J.R. Ellis

Glenn Research Center, Cleveland, Ohio

G.S. Sandlass

MTS Systems Corporation, Eden Prairie, Minnesota

M. Bayyari

Research Applications, Inc., San Diego, California

Specimens and Reusable Fixturing for Testing

Advanced Aeropropulsion Materials Under

In-Plane Biaxial Loading

Part 1—Results of Conceptual Design Study

NASA/TM—2001-211134

October 2001
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NASA/TM—2001-211134

October 2001

National Aeronautics and

Space Administration

Glenn Research Center

J.R. Ellis

Glenn Research Center, Cleveland, Ohio

G.S. Sandlass

MTS Systems Corporation, Eden Prairie, Minnesota

M. Bayyari

Research Applications, Inc., San Diego, California

Specimens and Reusable Fixturing for Testing

Advanced Aeropropulsion Materials Under

In-Plane Biaxial Loading

Part 1—Results of Conceptual Design Study
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

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Aeronautics and Space Administration.

Available electronically at http://gltrs.grc.nasa.gov/GLTRS
NASA/TM—2001-211134 1

SPECIMENS AND REUSABLE FIXTURING FOR TESTING ADVANCED

AEROPROPULSION MATERIALS UNDER

IN-PLANE BIAXIAL LOADING

PART 1—RESULTS OF CONCEPTUAL DESIGN STUDY

J. R. Ellis*

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

G.S. Sandlass†

MTS Systems Corporation

Eden Prairie, Minnesota 55344

M. Bayyari‡

Research Applications, Inc.

San Diego, California 92121

SUMMARY

A design study was undertaken to investigate the feasibility of using simple specimen designs and

reusable fixturing for in-plane biaxial tests planned for advanced aeropropulsion materials. Materials of

interest in this work include: advanced metallics, polymeric matrix composites, metal and intermetallic

matrix composites, and ceramic matrix composites. Early experience with advanced metallics showed that

the cruciform specimen design typically used in this type of testing was impractical for these materials,

primarily because of concerns regarding complexity and cost. The objective of this research was to

develop specimen designs, fixturing, and procedures which would allow in-plane biaxial tests to be conducted on a wide range of aeropropulsion materials while at the same time keeping costs within acceptable limits. With this goal in mind, a conceptual design was developed centered on a specimen

incorporating a relatively simple arrangement of slots and fingers for attachment and loading purposes.

The ANSYS finite element code was used to demonstrate the feasibility of the approach and also to

develop a number of optimized specimen designs. The same computer code was used to develop the reusable fixturing needed to position and grip the specimens in the load frame. The design adopted uses an

assembly of slotted fingers which can be reconfigured as necessary to obtain optimum biaxial stress states

in the specimen gage area. Most recently, prototype fixturing was manufactured and is being evaluated

over a range of uniaxial and biaxial loading conditions.

INTRODUCTION

One technique for investigating material behavior under complex stress states is to use in-plane

biaxial loading. Using this approach, cruciform specimens fabricated from plate or sheet material are

gripped at four locations and loaded along two orthogonal axes. Servohydraulic loading systems are used

in this application which are similar to those used for uniaxial testing. Thus, the technique has the advantage that the loading arrangement is relatively straightforward and uses equipment which has seen

 

*

Senior Research Engineer.

†

Structural Analyst.

3

Principal Research Engineer.
NASA/TM—2001-211134 2

extensive development over the past 30 years. Also, the test method allows a wide range of biaxial stress

states to be investigated with minimum complication from the load application viewpoint. For these reasons, the test method has been used to generate a sizable body of biaxial test data for both monolithic and

composite materials (refs. 1 to 29).

One difficulty facing these investigations has been the selection and/or development of the most suitable specimen design for the particular program. It should be noted that consensus standards do not exist

for this method of testing, and so the experimentalist is faced with a wide range of possibilities. A major

complication here is that use of the cruciform specimen configuration and associated gripping fixtures

results in “coupling” between the two loading directions. In the present research, specimens are positioned in the load frame using four hydraulic grips which rigidly constrain the specimen over the gripped

regions. It follows that loading applied in one direction is partially reacted by the specimen and partially

by the grips associated with loading in the second direction. One method of minimizing this effect is to

use specimen designs which incorporate fairly complicated arrangements of flexures as illustrated in figure 1. It has been demonstrated that flexures with low bending stiffness in the plane of loading can be

used to minimize the constraint imposed by specimen gripping. Also, it has been shown that the geometry

of the flexures can be optimized and tailored to give near-uniform stress/strain conditions in the gage area

for specific biaxial loading conditions.

One obvious disadvantage of using flexures is that regions of high stress concentration can be introduced into specimens in close proximity to the gage area. Of particular concern are stress concentrations

at the ends and intersection points of the flexures. This raises the possibility that failure can be initiated

outside of the gage area in regions where stress/strain conditions are ill defined. Traditionally, this problem has been addressed by incorporating a gage area within which specimen thickness is reduced significantly from the value in the gripped regions. In the case of plate specimens incorporating flexures,

experience has shown that thickness reduction factors as high as ten are needed to achieve acceptable performance. That is failure initiating within the gage area where stress/strain conditions are both relatively

uniform and relatively well defined.

Although the above approach has been used effectively in the case of conventional structural alloys, it

has proved impractical for the materials of interest in this work including: advanced metallics; polymeric

matrix composites; metal and intermetallic matrix composites; and ceramic matrix composites. Problems

include the unavailability of material in “large” product forms and also the difficulties associated with

machining complex three-dimensional geometries in complex multiphase materials. The aim of the present work was to develop an alternative approach involving use of a simplified specimen design and use

of reusable fixtures incorporating the design features needed to decouple the applied biaxial loading. A

further goal was to develop fixturing and procedures which would allow in-plane biaxial tests to be conducted on a wide range of advanced materials while at the same time keeping costs within acceptable

limits.

SPECIMEN DESIGN AND ANALYSIS

The current cruciform specimen design (fig. 1) developed at NASA for testing conventional structural

alloys served as a starting point for this work. In the new approach, the gripped regions of the current

design are replaced by four individual fixtures which incorporate slotted fingers to decouple the biaxial

loading. The gage section of the current design is replaced by a specimen incorporating a reduced gage

area and four sets of slots and fingers for attachment purposes. The focus of the preliminary design and

analysis work was on determining whether a specimen design with this configuration would meet two

straightforward design requirements. These were (1) that the maximum stress in the part should occur

within the gage area, and (2) that the stress/strain distribution in the gage area should be reasonably uniform, say, within ±5 percent of the mean. Details of the conceptual design and the results of specimen

design and analysis work are described in the following.
NASA/TM—2001-211134 3

Conceptual Design

A conceptual design for the new approach is shown in figure 2. One constraint on the overall size of

the assembly was that a 432¥432 mm envelope is available within the load frame for installation and

gripping purposes. Four slotted finger fixtures are shown attached to a specimen fabricated from a

229¥229¥6 mm plate. These dimensions were selected to give a relatively large gage area, 76 mm outside

diameter in the case of specimens with circular gage areas. This approach was adopted primarily with

instrumentation requirements in mind. The attachment method is not shown in figure 2 for simplicity of

drawing.

Details of a slotted finger attachment are given in figure 3. The design shown is idealized in that no

stress relieving blend radii were included so as to simplify finite element analysis of the complete assembly. This approach was acceptable because the focus of initial work was on the performance of the specimen rather than on the performance of the fixturing. The slotted finger attachments are assumed to be

gripped over 152¥38 mm2

 areas on both top and bottom surfaces. Earlier experiments using the current

NASA cruciform specimen design had shown that this arrangement met the loading requirements of

planned test programs. Experience gained in these earlier experiments was also used to size the finger and

flexure configuration shown in figure 3. The four finger arrangement was an obvious choice given the

need to locate a slot on the fixtures centerline and also given the need to maintain symmetry about the

fixtures centerline.

Details of the initial specimen design are given in figure 4. As noted earlier, it is assumed to be fabricated from a 229¥229¥6 mm plate. Perhaps the most important design feature is the arrangement of slots

and fingers used for attachment and loading purposes. It was recognized at the outset that the slot configuration would play a key role in obtaining an optimized specimen design. As indicated in figure 4, a slot

width of 10 mm was selected for initial feasibility studies. Other dimensions shown in symbolic form

were treated as variables in subsequent optimization analyses.

Stress Analysis Details

The ANSYS finite element code, version 5.4, was selected for this work, primarily because it features

an optimization package. The plan was to model 1/8 of the complete assembly with the six specimen

dimensions shown in figure 4 expressed as variables and to perform fully automated analyses until an

optimum set of specimen dimensions had been obtained. To facilitate this process, a command input file

was created using the ANSYS Parametric Design Language (APDL). This provides the means to create

finite element models in terms of variables, which in turn allows for easy and rapid design changes. Approximately 1000 lines of ANSYS commands were used to define parameters, generate the finite element

model, solve, evaluate results, and begin optimization looping.

As indicated earlier, external loading was applied to the assembly over 152¥38 mm2 areas. An equibiaxial stress state was introduced into the finite element model by constraining all surface nodes within

the gripped regions to displace 0.127 mm in the positive sense in the two loading directions. Similarly,

clamping within the specimen grips was simulated by constraining all surface nodes within the gripped

region to displace 0.005 mm in the thickness sense. Regarding the attachment method, the specimen and

the slotted finger fixtures were modeled as a single unit in the early analyses which focused on specimen

performance. Note that the material properties used in this work were handbook values for Inconel 718

and that the results of stress analyses are expressed in the form of von Mises equivalent stress throughout.

Stress Analysis Results

The results shown in figures 5 and 6 were obtained in one of a large number of stress analyses performed during the initial stages of the research. One interesting feature of the overall deformation behavior of the assembly shown in figure 5 is the ability of the finger and flexure arrangement to accommodate

large overall displacements and rotations without becoming overstressed. This flexibility is of course the

mechanism by which loading in the two directions is partially decoupled. As might be expected, analysis

of the results showed that stress concentrations occurred at three locations outside of the gage area. As

indicated in figure 6, these locations were the center slot, the outer slot, and the fillet region. Simply

stated, the optimization process involved varying specimen dimensions in a systematic manner until the
NASA/TM—2001-211134 4

maximum stress values at these locations were less than the average stress in the gage area, say, with a

20 percent margin of conservatism.

Analysis of the data shown in figures 5 and 6 indicated that this condition had partially been achieved

with the particular specimen design shown. The average and maximum stresses in the gage area were 392

and 397 MPa, respectively. The maximum stress levels in the center and the outer slots were 367 and

352 MPa, and the maximum stress in the fillet region was 382 MPa. Thus, this design met the design

requirement that the maximum stress should occur within the gage area. However, it was apparent that

additional work was needed to achieve the 20 percent margin of conservatism. The second design

requirement was that the stress distribution in the gage area should be uniform within ±5 percent of the

mean. Analysis of the data shown in figure 6 showed that the stress distribution in the gage area fell

within ±2.4 percent of the mean, easily meeting the target value.

Optimization Method

The combination of specimen dimensions used in obtaining the above result was as follows:

• Gage section radius (R1) = 41.28 mm

• Center slot length (SLA) = 35.50 mm

• Outer slot length (SLB) = 37.00 mm

• Fillet radius (FR) = 27.94 mm

• Gage area thickness (T1) = 1.25 mm

• Thickness transition radius (TR1) = 12.70 mm

The optimization process followed in obtaining these results was not straightforward and proved to be

extremely time-consuming. Evaluation of the various ANSYS optimization routines showed that in this

application, the routines had difficulty converging on optimum sets of values. The factorial routine was

found to be most useful for the present work as it allowed predetermined combinations of specimen

dimensions to be investigated in a straightforward manner. As described in the following, the “automatic”

process was supplemented by presenting the results of stress analysis in graphical form and by analyzing

the results by hand. This approach effectively narrowed the design space and allowed optimum data sets

to be determined more efficiently.

As a first step, fully automated stress analyses were conducted for up to thirty-six combinations of

center and outer slot length and gage section thickness. As illustrated in figure 7, these data were plotted

to establish the optimum combination of center and outer slot length. This was defined as the intersection

point giving the minimum stress condition at the two slot locations. It can be seen in figure 7 that the

optimum values of center and outer slot length established in this manner were 35.50 and 37.00 mm. One

important result was that the curves representing stress conditions at the two slot locations and at the fillet

region were found to be unaffected for the most part by changing gage area thickness. The most important

effect of changing this variable was to shift the position of the gage area curve in the vertical sense relative to the stress axis. Thus, selecting the optimum gage area thickness simply involved identifying the

curve that fell above the intersection point with some reasonable level of conservatism. The optimum

value of gage area thickness selected in this manner was 1.25 mm.

Additional stress analyses were then conducted to determine the optimum value of fillet radius. This

approach was possible because changing this variable did not have a major effect on the stress states at

the slots and within the gage area. As illustrated in figure 8, these results were also plotted to determine

the minimum feasible value of fillet radius which was 26.9 mm for the case shown. A value of 27.94 mm

was selected as being optimum for the particular specimen design as it provided some margin of

conservatism.
NASA/TM—2001-211134 5

Final Specimen Designs

Given this encouraging result, attention was shifted to the design of gripping and attachment methods

and to modifying the initial specimen design as found to be necessary. By way of background, it was

anticipated that load levels as high as ±222 kN would be needed in tests planned for aeropropulsion materials of interest. Relatively simple attachment methods using bolts, for example, as the primary means of

load transfer proved inadequate, primarily because of the previously noted size constraints. The approach

adopted to resolve this difficulty was to incorporate tapers on the specimen fingers to allow load transfer

by means of shear. This change was made reluctantly as it was viewed as introducing a major element of

complexity to the specimen design. A further change was that the width of the slots was increased to

reduce stress levels at the root locations and to increase margins of conservatism.

Details of the final specimen design featuring a circular gage area are given in figures 9 and 10. One

change from the initial design is that the width of the fingers is reduced from 19 to 16 mm. This allowed

the slot width to be increased from 10 to 14 mm. Further, an 8°00¢ ±15¢ taper was incorporated on the

gripped section to facilitate load transfer into the specimen (fig. 10). Optimization exercises similar to

those described above were conducted for two values of overall plate thickness, 19 and 25.4 mm. The

optimized set of dimensions for the two thicknesses are summarized in table I, and the results of stress

analyses are summarized in table II. The relative merits of the designs will be discussed later in the paper.

REUSABLE FIXTURING DESIGN AND ANALYSIS

The first objective of the fixturing design work was to identify the optimum attachment method for

specimens with the slot and finger configuration described above. A number of attachment methods were

considered during initial design studies and all but two rejected, primarily because of concerns regarding

complexity and cost. Work on the two most promising concepts was continued through detailed design

and in one case through manufacture. The preferred approach uses a yoke arrangement which has the

important advantage of not requiring any further modifications to the specimen designs described earlier.

The design and analysis process followed in achieving a final design is outlined as follows.

Design Details

As a first step, a number of changes were made to the slotted finger attachment (fig. 3) which served

as a starting point for this work. It was recognized that the design in its original form was going to be difficult and expensive to manufacture and, with this in mind, the original unit design was broken down into

nine subcomponents. These were eight fingers and a single mounting plate for assembly purposes. Details

of this assembly are shown in figures 11 and 12. Here it can be seen that the mounting plate incorporates

eight slots to accommodate the fingers and that setscrews are used for assembly purposes. The finger

design includes tapers on two surfaces to match the corresponding tapers on the specimen and the yoke. A

further design feature worth noting is the flats which were provided to ensure positive location between

the end of the specimen and the fingers. An undercut was included at the same location to ensure proper

specimen seating and also to provide some flexibility for specimen gripping.

The important features of the yoke gripping arrangement are shown in figures 13 to 15 where, for

simplicity, a single pair of fingers is shown attached to a rectangular block. The plan was to first subject

the fixturing to detailed evaluation under uniaxial loading. The prototype fixturing shown in these figures

was manufactured specifically for this purpose. The primary function of the yoke fixture is to prevent the

fingers separating under load and to prevent relative motion between the specimen and the fingers. Stated

differently, the yoke's function is to ensure that the end of the specimen stays in full contact with the

mating surfaces of the fingers under both tensile and compressive load-ings. This condition was to be

achieved by effectively clamping the ends of the specimen between finger pairs by applying suitable preload to the assembly. This preloading was to be achieved using the two preload bolts in conjunction with

the tapers on the mating surfaces of the fingers and the yoke. The first goal of analysis was to determine

whether effective clamping could be obtained without overstressing either the bolts or the yoke. Also, the
NASA/TM—2001-211134 6

stiffness and load transfer characteristics of the attachment method were to be investigated to establish the

useful loading range available with the design.

Stress Analysis Details

The ANSYS finite element code, version 5.4, was again used for this work. The plan was to model

one half of the assembly shown in figure 13 and to investigate the characteristics of the attachment

method over a range of uni-axial loading conditions. The effect of simply preloading the assembly was

the first loading case considered. Bolt preloading in these analyses was obtained by applying known displacements to the underside of the bolt head. Further, it was of interest to investigate how the stress state

resulting from preloading was modified by the superimposition of external loading. As in earlier analyses,

external loading was applied by constraining surface nodes in the gripped region to displace predetermined amounts in the loading direction. The magnitudes of these displacements were varied to simulate

strength tests under both tensile and compressive loading.

As with most general-purpose finite element codes, contact elements are available within ANSYS for

analyzing joints and attachments. Line contact elements were used in the present work to model the contact surfaces between the mating components. One complication with this approach is that a value of

contact stiffness has to be specified up front for these nonlinear analyses. Also, it is well known that the

correct choice of contact stiffness is critical in regard to the accuracy of the solution and also in regard to

the time taken to converge on a solution. To address this issue, a series of preliminary analyses was conducted investigating the effect of varying contact stiffness over the range 1.776¥10¢ to 1.776¥106 kN/mm.

The highest value was selected for the final analyses as it was shown to provide reasonably accurate solutions within acceptable time periods. As would be expected, a coefficient of friction value has to be specified which is judged typical for the surface condition of the mating parts under consideration. In the

absence of experimental data, a value of 0.1 was assumed for the majority of analyses and a limited number of spot checks were conducted using a value of 0.2. As in the case of the earlier work, elastic constants used in these analyses were handbook values for Inconel 718.

Stress Analysis Results

The results shown in figures 16 and 17 were obtained in one of a large number of stress analyses performed on the yoke assembly. These data were obtained using a contact stiffness of 1.776¥106 kN/mm, a

coefficient of friction of 0.2, and a bolt preload of 31.6 kN. Analysis of the results showed that the maximum stress in the yoke, 692 MPa, occurred at location (2) in figure 16. The maximum stress in the finger,

1792 MPa, occurred at location (4) in figure 17. Clearly, the preload assumed in this analysis was less

than ideal since it resulted in unacceptably high stresses in both the yoke and the finger. This situation

was corrected in subsequent analyses by using more realistic values of bolt preload. One result of changing this variable was to change the location of maximum stress. For example, in analyses using a bolt

preload of 5.816 kN and a coefficient of friction of 0.1, the maximum stress condition occurred at location

(1) in figure 16 and at location (3) in figure 17. The results of all analyses performed using a contact stiffness of 1.776¥106 kN/mm are summarized in table III.

Stiffness and Load Transfer Characteristics

The efficiency of the yoke attachment method was investigated by generating plots of applied grip

displacement versus the corresponding specimen load. Such a curve is shown in figure 18 for a bolt preload of 5.816 kN and a coefficient of friction of 0.1. As would be expected, the performance of the fixture

under tensile loading is significantly different from that under compressive loading. This is because the

load path between the specimen and the fingers is completely different for the two loading cases. Under

tension, a minor change in slope occurs at point (A) and a major change occurs at point (B) where slippage apparently occurs. Under compression, behavior is more straightforward with a minor change in

slope occurring at point (C). The above data are summarized in more quantitative form in table 4 along

with results obtained for other combinations of preload and coefficient of friction.
NASA/TM—2001-211134 7

An attempt was made to investigate the cause of the slope changes using the contact status option

available with ANSYS. Using this option, the status of contacting surfaces is given in three categories:

1. Gap closed, no sliding

2. Gap closed, sliding

3. Gap open

Data of this type were determined at frequent intervals during simulated loading for both the finger/yoke interface and the specimen/finger interface. The approach adopted in analyzing the data was

simply to identify any significant changes in contact status that occurred during the various stages of

loading. Overall, the data did not appear reliable and proved difficult to analyze. For example, there were

no obvious changes in contact status at load/displacement combinations corresponding to points (A) to

(C) in figure 18. One expected result was that the status at both interfaces was predominantly category

(1) for the case of preload only. Also, as expected, the status at the specimen/finger interface changed to

mixed (2) and (3) almost immediately on load application as a result of specimen straining. Beyond this,

the data were judged to have little value and will not be discussed further.

DISCUSSION

As noted in the introduction, the aim of this research was to develop specimen designs and fixturing

which would allow in-plane biaxial tests to be conducted on a wide range of aeropropulsion materials

including advanced metallics and composites. The plan was to develop optimized specimen designs with

relatively simple geometries to facilitate manufacture and to keep costs within reasonable limits. Further,

reusable fixturing was to be developed for specimen gripping and loading purposes which would incorporate the flexures needed to decouple the applied biaxial loading. The fixturing was to be manufactured

using conventional structural alloys, again with the goal of keeping costs within acceptable limits.

Inspection of figures 9 and 10 and tables I and II shows that the goal of developing a relatively simple

specimen design was met as a result of this research. The design feature which enabled this result was the

arrangement of slots and fingers used for attachment and loading purposes. As expected, the geometry of

the slots played a key role in obtaining optimized specimen designs. Over the course of the design process, the width of the slots was progressively increased to a final value of 14 mm with the aim of reducing

stress levels at the ends of the slots. This far, the slots have been configured using a simple circular detail

at the root location with ease of manufacture in mind. Clearly, the possibility exists that noncircular geometries could be used to give improved results.

Slot length also played an important role in the optimization process. It was shown that best results in

terms of stress distribution at the root locations were obtained when the shorter slot was located on the

specimen's centerline. It was also shown that increasing slot length caused increased stress levels at the

ends of the slots and reduced stress levels at the fillet radius. Best results were obtained for slot lengths in

the range 30.48 to 38.10 mm and fillet radii in the range 40.64 to 50.80 mm. Interestingly, these results

applied for all the various specimen thicknesses considered. The importance of these results is that it

allows some flexibility in the choice of gage area thickness (T1). For example, increased values of this

variable might be preferred in test programs investigating the effects of pre-existing notches or defects.

One advantage offered by the slotted finger attachment is that the flexures are located some distance

from the specimen gage area. This allows the use of generous fillet radii at the specimen corners to reduce

the stress concentrations at this location. As indicated in table I, fillet radii as high as 50.80 mm were used

to obtain feasible specimen designs. Such an approach is not possible with the current NASA cruciform

specimen design shown in figure 1. In this case, use of large fillet radii increases the stiffness of the outermost flexures resulting in unacceptably high stress concentrations at the corner locations.

The results summarized in table I show that it is possible to develop feasible specimen designs for a

range of specimen dimensions. Six designs are shown in this table with overall thicknesses of 19 and

25.4 mm and with gage area thicknesses ranging from 1.524 to 2.540 mm. One method of evaluating the

various designs is to normalize the maximum stresses at the slot and fillet radius locations using the average gage area stress. This procedure was followed with the results shown in table II. The normalized
NASA/TM—2001-211134 8

values give an indication of “margin of conservatism” and can be used to rank the various designs.

Adopting this approach, review of the data showed that most favorable results were obtained for center

and outer slot lengths of 30.48 and 30.78 mm. With one exception, the normalized values were 0.88 or

less, giving about 10 percent design margin.

The ranking process was carried one stage further by evaluating the results for various gage area

thicknesses. Best results were obtained for a 1.524 mm gage area thickness in the case of the 19 mm

specimen, and for a gage area thickness of 2.032 mm in the case of the 25.4 mm specimen. The margin of

conservatism for these particular designs was about 20 percent. The above result illustrates that the subject specimen design offers some flexibility in meeting the particular size requirements of test programs

investigating the behavior of advanced materials.

A number of candidate specimen configurations were evaluated during the conceptual design study in

addition to the single-step, circular design described this far. As summarized in appendix A, these designs

featured both circular and square gage areas and both single-step and two-step reductions in gage area

thickness (figs. 19 to 23). On advantage of the square gage area configuration was that it was found possible to obtain near-optimum designs using relatively long slot lengths (SLA and SLB) and relatively

small fillet radii (FR). The importance of this result is that both these features facilitate specimen gripping

in the reusable fixturing as greater working space is provided for the yoke fixtures. The advantage of the

two-step reduction in gage area thickness was that stress concentrations in the thickness transition region

were reduced significantly compared to those in single-step designs. Advantage can be taken of these

characteristics in research programs where specimen manufacturing costs are not a major concern. It is

planned to develop fully optimized designs in future work using the designs shown in figures 19 to 23 as

a starting point.

One limiting feature of the design/optimization work outlined above is that it focused entirely on a

single form of biaxial loading. This was the special case of equibiaxial tensile loading which was selected

in part to simplify the optimization process. One obvious question is whether the specimen designs optimized using this form of loading can be used without modification to investigate more general forms of

biaxial loading. As described in appendix B, an additional series of analyses was conducted on specimen

design 3.2 to address this question. Details are given in figure 24 of the approach used to investigate

behavior over a single quadrant of biaxial stress space while maintaining a reference state of stress at the

specimen center. The results of these analyses are shown in figures 25 to 30 and also in tables V to VII in

reduced form.

In summary, it was shown that the equibiaxial specimen design can be used without modification to

investigate deformation behavior under general forms of biaxial loading. This is assuming that all measurement and observation is limited to the 25.4 mm diameter circular region at the center of the specimen.

For strength and fracture tests, the situation is less straightforward since the magnitude and the location of

the maximum stress in the gage area varied markedly with the type of biaxial loading. In one case, the

deviation of gage area stress about the mean was as high as ±7 percent. Here, the preferred approach is to

modify the test setup so as to ensure that the original design requirements are met. One interesting possibility is that minor modifications can be made to the slotted finger attachment to bring stress levels at

critical locations back within acceptable limits. The obvious advantage of this approach is that it eliminates the need to modify the equibiaxial specimen design.

Turning to the design of reusable fixturing, the slotted finger attachment in its final form is shown in

figures 11 and 12. One important modification was that the original unit design was broken down into

nine subcomponents with the primary aim of simplifying manufacture. Subsequent to the design study,

eight slotted fingers were fabricated from Inconel 718 using the electrical discharge machining (EDM)

method. The wire EDM method was used to machine the somewhat complicated finger profile shown in

figure 12 in a single part about 32 mm wide. This part was then cut into two 16 mm widths to form a

matched pair of fingers. This approach ensured the symmetry of the finger pair about the central plane of

the fixture. The obvious concern here was load alignment and the need to minimize the effects of variability in machining.

A similar issue addressed during the manufacturing exercise concerned the tolerances specified for

the various tapered surfaces. As noted earlier, one important goal of the fixturing design was to ensure

that the end of the specimen stays in full contact with the fingers under both tensile and compressive

loading. For this condition to be achieved, analysis showed that careful attention had to be given to the

taper angles specified for the mating parts. Assuming a less than perfect machining job, it was shown that
NASA/TM—2001-211134 9

the taper angle on the finger should be less than that on the specimen and greater than that on the yoke.

For simplicity, an angle of 7°30¢ ±15¢ was selected for both taper angles on the slotted fingers. The taper

angle selected for the specimen was 8°00¢ ±15¢ and that selected for the yoke was 7°00¢ ±15¢. It remains

to experimentally verify that this approach will provide the required results in terms of gripping efficiency

and effective load transfer under both tensile and compressive loading.

Turning to the yoke attachment, the final design is shown in figures 13 to 15 and the results of stress

analysis are shown in figures 16 and 17 and in table III. It should be noted that a single value of contact

stiffness, 1.776¥106 kN/mm, was used throughout in this work. Initial analysis focused on investigating

the effect of varying bolt preload and coefficient of friction on the stress distribution in the assembly.

Stress analysis results are summarized in table III for two combinations of bolt preload and coefficient of

friction (m). Here, it can be seen that for (m) = 0.2 and bolt preload = 31.6 kN, the maximum stress in the

yoke is 692 MPa and that in the finger is 1792 MPa. Since the ultimate tensile strength for Inconel 718 in

aged condition is about 1448 MPa, the latter stress was known to be unrealistic. However, data for this

particular combination was retained as it provided useful insight regarding the load transfer characteristics

of the assembly for higher values of coefficient of friction and bolt preload.

More reasonable results were obtained for m = 0.1 and bolt preload = 5.816 kN. For this combination,

the maxi-mum stress in the yoke was 450 MPa and that in the finger was 718 MPa. These values were

judged acceptable as the 0.2 percent yield strength for Inconel 718 in aged condition is about 1172 MPa.

The analyses were carried one stage further by simulating the effect of specimen loading. This was done

by applying a range of grip displacements in both the tensile and compressive senses. One interesting

result was that superimposition of tensile loading had little effect on the bolt preload whereas compressive

loading caused the bolt preload to increase by about 20 percent. Stresses in the yoke were found to

increase by about 15 percent under tensile loading and to decrease by about 13 percent under compressive

loading. In contrast, stress levels in the finger increased by about 22 percent for both tensile and compressive loading. The important result here is that the major component of stress in the assembly resulted from

bolt preloading and that subsequent specimen loading had a relatively minor effect.

Data regarding the stiffness and load transfer characteristics of the assembly are shown in figure 18

and in table IV. Note that the data shown in this figure were determined for a coefficient of friction of 0.1

and for a bolt preload of 5.816 kN. It can be seen in figure 18 that at relatively low load levels, the initial

slope for tensile loading is 91.8 kN/mm and that for compressive loading is 92.8 kN/mm. Relatively small

changes in slope occurred at load (kN)/displacement (mm) combinations of 5.19/0.0559 in the case of

tensile loading and 5.36/0.0584 in the case of compressive loading. The 0.150 secant modulii for the two

loading directions were 88.6 and 90.33 kN/mm. Thus, the magnitude of the slope changes at points (A)

and (C) are relatively small, about 5 percent on average. Under tensile loading, a major change in slope

occurred at point (B) which corresponds to a load level of about 14.20 kN. Load carrying capability was

lost at this point giving an upper limit on the useful range of the fixture for the particular combination of

bolt preload and coefficient of friction considered. Under compressive loading, behavior was better

behaved with near-linear response extending to at least 22.50 kN.

Turning to the results summarized in table IV, similar behavior to that described above was observed

for higher values of coefficient of friction and preload. More specifically, for a coefficient of friction =

0.1 and a bolt preload = 11.62 kN, the initial slope in tension was 96.41 kN/mm and that in compression

was 91.44 kN/mm. Further, the 0.150 secant modulus for tensile loading was 91.26 kN/mm. The magnitude of these values were very close to those determined for a bolt preload = 5.816 kN indicating that the

value of initial slope is not a function of this variable. Under tensile loading, the change in slope occurred

at a load (kN)/displacement (mm) combination of 12.36/0.130. Apparently, increasing bolt preload by a

factor of two effectively doubled the initial linear range of the fixture. Inspection of table IV shows that

this trend was not continued when bolt preload was increased to 31.64 kN for a coefficient of friction of

0.2. In this case, increasing preload did not result in any increase in the linear range. One important result

here is that the stiffness characteristics of the fixturing are not a function of coefficient of friction or bolt

preload. Had this been the case, the design would not have been useful for in-plane biaxial testing.
NASA/TM—2001-211134 10

1. The feasibility of using specimen designs incorporating relatively simple arrangements of slots and

fingers for loading purposes was demonstrated by analysis for conventional structural alloys.

2. A number of optimized specimen designs were developed with gage area thicknesses ranging from

1.524 to 2.032 mm. These designs were suitable for investigating material behavior under

equibiaxial stress states.

3. Reusable fixturing was developed incorporating an assembly of slotted fingers which provide the

flexibility needed to decouple the applied biaxial loading. This assembly can be reconfigured as necessary to obtain optimum biaxial stress states in the specimen's gage area.

4. A yoke gripping arrangement was developed which facilitates specimen loading while avoiding the

need for holes or other forms of discontinuity in the specimen.

FUTURE WORK

The slotted finger and yoke fixtures will be subjected to detailed experimental evaluation under

uniaxial loading with the focus on stiffness and load transfer characteristics. Given a positive result, a

second series of experiments will investigate the performance of the fixturing under in-plane biaxial

loading.

CONCLUSIONS

The following conclusions were drawn from this design study aimed at developing improved specimen designs and fixturing for in-plane biaxial testing.
NASA/TM—2001-211134 11

APPENDIX A

CANDIDATE SPECIMEN DESIGNS FOR FUTURE WORK

It should be noted that a number of candidate specimen configurations were evaluated during the conceptual design study in addition to the designs described earlier. These configurations were based in part

on the current NASA specimen design shown in figure 1. Features of interest here include the square gage

area and the two-step reduction in gage thickness. As might be expected, the evaluation process showed

that these design features had both advantages and disadvantages. One disadvantage of square gage areas

is that unacceptably high stress concentrations can occur at the corners if careful attention is not given to

the radii at these locations. Also, use of a two-step reduction in gage thickness was known to complicate

manufacture and to lead to increased manufacturing costs. With these disadvantages in mind, work aimed

at developing the most cost effective design focused almost entirely on specimens with single-step, circular gage areas (figs. 9 and 10).

The conceptual design study did however identify one important advantage of the square gage area

configuration. It was found possible to obtain near-optimum designs without too much difficulty using

relatively long slot lengths (SLA and SLB) and relatively small fillet radii (FR). The importance of this

result is that both of these features facilitate specimen gripping in the reusable fixturing as greater working space is provided for the yoke fixtures (fig. 13). Note that these fixtures are partially located in the

specimen slots when assembled with the slotted finger attachments and used for biaxial testing. With this

advantage in mind, it appears that further consideration should be given to the square gage area configuration and fully optimized designs developed. A starting point for this work is the design shown in figures

19 and 20. The gage area dimensions shown were optimized during the conceptual design study and do

not require further work. It remains to determine optimum values of slot length and fillet radius using the

optimization procedures described earlier.

Also during the conceptual design study, the use of multistep reductions in gage area thickness was

shown to offer certain advantages over single-step designs. It was shown for example that stress concentrations in the thickness transition regions can be reduced significantly using the multistep approach.

Thus, advantage can be taken of this characteristic in research programs where specimen manufacturing

cost is not a major factor. With this option in mind, partially optimized designs featuring two-step reductions in gage area thickness are shown for further consideration in figures 21 to 23. As before, the gage

area dimensions were optimized during the conceptual design study and do not require further work. Fully

optimized designs can be obtained using these designs as a starting point by determining optimum values

of slot length (SLA and SLB) and fillet radius (FR). It should be noted that the two-step, square gage area

configuration might give best overall performance. This is assuming that this configuration in fully optimized form does indeed allow use of long slot lengths and small fillet radii. As noted earlier, the important consideration here is ease of specimen gripping in the reusable fixturing.
NASA/TM—2001-211134 12

APPENDIX B

SPECIMEN PERFORMANCE UNDER GENERAL FORMS OF BIAXIAL LOADING

One limiting feature of the design/optimization work described this far is that it focused entirely on a

single form of biaxial loading. This was the special case of equibiaxial tensile loading. One advantage of

using this type of loading was that it caused symmetrical stress states to be introduced into the specimen

and associated fixturing. This simplified the optimization process by effectively reducing the number of

variables involved. Regardless of such efforts, the process of developing fully optimized designs

remained complex and time consuming. Given this result, it was apparent that major savings in time and

effort would be realized if it could be demonstrated that the equibiaxial specimen design could be used

without modification to investigate more general forms of biaxial loading. Possible issues to be addressed

here included the location of the maximum stress in the assembly and also the uniformity of stress in the

specimen gage area.

The specimen configuration selected for further study was specimen type 3.2, details of which are

given in table I. One goal in conducting this work was to maintain a reference state of stress at the center

of the specimen gage area so as to allow meaningful comparison of performance under the various loading conditions investigated. The approach adopted in achieving this goal is shown schematically in

figure 24. Here it can be seen that a single value of von Mises equivalent stress, 345 MPa, was used

throughout. Further, six stress ratios (q) in the range + 45∞ were selected to investigate specimen performance over a single quadrant of biaxial stress space. In the case of isotropic materials, stress states in the

remaining quadrants can be inferred from the symmetry of the von Mises ellipse. The components of

stress, sx and sy, corresponding to the six reference conditions were calculated in a straightforward

manner using the relationships shown in figure 24 and the results of these calculations are summarized in

table V. It remained to establish the grip displacements needed to achieve the reference stress states in

planned finite element analyses.

As noted earlier, loading in the subject in-plane biaxial tests is introduced into specimens and associated fixturing by means of four hydraulic grips. These grips rigidly constrain the gripped region of the

fixturing over 152¥38 mm2

 areas (fig. 3). This was simulated in earlier finite element analyses by constraining all surface nodes in the gripped regions to displace predetermined amounts in the two loading

directions. Similarly, clamping within the specimen grips was simulated by constraining all surface nodes

within the gripped regions to displace 0.005 mm in the thickness sense. The plan was to use the same

general approach in the present investigation. To determine the required grip displacements, it was

assumed that stress components at the center of the gage area, sx and sy, are related to corresponding grip

displacements, Dx and Dy, by the expressions:

Dx = K1 sx + K2 sy (1)

Dy = K1 sy + K2 sx (2)

where K1 and K2 are constants.

Since K1 and K2 were unknown, it was necessary to conduct a preliminary finite element analysis to

effectively calibrate these expressions. The planned approach was to apply known grip displacements to

the model and to calculate the corresponding values of sx andsy. It was then possible to solve equations

(1) and (2) for K1 and K2.

Regarding the boundary conditions and loading used in the preliminary analysis, clamping in the rigid

grips was simulated by constraining surface nodes in the gripped regions using the approach described

above. Loading was introduced into the finite element model by applying a simulated grip displacement

of 0.127 mm in the x sense. The condition in the y sense was “gripped” but free-to-displace in the

y direction. The value of Dy calculated as a result of this loading was –0.0336 mm and the calculated

values of sx andsy were 320MPa and –100MPa. These values along with the known value of Dx were

substituted in Equations (1) and (2) and solved for K1 and K2 with the following results:

K1 = 4.03688¥10–4 (mm)(MPa)–1

K2 = 2.07884¥10–5 (mm)(MPa)–1

At this stage, it was possible to use equations (1) and (2) to determine the required grip displacements.

These values are summarized in table V along with the target stress values. The results obtained in
NASA/TM—2001-211134 13

subsequent finite element analyses are shown in figures 25 to 30 and in reduced form in tables V to VII.

The stress components, sx andsy, determined at the center of the gage area are summarized in table V

along with the target values. Comparison of the two data sets showed that the finite element results were

within +2 percent of target values in the case of sx and were within + 4 percent in the case of the sy stress

component. Similarly, the values of von Mises equivalent stress were found to be within +2 percent of the

target value. These differences were judged to be acceptable for the present comparative study.

The data presented in figures 25 to 30 were used to assess the uniformity of stress over the entire

specimen gage area with the results shown in table VI. As noted earlier, the optimized form of specimen

3.2 was obtained using equibiaxial, tensile loading which corresponds to stress ratio = +45.0°. Not surprisingly, the stress distribution for this loading case shown in figure 25 is highly uniform with stress levels falling within +0.5 percent of the mean over the entire gage area. Analysis of the data shown in figures

26 to 30 showed that the deviations of stress are significantly higher for the other stress ratios. More specifically, it can be seen in table VI that the deviations for q = 0∞, 15.0∞, and 30.0∞ fall in the range ±6 to

±7 percent. Clearly, these results do not meet the original design requirement that stresses within the gage

area should be uniform within + 5 percent of the mean. As expected, a much improved situation holds for

stress distributions within a 25.4 mm diameter circular region at the center of the specimen gage area. In

this case, deviations of stress fall within +1 percent of the mean for all six stress ratios. This result suggests that the equibiaxial design can be used to investigate deformation behavior under general forms of

biaxial loading provided measurement and observation is limited to the central 25.4 mm diameter circular

region.

In the case of experiments investigating strength and fracture behavior, the focus is more on the magnitude and the location of the maximum stress in the specimen. The results shown in figures 25 to 30 were

analyzed further with this particular viewpoint in mind. In this case, stress states were analyzed along individual axes to identify the magnitude and location of the maximum stress. The results of these analyses for

the x, y, and 45∞ axes are summarized in table VI. As expected, the location of the maximum stress is

highly dependent on the loading direction or stress ratio. In the case of equibiaxial loading, q = 45.0∞, the

maximum stress occurred on the 45∞ axis at the outside diameter of the gage area. For stress ratios of 0∞, 15.0∞, and 30.0∞, the maximum stress location fell on the x-axis, again at the gage section outside diameter.

Interestingly, this pattern of behavior was not repeated for negative stress ratios. For q = –22.5∞, the maximum stress location fell on the x-axis about 12.7 mm from the center of the specimen. In the case of

q = –45.0∞, the maximum stress was located exactly at the specimen center. Clearly, the behavior

described above complicates interpretation of any strength or fracture tests involving general forms of

biaxial loading.

Finally, attention is shifted to stress distributions over the entire specimen including the critical fillet

and slot locations. More specifically, the six locations of interest are the gage area, the fillet radius, and

the center and outer slots in both the x and y directions. The maximum stress values at these locations are

summarized in table VII for stress ratios in the range + 45.0∞ along with the average gage area stress. Note

that to facilitate comparison of the data, the maximum stress values were normalized using the average

gage area stress. The approach adopted in evaluating these data was to use the original design requirement

that the average gage section stress should exceed stress levels at other critical locations with at least a

20 percent margin. It can be seen in table VII that this design requirement was met reasonably well for all

stress ratios except q = +45.0∞. For this loading case, the design margin at the fillet radius was about

10 percent. Somewhat surprisingly this indicates that specimen design 3.2 as used in this series of analyses was not in fully optimized form. Clearly, further work is needed to identify the optimum value of fillet

radius needed to give the 20 percent design margin. A further result of interest is that the equibiaxial

loading case proved to be the most challenging in terms of achieving optimum stress distributions over

the entire specimen.

In summary, this study showed that the equibiaxial specimen design can be used without modification

to investigate deformation behavior under general forms of biaxial loading. This is assuming that all

measurements and observations are limited to the 25.4 mm diameter circular region at the specimen center. It was also shown that the equibiaxial specimen design can be used for other forms of testing for

stress ratios of +45.0∞, 0∞, –22.5∞ and –45.0∞. This recognized that data for q = 0∞ can be generated in a

straightforward manner under uniaxial loading using a much simpler specimen design and test setup. For

the remaining stress ratios, q = +15.0∞ and +30.0∞, some modifications to the test setup are necessary to

meet the original design requirements. One interesting possibility is that minor modifications can be made

to the slotted finger attachments to bring stress levels at critical locations back within acceptable limits.

The obvious advantage of this approach is that it eliminates the need to modify the equibiaxial specimen

design.
NASA/TM—2001-211134 14

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B.F. Dyson, Eds., HMSO, 1982, pp. 185–203.

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Properties of Composite Materials,” Multiaxial Fatigue, ASTM STP 853, K.J. Miller and

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Inter-national Conference on Biaxial Multiaxial Fatigue, Vol. 2, University Stuttgart, Paper No. 46,

1989, pp. 1–18.

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Materials–VI, Vol. 2 (ICM 6), Pergamon Press, Oxford, 1991, pp. 543–548.

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Using Cruciform Specimens,” Experimental Mechanics, Vol. 32, 1992, pp. 138–144.
NASA/TM—2001-211134 15

23. Demmerle, J. and Boehler, J.P.: “Optimal Design of Biaxial Tensile Cruciform Specimens,” J. of the

Mechanics and Physics of Solids, Vol. 41, No. 1, 1993, pp. 143–181.

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Materials,” Experimental Mechanics, Vol. 34, 1994, pp. 1–9.

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26. Masumoto, H., and Tanaka, M.: “Ultra High Temperature In-Plane Biaxial Fatigue Testing System

with In-Situ Observation,” Ultra High Temperature Mechanical Testing, R.F. Lohr, and M. Steen,

Eds., Woodhead Publishing Limited, Cambridge, 1995, pp. 193–207.

27. Bartolotta, P.A., Ellis, J.R., and Abdul-Aziz, A.: “A Structural Test Facility for In-Plane Biaxial

Testing of Advanced Materials,” Multiaxial Fatigue and Deformation Testing Techniques, ASTM STP

1280, S. Kalluri and P.J. Bonacuse, Eds., American Society for Testing and Materials, 1997,

pp. 25–42.

28. Trautmann, K.-H., Maldfeld, E., and Nowack, H.: “Crack Propagation in Cruciform IMI 834 Specimens Under Variable Biaxial Loading,” Multiaxial Fatigue and Defonnation Testing Techniques,

ASTM STP 1280, S. Kalluri and P.J. Bonacuse, Eds., American Society for Testing and Materials,

1997, pp. 290–309.

29. Dalle Donne, C., and Doker, H.: “Plane Stress Crack Resistance Curves of an Inclined Crack Under

Biaxial Loading,” Multiaxial Fatigue and Deformation Testing Techniques, ASTM STP 1280,

S. Kalluri and P.J. Bonacuse, Eds., American Society for Testing and Materials, 1997, pp. 243–263.
Notes: (1) Values in brackets are % deviations about the mean; (2) Normalization of Von Mises equivalent

stress obtained using average gage section stress.

NASA/TM—2001-211134 16

TABLE I.—SUMMARY OF SPECIMEN TYPES AND OPTIMIZED SPECIMEN

DESIGNS

Specimen details Optimized specimen dimensions, mm

Design with

25.4 mm overall

thickness, and

14 mm slot

width 3.3 283

(±2.8%)

1 241 0.85 248 0.88 248 0.88

Specimen

type T1 T2 SLA SLB FR R1

3.2 305

(±2.4%)

1 253 0.83 248 0.81 249 0.82

2.1 1.524 6.35 35.56 36.45 40.64 44.45

3.1 316

(±2.6%)

1 293 0.93 293 0.93 272 0.86

2.2 1.524 6.35 30.48 30.78 50.80 44.45

Design with

19 mm overall

thickness, and

14 mm slot

width 2.3 317

(±2.0%)

1 268 0.85 270 0.85 297 0.94

2.2 352

(±1.9%)

1 288 0.82 271 0.77 299 0.85

Design with 19 mm

overall thickness, and

14 mm slot width 2.3 2.032 6.35 30.48 30.78 50.80 44.45

2.1 361

(±2.7%)

1 326 0.90 330 0.92 346 0.96

3.1 2.032 12.70 35.56 36.45 40.64 48.46

Specimen

details

Specimen

type

MPa Normalized MPa Normalized MPa Normalized MPa Normalized

Gage section,

average

Center slot,

maximum

Outer slot,

maximum

Fillet radius,

maximum

3.2 2.032 12.70 30.48 30.78 45.72 48.46

TABLE II.—SUMMARY OF STRESS RESULTS AT CRITICAL LOCATIONS FOR OPTIMIZED

SPECIMEN DESIGNS

Von Mises equivalent stress at location shown

Note: L1 = 80.65 mm and TR1 = 25.4 mm throughout.

Design with 25.4 mm

overall thickness, and

14 mm slot width 3.3 2.540 12.70 30.48 30.78 45.72 48.46
NASA/TM—2001-211134 17

TABLE III.—STRESS ANALYSIS RESULTS FOR THE YOKE GRIPPING

ARRANGEMENT

Coefficient

of friction

Bolt preload,

kN

Grip

displacement,

mm

Bolt load,

kN

Specimen

force,

kN

Maximum

yoke stress,

MPa

Maximum

finger stress,

MPa

0 5.816 0 450 (1) 718 (3)

0.152 5.790 12.725 450 (1) 763 (3)

0.254 6.016 17.298 519 (1) 830 (3)

–0.152 6.966 –14.140 411 (1) 826 (3)

0.1 5.816

(0.381 mm)(5)

–0.254 6.962 –23.000 394 (1) 909 (3)

0 31.600 0 692 (2) 1792 (4)

0.152 31.620 12.721 704 (2) 1772 (4)

0.2 31.60

(0.762mm)

0.254 31.620 21.760 709 (2) 1765 (4)

Note: (1) and (2) see figure 15 for maximum stress locations in yoke; (3) and (4) see figure 16

for maximum stress locations in finger; (5) corresponding bolt head displacement in mm.

TABLE IV.—STIFFNESS AND LOAD TRANSFER CHARACTERISTICS OF THE YOKE

GRIPPING ARRANGEMENT

Coefficient

of friction

Bolt preload,

kN

Maximum grip

displacement,

mm

Initial slope,

kN/mm

0.150 secant

modulus,

kN/mm

Limit of proportionality

load (kN)/displacement

(mm)

5.816 0.254 91.8 88.6 5.19/0.0559

(0.381 mm)(2) –0.254 92.8 90.3 5.36/0.0584

0.381 96.4 91.26 12.36/0.130

0.1

11.62

(0.762mm) –0.351 91.44 (1) (1)

0.2 31.64

(0.762mm)

0.254 93.93 92.15 11.04/0.119

Note: (1) discontinuities in the load versus displacement data prevented determination of these

values; (2) corresponding bolt head displacements in mm

TABLE V.—GRIP DISPLACEMENTS GIVING REQUIRED

COMBINATION OF STRESS RATIO (q) AND VON MISES

EQUIVALENT STRESS ( s ) AT CENTER OF GAGE SECTION

Stress Calculated values Finite element results

ratio,

q

sx,

MPa

sy,

MPa

Dx,

mm

Dy,

mm

sx,

MPa

sy,

MPa

s,

MPa

45.0 345 345 0.146329 0.146329 352 352 352

30.0 397 229 0.164821 0.100635 403 235 351

15.0 385 103 0.157353 0.049581 389 107 348

0 345 0 0.139167 0.007163 347 2 346

–22.5 274 –113 0.108153 –0.040107 272 –114 343

–45.0 199 –199 0.076225 –0.076225 195 –202 344

Note: sx, sy are target stress components at center of gage section.

Dx, Dy are corresponding grip displacements in the x, y directions.
NASA/TM—2001-211134 18

TABLE VI.—SUMMARY OF STRESS STATES IN GAGE AREA FOR GENERAL FORMS OF BIAXIAL

LOADING

Overall variation of

stress in gage area

Stress states along individual axes

X-axis Y-axis 45∞-axis

Stress

ratio,

Q Average,

MPa

Deviation,

percent Maximum,

MPa

Average,

MPa

Maximum,

MPa

Average,

MPa

Maximum,

MPa

Average,

MPa

Maximum overall

stress and location,

MPa

45.0 354 + 0.5 355 353 355 353 356 354 356 MPa at OD

on 45∞ axis

30.0 347 + 6.0 366 358 353 341 353 351 366 MPa, at OD

on X-axis

15.0 340 + 7.0 364 354 348 332 348 346 364 MPa at OD

on X-axis

0 336 + 6.0 356 349 347 331 343 343 356 MPa at OD

on X-axis

–22.5 332 + 3.0 343 342 343 332 343 341 343 MPa, 12.7 mm

from center on

X-axis

–45.0 336 + 3.0 344 336 344 336 344 341 344 MPa at center

of gage area

TABLE VII.—STRESS STATES AT CRITICAL SPECIMEN

LOCATIONS FOR GENERAL FORMS OF BIAXIAL

LOADING

Maximum stress values at locations shown

X-direction

slots

Y-direction

slots

Stress

ratio,

Q

Average

gage area

stress,

MPa

Fillet radius,

MPa

Center,

MPa

Outer,

MPa

Center,

 MPa

Outer,

MPa

45.0 354

(1.0)

316

(0.89)

289

(0.82)

291

(0.82)

289

(0.82)

291

(0.82)

30.0 347

(1.0)

292

(0.84)

292

(0.84)

298

(0.86)

232

(0.67)

230

(0.66)

15.0 340

(1.0)

234

(0.69)

255

(0.75)

263

(0.77)

153

(0.45)

148

(0.44)

0 336

(1.0)

193

(0.57)

206

(0.61)

215

(0.64)

81

(0.24)

75

(0.22)

–22.5 332

(1.0)

151

(0.45)

129

(0.38)

154

(0.46)

9

(0.03)

26

(0.08)

–45.0 336

(1.0)

105

(0.81)

63

(0.19)

88

(0.26)

76

(0.23)

86

(0.26)

Note: Values in brackets are normalized stresses obtained using

the average gage area stress.
NASA/TM—2001-211134 19

Gripped region,

typical 4 places

Flexures

Figure 1.—Current NASA specimen design.

Gage area
NASA/TM—2001-211134 20

Figure 2.—Proposed test setup using simplified specimen design and

 reusable fixturing.

432 mm square

Note: Attachment method not shown for simplicity of drawing.

Specimen

gage area,

76 mm dia.

229x229x6 mm

plate

Specimen

Slotted finger

attachment
NASA/TM—2001-211134 21

Finger,

typical

4 places

Note: All dimensions in millimeters.

Flexures,

2.5, typical

16 places

Gripped area

(152x38)

152

10, typical

3 places

19, typical

4 places

46

38

106

152

10

26

57

Figure 3.—Slotted finger attachment: Initial design.

19, typical

16 places

106

5, slot radius,

typical 12 places

10, slot,

typical 12

places

229

(Partial section

on centerline)

Thickness

transition

detail

229

R1

FR

SLB

SLA

SLB

6

TR1

T1

Note: All dimensions in millimeters.

Figure 4.—Conceptual specimen design with circular gage area.
NASA/TM—2001-211134 22

von Mises

equivalent

stress, MPa

6

45

84

123

163

202

241

280

319

358

397

Figure 5.—Stress distribution in assembly.
NASA/TM—2001-211134 23

Figure 6.—Stress distribution in specimen.

Outer slot

Outer slot

Gage area Center slot

Fillet region

Center slot von Mises

equivalent

stress, MPa

6

45

84

124

163

202

241

280

319

358

397
NASA/TM—2001-211134 24

Figure 7.—Determination of optimum value of outer slot length.

von Mises equivalent stress, MPa

1000

900

800

600

500

700

400

300

200

100

35 55 40 45 50

Outer slot length, mm

Center slot

Outer slot

Fillet radius

Gage section Average von Mises

equivalent stress

Maximum von Mises

equivalent stress

Center slot length 35.50 mm

Fillet radius 25.50 mm

Gage area thickness 1.25 mm

Optimum value = 37.00 mm
NASA/TM—2001-211134 25

Figure 8.—Determination of optimum value of fillet radius.

von Mises equivalent stress, MPa

700

600

500

300

400

800

20 40 25 30 35

Fillet radius, mm

Minimum feasible

value = 26.9 mm Optimum value = 27.94 mm

Center slot

Fillet radius

Outer slot

Gage section Average von Mises

equivalent stress

Maximum von Mises

equivalent stress

Center slot length 35.50 mm

Outer slot length 37.00 mm

Gage area thickness 1.25 mm
NASA/TM—2001-211134 26

16, typical

16 places

106, typical

4 places

7, slot radius,

typical 12

places

14, slot,

typical 12

places

229, typical 2 places

R1

FR

SLB

SLA

SLB

Note: All dimensions in millimeters.

Figure 9.—Final specimen design with circular gage area: Plan view.
NASA/TM—2001-211134 27

Figure 10.—Final specimen design with

 circular gage area: Partial section on

 centerline.

T1

T2

TR1

13 mm, blend

radius, typical

2 places

2.5 mm, typical

2 places

8° 00' ± 0° 15',

typical 2 places

T0

49 mm

L1
NASA/TM—2001-211134 28

Figure 11.—Slotted finger attachment: Plan view.

152

152

14, typical

3 places

16, typical

4 places

37

106

41

Mounting plate

Slots are 2.50

wide with 1.25

radii at each end

Slotted

finger

Note: All dimensions in millimeters.
NASA/TM—2001-211134 29

Figure 12.—Slotted finger attachment: Side view.

Preload

bracket

33

9.5

152

34

9.5

7° 30' ± 0° 15',

typical 2 places

Mounting plate

Flat and

undercut,

typical 2

places

Slotted fingers

Note: All dimensions in millimeters.
NASA/TM—2001-211134 30

Figure 13.—Yoke gripping arrangement and setup for evaluation under axial

 loading.

Note: Taper angle on yoke = 7° 00' ± 0° 15'.

Preload bolt

Uniaxial specimen

Yoke

Top view

Side view

Water cooling

56 mm

27.5 mm

89 mm
NASA/TM—2001-211134 31

Figure 14.—Prototype fixturing in partially disassembled form.

Figure 15.—Prototype fixturing in assembled form.
NASA/TM—2001-211134 32

View on mid

section

Location

(2)

Location (1)

Note: Assumed coefficient of friction = 0.2 and grip displacement = 0.

von Mises

equivalent

stress, MPa

539

3

79

156

232

309

386

462

615

692

Figure 16.—Stress distribution in central section of yoke for 31.6 kN bolt pre-

 load.
NASA/TM—2001-211134 33

Figure 17—Stress distribution in tapered section of finger for 31.6 kN bolt pre-

 load.

Note: Assumed coefficient of friction = 0.2 and grip displacement = 0.

von Mises

equivalent

stress, MPa

5

203

402

600

799

998

1196

1394

1593

1792 Location (4)

Location (3)
NASA/TM—2001-211134 34 Specimen load, kN

4.5

0

–4.5

–13.5

–9.0

–18.0

–22.5

9.0

Secant modulus

= 90.33

Secant modulus

= 88.6

Initial slope = 92.8

Initial slope = 91.8

0.150

0.150

13.55

13.29

C

A

B

13.5

18.0

22.5

–25 20 25

Grip displacement, mm x10–2

Note: Assumed coefficient of friction = 0.1 and bolt preload = 5.816 kN.

–20 –15 –10 –5 0 5 10 15

Figure 18.—Stiffness and load transfer characteristics under tensile and compressive

 loading.
NASA/TM—2001-211134 35

Figure 19.—Specimen design with square gage area: Plan view.

16, typical

16 places

106, typical

4 places

7, slot radius

typical 12

places

14, slot

typical 12

places

229, typical 2 places

25.4

88.9

FR

SLB

SLA

SLB

Note: All dimensions in millimeters.
NASA/TM—2001-211134 36

Figure 20.—Specimen design with square gage

 area: Partial section on centerline.

Note: All dimensions in millimeters.

13.0, blend

radius typical

2 places

2.54, typical

2 places

8° 00' ± 0° 15'

typical 2 places

19.1

49.0

80.65

1.524

25.4

6.35
NASA/TM—2001-211134 37

Figure 21.—Specimen design with two-step square gage area: Plan view.

16, typical

16 places

106, typical

4 places

7, slot radius

typical 12

places

14, slot

typical 12

places

229, typical 2 places

25.4 19.1

88.9

64.0

FR

SLB

SLA

SLB

Note: All dimensions in millimeters.
NASA/TM—2001-211134 38

Figure 22.—Specimen design with two-step circular gage area: Plan view.

16, typical

16 places

106, typical

4 places

7, slot radius

typical 12

places

14, slot

typical 12

places

229, typical 2 places

FR

44.45

32.0

SLB

SLA

SLB

Note: All dimensions in millimeters.
NASA/TM—2001-211134 39

Figure 23.—Specimen design with two-step gage

 areas: Partial section on centerline.

Note: All dimensions in millimeters.

13, blend

radius typical

2 places

2.54, typical

2 places

8° 00' ± 0° 15'

typical 2 places

19.1

49.0

76.40

86.69

1.524

2.946

6.350

12.7

12.7
NASA/TM—2001-211134 40

Figure 24.—Stress ratios () used to investigate general forms of biaxial

 loading.

–45°

–22.5°

15°

30°

45°

y

x



6

1

5

4

3

2

Major axis

Minor axis

Where von Mises equivalent stress ()

 = (x

2 – x y + y2)

1/2 = 345 MPa

and stress ratio ()

 = tan–1 (y/x)
NASA/TM—2001-211134 41

Figure 25.—Stress distribution in specimen gage area: Stress ratio () = 45°.

von Mises

equivalent

stress, MPa

347

347

348

349

350

351

352

352

353

354

355

x

y

z
NASA/TM—2001-211134 42

Figure 26.—Stress distribution in specimen gage area: Stress ratio () = 30°.

x

y

z

von Mises

equivalent

stress, MPa

327

331

335

339

343

347

350

354

358

362

366
NASA/TM—2001-211134 43

Figure 27.—Stress distribution in specimen gage area: Stress ratio () = 15°.

x

y

z

von Mises

equivalent

stress, MPa

316

321

326

330

335

340

345

349

354

359

364
NASA/TM—2001-211134 44

Figure 28.—Stress distribution in specimen gage area: Stress ratio () = 0°.

x

y

z

von Mises

equivalent

stress, MPa

314

319

323

327

331

335

339

343

348

352

356
NASA/TM—2001-211134 45

Figure 29.—Stress distribution in specimen gage area: Stress ratio () = –22.5°.

x

y

z

von Mises

equivalent

stress, MPa

320

323

325

327

329

332

334

336

338

341

343
NASA/TM—2001-211134 46

Figure 30.—Stress distribution in specimen gage area: Stress ratio () = –45°.

x

y

z

von Mises

equivalent

stress, MPa

328

329

331

332

334

335

337

339

340

342

343
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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October 2001

NASA TM—2001-211134

E–12873

WU–708–31–13–00

52

Specimens and Reusable Fixturing for Testing Advanced Aeropropulsion

Materials Under In-Plane Biaxial Loading

Part 1—Results of Conceptual Design Study

J.R. Ellis, G.S. Sandlass, and M. Bayyari

In-plane biaxial testing; Advanced aeropropulsion materials; Cruciform specimen design;

Reusable fixturing; Finite element analysis; Optimization techniques; Attachment methods;

Prototype fixturing

Unclassified -Unlimited

Subject Category: 24 Distribution: Nonstandard

J.R. Ellis, NASA Glenn Research Center; G.S. Sandlass, MTS Systems Corporation, Eden Prairie, Minnesota 55344; and

M. Bayyari, Research Applications, Inc., San Diego, California 92121. Responsible person, J.R. Ellis, organization code

5920, 216–433–3340.

A design study was undertaken to investigate the feasibility of using simple specimen designs and reusable fixturing for in-plane

biaxial tests planned for advanced aeropropulsion materials. Materials of interest in this work include: advanced metallics, polymeric

matrix composites, metal and intermetallic matrix composites, and ceramic matrix composites. Early experience with advanced

metallics showed that the cruciform specimen design typically used in this type of testing was impractical for these materials,

primarily because of concerns regarding complexity and cost. The objective of this research was to develop specimen designs,

fixturing, and procedures which would allow in-plane biaxial tests to be conducted on a wide range of aeropropulsion materials while

at the same time keeping costs within acceptable limits. With this goal in mind, a conceptual design was developed centered on a

specimen incorporating a relatively simple arrangement of slots and fingers for attachment and loading purposes. The ANSYS finite

element code was used to demonstrate the feasibility of the approach and also to develop a number of optimized specimen designs.

The same computer code was used to develop the reusable fixturing needed to position and grip the specimens in the load frame. The

design adopted uses an assembly of slotted fingers which can be reconfigured as necessary to obtain optimum biaxial stress states in

the specimen gage area. Most recently, prototype fixturing was manufactured and is being evaluated over a range of uniaxial and

biaxial loading conditions.