Improvement of Critical Intergranular Fracture Stress by Increasing Carbon Content in Tempered Martensite Steels

Abstract

Effect of carbon (C) content (0.05 mass% to 0.3 mass%) on critical intergranular fracture stress of tempered martensite steel was investigated using 3 mass% manganese (Mn) steel. The critical intergranular fracture stress was obtained by calculating the maximum principal stress at fracture in a tensile test of circumferentially notched round bar specimen using elastoplastic finite element analysis. As a result, critical intergranular fracture stress of tempered martensite steel increased with increasing the C content. Therefore, the dominant factors of critical intergranular fracture stress were examined from the viewpoints of the amount of segregation of each element on prior-austenite grain boundaries and the grain size of the martensite substructure. The first result was found to be the effect of reducing the amount of Mn segregation by increasing the C content. This was thought to be because cementite acts as a solid solution site for Mn, and the amount of Mn in solid solution in the matrix phase is reduced by increasing the C content. The second result was found to be the effect of refining the substructure of martensite surrounded by high angle grain boundaries by increasing the C content. This indicates that grain size also affects crack initiation resistance in intergranular fracture by determining the stress concentration at the grain boundaries as the distance of dislocation accumulation.

1. Introduction

Modern social infrastructure requires steels with high strength to accommodate the increased size and reduced weight of structures. However, increasing the strength of steels often results in a decrease in low-temperature toughness, making it challenging to achieve high strength and high toughness simultaneously. Specifically, high-strength steels with a martensite microstructure can exhibit significantly low toughness due to intergranular fracture occurring along prior-austenite (γ) grain boundaries. This type of fracture commonly occurs in tempered martensite steels, which is well-known as temper embrittlement.^1,2,3,4) The main factor for this phenomenon is the segregation of phosphorus (P), an impurity, at prior-γ grain boundaries. For example, a study has reported that an increase in grain boundary segregation of P, as measured by Auger electron spectroscopy, leads to an increase in the ductile-to-brittle transition temperature in the Charpy impact test.⁵⁾ Moreover, the effect of grain boundary segregation of P has also been investigated from the perspective of fracture mechanics. Fracture mechanics defines the condition for the occurrence of intergranular fracture as the local acting stress exceeding the critical intergranular fracture stress inherent to the material. Studies have shown that the critical intergranular fracture stress, which is derived from the fracture stress in a four-point bending test or a tensile test of circumferentially notched round bar specimen, decreases.^6,7) From the above, it is effective to enhance the critical intergranular fracture stress by eliminating P impurities in steels. On the other hand, carbon (C), which is effective in increasing strength, is known to suppress intergranular fracture and improve toughness when segregated at grain boundaries.^8,9,10) Furthermore, C is known to interact with P at grain boundaries and reduce the amount of P segregation.^9,10,11,12) However, in tempered martensite steels, the solubility limit of C in matrix is low, resulting in the precipitation of cementite. As a result, the effect of C on improving toughness may be limited. On the contrary, increasing the C content has been shown to increase the ductile-to-brittle transition temperature.^3,5) However, this does not necessarily mean a decrease in the critical intergranular fracture stress, as increasing the C content also enhances strength of steels. It is known that an increase in the C content in a martensite microstructure leads to a refinement in the size of the substructure, specifically the packets and blocks.¹³⁾ This refinement may contribute to an increase in the critical intergranular fracture stress. However, conventionally, the influential grain in intergranular fracture is prior-γ grain, which serves as the crack propagation path, and the effect of martensite substructure has not been clarified. Therefore, the objective of this study is to investigate the effect of C on the critical intergranular fracture stress in tempered martensite steels, with a focus on the impact of martensite substructure grain size.

2. Experimental

Steel ingots having chemical compositions with C of 0.049, 0.099 and 0.31 mass% and manganese (Mn) of 3 mass% were produced in a vacuum melting furnace. The chemical compositions are shown in Table 1. Mn was added to obtain a martensite microstructure during quenching, as well as to assist intergranular fracture, thus facilitating the objective of this study.^15,16,17,18) The reduction of P was carried out to eliminate the interaction effect between C and P at grain boundaries. The ingots were hot rolled at temperatures above 1273 K to produce the plates with a thickness of 15 mm and were subsequently air-cooled to room temperature. Furthermore, the plates were held for 14.4 ks at 1573 K in an Argon (Ar) atmosphere furnace and were subsequently air-cooled to room temperature. The aim is to reduce Mn micro-segregation, which in turn will result in a reduction of test variability. Then, the plates were held for 3.6 ks at 1473 K, 1323 K, and 1223 K, respectively, in an Ar atmosphere furnace and subsequently quenched by immersion in water. The reason for changing the holding temperature is that substructure grain size is affected not only by carbon content but also by prior-γ grain size, so that both influences on substructure grain size can be evaluated separately. Afterwards, the plates were tempered for 14.4 ks at 823 K and subsequently underwent immersion in water. Additionally, to investigate the amount of cementite precipitation during tempering, the plates that were quenched at 1473 K were tempered at 823 K for 1.2 ks, 14.4 ks and 360.0 ks, respectively, and subsequently underwent immersion in water.

Table 1. Chemical compositions (mass%).

Alloy	C	Si	Mn	P	S	Al	N	O	Fe
0.05C	0.049	0.023	3.0	<0.002	0.0007	0.028	0.0011	<0.001	Bal.
0.1C	0.099	0.024	3.0	<0.002	0.0007	0.027	0.0010	<0.001	Bal.
0.3C	0.310	0.025	3.0	<0.002	0.0006	0.026	0.0011	<0.001	Bal.

To observe the microstructure, micro blocks with dimensions of 15 mm × 10 mm × 10 mm were cut from the middle of the plate thickness. The observation plane is perpendicular to the rolling direction. The prior-γ grain size was determined by the intercept method after the above micro blocks were mirror-polished and etched with nital. The micro blocks were then electropolished and analyzed using scanning electron microscopy (SEM) with backscattered electron diffraction (EBSD) to determine the circular equivalent diameter of areas surrounded by grain boundaries with a misorientation of 15° or more. JEOL JSM-6500F was used and the acceleration voltage was 15 kV. The substructure grain size in this study was determined by calculating the area average of the circular equivalent diameters. Additionally, the average aspect ratio of the substructure grain size was calculated by dividing the short diameter by the long diameter, which was determined by the ellipsoid approximation. The amount of cementite precipitation was measured as follows: the observation surface was mirror-polished, and backscattered electron images were taken at three locations in a 9 μm × 12 μm area in the middle of the plate thickness using SEM. JEOL JSM-7000F was used and the acceleration voltage was 5 kV. The areas of black contrast were then binarized by image analysis to determine the area fraction occupied by cementite precipitation.

Tensile tests were conducted to determine the strength of the plates. Two round bar specimens with parallel sections having a diameter of 6 mm were taken from the middle of the plate thickness. The longitudinal direction of the round bar specimens was parallel to the rolling direction. Tensile strength (TS) and yield stress (YS) were determined by conducting tests at a strain rate of 1×10⁻³ s⁻¹ and room temperature with a gauge length of 24 mm. YS was determined as 0.2% proof stress. Each TS and YS of the specimens was the average of two measurements.

The critical intergranular fracture stress was measured using the following method. Three circumferentially notched specimens shown in Fig. 1 and a smooth round bar without a notch were taken from the middle of the plate thickness. The longitudinal direction of these tensile specimens was parallel to the rolling direction. Low-temperature tensile tests were carried out in liquid nitrogen at 77 K with a gauge length of 30 mm and a strain rate of 5.6×10⁻⁴ s⁻¹ to measure the stress-strain curve. The circumferential notches were prepared to increase stress triaxiality under the notch and facilitate brittle fracture. The maximum principal stress at fracture of the circumferentially notched specimens was then calculated by elastoplastic finite element analysis (FEM) and used as the critical intergranular fracture stress. In this analysis, an axisymmetric model with 928 elements was created using the general-purpose software ABAQUS. An example of the calculation results of the FEM analysis is shown in Fig. 2. SEM images of the fracture surface after the circumferential notch tensile tests were taken to confirm the intergranular fracture surface and to confirm the presence of cementite precipitation on the intergranular fracture surface.

Fig. 1. Geometry of circumferentially notched round bar specimen used to measure critical intergranular fracture stress.

Fig. 2. Example of maximum principal stress distribution obtained by finite element analysis in the circumferentially notched specimen (Axisymmetric model of 0.3C alloy quenched at 1223 K). (Online version in color.)

The segregation of P, C and Mn at grain boundaries was measured by Auger electron spectroscopy for specimens quenched at 1473 K, 1323 K, and 1223 K. Notched round bar specimens with a diameter of 3 mm were taken from the middle of the plate thickness and fractured in a vacuum chamber cooled by liquid nitrogen. The specimens were then transferred to the stage of SEM, which was installed alongside in a vacuum, and the Auger electron signals were analyzed on the intergranular fracture surface at three non-cementite points on each of the three intergranular fracture surfaces. JEOL JAMP-9500F with an acceleration voltage of 10 kV, a current of 10 nA and a vacuum of 1×10⁻⁷ Pa was used. Auger peaks at 120 eV, 272 eV, 542 eV and 703 eV were used for P, C, Mn, and Fe, respectively. Segregation concentrations were determined using the relative sensitivity coefficient method,¹⁹⁾ which involves applying elements-specific weights to the respective peak intensities.

3. Experimental Results

3.1. Microstructure and Tensile Properties

The grain size, aspect ratio, and tensile test results of the specimens are presented in Table 2, and the EBSD inverse pole figure (IPF) maps are shown in Fig. 3. The prior-γ grain size was mainly determined by the quenching temperature, with only a slight dependence on the C content. However, increasing the C content resulted in the refinement of the substructure grain size. For example, after quenching at 1473 K, the prior-γ grain size of 0.05C, 0.1C and 0.3C steels was approximately 700 μm. Nevertheless, the substructure grain size was refined from 101 μm for 0.05C steel, to 70 μm for 0.1C steel, and 21 μm for 0.3C steel. This trend is similar to that reported previously.¹³⁾ The aspect ratio tended to increase at lower quenching temperatures. TS increased with an increase in the C content at the same quenching temperature and 0.3C steel demonstrated an increase in strength at lower quenching temperatures. On the other hand, the strength of the 0.05C steel increased with a decrease in quenching temperature from 1473 K to 1323 K, however decreased with a further decrease in quenching temperature from 1323 K to 1223 K. The lower C content is considered to have reduced the hardenability due to the finer γ grains, which resulted in bainite formation.

Table 2. Heat treatment conditions, grain size, aspect ratio, and tensile properties.

Alloy	Quenching temperature (K)	Tempering		Microstructure			Tensile properties
		Temperature (K)	Time (s)	prior-γ size (μm)	substructure size (μm)	substructure aspect ratio	YS (MPa)	TS (MPa)
0.05C	1473	823	14.4 k	691	101	0.22	497	573
	1323			146	59	0.27	502	581
	1223			41	37	0.32	436	533
0.1C	1473	823	14.4 k	695	70	0.24	563	652
	1323			135	38	0.26	558	650
	1223			38	21	0.32	563	654
0.3C	1473	823	14.4 k	712	21	0.20	657	807
	1323			109	16	0.27	672	820
	1223			37	8	0.34	690	823

Fig. 3. Inverse pole figure maps. Black lines correspond to grain boundaries with a misorientation of 15 degrees, which are high angle grain boundaries. (Online version in color.)

3.2. Critical Intergranular Fracture Stress

The nominal stress–nominal strain curves for the tensile tests of circumferentially notched specimens conducted at 77 K are presented in Fig. 4. Three tests were conducted for each level of testing. The test start point of the strain is shown staggered for each quenching temperature. The nominal stress–nominal strain curves show a round shape, indicating that work hardening progresses gradually from the bottom of the circumferential notch toward the center when the specimens are subjected to strain. On the other hand, clear yielding was observed in the tensile test of smooth round bar without a notch. At the same quenching temperature, an increase in fracture strength and fracture elongation was observed as the C content increased. For the same steel grade, the fracture strength and elongation mainly tended to increase with decreasing quenching temperature, particularly for 0.3C steel. The fracture surface of the tensile test of circumferentially notched specimen after testing is shown in Fig. 5. All specimens had predominantly intergranular fracture surfaces. Quenching at 1473 K resulted in almost entirely intergranular fracture. Conversely, the specimens quenched at lower temperatures (1323 K and 1223 K) had fracture surfaces that were partially mixed with cleavage fracture surfaces. This is due to the critical intergranular fracture stress increasing to a value close to the critical cleavage fracture stress at lower quenching temperatures. SEM images of the fracture surfaces with increased magnification are shown in Fig. 6. The intergranular fracture surface contained cementite in white contrast, all of which were less than 1 μm in size. To determine the critical intergranular fracture stress, the maximum principal stress at fracture was determined by elastoplastic FEM calculations using true stress–true strain curves obtained from tensile tests of smooth round bars at 77 K. The results are presented in Fig. 7 and Table 3. The critical intergranular fracture stress increased as the amount of the C content increased and as the quenching temperature decreased.

Fig. 4. Stress-strain curves of tensile tests of circumferentially notched specimens at 77 K. Three tests were conducted per test level. 1473 K, 1323 K, and 1223 K indicate the quenching temperature respectively.

Fig. 5. Fracture surfaces of tensile tests of circumferentially notched specimens at 77 K. All samples show intergranular fractures. The fracture surfaces of the specimens at the reduced quenching temperature have a mixture of partially cleavage fracture surfaces.

Fig. 6. Detailed intergranular fracture surface of tensile tests of circumferentially notched specimens at 77 K. Cementite is shown in white contrast.

Fig. 7. Relationship between critical intergranular fracture stress and carbon content. Higher carbon content and lower quenching temperatures improve critical intergranular fracture stress.

Table 3. Nominal breaking stress of the tensile test of circumferentially notched specimen at 77 K and critical intergranular fracture stress obtained from elastoplastic finite element analysis.

Alloy	Quenching temperature (K)	Tempering		Nominal breaking stress at 77 K			Critical intergranular fracture stress
		temperature (K)	time (s)	N1 (MPa)	N2 (MPa)	N3 (MPa)	N1 (MPa)	N2 (MPa)	N3 (MPa)
0.05C	1473	823	14.4 k	1593	1510	1413	1771	1747	1636
	1323			1459	1534	1417	1661	1704	1633
	1223			1613	1579	1573	1757	1722	1762
0.1C	1473	823	14.4 k	1641	1583	1452	1739	1804	1669
	1323			1485	1428	1651	1745	1740	1850
	1223			1658	1653	1641	1819	1869	1858
0.3C	1473	823	14.4 k	1920	1708	1909	2096	1959	2111
	1323			2005	1933	1980	2134	2113	2185
	1223			2005	2041	2018	2242	2248	2232

3.3. Grain Boundary Segregation

C, P, and Mn segregation at the prior-γ grain boundaries measured by Auger electron spectroscopy is presented in Fig. 8 for 0.05C, 0.1C and 0.3C steels with a quenching temperature of 1473 K and subsequent tempering at 823 K for 14.4 ks. The amount of C segregation remained almost constant as the C content increased. To confirm this, the relationship between the tempering time at 823 K and the amount of cementite precipitation was investigated. This investigation aimed to examine the amount of C in solid solution in the steels, which is associated with grain boundary segregation. The backscattered electron images are shown in Fig. 9 and the relationship between tempering time and cementite precipitation is shown in Fig. 10. The area fraction of cementite did not change at tempering times of 1.2 ks, 14.4 ks, and 360 ks at 823 K. If the microstructure is uniform in the depth direction of the observed surface, the area fraction measured in one section is equivalent to the volume fraction. The volume fraction is calculated as D_αC_add/(D_αC_add+D_θ(C_θ−C_add)), where C_add is the amount of added C in mass%, C_θ is the amount of C in cementite with a value of 6.69 mass%, D_θ is the density of cementite with a value of 7.68 g/cm³ and D_α is the density of steel with a value of 7.87 g/cm³. The volume fraction of cementite determined in this way was 0.75% for 0.05C steel, 1.52% for 0.1C steel, and 4.75% for 0.3C steel, which generally corresponds to the value measured here. Based on these results, in the steels tempered to 14.4 ks, for which the critical intergranular fracture stress was measured, all the supersaturated C that was present during quenching precipitated as cementite. Therefore, the amount of C in solid solution in ferrite was the solubility limit, which was calculated by thermodynamic calculation using Thermo-Calc with TCFE10 database to be 3.7 massppmC for the Fe-C-3 mass%Mn at 823 K with the exclusion of the graphite phase when specifying the phases, resulting in not affecting the amount of C segregation at prior-γ grain boundaries.

Fig. 8. Grain boundary concentration of C, P, and Mn measured by Auger electron spectroscopy for samples quenched at 1473 K and tempered at 823 K for 14.4 ks. The measurements were taken in local areas that did not contain cementite.

Fig. 9. Backscattered electron images of specimens polished to mirror surfaces quenched at 1473 K and tempered at 823 K. Cementite is shown in black contrast.

Fig. 10. Relationship between area fraction of cementite and tempering time for specimens quenched at 1473 K and tempered at 823 K. Lines are the calculated value when all C is precipitated as cementite. The specimens for 14.4 ks are fully precipitated.

The amount of P segregation at the grain boundaries remained nearly constant as the C content increased. The measured values are considered to be below the detection limit because the steels with reduced P content were used.

On the other hand, the amount of Mn segregation at the grain boundaries was 9.4 at% for 0.05C steel, 9.1 at% for 0.1C steel, and 6.3 at% for 0.3C steel. To analyze the reason for the decrease in Mn segregation as the C content increased, changes in the amount of Mn in solid solution in ferrite with increasing amount of the C content were calculated by thermodynamic calculation using Thermo-Calc with TCFE10 database with the exclusion of the graphite phase when specifying the phases. The amount of Mn in solid solution in ferrite at 823 K for Fe-C-3 mass%Mn was 2.7 mass% for 0.05C steel, 2.4 mass% for 0.1C steel, and 1.5 mass% for 0.3C steel. On the other hand, the remaining phase was cementite only, and Mn in solid solution in cementite was 44 mass% for 0.05C steel, 41 mass% for 0.1C steel, and 34 mass% for 0.3C steel. All these values indicate a high solid solution content. The relationship between the amount of solid solution and the amount of grain boundary segregation at equilibrium is commonly expressed using McLean‘s equilibrium segregation equation,²⁰⁾ shown in Eq. (1) below.

  

$$X^{gb,\infty }\approx \frac{x^{\alpha }\text{exp(}\mathrm{\Delta }{E}_X^{gb}/RT\text{)}}{1+x^{\alpha }\text{exp(}\mathrm{\Delta }{E}_X^{gb}/RT\text{)}},$$(1)

where X^gb,∞ is the concentration of grain boundary segregation at equilibrium, x^α is the concentration of segregated element in solid solution in ferrite, $\mathrm{\Delta }{E}_X^{gb}$ is the grain boundary segregation energy, R is the gas constant and T is the heat treatment temperature. The behavior of segregation in the non-equilibrium state represents a step towards reaching the equilibrium grain boundary segregation amount, determined by the diffusion coefficient of the segregating elements in ferrite. This behavior is often described using McLean’s non-equilibrium segregation equation,²⁰⁾ shown in Eq. (2) below.

  

$$\begin{array}{l}\frac{X^{gb}(t)-X^{gb}(0)}{X^{gb,\infty }-X^{gb}(0)}=\\ 1-\text{exp}\left(\frac{4Dt}{{(X^{gb,\infty }/x^{\alpha })}^2{d}^2}\right)\text{erfc}\left(\frac{2\sqrt{Dt}}{(X^{gb,\infty }/x^{\alpha })d}\right),\end{array}$$(2)

where X^gb(t) is the concentration of grain boundary segregation at finite time t, X^gb(0) is the concentration of initial grain boundary segregation, D is the diffusion coefficient of the segregating element, and d is the grain boundary width. In this study, each steel was heat-treated at the same temperature and it is unlikely that the Mn concentration of initial grain boundary segregation X^gb(0), the grain boundary segregation energy $\mathrm{\Delta }{E}_X^{gb}$ of Mn, the diffusion coefficient D of Mn, and the grain boundary width d vary with the amount of C, so Mn in solid solution x^α is considered to change the concentration of grain boundary segregation both in equilibrium and non-equilibrium conditions. As Mn in solid solution x^α decreases, the concentration of grain boundary segregation in equilibrium X^gb,∞ decreases from McLean’s equilibrium segregation equation shown in Eq. (1). Using $Y=2\sqrt{Dt}/((X^{gb,\infty }/x^{\alpha })d)$ in the non-equilibrium, the concentration of grain boundary segregation shown in Eq. (2) is expressed as (X^gb(t)−X^gb(0))/(X^gb,∞−X^gb(0))=1−exp(Y²)erfc(Y). The right-hand side of this function is shown to be a monotonically increasing function with respect to Y.²⁰⁾ Y can also be expressed as the following Eq. (3) by substituting McLean’s equilibrium segregation equation shown in Eq. (1).

  

$$Y\approx \frac{2\sqrt{Dt}\left(1+x^{\alpha }\text{exp(}\mathrm{\Delta }{E}_X^{gb}/RT\text{)}\right)}{d\text{exp(}\mathrm{\Delta }{E}_X^{gb}/RT\text{)}}$$(3)

From this Eq. (3), Y is a monotonically increasing function with respect to x^α. Therefore, as Mn in solid solution x^α decreases, Y also decreases and 1−exp(Y²)erfc(Y) also decreases. Consequently, the concentration of grain boundary segregation X^gb(t) in non-equilibrium eventually decreases. In other words, the cementite acts as a solid solution site for Mn, and an increase in the C content leads to a reduction in the concentration of Mn in solid solution in ferrite, thereby reducing the concentration of Mn segregation at grain boundaries.

These results reveal a novel observation: the critical intergranular fracture stress in tempered martensite steels increases with an increase in the C content. However, increasing the C content does not induce changes in C segregation, which strengthens prior-γ grain boundaries, or P segregation, which weakens them. These factors fail to explain the increase in the critical intergranular fracture stress. Furthermore, the increase in cementite also does not account for this phenomenon. Conversely, a plausible explanation lies in the reduction of Mn segregation at prior-γ grain boundaries resulting from the increased C content and the presence of finer martensitic substructure. Therefore, the effect of the C content on the increase in the critical intergranular fracture stress is investigated utilizing a model that considers the influence of Mn segregation and the refinement of the martensitic substructure. Additionally, the embrittlement caused by cementite is taken into consideration.

4. Discussions

The improvement mechanism of critical intergranular fracture stress by increasing the C content in tempered martensite steels is discussed in relation to grain boundary segregation and grain size. Firstly, the investigation of Auger electron spectroscopy results indicates that the concentration of C segregation at grain boundaries remains almost unchanged as the C content increases. Conversely, the concentration of Mn segregation at grain boundaries decreases with increasing the C content. In ferrite steels, previous measurements using Auger electron spectroscopy have indicated a reduction of 39 MPa in the critical intergranular fracture stress per 1 at% Mn segregation at grain boundaries within the range of 4–8 at% Mn segregation.¹⁵⁾ Additionally, our previous study has demonstrated that in tempered martensite steels containing 3 mass% to 5 mass% Mn, Mn segregation at grain boundaries reduces the critical intergranular fracture stress by 35 MPa per at% Mn within the range of 5–12 at% Mn segregation.¹⁸⁾ In subtracting the effect of the concentration of Mn segregation at grain boundaries, the effect on the critical intergranular fracture stress from zero Mn segregation has not been obtained, so in the present case the Mn segregation of the 0.05C steel was used as a reference to discuss the difference. The change in Mn segregation is estimated to be 0.3 at% lower for 0.1C steel and 3.1% lower for 0.3C steel when compared with 0.05C steel. Correspondingly, based on our previous data, the change in the critical intergranular fracture stress is estimated to be 11 MPa higher for 0.1C steel and 109 MPa higher for 0.3C steel when compared with 0.05C steel.

Next, the effect of grain size is considered. It has conventionally been reported that intergranular fracture toughness increases as prior-γ grains become finer. This is explained by the concept that refining prior-γ grains, which serve as the crack propagation path, enhances the resistance to crack propagation. The relationship between prior-γ grain size and the measured critical intergranular fracture stress in this study is shown in Fig. 11. When comparing the same steel grade, prior-γ grain refinement increases the critical intergranular fracture stress. However, when comparing the same prior-γ grain size, a higher C content corresponds to a higher the critical intergranular fracture stress. For example, the difference in the critical intergranular fracture stress between 0.05C steel and 0.3C steel with a prior-γ grain size of approximately 700 μm is 337 MPa. This difference is greater than the 109 MPa difference in the critical intergranular fracture stress between 0.05C steel and 0.3C steel through the difference of Mn segregation at grain boundaries. Consequently, it can be inferred that the change in the critical intergranular fracture stress cannot be solely explained by the conventional factors of Mn segregation at grain boundaries and prior-γ grain size.

Fig. 11. Relationship between critical intergranular fracture stress and prior-γ grain size. The white plots are the values obtained by subtracting the effect of the amount of Mn segregation at grain boundaries based on 0.05C. Critical intergranular fracture stress cannot be explained by prior-γ grain size and Mn segregation.

However, in cleavage fracture, it has been shown that grain size not only influences the crack propagation, but also plays a role in crack initiation.²¹⁾ Since the grain size corresponds to the length of the slip surface of the grain adjacent to the brittle particle on the grain boundary, it is understood that a longer slip surface length facilitates stress concentration on the brittle particle on the grain boundary due to the dislocation accumulation. Consequently, this heightened stress concentration leads to a higher susceptibility to crack initiation. The influence of grain size on crack initiation is expected to apply similarly to intergranular fracture, which is another form of brittle fracture. During crack initiation, stress concentration occurs on the brittle particle on the grain boundary. The crack then propagates along the grain boundaries, resulting in intergranular fracture, as well as along the (100) plane of ferrite, resulting in cleavage fracture. Furthermore, in contrast to ductile fracture, brittle fracture is predominantly governed by the weakest regions. Therefore, the longest slip surface length within the same grain is considered to impact brittle fracture. In other words, the major diameter of the substructure grain can influence intergranular fracture. The major diameter of the substructure grain is obtained by dividing the substructure grain circle equivalent diameter by the square root of the mean aspect ratio, which is analyzed as the effective substructure grain size for brittle fracture in this study. The relationship between effective substructure grain size and the critical intergranular fracture stress is shown in Fig. 12. By plotting the −1/2 power of the substructure grain size on the horizontal axis and the corresponding critical intergranular fracture stress, which is adjusted by subtracting the effect of Mn segregation based on 0.05C steel, on the vertical axis with white data points, it can be observed that they roughly correspond on a one-to-one basis. The solid line represents their linear approximation. This implies that, as illustrated in Fig. 13, the effective substructure grain size can influence crack initiation by determining the stress concentration at the grain boundaries as dislocation accumulation.

Fig. 12. Relationship between critical intergranular fracture stress and effective substructure grain size. The white plots are the values obtained by subtracting the effect of the amount of Mn segregation at grain boundaries based on 0.05C. The line is the approximation straight line to the −1/2 power of the effective substructure grain size.

Fig. 13. Conceptual diagram of the effect of major diameter surrounded by grain boundaries with misorientation of 15 degrees (effective substructure grain size) in tempered martensite steels on intergranular fracture. Effective substructure grain size affects crack initiation resistance in intergranular fracture by determining the stress concentration at the prior-γ grain boundaries as the distance of dislocation accumulation.

The certainty of this is further assessed by employing a model²²⁾ that investigates the critical fracture stress resulting from stress concentration at grain boundaries, while considering both grain size and brittle particle size. The critical fracture stress σ_c is determined by analyzing the energy release rate due to crack propagation in systems with dislocations accumulated along the grain slip plane, using the length of the brittle particle as the initial crack length, and is formulated as Eqs. (4) and (5) below.

  

$${\sigma }_c=\{\begin{array}{c}\frac{8\mu {\gamma }_p{d}^{-1/2}}{\left(1+1/\sqrt{2}\right)\left(1-\nu \right)k_y}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(t<C_c\right)\\ {\left(\frac{8\mu {\gamma }_p}{\pi \left(1-\nu \right)t}-\frac{k_y{}^{2}d}{8{\pi }^2{t}^2}\right)}^{1/2}-\frac{k_y{d}^{1/2}}{2\sqrt{2}\pi t}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(t\ge C_c\right)\end{array},$$(4)

  

$$C_c=\frac{\left(1+1/\sqrt{2}\right)\left(1-\nu \right)k_y^{2}d}{16\pi \mu {\gamma }_P},$$(5)

where μ=8.2×10¹⁰ N/m² is shear modulus, ν=0.3 is Poisson’s ratio, d is the length of dislocation accumulation, and t is the brittle particle size. k_y is the Hall-Petch coefficient, which is the slope of the grain size dependence of YS. γ_p represents the effective surface energy necessary for crack propagation along the (100) plane in ferrite originating from the crack in the brittle particle. If the brittle particle size is smaller than the critical size C_c, the accumulation of dislocations on the slip plane within a grain directly influences the critical fracture stress. The critical fracture stress is determined by the grain size with a power of −1/2. If the initial crack length is larger than C_c, the brittle particle is characterized as a potential crack and the critical fracture stress at its tip is reduced. Petch model is applied to analyze cleavage fracture. However, this model is derived from the rate of energy release rate resulting from crack propagation and does not incorporate information regarding the crack propagation plane. The effective surface energy represents the propensity for crack propagation. Therefore, the model is considered applicable to systems in which a well-defined critical fracture stress can be determined based on the effective surface energy. This implies that significant plastic deformation is absent in both cleavage and intergranular fracture, allowing for a clear definition of the critical fracture stress. Therefore, Petch model is employed in this study to qualitatively assess its ability to explain the observed phenomenon. The length of dislocation accumulation d is taken as the effective substructure grain size, the Hall-Petch coefficient k_y is 3.7 MPa/mm^−1/2, the average of 7.2 MPa/mm^−1/2 and 0.3 MPa/mm^−1/2 for 0.3C steel and 0.1C steel, respectively, determined by the slope of YS with respect to the substructure grain size. Hall-Petch coefficients of 3.6–5.9 MPa/mm^−1/2 have been reported for IF steel with a C content of 4–5 ppm.²³⁾ Similarly, a Hall-Petch coefficient of 2.6 MPa/mm^−1/2 has been reported for quenched martensite in Fe-18 mass%Ni with a C content of 4–7 ppm.²⁴⁾ Based on the previous thermodynamic calculations, the solubility limit of C for this study is determined to be 3.7 ppm. The determined Hall-Petch coefficient value is considered reasonable. The cementite size and effective surface energy are determined by fitting experimental values with the least-squares method in this study. The experimental values, in this context, refer to the values after subtracting the effect of Mn segregation at grain boundaries. The calculated and experimental values of the fitted critical intergranular fracture stress are shown in Fig. 14 and the relationship between effective substructure grain size and critical intergranular fracture strength in Fig. 15. The obtained cementite size is approximately 0.44 μm, which corresponds to the grain boundary cementite visible in white contrast in Fig. 5. The obtained effective surface energy is 7.0 J/m², which is lower than the typical effective surface energy of 10 J/m² for cleavage fracture. This indicates a situation where fracture takes place at grain boundaries rather than on the (100) plane in ferrite due to the presence of Mn segregation. The Mn segregation reduces the effective surface energy required for propagation along grain boundaries. Based on the findings above, it can be concluded that the model is capable of reasonably predicting the cementite size and the effective surface energy, with a coefficient of determination indicating a good fit to the experimental data. This suggests that the model effectively accounts for the influence of grain size on intergranular fracture. Traditionally, the discussion regarding the effect of grain size on intergranular fracture has primarily focused on prior-γ grains, which serve as the crack propagation path. However, it has been discovered that the major diameter of the region bounded by large-angle grain boundaries within prior-γ grains plays a crucial role in determining the crack initiation properties. This region affects stress concentration at grain boundaries by determining the length of dislocation accumulation.

Fig. 14. Relationship between fracture stress calculated by Petch model²²⁾ and critical intergranular fracture stress with Mn effect subtracted.

Fig. 15. Relationship between critical intergranular fracture stress and effective substructure grain size. The white plots are the values obtained by subtracting the effect of the amount of Mn segregation at grain boundaries based on 0.05C. The line is the result of fitting with Petch model.²²⁾

5. Conclusion

This study aimed to investigate the influence of the C content ranging from 0.05 to 0.3 mass% on the critical intergranular fracture stress in tempered martensite steels with a Mn content of 3 mass%. Additionally, the study explored the primary factors that contribute to the critical intergranular fracture stress, specifically focusing on grain boundary segregation and grain size. The following results were obtained.

(1) The critical intergranular fracture stress in tempered martensite steels increased with increasing the C content.

(2) The amount of Mn segregation at prior-γ grain boundaries decreased with an increase in the C content. This phenomenon was attributed to cementite serving as a solid solution site for Mn, and the increased C content leads to a reduction in the amount of Mn in solid solution in ferrite. However, the increase in the critical intergranular fracture stress could not be explained solely by the effect of reduced Mn segregation at grain boundaries due to the increased the C content.

(3) The refinement of the substructure grain size was confirmed through an increase in the C content. In addition, a direct correlation was observed between the major diameter of the substructure grains and the critical intergranular fracture stress with the influence of Mn corrected.

(4) The application of Petch model, which addresses the characteristics of crack initiation in cleavage fractures, was extended to intergranular fractures. The qualitative consistency between the model and experimental results was indicated by a coefficient of determination r² of 0.66. Specifically, it was discovered that the stress concentration at grain boundaries is determined by the major diameter bounded by high angle grain boundaries, as the distance of dislocation accumulation. This factor significantly influences the characteristics of crack initiation, even in the case of intergranular fractures.

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