Comprehensive Study of the Influence of the Bonding Temperature and Contact Pressure Regimes during Diffusion Bonding on the Deformation and Mechanical Properties of AISI 304

Process parameters for diffusion bonding are temperature, dwell time, and contact pressure. Temperature and contact pressure have opposite effects on deformation. The effect of temperature on deformation was investigated in steps of 20 K from 1015 to 1135 °C. Contact pressure and dwell time were 16 MPa and 4 h, respectively. The deformation increase steadily with temperature. Yield strength and tensile strength decrease slightly with temperature, which is attributed to grain growth. The elongation‐at‐fracture values are 100–105%. For 925 to 995 °C, values for elongation at fracture decrease. It was investigated if comparable mechanical properties can be obtained at a temperature of 850 °C only. Experiments with higher constant contact pressures were supplemented by tests with superimposed short load peaks. Similar and higher values for the yield strength were achieved. A correlation of yield strength, tensile strengths and elongation‐at‐fracture values with contact pressure and contact pressure regime was found. The values for elongation at fracture are significantly lower than those for higher temperatures. This even applies to parameter sets at different temperatures, leading to almost identical deformations. Reduced elongation‐at‐fracture values at 850 °C are attributed to microscopically small defects in the bonding plane and to notch effects.

DOI: 10.1002/adem.202100188 Process parameters for diffusion bonding are temperature, dwell time, and contact pressure. Temperature and contact pressure have opposite effects on deformation. The effect of temperature on deformation was investigated in steps of 20 K from 1015 to 1135 C. Contact pressure and dwell time were 16 MPa and 4 h, respectively. The deformation increase steadily with temperature. Yield strength and tensile strength decrease slightly with temperature, which is attributed to grain growth. The elongation-at-fracture values are 100-105%. For 925 to 995 C, values for elongation at fracture decrease. It was investigated if comparable mechanical properties can be obtained at a temperature of 850 C only. Experiments with higher constant contact pressures were supplemented by tests with superimposed short load peaks. Similar and higher values for the yield strength were achieved. A correlation of yield strength, tensile strengths and elongation-at-fracture values with contact pressure and contact pressure regime was found. The values for elongation at fracture are significantly lower than those for higher temperatures. This even applies to parameter sets at different temperatures, leading to almost identical deformations. Reduced elongation-at-fracture values at 850 C are attributed to microscopically small defects in the bonding plane and to notch effects. and a higher affinity of alloying elements may be reasons for this, e.g., when bonding different materials, or precipitations at grain boundaries for complex alloys are formed. [4][5][6][7][8] In the literature, only little attention is paid to the impact on deformation of leveling multiple surface roughnesses of multilayered devices. [3] This may be because that diffusion-bonded parts in most cases consist of a few layers only. It was shown by the authors that the impact of the number of layers on deformation cannot be neglected. [9,10] However, the main impact on deformation is the materials flow rate depending on the bonding temperature and contact pressure. Since the concentration of vacancies in metallic lattice follows an exponential function, it approximately doubles when increasing the bonding temperature by 20 K at about 80% of the melting range, causing a huge impact on deformation. Therefore, temperature measurement and homogeneity of the temperature are of great interest to the diffusion bonding process.
During diffusion bonding, due to high temperatures and long dwell times, the dislocation density is drastically reduced and grain growth occurs. The grain growth depends strongly on the absolute bonding temperature and exhibits no linear behavior. For example, for titanium, it was shown that excessive grain growth starts at 900 C. [11] According to the Hall-Petch relation, an increasing grain size will decrease strength since grain boundaries are obstacles limiting dislocation movement across the metallic lattice. [12] If materials exhibit no polymorphy, their microstructure is much coarser after diffusion bonding. Therefore, lower strength values can be expected for samples diffusion bonded at higher temperatures as shown in this article. [13] If cold work-hardened materials are used, recrystallization may facilitate grain growth across the bonding planes and limit grain growth, as polymorphy does in the case of mild steel. [14][15][16][17] During diffusion bonding in high vacuum, only limited cooling rates can be realized. For nickel-base alloys, however, this facilitates the formation of precipitations at grain boundaries, which is bad in terms of corrosion resistance. [18,19] Many publications reporting mechanical properties of diffusion bonds lack in information on deformation [20] or data for the statistical validation of given values. [14,15,21,22] Reduced elongation-at-fracture values and varying tensile strengths indicate that the bonding parameters influence the mechanical properties of the bonds. [20,23] Since bonding temperature and contact pressure have opposite effects, similar strength values can be achieved under different conditions.
For corrosion-resistant alloys, the formation, thickness, and composition of passivation layers strongly influence the ability of diffusion bonding. At low bonding temperatures and applying high contact pressures, asperities can help to destroy the integrity of passivation layers, promoting diffusion. In addition, grain growth is reduced at lower temperatures. The coefficient of diffusion, however, may drop several orders of magnitude, impeding grain growth across the bond line and filling the remaining pores.
Achieving adequate deformation during diffusion bonding for opposing values of bonding temperature and contact pressure does not guarantee reasonable elongation-to-fracture values, as shown here.
In consequence, diffusion bonding parameters must not only be optimized in terms of mechanical properties of the bond but also regarding the alloys' composition.
In this article, diffusion bonding experiments on austenitic stainless steel 304 at a low joining temperature of 850 C and varying contact pressure were performed. For reasons of comparison, an additional experiment was performed at 800 C, too.
Practically, it is difficult to adjust a contact pressure so that a certain percentage of deformation is obtained. Therefore, additional experiments were conducted combining a constant contact pressure with several short-term peak contact pressures. By superimposing of peak loads, where a much higher creep rate occurs, the bonding area at microscopic scale is increased, whereas the absolute amount of deformation is limited due to the short duration. In consequence, a higher creep rate due to deviation of temperature and the design of the part will not cause improper distortions either and will help to control the overall deformation.
The deformation and mechanical properties of bonding experiments at 850 C were compared to those obtained from experiments at a constant contact pressure of 16 MPa. For this, experiments within a temperature range of T ¼ 925-1135 C were performed.

Materials and Design of Experiments
As material, round stock 20 and 40 mm in diameter of austenitic stainless steel 1.4301 (AISI 304) was used. The delivery condition was solution annealed. From this, cylinders were turned 20 and 40 mm in height, respectively, at a tolerance of AE0.05 mm. For diffusion bonding experiments, two cylinders were stacked, so the aspect ratio was two for both diameters ( Figure 1). The dwell time was set to t ¼ 4 h. Since the maximum force of the furnace used was 20 kN, a contact pressure of 15.9 MPa results for the d ¼ 40 mm samples. For simplifying reasons, this contact pressure is rounded up to 16 MPa in this publication. Therefore, the samples of both diameters can be diffusion bonded in one furnace. www.advancedsciencenews.com www.aem-journal.com The bonding temperature was monitored and controlled using a thermocouple type S (Pt/PtRh10) consisting of two wires 0.3 mm in diameter and laser-welded at the tip. The wires were insulated by segments of alumina ferrules 4 mm in diameter with two internal holes. They were mounted on the sample by means of a small block made of molybdenum with a hole for it.
Starting at 1075 C, the bonding temperature was varied in steps of 20 K within a range where the deformation for the samples 40 mm in diameter was below 20% but high enough to limit measuring errors.
For samples bonded at T ¼ 850 C, a dwell time of t ¼ 4 h, contact pressures of more than 16 MPa, and a furnace with 200 kN maximum force were used. In a first step, different levels of contact pressure were investigated for comparison with deformations obtained at much higher bonding temperatures in the first set of experiments. After determining the contact pressure at 850 C where the material starts to deform, various experiments with peak loads were performed.

Characterization of Surface Roughness
The finely turned surfaces of the cylindrical samples were characterized by means of a Sensofar S neox by Sensofar Metrology, Terrassa, Spain, with respect to roughness. A combination of focus variation and confocal microscopy mode was used. In the center, an area of about 1.8 Â 1.3 mm was evaluated (Figure 2A,B). The line profile in Figure 2B shows roughness values of R a ¼ 4.6 μm and R t ¼ 31.8 μm. Areas with greater roughness are visible in the center of the sample, which is formed during cutting of tough austenitic stainless steel due to the formation of built-up edges at the lathe tool with decreasing cutting speed in the center.
A series of 29 images with 20% overlap each were stitched, covering the full sample diameter of 40 mm. To the whole sample, diameter of 40 mm, roughness values of R a ¼ 4.0 μm, and R t ¼ 52.2 μm apply ( Figure 2C).

Setup of Diffusion Bonding Experiments
For all diffusion bonding experiments, additional baffle plates made of TZM were used to protect the pressure dies from getting damaged. The baffle plates were coated with alumina suspension to prevent sticking at the samples. After placing the samples in the furnace, it was evacuated to a vacuum better than 1 * E-04 mbar. When reaching this threshold, the temperature was ramped up at a rate of 10 K min À1 . The load was applied after reaching the set point of temperature within 5 min. After diffusion bonding, the temperature was decreased at a rate of 10 K min À1 . Depending on the size and thermal mass of the furnace, the natural cooling rate was less than 10 K min À1 , starting at about 600 C.
For each set of parameters, one diffusion bonding experiment was performed.  All diffusion bonding experiments were performed in a furnace with a maximum bonding force of 20 kN. From this, to the samples 40 mm in diameter, a contact pressure of 16 MPa is applied. For samples 20 mm in diameter, however, a load of 5 kN was used to obtain identical contact pressures. The results of deformation are summarized in Table 1. Comparing the deformation for samples 40 mm in diameter obtained for T ¼ 1015 C to the standard bonding temperature of T ¼ 1075 C, a temperature rise of 60 K led to an increase in deformation of 250%. This underlines the nonlinear impact of temperature on deformation. Raising the temperature for another 60 K to 1135 C, the deformation doubles compared to T ¼ 1075 C and reaches nearly 20%. From other experiments, deformations were added for lower temperatures. For a bonding temperature of T ¼ 925 C only, the deformation starts vanishing and is about one fifteenth of that at T ¼ 1075 C. For such low deformation, no good mechanical properties were expected. Figure 3 shows the deformation for both sample diameters versus temperature. The deformation increased steadily for all samples, raising the bonding temperature in steps of 20 K. For some experiments, however, the increase in deformation was not increased steadily (bold values in Table 1). For d ¼ 40 mm, this was for T ¼ 995, 1015, and 1115 C, for d ¼ 20 mm for T ¼ 1095 and 1115 C.
At a bonding temperature of 850 C, no deformation can be detected.
From Table 1, it can be seen that there are only slight deviations in deformation for samples 20 and 40 mm in diameter. This is in contradiction to the findings in the study by Gietzelt et al. [9] It is attributed to small cross sections in combination with the high aspect ratio of AR ¼ 2. Thus, the friction at the pressure dies does not rule deformation behavior. Figure 4 shows the bonding cross section for a contact pressure of p ¼ 16 MPa and a dwell time of t ¼ 4 h for T ¼ 850 C, the standard bonding temperature of T ¼ 1075 C, and T ¼ 1135 C. For T ¼ 85 C, a poor bonding quality can be seen, displaying a line of pores due to zero deformation. For 1075 and 1135 C, however, the original bonding cross section cannot be detected anymore. It is marked by arrows indicating the bonding cross section at the outlines of the samples. For T ¼ 1135 C, the grain sizes are larger than for T ¼ 1075 C.
Since zero deformation was detected at T ¼ 850 C, p ¼ 16 MPa, and t ¼ 4 h, and parameters are far away from our experience, the sample was fixed in a bench vise and struck using a sledge. However, it could not be detached and, therefore, samples for tensile tests were manufactured.

Diffusion Bonding Tests at T ¼ 850 C for Constant and Superimposed Peak Contact Pressures
Diffusion bonding experiments at T ¼ 850 C were performed in furnace I (max. load 20 kN) for 16 MPa and in furnace II (max. load 200 kN) for higher contact pressures at samples 40 mm in diameter. These parameters were chosen due to the study by Elßner et al., [24] where good bonding results can be achieved  www.advancedsciencenews.com www.aem-journal.com by removing the passivation layers on austenitic stainless steel inside a glove box with inert atmosphere prior to bonding. In Table 2, different contact pressure regimes for diffusion bonding experiments performed at T ¼ 850 C are summarized. Since this joining temperature is 225 K lower than the joining temperature of T ¼ 1075 C, which is standard for austenitic stainless steels at the Institute for Micro Process Engineering, the contact pressure to achieve a reasonable deformation is much higher. It was found that for a contact pressure of p ¼ 16 MPa, no deformation occurred at 850 C. Raising the dwell time by fourfold to t ¼ 16 h resulted in no deformation, too.
At a contact pressure of p ¼ 32 MPa (40 kN), only a slight deformation of 0.31% was obtained. This means that a constant contact pressure of p ¼ 32 MPa at a dwell time of t ¼ 4 h does not cause serious deformation for this geometry. However, for complex geometries and mechanical microstructures, higher deformation may occur.
For a contact pressure of p ¼ 64 MPa (80 kN), the deformation rose to 8.38%, illustrating the nonlinear impact of contact pressure on deformation. This deformation is too high for parts consisting of a few layers only. From this observation, it was concluded that it is almost impossible to control the deformation for arbitrary designs while applying a constant contact pressure. However, short phases at higher contact pressure, at which a higher flow rate of the material applies, should be helpful bringing surfaces into intimate contact and controlling the deformation.
Therefore, for further experiments, a constant level of x ¼ 32 MPa of contact pressure was superimposed by short peak loads (see Figure 5). The dwell time was fixed at t ¼ 4 h. The contact pressure was raised within 1 min to the peak contact pressure, kept constant for a certain time (z), and afterward decreased again within 1 min back to p ¼ 32 MPa. Four peak contact pressures, one per hour, were applied. By the initial peak contact pressure, asperities were deformed, increasing the contact area at a microscopic scale. Peak contact pressures of y ¼ 64 MPa were applied for z ¼ 1 (sample 5) and z ¼ 5 min (sample 6), respectively, leading to reasonable deformation values. Also, for a peak contact pressure of y ¼ 96 MPa and a dwell time of z ¼ 1 min (sample 7), a reasonable deformation of 4.3% was obtained. It has to be pointed out, however, that this deformation is only about 50% of the deformation obtained for a constant contact pressure of p ¼ 64 MPa and a dwell time of t ¼ 4 h. However, a deformation of 4.3% is close to 4.13% obtained for T ¼ 1015 C and p ¼ 16 MPa. Therefore, mechanical properties, namely, tensile strength and elongation at fracture, of samples with comparable deformations but different bonding temperatures, were of great interest.
Similar experiments with superimposed peak contact pressure were performed, [25,26] however, at higher frequencies and shorter   www.advancedsciencenews.com www.aem-journal.com dwell times in between. However, the authors of this publication are convinced that after a peak load with intentional plastic deformation, a longer dwell time is required to fill pores by volume diffusion. Figure 6 shows the bonding quality at T ¼ 850 C for different contact pressures. In Table 2, flow rates for contact pressures of p ¼ 32 and 64 MPa, respectively, are calculated. Using these values for calculating expected deformations for experiments using short peak loads (sample 5 or 6) leads to significantly lower values. Obviously, non-negligible deformations occur during loading and unloading periods. Specific deformations for short increased contact pressures are higher than those for constant contact pressures and long dwell times.

Diffusion Bonding Tests for t ¼ 4 h at T ¼ 995, 975, and 925 C at p ¼ 16 MPa and T ¼ 800 C, p ¼ 64 MPa
During the tensile tests, it turned out that for all samples for the temperature range of T ¼ 1015 to1135 C, the elongations at fracture were constant, ranging from 100% to 105%.
For all diffusion experiments performed at T ¼ 850 C, however, regardless of the contact pressure or contact pressure regime, the elongation-at-fracture values were considerably reduced. In fact, this was an expected finding since the coefficient of diffusion is reduced by several orders of magnitudes at T ¼ 850 C. However, as to be discussed later, superimposed peak contact pressure can improve the mechanical properties considerably.
To bridge this huge gap in bonding temperature and to investigate the relation between bonding temperature, contact pressure, and deformation more closely, additional diffusion bonding experiments were performed in the range of T ¼ 925-975 C. In this range, a strong impact on elongation at fracture was found. Obviously, a further decrease in temperature at a constant contact pressure of p ¼ 16 MPa is not sufficient for obtaining a sound bond.
From the diffusion bonding results obtained at T ¼ 850 C with increasing contact pressure, it was deduced that an increased contact pressure may compensate decreasing elongation at fracture values at low temperatures if deformation during diffusion bonding is increased. To prove this assumption, an additional experiment at T ¼ 800 C and a contact pressure of p ¼ 64 MPa was performed.
In fact, whereas for a bonding temperature of T ¼ 850 C, the deformation was 8.38% at a contact pressure of p ¼ 64 MPa, at T ¼ 800 C, it decreased to 2.1%, which is a reasonable value.

Tensile Test Measurements
The geometry of a tensile test specimen is shown in Figure 7.
For fabrication, the height of diffusion bonding specimens after bonding must be sufficient regardless of the deformation. Here, even for a deformation of 20%, a tensile test specimen with larger cross section, e.g., with a diameter of 5 mm, could have been chosen. However, according to our experience, a diameter of 3 mm is sufficient for homogeneous results. Since the goal was to detect tiny deviations in bonding quality originating from imperfect deformation of surface roughness, the smaller geometry was chosen. The tensile test specimens were wire-cut electrical discharge machining (EDM) from diffusion-bonded samples, placing the bonding plane in the middle of the length of the tensile test specimen for arbitrary deformations (Figure 8).
Tensile tests were performed for all diffusion bonding experiments. Whereas only one diffusion bonding experiment was done for each set of bonding parameters, five samples for tensile tests were machined from each diffusion bonding sample for statistical reasons. Tensile tests were performed traverse controlled (dl/dt ¼ 2 mm min À1 ) using a universal testing machine from Instron, Norwood, USA, type 4505, equipped with a controller unit from Doli, Doli Elektronik GmbH, Munich, Germany.
In Table 3, yield strength, tensile strength, and elongation-atfracture values are given for all diffusion bonding experiments performed using samples d ¼ 40 mm, h ¼ 2 Â 40 mm, together with the standard deviation from five specimens each.
In addition, values for delivery condition and a heat treatment at T ¼ 1100 C and t ¼ 4 h are given. Comparing delivery and heat-treated condition, a reduction in yield strength by 25% is found. The tensile strength, however, is reduced by 10% only. This can be attributed to grain growth and reduced dislocation density after the heat treatment. In consequence, the material exhibits more cold work hardening during tensile tests. The travel distance of dislocations to the next obstacle, namely, the  www.advancedsciencenews.com www.aem-journal.com grain boundary, is larger, and the elongation at fracture is increased by 20% related to the delivery condition. It is noteworthy that the heat-treated sample has a significantly lower value for elongation at fracture than diffusionbonded samples in the temperature range between 1015 and 1135 C. Apparently, the deformation during diffusion bonding has a beneficial effect on the materials' microstructure.
From Table 3   For a contact pressure of p ¼ 64 MPa, a deformation of 8.38% was obtained which is too much for most technical applications. For a bonding temperature of T ¼ 850 C, a reasonable deformation seems to appear in a range between 32 and 64 MPa for the contact pressure, depending on the geometry of the part to be bonded. The yield strength increased by 13% to 316 MPa. However, due to a huge increase in the elongation at fracture from 16% to 78.1%, the tensile strength was raised by 30% from 491 to 639 MPa. The scattering of samples for all mechanical parameters is reduced in relation to its absolute values.
Comparing the mechanical properties obtained for the diffusion bonding experiment using T ¼ 850 C, p ¼ 64 MPa, and t ¼ 4 h, the values are fairly identical to those of the delivery state.
To assess if the deformation can be decreased to a technically reasonable value, an additional diffusion bonding experiment with a contact pressure of p ¼ 64 MPa but a decreased temperature of T ¼ 800 C was performed. A deformation of 2.1% was obtained, which is a reasonable value. Whereas the yield strength is comparable to delivery state as well as to 850 C, 64 MPa, and 4 h, the tensile strength dropped by 15% to 546 MPa, and the elongation at fracture was reduced to 21.6%, which is less than one third.
The results for bonding temperatures of T ¼ 800 and 850 C and constant contact pressures are summarized in Figure 9.

Experiments at T ¼ 850 C, Contact Pressure p ¼ 32 MPa, and Superimposed Peak Contact Pressures
As shown by the diffusion bonding experiments using constant contact pressures of 32 and 64 MPa, it is difficult in this way to achieve a predefined deformation for arbitrary geometries, e.g., for guaranteeing vacuum tightness. However, it shows that the impact of the contact pressure on mechanical strength and especially on elongation at fracture is enormous. Therefore, the idea arose to select the contact pressure for the main dwell time in such a way that only a small time-dependent deformation occurs. A contact pressure of p ¼ 32 MPa is appropriate since a deformation of only 0.31% occurred within t ¼ 4 h. Increasing the contact area at an atomic scale, however, should be achieved at much higher contact pressures, deforming asperities. Adjusting the dwell time at a high materials flow rate, the overall deformation can be controlled. For this, tests with constant contact pressures offered good approximate values. As peak contact pressures,  Elongation-at-fracture values increase continuously and are sufficient to prevent a catastrophic failure of parts. However, it remains below delivery condition, indicating binding flaws.
The deformation during diffusion bonding can be limited to reasonable values compared to a constant contact pressure of p ¼ 64 MPa. Figure 10 shows all data obtained for diffusion bonding experiments performed at T ¼ 850 C using superimposed peak contact pressures.

Experiments for Bonding Temperatures Ranging from T ¼ 1015-1135 C for t ¼ 4 h, p ¼ 16 MPa
As mentioned earlier, the bonding temperature and contact pressure have an opposite effect on the deformation. Identical deformations can be achieved at a low bonding temperature and high contact pressure as well as high bonding temperature and low contact pressure. The question arises whether there is a sound relation between deformation and mechanical properties.
For this, diffusion bonding experiments with variations in steps of T ¼ 20 K around a bonding temperature of T ¼ 1075 C were performed, covering a range of T ¼ 1015 to 1135 C. From Table 3, it can be seen that the deformation increases steadily with temperature. The yield strength and the tensile strength decrease slightly. This can be attributed to grain growth and the Hall-Petch relation.
The values for elongation at fracture, however, are constant within 100-105% for the whole temperature range.
It can be seen that good mechanical properties are obtained for T ¼ 1015 C and a deformation of 4.16%. The elongation at fracture is 104.7%, whereas for diffusion bonding at T ¼ 850 C and a short peak contact pressure of p ¼ 96 MPa, given a deformation of 4.3%, it is only 61.9%. From this, it can be concluded that a certain deformation is a necessary but not sufficient constraint for identical mechanical parameters. Figure 11 shows tensile test curves obtained for the temperature range of T ¼ 1015 to 1135 C. Since scattering between the five tensile test specimens is small, only one specimen per test condition is shown for clarity.

Experiments for t ¼ 4 h, p ¼ 16 MPa, and T ¼ 925, 975, and 995 C, respectively
To cover the temperature gap between T ¼ 850 and 1015 C, as well as the gap for elongations at fracture, additional experiments at intermediate temperatures were performed. Table 3 shows that the yield strength is maximum for T ¼ 925 C. This is attributed to the impact of grain growth with temperature. However, the tensile strength shows the opposite trend: it increases for rising temperatures whereas the standard deviation decreases. This is also in accordance with elongation-atfracture values increasing with temperature. High standard deviations for values of both elongation at fracture and tensile strength indicate imperfect bonding. Apparently, a contact pressure of p ¼ 16 MPa is too low to achieve a good and reproducible bond at temperatures of T ¼ 995 C and below within t ¼ 4 h. The yield strength for T ¼ 925 C, however, is identically to T ¼ 850 C, t ¼ 16 h at the same contact pressure of p ¼ 16 MPa as well as for p ¼ 32 MPa and t ¼ 4 h. The tensile strength for T ¼ 925 C, however, is in between these two experiments at T ¼ 850 C. For T ¼ 850 C and 32 MPa, the tensile strength is 7% higher (491 MPa) than for T ¼ 925 C (456.8 MPa) despite the fact that the values for elongation at fracture are nearby and the deformation from the bonding process is lower. However, the tensile strength for T ¼ 925 C shows a huge scattering (min./max. values for five specimens: 399/593 MPa). Here, further experiments could be performed considering the impact of surface roughness.
For T ¼ 995 C, the yield strength is 18% lower (254 MPa) than that for the experiment at T ¼ 850 C, p ¼ 32 MPa, and a peak contact pressure of p ¼ 96 MPa (310.8 MPa). It is worth mentioning that also the tensile strength is about 5% lower despite the fact that the elongation at fracture was raised from 61.9 to 84.4%. However,  www.advancedsciencenews.com www.aem-journal.com the deformation during the diffusion bonding process for T ¼ 995 C is only two thirds that of the experiment at T ¼ 850 C with a peak contact pressure of p ¼ 96 MPa. Figure 12 shows the curves for bonding experiments performed at T ¼ 925, 975, and 995 C. Due to huge differences in elongation-at-fracture and tensile strength values, different sets of parameters can clearly be distinguished.

Evaluation of the Relationship between Deformation and Elongation at Fracture
From Table 3, three areas of elongations at fracture can be distinguished: First, experiments with nearly no elongation at fracture, namely, for a bonding temperature of T ¼ 850 C in combination with a constant contact pressure of p ¼ 16 MPa, leading to zero deformation.
Second, experiments leading to elongations at fracture of about 100%, starting at a minimum bonding temperature of T ¼ 1015 C. The deformation increases continuously from 4.16 to 19.78% with temperature for a constant contact pressure of p ¼ 16 MPa.
Third, for varying temperatures and contact pressures as well as contact pressure regimes, the elongations at fracture and deformation vary in a wide range.
These experiments were ordered according to increasing deformations to evaluate if elongations at fracture follow the trend of deformation during diffusion bonding ( Figure 13). It can be stated that for experiments ranging within T ¼ 925-995 C and a constant contact pressure of p ¼ 16 MPa, the deformation and elongations at fracture drop steadily. Obviously, a contact pressure of p ¼ 16 MPa is too low to facilitate reasonable elongations at fracture.
In general, the elongations at fracture, even for higher deformations, are lower than the values obtained at a bonding temperature of T ¼ 1015 C and above, which have comparable deformations. The increase in contact pressure cannot compensate for the effect of a decreasing bonding temperature, since the diffusion coefficient is several orders of magnitude lower.

Evaluation of Fracture Surfaces
The tensile specimens for the temperature range T ¼ 1015-1135 C show a very high elongation at fracture and reduction in area. The remaining cross section shows a ductile fracture with dimples ( Figure 14).
More interesting is the evaluation of fracture surfaces of diffusion bonding experiments showing strong scattering of elongation-at-fracture values. Minimum and maximum values for elongation-at-fracture data for selected diffusion bonding experiments are given in Table 4.
For T ¼ 850 C, t ¼ 4 h, and p ¼ 32 MPa applying short peak contact pressures of p ¼ 64 MPa and a dwell time of t ¼ 5 min, machining grooves from turning are visible in the fracture surface despite of the fact that this sample possesses an elongation at fracture of 36.4%. The sample exhibiting the maximum elongation at fracture of 46.2% shows considerably less machining grooves. A reduction in area is not visible ( Figure 15). Obviously, these elongation-at-fracture values are within the proportional elongation range ( Figure 8C, middle). At the same time, the bonding quality is sufficient to deform the full cross-sectional length of the sample.
For T ¼ 850 C, t ¼ 4 h, and p ¼ 32MPA applying short peak contact pressures of 96 MPa and a dwell time of 1 min, the overview image of the cross section shows a homogeneous bonding state ( Figure 16). However, periodic structures are clearly visible. At higher magnification, scratches and remains from turning are visible. For minimum and maximum elongations at fracture of 54% and 68.1%, no obvious reduction in area is visible. An elongation of nearly 70% is obtained in the proportional elongation range.
Looking at samples diffusion-bonded between T ¼ 925 to 995 C at a constant contact pressure of p ¼ 16 MPa for t ¼ 4 h, a transition of fracture surfaces is found. At T ¼ 925 C, the difference in percentaged bonded cross sections is already obvious at low magnification for minimum and maximum elongations at fracture values of 5.4% and 35%, respectively ( Figure 17).
For T ¼ 975 C, the difference in bond quality for the samples with minimum and maximum elongations at fracture is clearly visible (Figure 18). However, for the sample with the maximum  www.advancedsciencenews.com www.aem-journal.com elongation at fracture of 35%, an incipient crack seems to have occurred outside the bonding plane. No necking appeared because the bonding plane could not transfer sufficient load. The greatest differences in bond quality occurred at T ¼ 995 C. The elongation-at-fracture values are 50% and 100%, respectively, for the worst and best sample. Sample 5 with 50% elongation at fracture shows severe grooves from turning whereas sample 3 bonded at T ¼ 975 C, having an elongation at fracture of 79.5%, shows nearly no defects. In contrast, sample 3 bonded at T ¼ 995 C and 100% elongation at fracture exhibits pronounced necking ( Figure 19).
Finally, it can be concluded that in the temperature range of T ¼ 925 to 995 C, the bond quality scatters extremely within five tensile samples. As long as machining grooves are visible on the bond surfaces, vacuum tightness cannot be expected despite sufficient mechanical properties.
Diffusion bonding experiments performed at T ¼ 850 C with superimposed peak contact pressures led to better results.

Conclusion and Outlook
Diffusion bonding can be performed successfully in a wide range of temperatures regarding mechanical properties. Even at a bonding temperature of T ¼ 850 C, it is possible to obtain   www.advancedsciencenews.com www.aem-journal.com reasonable elongations at fracture, preventing catastrophic failure of devices.
Diffusion bonding experiments performed in steps of 20 K showed the strong impact of the bonding temperature on deformation. Therefore, it is important to control the temperature precisely.
The experiments proved that it is difficult to define bonding parameters using constant contact pressure to reach a target deformation.
Superimposed short peaks of increased contact pressures lead to reasonable values of elongation at fracture in relation to macroscopic deformation and facilitate leveling of roughness asperities.  Remaining pores, however, must be filled by volume diffusion. From the experiments, it can be concluded that, at a dwell time of t ¼ 4 h, a bonding temperature of T ¼ 995 C does not fulfill this requirement. The elongation at fracture is strongly reduced compared to T ¼ 1015 C.
Obviously, an increase in contact pressure cannot fully compensate reduced bonding temperature either, even if comparable deformations are obtained. The reason is that the diffusion coefficient in the diffusion bonding temperature range is half for a decrease in 20 K according to the Arrhenius Equation (Equation (1)). [27]    It is emphasized that the deformation of the parts to be bonded changes significantly with the geometry. Therefore, these experiments do not necessarily give comparable results in terms of deformation for arbitrary geometries and aspect ratios.
For cylindrical samples of d ¼ 20 and 40 mm, respectively, no dependence of the deformation on cross sections was found. Contrary to the findings described in the study by Gietzelt et al., [9] this is attributed to the high aspect ratio of two and to the fact that the variation in cross sections is low.
Using nonpolymorphic materials, diffusion bonding is accompanied by grain growth. According to the Hall-Petch relation, decreasing yield strength and tensile strength have to be expected. Here, a heat treatment at T ¼ 1100 C, t ¼ 4 h decreased the yield strength by 25% to 227 MPa and the tensile strength by 10% to 588 MPa, respectively, compared to delivery condition. The elongations at fracture, however, were increased by 21% from 79% to 95.9%. Nevertheless, the mechanical properties meet the specifications of AISI 304 (1.4301) for different dimensions of half stock according to ASTM A276, which have a yield strength of more than 205 MPa, tensile strength of more than 515 MPa, and an elongation at fracture of more than 40%. [28,29] For diffusion bonding experiments performed in the temperature range of T ¼ 1015-1135 C, lower bonding temperatures are favorable in terms of yield strength. Starting from T ¼ 1015 C, the yield strength decreases, and elongation-atfracture values of at least 100% were obtained.
By decreasing the bonding temperature from T ¼ 1075-850 C, which is 225 K, and despite decreasing the diffusion coefficient by several orders of magnitude, good mechanical properties and high values for elongation at fracture can be achieved by adjusting the contact pressure and contact pressure regime. The yield strength was slightly increased since the grain growth was lower, even for long dwell times.
Bonding experiments performed between T ¼ 925 and 995 C for a dwell time of t ¼ 4 h and a constant contact pressure of p ¼ 16 MPa showed a strong impact of temperature on tensile strength and elongation at fracture. In addition, the standard deviations within the five tensile samples were enormous.
From a practical point of view, the question arises which elongation-at-fracture values are required to reliably exclude unexpected failure of diffusion-bonded components. Facecentered cubic materials in general exhibit very high intrinsic values for elongation at fracture due to the higher number of sliding systems for the dislocation movement. Therefore, for failure safety reasons, values for elongation at fracture for diffusionbonded components may be defined as for space-centered cubic materials, e.g., mild steels. From this, elongation-at-fracture values of more than 20% appear sufficient. However, these values must be met reliably and must not scatter strongly.
A different point is the application of diffusion-bonded devices, apart from the mechanical properties. Vacuum or water tightness cannot be guaranteed as far as remaining pores are present at the bonding plane. As revealed by the experiments, there is no strong correlation between deformation during diffusion bonding and a bonding plane free of pores.
For austenitic stainless steels containing 18% of chromium and 10% of nickel, a bonding temperature of T ¼ 1015 C is sufficient for diffusion bonding.
A quality criterion for a perfect diffusion bond is always grain growth across the bonding planes. In a previous publication, it was shown that the thickness of passivation layers has a huge impact on diffusion bonding results. [10] Due to the different crystallographic or amorphous structures of passivation layers, it hinders the diffusion of atoms across the bonding plane extremely. In addition, the composition of an alloy and its content of metals forming the passivation layer is important in terms of diffusion bonding. Bonding parameters, e.g., suited for an austenitic stainless steel containing 18% of chromium and 10% of nickel cannot be successfully adopted for a nickel-base alloy, e.g., Hastelloy C-22 (2.4602). Not only is the composition of the passivation layer different but also the deformation behavior is different.
As investigated in detail, [30] also the grain size and composition of an alloy have an impact on the deformation behavior at high temperatures.
To overcome these obstacles, the concept of short-term increased contact pressure might be helpful to penetrate passivation layers by surface asperities as well as to limit overall deformation.
Further investigations will be performed regarding the impact of the dwell time of peak contact pressures and its absolute level on the plastic deformation and the bonding result. Since the contact area on the atomic level is increased with time, increasing peak contact pressures or dwell times are also feasible as shown in Figure 5 (for y 1 < y 2 < y 3 < y 4 and/or z 1 < z 2 < z 3 < z 4 , respectively). The dwell time in between peak contact pressures, however, must be sufficient to fill remaining pores by volume diffusion.