Residual stress and its effect on failure in a DLC coating on a steel substrate with rough surfaces
Graphical abstract
Introduction
Diamond-like carbon (DLC) coatings prepared by physical vapor deposition (PVD) technology have been widely used in mechanical components due to their excellent tribological properties [1], [2], [3], [4]. The coating mechanical reliability is strongly influenced by residual stresses which originate from growth stresses, geometrical constraints, thermal gradients, and service stresses during the manufacturing process [5], [6]. As a general rule, the deposition of DLC is on smooth polished substrate [7]. Nevertheless, it is much difficult to reduce surface roughness of some mechanical components via grinding machine, such as complicated curved face parts (e.g., spiral bevel gear), which indicates coatings are commonly applied to relatively rough surfaces. It needs to be emphasized that deleterious stress concentrations may develop in the coating–substrate system with rough surfaces [8]. Therefore, the influence of surface roughness on coating residual stress should be of concern.
The generation of residual stresses frequently leads to local interfacial delamination (between coating and substrate) and coating cracking [8], [9], [10]. For DLC coatings on steel substrates, residual stresses measured to be in the range of − 0.03 to − 4 GPa [11] are too large to ignore. Moreover, the high compressive residual stress is to serve as a catalyst for coating–substrate system failures [8], [12]. The similar phenomenon on failures (interfacial delamination and coating cracking) of a PVD coating (TiB2) on a stainless steel substrate was obtained in a previous study [8], as shown in Fig. 1. It is remarkable that the surface roughness can greatly reduce the interfacial adhesion between a PVD coating and a steel substrate [13]. Thus, the selection of a typical weakly bonded coating–substrate system is critical to the investigation, which is in reason. Beyond that, for better prediction and evolution of the system failures, it is essential to have a study into effects of residual stress on interfacial delamination and coating cracking.
Due to the limited thickness of most PVD coatings, the above effects are difficult to quantify experimentally [8]. Finite element analysis (FEA) has been chosen as an attractive tool to simulate residual stresses and failures in coating–substrate system [14]. Also, it is useful for guiding the design process of DLC coatings by numerical simulation of the residual stress field [9]. A number of finite element models have been developed to study the residual stresses of PVD coatings. For instance, Haider et al. [14] and Wei et al. [15] investigated the thermal stress and the effect of interlayer material on thermal stress for TiN and DLC coatings, respectively. It was also found that the thermal stress induced in the coating for the rough substrate is higher as compared to that of the perfectly flat substrate [6], [7], [8]. However, convex and concave asperities in the model are represented by isosceles triangles [7], which is too simple, and the geometry parameters [6] are not clearly explained. It is worth noting that the residual stress in a PVD coating is the result of two major contributions: thermal stress and intrinsic stress [16], [17], [18], [19], [20]. Yet, the intrinsic stress is less considered in the previous numerical calculations for the investigation of realistic residual stresses. On the other hand, there are some numerical analyses on failure evaluation in the coating–substrate system caused by the high residual stress [8], [9]. The stress characteristics of the coating surface and interface were studied to evaluate the coating failures. This method can only predict the location of the most probable failure, while is not good for evolution of coating failures. Hence, these gaps will be the emphasis of the present paper.
In recent years, the cohesive zone model (CZM) has emerged as a powerful numerical procedure for the simulation of interfacial behavior [21], [22], [23]. It is able to adequately investigate the initiation and growth of separations if damage occurs. Also, the CZM does not represent any physical material, but describes the cohesive forces which occur when material elements are being pulled apart. Additionally, the extended finite element method (XFEM) is one of the most modern evolutions to analyze the crack problems [24], [25], [26]. It can approximate the discontinuous displacement field near cracks independently of the finite element mesh by using interpolation functions, which can describe the propagation of the crack.
The objective of the present paper is to study the residual stress developed in a system consisting of a DLC coating on a steel substrate combined with rough surfaces during deposition process by FEA, as well as effects of high residual stresses on coating-substrate failures. To logically and coherently analyze the problem, the paper is organized as follows. The description of the problem model is presented in Section 2. The numerical procedure is formulated in Section 3. The results and discussion, and concluding remarks are presented in 4 Results and discussion, 5 Conclusions, respectively. Importantly, numerical results will be compared with other emulational or experimental works.
Section snippets
Thermal stress equation in DLC coating
The thermal stress of DLC arises from the differences between thermal expansion coefficients of the coating and substrate (αc and αs, respectively) at the cooling stage. A thermal misfit elastic strain εth arises during PVD process when cooled down to room temperature Tr from deposition temperature Td, and could lead to residual stress expressed by the following equation [20]:where Ec and vc are the Young's modulus and Poisson's ratio of the coating,
Numerical calculation
In the real situation, both the coating and substrate surfaces are very complex. Thus, the uneven coating surface and interface are approximated by using an analytical sinusoidal function (Fig. 4) [39]. As shown in Fig. 4, the coating thickness hc is determined by the distance between the wave central lines of the coating and substrate. The roughness of coatings on industrial surfaces is mainly controlled by the substrate roughness and can be minimized by PVD technology [40]. Herein, the
Residual stress
To focus on the analysis of residual stress, the DLC coating with perfect adhesion performance is investigated in this section. The von Mises stress obtained from the simulation in the coating-substrate system with smooth surfaces (coating and interface) is showed in Fig. 7. The maximum von Mises stress is about 2.846 GPa, which evenly distributes in the whole coating except the region around the edge (stress concentration [43]). For the case of coating-substrate system with rough surfaces, it
Conclusions
The mechanical analysis of a system composed of a DLC coating on a steel substrate is performed by finite element method to investigate the residual stress produced under rough surfaces with a sinusoidal function. Also, effects of the high compressive residual stress on the interfacial delamination and coating cracking are studied. Several illustrative numerical examples are presented. According to the numerical results, the following conclusions can be drawn.
- 1.
The residual stress induced in the
Prime novelty statement
The residual stresses (thermal and intrinsic stresses) of a system consisting of a DLC coating on a steel substrate with rough surfaces are numerically analyzed. Also, effects of the high compressive residual stress on the interfacial delamination and coating cracking are investigated.
Acknowledgments
The authors would like to acknowledge the support from the China Scholarship Council (CSC), National Key Basic Research Program of China (973 Program, grant no. 2014CB046304), State Key Laboratory of Mechanical Transmission at the Chongqing University, and Department of Mechanical, Automotive and Materials Engineering at the University of Windsor.
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