Influence of Heat Treatment on Elinvar Properties of a 40NiCrTiAl Alloy

This study investigates the effect of heat treatment on the microstructure and Elinvar properties of a cold-rolled 40NiCrTiAl alloy. This study utilizes optical microscopy, scanning electron microscopy backscattered electron imaging, secondary electron imaging, and energy-dispersive X-ray spectroscopy analysis to observe the precipitation behavior and determine the composition within the material. The results show that the 40NiCrTiAl Elinvar alloy at aging temperatures of 600-700°C, spherical precipitates appear within the grains. At approximately 700°C and with an aging time of around 2 hours, the precipitate volume reaches a peak, and the Young’s modulus and Elastic modulus temperature coefficient also reach their respective peaks. These elastic performance indicators exhibit a strong linear relationship with the degree of precipitate formation. These findings are important for a deeper understanding of the application potential and performance optimization of this Elinvar alloy.


Introduction
The Elinvar effect, characterized by a constant elastic modulus regardless of temperature, is an interesting phenomenon observed in many alloys [1].Elinvar alloys are unique materials that exhibit temperature invariance of Young's modulus or other elastic constants over a wide temperature range, making them essential in various fields such as precision instruments, acoustic applications, and aerospace industry [2].So far, the Elinvar effect has been mainly observed in ferromagnetic alloys, antiferromagnetic alloys, shape memory alloys, and high-entropy alloys.Elinvar alloys can be classified into ferromagnetic alloys, paramagnetic alloys, and antiferromagnetic alloys based on their magnetic properties [3].
Studies have shown that some elements in Elinvar alloys exhibit smaller local thermal expansion [4], especially the local thermal expansion near Fe is much smaller than that near Ni and Cr.On the other hand, lattice distortions near Cr show a significantly larger deviation than thermal expansion and lattice strain near other elements [5], playing a crucial role in absorbing lattice distortions in the matrix.Through specific alloy design and aging treatment, phase separation of unstable phases and related microstructural transformations can be achieved in Elinvar alloys, allowing the alloy to exhibit Elinvar

Experimental Methods
The experiment utilized a 40NiCrTiAl alloy, which was produced by smelting in a vacuum induction furnace.The actual chemical composition of the alloy after smelting was Fe-40.32Ni-5.51Cr-2.63Ti-0.47Al-0.55Mn-0.4Si(wt.%).To ensure homogeneity, the ingot was reheated to 1200 °C for 20 min, and then forged at temperatures above 1000 °C .The dimensions of the as-forged billet were 1050 mm in length, 50 mm in width, and 12 mm in thickness.Subsequently, the as-forged billet was cold rolled into a sheet with a thickness of 6 mm.
The samples prepared for heat treatment was cut from the sheet.The temperature designed for the heat treatment was in the range of 400 to 900 °C .The recrystallization temperature for the experimental alloy was approximately 850 °C .Hence, when the temperature is higher than 850 °C , the heat treatment process was called annealing; when the temperature is below 850 °C , the heat treatment process was called aging treatment.The cooling process after heat treatment was water quenching.The metallographic sample was corroded with CuSO4 solution and the corrosion time was 1 minute.Observation and composition determination of the internal precipitation behavior of the material were carried out using Optical Microscopy (OM), Scanning Electron Microscopy (SEM) with backscattered electron imaging, secondary electron imaging, and Energy-dispersive X-ray Spectroscopy (EDS) analysis.
The Young's modulus temperature coefficient is a fundamental performance requirement for Elinvar alloys.In this experiment, the Young's modulus of the solid materials was measured at different temperatures using the transverse vibration method outlined in GBT22315-2008.The shape of the sample used for this measurement was a round rod with a length of 150 mm and a diameter of 5 mm.

Influence of Aging Temperature on Precipitation
During the aging process of the 40NiCrTiAl alloy, the main precipitate phase was the γ' phase.The precipitate phase γ' is the most significant strengthening phase in this alloy, and controlling the type and content of the γ' phase was the primary method used to achieve the adjustment of the temperature coefficient of Young's modulus [8].
Figure 1 shows SEM images of the grain morphology of the samples at different aging temperatures.The interior of the grain exhibits regular undulations, and the orientation within the same grain is generally consistent, while the orientation varies among different grains.In the samples at different temperatures, spherical precipitates can also be observed, with noticeable differences in Ti content compared to the matrix.
After measurements, it was found that at an aging temperature of 600 °C, the size of the precipitates was around 100 nm.At 650 °C, similar precipitates were present with little change in distribution density and size compared to 600 °C.However, there were larger spherical precipitates with sizes around 1-2 um, which were identified as TiC through EDS analysis.At 700 °C, spherical precipitates of around 100 nm in size were also observed, and their quantity was relatively higher compared to the previous temperatures.As the temperature increased to 900 °C, the number of precipitates in the matrix decreased, with most of the precipitates gathering at the grain boundaries.It can be observed that the variations of Elastic modulus temperature coefficient, the content of Ti in precipitate, and the content of Ni in the matrix are highly similar in figure 2 there is a direct relationship between the three.Hence, the degree of precipitation was positively correlated with the Ti content in the precipitates.At about 400-700 °C, the precipitated phase is in the growth stage, and the precipitated phase is formed in the internal matrix of the grains, this precipitation has a significant impact on the properties of the superelastic alloy, with the maximum peak of precipitation occurring around 700 °C .However, in the temperature range of approximately 700-900 °C , the precipitation phase dissolves within the grains, leading to a gradual decrease in the quantity within the matrix and the formation of Ti-enriched phases at the grain boundaries.This type of precipitation has a lesser impact on the properties of the superelastic alloy.The trends of Young's modulus and Elastic modulus temperature coefficient closely mirror the changes in the precipitation phase.The influence of the precipitation phase on the superelastic performance can be attributed to two aspects: firstly, as a strengthening phase, it enhances the Young's modulus, and secondly, as a regulating phase, it improves the temperature coefficient [9].
We are attempting to establish a theoretical model for analysis: For ferromagnetic superelastic alloys, their superelastic properties primarily come from the "ΔE effect".According to mechanics, the relationship between the bulk modulus B and the Young's modulus E of a material can be expressed as equations 1 and 2: B=V ( Where λ represents strain, since this study used the transverse vibration method for measurements, where λ is equal to 0 when measuring, so can be simplified to equation 3:

E=3B
(3) For general materials, neglecting the influence of internal defects such as grain boundaries and dislocations, the internal energy U value of the material mainly comes from its atomic interaction potential.However, for shape memory alloys, in addition to considering atomic interaction potential, the "ΔE effect" also needs to be taken into account.
Based on the information in figure 4, it can be observed that the extent of precipitation of the precipitate phase is almost consistent with the reduction in the host Ni.The degree of precipitation, denoted as x, can be expressed as a function of the Ti content in the precipitates, represented as ω (wt.%).The relationship can be described as x = pω + q, where p and q are constants, Therefore, it can be assumed that the reduction in host Ni can be linearly represented by the extent of precipitation of the precipitate phase: Bringing this into equation 3 yields equation 5: Substituting equation 5 into equation 2 yields equation 6: Differentiating with respect to temperature T, we obtain the expression for the temperature coefficient of Young's modulus as shown in equation 7: V dT (7) Due to the small and similar temperature changes observed in all experimental groups and the nearly complete coherency between the precipitate phase and the matrix, it can be assumed that different degrees of precipitation have little effect on the volume V. Therefore, in the experimental process, V can be approximated as a constant V0.This leads to equation 8: V 0 (8) According to Brozorth's theory, the expression for the Young's modulus caused by small stress is given by equation 9: The increase in the precipitation phase leads to a decrease in the Ni content, which significantly affects the saturation magnetostriction and the precipitation degree λs.Assuming that this relationship is linear with the Ni content, it will also be linear with x, as shown in equation 10.
Due to the small and similar temperature changes observed in all experimental groups, the variation of λs with temperature T can be approximated as a constant.Therefore, we can derive the equation as follows: Bringing x=pω+q into equation 12 gives the relationship between the βE and the Ti content ω in the precipitate, as in equation 13: Equation 12 indicates that βE exhibits a quasi-linear relationship with the precipitation degree x under experimental conditions.Figure 3 represents the variation curves of the temperature coefficient of Young's modulus with the content of Ti in precipitate.The value of βE increases with the increase of Ti content in the precipitate, and βE exhibits a quasi-linear relationship with the precipitation degree under experimental conditions.This is consistent with the experimental results.

Effect of Aging Temperature on Elinvar Performance
The main hysteresis properties of Fe-Ni Elinvar alloys are influenced by the aging temperature [10].Therefore, it is necessary to discuss the effects of temperature and time during the heat treatment aging process on the material's Elinvar properties.
Figure 4 depicts the variation curves of the Young's modulus, Elastic modulus temperature coefficient, and Frequency temperature coefficient (βf) of the material with aging temperature at 30 °C.The Young's modulus shows a clear upward trend within the temperature range of 400-700 °C, while it exhibits a significant downward trend in the range of approximately 700-900 °C.Around 700 °C, there is a peak in the aging strength of the specimen.The trends of the Young's modulus temperature coefficient and the Frequency temperature coefficient are generally similar.In the range of 400-500 °C , their temperature coefficients show small variations.In the range of 500-700 °C , they exhibit a significant upward trend.However, in the range of approximately 700-800 °C , they display a noticeable downward trend.The temperature coefficients also show relatively small variations in the range of 800-900 °C .Around 700 °C , there is a peak in the temperature coefficient of the specimen.

Effect of Aging Time on Elinvar Performance
Figure 5 represents the variation curves of Young's modulus, Elastic modulus temperature coefficient, and Frequency temperature coefficient of the specimen at 30 °C with respect to the aging time at 650 °C.From the graph, it can be seen that the Young's modulus shows an increasing trend during the 1-2 h aging process, followed by a decreasing trend during the 2-3 h aging process.A strength peak occurs at around 2 h of aging.The variations in the Elastic modulus temperature coefficient and the Frequency temperature coefficient follow a similar trend.The Elastic modulus temperature coefficient increases in the range of 1-2 h and decreases in the range of 2-3 h, there is also a peak around 2 h.

Conclusion
When the aging temperature of the material is between 600-700 °C, spherical precipitates with a size of around 100 nm can be observed inside the material grains.The Ti content in the precipitates can be used as an indicator to determine the degree of precipitation.It can be observed that precipitation reaches its maximum value at IOP Publishing doi:10.1088/1742-6596/2694/1/0120377 around 700 °C.When the temperature reaches approximately 900 °C, Ti-enriched precipitates appear at grain boundaries.At an aging temperature of around 700 °C and a time of approximately 2 hours, as the precipitate volume of the sample reaches its peak, the Young's modulus and Elastic modulus temperature coefficient also reach their peak values.These two performance indicators show a strong linear relationship with the degree of precipitation.

Figure 1 .
Figure 1.SEM images of the grain morphology of samples at different aging temperatures, (a) 600 °C, (b) 650 °C, (c) 700 °C, and (d) 900 °C.The main strengthening phase was the γ' phase (Fe, Ni)3(Al, Ti), which has a high Ti content compared to the matrix composition.By utilizing EDS to measure the component content of 20 precipitates and calculating the average value, the Young's modulus temperature coefficient, the content of Ti in precipitate, matrix Ni content, and aging temperature variation can be plotted as shown in figure 2.

Figure 2 .
Figure 2. Variation of Elastic modulus temperature coefficient, the content of Ti in precipitate, and the content of Ni in the matrix with aging temperature.

Figure 3 .
Figure 3. Variation curves of the temperature coefficient of Young's modulus with the content of Ti in precipitate.

Figure 4 .
Figure 4.The variation curves of Young's modulus, Elastic modulus temperature coefficient, and frequency temperature coefficient of the material with aging temperature at 30 °C.

Figure 5 .
Figure 5.The curves of the variation of Young's modulus, Elastic modulus temperature coefficient, and Frequency temperature coefficient of the specimen at 30 °C with respect to the aging time at 650 °C.
Conference on Mechanical Engineering and Materials Journal of Physics: Conference Series 2694 (2024) 012037