1 Introduction

It is well-known that the machinability of steel has great effect on cost reduction of products, productivity increase, and realization of up-speed, automation, and high precision of machine work. Control of non-metallic inclusions is one of the most effective methods to improve the machinability of steel.[1] One of the ways to improve machinability of steel is attained by realization of the inclusions mechanical properties.[2] The microvoids and microcracks are nucleated by stress concentration due to different mechanical properties between inclusions and matrix.[3,4] It is considered that soft inclusions in steel can promote ductile fracture of chip formation process.[5] However, hard inclusions which have high melting points in steel can reduce tool life seriously during cutting process because of abrasive wear.[6] Therefore, it is necessary to investigate the mechanical properties of inclusions in steel, as the basis of the investigation of the effects of inclusions on machinability.

In fact, few experimental methods are available to determine the mechanical properties of inclusions because of their small size. In recent years, nano-indentation tests[7–10] have been revealed suitable for measuring hardness, as well as elastic moduli of microscopic volumes of materials such as microstructure, thin-film structures, oxides, and inclusions.[11–32] Nano-indentation is simply an indentation test in which the length scale of the penetration is measured in nanometers (10−9 m) rather than microns (10−6 m) or millimeters (10−3 m), the latter being common in conventional hardness tests. However, in nano-indentation tests, the size of the residual impression is of the order of microns and too small to be conveniently measured directly. Thus, it is customary to determine the contact area by measuring the depth of penetration of the indenter into the specimen surface. This, together with the known geometry of the indenter, provides an indirect measurement of contact area at full load.[10]

This paper aims at investigating the effects of inclusions on machinability. In the first part of the paper, the hardness, elastic moduli, and load–displacement curves of BN, MnS, Al2O3, TiN, and matrices in free-cutting steels are measured by means of nano-indentation tests. Then, the effects of inclusions on machinability are discussed using nano-indentation results and thermodynamic calculations. Finally, errors of nano-indentation measurements and macrohardness tests are analyzed and discussed.

2 Experimental Procedure

The chemical compositions and states of samples for nano-indentation tests are shown in Table I.

Table I Chemical Composition (in mass pct) and State of Samples
Full size table

As-cast samples were obtained by crucible melting. Experiments were carried out in a tubular resistance furnace (SKL 16-8), as shown in Figure 1. A crucible in which Al2O3 with 99.99 pct purity was used had capacity of 1 kg. Argon gas of gas flow rate of 2 L min−1 was used to guarantee the inert atmosphere during the whole experimental process, and the experimental temperature was about 1873 K (1600 °C). The experimental material was 42CrMo steel and 20CrMo steel. The experimental processes are as follows: The crucible containing 1 kg steel was placed in a resistance furnace, and arc heating was conducted until the steel was wholly melted to the required temperature. Ferro boron (boron content is 20 pct) was added and nitrogen gas was injected into steel to achieve different N/B ratios. Sample 42CrMo-BN was controlled cooled to room temperature and the cooling curve is shown in Figure 2. Sample 42CrMo-TiN was natural cooled to room temperature and sample 20CrMo-BN was furnace cooled to room temperature. So, samples with different B and N contents were prepared.

Fig. 1
figure 1

Schematic diagram of tubular resistance furnace

Full size image
Fig. 2
figure 2

Schematic illustration of cooling curve of sample 42CrMo-BN

Full size image

In order to observe the morphology of MnS in the steel and measure the mechanical properties of the samples, AISI1215 bar with diameter of 36 mm was prepared.

15 mm3 cubes were taken from samples in various states for nano-indentation measurements. These cubes were polished by SiC papers and diamond suspensions. After polished, the observation of microstructure was carried out using metallographic microscope (52XA) after nano-indentation tests. In sample 20CrMo-BN or AISI1215, an area of around 216 mm2 was analyzed by image analysis system (IMAGE-PRO PLUS6.0) to obtain the area fraction of perlite at the 50 magnification.

Before nano-indentation tests, inclusions in cubes were characterized through scanning electron microscope (SEM; Zeiss Ultra55; Carl Zeiss, Oberkochen, Germany) and energy-dispersive spectroscopy (EDS; INCA X-MAX50; Oxford Instruments, Oxfordshire, U.K.). The morphologies of inclusions were observed and the chemical compositions of inclusions were obtained. Meanwhile, morphologies and chemical compositions of BN inclusions were characterized by transmission electron microscope (TEM; JEM-2010; JEOL, Tokyo, Japan) with an energy-dispersive spectroscope (EDS; INCA OXFORD; Oxford Instruments, Oxfordshire, U.K.). Samples for TEM were prepared by mechanical polishing and electrochemical thinning using electrolyte composed of perchloric acid and ethanol (volume ratio, 7:93).

Nano-indentation measurements of inclusions and matrices were performed by Nano-mechanical Test Instruments (Nano-indenter II; MTS, Eden Prairie, USA) with Berkovich tip indenter, as shown in Figure 3. It allows the application of loads from 1 to 70,000.00 μN and records the displacement as a function of applied loads with a high load resolution (75 nN) and a high displacement resolution (0.04 nm). Parameters of measurements were as follows: maximum depth h max = 500 nm, the Poisson’s ratio \( \nu \) = 0.3. In order to remove the size effects of nano-indentation,[33,34] the indentation depth was unified. In nano-indentation tests, each inclusion was measured 5 times to obtain the average hardness and elastic modulus. After the tests, the indentation load–displacement curves of inclusions and matrices were obtained.

Fig. 3
figure 3

Schematic diagram of the nano-indenter II

Full size image

3 Principle of Nano-Indentation

Based on the half-space elastic deformation theory, hardness (\( H \)) and elastic modulus (\( E \)) values can be extracted from the experimental data (load–displacement curves) using the Oliver–Pharr (O&P) method.[35–37] For the test, Berkovich tip indenter showing a face of 78.9 deg is used.

A schematic diagram of the elasto-plastic indentation is shown in Figure 4. \( h_{\text{c}} \) is the vertical distance along which contact is made (hereafter called the contact depth), \( h_{\text{f}} \) is the final depth of the contact impression after unloading. \( P \) is the indentation load, \( h_{ \hbox{max} } \) is the indenter displacement at peak load.

Fig. 4
figure 4

Schematic diagram of the elasto-plastic indentation

Full size image

A schematic of the load–displacement curve recorded during a nano-indentation test is presented in Figure 5. The plastic work done in the viscoelastic-plastic case is represented by the area \( A_{1} \) (OBC). The area \( A_{2} \) (CBC′) corresponds to the elastic work recovered during the unloading segment. In case of completely plastic material, the unloading curve is a straight line (BC′) and \( h_{\text{f}} = h_{\hbox{max} } \left( {A_{2} = 0} \right) \). \( S \) is the contact compliance (initial slope of the unloading load–displacement curve at the maximum depth of penetration (or peak load)) and \( P_{ \hbox{max} } \) is the peak load.

Fig. 5
figure 5

Schematic diagram of indentation load–displacement curve

Full size image

Once \( H \) is known, it can be used to assess the yield stress of the probed material as follows. According to Fischer-Cripps[10] who assumes that the contact is frictionless, \( H \) and maximum shear stress, \( \tau_{ \hbox{max} } \), is correlated as below:

$$ H = 2\tau_{ \hbox{max} } \left( {1 + \alpha } \right), $$
(1)

where \( \alpha \) = 70.3 deg is the equivalent cone angle of the Berkovich tip indenter (in radians). Using the Von Mises yield criterion, one can find the relationship between \( \tau_{ \hbox{max} } \) and the yield stress, \( \sigma_{y} \)[26,38]:

$$ \tau_{ \hbox{max} } = \sigma_{y} /\sqrt 3 $$
(2)

The \( \sigma_{y} \) can be obtained by Eq. [3]

$$ \sigma_{y} = H\frac{\sqrt 3 }{{2\left( {1 + \alpha } \right)}} $$
(3)

The “plasticity index,”, \( \psi \), of a solid body is usually a parameter which characterizes the relative plastic/elastic behavior of the material when it undergoes external stresses and strains. In the case of indentation contacts, one of the possible definitions for the plasticity index is shown in Eq. [4][39]

$$ \psi = A_{1} /\left( {A_{1} + A_{2} } \right), $$
(4)

where \( A_{1} \) is the area encompassed between the loading and unloading curves (equal to the plastic work done during the indentation) and \( A_{2} \) is the area encompassed by the unloading curve (viscoelastic recovery) (Figure 5). It follows that \( \psi \) = 1 (that is, \( A_{2} \) = 0) for a fully plastic deformation, \( \psi \) = 0 (that is, \( A_{1} \) = 0) for a fully elastic case and 0 < \( \psi \) < 1 for viscoelastic-plastic surfaces.

4 Experimental Results

4.1 Typical Inclusion Observation

In order to distinguish various inclusions in nano-indentation tests accurately, the typical morphologies of various inclusions were obtained by SEM and the chemical compositions of inclusions were tested by EDS. SEM photos and chemical compositions of typical inclusions are shown in Figures 6 and 7. Typical morphologies of inclusions observed during nano-indentation tests are shown in Figure 8. The morphologies of inclusions observed by SEM and nano-indentation tests are corresponded perfectly. The morphology properties of typical inclusions are obvious and easy to identify in nano-indentation tests. In sample 20CrMo-BN, most of the inclusions containing Al2O3 are the composite inclusions which contained MnS and Al2O3. To ensure that Al2O3 can be found in sample 20CrMo-BN, inclusions with the same constitution were chosen in nano-indentation tests, as shown in Figure 8(d). The morphology of BN inclusion observed by TEM (Figure 9) is similar to those in Figures 6(a) and 8(a).

Fig. 6
figure 6

Morphologies and chemical compositions of inclusions (a) BN in sample 42CrMo-BN, (b) TiN in sample 42CrMo-TiN, and (c) MnS in sample AISI1215

Full size image
Fig. 7
figure 7

SEM image and EDS analysis of typical composite inclusion (MnS and Al2O3) in sample 20CrMo-BN

Full size image
Fig. 8
figure 8

Typical morphologies of inclusions in nano-indentation tests (a) BN in sample 42CrMo-BN, (b) TiN in sample 42CrMo-TiN, (c) composite inclusion (MnS and Al2O3) in sample 20CrMo-BN, and (d) MnS in sample AISI1215

Full size image
Fig. 9
figure 9

TEM image and EDS analysis of typical BN inclusion in sample 42CrMo-BN

Full size image

4.2 Hardness and Elastic Moduli of Inclusions and Matrices

The hardness and elastic moduli of inclusions and matrices obtained by nano-indentation tests are shown in Table II. The Vickers hardness of matrices (average value of three tests) which obtained by Vickers hardness tests and that of inclusions which found by literature are also listed. In nano-indentation measurements, BN has the lowest hardness, MnS has a little higher hardness, the hardness of Al2O3 is higher than that of the matrix, and TiN has the highest hardness. The hardness of matrices is in the range of 2 to 4 GPa except sample AISI1215. The hardness of matrices is considerably higher than those of BN and MnS, lower than that of Al2O3 and about one-third of the hardness of TiN. Figures 6 through 8 show that the size of BN and MnS is higher than 5 μm, according to Tsui and Pharr,[40] the influences of substrate effect on the hardness and elastic moduli of them are negligible. However, according to Saha and Nix,[41] the hardness and elastic moduli of BN and MnS which obtained by nano-indentation tests are higher than the actual values. The size of TiN is about 5 μm, whereas that of Al2O3 is about 3 μm. Saha and Nix[41] revealed that the influence of substrate effect on the hardness and elastic modulus of TiN is negligible. However, the measured values of the hardness and elastic modulus of Al2O3 are lower than the actual values of them because of substrate effect.

Table II Hardness and Elastic Modulus of Inclusions and Matrices
Full size table

4.3 Load–Displacement Curves of Samples

In order to investigate the elastic–plastic of inclusions and matrices, the load–displacement curves are analyzed. Figures 10 and 11 show the load–displacement curves of inclusions and matrices, respectively. In order to make figures simplified, typical curves of each inclusion and matrix have been selected.

Fig. 10
figure 10

Load–displacement curves of inclusions (a) Al2O3 and TiN, (b) BN and MnS

Full size image
Fig. 11
figure 11

Load–displacement curves of matrices

Full size image

4.4 Microstructures of Matrices

Figure 12 shows the microstructures of matrices. The microstructures of 42CrMo-BN and 42CrMo-TiN are bainite and a small amount of acicular ferrite. The microstructure of 20CrMo-BN is pearlite and polygonal ferrite. For sample AISI1215, two-phase mixtures of pearlite and polygonal ferrite are obtained, the gray segment is MnS. In general, the hardness of bainite is higher than that of pearlite, and the hardness of ferrite is the lowest. The hardness of ferrite mainly depends on the contents of alloying elements and crystal defect.[43] The hardness of pearlite is largely influenced by the hardness of ferrite. Meanwhile, the hardness of bainite greatly depends on the ferrite in the bainite, the dispersion and distribution of carbide, solution strengthening of solute element and dislocation density, and carbon has a larger influence on solution strengthening than the other alloying elements. The area fraction of pearlite in sample 20CrMo-BN is about 50 pct, whereas that in sample AISI1215 is about 5.5 pct. The change of the area fraction of pearlite is the main factor which causes the Vickers hardness of sample 20CrMo-BN higher than that of sample AISI1215, although the solution strengthening of alloying elements also has certain influence.

Fig. 12
figure 12

Microstructures of matrices (a) 42CrMo-BN, (b) 42CrMo-TiN, (c) 20CrMo-BN, and (d) AISI1215

Full size image

5 Discussion

5.1 Elastic–Plastic Analyses of Inclusions and Matrices

The plasticity indexes of inclusions and matrices can be obtained by Eq. [4] and load–displacement curves. Figure 13 shows the plasticity indexes of inclusions and matrices. The plasticity indexes of matrices are high except sample AISI1215, which has low plasticity index similar to BN and MnS. Al2O3 has a higher plasticity than TiN. The results show that the ratios of elastic works in the total works of BN and MnS are high, which means BN and MnS have good elasticity. The values of plastic work, elastic work, and total work of BN and MnS are much less than those of other inclusions and matrices.

Fig. 13
figure 13

Plasticity indexes of inclusions and matrices

Full size image

The yield stresses of inclusions and matrices can be obtained by Eq. [3]. Table III shows the calculated values and published values of yield stresses of inclusions and matrices.[44,45] The calculated values of yield stresses of matrices are close to the published values. The yield stress is proportionate to the hardness.

Table III Yield Stresses of Inclusions and Matrices (GPa)
Full size table

5.2 Effects of Inclusions on Machinability

BN and MnS are sources of stress concentration in steel. As shown in Table II, the hardness of BN is lower than that of MnS and far lower than those of matrices. It can approximately regarded as cracks or holes in steel, which is the same as MnS. BN and MnS break the continuity of the matrix and act as internal notches because of their low hardness. They lead to stress concentration and change the state of stress of surrounding matrix, which make chips broken easily.

The elastic moduli and the elastic works of BN and MnS show that they have good elasticity. At the onset of cutting, the material particles of the removed surface layer and of the chip are subject to elastic deformation only.[2] The incompatibility of elasticity between the inclusions of good elasticity such as BN and MnS and the steel matrix of bad elasticity promotes the nucleation of cracks leading to rupture.[2] In addition, the growths and coalescence of microfissures make the steel easy to fracture, thus improve the cutting process.

BN has excellent lubrication performance. Pawlak et al.[46] and Kimura et al.[47] have revealed that BN is effective in reducing wear if used as a lubricant additive. Pawlak et al.[48] also showed that the addition of BN to the oil decreased the friction coefficient about twice compared to self-lubricated bearings lubricated only by oil. Previous work[49] prove that BN has the lubricant effect in cutting process.

BN and MnS can wrap the hard spots in steel, improve the machinability. Figure 14 shows the evolution of inclusions during solidification obtained by Thermo-calc (version TCW5) thermodynamic calculation program.[50,51] The data set of the thermodynamic parameters describing the Fe-C-Si-Mn-P-S-Cr-Mo-Al-Ti-O-N-B system of 42CrMo-BN steel and the Fe-C-Si-Mn-P-S-O-N system of AISI1215 steel were constructed based on the TCFE6 database of Thermo-calc. The inclusion phases considered in the calculation of 42CrMo-BN steel were SiC, AlN, BN, Si3N4, Ti2N, Cr3O4, Al2O3, MnO·Al2O3, MnO·SiO2, Mn2O2·SiO2, Si2O4·Al6O9, and MnS. However, the inclusion phases considered in the calculation of AISI1215 steel were SiC, Si3N4, Fe2O2·SiO2, MnO·SiO2, Mn2O2·SiO2, and MnS.

Fig. 14
figure 14

Thermodynamic calculation about evolution of inclusions during solidification (a) 42CrMo-BN and (b) AISI1215

Full size image

In sample 42CrMo-BN, the initial precipitation temperature of BN is 1684 K (1411 °C), which is lower than those of Al2O3 and TiN. The initial precipitation temperature of MnS is slightly lower than that of BN. In sample AISI1215, the initial precipitation temperature of MnS is lower than the liquidus, though the content of sulfur is high. Thus, the precipitation temperatures of BN and MnS are lower than those of Al2O3 and TiN under normal conditions, which reveal the reason why they can wrap Al2O3 and TiN theoretically. The actual evidence is shown in Figure 15, which has been reported in previous work.[52] Figure 15 shows that Al2O3 and TiN are the nuclei and BN is the wrappage. As shown in Table II, Al2O3 and TiN have higher hardness than matrices. They have the effects of abrasive wear on cutting tool during cutting process, which can reduce the tool life obviously. BN and MnS can avoid hard spots contact with cutting tool, thereby reducing the abrasive wear and improving the machinability of steel.

Fig. 15
figure 15

Mapping photo of typical inclusion in sample 42CrMo-BN

Full size image

5.3 Error Analysis of Nano-Indentation and Macrohardness Measurement

From the results obtained in this paper, the hardness, elastic modulus, and plastic index of sample AISI1215 are quite different from other matrices. The microstructure of sample AISI1215 is ferrite and pearlite. Based on the research of Choi et al.,[53] the nano-indentation hardness of ferrite in low-carbon steel (0.1C-0.26Si-1.5Mn-0.053V) is 2 to 3 GPa. According to the determination of Liu et al.,[54] the nano-indentation hardness of the deformation-induced ferrite and proeutectoid ferrite in Q235 steel (0.13C-0.19Si-0.49Mn-0.012P) is 2.0 to 2.5 and 1.8 to 2.1 GPa, respectively. The extents of solid solution strengthening effects of elements in steel on ferrite are: P > Si > Mn > Ni > Mo > V > W > Cr. The contents of Si and Mn of sample in the literature[51] are higher than those of the samples in the literature,[54] so that the nano-indentation hardness of ferrite in the literature[53] is higher. In this paper, the content of Si of sample AISI1215 (0.071C-0.005Si-1.23Mn-0.056P) is lower than that of the sample in the literature,[54] however, the content of Mn and P of sample AISI1215 is higher than that of the sample in the literature,[54] thus the nano-indentation hardness of sample AISI1215 should be significantly higher than that of the sample. Obviously, the nano-indentation tests of sample AISI1215 have certain error. Figure 16 shows the load–displacement curves of sample AISI1215 and MnS, it reveals that the trends of the curves are coincident. The only difference is that the load of curve of sample AISI1215 is a little higher than that of MnS. Therefore, it is thought that when the matrix of sample AISI1215 was tested by nano-indentation, its surface was matrix and inside was MnS, as shown in Figure 17(b). The surface which the indenter pressed into is matrix, whereas under the thin layer of matrix is MnS. Therefore, the hardness, elastic modulus, and load–displacement curve of sample AISI1215 obtained by nano-indentation test can not characterize the matrix of sample AISI1215.

Fig. 16
figure 16

Load–displacement curves of MnS and sample AISI1215

Full size image
Fig. 17
figure 17

Schematic diagram of (a) Vickers hardness measurement and (b) nano-indentation test for matrix of sample AISI1215

Full size image

The diameter distribution of inclusions in sample AISI1215 was obtained by metallographic microscope (52XA) and analysis software (UV-G), as shown in Figure 18. 236 inclusions in 0.15 mm2 have been counted and they are mainly MnS. The number of inclusions per unit volume was calculated by the number and size of inclusions and R. T. DeHoff’s equations[55] expressed by Eqs. [5] and [6]. The volume fraction of inclusions was calculated by Eq. [7]

$$ N_{\text{V}} = \frac{2}{\pi } \cdot \frac{{N_{\text{a}} }}{{\overline{d} }} $$
(5)
$$ \frac{1}{{\overline{d} }} = \frac{1}{n} \cdot \sum {\frac{1}{{d_{i} }}} $$
(6)
$$ V = \frac{\pi }{6}\overline{d}^{3} \cdot N_{\text{v}} , $$
(7)

where \( N_{\text{V}} \) is the number of inclusions per unit volume in specimen (m−3), \( N_{\text{a}} \) is the number of inclusions per unit area in specimen (m−2), \( d_{i} \) is the apparent particle size of ith inclusion among n inclusions (m), \( \overline{d} \) is the harmonic mean of inclusion particle size (m), and \( V \) is the volume fraction of inclusions.

Fig. 18
figure 18

Change of number of inclusions per area with diameter in sample AISI1215

Full size image

The volume fraction of inclusions in sample AISI1215 is 0.96 pct, which means that the situation presented in Figure 17(b) is possible to appear. Therefore, it is necessary to remove the effect of inclusions on nano-indentation tests when characterize the matrix of sample which has a lot of inclusions. Possible methods are continuous stiffness measurement and repeated experiments.

In this paper, sample AISI1215 is used to analyze the errors of Vickers hardness measurement. The area fractions of ferrite, pearlite, and MnS in sample AISI1215 are about 93.5, 5.5, and 1 pct, respectively. In Vickers hardness measurement, the hardness of sample AISI1215 not only depends on the chemical composition and microstructure, but also influenced by MnS which is largely existed in steel, the schematic diagram is shown in Figure 17(a). Compared with the matrix of steel, MnS has a lower hardness, which will reduce the Vickers hardness of steel. The macrohardness measurement of steel microstructure is influenced by inclusions in steel. However, the nano-indentation tests (repeated experiments) can reduce the influence significantly. When the steel contains a large number of soft inclusions, the hardness value of macrohardness measurement of steel microstructure is lower than those of nano-indentation tests, and vice versa. Thus, the value of macrohardness measurement should make corresponding correction. Using nano-indentation test is better to obtain the accurate hardness value of steel microstructure than macrohardness measurement.

6 Conclusions

  1. 1.

    The hardness and elastic moduli of inclusions and matrices of samples have been obtained by nano-indentation measurements. The results show that BN and MnS are very soft. The hardness of BN is lower than that of MnS, and both of them are considerably lower than those of matrices. Thus, they can act as sources of stress concentration in steel and make the chip broken easily. The hardness of Al2O3 and TiN is higher than those of matrices, which reveal that they are hard spots in steel.

  2. 2.

    The plastic indexes of inclusions and matrices have been obtained by load–displacement curves. The results and elastic moduli show that BN and MnS have good elasticity. The mismatch in elasticity of the BN and MnS with matrices promotes the nucleation of cracks leading to rupture.

  3. 3.

    Thermodynamic calculations and observations of typical inclusions prove that BN and MnS can envelop the hard spots (Al2O3, TiN) in steel and reduce the abrasive wear on cutting tool during cutting process.