October 2011

NASA/TM–2011-215882

Failure Assessment Diagram for Titanium Brazed Joints

Yury Flom, Justin S. Jones, Mollie M. Powell, and David F. Puckett
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October 2011

Yury Flom

Goddard Space Flight Center, Greenbelt, MD

Justin S. Jones

Goddard Space Flight Center, Greenbelt, MD 

Mollie M. Powell

Goddard Space Flight Center, Greenbelt, MD

David F. Puckett

Goddard Space Flight Center, Greenbelt, MD

NASA/TM–2011-215882

Failure Assessment Diagram for Titanium Brazed Joints
Available from:

NASA Center for AeroSpace Information National Technical Information Service

7115 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161

Trade names and trademarks are used in this report for identification only. 

Their usage does not constitute an official endorsement, either expressed 

or implied, by the National Aeronautics and Space Administration.
*- Brush and Wellman trade name for 62%Be 38%Al metal matrix composite 

FAILURE ASSESSMENT DIAGRAM FOR TITANIUM BRAZED JOINTS 

ABSTRACT 

The interaction equation was used to predict failure in Ti-4V-6Al joints brazed with Al 

1100 filler metal. The joints used in this study were geometrically similar to the joints in 

the brazed beryllium metering structure considered for the ATLAS telescope. This study 

confirmed that the interaction equation Rσ ൅ R = 1, where Rσ and R are normal and 

shear stress ratios, can be used as conservative lower bound estimate of the failure 

criterion in ATLAS brazed joints as well as for construction of the Failure Assessment 

Diagram (FAD). 

1.0 INTRODUCTION 

The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) will use the Advanced 

Topographic Laser Altimeter System (ATLAS) to meet its scientific objectives. An 

integral part of the ATLAS instrument is the optical 532 nm telescope which is fabricated 

from beryllium. A structural element of the ATLAS telescope is a metering tower that 

provides support for the secondary mirror. The ICESat-2 program is considering brazing 

as a possible way of assembling the metering structure. When attempting to evaluate 

the load carrying capabilities of the beryllium brazed joints, it was realized that existing 

practices of structural analysis are lacking simple engineering methodology for 

estimating strength margins of brazed joints subjected to combined normal and shear 

stresses. 

A study was initiated to develop a simple practice of conservative estimate of strength 

margins in the brazed joints. Due to the cost and health considerations, it was decided 

to perform this study on Ti/Al/Ti rather than Be/Al/Be system then apply the results of 

this study to other systems representing the flight applications. 

Earlier work [1, 2] demonstrated that interaction equations could be used for failure 

assessment of the Albemet 162* joints brazed with AWS BAlSi-4 filler metal as well as 

stainless steel joints brazed with silver-based filler metals. 

This memorandum provides a summary of work performed in this study and 

demonstrates that interaction equations used earlier could also be applied for failure 

assessment of Ti/Al/Ti brazed system. 
2 

2.0 APPROACH 

A two part approach similar to [1] was also used in this study. In the first part, design 

values of tensile σo and shear o strength (allowables) were determined. These 

allowables were used to construct interaction equation (1). The second part was 

performed to verify that this equation can be used as a lower bound FAD for Ti/Al/Ti 

brazed joints. A semi-empirical interaction equation proposed in [1,2] is shown below: 

ߪ

௢ߪ

൅  

߬

߬௢

 ൑ 1

In this equation σ and  are the maximum normal tensile and shear stresses acting on 

the filler metal layer within the brazed joint. σo and o were determined experimentally. 

Equation (1) was validated by testing brazed T-specimens under combined tensile and 

shear loading configurations. Tensile and shear stresses acting on the brazed joints 

were calculated using the finite element analysis FeMAP program as well as 

engineering mechanics of materials equations (hand calculations), as described in the 

Appendix. An image-based strain measurement technique was employed during the 

mechanical tests to validate the results of the finite element analysis. 

3.0 EXPERIMENTAL PROCEDURE 

3.1 Test Specimens 

Each specimen was given a unique identification to represent the test configuration. 

Test specimen identifications are explained in Table 1. 

Table 1. Test Specimen Identification 

Spec. ID Example descriptions

B-1 Butt brazed specimen # 1 

L1T1 Lap shear specimen # 1, nominal overlap length = 1T 

L3T4 Lap shear specimen # 3, nominal overlap length = 4T 

T-1 T-specimen # 1 

All test specimens were fabricated from the Ti-6Al-4V alloy. Tensile and lap shear test 

specimens (Fig.1) were fabricated and tested to determine tensile and shear allowables. 

A T-specimen designed and fabricated to test the brazed joints under the combined 

action of shear and normal stresses is shown in Fig. 2. 

(1) 
3 

Fig.1 Lap shear (a) and butt tensile (b) specimens used in this effort to derive tensile 

and shear allowables. All dimensions are in inches. 

Fig. 2 T-specimens used for testing brazed joints under various loading configurations. 

Dimensions are in inches. 
4 

Brazing was performed in the vacuum furnace. All specimens were brazed with a 0.002 

in (0.05 mm) foil of Al 1100 filler metal, preplaced between the faying surfaces of the 

braze joint prior to brazing. Typical time-temperature records of the brazing cycles are 

shown in Figure 3. 

Fig.3 Time-temperature profile of the typical braze cycle 

3.2 Mechanical testing 

All specimens were tested on an Instron 4485 universal test frame. A total of six butt 

brazed specimens were tested. One specimen, marked B-6, had a noticeable 

misalignment and failed at a very low load. Consequently, it was considered an outlier 

and was ignored in estimating the tensile allowable. There were 4 groups of 3 lap shear 

specimens tested. Each group had the same nominal overlap length starting with 1T 

and ending with 4T, bringing a total number of lap shear specimens tested to 12. The 

purpose of testing various overlap lengths was to identify the lowest shear strength, as 

explained in more detail in [3]. 
5 

The actual overlap length varied somewhat, since maintaining exact overlaps was not 

critical for the purpose of this investigation. Test results of the tensile tests are 

summarized in Table 2 while the results for the lap shear specimens are presented in 

Table 3. 

Table 2 Butt Brazed Specimens Tensile Test Results 

SPEC 

ID 

MAX LOAD, 

lbs 

AREA, 

in2

TUS, 

ksi (MPa)

AVG TUS,

ksi (MPa) 

MIN TUS, 

ksi (MPa) 

3 Sigma TUS,** 

ksi (MPa) 

B1 1599 0.071 23 (155) 

24 (166) 22 (153) 16 (110) 

B2 1623 0.071 23 (158) 

B3 1573 0.071 22 (153) 

B4 2036 0.071 29 (198) 

B5 1791 0.071 25 (174) 

B6* 757 0.071 11 (74) 

*-Outlier; ** - 3 Sigma TUS = AVG – 3xSTDEV; STDEV = 2.7 ksi (18.6 MPa) 

Table 3 Lap Shear Specimens Pull Test Results 

SPEC. 

ID 

MAX 

LOAD, 

lbs 

OVERLAP, 

in 

OVERLAP, 

T 

WIDTH, 

in 

AREA, 

in2

SHEAR 

STRESS*, 

ksi 

SHEAR 

STRESS, 

MPa 

L1T1 1287 0.158 1.1 0.5 0.08 16.3 112.4 

L2T1 1083 0.175 1.2 0.5 0.09 12.4 85.4 

L3T1 1150 0.182 1.3 0.5 0.09 12.6 87.2 

L1T2 1811 0.324 2.3 0.5 0.16 11.2 77.1 

L2T2 1740 0.308 2.2 0.5 0.15 11.3 78.0 

L3T2 1690 0.283 2.0 0.5 0.14 11.9 82.4 

L1T3 2448 0.421 3.0 0.5 0.21 11.6 80.2 

L2T3 2136 0.417 2.9 0.5 0.21 10.2 70.7 

L3T3 2392 0.446 3.1 0.5 0.22 10.7 74.0 

L1T4 3501 0.582 4.1 0.5 0.29 12.0 83.0 

L2T4 3426 0.581 4.1 0.5 0.29 11.8 81.4 

L3T4 3828 0.573 4.0 0.5 0.29 13.4 92.2 

*- Shear stress calculated as maximum load divided by the overlap area. 

In order to test T-specimens under combined tensile and shear loads, special 30 ̊ and 

45 ̊wedge fixtures were fabricated (see Fig. 4). By interchanging the different wedges 

and by varying the angle of rotation of the T-specimen, a total of 6 different loading 

configurations were established for this study, as indicated in Table 4. 
6 

Fig.4. Different loading configurations of the brazed T-specimens. Wedge angle α was 

either 30 ̊ or 45 ̊. Rotation of the T-specimen on the face of the wedge provided desired 

combined loading. 

Table 4 T-specimens Test Results 

ID Loading 

case

Wedge 

angle,  ̊

Rotation 

angle,  ̊

Max Load 

F, lbs (kN)

Axial Components of F 

Fx, lbs (kN) Fy, lbs (kN) Fz, lbs (kN)

T1 W45R0 45 0 3369 (15.0) 0 -2382 (-10.6) 2382 (10.6)

T2 W30R0 30 0 3649 (16.2) 0 -3160 (-14.1) 1825 (8.1)

T3* W30R90 30 90 211 (0.9) 183 (0.8) 0 106 (0.5)

T4* W30R60 30 60 328 (1.5) 246 (1.1) -142 (-0.6) 164 (0.7)

T5 W30R90 30 90 414 (1.8) 359 (1.6) 0 207 (0.9)

T6 W30R120 30 120 383 (1.7) -287 (-1.3) 166 (0.7) 192 (0.9)

T7 W45R90 45 90 395 (1.8) 279 (1.2) 0 279 (1.2)

T8 W30R60 30 60 493 (2.2) 370 (1.6) -213 (-0.9) 247 (1.1)

*- these two specimens had braze flaws 
7 

At least one T-specimen was tested in each configuration. Four out of sixteen original 

plates used for brazing the T-specimens came distorted. The distortion of the plates 

prohibited proper contact between the faying surfaces. Rather than discarding the 

plates, it was decided to go ahead and braze these four plates with the understanding 

that the resultant T-specimens may be flawed. These specimens became T-3 and T-4 

and were tested in the W30R90 and W30R60 configurations, respectively. The 

rationale behind testing the flawed specimens was an opportunity to compare their load 

carrying capability against higher quality brazed joints. Consequently, each flawed Tspecimen was tested along with a regular specimen in the same loading configuration. 

The T-specimen deformation was measured using an AramisTM digital image correlation 

(DIC) system. This system uses two cameras in stereo, combined with a softwarebased geometric calibration which measures the precise relative angles and focal 

distances of the cameras to provide three-dimensional displacement information, as 

shown in Fig.5. For any location within the calibrated volume (defined to be on the 

order of the sample dimensions) which is viewable from both cameras, the threedimensional displacements and full-field strains from objects under load can be 

measured. 

Fig.5 A schematic view of the ARAMISTM DIC setup. 
8 

DIC measures strain by tracking the positions of identifiable features on the object’s 

surface throughout the image sequence through the use of a virtual grid of markers 

which is superimposed onto the images within the software. While the measurement 

itself is non-destructive and non-invasive, DIC tracking is often aided by application of a 

stochastic speckle pattern or dry powder to the surface of the specimen which provides 

the locally unique, trackable features on the surface. For this study, the flat surfaces of 

the T-specimens were painted with a white background and a black speckle pattern, as 

shown in Fig.6 

Fig. 6 Test setup showing the speckled T-specimen loaded into the test fixture. 

During the test, the DIC system captured images at a rate of 0.5 Hz. Load data was 

also collected simultaneously through the Instron® load cell and was later correlated 

with the imaging data. The samples were loaded at a quasi-static, constant rate of 

displacement until failure. 

3.3 Finite Element Analysis 

Finite Element Analysis (FEA) of the T-specimens was performed using the engineering 

analysis software tool FeMap (Finite element Modeling and Post-processing). FeMap is 

sold by Siemens PLM Software and provides modeling tools as well as post processing 

capabilities. FeMap utilizes the engineering analysis software NX Nastran which is also 

distributed by Siemens. The global models were constructed using the dimensions from 

the actual test specimens (dimension can be found in Fig. 2 above). The global axis in 

relation to the specimen can be seen in Figure 7. This global axis was maintained 
9 

throughout all models and coincides with the global axis used by the DIC system. Each 

model was meshed with tetrahedral shaped elements at 0.24 inch in size. 

Rigid body constraints were used to simulate the bolts holding the T-specimens to the 

wedge fixtures and were fixed in all directions and rotations. A rigid body was also used 

to simulate the ball fixture used to load the T-specimen. The center node of the rigid 

body was placed at the center location of the ball for each different T-specimen test 

configuration. The loading for each test configuration was then placed on this center 

node. The breaking load found during mechanical testing was used to analyze each 

model and to calculate the shear and tensile stresses within the braze joint. The FEAcalculated shear and tensile stresses were then compared to hand calculations. For 

added confidence, the deformation data obtained from FeMAP were compared to the 

deformation data provided by the DIC. 

Fig.7 Global FEA model of T-specimen 

4. RESULTS AND DISCUSSION 

4.1 Mechanical Tests - Butt and Lap Shear Specimens 

Tensile Ultimate Strength (TUS) of tested butt brazed specimens varied between 22 

and 29 ksi (153 and 198 MPA), as shown in Table 2. The number of specimens was too 

small for a meaningful A- or B-basis statistical analysis; it was felt, however, that the 

number of the test specimens was sufficient for verifying the methodology. 

Consequently, the tensile stress ratio can be determined using average, minimum, or 

the three sigma value of TUS given in Table 2, above. 
10 

Shear strength was measured on single lap shear specimens having different overlap 

lengths, as per AWS C3.2 [3]. The test results shown in Table 3 are plotted as a 

function of the overlap length in Fig.8. As one can see, the data generally follows the 

well-known experimental trend observed while testing numerous lap joints regardless of 

the joint geometries: as overlap length increases the average shear strength of the 

brazed joint decreases [4]. 

Fig.8 Plot of the lap shear test results vs. overlap length. 

It is not completely clear why there is a slight increase in shear strength observed on 

the specimens with the longest overlap tested. Since the specimens with the same 

overlap were brazed in one batch, there could be a batch-to-batch variability in brazed 

joint strength. A slight overheating during brazing could result in reduction of the brazed 

joint strength causing an artificial “dip” in data shown in Fig. 8. This artifact, however, 

has very little impact on the present study. For the purpose of calculating the shear 

stress ratio, the lowest experimentally observed average shear strength of the lap shear 

specimens should be used in order to have a conservative estimate. The lowest shear 

strength observed in this study is about 10 ksi (70 MPa). This value is still higher than 

the 8 ksi (55 MPa) shear strength of 1100 Al reported elsewhere [5]. Therefore, the 

shear stress ratios can be determined using either 10 or 8 ksi (70 or 55 MPa). Value of 

8 ksi was selected as more conservative. 
11 

4.2 Mechanical Tests – T-specimens 

Results of mechanical testing of the T-specimens are shown in Table 4. As expected, 

the failure loads of the flawed specimens T3 and T4 were significantly less than the 

flaw-free specimens subjected to identical loading cases. Typical fracture surfaces of 

the T-specimen brazed joints are shown in Fig. 9. The total lack of braze area found in 

specimens T3 and T4 were estimated to be approximately 26% and 14%, respectively, 

based on a digital area threshold analysis of the cross-section. 

Fig.9 Typical fracture surfaces (top) of the fractured T-specimens showing the entire, 

end-to-end brazed joints. The lower images showed fracture surfaces containing lack of 

braze in T3 and T4 specimens. Horizontal plates containing the braze joint “foot print” 

were used to take these photographs. 

Results of comparison between displacements obtained independently from FEA and 

DIC analysis are shown in Table 5. As one can see, total displacements at specific 

locations on the T-specimens at failure loads calculated by these two methods are 

within 2.5% for specimens T4 -T8. 
12 

Table 5 FEA vs. DIC Total Displacement Comparison 

Method T3 T4 T5 T6 T7 T8 T3 

reduced 

T4 

reduced 

FeMap, in 0.056 0.067 0.098 0.069 0.070 0.097 0.056 0.068 

DIC, in 0.055 0.068 0.098 0.068 0.068 0.096 0.055 0.068 

Difference, 

% 1.8 1.5 0.0 1.5 2.9 1.0 1.8 0.00 

Such a good match gives high confidence that the FEA models and results are correct. 

Figure 10 shows images of the deformed T-specimens at failure generated by FEA and 

DIC. 

Fig.10 Images of the deformed T-specimens at failure generated by DIC and FEA. 

Quite unexpected is a close agreement between FEA and DIC results for the flawed T3 

and T4 specimens. Since initial FEA models for T3 and T4 specimens did not take into 

account reduction in braze area due to lack of braze (LOB), the only conclusion one can 

make is that the stiffness of the flawed T3 and T4 specimens was not affected by the 

lack of braze, even as high as 26%! Indeed, a comparison of the load vs. crosshead 

displacement records of T4 vs T8 and T3 vs.T5, as shown in Fig. 11, demonstrates a 

very small difference in stiffness between the flawed and non-flawed specimens. 
13 

Fig.11 Tensile tests of the T3 and T4 brazed specimens containing flaws are compared 

with the flaw-free T5 and T8 specimens (dashed line) tested in identical loading 

configurations. Note a small difference in stiffness between the flawed and flaw-free 

specimens. Arrows indicate fracture of the flawed T3 and T4 specimens. 
14 

In an attempt to account for LOB in the finite element analysis, FEA models for T3 and 

T4 specimens were modified by reducing the braze area by 26% and 14% accordingly. 

This was accomplished by uniformly reducing the brazed joint width in the modified T3 

and T4 FEA models, as shown in Fig.12. 

Fig.12 A schematic showing lack of braze modeled by simple reduction of the braze 

width from b to b1

The FEA results can be found in Table 6; for the “reduced area”, T3 and T4 are denoted 

by T3 - reduced and T4 – reduced. For comparison, the results of hand calculations are 

provided in Table 7. 

Table 6 FEA Results 

Specimen ID 

Failure 

Load 

(lb) 

Max 

Princ 

(MPa) 

Max 

Princ 

(ksi) 

σ

Ratio, 

Rσ

Max 

Shear 

(MPa) 

Max 

Shear 

(ksi) 



Ratio, 

R

T1 3369 89 12.9 0.8 43 6.2 0.8

T2 3649 118 17.1 1.1 57 8.2 1.0

T3 (Flawed) 211 124 17.9 1.1 62 9.0 1.1 

T4 (Flawed) 328 161 23.4 1.5 89 12.9 1.6 

T5 414 243 35.2 2.2 121 17.6 2.2 

T6 383 197 28.5 1.8 101 14.6 1.8 

T7 395 197 28.6 1.8 99 14.3 1.8 

T8 493 254 36.8 2.3 130 18.9 2.4 

T3 reduced 211 253 36.6 2.3 133 19.3 2.4 

T4 reduced 328 267 38.7 2.4 147 21.3 2.7 
15 

Table 7 Hand Calculated Principal Stresses and Stress Ratios 

ID Loading 

case 

Failure 

load, 

(lbs) 

σ1

(ksi)

σ1

(MPa)

max

(ksi)

max,

(MPa)

σ

Ratio, 

Rσ



Ratio, 

R

T1 W45R0 3369 12.6 87 7.1 49 0.8 0.9 

T2 W30R0 3649 17.4 120 9.7 67 1.1 1.2 

T3 

(flawed) W30R90 211 18.5 127 9.8 67 1.2 1.2 

T4 

(flawed) W30R60 328 25.2 174 13.4 92 1.6 1.7 

T5 W30R90 414 36.2 250 19.2 132 2.3 2.4 

T6 W30R120 383 30.1 207 15.9 110 1.9 2.0 

T7 W45R90 395 28.6 197 15.1 104 1.8 1.9 

T8 W30R60 493 37.8 261 20.1 139 2.4 2.5 

A good match between FEA and DIC displacements for the “reduced” specimens as 

well as closer proximity of failure stresses to their T5 and T8 counterparts indicate that 

the flawed T3 and T4 discontinuities can be reasonably well represented by the reduced 

area FEA models. 

The data from Table 6 is plotted as normal stress vs. shear stress and as stress ratios 

in Figure 13 while the hand calculations are plotted in Figure 14. A combined plot 

representing the FEA and hand calculation results are shown in Fig. 15. As one can see 

there is a good agreement between FEA and hand calculated stress values and/or 

stress ratios. Stress ratios Rσ and R were calculated as: 

ܴఙ ൌ  

ଵߪ

଴ߪ

  ܽ݊݀  ܴఛ ൌ ߬௠௔௫

߬଴

 ,

where σo and o are 16 ksi (110 MPa) and 8 ksi (55 MPa) respectively. 

For convenience, the results of lap shear and butt-brazed pull tests (Tables 2 and 3) are 

also plotted along their respective axis in Figures 13-15. Since the strength of the 

standard test specimens is typically reported in terms of the average values, determined 

as failure force divided by the total area of the brazed joint (3), the data points 

representing these specimens in Figures 13-15 are also based on average values. 
16 

Fig.13 FEA results for T-specimens plotted as stresses (a) or stress ratios (b). 
17 

Fig.14 Hand calculated results for T-specimens plotted as stresses (a) and stress ratios 

(b). 
18 

Fig. 15 Shows a good agreement between FEA and hand calculations plotted in terms 

of stresses (a) or stress ratios (a). Trend lines (dashed) are also shown for convenience 
19 

Several interesting observations can be made when examining the graphs in Figs.13 - 

15. 

 It appears that all T specimens subjected to combined normal, bending, shear 

and torsional loads, such as specimens T3 – T8, all fall on the same straight 

trend line emanating from the origin. This means that the ratio of maximum 

normal principal and maximum shear stresses remains the same regardless of 

the loading configurations. 

 It appears that a relative position of the data point along the trend line is related 

to the strength or quality of the brazed joint. Note that specimens T8 and T4, as 

well as T5 and T3 were tested under identical loading configurations. The major 

difference between them, however, was the fact that brazed joints in T3 and T4 

had 26 and 14% lack of braze. Consequently, these flawed specimens failed at 

significantly lower stresses while remaining on the same trend line. 

 As one can see all the data points are located fairly far (even the flawed T3 and 

T4 specimens) from the Safe Zone. This indicates a fairly conservative selection 

of the FAD line. 

 When the braze areas in the FEA models for T3 and T4 flawed specimens are 

reduced by 26 and 14%, the estimated failure stresses increase and move up 

along the same lines closer to the T5 and T8 specimens tested under loading 

configurations identical to T3 and T4 respectively. This indicates that lack-ofbraze discontinuities (at least of the type observed in T3 and T4) can be 

reasonably modeled by reducing the total braze area. 

 Since the trend line is a straight line radiating from the origin, only one point is 

necessary to define an angular position of such line. A position of such point on 

the plot can be established from FEA analysis of the actual brazed assembly 

using a global FEA model subjected to the design loading conditions. 

Based on these observations, the following procedure of estimating margins of 

safety for brazed joints in a structure can be recommended: 

1. determine tensile and shear allowables by testing standard brazed test 

specimens and construct FAD line; 

2. using FEA determine 1st principal and max shear stresses acting on the braze 

plane in the actual structural brazed joint subjected to design loads; 

3. connect the origin with the point determined in 2) and construct a trend or 

braze joint line; 

4. an intercept of FAD line and the braze joint line corresponds to a zero safety 

margin condition; 

5. fabricate a small number (two or three) of identical or “realistic” specimens 

representing actual brazed joint geometry and test them to failure under 
20 

identical loading conditions. This step will help to determine the actual normal 

and shear stresses causing failure and define the location of the failure point 

on the braze joint line. If the actual level of stresses causing failure is of no 

consequence, this step can be omitted 

This procedure is illustrated graphically in Fig. 16. 

Fig. 16 Illustration of a structural evaluation of the brazed assembly. FAD is 

constructed based on experimental determination of shear o and tensile σo

allowables. Area inside the FAD line is a safe combination of stresses, or the safe 

zone. 1st principal and maximum shear in the brazed joint of interest subjected to the 

design loads are estimated by FEA using global model of the brazed assembly. 

Point A represents these stresses σA and A normalized over their respective 

allowables. The trend or braze joint line is constructed by connecting O and A. 

Intercept of the braze joint line with FAD gives point B representing zero Margin of 

Safety (MS). MS is estimated as (OB/OA) – 1; Point C represents the actual 

stresses at failure estimated from testing of the “realistic” specimens representing 

the brazed joint geometry and loading conditions. 
21 

Since the data points corresponding to all T3 – T8 specimens are located on the 

same braze joint line, it would be logical to expect the data points representing 

failure conditions of these specimens to form a closely spaced cluster located on the 

braze joint line. However, as one can see, these data points are spread quite far 

apart, particular T1 and T8. It is plausible that one of the reasons for such scatter in 

the T specimens test data is the propagation of error effect. Since the test results for 

standard butt tensile and lap shear brazed specimens show considerable scatter, it 

is reasonable to expect no lesser scatter when testing the specimens under more 

complicated loading conditions. A rigorous statistical analysis of propagation of error 

is difficult to perform since the exact functional relationship between normal and 

shear stresses and actual failure criterion is not known. Another possible reason for 

such scatter is a different sensitivity of the brazed joints to various types of stresses. 

5. CONCLUSIONS 

1. The Failure Assessment Diagram (FAD) based on eq.(1) can provide a very 

conservative estimate of safe static load carrying capabilities of the brazed 

joints; 

2. The applicability of FEA analysis to determine the 1st principal and maximum 

shear stresses for a complex loading geometry was validated using DIC 

analyzed experimental results. 

3. Such conservatism is justified by a large scatter in mechanical properties of 

the brazed joints, even when determined by testing the standard test 

specimens; 

4. A degree of conservatism of FAD can be controlled by the level of 

conservatism used to estimate brazed joint allowables. For example, A-basis 

allowables will result in the most conservative FAD; 

5. It appears that safety margins of the brazed joints can be estimated by using 

the simple engineering procedure proposed in this study. More work is 

required to verify that this procedure is applicable for other base – filler metal 

brazed joint combinations and structures. 

Acknowledgements 

The authors would like to thank IceSAT 2 project for sponsoring this study. Many 

thanks also go to Sheila Wall, Séké Godo, Wayne Chen and Babak Farrokh (code 

542) for their assistance with FEA and hand calculations. 

 
22 

Appendix

Normal and shear stresses acting on the braze plane in brazed joints were hand 

calculated using engineering mechanics [6,7]. Figure 17 illustrates the steps and 

nomenclature used to develop the necessary equations for normal and shear 

stresses. X, Y, and Z components of the applied force P can be calculated as: 

ܲ௫ ൌ ܲ ൉ cos   ൉ sin 

ܲ௬ ൌ ܲ ൉ cos   ൉ cos 

ܲ௭ ൌ ܲ ൉ sin 

First, for convenience, the point A where the test load is applied is relocated to the 

center of cross section, point B. To compensate for this relocation, three moments need 

to be introduced: 

ܲ௫ ൉ ሺ݀ଶሻ , ܲ௭ ൉ ሺ݀ଵሻ ܽ݊݀ ܲ௬ ൉ ሺ݀ଶሻ

Normal or axial stress on the braze plane is due to axial component Pz due to bending. 

The general form of the equation used to calculate normal stress acting at points 1 

through 8 in the braze plane is: ௉೥

஺ ൅ ∑ ெ൉௖

ூ

Where Aൌb൉h  is the area of the brazed joint footprint. The second term, in this equation, 

is a sum of all bending stresses and c represents the distance to neutral axis for each of 

the bending stresses and equals either h/2 or b/2. For example, normal stress at point 

1 can be calculated as: 

ߪ௭ ൌ ܲ௭

൅ ܣ

െܲ௭ · ݀ଵ · ቀ݄

2ቁ

௫௫ܫ

൅

െܲ௫ · ݀ଶ · ቀܾ

2ቁ

௬௬ܫ

൅

െܲ௬ · ݀ଶ · ቀ݄

2ቁ

௫௫ܫ

 ,

Where ܫ௫௫ ൌ(b·h3)/12 and ܫ௬௬ ൌ (b3·h)/12 are moments of inertia. Shear stresses due to 

shear and torsion have their maximum values at mid-points of each side, such as points 

2,5,7 and 8 (see Fig. 17). For example, a total shear stress at points 2 and 5 can be 

calculated as: 

߬௫௬ ൌ  

1.5 · ܲ௬

ܾ·݄ ൅

3·ܲ௫ · ሺ݀ଵሻ

8 · ቀ

݄

2ቁ · ቀ

ܾ

2ቁ

ଶ · ቈ1 ൅ 0.6095 · ൬

ܾ

݄

൰ ൅ 0.8865 · ൬

ܾ

݄

൰

ଶ

െ 1.8023 · ൬

ܾ

݄

൰

ଷ

൅ 0.91 · ൬

ܾ

݄

൰

ସ

቉

Shear stresses at mid-points 7 and 8 can be calculated as: 

߬ ൌ

1.5 · ܲ௫

ܾ·݄
23 

 a) b) 

 c) d) e) 

Fig. 17 Several sketches that help to better understand hand calculation process. Test 

load was applied in a direction represented by force P, as shown in sketch (a). The load 

components PX, PY and PZ are transferred to the center B and the new moments are 

introduced (b). Sketch (c ) shows how torsion is developed in the braze plane due to 

component PX acting over distance d1. Sketch (d) is a vertical cross section of the Tspecimen showing bending moment PX • d2. Finally, sketch (e) shows the braze plane 

and all locations where normal and shear stresses were calculated. 
24 

Results of hand calculations are shown in Table 6. Principal stresses and maximum 

shear stresses at each location 1 through 8 were calculated using the following 

expressions: 

ߪଵ, ߪଷ ൌ ఙ೥

ଶ േ ටቀ

ఙ೥

ଶ ቁ

ଶ

൅ ߬௫௬

ଶ, 

Where σ1 and σ3  are first (maximum) and third (minimum) principal stresses 

accordingly. For the purpose of calculating principal normal stresses, a conservative 

assumption is made that maximum shear stress xy is acting over entire braze plane. 

Maximum principal shear stresses calculated as: 

߬௠௔௫ ൌ  

|ߪଵ െ ߪଷ|

2

First principal normal and maximum principal shear stresses calculated as described 

above are listed in Table 7 and plotted in Fig.14 

References 

1. Flom, Y., Wang, L., Powell, M. M., Soffa, M. A., and Rommel, M. L., Evaluating 

Margins of safety in Brazed Joints, Welding Journal, 88(10), p. 31-37, 2009 

2. Flom, Y., Failure Assessment Diagram for Brazed 304 Stainless Steel Joints, 

NASA/TM-2011-215876, June 2011 

3. C3.2M/C3.2:2008, Standard Method for Evaluating the Strength of Brazed Joints, 

American Welding Society, Miami, Fla. 

4. Brazing Handbook, Fifth Edition, American Welding Society, Miami, Fla, 2007 

5. Welding Kaiser Aluminum, First Edition, Kaiser Aluminum and Chemical Sales, 

Inc., Kaiser Center, Oakland, 1967 

6. Dowling, N. E., Mechanical Behavior of Materials: Engineering Methods for 

Deformation, Fracture, and Fatigue, Prentice Hall Inc., New Jersey, 1993 

7. Young, W. C., and Budynas, R. G., Roark’s Formulas for Stress and Strain, 

Seventh Edition, McGraw-Hill, 2002 

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Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39-18 

26-10-2010 Technical Memorandum

 Failure Assessment Diagram for Titanium Brazed Joints Yury Flom, Justin S. Jones, Mollie M. Powell, and David F. Puckett 

Goddard Space Flight Center 

Greenbelt, MD 20771 

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

NASA/ GSFC NASA TM–2011-215882

Unclassified-Unlimited, Subject Category: 

Report available from the NASA Center for Aerospace Information, 7115 Standard Drive, Hanover, MD 21076. (443)757-5802 

The interaction equation was used to predict failure in Ti-4V-6Al joints brazed with Al 1100 filler metal. The joints used in this study 

were geometrically similar to the joints in the brazed beryllium metering structure considered for the ATLAS telescope. This study 

confirmed that the interaction equation Rσ + Rt = 1, where Rσ and Rt are normal and shear stress ratios, can be used as conservative 

lower bound estimate of the failure criterion in ATLAS brazed joints as well as for construction of the Failure Assessment Diagram 

(FAD).

Brazing, Structural Analysis, Interaction Equations, Failure Assessment Diagrams, Titanium

 Unclassified Unclassified Unclassified Unclassified

 24 Yury Flom (301) 286-3274