Effect of Carbon Content on Toughness of Tempered Martensitic Steels Analyzed by Toughness Prediction Model

Abstract

To evaluate the effect of carbon content on the toughness of tempered martensite, the critical crack tip opening displacement (CTOD) was evaluated for 0.1/0.3/0.5C-1.5Mn-1.0Mo (mass%) steels. The critical CTOD was the highest for 0.5C steel because of grain refinement rather than strengthening and cementite coarsening. The results were analyzed by a toughness prediction model that considered the strength, grain size, and cementite size. This model incorporated the microstructure information, stress distribution calculated using the finite element method (FEM), and fracture process criteria. It calculated the fracture point at which the local stress and local strength of the material correspond. The fracture process was divided into the following three stages: Stage I, cementite cracking; Stage II, microcrack propagation into the cementite and ferrite boundary by stress concentration caused by dislocation pileup along the major axis of the martensite block; and Stage III, crack propagation into the first intersecting 15°-oriented boundary with the crack length of the minor axis of the martensite block. The model calculation reflected experimental trends, revealing that the bottleneck in the fracture process was Stage III. Therefore, the refinement of the minor axis of the block was effective for toughness improvement.

1. Introduction

High-strength steel is increasingly required to make large and lightweight structures. Toughness is another important property of such steel. To properly understand fracture toughness, it is important to understand the role of the steel microstructure in the fracture process.

Petch reported that the fracture stress is dependent on the grain size of ferrite and the size of cementite.¹⁾ Lin considered that multiple fracture processes are related to the particle size and grain size.²⁾ Ritchie presented a relationship between the local fracture stress a few grains ahead of the crack tip and the fracture toughness.³⁾ However, such models did not consider the fracture toughness variation caused by the microstructural distribution. Beremin presented a fracture probability model based on the weakest-link theory to represent toughness variation.⁴⁾ However, this model was based on continuum theory; therefore, it did not clarify the relationship between the microstructure and the fracture toughness.

To address these issues, Shibanuma presented a toughness prediction model for ferrite-cementite steel that considered the fracture process and microstructure information.⁵⁾ This model could predict the toughness variation, which was found to be related to the microstructure. Hiraide and Shibanuma also applied this model to ferrite–pearlite microstructure and obtained accurate prediction results.^6,7) Further, Kawata presented a toughness prediction model for bainite-MA (martensite-austenite constituent) steel.⁸⁾ However, such models are not applicable to martensitic steels used in high-strength steels. Therefore, we observed the fracture process in tempered martensite steel and presented a toughness prediction model in our previous paper.⁹⁾

The carbon content affects various toughness-controlling factors such as strength, grain size, and cementite size; however, the dominant controlling factor is not known. In this study, to investigate the effect of carbon content on the toughness of tempered martensite, the effects of strength, grain size, and cementite size on toughness were evaluated experimentally and with a toughness prediction model.

2. Experimental

2.1. Tested Material

Ingots were produced by laboratory vacuum melting and were comprised of 0.1/0.3/0.5C-1.5Mn-1.0Mo (mass%) steel. Table 1 shows the chemical composition of the ingots. Their size was 120 mm in thickness, 120 mm in width, and 400 mm in length. They were hot-rolled into 25-mm-thick plates. The plates were heated at 1250°C for 30 min to ensure uniformity in the diameter of austenite grains. Then, they were quenched from 1250°C to obtain a martensite structure, followed by tempering at 650°C for 40 min.

Table 1. Chemical composition (mass%).

C	Si	Mn	P	S	Mo	t-Al	t-N	O
0.10	0.015	1.46	<0.002	0.0005	1.01	<0.002	0.0009	0.0016
0.29	0.014	1.50	<0.002	0.0004	1.01	<0.002	0.0007	0.0027
0.50	0.011	1.46	<0.002	0.0004	1.01	<0.002	0.0007	<0.0010

2.2. Characterization of Microstructure

Grain sizes were measured by electron backscatter diffraction (EBSD). 15°-oriented grains were defined by boundaries with a misorientation angle of at least 15°. As the grain shape was not equiaxed, the diameter distributions of the major and minor axes were measured. Cementite was observed by scanning electron microscopy (SEM), and size distributions were measured from binarized images. The cementite size was defined as the diameter of the minor axis because cementite cracked easily along this axis.

2.3. Tensile Testing

Tensile tests were conducted with 10 mmφ round bar specimens. The test temperature was 20°C. For 0.1C steel, low-temperature tensile tests were also conducted at −110°C and −150°C. The stress-strain curve was measured, and the 0.2% proof stress (PS) was determined from the point where the plastic strain was 0.2%. These material properties were used in finite element method (FEM) analysis to calculate the stress distribution in crack tip opening displacement (CTOD) specimens. For the other temperatures tested above, 0.2%PS was predicted by Gotoh’s formula,¹⁰⁾ which was found to have good accuracy for the tested data of 0.1C steel, as shown in Fig. 1.   

$$\begin{array}{l}{\sigma }_y=\\ {\sigma }_{y0}\text{exp}\left[\left(497.5-68.9ln{\sigma }_{y0}\right)\left({\displaystyle \frac{1}{T\left[°\mathrm{C}\right]+273}}-{\displaystyle \frac{1}{293}}\right)\right]\left[\text{MPa}\right]\end{array}$$(1)

Fig. 1.

Prediction result of 0.2%PS by Gotoh’s formula for 0.1C steel. (Online version in color.)

Here, σ_y0 is the 0.2%PS at room temperature and T, the test temperature. Before the yield point, elastic deformation was assumed, and after it, plastic deformation was assumed, using Swift’s formula.   

$$\sigma ={\sigma }_y{\left(\frac{{\epsilon }_p+0.002}{0.002}\right)}^n$$(2)

Here, ε_p is the plastic strain and n, the work-hardening exponent. n was interpolated and extrapolated to the test temperatures.

2.4. Crack Tip Opening Displacement Test

CTOD tests were conducted by the three-point bending method according to the WES¹¹⁾ standard. As shown in Fig. 2, the specimen was 20 mm thick, 40 mm wide, and 180 mm long. It had a 20 mm-long crack, the last 2 mm of which was introduced as a fatigue crack. The test temperature was varied between −196°C and −80°C. The critical CTOD was defined as the CTOD value at which fracture occurred. Two CTOD tests were conducted at each temperature to accommodate variations in the critical CTOD. The CTOD was calculated using the following formula:   

$$\delta =\frac{K^2\left(1-{\nu }^2\right)}{2E{\sigma }_y}+\frac{r_p\left(W-a\right)V_p}{r_p\left(W-a\right)+a}$$(3)

Fig. 2.

Specimen to evaluate the CTOD in the three-point bending test.

Here, K is the stress intensity factor; r_p, the rotational factor (=0.44); ν, Poisson’s ratio; E, Young’s modulus; W, the specimen width; a, the crack length; and V_p, the plastic component of the opening displacement at the crack edge.

2.5. Finite Element Method Analysis

FEM analysis was conducted for the CTOD specimens using the commercial software Abaqus 6.14. The model was a three-dimensional elasto-plastic model. Figure 3 shows the FEM mesh division of one-quarter of the model, assuming longitudinal and through-thickness symmetry. The minimum element size was 0.1 mm along the crack propagation direction, the number of nodes was 6440, and the number of elements was 4746. To obtain the stress value at any time and point, the stress field near the crack was calculated as a function of time. The stress values between each node were also calculated by interpolation.

Fig. 3.

FEM mesh division of three-point bending specimen (1/4 symmetry model). (Online version in color.)

2.6. Observation of Fracture Surface

The fracture surface was observed to identify the fracture initiation point by SEM. The fracture initiation point was analyzed by energy-dispersive X-ray spectroscopy (EDS). EBSD analysis was conducted on the plane that crossed the fracture initiation point. The lengths of the dislocation pileup and crack propagation unit were determined based on the orientation and fracture configuration.

3. Results

Figure 4 shows EBSD inverse pole figure (IPF) maps, which are used to determine the block size distribution in the microstructure. The prior austenite grain size is approximately 100–200 μm. The microstructure is martensite, with a finely divided block and packet structure. As the carbon content is increased, the 15°-oriented grains are refined. In 0.1C steel, there are coarse bainite grains. Figure 5 shows the 15°-oriented grain size distribution. Here, the circle equivalent diameter converted from the major and minor diameters is shown. The total number of grains observed is 6811–11121 in the observation area of 800² μm². The overall distribution profile does not differ between 0.1C steel and 0.3C steel; however, the former has a longer tail near the maximum diameter than the latter. Figure 6 shows SEM images in which cementite has precipitated everywhere in the block-shaped structure. With an increase in the carbon content, the cementite size and the number of cementite particles both increase. Figure 7 shows the cementite size distribution. The total number of particles observed is 4791–7064 in the observation area of 20² μm². The maximum sizes in 0.1C steel and 0.3C steel are almost equal. Figure 8 shows the effect of carbon content on the strength and microstructure. The 15°-oriented grain size and cementite size were the 99th percentile value. With increasing carbon content, 0.2%PS increased, 15°-oriented grain size decreased, and cementite size increased. In the toughness prediction model, the 15°-oriented grain size and cementite size distribution were used.

Fig. 4.

EBSD inverse pole figure maps. (Online version in color.)

Fig. 5.

Cumulative area frequency of 15°-oriented grain size. (Online version in color.)

Fig. 6.

Scanning electron micrographs showing the cementite particle distribution.

Fig. 7.

Cumulative area frequency of cementite particle size. (Online version in color.)

Fig. 8.

Effect of carbon content on the strength and microstructure. (Online version in color.)

Figure 9 shows the effect of carbon content on critical CTOD. The dashed line in Fig. 9 shows the envelope of the minimum value. The critical CTOD increases with the temperature. A comparison of the minimum values of the critical CTOD indicates that 0.5C steel is the toughest. From the present experiment, it is inferred that the positive effect of grain refinement on toughness is stronger than the negative effects of strengthening and cementite coarsening. Toughness variation is the largest in 0.1C steel, possibly because of the large variation in grain sizes.

Fig. 9.

Effect of carbon content on the critical CTOD. (Online version in color.)

4. Modeling

The fracture process of tempered martensite was demonstrated in our previous paper⁹⁾ based on the observation of the fracture surface. As shown in Fig. 10,⁹⁾ by following the river pattern and conducting EDS analysis, the fracture initiation point was identified as cementite. The EBSD analysis of the cross-section across the fracture initiation point indicated that the crack propagated along with a change in direction at the block boundary, because cracks easily occur in the (100) plane. Therefore, the crack propagation unit was considered to be near the minor axis of the block. Focusing on the block where fracture occurred, the major axis was the same as that along the <111> direction. In addition to this observational result, it was also derived from martensitic crystallography that the block grows toward the <111> direction.¹²⁾ Therefore, in the worst case for fracture toughness, the stress was assumed to concentrate due to dislocation pileup along the major axis of the block. Considering the above phenomena, as shown in Fig. 11,⁹⁾ fracture was considered to occur in the following three stages:

Fig. 10.

Fracture surface of CTOD test for 0.3C steel (−196°C), (a) near fracture initiation point, (b) magnification of (a). (Online version in color.)

Fig. 11.

Modeling of micro-fracture process. (Online version in color.)

Stage I: Cementite cracking

Stage II: Microcrack propagation into the cementite and ferrite boundary by stress concentration due to the dislocation pileup along the major axis of the block

Stage III: Crack propagation into the first crossing 15°-oriented boundary (near minor axis of the block)

As shown in Fig. 12,⁹⁾ the toughness prediction model incorporates the size distribution of 15°-oriented grains and cementite, the stress distribution calculated from the tensile properties, and fracture process criteria. This model is a type of Monte-Carlo simulation. Therefore, microstructures are assigned according to the probability density functions which are derived from Figs. 5 and 7 with each calculation. The model calculates the fracture toughness using the displacement when fracture occurs. The calculation methods are as follows:

Fig. 12.

Overview of toughness prediction model. (Online version in color.)

4.1. Measurements for Microstructure

The grain size was measured by EBSD as a 15°-oriented defined boundary. The cementite size was measured by SEM and binarized to identify cementite. Size distributions for both were obtained.

4.2. Assignment of Microstructure

A high stress was assumed to concentrate near the crack front area; therefore, the crack front was selected as the calculation area. This area was divided into calculation cells of 50 μm in size so that the stress distribution would be almost flat in a cell. For each cell, grains were assigned from the grain size distribution until the cell was completely filled. Moreover, cementite particles were assigned from the cementite size distribution until their number density met the measured value.

4.3. Definition of Fracture Stress

The fracture stress for Stage II was defined by inputting the maximum major diameter and cementite size into Petch’s formula.¹⁾   

$${\sigma }_{F\mathrm{I}\mathrm{I}}=\{\begin{array}{cc}{\displaystyle \frac{4E{\gamma }_{\mathrm{I}\mathrm{I}}}{\left(1+{\displaystyle \frac{1}{\sqrt{2}}}\right)\left(1-{\nu }^2\right)k_y\sqrt{s}}}\mathrm{\hspace{0.17em} }\hspace{1em}\hspace{1em}\hspace{1em}& \left(t_{\theta }<c_c\right)\\ \sqrt{{\displaystyle \frac{4E{\gamma }_{\mathrm{I}\mathrm{I}}}{\pi \left(1-v^2\right)t_{\theta }}}-{\displaystyle \frac{{k_y}^{2}s}{8{\pi }^2{t_{\theta }}^2}}}-{\displaystyle \frac{k_y\sqrt{s}}{2\sqrt{2}\pi t_{\theta }}}& \left(t_{\theta }\ge c_c\right)\end{array}$$(4)

Here, γ_II is the effective surface energy at the ferrite-cementite interface (=10 J/m²); k_y, the Hall–Petch coefficient (=21 N/mm^3/2); s, the maximum major diameter; and t_θ, the cementite thickness. Moreover, c_c, the threshold cementite size affecting σ_FII, was defined by the following formula:   

$$c_c=\frac{\left(1+\frac{1}{\sqrt{2}}\right)\left(1-v^2\right)k_{y}s}{8\pi E{\gamma }_{\mathrm{I}\mathrm{I}}}$$(5)

The fracture stress for Stage III was defined by employing the maximum minor diameter in Griffith’s formula.¹³⁾   

$${\sigma }_{F\mathrm{I}\mathrm{I}\mathrm{I}}=\sqrt{\frac{\pi E{\gamma }_{\mathrm{I}\mathrm{I}\mathrm{I}}}{\left(1-v^2\right)D}}$$(6)

Here, γ_III is the effective surface energy at the ferrite-ferrite interface and D, the maximum minor diameter. As γ_III was assumed to be temperature-dependent, as shown in Fig. 13, San Martin’s result was quoted.¹⁴⁾

Fig. 13.

Effective surface energy for Stage III by San Martin & Rodriguez-Ibabe. (Online version in color.)

The stage with higher fracture stress between σ_FII and σ_FIII became the bottleneck process in each cell. In Stage I, the cracking condition was not considered because it was thought to occur easily; further, there were numerous cementite particles in the tempered martensite steel. Therefore, only Stages II and III were considered in this model. However, the cementite thickness for Stage II was obtained from the cementite distribution.

4.4. Calculation of Fracture Toughness

CTOD was increased in steps small enough to assure prediction accuracy. In effect, the CTOD range from 0.001 mm to 0.2 mm was divided into 100 steps in the FEM calculation. The stress distribution was obtained by the method mentioned in section 2.5. Figure 14 shows examples of stress distributions calculated by FEM. By comparing the fracture stress of the bottleneck process and local stress in each cell, the cells were searched for those that satisfied the fracture condition of the local stress exceeding the fracture stress. Here, the local stress was calculated by multiplying the cosine of the minimum angle between the loading direction and one of three (100) plane directions. If such a point was identified, the CTOD was regarded as critical CTOD. Otherwise, CTOD was increased until the fracture condition was satisfied or CTOD reached its upper limit where brittle fracture did not occur.

Fig. 14.

Examples of stress distributions calculated by FEM for 0.1C steel at −110°C. (Online version in color.)

5. Calculation Result

By only inputting the tensile property and microstructure information, the critical CTODs were calculated. The model calculation was repeated three times for each condition. As shown in Fig. 15, the calculated critical CTODs were temperature-dependent, and the results indicated that 0.5C steel was the toughest. This result agreed with the experimental results shown in Fig. 9. This dependency on temperature was attributed to the increase in yield stress at a lower temperature and increase in surface energy for σ_FIII at a higher temperature. For example, the temperature dependency of the local stress and fracture stress is shown in Fig. 16 for 0.5C steel. The bottleneck process is identified as Stage III, because σ_FIII is higher than σ_FII at all temperatures. This trend was similar for the other steels tested in this study.

Fig. 15.

Effect of carbon content on critical CTOD reproduced by model calculation. (Online version in color.)

Fig. 16.

Temperature dependency of local stress and fracture stress for 0.5C steel. (Online version in color.)

Carbon content is thought to affect toughness as follows. With increasing carbon content, the grains are refined and cementite coarsens. As a result, σ_FII is decided by the balance of grain refinement and cementite coarsening. On the other hand, σ_FIII only increases by grain refinement. As the bottleneck process is Stage III, toughness does not decrease even when σ_FII decreases due to cementite coarsening. Moreover, referring to Petch’s result,¹⁾ σ_FII is hardly affected by cementite sizes below 0.5 μm for grain diameters larger than 30 μm. The largest cementite size was 0.3 μm in this study. With increasing carbon content, the increase in fracture stress led to the improvement of the fracture toughness; however, the yield stress also increased, which was disadvantageous for toughness.

A comparison of the experimental and the calculated critical CTODs is shown in Fig. 17. The correspondence was made by using the same number of data between experiment and calculation. One-to-one correspondence is used to evaluate the tendency of the model calculation; however, it should be noted that it is less meaningful because both are probabilistic. Generally, there was good agreement between the two for a wide range of critical CTODs. One reason for the slightly underestimated values may be because the length of the dislocation pileup along the major axis of the block is assumed to be greater than the actual length. However, the length of the dislocation pileup may be smaller because martensite has a high dislocation density. Another reason is that the difference was not considered between the direction of the major axis of the block and the loading direction. If the direction difference is 45°, the dislocation pileup is the maximum because the local shear stress is maximized. However, the direction of the major axis of the block may not always be disadvantageous for fracture. In other words, the worst case was assumed for conservative predictions in this study. With regard to the two outliers whose experimental critical CTODs were over 0.1 mm, the experimental V_p of 0.1C steel was 0.42 mm and that of 0.5C steel was 0.22 mm. These values were larger than that of other data in which V_p was smaller than 0.05 mm. Therefore, these underestimations are considered to be the effect of ductile fracture evolution because ductile fracture is not addressed in the FEM calculation. In this higher CTOD region, ductile fracture is actually thought to occur prior to brittle fracture.

Fig. 17.

Comparison of experimental and calculated values of critical CTOD. (Online version in color.)

6. Conclusion

The effect of carbon content on the toughness of tempered martensite was analyzed using a toughness prediction model that considered the strength, grain size, and cementite size. The following conclusions were obtained.

• The critical CTOD was the highest for 0.5C steel owing to grain refinement rather than strengthening and cementite coarsening. This trend was also reproduced by the model calculation.

• The bottleneck process was Stage III; therefore, refinement of the minor axis of the block is beneficial for toughness improvement.

Further studies should focus on the modeling of cementite cracking and in situ stress distribution measurements just before fracture as well as the evaluation of the variations related to the microstructural distribution.

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