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Evaluation of Elastic-Plastic Deformation Behavior of Lath Martensite by Nanoindentation Technique
2024 Volume 64 Issue 2 Pages 482-485
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2024 Volume 64 Issue 2 Pages 482-485
It is well known that ferritic steels yield discontinuously with a clear yield point, while martensitic steels yield continuously with a low elastic limit followed by significantly large strain hardening. To evaluate the unique elastic-plastic deformation behavior of martensitic steels easily and accurately, nanoindentation tests were conducted using martensitic steels with lath martensitic structure, and the obtained results were then compared with that of ferritic steel while taking into account the pop-in phenomenon. In the normal load-displacement curves, ferritic steel had pop-in clearly, but no pop-in was observed for martensitic steels, regardless of carbon content. However, the analysis based on Hertz’s contact theory made it possible to quantitatively evaluate the elastic limit of martensitic steel as well as ferritic steel. As a result, it was found that the elastic limit of martensitic steel is much lower than that of ferritic steel, and the plastic strain at yielding is also quite small. The plastic deformation behavior based on dislocation theory suggests that the yielding of ferritic steels is governed by dislocation nucleation and subsequent dislocation avalanche. In contrast, the yielding phenomenon of martensitic steels might be greatly influenced by the motion of pre-existing mobile dislocations introduced through martensitic transformation.
Since the crystal structure of iron has face-centered cubic structure (fcc) at high temperatures and body-centered cubic structure (bcc) at low temperatures, fcc-bcc solid-solid phase transformation occurs spontaneously during the cooling process. The transformation mechanism of the fcc-bcc phase transformation strongly depends on the cooling rate; ferrite forms by diffusional transformation when the cooling rate is low, while martensite prefers to form by non-diffusional transformation when the cooling rate becomes higher. Although both transformation products are basically bcc, martensite shows significantly higher strength than ferrite due to the introduction of high-density dislocations,1) the formation of fine-grained substructure,2) and the supersaturated solid solution of carbon (C).3,4) However, while ferrite yields discontinuously with a yield point, martensite exhibits high tensile strength through continuous yielding characterized by a relatively low elastic limit and subsequent large strain hardening. Therefore, to use martensitic steels as high-strength structural steels, it is necessary to accurately evaluate the elastic limit and control the characteristic strain-hardening behavior of martensitic steels. A macroscopic mechanical test using a uniaxial tensile test is commonly used to evaluate the mechanical properties of martensitic steels. Especially, stress relaxation test,1,5,6,7,8) in which the crosshead is stopped at stress near the elastic limit, and the decrease in load caused by plastic strain is measured, is also used to evaluate the elastic limit. However, this method is not always easy, because it is sometimes difficult to prepare a specimen of sufficient dimensions from a fully quenched material. Furthermore, it has been reported that the elastic limit of martensitic steels is strain rate dependent,8) making repeated testing under different conditions more labor intensive. On the other hand, the analysis of elastic-plastic deformation behavior of metallic materials by nanoindentation test has attracted attention in recent years. The nanoindentation test can locally and repeatedly evaluate mechanical properties such as hardness and elastic modulus by controlling a very small indentation load and measuring the corresponding indenter penetration depth. In addition, the position of the indenter can be controlled selectively with extremely high precision by using the imaging function of a scanning probe microscope. Furthermore, a discontinuous increase in displacement, called pop-in, is often observed in load-controlled nanoindentation tests. The pop-in can occur for various reasons, but several researchers9,10,11,12) have pointed out that it corresponds to the onset of plastic deformation due to a dislocation avalanche. Considering these characteristics, the nanoindentation test is expected to provide an easy and accurate evaluation of the elastic limit of martensitic steels. In this study, we attempted to evaluate the elastic limit of martensitic steels with lath martensitic structure by nanoindentation tests. In addition, the elastic-plastic deformation behavior was compared with ferritic steels while taking the pop-in phenomenon into account, and the plastic deformation mechanism in martensitic steel was discussed.
An interstitial-free 16%Ni martensitic steel13) (0C martensite) and an ultra-low carbon ferritic steel with 100 ppm C (ULC ferrite) were used (mass%). 0C martensite was cut from a hot-rolled sheet in which Ni segregation was removed by hot forging and subsequent sufficient homogenization treatment. After austenitization at 1373 K for 1.8 ks, the specimens were immediately water quenched to obtain lath martensitic structure fully. ULC ferrite cut from a cold-rolled sheet was solution treated at 973 K for 1.8 ks to achieve recrystallization and subsequent grain growth followed by air cooling. Microstructural observation and nanoindentation test were conducted on the cross-sections of the specimens in the normal direction and the transverse direction for rolling, respectively. Especially, a substructure of lath martensite was observed using a field emission-type scanning electron microscope (FE-SEM, JSM-7001F, JEOL Ltd.), and the crystal orientation was analyzed by electron backscattered diffraction (EBSD). The EBSD pattern obtained by the dedicated detector was analyzed using OIM Data Collection ver. 7.1.0. The obtained data was displayed as an inverse pole figure (IPF) map using OIM Analysis ver. 7.3.0 software developed by TSL Solutions. In EBSD analysis, the working distance was fixed at 15.0 mm, the acceleration voltage was set at 15.0 kV, and the step size was 0.02 μm. To investigate the effect of C on martensitic steel, 5%Mn-0.1%C steel14) (0.1C martensite) was also prepared as a comparison material and subjected to the same heat treatment as 0C martensite. Nanoindentation tests were performed using a nanoindentation system (Hysitron TI Premier developed by BRUKER). Finally, the sample surface for the nanoindentation test was polished with colloidal silica of 12 nm radius. After the final preparation, the surface roughness was averagely measured at approximately 3.0 nm. The test was performed mechanically on a square grid of 64 points in an arbitrary observation area. A Berkovich indenter was used, and the distance between the measurement points was set to 10 μm. Load-displacement curves (P–h curves) were obtained with controlled loading and unloading rates of 600 μN/s, maximum load of 3000 μN, and duration of 2 s at the maximum load. Displacements were monitored every 5.0 ms. The composite elastic modulus E and nano-hardness Hn were evaluated from the obtained P–h curves. Especially, the critical loads discussed later were measured using more than twenty reliable P–h curves.
Figure 1 shows the optical microstructure and Vickers hardness of (a) 0C martensite, (b) 0.1C martensite, and (c) ULC ferrite. Although microstructural features of the substructure were affected by C addition, both 0C martensite and 0.1C martensite show typical lath martensitic structure, and their prior austenite grain size were measured at 121 μm and 102 μm, respectively. On the other hand, ULC ferrite exhibited an equiaxial-grained ferritic structure with an average grain size of 90.2 μm. The comparison of Vickers hardness, ULC ferrite < 0C martensite < 0.1C martensite, indicates that martensitic steels are harder than ferritic steels and that adding C further increases the hardness of the martensitic steels, as is generally known. In addition, the surface of 0C martensite after indentation tests is shown in (d) as bcc crystal orientation map obtained by EBSD. It was found that the size of the indentation mark was approximately 1.0 μm, which is smaller than the block and sub-block widths of lath martensite. In the following, only data measured at a point far enough from the boundaries were selectively analyzed.
Figure 2 shows representative P–h curves for 0C martensite, 0.1C martensite, and ULC ferrite. Comparing three materials at the maximum load, ULC ferrite, 0C martensite, and 0.1C martensite show a decrease in displacement in that order, indicating greater deformation resistance. In fact, the average Hn was 1.8 GPa, 3.2 GPa, and 4.6 GPa, respectively, which agrees with the order of the macroscopic Vickers hardness (see Fig. 1). As indicated by the arrow in the magnified P–h curve, a clear discontinuous change in displacement due to pop-in was observed in the low load region for ULC ferrite. In contrast, 0C martensite and 0.1C martensite showed a continuous displacement change in all load ranges, and no clear pop-in was observed.
When two spherical bodies are in elastic contact, the relationship between the load P and the relative displacement h at the contact zone can be expressed by Eq. (1) using E and the curvature radius of indenter tip R, according to Hertz’s contact theory.15)
| (1) |
Here, we obtain the following equation by taking the logarithm of Eq. (1).
| (2) |
This equation shows that the logarithm of P and h have a linear relationship in the elastic deformation range. The low load region of Fig. 2 is displayed as a logarithm of the P–h curve in Fig. 3. A straight line with a slope of 3/2 is also displayed in this figure. Considering the surface roughness, it should be noted that the detection limit of the nanoindentation system for this study is about 3.0 nm in depth. Therefore, data below this limit are thought to contain errors. First, focusing on the deformation behavior of ULC ferrite, log P–log h shows a good linear relationship with a slope close to 3/2 in the region lower than the load at which pop-in occurs (Ppop-in) indicated by the arrow. This strongly suggests that Ppop-in is the elastic limit of ferritic steel and that the steel deformed elastically at lower loads. The Ppop-in was 146±14 μN, and the increase in discontinuous displacement caused by the pop-in was Δh = 15 nm. On the other hand, for the two martensitic steels, similar linearity is observed in the very low load region below the critical load Pc, and a very small displacement increase of Δh ~ 1.5 nm is observed. In other words, it is possible to evaluate the critical load for an elastic limit of martensitic steel, as well as ferritic steel, by applying Hertz’s contact theory. It is important to note that Pc is 23±4 μN for 0C martensite and 37±6 μN for 0.1C martensite, slightly increasing with increasing C content, but clearly smaller than Ppop-in for ferritic steel, and its Δh is also very small. In the following, the low elastic limit and small plastic strain of martensitic steels were briefly discussed based on dislocation theory. As a side note, the difference in the absolute value of P for a given h in Fig. 3 is due to the difference in the composite elastic modulus among materials, 181.9 GPa (0C martensite), 202.3 GPa (0.1C martensite), and 204.7 GPa (ULC ferrite), as Eq. (2) indicates.
In nanoindentation tests, the maximum shear stress τmax just below the indenter can be estimated by the following equation.
| (3) |
By substituting R = 250 nm, Pc, and Ppop-in estimated from Eq. (1) and Fig. 3 into the equation, τmax at the onset of plastic deformation in 0C martensite and ULC ferrite is 4.13 GPa and 8.31 GPa, respectively. The τmax of ULC ferrite is close to the ideal shear strength of ferrite τm, which can be approximated as μ/10 using the shear modulus μ = 80 GPa. On the other hand, Leipner et al.11) proposed that the critical stress τc for dislocation nucleation can be obtained by Eq. (4) through nanoindentation tests using GaAs wafers and transmission electron microscopy observations.
| (4) |
e, b, r0, and ν are Euler number, the length of Burgers vector, the radius of the dislocation core, and Poisson’s ratio. Substituting μ = 80 GPa, r0 = b/3, and ν = 0.3 into Eq. (4), τc for ULC ferrite was estimated to be 9.7 GPa, which is in close agreement with τmax. In other words, in the nanoindentation test for ULC ferrite, after elastic deformation in the dislocation-free area, dislocations nucleate at a high-stress state close to the ideal shear strength, and pop-in is considered to have occurred due to dislocation avalanche, as illustrated in Fig. 4(a). The double cross-slip model16) may be applied to the dislocation avalanche mechanism. On the other hand, in 0C martensite and 0.1C martensite, plastic deformation starts at shear stress τmax, which is clearly lower than τm and τc. This experimental fact suggests that in the nanoindentation test for the martensitic steels, high-density dislocations had already existed under the indenter and provided plastic deformation directly (Fig. 4(b)).
When plastic deformation proceeds by dislocation motion, the amount of shear strain γ can be described by the following equation, using the density ρ and the average moving distance x of dislocations, and b.
| (5) |
If newly-formed dislocations move x immediately, the plastic deformation depends on the rate of increase of dislocation density and thus the shear strain rate can be described by the following equation with time t.
| (6a) |
In contrast, if ρ contributing to shear strain is constant with respect to t, the strain rate is controlled by the velocity of moving dislocations. Therefore,
| (6b) |
Equations (6a) and (6b) are the deformation models controlled by multiplication and mobility of dislocation, respectively.17) The deformation of ferritic steels can be given by Eq. (6a) because plastic deformation might begin in a dislocation-free area. Therefore, the amount and rate of displacement at the onset of plastic deformation are considered to be controlled by the rate of increase of dislocation density dρ/dt. This is consistent with the report that the avalanche of dislocations causes the displacement burst at the pop-in. On the contrary, martensitic transformation in steels introduces high-density dislocations of 1015−1016 m−2, and some of their short-range motion as mobile dislocations can generate sufficient plastic strain.1,5,6,7,8) Therefore, in martensitic steels, the effect of newly-formed dislocations is small, and the onset of plastic deformation will be controlled by the average dislocation velocity of mobile dislocations dx/dt, as indicated by Eq. (6b). Considering the above differences in deformation models, it is understandable that a clear pop-in appears not in martensitic steel but in ferritic steel. In addition, it has been reported that when the dislocation velocity is the rate-determining factor of the yield phenomenon, the yield stress shows a strain rate dependence,17) which can explain the strain rate dependence of the elastic limit of martensitic steel8) without contradiction. On the other hand, it has been recently pointed out that microscopic internal stresses generated via martensitic transformation affect the yielding behavior of martensitic steels. In fact, Fukui et al.13) performed nanoindentation tests on a microscopic region where the transformation-induced internal stress was released by focused ion beam processing and reported that the displacement decreased at low loads. Although the Pc of the martensitic steels was not evaluated as in the present experiment, if internal stresses assist dislocation motion, this may act as a factor to reduce the elastic limit, in addition to the presence of high-density of pre-existing mobile dislocations. After mobile dislocations begin moving in martensitic steels, they will entangle with each other leading to dislocation cells or reach lath boundaries immediately. Some researchers reported the anisotropic deformation of lath martensite.18,19,20,21) Nambu et al.18,19) investigated the anisotropic deformation behavior by scanning electron microscopy with digital image correlation and revealed that the slip system is strictly restricted by lath morphology, i.e., in-lath-plane slip. The inhibition of dislocation motion by the formation of dislocation cell and lath structure leads to significant large strain hardening in martensitic steels.
In this study, the possibility of evaluating the elastic limit of martensitic steels by nanoindentation tests was clarified. However, τmax for 0C martensite estimated by Pc (4.13 GPa) is much higher than the shear stress to move pre-existing dislocations. This is maybe because the local stress state below the indenter is more complexed by substructure of lath martensite, and the mobile dislocations may be heterogeneously distributed locally. Therefore, it must be said that the mechanical evaluation by nanoindentation is qualitative so far. Further experiments and more precise stress analysis will be necessary for the material design of martensitic steels in the future.
For easy and accurate evaluation of the elastic limit and understanding of the elastic-plastic deformation mechanism of martensitic steel, nanoindentation was performed on martensitic and ferritic steels. The obtained results are summarized as follows:
(1) In the load-displacement curves obtained by nanoindentation, ferritic steel has a clear pop-in, but no clear pop-in is observed for martensitic steel, regardless of the carbon content.
(2) Hertz’s contact theory can qualitatively evaluate the elastic limit of not only ferritic steel but also martensitic steel. As a result, it is found that martensitic steel yields at stress clearly lower than that of ferritic steel, and a very small plastic strain is generated at the yielding.
(3) The yield stress of the martensitic steels is caused by the pre-existing mobile dislocation motion, whereas the dislocation nucleation and dislocation avalanche govern the yield stress of the ferritic steels. Therefore, the amount of small plastic strain at yield is governed by the dislocation velocity in martensitic steels.
This work was supported by JST, PRESTO, Grant Number JPMJPR2099, Japan.
