Stress analysis of specimen with a reinforced thin layer

The paper presents an analysis of the stress state in the tensile test sample. The test sample has a hardened surface layer with chemic heat treatment – cementation. The analysis was carried out for various thicknesses of the reinforced cemented layer. If the whole thickness of the material is not cemented, the fracture is near the grip section of the specimen. The analysis results explain the cause of this fracture.


Introduction
The surface of components or tools is very often adjusted using processes such as heat-treatment or chemical-heat treatment [1]. The treatments change the properties of material. Surface of the material usually become more hardened [2]. In the case of intricately shaped parts of the component, the interaction between treated surface and deeper tough interior material may affect a reduction in the overall strength of the component [3,4]. To achieve the most efficient properties of the component appropriate to industry [5], there is necessary to propose a correct ratio between thicknesses of the hardened surface layer and interior non-treated material [6]. The ratio could be determined using the program SYSWELD, but in the case of complex-shaped component, the generation of the model is accompanied by complications [7].
The paper focuses on stress distribution in components loaded to tension, which surface is heattreated or chemical-heat treated. The components are made of chromium-manganese steel 16CrMn5 with the adjusted surface layer. The objective of the paper is to examine the stresses in the component during constant loading with changing the thickness of the adjusted material.
The analysis of the heat transfer in the program Ansys Workbench was performed to determine the shapes of adjusted material, transition area and material that is not affected by carburization process [8].
In the process of carburization, the temperature distribution described by the differential equations for thermal conduction (1) and diffusion (2) control the thickness of the adjusted layer [9, 10]: where α is thermal conduction coefficient and D is diffusion coefficient. The differentiation between partial differential equations (1) and (2) is solely based on the usage of specific constants. It means, that the mathematical formulation of carbon atoms absorption into steel procedure is similar to the process of heat conduction. Therefore, the geometric shape of a model (carburized and non-carburized material) was determined from the simulation of heat conduction. Subsequently, this analysis was connected to a static analysis of specimen loaded to tension with defined geometry (figure 1). Different material properties were assigned to treated surface and interior part of the specimen, which correspond to the carburized and non-carburized steel 16CrMn5.

Model preparation
The content of the alloying elements in the specimen made of Chromium-Manganesesteel16CrMn5 is given in Table 1. Selected mechanical properties of 16CrMn5 steel in carburized and non-carburized state are in Table 2. Another properties of Chromium-Manganese steel, which are assumed in the simulation are:  thermal expansion coefficient 10 -6 (K -1 )  thermal conductivity 41 (W m -1 K -1 )  specific heat capacity 460 (J kg -1 K -1 ) For both types of materials were defined corresponding curves on σ -ε graph in the Material Data of software Ansys Workbench (Figure 2). For tensile test simulation of the specified specimen shape (Figure 1) modeled using CAD programs [11,12] was created the temperature-dependent material model (figure 3) in the following steps. The heat conduction simulation determined temperature limits at which material has various mechanical properties [13]. At a temperature not exceeding 24.3 °C, the specimen has the mechanical properties of non-carburized steel. The properties of carburized steel were assigned to the material with temperatures more than 24.5 °C. The transition area, which was identified at temperatures between 24.3 °C and 24.5 °C, had mechanical properties determined by program ANSYS Workbench. The program determined them in pursuance of input values, which were specified for both materials.

Stress distribution analysis
The first assessed specimen was composed solely of non-treated steel. The loading force was 20 000 N. The maximal stress occurs in the narrowest part of the specimen (figure 4).
The following simulations were performed on specimens with the carburized surface layer. The model preparations consist of the increasing thickness of the hardened layer in simulation of heat conduction. The specimens were loaded to force from 20 kN to 30 kN. In each figure of the specimen model, the red colour represents carburized material, green colour illustrates the transition area and the blue colour introduces non-carburized steel. Firstly, the specimen with a 0.2 mm thick carburized surface layer was assessed (figure 5).  In the case of the specimen with a 0.2 mm thick carbonized layer, the maximal stress appears throughout the length of the narrowest part of the specimen. Figure 6 shows the stress state at the time of 1.7 s, which corresponds to the loading force of 27 kN. The increase of loading force effect to the gradual spread of stress from the narrowest part to the head of the specimen.
Secondly, the carburized layer was 1.2 mm thick at the narrowest part of the specimen. Figure 7 shows the geometry model obtained from the simulation of heat conduction.  In comparison to previous one, the maximal stress in specimen reinforced with 1.2 mm thick carburized layer exceeds into deeper location of specimen in the narrowest specimen part. In addition, stress at the head of specimen increase. Figure 8 shows the stress distribution in the specimen at loading force 27 kN. Finally, the last specimen has carburized material over the entire cross-section. Non-carburized material was located only at head part of specimen. The thickness of the carburized material at the roundings of specimen was 0.7 mm (Figure 9).

Conclusion
The simulation confirmed the experimental results, which resulted in breakage of the specimen at the rounding regions. The case for breakage of the specimen is the insufficient depth of the hardened layer at the head part of the specimen.