Numerical analysis on the residual stress distribution and its influence factor analysis for Si3N4/42CrMo brazed joint
Introduction
High strength ceramic-metal joints are employed in a great variety of industrial applications, such as electronic packaging, manufacturing of engines and turbines [1]. Various techniques for joining ceramics to metals are available. Among them, brazing has received extensive attention due to its simplicity, high strength, excellent heat resistance as well as the perfect adaptability of joint size and shape, as reported by Suganuma [2]. However, because of the large difference in the physical and mechanical properties between ceramic and metal, residual stresses generate inevitably as the bonded assembly cools from the joining temperature to room temperature. The magnitude and influence of these thermal stresses can be particularly high because of the large difference in the coefficients of thermal expansion (CTE) and Young's moduli of the different materials [3]. Of particular note are tensile stresses induced in the ceramic at the surfaces of the joined components. These stresses can cause the propagation of cracks in the ceramic and the formation of characteristic ‘dome-shaped’ crack profiles, detaching most of the ceramics from the metals. Therefore, it is necessary to evaluate the stress distribution and to minimize the residual stresses in the ceramic-metal brazed joints. Reinforced particles with low CTE have been successfully incorporated into Ag–Cu–Ti brazing alloy for acquiring high quality brazed joints. SiC was incorporated in Ag–Cu–Ti brazing alloy for joining Si3N4 ceramic by He [4]. The highest average three-point bending strength of 506.3 MPa was retained with 8 wt.% Ti and 5 vol.% SiC, which was approximately 153.15% higher than the average strength for the filler without SiC particles. Reliable brazed joints of Si3N4 ceramics to TiAl intermetallics were successfully produced using a composite filler modified by adding Si3N4 particle into the Ag–Cu–Ti filler alloy [5]. The shear strength of brazed joints increased and then decreased with the increase of Si3N4 content. The maximum value reached 115 MPa when the content of Si3N4 was 3 wt.%.
In the past few years, much effort based on the experimental techniques has been devoted to studying the stress distribution of ceramic/metal joints. Diffraction techniques, such as neutron diffraction or (small area) X-ray diffraction (XRD) technique was developed to study the residual stress (strain) distribution in the brazed joints, such as in zirconia-iron joints, polycrystalline alumina and stainless steel joints, or vanadium/ alumina joints [6], [7], [8], [9]. Other indirect precise methods including Vickers indentation fracture (VIF) method and layer removal techniques have been also reported in the literature. Hattali adopted VIF method to measure the residual stress distribution after solid state bonding of Al2O3- HAYNES® 214™ joints [10]. The VIF method confirmed that changes in the nature of alumina in the immediate vicinity of the interface occurred during bonding processes. Cheng and Finnie has proposed an analytical solution to examine the accuracy of the layer removal technique [11]. They suggested that the layer removal method could be used for measuring residual stress for cases in which the ratio of the strip height to the half dimension of the localized residual stress zone. In parallel, a variety of analytical and numerical models have been developed to understand and optimize the residual stress state in the brazed joints [12], [13], [14], [15], [16], [17]. Gong developed a finite element model to simulate the brazed residual stress in a stainless steel plate-fin structure applied to recuperators in microturbines [15]. Kim also adopted the finite element analysis to examine the variations of the residual stress distribution for Si3N4/stainless steel joints with various interlayer [16]. Chen developed a three-dimensional finite element analysis for determining the residual stresses of a three layered stainless steel plate-fin structure fabricated by nickel-based brazing [17]. Even that a great number of works have been conducted on the comparison between experimental measurements and FE simulation, a persuasive way to compare the simulation work with the mechanical properties of the ceramic-metal brazed joints is still needed.
Based on the finite element method software ABAQUS, this study presents characteristic residual stress distribution in brazed Si3N4-42CrMo structures. Additionally, the possibility of reducing residual stresses and increasing the four-point bending strength by Ag–Cu–Ti+TiNp (p = particle) composite filler of different TiNp contents was studied numerically and experimentally. A good correlation was found between the FE calculation and the experimental results. In addition, the effect of the thickness of brazing layer and interfacial reaction layer on the stress distribution and joint strength of the Si3N4/42CrMo joint was also investigated. The aim of this work is to provide a reference for decreasing the residual stress and optimizing the joint strength for ceramic–metal brazed structures.
Section snippets
Materials
Si3N4 ceramics and 42CrMo steels were used as the base materials. The ceramic materials used in this work were commercially polycrystalline Si3N4 (Shanghai Institute of Ceramics, Shanghai, China). The ceramic and steel for brazing were cut into rectangular specimens with the dimensions of 3 × 4 × 18 mm3. The composite braze was composed of commercially available Ag-28Cu (wt.%) alloy powder with a mean particle size of 50 µm, Ti powder with an average size of 50 µm and TiN particles (TiNp) with
Residual stress distribution in Si3N4/42CrMo joint after cooling
In Fig. 2, the contour plots of the computed residual stresses after cooling, including the von Mises stress, the axial stress, σxx, the maximum principal stress, σ1, and the shear stress, τxy, in the brazed joint without TiNp are demonstrated. It can be seen that the maximum residual stresses occur in the vicinity of the substrates/filler alloy interfaces. The von Mises stress (Fig. 2a) in the Si3N4 /42CrMo joint has a symmetrical distribution along the substrate/filler interface and the
Experimental validation of the built finite element model
To validate the finite element model built in this study, the results of the simulations are reported along with the mechanical properties of several considered brazing systems. Five different volume fractions of TiNp (0, 2, 5, 10 and 15 vol.%) in the filler alloy were considered in the FE simulation. Tensile maximum principal stresses appear at the bottom corner of ceramic according to the above simulations. The larger the tensile stress in this region is, the lower the experimental nominal
The effect of brazing seam thickness and interfacial reaction layer
The brazed residual stress in the Si3N4/42CrMo joining structure is mainly affected by the TiNp content, brazing layer thickness, interfacial reaction layer thickness and physical dimension and shape of the structure. As that the dimension and shape of the joint can vary a lot, these two factors are not the scope of this research. The aim of this section is to investigate the effect of the brazing seam thickness and interfacial reaction layer thickness on the stress distribution and mechanical
Conclusions
The residual stresses were studied in the Si3N4/42CrMo joints brazed by TiNp modified Ag–Cu–Ti active filler. An elastic–plastic FE model was developed to simulate the joint behavior both during the cooling process and four-point bending test. The roles of the TiNp content, brazing layer thickness and interfacial reaction layer thickness on the residual stresses were investigated. The following conclusions were drawn.
- (1)
For the Si3N4/42CrMo joint after cooling, peak tensile axial residual stresses
Acknowledgment
This work was financially supported by the National Natural Science Foundation of China under Grant nos. 51872060, 51621091 and U1537206.
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