Phenomenon of High Extension Observed in Grey Cast Iron after Micro-rolling

Abstract

Grey cast iron is traditionally thought to not deform plastically, because of the presence of a large number of graphite flakes, which act as crack initiation sites. Therefore, researchers had given up efforts to study its formability. However, our research suggests that, when the thickness of grey cast iron samples is decreased to 400 µm, they can be elongated by cold rolling, with the extension being as high as 156%, which is well beyond the forming limit of grey cast iron. This phenomenon confirms that the plasticity size effect occurs in thin grey cast iron samples, breaking the ceiling of their intrinsically low plasticity. We use classical plasticity theory and the surface-layer ratio theory to investigate the mechanism responsible for the deformation that occurs during micro-rolling. We also propose a method for improving the plasticity of extra-brittle materials.

1. Introduction

Owing to the rapid developments in product miniaturization, micro-manufacturing is increasingly becoming an important process.¹⁾ As one of the most promising micro-manufacturing techniques, micro-forming is being used widely because of its high production rate and low cost. However, when the size of the workpiece is decreased from the macro-scale to the micro-scale, the workpiece displays a strong size effect, such that its deformation and fracture behavior change with its size. Consequently, the size effect influences the forming performance of the material as well as defect formation in it, because fewer grains are present in the deformation zone. Because classical plasticity theory cannot predict the effect of size on material behavior, knowledge and technical knowhow regarding traditional metal-forming processes can not be transferred directly to the micro-scale.²⁾ Therefore, understanding the size effect and how it influences the material deformation behavior is vital to improving product quality and preventing defects.

Since Armstrong³⁾ first reported the effect of the thickness-to-grain size ratio on the mechanical properties of materials at the micro- and macro-scale, researchers have performed many studies on the size-dependent flow and fracture behaviors of materials. Fleck et al.⁴⁾ performed micro-torsion tests on polycrystalline copper wires; their results showed that wires with smaller diameters exhibited greater torsion strength. Based on micro-tensile tests, Chen et al.⁵⁾ reported that, for micron-sized Ag wires, the strength depends to a significant degree on the grain and specimen size. Similar results were reported by Miyahara.⁶⁾ In addition to these studies, investigations have been performed on other interesting micro-forming processes such as bending,^7,8) drawing,^9,10,11) indentation,¹²⁾ cutting,^13,14) compression,¹⁵⁾ extrusion,¹⁶⁾ punching,¹⁷⁾ and micro-rolling.^18,19) In particular, the interesting phenomenon resulting from micro-rolling is receiving increasing attention.^20,21) In view of this, we suggest that it should be possible to plastically deform grey cast iron, which has long been regarded a brittle material that does not exhibit formability, at room temperature by micro-rolling.

For this purpose, we developed a four-high micro-foil mini mill (termed a 3M mill), which can roll extremely thin strips. In this study, 400-μm-thick and 1200-μm-thick grey cast iron samples were rolled by the 3M mill at room temperature. We found that the 400-μm-thick grey cast iron sample could be cold-rolled without undergoing edge cracking; after repeated rolling, the degree of extension was as high as 156%. On the other hand, the 1200-μm-thick sample did not show high extensibility, as it underwent edge cracking after being extended by only 6%. These observations are attributable to the plasticity size effect rather than the inherent ductility of grey cast iron.

2. Experimental Methods

2.1. Sample Preparation for Micro-rolling and Microstructural Observation

The material used in this study was the grey cast iron HT150, which has a composition of Fe-4.2C-2.1Si (wt%). Two samples (10 × 30 × 1.2 mm³ and 10 × 30 × 0.4 mm³) were cut from a grey cast iron bar. After the completion of the rolling process, metallographic samples were prepared by mechanical grinding and polishing. The microstructure of the grey cast iron HT150 was observed using a longitudinal section with an Olympus GX51 optical microscope; the test sample was first etched with a solution containing 96 vol% alcohol and 4 vol% nitric acid for 20–30 s.

2.2. Micro-rolling Experiment

The rolling experiment was carried out using the above-mentioned laboratory-developed 3M mill (Micro-foil Multi-functional Mini mill), as shown in Fig. 1 and Supplementary Figs. S1 and S2. The roll diameter is 50 mm for the work rolls and 120 mm for the backup rolls, and the roll barrel is 120 mm in diameter. It should be emphasized that the experiment was performed at room temperature and that no intermediate annealing treatment was performed during the micro-rolling process. The micro-rolling schedule for the grey cast iron sample 400 μm thick is shown in Table 1.

Fig. 1.

3M mill used for rolling grey cast iron samples.

Table 1. Micro-rolling schedule for 400-μm-thick grey cast iron sample.

Rolling pass No.	Thickness before rolling, μm	Thickness after rolling, μm	Working ratio, %	Rolling speed, m/s
1	400	286	28.5	0.04
2	286	213	25.4	0.04
3	213	157	26.5	0.04
4	157	117	25.5	0.04

3. Results

3.1. High Extension of Grey Cast Iron

The degree of extension by rolling is expressed as β=(l−l₀)/l₀ (where l₀ and l are the sample lengths before and after rolling, respectively). Figure 2 shows a scanning electron microscopy (SEM) image of an impact fracture on an HT150 sample. It can be observed that graphite particles 125 μm in length and 42 μm in width are distributed like flakes in the sample. After one pass, these flake-like graphite particles resulted in edge cracking in the 1200-μm-thick sample under the action of the applied load (Fig. 3). As result, further rolling was not performed on this sample. The degree of extension was found to be only 6%. However, it was found that the 400-μm-thick grey cast iron sample could be cold-rolled without undergoing edge cracking, as shown in Fig. 4. After four passes, the degree of extension was as high as 156%, and the rolled sample could be bent elastically (Fig. 5).

Fig. 2.

Morphology of flake-like graphite particles in grey cast iron HT150.

Fig. 3.

Grey cast iron sample with thickness of 1.2 mm showing edge cracks after cold rolling at extension of 6%.

Fig. 4.

Grey cast iron samples with different degrees of extension before and after being micro-rolled.

Fig. 5.

Grey cast iron sample 400 μm in thickness after being micro-rolled; the sample could be bent elastically.

3.2. Microstructural Evolution of Grey Cast Iron during Micro-rolling

Figure 6(a) shows the microstructure of the grey cast iron HT150 before cold rolling; several bent black graphite particles can be seen distributed in the sample, in addition to the equiaxed ferric grains and the pearlite colony. After one pass, both the ferrous grains and the graphite particles were quashed and arranged in the rolling direction, as shown in Fig. 6(b). After three passes, the ferrous grains were quashed further, and the initially bent graphite particles became flat, as shown in Fig. 6(c). After four passes, the graphite flakes became flatter and thinner, as shown in Fig. 6(d).

Fig. 6.

Microstructures of longitudinal sections of plastically deformed grey cast iron samples with different degrees of extension. (a) As-cast, (b) β = 28% (after one pass), (c) β = 104% (after three passes), and (d) β = 156% (after four passes).

4. Discussion

4.1. Role of Negative-gap Rolling

The obtained experimental results indicated that, for the same composition, microstructure, and processing technology, the degree of extension of grey cast iron depends primarily on the sample thickness. For example, when the initial thickness of the sample was 400 μm, the degree of extension was as high as 156%. A theoretical analysis suggested that, when the thickness of the rolled product is less than or equal to the sum of the degrees of elastic deformation of the roll mill stand and the roll system in the vertical direction, negative-gap rolling must be used, in order to ensure that compressive deformation takes place. During negative-gap rolling, an appropriate pressure is applied on the upper and bottom rolls to force the two rolls to come into contact before the sample is bit into the rolls. Once the sample has been bitten into the rolls, the higher degree of elastic deformation of the rolling mill results in the formation of a load roll gap within the range of the width of the rolled product (Fig. 7(a)), and the load roll gap is nearly equal to the product thickness. Moreover, the sections of the upper and bottom rolls that do not touch the sample being rolled still touch each other (Fig. 7(b)). Consequently, the rolled sample is prevented from flowing in the transverse direction (y-direction), and a compressive stress σ_y acts on the side surfaces of the rolled sample. Thus, it can be concluded that the side surfaces of the rolled product are subjected to three-dimensional compressive stresses (Fig. 7(c) and Supplementary Fig. S3), and it is thus difficult for edge cracks to form on these surfaces. In contrast, during normal-gap rolling (Fig. 8(a)), the sections of the upper and bottom rolls not touching the sample do not touch each other (Fig. 8(b)). Therefore, a bulging edge is formed on the side surfaces of the rolled sample, because of inhomogeneous plastic deformation. Further, this bulging edge is subjected to a one-dimensional compressive stress, as shown in Fig. 8(c) and Supplementary Fig. S4. In contrast to the three-dimensional compressive stress state, the one-dimensional tensile stress state results in the ready formation of edge cracks.

Fig. 7.

Characteristics of negative-gap rolling. (a) Sections of upper and bottom rolls not touching the rolled product touch each, so the rolled product is prevented from flowing in transverse direction. (b) A bulging edge is not formed on side surfaces because of the action of compressive stress σ_y. (c) Side surfaces of rolled product are subjected to three-dimensional compressive stresses. (d) Grey cast iron rolled sample without edge cracking.

Fig. 8.

Characteristics of normal-gap rolling. (a) Rolled product can flow in transverse direction. (b) Bulging edge is formed on side surfaces because of inhomogeneous plastic deformation. (c) Bulging edge on side surfaces of rolled product is subjected to one-dimensional tensile stress. (d) Several edge cracks are formed on side surfaces because of this one-dimensional tensile stress.

It was observed that, when the 1200-μm-thick grey cast iron sample was rolled with a normal gap, its side surfaces were subjected to a one-dimensional tensile stress. Further, grey cast iron has a low tensile strength. Therefore, a few cracks formed on the side surfaces of the rolled sample owing to the tensile stress (Fig. 8(d)). In contrast, the 400-μm-thick sample was rolled with a negative gap; negative-gap rolling is different from normal-gap rolling when it comes to the stress state, as discussed above. Therefore, no edge cracks were formed during the rolling process (Fig. 7(d)). Hence, it can be concluded that negative-gap rolling is essential in the case of grey cast iron if one wishes to achieve high extensibility.

4.2. Role of Hydrostatic Stress during Micro-rolling Process

With respect to the micro-rolling process, it is advantageous to consider the following four assumptions when developing a corresponding mathematical model:

(1) Consider the rolling process as the upsetting process between two plates.

(2) Acknowledge the fact that the width of the flat product remains almost unchanged (i.e., acknowledge the plane-strain flow phenomenon).

(3) Assume that the compressive stress σ_x is distributed homogeneously in the thickness and width directions of the rolled product.

(4) Assume that the friction between the rolls and the rolled product obeys Coulomb’s law of friction.

Based on these assumptions, stone²²⁾ presented the formula (see Supplementary Fig. S5)   

$${\sigma }_z=2k{e}^{\frac{fl\pm 2fx}{h}},$$(1)

where σ_z is the normal stress (compressive) in the z-direction, k is the metal’s flow strength with respect to pure shear f is the friction coefficient, x, which is measured from the line connecting the roll centers, indicates the distance in the direction of rolling, and h is the thickness of the rolled product.

Equation (1) shows that the normal stress, σ_z, increases with a decrease in the thickness of the rolled product. Here, we defined the parameter λ as the ratio of the contact area between the two rolls and the rolled product to the volume of the rolled product (λ is also called the contact-specific surface area). When considering an element with a length of d mm, width of b mm, and thickness of h mm in the deformation zone, the value of λ can be computed by   

$$\lambda =\frac{2d\times b}{h\times d\times b}\text{=}\frac{2}{h}.$$(2)

It can be seen from Eq. (2) that the thinner the rolled product is, the larger is the value of λ. For example, the value of λ for a hot-rolled continuous cast slab with a thickness of 200 mm is approximately 0.01 mm⁻¹; that for a cold-rolled strip with a thickness of 2 mm is approximately 1 mm⁻¹; and that for a thin foil with a thickness of 2 μm is approximately 1000 mm⁻¹. The ratio of their λ values is 1: 100: 100000. Therefore, the contact-specific surface area, λ, cannot be ignored when rolling thin samples. Substituting Eq. (2) into Eq. (1) gives   

$${\sigma }_{\text{z}}=\text{2}k{e}^{\lambda (0.5fl\pm fx)}.$$(3)

Equation (3) suggests that there exists an exponential relationship between σ_z and λ; the compressive stress σ_z increases with λ. Thus, thinner rolled products are subjected to a larger compressive stress σ_z. Here, we emphasize that, for an extremely thin rolled product in the deformation zone, the contact surface area is far larger than the area of the side surface. The ratio of the contact surface area to the side surface area is approximately equal to the ratio of the width to the thickness. For example, for a thin foil sample 100 mm in width and 0.01 mm in thickness, the ratio of the side surface area to the contact surface area is 1/10000. In this case, the side surface area can be ignored for practical matters, and the contact-specific surface area is considered the specific surface area (namely, the surface area per unit volume).

Based on the above-described results, it was concluded that the compressive stress σ_z increases with a decrease in the thickness of the rolled product. Next, we investigated the changes in the stresses σ_x and σ_y with a decrease in the thickness of the product to be rolled. For this, the well-known Tresca yield criterion was used.   

$${\sigma }_z-{\sigma }_x=2k,$$(4)

where, σ_z is the compressive stress in the z-direction, σ_x is the compressive stress in the rolling direction, and the k is the yield strength with respect to shear.

Equation (4) shows that, during the rolling process, the compressive stress σ_x increases with an increase in the compressive stress σ_z. In addition, the flat rolling of a thin sample can be considered as a plane-strain deformation, because the length of contact between the rolls and the rolled product is much smaller than the width of the rolled product. When the rolled product is thinned in the deformation zone, extension occurs freely in the x-direction, whereas transverse expansion in the y-direction is constrained. Meanwhile, for plane-strain-related deformation,   

$${\sigma }_{\text{y}}=\frac{{\sigma }_{\text{x}}+{\sigma }_{\text{z}}}{2}.$$(5)

Considering Eqs. (3), (4), and (5), it can be seen that σ_x, σ_y, and σ_z increase with a decrease in the thickness of the rolled product. Therefore, the hydrostatic stress, p, given by Eq. (6), also increases accordingly.   

$$p=\frac{{\sigma }_{\text{x}}+{\sigma }_y+{\sigma }_{\text{z}}}{3}$$(6)

These results indicate that a large hydrostatic stress is generated during the rolling of thin samples. A large hydrostatic stress would inhibit the formation and propagation of micro-cracks and micro-holes within the rolled product; this is what results in grey cast iron exhibiting high extensibility at room temperature. The brittle-ductile transition of grey cast iron observed during the micro-rolling process, which can be accounted for by conventional theory, is thus called a size effect of the first order.²³⁾

4.3. Role of Surface Grains

Both conventional and micro-scale samples can be assumed to be composed of two parts, namely, surface grains and internal grains. With this in mind, the surface layer of the sample to be rolled is considered to consist of surface grains, while the interior is considered to consist of internal grains (Fig. 9(a)). When the sample to be rolled is in the rolling deformation zone, the ratio of the volume of the surface layer touching the upper and bottom rolls to the total volume is called the surface-layer ratio, ω, and is given by the following formula   

$$\omega =\frac{2l\times b\times t}{l\times b\times h}=\frac{2t}{h},$$(7)

where l, b, and h are the length, width, and thickness of the sample being rolled in the deformation zone, and t is the thickness of the surface grains of the sample.

Fig. 9.

Schematic showing proportions of surface grains in samples having different thicknesses. (a) Ordinary sample to be rolled. (b) Thin sample to be rolled. (c) Extremely thin sample to be rolled and having only two rows of grains in thickness direction. (d) Extremely thin sample to be rolled and having only one row of grains in thickness direction.

Substituting Eq. (2) in (7), we get   

$$\omega =\frac{2t}{h}=\lambda \cdot t.$$(8)

For an ordinary rolled product with a thickness H and having surface grains with a thickness t (Fig. 9(a)), the surface-layer ratio is 2t/H or λ_H·t. Similarly, for a thin rolled product (Fig. 9(b)) with a thickness h and having surface grains with a thickness t, the surface-layer ratio is 2t/h or λ_h·t. When the thickness of an extremely thin rolled product is much lower than that of an ordinary rolled product (namely, h << H), the surface-layer ratio of the former will be much larger than that of the latter, namely,   

$${\omega }_{\text{h}}=\frac{2t}{h}>>{\omega }_{\text{H}}=\frac{2t}{H}\mathrm{\hspace{0.17em} }\mathrm{o}\mathrm{r}\mathrm{\hspace{0.17em} }{\lambda }_{\text{h}}>>{\lambda }_{\text{H}},$$(9)

where ω_h is the surface-layer ratio of the extremely thin rolled product, ω_H is the surface-layer ratio of the ordinary rolled product, λ_h is the contact-specific surface area of the extremely thin rolled product, and λ_H is the contact-specific surface area of the ordinary rolled product.

Equation (9) shows that the thinner the sample to be rolled is, the larger is the contact-specific surface area (λ) as well as the surface-layer ratio (ω). Therefore, three extreme cases are considered:

(1) When the thickness of the surface grains is much lower than that of the sample to be rolled (Fig. 9(a), namely, the ordinary rolling process), the surface-layer ratio, ω, is almost equal to zero, suggesting that the effect of the surface grains can be ignored.

(2) When rolling a thin sample, the surface-layer ratio, ω, is t/h and the surface grains have an effect (Fig. 9(b)).

(3) When rolling an extremely thin sample having only two rows of grains in the thickness direction (Fig. 9(c)), the entire sample can be considered to be composed of surface grains.

In this case, the surface-layer ratio, ω, has a maximum value of 1. Thus, the surface grains play a dominant role in determining the mechanical properties of the ultrathin rolled product. Likewise, if only one row of grains is distributed in the thickness direction of the sample to be rolled (Fig. 9(d)), the surface-layer ratio, ω, is still 1.

Therefore, the surface-layer ratio for the different scenarios is given as follows:   

$$\omega =\{\begin{array}{cc}0& t<<H\\ \frac{t}{h}& t<h\\ 1& t=\frac{h}{2}\end{array}$$(10)

During plastic deformation, the deformation behaviors of the surface grains and internal grains are different because of the occurrence of dislocations, such as dislocation pileups within the sample and dislocation emissions from the surface. In addition, for a thinner sample, during the rolling process, micro-voids within the sample can move to the sample’s surface more easily and disappear, resulting in the cessation of the damage due to the micro-voids. Thus, the larger the value of ω is, the lower is the damage due to these micro-voids. This specific phenomenon occurring at the sample’s surface is difficult to account for using conventional theory and is thus considered a size effect of the second order [23].

On the basis of the above-mentioned experimental results and theoretical analyses, we concluded that the surface-layer ratio is an important parameter affecting the plasticity of metals. When the thickness of a sample is decreased to a certain critical value, the size effect occurs, and the plasticity of the material increases. In this study, the 400-μm-thick grey cast iron sample was thin enough to correspond to this critical value, but the 1200-μm-thick sample was not. However, it is essential to further investigate how the critical value changes under different deformation conditions and what the underlying mechanism of this size effect of the second order is.

5. Conclusions

A sample of grey cast iron 400 μm in thickness could be successfully elongated by micro-rolling, with the extension being as high as 156%. This broke the inherent plastic limit of grey cast iron. This interesting result is attributable to the size effect occurring during the micro-rolling process. On the basis of the characteristics of the micro-rolling process, we propose that negative-gap rolling and the hydrostatic stress are the two factors responsible for inhibiting the formation of edge cracks and the propagation of internal defects. In addition, micro-rolling results in a higher surface-layer ratio than ordinary rolling. For samples with larger surface-layer ratios, a greater number of defects such as dislocations and micro-voids move to the sample surfaces during the rolling process, where they decrease in number or even disappear completely. As a result, the fracturing of such samples is delayed and the samples exhibit higher plasticity.

Acknowledgments

The authors thank the Applied Basic Research Program of Changzhou (CJ20160032), Natural Science Foundation of Jiangsu Province of China (No. BK20131123), and the National Natural Science Foundation of China (No. 51374069).

References

• 1)   H. G.  Craighead: Science, 290 (2000), 1532.
• 2)   F.  Vollertsen,  H. S.  Niehoff and  Z.  Hu: Int. J. Mach. Tools Manuf., 46 (2006), 1172.
• 3)   R.  Armstrong: J. Mech. Phys. Solids, 9 (1961), 196.
• 4)   N.  Fleck,  G.  Muller and  M.  Ashby: Acta Metall. Mater., 42 (1994), 475.
• 5)   X.  Chen and  A.  Ngan: Scr. Mater., 64 (2011), 717.
• 6)   K.  Miyahara,  C.  Tada,  T.  Uda and  N.  Igata: J. Nucl. Mater., 133 (1985), 506.
• 7)   K. C.  Chan and  S. H.  Wang: J. Mater. Process. Technol., 91 (1999), 111.
• 8)   J.  Stölken and  A.  Evans: Acta Mater., 46 (1998), 5109.
• 9)   H. L.  Costa and  I. M.  Hutchings: J. Mater. Process. Technol., 209 (2008), 1175.
• 10)   F.  Gong,  B.  Guo,  C. J.  Wang and  D. B.  Shan: Microsyst. Technol., 16 (2010), 1741.
• 11)   Y.  Saotome,  K.  Yasuda and  H.  Kaga: J. Mater. Process. Technol., 113 (2001), 641.
• 12)   K. W.  McElhaney,  J. J.  Vlassak and  W. D.  Nix: J. Mater. Res., 13 (1998), 1300.
• 13)   C. F.  Cheung,  W. B.  Lee and  W. M.  Chiu: Wear, 237 (2000), 274.
• 14)   W. B.  Lee,  C. F.  Cheung,  L. K.  Chan and  W. M.  Chiu: J. Mater. Process. Technol., 66 (1997), 63.
• 15)   M. D.  Uchic,  D. M.  Dimiduk,  J. N.  Florando and  W. D.  Nix: Science, 305 (2004), 986.
• 16)   U.  Engel and  R.  Eckstein: J. Mater. Process. Technol., 125 (2002), 35.
• 17)   M.  Song,  K.  Guan,  W.  Qin,  J. A.  Szpunar and  J.  Chen: Mater. Sci. Eng. A, 606 (2014), 346.
• 18)   D. K.  Xu,  M. K.  Ng,  R.  Fan,  R.  Zhou,  H. P.  Wang,  J.  Chen and  J.  Cao: Int. J. Adv. Manuf. Technol., 78 (2015), 1427.
• 19)   Q. B.  Yu,  X. H.  Liu and  D. L.  Tang: Sci. Rep., 3 (2013), 3556.
• 20)   Q. B.  Yu,  X. H.  Liu,  Y.  Sun,  M.  Song and  Y. M.  Gao: Sci. Sin. Technol., 11 (2015), 1187.
• 21)   D. L.  Tang,  X. H.  Liu,  M.  Song and  H. L.  Yu: PLoS One, 9 (2014), 106637.
• 22)   M.  Stone: Iron Steel Eng., 30 (1953), 1.
• 23)   M.  Geiger,  F.  Vollertsen and  R.  Kals: CIRP Ann. Manuf. Technol., 45 (1996), 277.