Stress estimation in brazed Al2O3-FeNi42 joints by means of FEM and automated grating interferometry
Dariusz Golanski , Wladyslaw Wlosinski, Pawel Cegielski, Andrzej Kolasa 1),
Malgorzata Kujawinska, Leszek Salbut 2)
Abstract
One of the key issues affecting the reliability and durability of ceramic-metal joints (C-M) is the knowledge of stress state generated upon their fabrication or during service life.
The mismatch in thermal, physical and mechanical properties between ceramics and metals often results in stress concentration in a brittle ceramic member and may lead to cracking and damage of the joint.
To evaluate the stress state in C–M brazed joints both analytical methods, mostly based on the finite element method (FEM), and experimental techniques (e.g. X-ray, or strain gauge metering) are used but both approaches have some limitations.
In this paper we have presented the joint approach which utilizes FEM calculations matched with the automatic grating interferometry method (GI). The GI method allows for full-field and non-contact measurements of in-plane displacements with high spatial resolution and high sensitivity. This method seems to be suitable tool for analyzing ceramic-to-metal joints in which stress is often highly localized in narrow regions laying in ceramic elements.
We have used the GI method to determine displacement field in a small interface zone of brazed Al2O3-FeNi42 joints which subsequently have been fetched into the FEM analysis for stress estimation.
It is expected that coupling GI with FEM could be a promising approach to establish a hybrid method of stress estimation by transferring measured displacement data into FEM analysis.
1) Warsaw University of Technology, Institute of Materials Processing, Dept. of Joining Engineering
2) Warsaw University of Technology, Institute of Mechatronics and Photonics
1. INTRODUCTION
The recent advances in material science allowed to produce ceramic materials which are used in many engineering applications. This is due to the development of a new generation of advanced ceramics which include such common materials like Al2O3, SiC, Si3N4, ZrO2 and others. These materials may give the extra wear and corrosion resistance or may be used as thermal or electric insulators.
Very often the ceramics must be bonded with metals. There are several joining processes used for this purpose and the joining procedures are generally well known. However, joining ceramics with metals still makes some problem. This is mainly due to the difference in the physical and chemical properties of ceramics and metals. These may include insufficient wetting of ceramic by a brazing metal, low conductivity, low thermal expansion coefficient, poor machinability and others.
One of the most important issue in ceramic-to-metal joints is often the existence of high tensile residual stress concentration in a brittle ceramic element. This stress is developed during cooling of a C–M joint from bonding to room temperature and is mainly affected by the difference in the coefficients of thermal expansion (CTE) between ceramic and metal (1). The high residual stress in ceramic may lower the strength of a C–M joint and even lead to the cracking of ceramic and failure of the joint (2).
The stress minimization in this kind of joints is one of the key parameter in achieving sound and durable joints. To evaluate the stress state in C–M brazed joints analytical methods based on the finite element method (FEM) are used (3,4). This method allows to calculate the stress field in any cross section of the C–M joint which is very helpful to identify the regions with stress concentration. On the other hand, there are some experimental methods used for determination of stress in C–M joint like X–ray diffraction or strain-gauge resistance meters. Both analytical and experimental methods have some limitations: the experiment usually is expensive and the stress is determined in only few points, while the finite element method is based on a model having several simplifications or requires the knowledge of temperature dependent material properties.
In this paper we try to introduce both experimental and numerical procedures which applied simultaneously would give us valuable information about displacement field in tested brazed ceramic-to-metal joints. Having the displacement field, resulting from a given load case, we are a short step from obtaining strain and stress distribution in analyzed joints, specifically in crucial regions of a C-M joint. This way a hybrid experimental–numerical method could be possible to build for the stress evaluation in ceramic-metal joints. The testing procedure has been applied on brazed ceramic-metal joints under four-point bending load.
The experimental tool used for this purpose is the automated grating interferometry method (GI) for in-plane displacement and strain measurements, while the finite element method was used as a numerical one. The GI method allows for full-field and non-contact measurements with high spatial resolution and high sensitivity. This method seems to be suitable tool for analyzing ceramic-to-metal joints in which narrow regions with stress concentration often exist in ceramic member. Moreover, the raw displacement data from experiment could further be used as the input data for the finite element analysis making the stress evaluation in C-M joints more reliable.
2. Material and samples
The materials used for C–M joints were 99.97% alumina and FeNi42 alloy in the forms of rectangular beams. The samples were brazed in vacuum using the Ag72.5Cu19.5In5Ti3 (CB1) active filler metal with thickness of 0.1 mm. The C–M joint configuration is shown in Fig. 1.
Fig. 1. The shape and dimension of brazed Al2O3–FeNi42 joints.
Brazing was conducted in the vacuum chamber of diffusion welding machine UZD1. The brazing parameters were: brazing temperature (Tb=860°C), vacuum (v=1¸2·10-3 Pa) and brazing time (tb=600 s). The cooling rate of C–M joints was set and controlled below 10°C/min.
The shape and dimensions of ceramic-metal samples were chosen in order to conduct the flexure tests. For this reason the FeNi42 alloy having the coefficient of thermal expansion a=4.7·10-6 1/°C close to Al2O3 samples (a=5.6·10-6 1/°C) was selected as the metal. That would allow to minimize the effect of residual stresses on the bending results obtained by finite element method and compared with experiment.
3. Loading configuration
We have used 4–point bending test of Al2O3–FeNi42 brazed joints in order to measure the displacement field in the joint. The bending configuration shown in Fig. 2 is based on the 3 x 4 mm beam which is commonly used for testing ceramics as present by ASTM C1161–USA. The grayed area from the ceramic–metal interface in Fig. 2 shows the zone within which the measurements by means of grating interferometry were performed. Prior to measurements of C–M joints the whole experimental system has been calibrated in flexure test of single Al2O3 beam and validated with the theoretical beam analysis and FEM calculations which was described and discussed in (5). In order to minimize the effect of residual stresses on the bending results the FeNi42 alloy with low coefficient of thermal expansion (4.7×10–6 1/K) was selected. The brazing residual stresses that arise in Al2O3–FeNi42 joints, mainly due to the difference in coefficient of thermal expansions between ceramic and metal upon cooling, have been calculated by FEM. The highest tensile stress concentration in ceramic part was below 35 MPa (5).
Fig. 2. Configuration of Al2O3–FeNi42 brazed joints in 4–point bending test with the area under GI measurement marked by gray rectangle.
4. Grating interferometry principles
The setup of grating interferomery system (6,7) are shown in Fig. 3. The two mutually coherent and collimated beams A and B illuminate symmetrically the cross–type, high frequency specimen grating SG fixed to the specimen under test S. If the first diffraction angle of the grating is equal to the angle of incident beams then the +1 and –1 diffraction order beams A’ and B’, respectively, go along the normal to the specimen surface, interfere and produce the fringe pattern with information about in–plane displacement component in perpendicular to the grating line direction. The intensity distribution at the image plane P can be expressed as:
(1)
where: I(x,y) is the intensity, d is grating period, a(x,y) is background, b(x,y) is local contrast of the fringes, u(x,y) and v(x,y) are the functions describing the in–plane displacements in x and y direction respectively. It is clearly shown that maxima of fringes are formed when u(x,y)=Nd/2, where N=0,1,2,..... is the fringe number. It means that the interferogram is the displacement map with basic sensitivity equal to half of the specimen grating period. Here the grating with frequency 1200 lines/mm is applied, which gives 417 nm per fringe.
Fig. 3. Principles setup of grating interferometry
The optomechanical arrangement of grating interferometry applied for testing of the four–point bending C–M beam is shown in Fig. 3b [B]. In this setup, two pairs of beam AB and CD are used for obtaining two orthogonal in–plane displacement components: u(x,y) (for AB), or v(x,y) (for CD). The CCD matrix with telecentric imaging system (O1 and O2) observes the fringe pattern which can be recorded on the videotape or stored directly to the frame–grabber for further processing.
The interferogram is analyzed by the spatial carrier phase shifting method SCPSM (7). SCPSM requires a single fringe pattern with proper number of carrier fringes introduced by proper tilt of mirror M1 (for u(x,y)) and mirrors M3 or M2 (for v(x,y)). Here the five point SCPSM algorithm is applied and the displacement module (d/2) is calculated according to the formula:
(2)
where I(x+i,y) are the values of intensities in the sequential pixels within the five point sampling window. The calculations for v(x,y) displacement are performed according to the same method but with usage the sampling window in y–direction i.e. for I(x,y+i).
The strains ex and ey and txy are calculated by numerical differentiation of discrete displacement maps according to relation:
(3)
(4)
5. Coupling of GI with FEM analysis
We have coupled the FEM analysis with the automated grating inteferometry according to the diagram presented in Fig. 4.
Fig. 4. The scheme of experimental data conversion into FEM mesh, accepted as the boundary condition in further C-M joint modeling.
Figure 4 presents the methodology for experimental data conversion into files required as the boundary conditions e.g. for 3D strain/stress FEM modelling of C-M joint. In the first stage again data pre-processing procedures are applied to improve the S/N ratio in displacement/strain maps. These maps are the files of discrete values at the regular mesh with usual dimension of 512 x 512 or 256 x 256 points. The co-ordinates of experimental domain have to be provided in order to assure the proper localisation of these data within FEM mesh. The FEM mesh has lower resolution and nodes are often not uniformly spaced. In order to use experimental data, their number have to be reduced and the values in the FEM node location have to be determined. Additionally the points with mask (no data available) have to be marked as the nodes with unlocking degrees of freedom. The experimental data inserted into FEM nodes provide the information for calculation of the displacement/strain maps within extended (full object) domain and can be used as the boundary conditions for determination of 3D FEM strain/stress analysis.
Here, this technique is applied for strain determination by FEM on the base of experimental local in-plane displacement 2-D maps. The comparison between strains obtained directly from experiment (moiré interferometry), by FEM and using hybrid technique is shown in Fig.5.
Fig. 5. The profiles of ex strain across the C-M joint : ♦ moiré interferometry (GI), ▲FEM and ● hybrid results.
These exemplary results are obtained for specimen manufactured under conditions:
Tb=860°C and tb=10 min. The low level of experimental strains is caused by smoothing the strain gradients by:
– filtering procedures used on displacement and strain maps for decreasing the noise,
– relatively big differentiation base (Δx = 0.08 mm) determined by the CCD spatial sampling of an interferogram.
The hybrid result shows the highest strain in the joint area and relatively small noise (the hybrid procedure smoothes the effect of strain modulation in the vicinity of the joint). From Fig. 6 we may notice a sudden change in strain profile at the C-M interface. Here, we may notice the highest difference between all three curves, which implies that the C-M interface together with the filler metal are playing the dominant role in correct verification of applied models. Despite that, all results fall into common value range which shows that the application of experimental and numerical methods can be matched together in order to develop a joint method for strain and stress determination in brazed ceramic-metal joints.
a)
b)
Fig. 7. Distribution of a) displacement field and b) resulting stress in x direction in analyzed FeNi42-CB1-Al2O3 zone marked as in a rectangle in Fig.2 and Fig.6.
The resulting stress distribution in x direction has been shown in Fig. 7b. The stress map covers the region of displacement data fetched into the FE analysis from the GI measurement (grayed area in Fig.2). According to the data from Fig.6 the stress concentration exists in ceramic region laying close to the bonding line.
The advantage of such stress estimation lays also in fact that the final results include the residual stress cumulated in C-M joints generated upon cooling from bonding to room temperature.
5. CONCLUSIONS
The joining process of ceramic and metal provides several problems due to significant difference in the physical and chemical properties of these materials and complicated technological procedure involving high temperature, pressure and time dependencies.
Initial tests show that the experimental part could be coupled with analytical one by transferring the raw results of displacements values from GI measurements into the FE code for subsequent strain and stress analysis. This is presented in Fig. 12 for the ex strain cross-section through the C-M interface at a given load of 100 N. The hybrid results were taken by introducing measurement results of displacement field from the C-M interface region about 3 mm width into the finite element model with a fine mesh and dimension equaled to the measurement zone.