1. Introduction
As the key components of the rolling mill of the steel rolling production line, with the continuous development of the steel rolling industry, the requirements for the hardness and wear resistance of the rolls in industrial production are getting higher and higher. Cr5 alloy steel has been widely used in the production of modern rolls as a substitute for 60CrMnMo, 50CrNiMo, 70Cr3NiMo and Cr4 [
1] due to its good hardness, wear resistance and resistance. Fatigue performance has always been one of the key research topics for roll steels in the iron and steel production industry. Many scholars from all over the world have conducted a lot of research into the mechanical properties and fatigue resistance of Cr5 alloy steel and have achieved certain results. Junkai Fan et al. [
2] determined the forming properties of Cr5 alloy steel by studying the mechanical properties of Cr5 alloy steel. Qing Gu et al. [
3] determined the mechanical properties of Cr5 alloy steel by studying the fatigue behaviour of Cr5 alloy steel. M. Surendran [
4] and others determined the fatigue characteristics of Cr5 alloy steel by studying the hoop stress of Cr5 alloy steel. Many scholars conducted in-depth research on the mechanical properties of Cr5 alloy steel, which are beneficial to actual industrial production to a certain extent. However, there have been few studies on the damage performance of this material. Therefore, the current hot forming production plan for Cr5 rolls is often made by trial and error based on actual production experience, and there is no effective method to control crack defects.
Damage mechanics is a discipline that studies the process of material damage evolving with deformation until it is destroyed. It is believed that there are micro-defects distributed inside the material, such as dislocations, micro-cracks, micro-voids, etc. These micro-structures of different scales are typical damage performance [
5]. Y.C. Huang et al. studied the damage mechanism of 42CrMo steel and found that the growth and accumulation of pores were the main reasons for alloy fracture [
6]. Y.C. Lin et al. studied the fracture mechanism of nickel-based superalloys. They found that the higher the nucleus density formed by micropores is, the worse the plastic deformation ability of the material is, and that the combination of micropores was one of the reasons for the final ductile fracture [
7]. Kaimeng Wang et al. conducted tensile experiments on nickel-based superalloys and found that pores were mainly formed around grain boundaries and carbides in grains, and the fracture morphologies are characterized by transgranular fracture and intergranular fracture [
8]. Many scholars have conducted in-depth research on the formation mechanism of material cracks which is beneficial to reduce or eliminate the initiation of material damage during plastic deformation. However, no damage model was used to describe the damage behaviour of the materials.
In recent decades, many scholars have performed systematic research on the mechanism of crack generation and the establishment of related models in the material forming process. Freudenthal [
9] believed that when the material strain energy reached a critical value, the material would fracture, and proposed the Freudenthal damage model. Cockcroft and Latham [
10] believed that the maximum tensile stress in the material deformation process was the cause of material fracture, and proposed the Cockcroft and Latham (CL) damage model. Oyane [
11] believed that the pores were produced by the large deformation or the influence of the second phase particles, and proposed the Oyane damage model which considers stress triaxiality. Weitao Jia [
12] used the Freudenthal damage model to study the deformation and fracture behaviour of as-cast AZ31B Mg alloy. Qiang Li [
13] used the Cockroft and Latham fracture criterion to study the surface cracking of Fe-Cu-C steel. Feuerhack et al. [
14] used the Cockcroft and Latham damage criterion to study crack location and shape during extrusion. Aditya Rio Prabowo et al. [
15] analysed the reliability of the Cockcroft and Latham damage criterion. Wu Ying et al. [
16] used the Oyane fracture criterion to compare and analyse the dent defect failure of the X80 pipeline; Yu Zhang et al. [
17] used the Oyane fracture criterion to study the damage and cracking characteristics of AISI 410 stainless steel at high-temperature. Zbigniew Pater [
18] used the Oyane damage criterion to systematically study the critical damage value of 100Cr6 steel. Many scholars used the above damage models to effectively predict the damage behaviour during the material forming process which played a guiding role in controlling the damage defects in production. However, these damage models use the correlation function of strain and stress to calculate the damage parameters, and the prediction accuracy is slightly lower [
19].
The Lemaitre damage model in damage mechanics was proposed based on the thermodynamic dissipation potential of the material. This phenomenological method has been used to describe the damage of the material, which is closer to the real physical situation, and can more accurately describe the damage evolution behaviour of the material. Manizheh Aghaei et al. [
20] studied the tensile process of DP600 steel based on the Lemaitre damage model, and described the micromechanical behaviour of DP600 steel under tensile load. Based on the Lemaitre damage model, Sheng Cai et al. [
21] studied the blanking process of T6, and the damage of the material during the blanking process was simulated. Yogeshwar Jasra et al. [
22] studied the cracking process of AISI 304 stainless steel based on the Lemaitre damage model, and obtained the failure characteristics of AISI 304 stainless steel. Ashwani Verma et al. [
23] simulated the tensile process of the dual-phase steel based on the Lemaitre damage model, and obtained the damage parameters of the dual-phase steel in the tensile state. Based on the Lemaitre damage model, the fatigue life of the alloy was studied and predicted by L.M. Araújo et al. [
24]. Kazem Malekipour et al. [
25] observed and simulated the damage evolution process of AISI 316L parts based on the Lemaitre damage model. The axial stretching process was simulated, and the damage evolution law of the thin-walled steel pipe was obtained by Sheng He et al. [
26]. Many scholars have used the traditional Lemaitre damage model to accurately predict the damage behaviour of different forming processes. Tandon Puneet et al. [
27] simulated the establishment of progressive sheet metal forming process based on the Lemaitre damage model and investigated the effectiveness of the Lemaitre damage model in the simulation of the ISF process. However, this model can only be used for the calculation and prediction of damage defects in the cold forming process of metal materials. Because this model does not affect the crack initiation and propagation process of temperature and strain rate during the high-temperature forming process, it cannot be used for the calculation and prediction of damage defects in the high-temperature forming process; On the other hand, this damage model lacks consideration of the effect of temperature-induced elastic modulus changes on material damage [
28].
The traditional Lemaitre damage model does not consider the effect of temperature and strain rate on damage, and it is difficult to predict damage behaviour at high temperature. In this paper, considering the influence factors of temperature and strain rate, the high-temperature Lemaitre damage model of Cr5 alloy steel is improved and established, and its high temperature damage map is drawn to accurately predict the damage initiation of Cr5 alloy steel at high temperature.
In order to study the damage law of Cr5 alloy steel at high temperature, the hot tensile test and high temperature elastic modulus measurement test of Cr5 alloy steel were carried out. Based on the test data, a high-temperature Lemaitre damage model of Cr5 alloy steel considering the temperature and strain rate was established to predict its high-temperature damage behaviour. The high-temperature damage model of Cr5 steel was embedded in the finite element software FORGE® to simulate the tensile test of the Cr5 alloy steel. The accuracy of the established high-temperature damage model was verified by comparing the displacement–loads and fracture lengths of the simulation and the test. In order to avoid the crack defect of the Cr5 roll during hot forming, the corresponding Lemaitre high-temperature damage model damage map was proposed.
5. Conclusions
In order to accurately predict the crack defects of the Cr5 alloy steel during high-temperature forming. In the present study, the thermal tensile test and elastic modulus measurement experiment of Cr5 alloy under the conditions of 800–1150 °C and 0.01–5 s−1 were carried out, and the high-temperature damage model and damage diagram of the Cr5 alloy steel Lemaitre were established.
The elastic modulus E value of the Cr5 alloy steel decreases with the increase in temperature in the temperature range of 800–1150 °C. This is because when the temperature rises, the atomic spacing inside the material increases, the thermal motion of molecules increases, and then the ability to resist external elastic deformation is weakened. The test results show that the decrease in elastic modulus at high temperature increases the damage resistance factor S. In order to more accurately describe the effect of temperature on the elastic modulus, the functional relationship between the elastic modulus of the Cr5 alloy steel and temperature is determined.
Considering the influence of the temperature and strain rate on the damage of Cr5 alloy steel, Zener–Hollomon coefficient was introduced, the parameters of Lemaitre high-temperature damage model were measured, and the Lemaitre damage model of the Cr5 alloy steel at a high-temperature stage was founded.
The established high-temperature damage model was embedded in a Forge® finite element software through the program’s secondary development method to carry out the numerical simulation calculation of the strength of the experimental samples. Comparing the difference between the simulation and the test displacement–load curve, the obtained correlation coefficient (R2) was 0.987. The fracture gauge length of the tensile specimen differed by 1.28% and the fracture morphology was basically consistent. This shows that the high-temperature damage model of the Cr5 alloy steel Lemaitre established in this paper has high accuracy in predicting the damage behaviour of this material. Finally, the damage map of Cr5 alloy steel at the high-temperature stage was constructed. The relationship between the damage parameters of the high-temperature damage model of Cr5 alloy steel and the deformation temperature and strain rate were analysed. This provides an effective method for controlling crack defects in the Cr5 alloy steel during high-temperature plastic deformation. In this paper, a high temperature damage model is established for Cr5 alloy steel. In the future, the production process of the Cr5 large roller will be simulated and verified in real industry.