Influence Factors for the Determination of Vermicular Graphite Ratio in Cast Iron Measured by Ultrasonic Method
2018 Volume 59 Issue 7 Pages 1186-1191
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2018 Volume 59 Issue 7 Pages 1186-1191
The ultrasonic method was used to detect vermicular graphite ratio according to the relationship between them. However, there is little report how the factors affect the vermicular graphite ratio detection and ultrasonic velocity measurement. In this paper, using ECHOMETER1076 ultrasonic tester, stylus surface roughness tester and quantitative metallography, the influences of sample two-plane parallelism, probe incident angle, coupling agent type, surface roughness and matrix on the ultrasonic velocity were further studied by experiments and simulation. The parallelism and probe incident angle were found to have important influence on the ultrasonic velocity, increasing more than 4.58 m/s every 0.1°. Contrarily, the influence of coupling agent, surface roughness less than 5 and pearlite percentage were little, and even neglected. So, the parallelism and probe incident angle must be kept as small as possible and the surface roughness is not more than 5. This provide a basis for accurately measuring the ultrasonic velocity and predicting the vermiculate graphite ratio.
The tensile strength and yield strength of vermicular cast iron are higher than that of gray iron and lower than that of nodular cast iron. Its thermal conductivity, thermal fatigue resistance, machinability and shock absorption are similar to grey cast iron,1) and its liquidity and feeding are better than nodular cast iron. Those good properties make it be widely used in the field of high mechanical thermal stress, such as cylinder body, cylinder head and brake of large diesel engine.2) Its good compactness makes it especially suitable for the hydraulic parts. However, the problem of producing vermicular cast iron is difficult to control the vermicular graphite ratio. During the production process, in order to avoid a lot of flake graphite arising from lack modification and too much nodular graphite due to excessive modification,3) there is a need to quickly and accurately detect the vermicular graphite ratio, and thus adjust the quantity of the vermicular agent in time.
Quantitative metallographic method is one of the most commonly used to detect vermicular graphite ratio.4) Although it can detect the vermicular graphite ratio accurately, it is very slow, time-consuming and laborious, and it is not easy to achieve on-line detection.
Ultrasonic method is a promising method to detect vermicular graphite ratio of vermicular cast iron rapidly and online. The method is based on the pre-established relationship between the ultrasonic velocity and the vermicular graphite ratio of cast iron, and the ultrasonic velocity is used to predict the vermicular graphite ratio quickly.5) Therefore, the measurement of ultrasonic velocity is very important because it is directly related to the accuracy of detecting vermicular graphite ratio. At present, a lot of researches were focused on the ultrasonic system of detecting vermicular graphite ratio and the relationship model between ultrasonic velocity and vermicular graphite ratio, and some progress had been made.6–8) The relationship between ultrasonic velocity and vermicular graphite ratio were divided into three sections to be described, including two straight lines and one transitional curve, and corresponding mathematical regression relation model was given. However, because the range of the transitional curve is very narrow, which requires accurate measurement of ultrasonic velocity. In addition, although the influence of matrix and defects on the ultrasonic velocity was mentioned,9) there were few reports how the factors affect the ultrasonic velocity and thus vermicular graphite ratio.
In order to solve the above problem, the factors of the sample two-plane parallelism, probe incident angle, coupling agent type, surface roughness and matrix on the ultrasonic velocity were further studied by experiments and simulation, which will lay a foundation for measuring ultrasonic velocity and detecting the vermiculate graphite ratio accurately.
The longitudinal wave, transverse wave and surface wave can propagate in solid medium such as vermicular cast iron. When the wave length is much less than the size of solid medium, the propagation velocity of the ultrasonic longitudinal wave in solid medium can be expressed as eq. (1).10)
| \begin{equation} v = \sqrt{\frac{E(1 - \mu)}{\rho(1 + \mu)(1 - 2\mu)}} \end{equation} | (1) |
The Poisson’s ratio μ and density ρ of vermicular cast iron are 0.27–0.28 and (7.05–7.1) × 103 kg/m3. Their small changes have little influence on the ultrasonic velocity v. Therefore, according to eq. (1), the ultrasonic velocity v is mainly decided by the Young’s elastic modulus E of vermicular cast iron which has a big change range from 127400 MPa to 156800 MPa. And the Young’s elastic modulus E has direct relation to vermicular graphite ratio.
Therefore, when the carbon equivalent is constant, the change of the graphite shape and size will lead to the change of elastic modulus E, that is, the change of vermicular graphite ratio will lead to the change of ultrasonic velocity in vermicular cast iron. Once the modification of vermicular cast iron is lack or excessive, the mechanical properties of castings will decrease greatly, and the elastic modulus E and ultrasonic velocity will also change with the quantity of flake graphite or nodular graphite. So, the vermicular graphite ratio of vermicular cast iron can be predicted by the ultrasonic velocity, and accurate measurement of ultrasonic velocity is very important.
The experimental materials are the cylinder head, cylinder and the specimen attached to those, from which the experimental samples are cut and machined. The Echometer1076 ultrasonic velocity tester was used to measure the ultrasonic velocity in the sample, and the stylus surface roughness tester was used to measure the sample roughness Ra, and the quantitative metallography was used to measure the sample microstructure.
The frequency of the ultrasonic probe is very important to measure the ultrasonic velocity. According to the relation between the direction angle and the wavelength, the shorter the wavelength of the ultrasonic probe is, the better the directivity of the acoustic beam is, the more concentrated the acoustic energy is and the smaller the energy attenuation is. However, the attenuation in the cast iron is also directly related with the grain size and properties of castings.11) When the wavelength is equal to or smaller than the grain size, the absorption attenuation and scattering attenuation are very significant, which not only reduces the ultrasonic penetration capability, but also makes difficult to accurate measurement because of the grain boundary reflection. Therefore, the probe frequency is not too low, otherwise it will make the spread attenuation of sound beam increase. Contrarily, the frequency is not too high, otherwise it will make the absorption attenuation and scattering attenuation increase due to the relatively coarse grain in cast iron. So, the probe with the frequency of 2 MHz and the diameter of 20 mm was used to measure the experimental samples.
When the upper plane of the experimental sample is not parallel to the lower plane, the ultrasonic velocity will be affected. Considering that the parallelism of sample two planes cannot be accurately got by machining, the ANSYS finite element simulation method is applied to study the influence of the sample two-plane parallelism on the ultrasonic velocity.
Since the propagation mode and path of ultrasonic waves in two-dimensional model are the similar to those in three-dimensional model, it is possible to establish the two-dimensional model to study the influence of two-plane parallelism, which will not only reduce the calculate time, but also clearly give the propagation process of the ultrasonic wave.
The two-plane parallelism of the experimental sample is characterized by the included angle between the upper plane and lower plane, as shown in Fig. 1. The included angle α increases from 0 to 5° with the step of 0.5°, and the parameters of the model are as follows. The density is 7.1 × 103 kg/m3, the elastic modulus is 153000 MPa, and the Poisson’s ratio is 0.27. The size of the model is 30 mm × 30 mm × 0.1 mm, and the grid size is 1/100 of the wavelength. During the propagation in vermicular cast iron, the sound pressure of ultrasonic was shown in Fig. 2. Figure 2(a) to Fig. 2(f) express the propagation process from transmitting ultrasonic waves to receiving echoes, respectively.
Diagram of expressing two-plane parallelism by their included angle.
Sound pressure map during ultrasonic propagation in cast iron sample: (a)–(f) express the propagation process from transmitting sound waves to receiving echoes.
The propagation process can be explained as follows. If the function u(x, t) is defined as the particle displacement in the sample, it will change under stress due to the isotropy of vermicular cast iron. After the Lame constant is introduced, the motion equation of the particle in ultrasonic field can be expressed as:
| \begin{equation} \rho\frac{\partial^{2}u_{i}}{\partial t^{2}} = (\lambda + \mu)\frac{\partial}{\partial x_{i}}\frac{\partial u_{i}}{\partial x_{j}} + \mu\frac{\partial^{2}u_{i}}{\partial x_{j}^{2}}\quad i,j = 1,2,3 \end{equation} | (2) |
According to Helmholtz decomposition, after taking u = ∇ϕ + ∇ψ into the eq. (2), the eq. (3) can be obtained.
| \begin{equation} \left. \begin{array}{l} \nabla^{2}\phi = \dfrac{1}{C_{l}^{2}}\dfrac{\partial^{2}\phi}{\partial t^{2}}\\ \nabla^{2}\psi = \dfrac{1}{C_{s}^{2}}\dfrac{\partial^{2}\psi}{\partial t^{2}} \end{array} \right\} \end{equation} | (3) |
According to the eq. (3), the ultrasonic propagation in the two-dimensional model is in the form of several concentric circles. When a series of ultrasonic waves propagate to the bottom of the sample, they will reflect back because of the different acoustic impedance on the interface. The reflecting waves also satisfy the eq. (3), then a series of concentric circle waveforms can be received. Due to the ultrasonic attenuation in the sample, the sound pressure of the reflecting wave is far less than that of the incident wave, and the relationship between the sound pressure and the propagation time was shown in Fig. 3. The maximum sound pressure is designated as the echo peak, and the corresponding time is taken as the ultrasonic propagation time in the sample. So, the ultrasonic velocity can be calculated according to the propagation time and the propagation distance.
Change curve of sound pressure versus propagation time.
In Fig. 3, the propagation time corresponding to the echo peak is 1.1232 × 10−5 s, and the propagation distance is 30 mm × 2 = 60 mm. So, the calculated ultrasonic velocity is 5341.9 m/s. By analogy, after the different included angle α was given, the different simulation results can be obtained, as shown in Fig. 4. Since the most likely range of the included angle in actual production is 0–0.5°, the subdivision is carried out every 0.05° in this range, and the result was shown in Fig. 4(b).
Influence of two-plane parallelism on ultrasonic velocity: (a) relationship between v and α; (b) partial magnification of α = [0, 0.5].
It can be seen from Fig. 4 there is a linear relationship between the ultrasonic velocity and the included angle. When the included angle increases 0.1°, the ultrasonic velocity will increase about 4.58 m/s, and the corresponding detection error is 0.086%. If the included angle is changed from 0 to 0.5°, the ultrasonic velocity will rise from 5342 m/s to 5366 m/s, and the difference is 24 m/s, which cannot be ignored for the measurement of ultrasonic velocity. Therefore, the included angle should be controlled in a smaller range as far as possible.
4.2 Influence of probe incident angle on ultrasonic velocityThe same method of analyzing the influence of the included angle was used to study the influence of the probe incident angle on the ultrasonic velocity. The probe incident angle is defined as the angle between the probe axis and the vertical line of the sample incident plane. The simulation results were shown in Fig. 5. It can be seen the ultrasonic velocity has an approximately linear decrease with the increase of the probe incident angle, which is opposite to the sample two-plane parallelism. If the incident angle increases every 0.1°, the ultrasonic velocity will decrease about 4.92 m/s. When the probe incident angle increases from 0 to 0.5°, the ultrasonic velocity will drop from 5343 m/s to 5317 m/s with the difference of 26 m/s. The influence of the probe incident angle also cannot be ignored. So, the probe incident angle should be smaller as far as possible in order to reduce the influence on the ultrasonic velocity.
Influence of probe incident angle on ultrasonic velocity: (a) relationship between v and β; (b) partial magnification of β = [0, 0.5].
Samples with different surface roughness were obtained by grinding. After first grinding, the roughness and ultrasonic velocity was measured, and then grinding again and measurement again until it is near to the as-cast roughness. Finally, the experimental data of different surface roughness and corresponding ultrasonic velocity were obtained, as shown in Fig. 6.
Influence of sample surface roughness on ultrasonic velocity.
As can be seen from Fig. 6, when the surface roughness Ra is less than 5 µm, the ultrasonic velocity almost does not change. When the surface roughness Ra is more than 5 µm, the ultrasonic velocity decreases with the increase of the surface roughness. If the average surface roughness increases 1 µm, the ultrasonic velocity will decrease about 3 m/s.
The influence of the surface roughness on ultrasonic propagation can be explained physically. Ultrasonic waves are emitted from the probe and transmitted back and forth in the cast iron sample, and then it is received by the probe. In this process, the ultrasonic passes through the rough interface of the sample two times, which will lead to the diffuse scattering, reducing the echo amplitude. When the surface roughness reaches a certain threshold, the distortion of the measurement results will occur, resulting in a sharp decline in the ultrasonic velocity. On the other hand, the coarser the sample surface is, the longer the reflection time of the ultrasonic on the coarse surface is, which will lead to the decrease of the ultrasonic velocity. Therefore, to avoid the influence of surface roughness on the ultrasonic velocity, the surface roughness Ra must be less than 5 µm. Fortunately, the requirement can be meet by the conventional machining. Under this condition, the influence of surface roughness on ultrasonic velocity can be neglected.
4.4 Influence of coupling agent type on ultrasonic velocityThe following coupling agents are used: the original coupling agent of Echometer 1076 ultrasonic velocity tester, water, sodium silicate, 45# transformer oil, L-AN46 oil and propanetriol. The ultrasonic velocity for 10 samples is measured by using those coupling agents, respectively, and the experimental results are shown in Fig. 7.
Influence of coupling agent type on ultrasonic velocity.
Figure 7 illustrates that the coupling agent type has little effect on the ultrasonic velocity. This provides a basis for choosing the convenient coupling agent when the vermicular graphite ratio of cast iron was on-line predicted.
The main function of the coupling agent is to eliminate the air between the ultrasonic probe and the experimental sample, and to prevent the air from affecting the ultrasonic transmission. The influence of coupling agent on the ultrasonic velocity is mainly attributed to different acoustic impedance for different coupling agent, and thus it will cause the difference of echo energy or amplitude. Therefore, for the same sample and different kind of coupling agents, the measured ultrasonic velocity is not exactly the same, as shown in Fig. 7. On the other hand, the coupling agent layer is usually very thin, and thus the ultrasonic propagation distance in the coupling agent is very short. Therefore, it has little influence on the ultrasonic velocity. Furthermore, the acoustic impedance of several other coupling agents except the original coupling agent are available and are between (0.13–0.3) × 106 g/cm2 s, which is very small compared with the acoustic impedance of cast iron of (2.5–4.0) × 106 g/cm2 s. So, the influence on the ultrasonic velocity is not significant. In addition, it can be deduced from the above analysis that the acoustic impedance of the original coupling agent is also between (0.13–0.3) × 106 g/cm2 s.
4.5 Influence of matrix on ultrasonic velocityThe previous research12,13) showed the ultrasonic velocity of ferrite matrix is low and the ultrasonic velocity of pearlite matrix is high when the graphite shape is similar. And the ultrasonic velocity increases slightly with the increase of the pearlite percentage. For common vermicular cast iron, the pearlite percentage is low because of high carbon equivalent, which is generally 20%–30%. When the pearlite increased to 70%–80%, the ultrasonic velocity increased only 0.25%–0.4%. So the influence of pearlite percentage on the ultrasonic velocity in vermicular cast iron is very small.
The above research can be explained as follows. Pearlite is composed of lamellar ferrite and hard cementite. Because the cementite area has no graphite precipitation, and thus the matrix propagation path increases where the ultrasonic propagation velocity increase. On the other hand, the binding ability between graphite and ferrite is poor, and this will greatly weaken the bonding ability. So, the ultrasonic vibrations of graphite particle and matrix disaccord, which will lead to the decrease of ultrasonic velocity. Therefore, the propagation velocity in ferrite matrix is less than that in pearlite matrix, namely, with the increase of pearlite percentage, the ultrasonic velocity increases slightly. But compared with the change of graphite shape, it is not enough to have a great influence on the elastic modulus of vermicular cast iron, and ultrasonic velocity will not increase too much.
Experiments was used to verified the above analysis. The samples were divided into different groups according to similar vermicular graphite ratio by quantitative metallography, and the ultrasonic velocity was measured, and then the pearlite percentage was measured according to the GB/T 26656-2011. The experimental results were shown in Fig. 8. Obviously, when the pearlite was changed from a minimum of 24% to a maximum of 87%, the maximum velocity increase is about 22 m/s and 0.41%. When the range of pearlite percentage is not big, such as 60%–90%, the slight increase of ultrasonic velocity with the increase of pearlite is not obvious. The reason is that the small change of matrix is covered by the graphite shape change and experimental error. For industrial production, the pearlite of each batch of castings is generally in a certain range, for instance, the pearlite of truck engine cylinder and piston ring is generally 70%–80% due to the strength and wear resistance while the pearlite of the exhaust manifold is about 20%–30% due to toughness. Therefore, the influence of matrix on ultrasonic velocity is almost negligible.
Influence of pearlite percent on ultrasonic velocity.
This work was supported by State Key Laboratory of Engine Reliability, and Harbin special fund for scientific and technological innovation (2017RAGGJ012). The authors would like to acknowledge it.
