Previous work: Mechanical characterization by standard methods (^{Alcaraz, 2012})

The materials under study are cast steels from two different cable anchorages (see Figure 3), where the chemical composition, microstructural details, and tensile and fracture toughness properties were determined according to current standards. The chemical composition was obtained by applying the optical spark emission technique under the ^{ASTM E1019} and ^{ASTM E415} standards. The microstructure characterization was performed by optical microscopy after specimen polishing and chemical attack with Nital-3%. A total of 9 rectangular specimens from anchorage 1 and 34 rectangular specimens from anchorage 2 were prepared for tensile testing according to the ^{ASTM E8} standard. In addition, plane-strain fracture toughness K_IC was determined following the guidelines of the ^{ASTM E399} standard; SE(B) three-point bend specimens were fabricated with a maximum thickness allowed by the limited dimensions of the respective anchorages. Thus, from anchorage 1, two 52-mm-thick specimens were obtained, whereas one specimen of 60 mm thickness was fabricated from anchorage 2.

Small punch technique characterization

As mentioned, a widely used correlation for assessing the fracture toughness of metallic materials by means of the small punch technique is given by Eq. (1). This expression, which relates the fracture parameter J_IC with the equivalent fracture strain ε_qf, has proved to give good approximations. In fact, fitting coefficients k and J₀ for several materials have been reported by some authors (^{Mao, 1987}; ^{Wang, 2008}; ^{Guan, 2011}). In the present work, the fitting parameters mentioned above have been used for the fracture toughness estimation of the cast steels under study, and they are shown in Table 1.

Moreover, additional k and J₀ values were also obtained by using (ε_qf, J_IC) values from anchorage 2 and corresponding low-alloy steel values from literature (^{Guan, 2011}), see Table 2, where the main alloying element was Chromium (Cr). It is worth mentioning that (ε_qf, J_IC) values from weld steels were not considered from such reference because the steel under study is a cast steel without welding. The ε_qf value from anchorage 2 was calculated by using Eq. (2), while J_IC was obtained by means of Equation (3), where E is Young’s modulus and v represents Poisson’s ratio of the material.

The small punch test specimens considered were 10×10 mm² squares of 0.5 mm thickness. Eigth test pieces were prepared from anchorage 1 and eigth samples from anchorage 2. The testing machine used was a Zwick Roell single-column equipment, model BT1-FR2.5TS.140, 2500 N loading capacity. The SPT compression tests were performed at room temperature under displacement control by using TestExpert software (Zwick Roell) at a speed of 0.6 mm/min as recommended (^{CWA 15627, 2008}).

Mechanical characterization by standard methods

Chemical analysis results from previous work of the two cable anchorage steels are shown in Table 3. Based on their alloying elements, the materials were classified as low-alloy cast steels, where anchorage 1 is named 1Cr-0.5Ni, and anchorage 2 as 0.8Cr-0.6Ni. Figure 4 presents metallographic examinations from the two anchorages. In both cast steels, a characteristic ferrite-pearlite microstructure is observed; however, some differences can be distinguished concerning the phase distribution, possibly due to a deficient heat treatment (^{López, 2009}). Also, some sulfides and pores are also observed (Figure 5), as well as macroscopic discontinuities (Figure 6).

Figure 4 Microstructure in anchorage 1 (left) and anchorage 2 (right), 200X. 

Figure 5 Sulfides (white arrow) and pores (black arrow) observed in both anchorages (^{Alcaraz, 2012}). 

Figure 6 Macro-pores and cavities observed in both anchorages (^{Alcaraz, 2012}). 

The tensile mechanical properties obtained from previous work are shown in Table 4. It is observed that the steel from anchorage 1 has a yield and ultimate strength higher than those of anchorage 2; however, the ductility is higher for the cast steel from anchorage 2, as evidenced by the elongation percent. Figure 7 shows stress-strain curves for the two cast steels for comparison purposes. The stress-strain curve from anchorage 1 is typical of high-resistance steel, whereas the corresponding curve for anchorage 2 is representative of high-ductility steels with extensive plastic strain prior to fracture.

Figure 7 Stress-strain curves for both anchorages. 

The fracture toughness testing results according to ASTM E399 standard are shown in Table 5. By comparing fracture toughness K_IC values for both anchorages, anchorage 2 presents a higher value than anchorage 1. The difference can be explained by the high ductility exhibited by anchorage 2 with respect to anchorage 1; see Table 4.

Small Punch Test Characterization

Load-displacement curves obtained from small punch testing for both anchorages are shown in Figure 8. These curves display a characteristic ductile behavior for both steels (^{Lacalle, 2012}). Some clear differences can be appreciated between both curve sets if the maximum values of load and displacement are considered. The set of curves for anchorage 1 exhibits lower load and displacement values than the corresponding values for anchorage 2. According to this result, the SPT technique yields load-displacement curves with good repeatability and thus can make a capable distinction between the two types of cast steels; nevertheless, the maximum load values slightly fluctuate. This last behavior is linked to local strain concentrations arising before the maximum load is reached, leading to material instabilities (^{Lacalle, 2012}).

Figure 8 SPT load-displacement curves for steel specimens in anchorage 1 (left) and anchorage 2 (right). 

The failure morphology displayed by the small punch specimens for both anchorages showed a hemispherical surface, and fracture occurred along the circumference where the strain is highest; see Figure 9. This failure mode is typical of ductile steels.

Figure 9 Fracture morphology in small punch specimens in anchorage 1 (left) and anchorage 2 (right). 

To analyze the SPT fracture toughness results, the equivalent fracture strain ε_qf is used. This parameter is calculated from a modified version of Eq. (2) (^{Mao, 1987}), which is given as

Where d* is the displacement at fracture, which is obtained from the load-displacement curves for the fractured specimens. Thus, d* and ε_qf values for the specimens from anchorages 1 and 2 are shown in Table 6. By observing the displacement values d* from both anchorages, it is then clear that the cast steel from anchorage 2 shows higher ductility, as previously concluded from Figure 8 and Table 4.

Table 7 shows the results obtained when the equivalent fracture strain, ε_qf (Table 6), is introduced into the different correlation models given in Table 1. Corresponding K_IC values are obtained by using Eq. (3) and compared with the K_IC value found from the standard fracture mechanics technique (^{ASTM E399, 2004}). It is observed that the K_IC values from empirical relationships (^{Wang, 2008}; ^{Guan, 2011}) support once again the higher toughness of anchorage 2. However, by comparing such values with the K_IC reference value obtained from the standard ^{ASTM E399} technique, the SPT K_IC values are more than 60% higher. On the other hand, when the parameters are substituted into the relationship proposed (^{Mao, 1987}) for the materials under study, negative K_IC values are obtained, which have no physical meaning. This difference can be attributed to materials used in correlations since coefficients can be different. In addition, specimen thickness and device dimensions have an important effect on the results. In fact, this is one of the reasons why the European Committee for Standardization (^{CWA 15627, 2008}) recommends unifying these parameters.

To achieve better estimates of the fracture toughness values for the cast steels under study, k and J₀ values were obtained by using an additional correlation with (ε_qf , J_IC) values (^{Guan, 2011}), along with corresponding values from anchorage 2; see Table 2. Figure 10 shows a J_IC-ε_qf plot from such data, along with the trend line with fitting parameters k=340.27 and J₀ =54.19 and correlation coefficient R²=0.9511. Thus, the new empirical relationship results in Eq. (5).

Figure 10 Equivalent fracture strain ε_af-fracture toughness J_IC correlation. 

This new correlation was tested by substituting the ε_qf value from anchorage 1 to obtain a new K_IC value, which is 40.87 MPa∙m^1/2. A better approximation was reached, with 4% error compared to previous models. Thus, for the anchorage cast steels under study, the empirical model (5) is proposed for fracture toughness assessment by the small punch technique.

Finally, Figures 11 (obtained from previous work) and 12 show fractographs from standard and small punch tested specimens, respectively. The fracture surface from the standard specimen shows trans-granular cleavage with ductile tearing, which is associated with a triaxial stress state (^{Alcaraz, 2012}). In contrast, the fracture surface from the SPT specimen exhibits ductile tearing with a considerable quantity of micro-voids. This type of fracture can be associated with a biaxial stress state (insignificant third stress component), which yields extensive plastic deformation throughout the reduced thickness of the SPT specimen.

Figure 11 Fractograph for a standard specimen showing cleavage behavior plus dimples and tear ridges (^{Alcaraz, 2012}). 

Figure 12 Typical fractograph for SPT specimens: (a) through-thickness fracture, (b) Detail of the rectangule in (a) exhibites ductile failure by micro-void growth and coalescence.