Effects of Carbon Content and Grain Orientation on the Crack Growth Behaviour in Magnesia-carbon Refractory Bricks

Yuta Hino; Shaowei Zhang

doi:10.2355/isijinternational.54.2221

Abstract

Effects of carbon content and loading direction/grain orientation on the crack growth resistance of MgO–C refractories were examined via evaluating R-curve, critical stress intensity factor and bridging stress derived from the results of three point bending testing on single edged notched beam samples. The results indicated that crack growth resistance, critical stress intensity factor and bridging stress all increased with increasing the carbon content in the refractories, and were greater in the loading direction horizontal to than perpendicular to the sample pressing direction. Nevertheless, the stress intensity factor at crack initiation was similar in all cases of samples containing different levels of carbon. Based on these, it can be concluded that an MgO–C refractory with a higher carbon content would have better resistance against crack propagation after initiation, but would not show obvious improvement in its resistance against crack initiation.

1. Introduction

Magnesia-carbon (MgO–C) bricks are un-fired refractories composed of mainly magnesia aggregates and fines, graphite flake and antioxidants additives. They possess much better corrosion resistance against steel-making slags as well as improved thermal shock/spalling resistance compared to fired carbon-free counterparts, thus have been and are still being used extensively to line key steel-making vessels such as converters and steel ladles.^1,2,3,4)

Thermal spalling is generally identified as one of the main mechanisms responsible for the damage of a refractory during service. As mentioned above, compared to the fired carbon-free counterparts, unfired MgO–C bricks have much better thermal shock/spalling resistance. Nevertheless, upon subjection to cyclic thermal changes at steel-making temperatures, some cracks due to large thermal stress could still be generated and subsequently propagated, resulting in some damages on the refractories. Such damage usually is not instantaneous but develops progressively with time. To prevent this kind of damage so as to improve service lives of refractories and steel-making vessels, cracks generation and propagation in the refractories need to be investigated, along with quantitative evaluation on the affecting factors underpinning. Considering this, it is important to find out the relationship between thermal cycling and refractories failures based on the principle of fracture mechanics. Although thermal shock resistance itself has been qualitatively studied by many researchers,^{5,6,7,8,9,10)} little work has been done on quantitative analysis of crack propagation in a refractory.

Considering that thermal spalling damage arises from thermal stress changes induced by the cyclic heat input and discharge, the first author examined the fracture behaviours of some types of refractories from the viewpoint of fracture mechanics.^11,12,13) One of these studies evaluated the relationship between fatigue failure and thermal spalling resistance of MgO–C refractories. It clarified that the strong ability of the refractories to resist dynamic fatigue failure is one of the main reasons for their excellent resistance against thermal shock.¹¹⁾ The crack growth behaviour in the refractories was also investigated via correlating the crack growth rate with stress intensity factor, i.e., K–V diagram.¹³⁾ In addition, the effect of carbon content in the refractories on the crack growth behaviour and fatigue failure was examined. The results indicated that increase in carbon content reduced the crack growth rate and improved fatigue lives. The bridging force acting on carbon particle was considered to be responsible for the dependency of crack growth rate on carbon content. In order to investigate the relationship quantitatively, crack growth resistance indicated by R-curve, needs to be determined and evaluated. However, the work on this was very limited, in particular, in the case of MgO–C refractory bricks.¹⁴⁾

On the other hand, MgO–C bricks are usually manufactured via uniaxial pressing using a friction press, therefore, grains, in particular, graphite flakes, often tend to orientate in the microstructure of the refractories,^15,16,17) resulting in anisotropic mechanical properties. The effect of orientation on mechanical strength was examined before.^15,16,17) However, to the knowledge of the present authors, its effect on the crack growth resistance of the refractories has not been investigated.

Therefore, in this study, three-point bending testing on MgO–C brick samples containing different levels of carbon was carried out under different loading conditions. Subsequently, R-curves of the refractories were determined and further evaluated based on the principle of fracture mechanics, and the effects of carbon content and grain orientation in the refractories on their crack growth resistance were discussed.

2. Experimental

Sintered MgO aggregates (purity: 98%, average diameter: 1.15 mm) and fine particles (purity: 98%, average diameter: 0.07 mm) and graphite flakes (purity: 97%, average diameter: under 0.15 mm) were used as the main raw materials, and phenolic resin was used as the binder. MgO and C were mixed respectively in weight ratios of MgO:C = (100-x):x (x = 10, 15, and 20 wt%) and then combined with 3% phenolic resin in a mixer. The mixed powder batch was fed into a steel die and pressed using a friction press to form a brick sample with standard dimensions, i.e., 114 (width) × 65 (height) × 230 mm (length). The brick was further cut into smaller pieces of samples of 20 (width, B) × 20 (height, W) × 200 mm (length, L), which were heat-treated at 1623 K for 3 h in a carbon monoxide atmosphere prior to mechanical testing. The apparent porosities of samples after heat-treatment are shown in Table 1. Apparent porosity increased with increasing carbon content in brick. A single notch about 1 mm wide and 10 mm deep was introduced in the middle of the lower part of a heat-treated sample using a diamond saw. Such an SENB (single edged notched beam) sample was subjected to three-point bending testing using the experimental set-up shown in Fig. 1. The span between the two loading points was fixed at 150 mm and the loading speed was 0.05 mm/min. The displacement corresponding to each applied load was recorded, and photographs monitoring the loading process were taken every 15 seconds. One of the photographs is shown in Fig. 2 as an example. From the image analysis, changes of notch width from the initial 1 mm were estimated. R-curves were established and used for further evaluation. Moreover, in order to evaluate the effect of grain orientation in the microstructure on crack growth resistance, samples were loaded in two directions, one parallel to the pressing direction (Fig. 3 <A>, referred to as direction <A>), and the other perpendicular to the pressing direction (Fig. 3 , referred to as direction ). Three point–bending test using plain samples without notches were also carried out in order to evaluate the modulus of rapture and static modulus of elasticity. To assist understanding the fracture procedure, fracture surfaces of some typical samples after bending testing were observed by using a scanning electronic microscope (SEM).

Table 1. The apparent porosity of sample after heat-treatment.

	MgO-10%C	MgO-15%C	MgO-20%C
Apparent porosity	8.07%	8.60%	9.69%

Fig. 1.

Experimental set-up for R-curve evaluation.

Fig. 2.

Photograph of notch in SENB specimen taken in the test.

Fig. 3.

Experimental conditions for three point bending test of SENB.

3. Results

Shown in Figs. 4 and 5 are respectively modulus of rapture (MoR) and static modulus of elasticity (E) of unnotched samples, determined from their load-displacement curves (not shown). E is calculated by using Eq. (1).²⁴⁾

E= L 3 ( ΔP ) 4B W 3 ( Δu )

(1)

Fig. 4.

Modulus of Rapture values of samples with various contents of carbon.

Fig. 5.

Static modulus of elasticity values of samples with various contents of carbon.

where, ΔP is variation in load, and Δu is variation in displacement.¹⁸⁾ As shown in Fig. 4, in the same loading direction, MoR increased with increasing the carbon content. On the other hand, according to Fig. 5, E decreased slightly with increasing the carbon content. Furthermore, both MoR and E in the direction <A>, i.e., parallel to the brick pressing direction, were greater than those in the direction , i.e., perpendicular to the brick pressing direction.

Figures 6, 7, 8, 9 further show the relationships between load level and change in notch width in the cases of samples containing 10–20%C in direction <A>, and 20%C in direction . As shown in Figs. 6, 7, 8, the maximum load value increased with increasing the carbon content. Comparison of Figs. 8 and 9 reveals that the maximum load in the direction <A> was larger than that in the direction , and after the peak load, the load values in both directions <A> and decreased gradually with increasing the notch width in the case of MgO-20%C sample but decreased relatively more rapidly in the cases of samples containing 10 and 15%C.

Fig. 6.

Relationship between load and notch width change in the case of sample MgO-10%C (in the direction <A>).

Fig. 7.

Relationship between load and notch width change in the case of MgO-15%C (in the direction <A>).

Fig. 8.

Relationship between load and notch width change in the case of MgO-20%C (in the direction <A>).

Fig. 9.

Relationship between load and notch width change in the case of MgO-20%C (in the direction ).

4. Discussion

4.1. Evaluation of R-curve and Critical Stress Intensity Factor

Due to the wide range of particle size distribution (from mm-sized aggregates to micron-sized fines) and relatively high levels of porosity in the samples, it is difficult to directly detect micro-cracks in them and monitor the crack extension during the bending test process. For this reason, the crack extension was estimated indirectly from the notch width change which was measured semi-continuously, as described below. Then, based on the results, R-curves can be established and used to discuss the effects of carbon content and grain orientation on the crack growth behaviour.

According to ASTM 399,¹⁹⁾ crack length and crack mouth open displacement (CMOD) V are correlated with each other by Eqs. (2) and (3),

V( a / W ) =V⋅( WBE LP ) = WBE LS

(2)

V( a / W ) =6( a / W ) ( 0.76-2.28( a / W ) +3.87 ( a / W ) 2 -2.07 ( a / W ) 3 + 0.66 ( 1-( a / W ) ) 2 )

(3)

The load (P) to V ratio (referred to as S (Eq. (4))) is constant in the initial stage before the crack starts to extend, but starts to change once the crack does so.

S= P V

(4)

S can be calculated from the plots in Figs. 6, 7, 8, 9, and the value of V( a / W ) can be obtained by substituting S values, elastic modulus values (Fig. 5) and dimensional sizes of samples into Eq. (2). Then, the value of a/W can be obtained by substituting the V( a / W ) value into Eq. (3). Finally, the crack length can be determined. As for the crack growth resistance K_R, it can be calculated by using Eqs. (5) and (6).²⁰⁾

K R = 3PL 2B W 2 a ⋅F( a / W )

(5)

F( a / W ) =1.964-2.837( a / W ) +13.71 ( a / W ) 2 -23.25 ( a / W ) 3 +24.13 ( a / W ) 4

(6)

Figure 10 presents R-curves for samples containing 10, 15, and 20%C in the direction <A>, determined by using the method described above. And Fig. 11 compares R-curves of the sample containing 20%C in the direction <A> and direction . Here, the material with a higher intercept value on the R-curve has a higher resistance against crack initiation, and that with a higher slope value on the R-curve has a better resistance against crack growth. According to Fig. 10, the slope on the R-curve increased with increasing the carbon content. However, the intercept changed very little. These results indicated that the crack growth resistance, K_R, increased with increasing the carbon content, whereas the crack initiation resistance changed little with increasing the carbon content. Moreover, as indicated by Fig. 11, crack growth resistance for the sample containing 20%C in the direction <A> was higher than in the direction .

Fig. 10.

R-curves of MgO–C samples containing 10, 15 and 20%C respectively.

Fig. 11.

R-curves of the MgO–C sample containing 20%C in the directions <A> and .

In addition, the crack growth resistance can be further evaluated quantitatively via determining the critical stress intensity factor in terms of the Griffith’s theory.¹⁸⁾ K_R, is correlated with crack extension length and modulus of rapture by Eq. (7), where, σ _i is the modulus of rapture (more precisely, the load at the deviation point on a load-displacement curve) and Δa is crack extension.

K R = σ i π( a 0 +Δa )

(7)

Thus,

K R 2 =π σ i 2 Δa+π σ i 2 a 0 =π σ i 2 Δa+ K i

(8)

Equation (8) reveals that the square of K_R changes linearly with crack extension length. Therefore, by squaring K_R values shown in Figs. 10 and 11, the critical stress intensity factor (K_max) can be obtained via the following procedure.

First, the modulus of rapture (i.e., σ _i) is calculated from the peak load shown on the load-displacement curve of unnotched sample, and the intercept point of R-curve with the vertical axis is identified (Fig. 12). From this intercept point, the value of stress intensity factor at the onset of crack growth is obtained. Next, a straight line passing through this intercept point and having the inclination of π σ i 2 is drawn (Fig. 12). From the intercept of this line with the horizontal axis, the apparent initial crack length, a₀ that is corresponded to the distance between the intercept of this line with the horizontal axis and the origin, is found. Then, a tangent line, passing through the point of a₀ to the R-curve, is drawn. Finally, from the contact point, the critical stress intensity factor K_max could be determined. K_max indicates the critical point at which the fracture mode of a material starts to change from stable to unstable. With increasing K_max, the crack extension will be reduced and the occurrence of an unstable fracture will become harder.

Fig. 12.

Determination of the critical stress intensity factor.

Figure 13 compares K_max values obtained from the R-curves shown in Figs. 10 and 11. In the same direction, K_max increased with increasing the carbon content in the sample. In particular, in the direction <A>, K_max in the case of the sample containing 20%C was more than twice as great as that in the case of the sample containing 10%C. Also, similarly to that indicated by Fig. 11, K_max for the sample containing 20%C in the direction <A> was greater than that in the direction . However, K_max for the sample containing 20%C in the direction was larger than that for the sample containing 10%C in the direction <A> and the sample containing 15%C in the direction <A>. These results additionally confirmed that a sample containing higher carbon content would have better crack growth resistance than that containing lower carbon content, even when the loading direction relative to the sample was different.

Fig. 13.

Comparison of critical stress intensity factor.

The values of stress intensity factor indicating the crack initiation resistance were also obtained from R-curves (Fig. 14). The carbon content did not show obvious effect on the stress intensity factor. Only the sample containing 20%C in the direction <A> showed slightly higher value of stress intensity factor than in the direction and other samples. In other words, no obvious carbon content dependence of the stress intensity factor at crack initiation in the samples was observed.

Fig. 14.

Comparison of stress intensity factor at crack initiation.

From above discussion, it could be concluded that increasing carbon content in an MgO–C refractory would improve its resistance against the propagation of cracks after initiation, but have little effect on its resistance against crack initiation.

4.2. Calculation of Bridging Stress

As shown in Fig. 10 and described above, the crack growth resistance of MgO–C refractories increased with increasing their carbon contents, which could be attributed to the bridging effect from the grains in their microstructure. To further evaluate the effect of carbon content in samples on the crack growth resistance, the bridging stress, i.e., the force of crack closure, is calculated based on R-curves. The relationship between bridging stress (σ _b) and K_R is expressed as,^{14,21,22,23,24)}

K R = K IC + 2 2π ∫ 0 Δa ( σ b x ) dx

(9)

By simply assuming that σ _b is homogeneous over the whole fracture surface and by further integrating Eqs. (9), (10) is obtained.

K R = K IC +4 σ b Δa 2π

(10)

According to Eq. (10), σ _b can be estimated empirically as described below. First, K_R is plotted versus the square root of crack extension, Δa (Fig. 15). As seen from Fig. 15, the former increased linearly with increasing the latter to a critical point but became almost constant beyond this critical point. Next, a regression line is drawn based on the data before the critical point (Fig. 15). σ _b is then determined from the slope of this regression line. In addition, the length of grain bridging is determined from the critical point where occurrence and disappearance of the bridging stress are balanced.

Fig. 15.

Relationship between K_R and crack extension.

Figures 16 and 17 give respectively values of σ _b and length of grain bridging. The former reveals that bridging stress increased with increasing the carbon content. Furthermore, corresponding to the tendency revealed by Fig. 13, the bridging stress for the sample containing 20%C in the direction <A> was larger than in the direction . On the other hand, the stationary grain bridging length increased with increasing the carbon content as well as bridging stress, whereas there was no difference between the grain bridging lengths in the direction <A> and direction (Fig. 17). From these results, it is considered that the stationary length of grain bridging simply depends on the carbon content, or, more precisely, on the number of graphite flakes present on the fracture surface.

Fig. 16.

Comparison of bridging stress.

Fig. 17.

Comparison of stationary length of grain bridging.

4.3. Further Consideration on the Effects of Carbon Content and Orientation on the Crack Growth Resistance

Backscattered Electron images of around the centre area of fracture surfaces of samples containing 10% and 20%C in the direction <A> are shown in Fig. 18, revealing that laminar structures, oriented obviously in the direction perpendicular to the loading direction. Such oriented structures were resultant from the uniaxial pressing during consolidation of the brick sample. Compared to the case of the sample containing 10%C, a finer laminar structure and more complicated concave-convex morphologies were observed on the fracture surface of the sample containing 20%C. As confirmed by Fig. 17 and discussed above, the bridging stress increased with increasing the carbon content in the bricks because of increased number of carbon particles contributing to the grain bridging. On the other hand, in terms of Fig. 18, refraction or divergence of crack also could occur due to the presence of carbon, thus preventing the crack propagation and resulting in more complicated fracture surface.

Fig. 18.

Backscattered electron images of fracture surfaces of a) MgO-10%C and b) MgO-20%C, in the direction <A>.

Next, the effect of grain orientation on the crack growth will be discussed. A typical microstructure of MgO-20%C brick after heat treatment is shown in Fig. 19. As mentioned in section 1, MgO–C brick is manufactured via uniaxial pressing in general. The uniaxial pressing arranges the graphite flakes mostly perpendicular to the pressing direction as observed in Fig. 19. This fact implies that the tests have been carried out with the graphite flakes perpendicular and parallel to the loading direction for the <A> and in the press conditions, respectively. Figure 20 shows schematically the stresses acting on carbon particles when MgO–C bricks are loaded in the a): direction <A> and b): direction , respectively. As described above, the graphite flakes has the morphologies of flakes and plates. In Fig. 20, d, l, and h show width, length and height of the graphite flakes, respectively, in a microscopic scale. Irwin’s theory is available assuming that the directions of the carbon flakes on the fracture surface are completely perpendicular and horizontal to the loading directions, which correspond to the <A> and in the test conditions, respectively. According to Irwin’s theory,²⁵⁾ the fracture of SENB specimen in the present case can be regarded as mode I, so the bridging grains are under a tensile stress. In this situation, bridging stress in the direction <A> is assumed to be almost the same as that in the direction . It can be deduced that the lower surface of carbon particle on the fracture surface should be subjected to a bending stress in addition to the bridging stress. By further assuming that the bending stress acting on the carbon particle is the same as that on a normal beam, it can be correlated to the width or height of the sample as indicated by Eq. (11).²⁶⁾

F <A> ∝ P d h 2 , F ∝ P h d 2

(11)

Fig. 19.

Backscattered electron images of microstructure of MgO-20%C after heat treatment (before testing).

Fig. 20.

A schematic diagram showing the stresses acting on a carbon particle in the a): direction <A> and b): direction , respectively.

Thus, it can be expected that for a given load level, the stress acting on a particle whose height is larger than the width (namely the particle with a higher aspect ratio, as in the direction ), will be larger than on a particle whose height is smaller than the width (as in the direction <A>). Consequently, more carbon particles will be broken down on the fracture surface in the direction than in the direction <A>, further making it easier for the crack to propagate in the former case due to the practically decreased bridging stress.

Based on the results shown in Figs. 10, 11, 12, 13, 14, 15, 16, 17 and the relevant discussion above, it can be concluded that MgO–C bricks with higher carbon contents would have higher crack growth resistance because of more carbon particles contributing to grain bridging and the increased crack refraction in the refractories. This is one of the main reasons for the excellent thermal shock resistance of MgO–C bricks containing high levels of carbon.

5. Summary

Effects of carbon content and grain orientation (loading direction) on the crack growth resistance of MgO–C bricks were investigated via evaluating R-curve, critical stress intensity factor and bridging stress. The main results can be summarised as follows:

1) Crack growth resistance increased with increasing the carbon content of the refractories. Correspondingly, critical stress intensity factor and bridging stress also increased.

2) Crack growth resistance, critical stress intensity factor and bridging stress in the loading direction horizontal to the sample pressing direction were greater than those in the loading direction perpendicular to the sample pressing direction.

3) Carbon content in the refractories had little effect on the stress intensity factor at crack initiation, i.e., it had little effect on the resistance against crack initiation.

Nomenclature

a: Depth of notch in SENB sample (m)

a₀: Apparent initial crack length in sample (m)

B: Width of SENB testing sample (m)

d: Width of graphite particle (m)

E: Static modulus of elasticity (MPa)

h: Height of graphite particle (m)

K_i: Stress intensity factor at crack propagation starting (MPa·m^1/2)

K_max: Critical stress intensity factor (MPa·m^1/2)

K_R: Crack growth resistance (MPa·m^1/2)

L: Span (m)

l: Stational length of grain bridging (m)

MoR: modulus of rapture (MPa)

P: Load (N)

S: The ratio of load to width of notch (–)

u: displacement (mm)

V: Width of notch in SENB sample (mm)

W: Height of SENB testing sample (m)

Δa: crack extension (mm)

Δu: difference of displacement (mm)

ΔP: difference of load (N)

Δu: change of notch width (mm)

σ _i: Modulus of rapture (the stress at the deviation point on a load displacement curve) (MPa)

σ _b: Bridging stress (MPa)

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