Water quenching cracking mechanism and prevention of steels

ABSTRACT Quenching is often an essential step in heat treatment of steels for enhancing strength. Water quenching which is low cost and free of pollution risk instead of oil quenching or polymer aqueous solution quenching which is high cost and has high pollution risk will be widely used in heat treatment enterprises. However, the problem of easy cracking of low alloy steels (especially medium carbon low alloy steels) quenched in water has long been a concern for many researchers. The finite element simulation (FES) is used to predict transient stress at cracking position during quenching of an AISI 4140 steel cylinder sample and found that the transient tangential tensile stress at cracking position was only 350 MPa which is smaller than half of the yield strength (775 MPa) of AISI 4140 steel. Such a low tensile stress causing quenching cracking is surprising. To ascertain the underline reasons, a phase-field finite element (PFFE) model is established to investigate the microscopic stress distribution produced by martensitic transformation. The results indicate that the microscopic stress at the junction of the lath martensitic variants in AISI 4140 steel exceeded 800 MPa, and thus such a high microscopic stress is considered as the origin of quenching cracking. By using two examples, our work further clarifies the basic principle of the water–air alternative timed quenching (ATQ) process invented by us as a process suitable for engineering applications with the ability to avoid water quenching cracking and ensure mechanical properties.


Introduction
Quenching is one of the most important heat-treatment process steps for raising the strength of low alloy steels [1].It is a process of rapid cooling from high-temperature austenite to room temperature to obtain high-strength martensite or bainite metastable microstructure [2,3].Clean and cheap water quenching instead of oil quenching or polymer aqueous solution quenching which is high cost and has a high pollution risk will become a trend in the heat treatment industry because of international requirements to reduce carbon emissions.
However, since the cracking issue of low alloy steel (especially medium carbon low alloy steel) parts induced by water quenching with a high cooling rate has not been solved, the oil or polymer aqueous solution with a low cooling rate is still widely used in various countries in the world [4].Water-air alternative timed quenching (ATQ) process proposed by our team 18 years ago has been successfully applied to treat various large-size alloy steel parts in China [5].
The finite element simulation (FES) of the stress field was established based on the simulations of the temperature field and the microstructure field, and the process design of water quenching based on finite element simulation achieves success in engineering [4].In the development of FES, transformation plasticity (TP) is one of the difficult issues that need to be addressed to obtain a precise prediction of the transient stress.TP is an irreversible strain observed when metallurgical transformation occurs under a small external stress lower than the yield stress.
For this purpose, an exponent-modified (Ex-Modified) normalized function describing the TP strain was proposed [1], showing that the Ex-Modified normalized function better describes the TP kinetics than Abrassart's, Desalos's and Leblond's functions, in turn, the FES for the residual stress distributions in quenched AISI 4140 cylinders with two diameter sizes better agrees with XRD measurements [6].Besides, the FES was used to predict the cracking position by maximum transient stress during the quenching of an AISI 4140 steel cylinder sample, which is consistent with experimental observation.Meanwhile, the occurrence time of quenching cracking also was precisely determined by acoustic emission (AE) technology.
However, the transient tangential tensile stress at the cracking position is only 350 MPa [7] which is smaller than half of the yield strength (775 MPa) of AISI 4140 steel.Such a low tensile stress causes quenching cracking, which is surprising.For this reason, we wonder whether the microscopic stress generated by martensitic transformation may be much larger than the macroscopic stress predicted by FES.Then the phase-field finite element (PFFE) model is established to investigate the distribution of the microscopic stress produced by martensitic transformation in AISI 4140 steel under the tensile loading, and particular attention is paid to the microscopic stress at the junction of lath martensitic variants, from which the mechanism of quenching cracking will be explored in martensitic steels and the process of avoiding cracking will be proposed.

Model formulation
In the phase field model of martensitic transformation, the order parameter h is used to describe the martensite variant.The evolution of the order parameter can be described by the Cahn-Allen equation [8,9].It can be written as follows: where L is the kinetic coefficient [10] and j h m (r, t) is the Langevin noise term.G is the Gibbs free energy of the system and can be divided into three parts: chemical free energy G ch , gradient energy G gr and elastic strain energy G el , then G can be written as [11,12]: The chemical energy, according to the Ginzburg-Landau theory, can be written as follows [13][14][15]: where B and C are constants, and A can be written as A(T) = a 0 (T − M f ), M f represents the end temperature of the martensitic transformation, a 0 is a constant.The gradient energy can be expressed as follows [16,17]: where b ij (p) is the gradient energy coefficient and ∇ is the differential operator.The elastic strain energy can be expressed as [18,19]: where s ij is the elastic stress, C ijkl is the elastic coefficient tensor and 1 el ij is the elastic strain tensor.
There are three ways to solve the partial differential equations: finite difference method, Fourier spectral method and finite element method.Unlike the finite difference method, where the choice of time step affects stability and accuracy, and the Fourier spectral method, which is limited to problems with periodic boundary conditions, while the finite element method overcomes these constraints.By dividing the domain into finite elements, FEM accommodates complex geometries and irregularly shaped domains, making it a flexible and powerful numerical technique.In this paper, the partial differential equation (Equation 1) is solved using the phase field finite element method with the Comsol software to get the evolution of martensite and its associated stress field [20,21].The mesh is a quadrilateral grid and the mesh size is set as 0.1 um.The parameters of the martensitic transformation coupling with phase filed finite model are set as follows: Figure 2 shows the microstructure evolution of martensite in AISI 4140 steel and its associated stress field when the steel quenching to 300 K (T q ).As shown in Figure 2(a-d), the martensite gradually grows with the change of quenching time from 1 to 10 s.The equivalent stress at the junctions of lath martensitic variants is higher than other martensite region during the formation of martensite in Figure 2(e-h).

Stress evolution during the formation of lath martensitic variants
To quantitatively investigate the stress distribution during the formation of martensite, the evolution of the equivalent stress is drawn with the quenching time along the lines A-B marked in Figure 2(d) and the asterisks marked in Figure 2(h), as shown in Figure 3(a) and (b), respectively.Figure 3(a) shows that the stress distribution in the martensite region gradually increases, caused by the accumulation of transformation stress, with the change of quenching time from 1 to 10 s.Moreover, the stress at the junctions of lath martensitic variants (point C) is higher than intergranular stress (point D).The above result indicates that the microscopic stress at the junction of the lath martensitic variant exceeds 800 MPa, which is much larger than the macroscopic stress of 350 MPa calculated by FES, and thus such microscopic stress is considered as the origin of quenching cracking.
Figure 4 shows the microstructure evolution of martensite and its associated stress field when the steel quenching to 440 K. Compared with the results in Figure 2, with the quenching temperature (T q ) increases, the volume fraction of martensite is less than that of martensite at quenching temperature of 300 K in the same quenching time, as shown in Figure 4(d), which is caused by the decrease of the driving force for martensitic transformation.Figure 4(e-h) shows the equivalent stress formed in the transformation process, which is much less than that of the corresponding position at a quenching temperature of 300 K.
The equivalent stress distributions at different T q mentioned above are summarized in Figure 5, in which the red line and black line represent the equivalent stress distribution along the lines A-B marked in Figure 2(d) and the lines E-F marked in Figure 4(d), respectively.Figure 5 shows that the microscopic stress produced by martensitic transformation decreases with the increase of quenching temperature.
Figure 6 shows the evolution of equivalent stress distribution along lines A-B marked in Figure 2(d) after quenching at 300 K with different tempering temperatures.With the increase of tempering temperature, the equivalent stress along A-B gradually decreases, indicating that the tempering process is added after the quenching process to further reduce the microscopic stress caused by martensitic transformation.

Process optimization to avoid cracking
Based on the above results, it can be seen that an increase of the quenching temperature and the addition of the tempering process after quenching can effectively reduce the microscopic stress caused by martensitic transformation.ATQ process just contains the above two factors.For example, the finite element simulation of the stress field of the AISI 4140 steel cylinder was carried out with a water quenching-air cooling-water quenching process (810°C austenitizing temperature, water quenching time 6 s, air  cooling time 300 s, water quenching time 60 s to room temperature).Figure 7 shows that the size of the cylindrical sample is 139 mm long, the radius is 8 mm, the mesh is 1/4 of the cylindrical cross-section, and the sampling position is a point on the circumference of the surface, as shown position indicated in Figure 7.
The cooling curve and corresponding principal stress distribution diagrams of the ATQ process are shown in Figure 8(a) and (b), respectively.It is clear from Figure 8(a) that the ATQ process has a quenching temperature T q = 170°C (443 K) and tempering temperature T t = 400°C (673 K).ATQ process has a higher quenching temperature than room temperature accompanying with lower quenching stress (300 MPa in Figure 8b) than 350 MPa produced by direct water quenching to room temperature (Graph omission), and tempering further reduces quenching stress (Figure 8b).The decrease of macroscopic stress form FES reduces correspondingly the microscopic stress produced by martensitic transformation easy to cause cracking.It is worth pointing out that it can be known from Figure 6 that a high tempering temperature is favorable for the reduction of microscopic stress; however, the high tempering temperature will lead to the reduction of the strength of martensitic matrix and the decomposition, ferrite + cementite, of untransformed austenite, and thus a proper tempering temperature and hold time must be considered for excellent strength and ductility of martensitic steels.
In general, the ATQ process designed by FES has a higher quenching temperature than room temperature and tempering step, which effectively reduces quenching macro-stress, correspondingly reducing the micro-stress at the junction of the lath martensitic variants, meanwhile, by FES design of quenching temperature (related to the volume fraction ratio of martensite and austenite) and tempering temperature and time (related to the strength of martensite and the stability of untransformed austenite), which ensure the strength and toughness of steel parts, and thus this is the basic principle of ATQ process suitable for engineering application with the ability to avoid cracking and ensuring mechanical properties.The 42CrMo 4 marine crankshaft is an important power part.Traditional quenching cooling methods, such as oil quenching and polymer aqueous solution quenching, cannot meet the performance requirement.Because of its complex shape and the large difference of cross-section size of the crankshaft, direct water quenching is easy to lead to the quenching cracking, so the ATQ process was used to treat the 42CrMo 4 marine crankshaft [22].Multi-cycle water quenching and air cooling were designed to avoid cracking of crankshaft and ensuring mechanical properties.Figure 9 shows the cooling curve of the crankshaft surface, in which precooling is to reduce the temperature gradient of the crankshaft and accelerate the subsequent cooling rate.The start temperature (M s ) of martensitic transformation for 42CrMo 4 is about 280°C.The quenching temperature (T q ) obtained by the first water cooling is much higher than room temperature, but less than M s , meaning the formation of martensite, so does subsequent T q obtained by water cooling.While air cooling between water cooling results in the self-tempering of martensite.Each time the martensite self-tempering temperature gradually reduces.To avoid the reduction   of the strength of the martensitic matrix and the decomposition, ferrite + cementite, of untransformed austenite, the tempering temperature cannot be too high.It is clear that the quenching temperature being much higher than room temperature and several self-tempering of martensite will effectively reduce the microscopic stress produced by martensitic transformation.The ATQ process designed to avoid the cracking of the crankshaft and ensure its mechanical properties, as shown in Table 1.

Figure 1
Figure1shows the initial simulation condition of the model.The boundaries of the domain adopt fixed constraints.A circular martensitic embryo is pre-positioned in the austenite parent phase to create an energy fluctuation area to induce the formation of the martensite phase.Figure2shows the microstructure evolution of martensite in AISI 4140 steel and its associated stress field when the steel quenching to 300 K (T q ).As shown in Figure2(a-d), the martensite gradually grows with the change of quenching time from 1 to 10 s.The equivalent stress at the junctions of lath martensitic variants is higher than other martensite region during the formation of martensite in Figure2(e-h).To quantitatively investigate the stress distribution during the formation of martensite, the evolution of the equivalent stress is drawn with the quenching time along the lines A-B marked in Figure2(d) and the asterisks marked in Figure2(h), as shown in Figure

Figure 1 .
Figure 1.The initial condition of the model with the martensitic embryo in the two-dimensional square domain.

Figure 2 .
Figure 2. Evolution of the martensite microstructure with its associated stress field with the quenching time at the quenching temperature T q = 300 K: (a-d) martensite; (e-f) equivalents stress; (a, e) 1 s; (b, f) 2 s; (c, g) 5 s; (d, h) 10 s.

Figure 4 .
Figure 4. Evolution of the martensite microstructure with its associated stress field with the quenching time at the quenching temperature T q = 440 K: (a-d) martensite; (e-f) equivalents stress; (a, e) 1 s; (b, f) 2 s; (c, g) 5 s; (d, h) 10 s.

Figure 5 .
Figure 5.The equivalent stress distribution along the lines A-B and lines E-F marked in Figure 2(d) and Figure 4(d), respectively, after the martensite formed in the domain.

Figure 6 .
Figure 6.The equivalent stress distribution along the lines A-B marked in Figure 2(d) after the quenching process and then tempering at different temperatures.

Figure 7 .
Figure 7. Length, radius and sampling position of the cylinder.

Figure 8 .
Figure 8.The (a) cooling curve and (b) equivalent stress distribution diagrams of the ATQ process.

Figure 9 .
Figure 9.The cooling curve of the crankshaft surface.

Table 1 .
The mechanical properties of crankshaft after quenching and tempering.