture process. Later, Tvergaard and Needleman [20,21] modified the model and obtained the 3

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Fig. 3. FEM diagram of sample.

widely used GTN damage model. The GTN yield function is expressed by equation (1). � � �2 � σ eq 3 q2 σ h 2 1 q3 ðf * Þ ¼ 0 φ¼ þ 2q1 f * cosh (1) 2 σm σm

σ eq ¼

pffiffiffiffiffiffiffiffiffiffiffi .pffiffi 2 3Sij Sij

pl

dε m ¼

ð1=q1 ​ fc Þ ðfF fc Þ

σ : d εp f Þσ m

(6)

ð1

With increasing plastic deformation, the original voids grow, and new ones nucleate. Therefore, the damage evolution process can be divided into two parts: changes in the void volume fraction caused by nucleation of new voids (dfn) and changes in the void volume fraction caused by the growth of original voids (dfg), as follows:

(2)

When q1 ¼ q2 ¼ q3 ¼ 1, the GTN damage model degenerates into the original Gurson model. When the equivalent void volume fraction f* ¼ 0, the material shows no degradation in toughness and the GTN damage model degenerates into the standard Von Mises yield function. Here, f*is a damage function describing the aggregate effect of void growth, and is defined as: � f f � fc f* ¼ (3) fc þ kðf fc Þ f > fc k¼

(5)

pl

f Þσm dε m ¼ σ : dεp

ð1

(7)

df ¼ dfn þ dfg

Assuming that the matrix material is incompressible, microvoid growth is macroscopically expressed as material volume expansion. Therefore, the increase in the void volume fraction caused by void growth is generally given by the volume expansion of the matrix ma­ terial. Hence, dfg is only correlated with the hydrostatic component of the macroscopic plastic strain:

(4)

dfg ¼ (1

In ductile porous materials, the plastic flow of metal is related both to the void volume fraction (f) and the cumulative plastic strain εplm of the matrix material. The equivalent plastic strain evolution equation of the matrix is obtained using the equivalent plastic work principle, as shown in equation (5).

(8)

f)dεp: I

Needleman [22,23] gave a general expression for dfn based on analysis of the factor controlling void nucleation: 1 dfn ¼ M1 dσ m þ M2 dσ : I 3

(9)

It is assumed that the nucleation mechanism and normal distribution are controlled by plastic strain. Hence, equation (9) degenerates to: (10)

pl

dfn ¼ M1 dσ m ¼ Adε m Here,

� " fN A ¼ pffiffiffiffiffi exp SN 2π

1 2

ε plm SN

εN �2 #

(11)

3.2. Numerical model The commercial software Abaqus/Explicit contains a subroutine for the GTN damage model. This study used the Abaqus simulation method to perform numerical simulations. The FEM analysis was performed using ABAQUS code. As the tensile specimens had axial symmetry, the FEM of the specimen was based on the 1/2 section of the specimen and modeled using an axisymmetric CAX4R element. For the gauge length segment (12 mm � 4 mm), the element shape was defined using a quadrilateral structural division technique. To ensure good simulation accuracy, the model gauge segment was mesh encrypted, with an average mesh density of 63.42 element/mm2. The model had 3799 nodes and 3658 elements. Before the simulation was run, the model was given an isotropic solid section property, a displacement constraint was imposed on the FEM, and a displacement load of 10 mm/s was applied in the y-axis direction. The proposed FEM for the uniaxial tensile test

Fig. 4. Mosaix puzzle of as-received Casting A for fN: (a) As-received Casting A; (b) The complete view of as-received Casting A; (c) One of the complete view of as-received Casting A; (d) Extracting MnS phase based on binary method. 4

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the damage evolution behavior of ductile materials. There are nine GTN parameters (q1, q2, q3, εN, SN, fN, f0, fc, fF). Based on other relevant works [24,25], the assumptions that q1 ¼ 1.5, q2 ¼ 1, q3 ¼ 2.25, SN ¼ 0.1, and εN ¼ 0.3 are thought to be realistic. Here, we used metallographic image analysis to obtain the value of fN, and RSM to calibrate the parameters f0, fc, and fF. Using a Zeiss intelligent automatic metallographic microscope (Axio Imager M2m) at 200 � magnification, the metallographic structure of the original sample (Fig. 4(a) blue region) was taken by the MosaiX puzzle of the whole sample. The ProImaging metallographic analysis software was used to analyze the statistics of the MnS content in each measured area (Fig. 4 (c)) based on the binary extraction method. Fig. 4 (d) shows the extraction of the MnS phase and MnS area statistics, from which we derived an average fN content of MnS in the original sample of 0.0124, with a standard deviation of 0.0027, i.e., fN ~ N(0.0124, 0.00272). The remaining three key damage parameters (f0, fc, fF) at elevated temperatures were calibrated using RSM. The RSM was developed by British statisticians Box and Wilson, and is a combination of mathe­ matical and statistical methods [26]. It is used to analyze the influence of multiple variables on testing, modeling, and data analysis. To date, there is no set of widely recognized methods for determining the GTN parameters. In this study, the three parameters at high temperature were difficult to determine. The values obtained using orthogonal tests are limited by the level of the factor, However, using RSM can avoid such problems while also considering the interaction between the parameters (e.g., the selection of f0 and fN affects fc and fF) [27]. Therefore, this study used the kind of simulation combining with FEM and the central composite design (CCD) of RSM. From the experimental and simulated σ–ε curves, three special points (stress peak point, failure point, strain intermediate point) are taken, as shown in Fig. 5. The response value equation (RN) is established by taking the difference between the stress or strain values of the corresponding points from the experimental and simulated data, as shown by equation (12). In this case, RN is the Nth (N ¼ 1, 2, 3, 4, 5, 6) response value equation, bi and bii are the interaction effect coefficients of Xi and Xii, where Xi and Xii are the GTN damage parameters (f0, fc or fF). Smaller absolute values of RN indicate a smaller difference between the corresponding points, where these points coin­ cide if RN ¼ 0. In this way, the consistency between the experimental and predicted curves can be obtained [16]. To save space, the data for Casting A at 1200 � C are merely listed. As shown in Table 2, 15 runs for three factors (f0, fc and fF) and three levels (low, medium and high) were obtained using CCD of RSM. The expression for the response value RN obtained using the exper­ imental design software Design-Expert 8.0.6 is as follows.

Fig. 5. Representation of six reference points regarded to obtain responses from simulation runs: Experimental stress peak point (P1), Numerical stress peak point (P1΄ ), R1 ¼ εp -εp΄, R2 ¼ σ p -σ p΄; Experimental strain intermediate point (P2), Numerical strain intermediate point (P2΄), R3 ¼ εm - εm΄, R4 ¼ σ m σm΄; Experimental failure point (P3), Numerical failure point (P3΄), R5 ¼ εf - εf΄, R6 ¼ σf - σ f΄. 4 X

RN ¼ b0 þ

4 X

bi Xi þ i¼1

i¼1

bii X 2i þ

3 4 X X

(12)

bij Xi Xj i¼1 j ​
specimen is depicted in Fig. 3. The simulation process used explicit dynamic analysis, which allows for large displacement deformations, where the damage effect can be considered and crack propagation can be simulated via stiffness reduction. To achieve a good consistency between the simulation and experi­ ments, the distribution of inclusions in the matrix was considered here. Since the distribution of inclusions was completely random in the ma­ terial after smelting, it satisfied the normal distribution fN ~ N (μ, σ2), where N is normality, and μ and σ are the average and standard devia­ tion of fN, respectively. The gauge length of the FEM was divided into 192 sections, as recommended in a previous study [12], where each section was assigned a different fN value. The fN value was obtained from metallographic analysis of the original experimental material, as described in Section 3.3. 3.3. Identification of GTN parameters Appropriate GTN parameters are necessary to accurately describe Table 2 The CCD arrangement and responses for tensile simulation of Casting A at 1200 � C. Runs

f0

fc

fF

R1

R2

R3

R4

R5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.9945 0.9918 0.9990 0.9918 0.9972 0.9945 0.9945 0.9945 0.9900 0.9918 0.9972 0.9972 0.9945 0.9918 0.9972

0.0300 0.0419 0.0300 0.0181 0.0181 0.0300 0.0500 0.0300 0.0300 0.0181 0.0419 0.0181 0.0100 0.0419 0.0419

0.2500 0.2399 0.2250 0.2399 0.2399 0.2250 0.2250 0.2000 0.2250 0.2101 0.2101 0.2101 0.2250 0.2101 0.2399

0.00817 0.00714 0.01475 0.00817 0.00714 0.00512 0.00512 0.00512 0.00817 0.00714 0.01947 0.00817 0.00512 0.00817 0.00714

1.05232 1.4009 1.63125 1.05232 1.4009 0.69712 0.69712 0.69712 1.05232 1.4009 0.45155 1.05232 0.69712 1.05232 1.4009

0.00284 0.0557 0.03397 0.01249 0.07454 0.02092 0.00208 0.06813 0.05611 0.01239 0.08024 0.006605 0.08429 0.07646 0.01613

1.23136 0.53118 0.594 1.18374 0.09833 1.97068 1.47658 1.45511 0.81571 0.52248 1.93123 1.27774 1.36656 0.82118 0.45882

0.01386 0.10426 0.05319 0.03315 0.14194 0.03672 0.00928 0.14138 0.12039 0.03192 0.14101 0.00504 0.17369 0.14475 0.03939

5

R6 24.9858 22.9828 16.317 24.6377 26.0665 27.1886 21.6373 26.4007 25.9699 26.2053 24.383 25.2547 19.9381 25.2127 15.4342

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Table 3 The final GTN damage parameters and k of Casting A and B at different temperatures. Temperature/� C 900 1000 1100 1200

Casting A

Casting B

f0

fc

fF

k

f0

fc

fF

k

0.0005 0.0026 0.0016 0.0032

0.0075 0.0010 0.0140 0.0181

0.1250 0.2000 0.2164 0.2399

5.6099 3.3451 3.2246 2.9241

0.0048 0.0060 0.0065 0.0082

0.0074 0.0100 0.0100 0.0102

0.0920 0.1200 0.2350 0.2678

7.7928 5.9697 2.9185 2.5481

8 > > > > > > > > R1 ¼ 450:6714 þ 908:3511f0 0:1896fc 0:9099fF þ 3:2092 � 10 11 f0 fc þ 8:2897 � 10 > > > > > þ1:2750 � 10 12 fc fF 457:5903f 20 þ 3:1595f 2c þ 2:0221f 2F > > > > > > R2 ¼ 381:4450 þ 900:6267f0 0:0620fc 0:2978fF þ 4:9474 � 10 10 f0 fc þ 3:7167 � 10 > > > > > þ8:8182 � 10 11 fc fF 518:8332f 20 þ 1:0341f 2c þ 0:6618f 2F > > > > > R3 ¼ 943:4189 þ 1891:3910f0 þ 38:6307fc þ 73:3928fF 49:1046f0 fc 75:5819f0 fF > > > < þ ​ 20:8031f f 947:5151f 2 þ 35:3071f 2 þ 1:6085f 2 c F

0

c

11

f0 fF

10

f0 fF

F

> R4 ¼ 1693:2010 þ 4033:8463f0 8799:2571fc 631:2516fF þ 8785:4089f0 fc > > > > > þ670:8401f0 fF 637:8527fc fF 2348:8284f 20 þ 3044:4656f 2c 25:1020f 2F > > > > > R5 ¼ 1436:1664 þ 2874:4310f0 þ 77:4509fc þ 147:6955fF 98:2093f0 fc ​ 151:1637f0 > > > > > > þ41:6062fc fF 1437:4399f 20 þ 67:4546f 2c þ 1:1950f 2F > > > > > R6 ¼ 2:5167 � 105 4:9243 � 105 f0 þ 21399:0503fc 61472:8705fF 19337:6813f0 fc > > > > > þ61915:4954f0 fF 9152:4437fc fF þ 2:4062 � 105 f 20 922:1493f 2c þ 442:0165f 2F > > > > > :

Appropriate GTN damage parameters were obtained by minimizing RN, while k was calculated using equation (4). The final GTN damage parameters and k of Casting A and B are shown for different tempera­ tures in Table 3. Then, the final GTN parameters and initial constitutive relationships for Casting A and B were used in the FEM established in Abaqus. The curves of the final experimental and numerical simulation analyses were in good agreement, as shown in Fig. 6. In Fig. 6(a), the positions of maximum damage (The result of experiment under 900 � C is just as an example) of the matrix in the fractured sample and FEM were similar.Hence, the GTN damage parameters determined by RSM accu­ rately simulated the process of deformation, damage, and fracture of the matrix at different temperatures.

fractured specimens to identify the fracture morphology. The SEM im­ ages of the fracture surface morphology obtained after testing at different temperatures are shown in Fig. 9. The fracture surface mor­ phologies of Casting A and B at 900 � C, as shown Fig. 9 (a1)-(a3) and (e1)-(e3), were quite different. The fracture of Casting A had a large cross-sectional area, but was shallow, indicating that only minor plastic deformation occurred during fracture, and the fracture time was rela­ tively short. SEM observation of the Casting A fracture surface showed many small dimples, which often contained MnS particles. The fracture surface of Casting A and B samples showed similar characteristics at the three other temperatures. It is known from fracture mechanics that microvoids are formed near cavity defects or secondary phase particles during deformation at room temperature. However, higher deformation temperatures can result in the movement of dislocations and migration of grain boundaries. During deformation, the initiation of voids occurs near defects, and also at grain boundaries, followed by growth and coalescence of the voids to form microcracks, which degrades the continuity of the matrix. Compared with Casting B, there were a large number of MnS particles in Casting A, which provided nucleation points for the initiation of voids, which promoted void nucleation, coalescence, and the formation of micro­ cracks, and accelerated the formation of macroscopic fractures. In conclusion, the presence of MnS particles accelerates fracture failure of the material [28,29]. The blue arrow in Fig. 9 (a3) shows many MnS inclusions clustering together. This is because the stress intensity at the interface between the MnS particles and the matrix is different from the interfacial strength of the matrix, where the weaker areas are more likely to debond and initiate voids. During increasing applied load, the voids grow, aggregate, and eventually the matrix fractures plastically to form a secondary crack. Compared to Casting A, the shear lip area, dimple diameter, and dimple depth of the fractures in Casting B were larger, and the number of dimples was smaller. Numerous ripple slip bands were observed near the dimple, as shown by the red arrow in Fig. 9 (e3), indicating that large

4. Results and discussion 4.1. Macroscopic mechanical properties and fracture analysis Fig. 7 shows the true stress–strain curve obtained from the uniaxial tensile test of Casting A and B samples at high temperature. The specific parameters of the experimental fracture strain (εf), peak stress (σ p), and reduction in area (ψ ) of the two samples at each temperature are shown in Table 4. In addition, Fig. 8 shows the difference in experimental performance indicators between Casting A and B at different tempera­ tures, where Δεf ¼ εAf - εBf , Δσp ¼ σ AP - σ BP , and △ψ ¼ ψ A ψ B . It can be seen from Table 4 and Fig. 8, in the range of 900–1200 � C, △εf < 0, and △σp > 0, indicating that the plasticity of Casting A was less than that of Casting B, while the strength was opposite; as the temper­ ature increased, Δεf increased (Δεf is negative), while Δσ p decreased. Therefore, as the temperature increased, the plasticity difference be­ tween Casting A and B increased, while the difference in strength be­ tween Casting A and B decreased. The specific reasons for this will be discussed in detail in Section 4.2 and 4.3. To investigate the effect of temperature and inclusions on matrix deformation and fracture behavior, SEM analysis was performed on the 6

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Fig. 7. True stress-strain curves of Casting A and B at different temperatures.

plastic deformation of the material. The combined effects of MnS in­ clusions on the matrix material determine the strength and plasticity of Casting A at different temperatures. Fig. 11 shows kernel average misorientation (KAM) and inverse pole figure (IPF) maps of Casting A and Casting B near the fracture [30] at different temperatures (see Fig. 10). The LAGBs in the IPF maps had an orientation angle of 2–10� and are shown by the fine black lines, while the high-angle grain boundaries (HAGBs) had an orientation angle greater than 10� , and are shown by the thick black lines. KAM maps are mainly used to analyze local misorientation. A filter size of 3 � 3 was used, which means that the average of the difference between the orientation of the intermediate points and the surrounding 8 pixels was used as the average orientation difference. All points on the map were processed using this same algorithm. The color of the regions with larger orientation differences are indicated in red, which qualitatively in­ dicates the effect of dislocation plugging on the stress in the matrix. The stress value in the matrix increases with changes in color from blue to red. Fig. 12(a) is the result of counting the number of grains in Casting A and Casting B at 500 � magnification. Fig. 11 (b1) and (b2) show that the Casting A samples contained many MnS inclusion particles (white areas in the KAM diagram). When the sample is plastically deformed, the failure of the MnS–matrix interface provides conditions for void initiation and reduces the conti­ nuity of displacement and stress during deformation of the matrix. In addition, it also hinders dislocation motion, resulting in dislocation accumulation, pinning, and rearrangement, which is macroscopically expressed as an increase in plastic deformation resistance. The accu­ mulation of dislocations near MnS inclusions provides the driving force for dynamic recrystallization (DRX) nucleation. The grain size of the Casting A sample at 900 � C was significantly higher than that of the original sample, and also higher than that of the Casting B sample at the same temperature. Comparing Fig. 11 (b2) and (g2), it is clear that there were large differences in the number and size of voids in the Casting A and Casting B samples. This is because the presence of MnS particles promotes DRX, increases the grain boundary density, hinders the growth of voids, in­ creases the plastic deformation time to some extent, delays the fracture failure, and increases the plasticity of the material. This is why the dif­ ference in plasticity between the two materials at 900 � C is not large. However, due to the presence of MnS inclusions, many dislocations were introduced in the Casting A sample during plastic deformation (as shown in Fig. 11 (b1) and (g1)), resulting in a larger deformation resistance than for Casting B. This explains why the strength of the two materials differed greatly at 900 � C (from Fig. 8, △σ p ¼ 5.58 MPa at 1200 � C, but △σ p ¼ 27.75 MPa at 900 � C).

Fig. 6. Comparison of experimental and simulated stress-strian curves at different temperatures: (a), (b) Respectively, comparison of experimental and GTN damage model stress-strian curves of first failed elements of Casting A, Casting B.

plastic deformation occurred at high temperature. Based on these ob­ servations at 900–1200 � C, we concluded that, due to the presence of MnS particles, the fracture point of the material advanced, so εf of Casting A was always smaller than that of Casting B. Fig. 9 (a1)-(h1) show SEM images of the fractures of the two spec­ imen types after tensile testing at 900–1200 � C. With increasing tem­ perature, both Casting A and B showed a reduction in fracture area, and increase in dimple diameter and depth, indicating a higher degree of plastic deformation. Comparing Fig. 9(a1) and (e1), (b1) and (f1), (c1) and (g1), and (d1) and (h1), it was clear that the fracture area of Casting A was always smaller than that of Casting B (△ψ < 0), indicating that the plasticity of Casting B was higher than that of Casting A at high temperatures. However, difference in ψ between 900 � C and 1200 � C for Casting A was 21.76%, and for Casting B was 26.99%. The presence of MnS reduced the temperature sensitivity of the plasticity of the material. As shown in Fig. 8, △ψ gradually increased with increasing tempera­ ture, which will be discussed in detail in Section 4.2. 4.2. EBSD analysis at different temperatures EBSD data was analyzed to yield information about the crystallo­ graphic orientation and produce low-angle grain boundary (LAGB) and local misorientation maps of the two materials at different temperatures. These data showed that the presence of MnS inclusions promoted the initiation of voids, along with displacement and stress discontinuity during deformation of the matrix, which increased the probability of dislocation accumulation and improved deformation resistance during 7

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Table 4 Experimental εf, σ p and ψ of Casting A and B at different temperatures. Temperature/� C

Casting A

Casting B

εf

σp (MPa)

ψ

εf

σp (MPa)

ψ

900 1000 1100 1200

0.4608 0.5059 0.5205 0.5734

164.02 104.47 76.28 49.863

53.81 67.13 67.75 75.57

0.4791 0.5175 0.6052 0.7124

138.27 95.85 65.29 44.28

59.30 67.85 79.74 86.29

It can be seen from Fig. 12(b) that at 900 � C and 1000 � C, the Casting B sample had larger k values than those of the Casting A sample during plastic deformation, which is entirely due to the grain size distribution of the Casting A sample at these temperatures. The number of grains and grain boundary density were significantly higher than that of the Casting B sample, which impeded void growth and partially improved the plasticity of the material. At higher temperature (1100–1200 � C), stronger DRX softening occurred in Casting A. As shown in Fig. 7, the true stress–strain curve showed that the stress decreased after reaching a peak value. The stress strengthening effect of MnS inclusions on dislocation plugging gradually became weaker than the DRX stress softening effect. Fig. 11 (b1), (c1), (d1), (g1), (h1), and (l1) show a large number of fine grains, indicating the occurrence of DRX nucleation. However, Fig. 11 (e1) and (m1) show very small KAM values, along with large grains and twins. For both Casting A and B at 900–1200 � C (Fig. 12(a)), the number of grains first increased and then decreased with increasing temperature, indicating that DRX nucleation increased the number of grains. Subsequently, the number of grains decreased due to the large grains annexing the finer ones, while the nucleation of new DRX grains was insignificant. The stress in the matrix continuously reduced due to changes in the microstructure that consumed a large amount of defor­ mation energy; for example, substructures forming inside the original grain boundary, the original grain continuously absorbing dislocations and changing orientation, resulting in the formation of HAGBs or twins, which then recrystallize into new grains via continuous DRX [31]. Eventually, the difference in strength between the two materials grad­ ually decreases. In addition, due to grain growth and twin formation at 1100 � C and 1200 � C in Casting A, the number of grains and grain boundary density in the matrix were lower than those of Casting B, resulting in a decrease in the formation, growth, and coalescence of voids [32,33]. Hence, the acceleration factor of void growth was higher for Casting A than Casting

Fig. 9. SEM morphologies of the fracture surface obtained after testing at different temperatures.

B (Fig. 12(b)), while the MnS inclusions in Casting A resulted in defor­ mation discontinuity during deformation, and an increase in the prob­ ability of void coalescence. Finally, the Casting B sample became more plastic than Casting A. In summary, during high-temperature deformation, stress strength­ ening caused by MnS inclusions and stress softening caused by DRX both contributed to the strength of the material. The promotion of void initiation and growth by MnS inclusions and the inhibition of void growth and coalescence by DRX together determine the plasticity of the material. Hence, a large difference in strength and plasticity between the two materials at different temperatures was observed. In addition, an interesting phenomenon was observed during the experiments regarding the regularity of the deformation behavior of single-crystal and polycrystalline MnS particles. Fig. 13(a) shows the original structure of Casting A without deformation, which consisted on

Fig. 8. Difference in macroscopic mechanical properties of Casting A and B at different temperatures. 8

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This can be explained considering the interface strength and orien­ tation relationship. First, the interfacial strength between the MnS particles and matrix is different for single-crystal and polycrystalline MnS particles, where the weaker areas are more likely to cause voids. Fig. 13(b)–(e) show that the voids tended to initiate at the interface between MnS particles and the matrix or inside polycrystalline MnS particles, while voids inside single-crystal MnS particles were less likely to occur. Second, the crystal orientation relationship of the MnS parti­ cles was different to the stress direction acting at the time of fracture. That is, polycrystalline MnS particles slipped in different directions after being split into multiple orientations, while single-crystal MnS particles slid only along the easiest slip system. 4.3. Analysis of the relationship between k and temperature From the physical meaning of fc and fF in the GTN damage model, it can be seen that these two parameters are crucial for describing the rapid decline of the strength and plasticity of the material in the final stages. Table 3 shows that, as the temperature increased, fc gradually increased; hence, the time taken to reach the critical coalescence void volume fraction increased. With this softening effect caused by DRX, the driving force of void evolution, viz., deformation-induced local stress concentration, was greatly relieved, subsequently hindering void growth and coalescence [32,33]. The value of fF also increased with increasing temperature because dislocation motion and atomic diffusion in the material are enhanced at high temperatures, which enhanced the plasticity of the material and increased the time to reach fracture failure.

Fig. 10. Fracture area diagram.

intact single-crystal and polycrystalline MnS particles. During hightemperature plastic deformation at 900–1200 � C, single-crystal MnS particles slid parallel to the load direction, while polycrystalline MnS particles split into two pieces and then slid parallel to the load direction (see Fig. 13(b)–(e)). In the diagram, different colors represent different orientations of polycrystalline MnS particles; the color of the arrow is consistent with the orientation color of the grain, and the arrow represents the sliding direction of the grain.

Fig. 11. Casting A and B undeformed and deformed KAM and IPF maps: (a1), (f1) KAM maps of as-received Casting A, B at 500 � ; (a2), (f2) IPF maps of as-received Casting A, B at 500 � ; (b1), (c1), (d1), (e1) and (g1), (h1), (l1), (m1) Respectively, KAM maps of Casting A and B at different temperatures at 2000 � ; (b2), (c2), (d2), (e2) and (g2), (h2), (l2), (m2) Respectively, IPF maps of Casting A and B at different temperatures at 2000 � . 9

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(4), where q1 ¼ 1.5). In the temperature range of 900–1200 � C, we compared the mechanical curve, SEM images of the fracture surface, and EBSD maps near the fracture of Casting A and B. The damage due to failure of Casting A was advanced due to the presence of MnS particles, and the fc and fF values (i.e., k) were a visual representation of this. That is, at the same temperature, the presence of MnS in Casting A resulted in a different k value than that of Casting B, which reflects the effect of MnS on the evolution of voids in the matrix. Fig. 12(b) shows that in the temperature range of 900–1200 � C, k gradually decreased with increasing temperature, where the rate of void growth in the material increased slowly. Section 4.2 showed that DRX occurred in the material at 900 � C, it was weak and had only a minor effect on void growth, resulting in a high k value. However, above 1100 � C, DRX was stronger in the material, and its restriction of void growth was increasingly obvious, which decreased k. This was due to void growth being a result of local stress concentration. The softening effect of DRX reduces local stress concentration, which inhibited void growth around DRX grains [32,33]. When the temperature increased from 900 � C to 1200 � C, temperature-induced DRX increasingly restricted void evolution, which increased the plasticity of Casting A. Therefore, for the metal studied here, a decrease in k with increasing temperature is inevitable. We propose that k can reflect the compre­ hensive effect of both MnS inclusions and temperature on the evolution of voids in the matrix. In addition, the relationship between k and temperature can provide researchers with a correlation between the temperature and GTN damage model. Our findings are expected to provide a research direction for further in-depth quantitative analysis of the damage behavior of the matrix at high temperatures during deformation. 5. Conclusions 1. The RSM was used to obtain GTN damage parameters of steels with and without MnS inclusions at different temperatures. The results of a simulation of uniaxial tensile specimens at high temperatures agreed well with experimental results. 2. In the process of high-temperature plastic deformation, the presence of MnS particles induces void nucleation, promotes void initiation and growth, increases the probability of void coalescence, and

Fig. 12. (a)Grain number of Casting A and B at different temperatures at 500 � ; (b) k of Casting A and B at different temperatures.

The GTN damage parameters f0, fc, and fF are the void volume fractions that characterize the process of void growth. While f0 hardly changes with temperature, fc and fF are dependent on k (see equation

Fig. 13. Deformation of single crystal and polycrystalline MnS particles: (a)SEM and IPF of as-received Casting A; (b)–(e) Respectively, SEM and IPF images of Casting A at 900, 1000, 1100, 1200 � C. 10

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reduces the plasticity of the material, which finally results in earlier fracture. Meanwhile, the presence of MnS reduces the temperaturedependence of the plasticity of the material. 3. Under high-temperature deformation, stress strengthening caused by MnS inclusions and stress softening caused by DRX determine the overall strength, while the promotion of void initiation and growth by MnS inclusions, and the inhibition of void growth and coalescence by DRX jointly determine the plasticity. 4. The deformation behavior of single-crystal and polycrystalline MnS particles was determined by the interface strength and orientation. During plastic deformation, single-crystal MnS particles slipped parallel to the loading direction, while polycrystalline MnS particles split into two pieces and slipped parallel to the loading direction. 5. The parameter k reflects the comprehensive effect of MnS and tem­ perature on the evolution of voids in the matrix.

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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. Acknowledgements This research was supported by the National Natural Science Foun­ dation of China (Grant No. 51575475 and Grant No. 51675465). References [1] Andr� e Luiz Vasconcellos da Costa e Silva, Non-metallic inclusions in steels-origin and control, journal of materials research and technology, J. Mater. Res. TechnolJMRT 7 (2018) 283–299. [2] A. Ghosh, S. Sahoo, M. Ghosh, R.N. Ghosh, D. Chakrabarti, Effect of microstructural parameters, microtexture and matrix strain on the Charpy impact properties of low carbon HSLA steel containing MnS inclusions, Mater. Sci. Eng., A 613 (2014) 37–47. [3] X. Li, J. Zhang, S. Shen, Y. Wang, X. Song, Effect of tempering temperature and inclusions on hydrogen-assisted fracture behaviors of a low alloy steel, Mater. Sci. Eng., A 682 (2017) 359–369. [4] M. Wu, W. Fang, R. Chen, B. Jiang, H. Wang, Y. Liu, H. Liang, Mechanical anisotropy and local ductility in transverse tensile deformation in hot rolled steels: the role of MnS inclusions, Mater. Sci. Eng., A 744 (2019) 324–334. [5] J. R. Shi, Z. Wang, L. Qiao, X. Pang, Microstructure evolution of in-situ nanoparticles and its comprehensive effect on high strength steel Mater. Sci. Technol. 35 (2019) 1940–1950. [6] A. Ghosh, P. Modak, R. Dutta, D. Chakrabarti, Effect of MnS inclusion and crystallographic texture on anisotropy in Charpy impact toughness of low carbon ferritic steel, Mater. Sci. Eng., A 654 (2016) 298–308. [7] A.E. Mayer, P.N. Mayer, Weak increase of the dynamic tensile strength of aluminum melt at the insertion of refractory inclusions, COMP MATER SCI 114 (2016) 178–182. [8] J. Guan, L. Wang, C. Zhang, X. Ma, Effects of non-metallic inclusions on the crack propagation in bearing steel, Tribol. Int. 106 (2017) 123–131. [9] Z. Gao, Y. Zhou, K.Y. Lee, Crack–inclusion problem for a long rectangular slab of superconductor under an electromagnetic force, COMP MATER SCI 50 (2010) 279–282.

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