Investigation of Micro-crack Initiation as a Trigger of Cleavage Fracture in Ferrite-pearlite Steels

Abstract

This study presents investigations of the micro-crack formation in pearlite microstructure as a trigger of unstable cleavage crack propagation in ferrite-pearlite steel. In order to clarify the micro-crack formation mechanism, a trace analysis was conducted to compare the direction of crack surface with those of cleavage and slip planes of ferrite in pearlite. It is found that any directions of crack surface were not coincident with those of {100} planes. On the other hand, all of the directions of crack surfaces showed good agreement with those of {110} planes. The result showed a probability that the micro-cracks in pearlite are formed by the shear fracture on slip planes in ferrite. The condition of unstable propagation from a micro-crack in pearlite into a neighbor ferrite grain was investigated. Effective surface energy was estimated by the crack length obtained by SEM observation and the local stress calculated by finite element analysis. The result showed the estimated effective surface energy of a propagation from micro-crack in pearlite into ferrite matrix is larger than that of cleavage crack propagation across boundary between ferrite grains. A probability of the micro-crack formation in pearlite was quantified by the measurement of micro-cracks in steels having various ferrite-pearlite microstructures and finite element analysis. As a result, the probability of micro-crack formation could be effectively estimated as a function of only the equivalent plastic strain, independently from temperature, volume fraction of pearlite and loading condition.

1. Introduction

A brittle fracture in a steel structure is caused by a cleave fracture of microstructures and sometimes leads a serious damage. We therefore must certainly prevent the brittle fracture in the fundamental structures.

In general, a material resistance for brittle fracture initiation is called as “fracture toughness”. It has been widely known that a fracture toughness depends on the grain size.¹⁾ It is also known that a brittle phase such as cementite becomes a fracture initiation site, and thus the fracture toughness depends on the size of brittle phase.²⁾ According to these facts, it is important to establish a theory to quantitatively predict the relationship between microstructures and fracture toughness for material developments.

The cleavage fracture of steel is generally interpreted by the weakest link mechanism which is completely different from yielding and work hardening. The fracture toughness is thus accompanied by the scatter as an intrinsic feature. Pineau and his co-workers proposed a formulation of the fracture probability using Weibull distribution function, called as the “Beremin model”.^3,4) The effectiveness of the model has been widely recognized and the standardizations on fracture probability based on the model has progressed.^5,6,7) This is because the model enables quantitative evaluation of the scatter and the size effect on fracture toughness, even though the studies in the past were limited within the empirical experiences. As the existence of small defects in the microstructures was assumed in advance in the original model, some modifications were proposed by introducing an effect of strain considering initiation of the small defects.^8,9,10,11) However, the relationship between microstructure and fracture toughness has not been essentially clarified by these models.

On the other hand, Shibanuma et al. recently proposed a model to predict fracture toughness of ferrite-cementite steels.^12,13,14,15) This model requires only two kinds of material information: distributions of ferrite grain and cementite particle sizes and a true stress-strain curve, without any adjustable parameters. The model is composed of two parts, i.e. the preparatory part and evaluation part. In the preparatory part, an active zone is discretized into volume elements. The microstructures of each volume element were modeled based on their size distributions using the Monte Carlo method. The applied stress and strain at each volume element were calculated by using macroscopic finite element analysis. In the evaluation part, the fracture initiation was evaluated based on the formulations of microscopic fracture process of three stages: (I) nucleation of a crack at the cementite particle;¹⁶⁾ (II) propagation of the crack at the cementite into the ferrite matrix and formation of a cleavage crack;¹⁷⁾ (III) propagation of the cleavage crack across a ferrite grain boundary.¹⁸⁾ An application of this model is however limited only to ferrite-cementite steel. It is therefore required to extend the application of the model to actually used steels, which have more complicated microstructures.

Ferrite-pearlite steel is one of the most widely used steels. Hiraide et al. tried to develop a model to predict fracture toughness of the ferrite-pearlite steel,¹⁹⁾ as a modification of the model proposed by Shibanuma et al.^14,15) The model was based on the microscopic fracture processes of three stages, in the same manner as that proposed by Shibanuma et al.:^14,15) (I) micro-crack formation in pearlite; (II) propagation of the micro-crack into ferrite matrix and formation of a cleavage crack; (III) propagation of the cleavage crack across a ferrite grain boundary, as shown in Fig. 1. The prediction results showed a good accuracy for the influences of ferrite grain size and temperature on fracture toughness. However, the prediction results of the influence of volume fraction of pearlite on fracture toughness were overestimated than the experimental ones. It is therefore necessary to reconsider the above formulations in the stages (I) and (II), in order to accurately predict the influence of volume fraction of pearlite on fracture toughness.

Fig. 1.

Cleavage fracture initiation process of ferrite pearlite steel. (Online version in color.)

It is well known that the cleavage fracture in a ferrite-pearlite steel initiates at a micro-crack formed in pearlite.^19,20,21,22) However, detail of the micro-crack formation process and conditions of the subsequent unstable cleavage fracture initiation were not sufficiently studied in the past. One of the major reasons results in the complicated lamellar structure of pearlite. Miller and Smith clarified that continuous cracking of cementite plates composed of the lamellar structure occurs prior to a micro-crack initiation in pearlite particle. In addition, nanoscale numerical simulations such as the molecular dynamics simulations were recently reported to clarify the micromechanics in the lamellar structure.²³⁾ However, it is difficult to quantify the relationship between the microscale or nanoscale phenomena clarified by these studies and the macroscopic fracture toughness due to too large scale gap between them. It is therefore actually effective to quantify the condition of micro-crack formation in pearlite and the subsequent unstable cleavage crack propagation using only the macroscopic parameters such as stress and strain obtained by the continuum mechanics theory.

According to the above background, the present paper describes foundational investigations in order to establish a theory to quantitatively predict the fracture toughness of ferrite-pearlite steels based on the microstructural information. We firstly observe a detailed micro-crack formation in pearlite, and secondly discuss a mechanism of the formation of micro-crack and a condition of the subsequent unstable cleavage crack propagation. We finally qualify probability of the micro-crack formation in pearlite, which is independent from temperature and loading condition, by the measurement of micro-cracks in steels having various ferrite-pearlite microstructures and finite element analysis.

2. Observation of Micro-cracks Working as Fracture Initiation Site

In this section, we show a detailed observation of a micro-crack in pearlite, which is important for a cleavage fracture initiation site. We conducted a fracture test using double-notched three point bend test specimen, which can preserve the condition just before fracture initiation near the notch root. Based on the results of the observation, the formation of micro-crack in pearlite and a condition of the subsequent unstable cleavage fracture initiation are discussed.

2.1. Test Steel

We employed JIS SM490A steel, which is widely used as a structural steel. The steel is call as ‘Steel S’. Chemical compositions of Steel S is shown in Table 1. Figure 2 shows an optical micrograph of the steel after the surface was polished and etched by nital.

Table 1. Chemical composition and tensile properties of Steel S.

(a) Chemical composition [mass%]

C	Si	Mn	P	S	V
0.15	0.36	1.35	0.015	0.005	0.034

(b) Tensile properties

YP [MPa]	TS [MPa]	EL [%]
241	527	30

Fig. 2.

Optical micrograph of Steel S.

2.2. Three Point Bend Tests Using Double-notched Specimen²⁴⁾

In the three point bend test using double-notched specimen, a cleavage fracture is initiated at one of two notch roots. That is, a damage condition just before fracture initiation can be preserved at the other notch root.²⁴⁾ Figure 3 shows configuration of the specimen. The span of the tests is 120 mm. Test temperature is set as −130°C in liquid nitrogen atmosphere. Loading rate is 1 mm/min. Notch mouth opening displacement is measured by a clip-gauge.

Fig. 3.

Double-notched specimen. (Online version in color.)

Figure 4 shows the relationship between load and clip gauge displacement. When the load is 21.7 kN and clip gauge displacement is 0.85 mm, a cleavage fracture was initiated at one of the notch roots. It is expected that the damage condition just before fracture initiation can be preserved at the other notch root at this time.

Fig. 4.

Load-displacement curves of three-point bending test using double-notched specimen of Steel S.

2.3. Estimation of Micro-crack Formation Mechanism

After the three point bend test, a sample for observation was extracted from the neighborhood of the preserved notch root as shown in Fig. 5. The observation surface was polished by the cross-section polisher (CP). Micro-cracks were observed on the surface of 1 mm×0.8 mm by the FE-SEM.

Fig. 5.

Sample for observation of micro-cracks. (Online version in color.)

Five micro-cracks were found in the observation region. Typical SEM images of micro-cracks are shown in Fig. 6. The crack tips got dulling, which was expected to be caused by the plastic deformation after micro-crack formations. On all of the observed crack surfaces, we observed roughness caused by the fracture surface of lamellar structure of pearlite. That is, the micro-cracks in the ferrite-pearlite steel was formed across the pearlite grains (see the results of EBSD analysis shown in Table 2). Many defects such as cracks or voids with tens of nanometers in size were found in front of the respective micro-crack tip. On the other hand, any crack across the ferrite grain was not found in the observation region. These facts reach the following two suggestions for the assumed three stages of microscopic process of the cleavage fracture initiation as shown in Fig. 1: (I) nucleation of a crack at the cementite particle and (II) propagation of the crack at the cementite into the ferrite matrix are bottleneck processes of the cleavage fracture initiation; the ferrite grain boundary scarcely works as a barrier for (III) propagation of the cleavage crack across the ferrite grain boundary.

Fig. 6.

SEM images of micro-cracks in pearlite structure of Steel S.

Table 2. EBSD images near micro-cracks together with {100} plane or {110} plane traces. (Online version in color.)

In order to clarify the mechanism of the micro-crack formation in pearlite, a trace analysis was conducted to compare the direction of micro-crack and cleavage or slip plane, based on a crystal orientation of ferrite in the pearlite obtained by the EBSD analysis.²⁵⁾ A cleavage surface of crystal is generally formed in a low Miller index plane and it is well known that {100} is the cleavage plane of BCC metal including ferrite. It is also well known that {110} is the dominant slip plane of BCC metal.²⁶⁾ According to the above knowledge, we assumed {100} for the cleavage plane and {110} for the slip plane in the trace analysis.

Table 2 shows the inverse pole figure (IPF) map and image quality (IQ) maps with the traces of {100} and {110}, respectively. The cracks in (a), (b) and (c) in Table 2 are corresponding with those of secondary electron images in Fig. 6. As a result, the directions of cracks did not show agreement with one of the traces of {100} except the case of (c). On the other hand, all of the directions of cracks showed good agreement with one of the traces of {110}. The results indicates that a micro-crack in pearlite is likely to be formed on a slip plane. Therefore, it can be expected that a micro-crack in pearlite, which works as a trigger of the cleavage fracture initiation, is formed by the shear fracture. A certain micro-crack was formed along a lamellar structure but another micro-crack was formed with a wide variation of angles including approximately right angle to a lamellar structure. A specific correlation between the directions of lamellar structure and micro-crack was thus not found in the results.

2.4. Evaluation on Unstable Cleavage Fracture Condition from Micro-crack

As mentioned in Section 1, the condition of unstable cleavage crack propagation from a micro-crack in pearlite to the neighboring ferrite has been scarcely clarified. In this section, the fracture condition is investigated based on the Griffith theory, which is the most fundamental theory for the cleavage fracture initiation.^{3,4,5,6,7,17,27)} Although the Griffith theory was originally established for an elastic body, the modification where the surface energy in the original formulation is replaced with effective surface energy, which is the sum of the pure surface energy and the plastic work, has been investigated for a long time. The modification has been widely applied for the evaluation on the cleavage fracture initiation in steels.^{3,4,5,6,7,17)}

According to the Griffith theory, if a fracture initiates in a solid with a penny-shaped crack when applied remote stress reaches the fracture stress σ_f , the effective surface energy γ is given as   

$$\gamma =\frac{{\sigma }_{\text{f}}^2\left(1-{\nu }^2\right)D}{\pi E}$$(1)

where D is the crack diameter, ν is the Poisson’s ratio (=0.3) and E is the Young’s modulus (=210 GPa).

In the observation results of the previous section, it is indicated that the micro-crack, which is a cleavage fracture initiation site in a ferrite-pearlite steel, was formed by the shear fracture. All of the observed micro-cracks were formed in pearlite and were arrested without propagation into the neighboring ferrite grains. That is, these micro-cracks did not satisfied the fracture condition of the propagation of a micro-crack in pearlite into ferrite matrix (Stage (II)). The relationship between true effective surface energy γ_Pα and the tentative effective surface energy ${\gamma }_{\text{P}\alpha }^{\prime }$ is given in Eq. (2). The tentative effective surface energy ${\gamma }_{\text{P}\alpha }^{\prime }$ is defined by replacing the crack diameter D and the fracture stress σ_f, with the observed micro-crack length L and the local stress σ in Eq. (1).   

$${\gamma }_{\text{P}\alpha }>{\gamma }_{\text{P}\alpha }^{\prime }\left(=\frac{{\sigma }^2\left(1-{\nu }^2\right)L}{\pi E}\right)$$(2)

In order to evaluate ${\gamma }_{\text{P}\alpha }^{\prime }$, a finite element analysis to simulate the three-point bend test using the double notched specimen was conducted. The analysis was conducted using the first order hexahedral element with full-integration considering the finite deformation theory by ABAQUS.³⁰⁾ Stress-strain relationship was obtained by a tensile test using a round bear specimen. As shown in Fig. 7, a quarter-symmetry finite element model was used. An example of the results of deformation and the maximum principal stress distribution neat the notch root are shown in Fig. 8.

Fig. 7.

Finite element mesh of the double-notched specimen. (Online version in color.)

Fig. 8.

Distribution of maximum principal stress and deformation near the notch root at the center of thickness obtained by finite element analysis of three-point bending test using double-notched specimen. (Online version in color.)

The local stress σ in Eq. (2) is assumed as the maximum principal stress at the location of the corresponding micro-crack observed in the previous section. The results of ${\gamma }_{\text{P}\alpha }^{\prime }$ calculated from a set of local stress σ and micro-crack length L are shown in Table 3. The maximum value of ${\gamma }_{\text{P}\alpha }^{\prime }$ was 60 J/m², so that the true effective surface energy was estimated as γ_Pα>60 J/m² at the test temperature of −130°C.

Table 3. Assumed effective surface energy obtained by SEM observation and finite element analysis.

Crack	(a)	(b)	(c)	(d)	(e)
Crack length L [mm]	0.020	0.013	0.011	0.009	0.008
Max. principal stress σ [MPa]	1464	1592	1655	1567	1566
Assumed effective surface energy ${\gamma }_{\text{P}\alpha }^{\prime }$ [J/m2]	60	46	43	29	26

Although the quantification of the effective surface energy γ_Pα for propagation of a micro-crack in pearlite into the ferrite matrix (Stage (II)) has not been reported as far as the authors know, the effective surface energy γ_αα for the propagation of a cleavage crack across a ferrite grain boundary (Stage (III)) was quantified by San Martin and Rodriguez-Ibabe.¹⁸⁾ Comparison between the results of γ_Pα obtained by the present study and those of γ_αα obtained by San Martin and Rodriguez-Ibabe are shown in Fig. 9. At the temperature of −130°C, which is the test condition of the present study, the result of San Martin and Rodriguez-Ibab was approximately γ_αα=60 J/m². The results was coincident with the obtained maximum value of the ${\gamma }_{\text{P}\alpha }^{\prime }$ in the present study. According to γ_Pα>${\gamma }_{\text{P}\alpha }^{\prime }$ as shown in Eq. (2), we obtained γ_Pα>γ_αα. That is, it is recognized that the effective surface energy for the propagation of a micro-crack in pearlite into the ferrite matrix is larger than that for the propagation of a cleavage crack across a ferrite grain boundary. Pearlite is generally regarded to be more brittle than ferrite. Therefore, this knowledge appears to be in conflict with the result of γ_Pα>γ_αα. One of the possible major reasons is due to two different kinds of crack formations, i.e., a shear crack in the pearlite grain for γ_Pα and a cleavage crack in the ferrite grain for γ_αα. In the micro-crack formation in the pearlite, it is expected that the dulling of the crack tip was caused by plastic deformation due to stable shear fracture in the pearlite. Such a dulled crack tip requires larger driving force to propagate into the adjacent ferrite grain, compared with a sharp crack tip accompanied which the cleavage fracture. Therefore, it is found that there is a possibility of γ_Pα>γ_αα in ferrite-pearlite steel.

Fig. 9.

Assumed effective surface energy ${\gamma }_{\text{P}\alpha }^{\prime }$ compared with γ_αα obtained by San Martin and Rodriguez-Ibabe.¹⁸⁾ (Online version in color.)

3. Quantification of Micro-crack Formation

In this section, we first show an observation of micro-cracks under various temperature and loading conditions using steels having various ferrite and pearlite grain sizes. We then show a quantification of the micro-crack formation as a basis to establish a theory to predict fracture toughness of ferrite-pearlite steels based on their microstructural information.

3.1. Test Steels¹⁹⁾

We employed three types of test steels which have different sizes of ferrite and pearlite grains each other in the same as those in the author’s previous study.¹⁹⁾ The chemical compositions, heat treatment conditions and mechanical properties are shown in Table 4. It can be regarded that their compositions are the same except carbon concentration. Figure 10 shows optical micrographs of the respective steels after polishing and etching. It is found that pearlite bands were formed in all of steels.

Table 4. Chemical composition, heat treatment condition and tensile properties of Steel A, B and C.

(a) Chemical composition [mass%]

Steel	C	Si	Mn	P	S	Al	N
A	0.18	0.15	0.99	<0.002	0.0005	0.019	0.0008
B	0.18	0.15	0.99	<0.002	0.0005	0.019	0.0008
C	0.09	0.15	0.99	<0.002	0.0005	0.019	0.0008

(b) Heat treatment condition

Steel	Normalizing			Cooling
	Rolling	Heating	Holding
A	Hot rolling	900°C	1 h	Air
B		1000°C
C		900°C		Accelerated cooling

(c) Tensile properties

Steel	YP [MPa]	TS [MPa]	EL [%]
A	241	527	24
B	209	522	36
C	211	455	43

Fig. 10.

Optical micrographs of Steel A, B and C.

The pearlite band thickness was measured by the image analysis for optical micrographs. The images were binarized, and the area of 4px (2.08 μm) in width was then extracted with 50px (26.04 μm) interval in the pearlite band direction. The pearlite band thickness was evaluated as the height of the equivalent rectangle of the measured area of 4px in width. A schematic diagram of the measurement process is shown in Fig. 11. The obtained distributions of the pearlite band thickness are shown in Fig. 12, and the average and maximum pearlite band thickness are shown in Table 5. It is noted that the vertical axis of the graphs in Fig. 12 denotes the cumulative probability of equivalent area fraction, which is defined as the cumulative probability of area fraction assuming the aspect ratio of the pearlite grain is constant.

Fig. 11.

Image analysis to obtain pearlite band thickness. (Online version in color.)

Fig. 12.

Distributions of pearlite band thickness of Steel A, B and C. (Online version in color.)

Table 5. Representative pearlite band thickness [μm].

Steel	Average	Maximum
A	14.0	85.4
B	17.8	68.5
C	9.2	31.3

3.2. Tensile Tests Using Circumferential Notched Round Bar Specimens

In order to efficiently make micro-cracks, tensile tests using circumferential notched round bar specimens were conducted. The specimen configuration is the same as those in the author’s previous study¹⁶⁾ as shown in Fig. 13. The notch root radius is defined as 15 mm. The test temperatures are −160°C, −120°C and −80°C and the loading rate is 2 mm/min, which is regarded as a quasi-static condition. In the author’s previous study, the three-point bending tests using notched specimen made by various ferrite-pearlite steels under various temperatures were conducted, and all the test results showed that the equivalent plastic strain at the fracture initiation sites was satisfied with ε_p<0.3.¹⁹⁾ Considering these results, the applied load is limited corresponding to −ε_p of 0.7–0.8 on the minimum section. These conditions were determined by the gauge length obtained by a preliminary finite element analysis. Under the conditions of −120°C and −160°C for steel A and −160°C for steel B, the cleavage fractures were initiated before the equivalent plastic strains reach the respective set values of the gauge lengths, so that the values at the times of the respective fracture initiations were employed for the following evaluation. The finite element analysis was carried out considering the finite deformation theory. The finite element mesh was modeled using first order quadrilateral element with full-integration and considering axial symmetry for the circumferential direction and plane symmetry for the axial direction. Examples of the equivalent plastic strain and equivalent stress on deformed notched tensile specimen are shown in Fig. 14.

Fig. 13.

Circumferential notched tensile specimen.

Fig. 14.

Equivalent plastic strain and equivalent stress on deformed notched tensile specimen obtained by finite element analysis (Steel A, −120°C). (Online version in color.)

3.3. Measurement of Micro-crack and Quantification of its Formation Probability

The measurement of the micro-cracks was conducted by SEM observation. According to the result of the finite element analysis as shown in Fig. 14, it is found that both the strain and stress were approximately constant in the orthogonal direction of axis. Therefore, the specimens were cut in the axial direction, and the number of micro-cracks were measured by scanning the sections along the direction.

The applied stress and strain can be varied by changing the scanning location in the axial direction, so that the measurement was conducted under three or four conditions of applied stress and strain for some of the specimens. An example of the SEM images of the micro-cracks is shown in Fig. 15.

Fig. 15.

Micro-cracks obtained by tensile tests using notched specimen (Steel A, −160°C). (Online version in color.)

The results of EBSD analysis in the section 2.3 indicated that a micro-crack is formed due to slip of ferrite in pearlite. According to the results, the experimental results were analyzed based on an assumption that the maximum shear stress or equivalent plastic strain is a governing factor of the micro-crack formation.

There is a difference between the maximum shear stress in the pearlite and that in the ferrite matrix due to the layered structure of the ferrite-pearlite steel. It is difficult to obtain the respective accurate constitutive equations of ferrite and pearlite. Thus, the simple estimation formula proposed by Ohata et al.³¹⁾ was employed to estimate the maximum shear stress in pearlite. The estimation formula, which assumes the relationship between the yield strengths of ferrite ${\sigma }_{\text{Y}}^{\text{F}}$ and that of pearlite ${\sigma }_{\text{Y}}^{\text{P}}$, are given using the average yield strength σ_Y and the volume fraction of pearlite $V_{\text{f}}^{\text{P}}$, as   

$$\frac{{\sigma }_{\text{Y}}^{\text{F}}}{{\sigma }_{\text{Y}}^{\text{P}}} = \frac{198}{276}$$(3)

  

$${\sigma }_{\text{Y}}=\left(1-V_{\text{f}}^{\text{P}}\right) {\sigma }_{\text{Y}}^{\text{F}}+V_{\text{f}}^{\text{P}}\hspace{0.17em}{\sigma }_{\text{Y}}^{\text{P}}$$(4)

The value of the right hand side in Eq. (3) derives from the results of the hardness tests for the respective ferrite and pearlite.³¹⁾ Summarizing Eqs. (3) and (4), we obtain   

$${\sigma }_{\text{Y}}^{\text{P}}=\frac{276}{198+78V_{\text{f}}^{\text{P}}} {\sigma }_{\text{Y}}$$(5)

In the plastic region, the relationship between σ_Y and ${\sigma }_{\text{Y}}^{\text{P}}$ shown in Eq. (5) can be directly applied to that between τ_max and ${\tau }_{\text{max}}^{\text{P}}$, as   

$${\tau }_{\text{max}}^{\text{P}}=\frac{276}{198+78V_{\text{f}}^{\text{P}}} {\tau }_{\text{max}}$$(6)

According to Eq. (6), it is found that the lower volume fraction of pearlite makes the higher stress concentration in pearlite.

On the other hand, the equivalent plastic strain in pearlite is coincident with that in the neighborhood ferrite matrix in the case that the loading direction is in-plane of the layered structure. That is, the relationship between the equivalent plastic strain in pearlite ${\epsilon }_{\text{q}}^{\text{P}}$ and the average equivalent plastic strain ε_q is given as   

$${\epsilon }_{\text{q}}^{\text{P}}={\epsilon }_{\text{q}}$$(7)

Based on the above conditions, temperature, the equivalent plastic strain, the maximum shear stress, a total pearlite band length in the observation region and the probability of the micro-crack formation in ferrite-pearlite steels were discussed below. The total pearlite band length was estimated by using the average pearlite band thickness shown in Table 5 and the volume fraction estimated by chemical compositions shown in Table 4. Details of the data is shown in Table A in the appendix.

The respective relationships between the probability of micro-crack formation and (a) the maximum shear stress as well as (b) the equivalent plastic strain are shown in Fig. 16. The probability of micro-crack formation had a large scatter for the same the maximum shear stress as shown in Fig. 16(a). In particular, we can find the tendency that the lower temperature gave the lower probability of micro-crack formation at the same maximum shear stress for the respective steels. That is, it is found that the probability of micro-crack formation could not quantified as a function of the maximum shear stress. On the other hand, we can find a good correlation between the probability of micro-crack formation and the equivalent plastic strain as shown in Fig. 16(b), though there was a certain scatter under the condition of the equivalent plastic strain of less than 0.4 due to the limited number of micro-crack formations. That is, the probability of micro-crack formation can be quantified as a function of only the equivalent plastic strain independently from temperature, volume fraction of pearlite and loading condition.

Fig. 16.

Quantification results of probability of cracking in pearlite structure. (Online version in color.)

Even though the same plastic strain are produced in both ferrite and pearlite, a micro-crack is formed in pearlite due to the lower ductility of pearlite than that of ferrite. It was clarified in the past study²³⁾ that the continuous cracking of cementite plates composed of lamellar structure occurred prior to a micro-crack initiation in pearlite particle. The probability of micro-crack formation in pearlite can be quantified by the equivalent plastic strain but not the maximum shear stress. This fact suggests that the micro-crack in pearlite cannot be formed just after shear slip initiation but can be formed accompanied with a certain plastic deformation.

Based on the above results, the probability of micro-crack formation per unit pearlite band length p can be approximated as a function of only the equivalent plastic strain ε_q as   

$$p=5.5{\epsilon }_{\text{q}}^3+{\epsilon }_{\text{q}}$$(8)

The relationship between p and ε_q in Eq. (8) is shown in dotted line in Fig. 16(b). It is expected that the evaluation formula of Eq. (8) can modify the accuracy of the fracture toughness prediction of the ferrite-pearlite steel in the past study.¹⁹⁾

4. Conclusions

In the present study, the fundamental investigation for a micro-crack initiation as a trigger of cleavage fracture in ferrite-pearlite steel were carried out. The concluding remarks are described as follows.

Firstly, in order to clarify the formation of micro-crack mechanism, a trace analysis using the EBSD method was conducted to compare the direction of crack surface with those of cleavage and slip planes of ferrite in pearlite. It is found that any directions of crack surface were not coincident with those of {100} planes. On the other hand, all of the directions of crack surfaces showed good agreement with those of {110} planes. The result indicated that a micro-crack in pearlite were formed by the stable shear fracture on a slip plane in ferrite.

Secondly, the condition of unstable propagation from a micro-crack in pearlite into a neighbor ferrite matrix was investigated. Effective surface energy was estimated by using the crack length obtained by SEM observation and the local stress calculated by finite element analysis. The result showed the estimated effective surface energy of a propagation from micro-crack in pearlite into ferrite matrix was larger than that of a cleavage crack propagation across the boundary between ferrite grains estimated by San Martin and Rodriguez-Ibabe.¹⁸⁾

Finally, a probability of micro-crack formation in pearlite was quantified by the measurement of micro-cracks in steels having various sizes of ferrite and pearlite grains. As a result, the probability of micro-crack formation could be effectively approximated as a function of only the equivalent plastic strain, independently from temperature, volume fraction of pearlite and loading condition.

Acknowledgements

The authors sincerely appreciate funding support from 24th ISIJ Research Promotion Grant (incl. Ishihara/Asada Grant) and technical support from “Nanotechnology Platform”(project No. 12024046) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Appendix

Table A shows details of the measurement results of micro-cracks in Steel A, Steel B and Steel C in Section 3.3.

Table A. Results of micro-crack measurement.

(a) Steel A

Temperature [°C]	−160	−120			−80
Maximum shear stress [MPa]	555	194	373	451	435
Equivalent plastic strain	0.63	0.01	0.20	0.54	0.76
Observation area [mm2]	0.515	–	0.281	0.284	0.418
Pearlite band length [mm]	9.92	–	5.40	5.48	8.06
Num. of micro-cracks	20	0	2	6	32
Probability of cracking [mm−1]	2.02	0.00	0.37	1.10	3.97

(b) Steel B

Temperature [°C]	−160	−120				−80
Maximum shear stress [MPa]	512	348	435	478	491	463
Equivalent plastic strain	0.37	0.15	0.38	0.66	0.80	0.73
Observation area [mm2]	0.571	0.706	0.627	0.522	0.576	0.496
Pearlite band length [mm]	8.63	10.68	9.49	7.90	8.71	7.50
Num. of micro-cracks	9	2	4	20	30	19
Probability of cracking [mm−1]	0.81	0.19	0.32	2.53	3.45	2.53

(c) Steel C

Temperature [°C]	−160	−120			−80
Maximum shear stress [MPa]	521	406	451	463	436
Equivalent plastic strain	0.77	0.38	0.64	0.75	0.75
Observation area [mm2]	0.477	0.785	0.529	0.353	0.493
Pearlite band length [mm]	6.97	11.49	7.73	5.17	7.21
Num. of micro-cracks	26	6	13	18	19
Probability of cracking [mm−1]	3.73	0.26	1.68	3.48	2.64

References

• 1)   W. C.  Leslie, trans. by N. Koda, H. Kumai and T. Noda: The Physical Metallurgy of Steels, Maruzen, Tokyo, (1985), (in Japanese).
• 2)   D. A.  Curry and  J. F.  Knott: Met. Sci., 12 (1978), 511.
• 3)   F. M.  Beremin: Metall. Mater. Trans. A, 14 (1983), 2277.
• 4)   A.  Pineau: Int. J. Fract., 138 (2006), 139.
• 5)  ASTM E1921: 2013, Standard test method for determination of reference temperature, to, for ferritic steels in the transition range.
• 6)  ISO 27306: 2009, Metallic materials-Method of constraint loss correction of CTOD fracture toughness for fracture assessment of steel components.
• 7)   F.  Minami: Procedia Mater. Sci., 3 (2014), 337.
• 8)   H.  Mimura: J. High Press. Inst. Jpn., 39 (2001), No. 5, 281.
• 9)   S. R.  Bordet,  A. D.  Karstensen,  D. M.  Knowles and  C. S.  Wiesner: Eng. Fract. Mech., 72 (2005), No. 3, 435.
• 10)   S. R.  Bordet,  A. D.  Karstensen,  D. M.  Knowles and  C. S.  Wiesner: Eng. Fract. Mech., 72 (2005), No. 3, 453.
• 11)   Y.  Haramishi,  T.  Tagawa,  E.  Abe,  H.  Mimura and  T.  Miyata: Q. J. Jpn. Weld. Soc., 23 (2005), 130.
• 12)   K.  Shibanuma,  S.  Aihara,  M.  Matsubara,  H.  Shirahata and  T.  Handa: Tetsu-to-Hagané, 99 (2013), 40.
• 13)   K.  Shibanuma,  S.  Aihara,  M.  Matsubara,  H.  Shirahata and  T.  Handa: Tetsu-to-Hagané, 99 (2013), 50.
• 14)   K.  Shibanuma,  S.  Aihara and  K.  Suzuki: Eng. Fract. Mech., 151 (2016), 161.
• 15)   K.  Shibanuma,  S.  Aihara and  K.  Suzuki: Eng. Fract. Mech., 151 (2016), 181.
• 16)   K.  Shibanuma,  S.  Aihara and  S.  Ohtsuka: ISIJ Int., 54 (2014), 1719.
• 17)   N. J.  Petch: Acta Metall., 34 (1986), 1387.
• 18)   J. I.  San Martin and  J. M.  Rodriguez-Ibabe: Scr. Mater., 40 (1999), 459.
• 19)   T.  Hiraide,  K.  Shibanuma and  S.  Aihara: Tetsu-to-Hagané, 101 (2015), 50.
• 20)   L. E.  Miller and  G. C.  Smith: J. Iron Steel Inst., 208 (1970), 998.
• 21)   Y. J.  Park and  I. M.  Bernstein: Metall. Trans. A, 10A (1979), 1653.
• 22)   A.  Valiente,  J.  Ruiz and  M.  Elices: Eng. Fract. Mech., 72 (2005), 709.
• 23)   T.  Shimokawa,  T.  Oguro,  M.  Tanaka,  K.  Higashida and  T.  Ohashi: Mater. Sci. Eng. A, 598 (2014), 68.
• 24)   T.  Tagawa,  T.  Miyata,  S.  Aihara and  K.  Okamoto: Tetsu-to-Hagané, 79 (1993), 1183.
• 25)  EDAX Inc.: OIM Analysis ver. 6.1, Mahwah, New Jersey, (2011).
• 26)  The Iron and Steel Institute of Japan: Tekko-binran (Handbook of iron and steel), 1st ed., ISIJ, Tokyo, (1981), 438 (in Japanese).
• 27)   T.  Anderson: Fracture Mechanics, 3rd ed., CRC Press, Boca Raton, FL, (2005).
• 28)   M.  Yamaguchi: Bull. Iron Steel Inst. Jpn., 15 (2010), 755.
• 29)   J.  Kameda and  C. J.  Mcmahon, Jr.: Metall. Trans. A, 12A (1981), 31.
• 30)  SIMULIA, Abaqus Analysis User’s Manual Version 6.14, Dassault Systemes, Vélizy-Villacoublay, (2014).
• 31)   M.  Ohata,  H.  Shoji and  F.  Minami: Tetsu-to-Hagané, 99 (2013), 573.