Influence of Cross Section Thickness and Aspect Ratio on Deformation during Diffusion Bonding and Impact of Metal Diffusion and Evaporation on Temperature Measurement Accuracy

Diffusion bonding is often used on pre-machined parts to generate internal cavities, e.g. for cooling injection molding tools close to the mold cavity. Only then, the workpieces are finished to their final dimensions. In the case of micro-process devices, however, it is essential to precisely control the deformation, as otherwise uncontrollable pressure losses will occur with channel cross-sections in the sub-millimeter range. Post-processing is not possible. The most important process parameters for diffusion bonding are temperature, dwell time and contact pressure, with the bonding temperature and contact pressure acting in opposite directions and showing a strong non-linear dependence on deformation. In addition, the deformation is influenced by a number of other factors such as the absolute size of the crosssection and the aspect ratio of the parts, the dimensions and distribution of the internal cross sections and the overall percentage of the cross-section to be bonded. In micro process engineering, small material cross-sections in the range of the materials microstructure can facilitate additional deformation mechanisms such as grain boundary sliding, which are not relevant at all for larger structures. For parts consisting of multiple layers, tolerances in thickness and roughness of multiple surfaces must be levelled, contributing to the percentaged deformation. This makes it difficult, especially in micro process engineering and in single or small series production, to determine Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 February 2020 doi:10.20944/preprints202002.0457.v1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. 2 suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components. Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts. For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved. In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.

suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components.
Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts.
For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved.
In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.
Keywords: diffusion welding, diffusion bonding, cross section width, aspect ratio, material thickness, thermocouple aging

Introduction
Diffusion welding is often used to create complex buried structures and channels in components.
In mechanical engineering, dimensions in the range of some tenth of a millimeter are relevant.
Typically, it is not necessary to control the deformation very exactly. Instead, only the functionality must be guaranteed, e.g. with cooling structures close to the mold cavity.
Furthermore, for massive parts such as injection molding tools, the deformation responds not very sensitive to bonding parameters, and these parts are only finished to their final dimensions afterward bonding. The joints are of interest with regard to existence of remaining pores and watertightness only. Therefore, there is hardly any literature dedicated to deformation control during diffusion bonding. In micro-process engineering, however, the mechanical dimensions are in the sub-millimeter range and thus in the order of magnitude of the materials microstructure. In addition, such devices are usually composed of a large number of microstructured thin layers.
There is no continuous joining surface, but only a fraction of the cross-section of the material is passing through the component over its entire height. Due to the small dimension of these columns, deformation mechanisms such as grain boundary gliding may occur, which do not contribute to the deformation for larger components and cross sections. Additionally, for micro process devices, depending on the design, the joining cross section may vary from layer to layer and the question of force transmission, force distribution over several layers and achieving a reproducible joining result over the whole part, occurs. [1] As the number of layers and the component overall cross section increases, also tolerance considerations applies. Since the variation of the thickness of cold rolled sheet material is in the range of 20-50 µm, it cannot be neglected. [ 2 ] With increasing lateral dimensions, manufacturing tolerances may add up or are balanced, causing a poor reproducibility for diffusion bonding of parts of identical design and subjected to the same bonding parameters, in terms of vacuum tightness and percentaged deformation. In practice, locally a much higher contact pressure may apply at the beginning, responsible for increased local deformation and blocking of internal microstructures, before the whole cross section is subjected to an uniform contact pressure. For relatively thin components with a large cross-section, which contain complex internal structures such as constrictions lying one behind the other, the pressure drop for different batches of diffusion-bonded parts may vary greatly and exceed the limits of technical specification.
Beside tolerance considerations of sheet thickness, for multilayered parts, many surface roughnesses must be leveled to make contact at atomic scale. Surprisingly, in the literature only little attention is paid to levelling multiple surface roughnesses of multilayered devices and its impact on deformation. Unfortunately, the deformation depends on many other parameters too, such as the design, e.g. aspect ratio and width of the cross sections to be joined. Hence, the specification of a percentaged deformation for multilayered devices may not be a suitable criterion to guarantee vacuum-tightness.
In [3], we examined the influence of the number of layers per construction height in comparison to components made of two pieces only as well as the impact of overall cross section and aspect ratio on deformation. However, the roughness values of surfaces were not characterized. In [4], Zhang et al. investigated the deformation behavior of asperities during diffusion bonding of milled surfaces possessing a surface roughness Ra=1.6 µm at T=1080°C, t= 20 min and varying contact pressures of 5, 10, 15 and 20 MPa, respectively, in terms of remaining pores. However, unfortunately, different roughness values were not investigated and compared. In [5], we investigated the depth of singular scratches on vacuum tightness and compared the impact of a constant contact pressure to a contact pressure superimposed by short peak loads. However, the influence of the absolute width of joining cross sections on the deformation behavior has not yet been investigated systematically.
In addition to all the parameters mentioned above, the composition of the material has an impact on diffusion and formation of passivation layers, affecting deformation, grain growth across the bonding planes and diffusion bonding result. Therefore, a certain bonding temperature, bonding time and contact pressure do not lead to a reproducible deformation for different parts and materials.
In this paper, test parts possessing a constant bonding area but different dimensional width of material at constant height were investigated. For comparison reasons, three samples with an aspect ratio of about three were bonded for comparison reasons.
During the experiments, it became clear that also inaccuracies in temperature measurement in particular can be responsible for very different deformation values. The reason is that the diffusion coefficient changes strongly non-linearly in the considered temperature range.

Materials and Design of Experiments
As material, austenitic stainless steel 1.4301 (AISI 304) with a sheet thickness of 2 mm was used.
To investigate the influence of the lateral dimension independent of the bonding cross-section, a set of samples with a constant cross-section of 5026.6 mm² , corresponding to a diameter of 80 mm, were used. In order to save material, overlapping annular test specimens were designed for this purpose (Tab. 1). Later on and in order to compare the deformation for a constant aspect ratio of about three, different numbers of sheet layers were stacked for selected samples (Tab. 3). Since layers for two annular samples were laser cut in a second run, the dimensions differed slightly.

Tab. 3: Measured geometric dimensions of annular samples with an aspect ratio of approximately three.
Cross section calculated using d0 and material width. Deviation related to 5026.6 mm² .

Experiments and Results
For all diffusion bonding experiments, additional baffle plates, made of TZM, were used, to protect the compression dies from damaging. These plates were coated by multiply spraying runs using alumina suspension and subsequent drying to prevent sticking at the samples at high temperatures. After placing the samples in the furnace, it was evacuated to a pressure smaller than 1*E-04 mbar. When reaching the criterion, the temperature was ramped up at a rate of 10 K/min for experiments performed in furnace II and 5 K/min in furnace III, used for larger formats (Tab. 4). The load was applied after reaching the set point of temperature within 5 min.
All diffusion bonding experiments were performed at T= 1075°C, t= 4 h and p= 15 MPa. After diffusion bonding, the heating was turned off and the furnaces cooled down naturally according to their thermal mass.

Impact of Material Width on Deformation for Annular Test Samples of constant Height
Tab. 4 shows the measured heights of the samples consisting of ten layers, before and after diffusion bonding. Before diffusion bonding, the ten sheets were fixed using a pulsed laser for alignment reasons. Five spots for the height were measured (Fig. 1). For the round sample, the For furnace III, the deviation of flatness is nearly constant due to higher stiffness of this setup, independent of the sample diameter, leading to a decreasing flatness to diameter-ratio.
Furthermore, it can be seen that the impact of the flatness deviation on the accuracy of the deformation is much higher for furnace II compared to furnace III.  If the percentage deformation is related to the material widths, there is a strong increase for decreasing material cross-sections. However, as the height was constant, the aspect ratios were not constant but increasing. Therefore, the deformation related to the material width was also normalized to an aspect ratio of one.  For the normalized deformation versus material width, a very good agreement with a potential function is obtained. It was found that the regression coefficient of the trend line drops if the deformation for the cylindrical samples was not taken into account. This affirms that the deformation is described well by a potential function and for small material cross-sections, the deformation increases extremely strongly.

Fig. 2: Relation between material width and percentaged deformation at constant height.
For the diffusion bonding experiments, different deformation conditions have to be considered, because the round specimen can only be deformed to the outside. It was noticeable that the barrel-shaped distortion of the outline of annular specimens occurred only to the outside and not to the inside (Fig. 3). However, the inner contour did not correspond to that of the parallelshifted, convex outer contour. Rather, vertical or even slightly convex areas are visible at the top and bottom. In the middle of the ring height, however, the contour is concave. It is concluded, that this is attributed to deformation obstruction due to friction on the compression dies during deformation.

Fig. 3: Characteristic shape of distortion of annular samples. Left: Overview. Right: Cross section
Due to the lack of material data, e.g. elastic modulus, yield strength and tensile strength, for the austenitic stainless steel 1.4301 at the diffusion bonding temperature of 1075°C, the deformation behavior of the ring-shaped sample with an aspect ratio close to three at room temperature was simulated. For this, ANSYS 2019 R1 was used. The simulation was carried out assuming an elastic-plastic material behavior, whereby the load level was adjusted in a way that the deformation obtained in the practical diffusion bonding experiment was achieved. Fig. 4 shows that the inner contour of the simulation of the deformation behavior of the annular sample corresponds qualitatively well with the observed profile of the diffusion-bonded sample in Fig.   3. It does not exactly follow a concave curvature. Rather, the sample is restricted in its deformation on the upper and lower side due to the mechanically very stiff compression dies and the friction that occurs in between. In contrast to the outer contour, the inner side is first vertical to convex before it changes to a concave curvature in the middle of the sample height.

Annular Samples with an Aspect Ratio of approximately three
For comparison reasons for diffusion bonding of samples with a constant aspect ratio of about three, to sample "Annular 5" of the first set of experiments, two additional samples were added, consisting of more layers (Tab. 5). Diffusion bonding samples were prepared by laser cutting as described in section 3.1 It was noticed that the deformation of the new samples of "Annular 1" and "Annular 3", with 24 and 15 layers to achieve an aspect ratio of approximately three, respectively, deviated strongly from the deformation of sample "Annular 5" of the first batch, which has an aspect ratio of about three, too.
Therefore, an additional experiment with the geometry of "Annular 6" and nine layers was performed. The deformation obtained from this last experiment fitted into the results of the other experiments at an aspect ratio of about three. Comparing the samples with an aspect ratio of about three, namely Annular 1 and 3, respectively, to Annular 6 bonded the second batch, the deformation is nearly constant whereas the deformation normalized to the materials width steadily increases for decreasing material width (Fig. 5). Comparing Tab. 6 to Tab. 5, it can be seen that the deformation for samples of a constant aspect ratio of three generally is much higher. For an aspect ratio of three, for Annular 1 the deformation is fourfold compared to an aspect ratio of 1.20 from Tab. 5. For "Annular 3", the deformation is tripled related to an aspect ratio of two.

Experiments to clarify the Discrepancy of the Deformation
However, when comparing the deformation of Annular 5 with the deformations of other samples with an aspect ratio of three in Tab. 6, it is obvious that the deformations do not show a linear dependence. The deformations obtained in different test series seem irregular.
As mentioned above, the first set of samples was made in one batch and the second batch of samples with an aspect ratio of about three were performed in a series of experiments later.
In between, in furnace III several runs were performed, including diffusion bonding of eight identical parts for an industrial partner possessing a completely different design and consisting of a few hundreds of layers. By comparing the deformation of these consecutively diffusion bonded parts, it was recognized that the deformation increased with the numbers of runs. The deformation of the last part was 1.5 % higher than for the first one (Tab. 7). Actually, diffusion bonding of the additional bonding experiment of Annular 6 with an aspect ratio of three was performed 12 runs later than the diffusion bonding of "Annular 5" with ten sheet layers.
When searching for the causes for the diverging results, the authors also considered temperature measurement by means of thermocouples.
Contrary to widespread opinion, the thermoelectric voltage is not only generated at the contact point of the two thermoelectric wires made of different materials. Rather, additional thermoelectric voltages are generated along the profile of the temperature gradient. [6,7] The diffusion bonding process is performed under vacuum. Anyone who deals with diffusion bonding or heat treatment at high temperatures knows about debris in furnace chambers.
Furthermore, it is generally known that chromium and its oxides in particular has a low vapor pressure. [8,9] Also different metals may be subjected to evaporation depending on its content  Fig. 7 and Tab. 8, respectively.   (Fig. 6, right) with areas of interest.
Tab. 8: Composition of precipitation (Fig. 6, right), determined by EDX. Elements marked with * were manually added. Surprisingly, from Tab. 8, it can be seen that the precipitations consisted mainly of manganese, despite its content in austenitic stainless steel is specified to be below 2 wt-%. Since the melting point of manganese at 1246°C is the lowest of all alloying elements of stainless steel, obviously its partial pressure is highest. On the other hand, surprisingly, the content of chromium was rather low. The copper content is attributed to former diffusion bonding runs. If diffusion bonding, e.g. of copper, is carried out at significantly lower temperatures. Evaporated copper migrates to the outside at subsequent diffusion bonding at higher temperatures in accordance with the temperature profile.
This observation means that the composition of thermocouple wires may change depending on the diffusion bonded metal and number of runs.
The individual thermocouple wires are isolated using 2-bore insulator pieces made of alumina for flexibility reasons. There is sufficiently space left in between for condensation of metal vapors. Despite their different positions, all three sample-thermocouples are normally within a temperature range of 5 K (Fig. 6, left).
In a first step, a Pegasus 4853 Advanced by Isotech, UK, supplied by Klasmeier, was used to check the thermocouples. The Pegasus was placed on an elevating platform in front of furnace III and the thermocouples were inserted into the calibrator block. It was started to three temperature setpoints at 1000, 1100 and 1200°C, respectively. It was found that the temperatures of the furnace thermocouples were between 300 to 400 K below the set points (!).
In a next step, one thermocouple was replaced. Subsequently, a diffusion bonding test under vacuum at T = 1100°C for t= 1 h was carried out. New TC 1 was used for temperature control.
It was found that old TC 2 was 23 to 29 K and TC 3 was 12 to 18 K below 1100°C. Furthermore, it can be seen from the curves, that the temperature of the old thermocouples is not constant but decreases with time (Fig. 8). In another publication evaluating the impact of bonding temperature on deformation, it was shown that a temperature raise of 20 K led to an increase in deformation of about 3%.
[10] For that reason, EDX-measurements were carried out on old cut-off TC 1. A microprobe JEOL JXA 8530F, equipped with an EDX-system EX-94310F4L1Q by Jeol with an energy resolution of 129 eV was used. At a voltage of 15 keV and a current of 3.2 nA, 2.500-3.000 counts per second were obtained. In Fig. 9, surfaces of the sensing tip, the platinum-wire and the Pt/10% rhodium-wire together with the measuring spots are displayed. In Tab. 9a-c, the results of EDX-measurements are summarized. For the tip of the TC (Fig. 9, left) it can be seen that spot 1 to 3 represent the Pt-wire. Spot 4 is in the transition range to the Pt/10%Rh-wire, whereas spot 5 represents the Pt/10%Rh-wire. Especially at the tip, large amounts of impurities by different metals such as iron, copper and chromium, are found due to diffusion and evaporation from the work pieces. Calcium and potassium may be attributed to skin excretions. For the Pt-wire less contaminants were found than for the Pt/10%Rh-wire. This might be attributed to the fact, that it is not clear, which spots of both wires in respect to the gaps between the alumina insulator pieces were investigated. For the Pt/10%Rh-wire, the Pt-Rh-ratio was found to be 10:1. This allows the following conclusions to be drawn: • First, the temperature measurement using the Pegasus leads to completely different temperature values. Obviously, normal atmosphere and different temperature gradients along a thermocouple due to a varying measurement setup does not lead to comparable temperature measurement results.
• Second, the thermocouples are subject to aging. Since the thermoelectric voltage is not generated exclusively at the sensing tip, cutting off and reshaping the sensing tip before each bonding run does not ensure exact temperature measurement.
• Thirdly, since it is economically not feasible to replace the complete thermocouples after each run, the temperature measurement is always subject to uncertainty. For this reason, it is not possible to predict reliably the deformation of new component designs based on the deformation obtained from previously diffusion bonded components.
• Fourthly, the deformation, as investigated in this paper and as described above, depends strongly on the component geometry.
Therefore, a generally applicable and reliable design of the diffusion bonding process itself, which guarantees a reproducibly successful diffusion bonding with limited deformation for parts containing complex mechanical microstructures, independent of the component design and accuracy of the temperature measurement, is important.
For this, there seem to be two possible ways: • First, the constant contact pressure should be temporarily increased to a level where the flow rate of the material is high in order to level thickness tolerances and surface roughnesses of multilayered parts and enlarging the contact area at the atomic level.
Due to a short dwell time, the deformation and the impact on the component are limited.
• Secondly, the possibility to define a maximum permissible absolute deformation per diffusion bonding program step as criteria to proceed to the next program step, in parallel to the specified dwell time. A prerequisite for this is that the component to be diffusion bonded has a minimum height due to limited distance measuring accuracy during the bonding process.
Thereby, it seems advantageous to select the constant contact pressure in a range where only a moderate strain rate of the material applies. The deformation of roughness peaks and the expansion of the contact area on the atomic scale, on the other hand, occurs predominantly during the short-term peak load. This increased contact pressure should be chosen two to three times as high. During the predominant duration of the overall dwell time at lower contact pressure, atomic diffusion takes place, closing pores at a considerably lower volume diffusion coefficient. This is also the difference to the procedure proposed in [11,12]: The sole multiple application of peak loads does not necessarily lead to the filling of remaining pore spaces.
Instead, longer dwell times are required between peak loads.