Biaxial testing apparatus

A new apparatus and method for applying a biaxial load to a flat plate test specimen is disclosed. A rhombus-shaped four-bar linkage is attached at one vertex to a fixed attachment point and a uniaxial tensile force is applied to the opposite vertex. The test specimen is placed inside the four-bar linkage and is attached to the four bar linkage by load transfer members connected at one end to the links of the four bar linkage and at their other end to grips holding the test specimen. In one embodiment, load transfer members parallel to the applied uniaxial tensile force are attached to test specimen grips adjacent to the link attachment points of the load transfer members and perpendicular load transfer members are attached to test specimen grips opposite their link attachment points. Application of the uniaxial tensile force then produces a biaxial tensile force in the test specimen. By attaching all load transfer members to test specimen grips adjacent to their link attachment points, a biaxial stress state tensile in one direction and compressive in a perpendicular direction can be accomplished.

BACKGROUND OF THE INVENTION 
The present invention relates generally to testing apparatus, and more 
specifically to apparatus and methods for applying a biaxial load to a 
flat test specimen. 
Prior art methods for applying a biaxial load to a test specimen require 
either two or more separate actuators, complex specimen configurations, or 
pressurization techniques. A common method for creating a biaxial stress 
state requires a loading apparatus having two orthogonally mounted 
actuators. A specimen is attached to the two actuators to produce loads 
along two orthogonal axes. A particular disadvantage of this approach is 
the high cost of the equipment, which often must be custom made. 
A cruciform, or cross-shaped, specimen has also been used in the biaxial 
stress testing prior art. The orthogonal arms of the cruciform are both 
put under a tensile load with the central portion of the intersecting 
region being the test area undergoing a biaxial stress. The disadvantages 
of this method are that two or more loading devices are required and 
excess material and fabrication time are required for the specimen 
compared to a straightforward flat plate. 
Another prior art method for biaxial loading is pressurizing the inside 
surface of a cylindrical specimen and applying compressive loads to the 
end of the specimen. One disadvantage of this method is that the specimen 
must be cylindrical, requiring more material and fabricating time than a 
simple flat plate specimen. Another disadvantage is the high cost of the 
equipment necessary to pressurize the cylinder. 
Thus it is seen that there is a need for a simple, straightforward 
apparatus and method for applying a biaxial stress to a flat plate test 
specimen. 
It is, therefore, a principal object of the present invention to provide 
such a simple and straightforward apparatus and method. 
It is a feature of the present invention that it is compatible with 
conventional uniaxial test equipment. 
It is an advantage of the present invention that it is inexpensive to make, 
to use and to fabricate test specimens. 
It is another advantage of the present invention that it allows a wide 
variety of load combinations. 
These and other objects, features and advantages of the present invention 
will become apparent as the description of certain representative 
embodiments proceeds. 
SUMMARY OF THE INVENTION 
In accordance with the foregoing principles and objects of the present 
invention, a novel apparatus and method for applying a biaxial stress to a 
flat plate test specimen is described. The unique discovery of the present 
invention is that a uniaxial tensile load can be converted to a biaxial 
stress state on a flat plate test specimen by use of load transfer members 
attached at one of each of their ends to respective links of a four-bar 
linkage and at their other ends to a flat plate test specimen enclosed by 
the four-bar linkage. By choosing the lengths of the load transfer members 
so that they either attach directly to adjacent sides of the test 
specimen, or overlap the test specimen to attach to opposite sides of the 
test specimen, a biaxial load will be applied to a test specimen that, 
depending on the selection of attachment points on the test specimen, may 
be compressive in two perpendicular directions, tensile in two 
perpendicular directions or compressive in one direction and tensile in a 
perpendicular direction. By varying the attachment locations of the load 
transfer members on the links of the four-bar linkage, different ratios 
between the horizontal and vertical components of a stress tensor can be 
achieved. 
Accordingly, the present invention is directed to a test apparatus for 
applying a biaxial load to a test specimen, comprising a four-bar linkage 
for enclosing the test specimen, the four-bar linkage having a first, 
second, third and fourth vertex, a first link between the first and second 
vertices, a second link between the second and third vertices, a third 
link between the third and fourth vertices, and a fourth link between the 
fourth and first vertices, and a pair of load transfer members attached at 
respective first ends to the first and second links, a second pair of load 
transfer members opposing the first pair of load transfer members and 
attached at respective first ends to the third and fourth links, a third 
pair of load transfer members attached at respective first ends to the 
fourth and first links, and a fourth pair of load transfer members 
opposing the third pair of load transfer members and attached at 
respective first ends to the second and third links. The four-bar linkage 
may form a rhombus. The respective lengths for the first, second, third 
and fourth load transfer members may be such that the first and second 
pairs of load transfer members attach at respective second ends to sides 
of the test specimen adjacent to the point of attachment of the first ends 
of said pairs of load transfer members, and the third and fourth pairs of 
load transfer members attach at respective second ends to sides of the 
test specimen opposite the point of attachment of the first ends of said 
pairs of load transfer members. The respective lengths for the first, 
second, third and fourth load transfer members may also be such that the 
first and second pairs of load transfer members attach at respective 
second ends to sides of the test specimen adjacent to the point of 
attachment of the first ends of said pairs of load transfer members, and 
the third and fourth pairs of load transfer members attached at respective 
second ends to sides of the test specimen adjacent to the point of 
attachment of the first ends of said pairs of load transfer members. 
The present invention is also directed to a method for applying a biaxial 
load to a test specimen, comprising the steps of enclosing the test 
specimen inside a four-bar linkage, wherein the four-bar linkage has a 
first, second, third and fourth vertex, a first link between the first and 
second vertices, a second link between the second and third vertices, a 
third link between the third and fourth vertices, and a fourth link 
between the fourth and first vertices, attaching each of four sides of the 
test specimen to, respectively, a first pair of load transfer members 
attached at respective first ends to the first and second links, a second 
pair of load transfer members opposing the first load transfer member and 
attached at respective first ends to the third and fourth links, a third 
pair of load transfer members attached at respective first ends to the 
fourth and first links, and a fourth pair of load transfer members 
opposing the third pair of load transfer members and attached at 
respective first ends to the second and third links, attaching the first 
and second pair of load transfer members at respective second ends to 
sides of the test specimen adjacent to the point of attachment of the 
first ends of said pair of load transfer members, attaching the third and 
fourth pair of load transfer members at respective second ends to sides of 
the test specimen opposite the point of attachment of the first ends of 
said pair of load transfer members, and while holding the first vertex in 
a fixed position, applying a uniaxial force to the third vertex in a 
direction opposite from the first vertex. The four-bar linkage may form a 
rhombus. 
The present invention is further directed to a method for applying a 
biaxial load to a test specimen, comprising the steps of enclosing the 
test specimen inside a four-bar linkage, wherein the four-bar linkage has 
a first, second, third and fourth vertex, a first link between the first 
and second vertices, a second link between the second and third vertices, 
a third link between the third and fourth vertices, and a fourth link 
between the fourth and first vertices, attaching each of four sides of the 
test specimen to, respectively, a first pair of load transfer members 
attached at respective first ends to the first and second links, a second 
pair of load transfer members opposing the first load transfer member and 
attached at respective first ends to the third and fourth links, a third 
pair of load transfer members attached at respective first ends to the 
fourth and first links, and a fourth pair of load transfer members 
opposing the third pair of load transfer members and attached at 
respective first ends to the second and third links, attaching the first 
and second pair of load transfer members at respective second ends to 
sides of the test specimen adjacent to the point of attachment of the 
first ends of said pair of load transfer members, attaching the third and 
fourth pair of load transfer members at respective second ends to sides of 
the test specimen adjacent to the point of attachment of the first ends of 
said pair of load transfer members, and while holding the first vertex in 
a fixed position, applying a uniaxial force to the third vertex in a 
direction opposite from the first vertex. 
The present invention is still further directed to a method for applying a 
biaxial load to a test specimen, comprising the steps of enclosing the 
test specimen inside a four-bar linkage, wherein the four-bar linkage has 
a first, second, third and fourth vertex, a first link between the first 
and second vertices, a second link between the second and third vertices, 
a third link between the third and fourth vertices, and a fourth link 
between the fourth and first vertices, attaching each of four sides of the 
test specimen to, respectively, a first pair of load transfer members 
attached at respective first ends to the first and second links, a second 
pair of load transfer members opposing the first load transfer member and 
attached at respective first ends to the third and fourth links, a third 
pair of load transfer members attached at respective first ends to the 
fourth and first links, and a fourth pair of load transfer members 
opposing the third pair of load transfer members and attached at 
respective first ends to the second and third links, attaching the first 
and second pair of load transfer members at respective second ends to 
sides of the test specimen opposite the point of attachment of the first 
ends of said pair of load transfer members, attaching the third and fourth 
pair of load transfer members at respective second ends to sides of the 
test specimen opposite the point of attachment of the first ends of said 
pair of load transfer members, and while holding the first vertex in a 
fixed position, applying a uniaxial force to the third vertex in a 
direction opposite from the first vertex.

DETAILED DESCRIPTION 
Referring now to FIG. 1 of the drawings, there is shown a schematic view of 
a four-bar linkage 10 and associated load transfer members 12 and 14 
attached to a set of grips 16 and 18 holding a flat plate test specimen 
20. The main structure of the invention is four-bar linkage 10. Four-bar 
linkage 10 is attached at a vertex 22 to a rigid attachment point 23. A 
tensile force 26 is applied to a vertex 24 opposite vertex 22 to actuate 
four-bar linkage 10 and apply a load to test specimen 20. 
Four load transfer members 12 are pinned at one of their ends to four-bar 
linkage 10 as shown in FIG. 1. The other ends of load transfer members 12 
are attached to adjacent grips 16 to uniformly distribute a tensile load 
to the specimen. The other four load transfer members 14 are pinned to 
four-bar linkage 10 as shown and their other ends are attached to 
respective grips 18 on the opposite sides of flat plate specimen 20 from 
the four-bar linkage attachment points. 
In this preferred embodiment, four-bar linkage 10 is a rhombus. Flat plate 
test specimen 20 is oriented so that an imaginary line passing through 
opposite vertices of four-bar linkage 10 will bisect the four sides of 
specimen 20. 
This attachment arrangement converts vertical tensile force 26 into a 
biaxial tensile load in specimen 20. The location of vertical load 
transfer members 12 and horizontal load transfer members 14 with respect 
to their attachment points on four-bar linkage 10 determine the ratio 
between the horizontal and vertical components of the resulting stress in 
test specimen 10. 
An alternative mode of the invention is to connect each horizontal load 
transfer member 14 to its respective adjacent specimen grip 18 rather than 
to its respective opposite specimen grip 18. In this configuration, a 
tension-compression stress state will be applied to flat plate specimen 
20. Similarly, the stress state can be made compression-compression by 
then connecting each vertical load transfer member 12 to its respective 
opposite specimen grip 16 instead of to its respective adjacent specimen 
grip 16. Varying the connection point locations of the load transfer 
members with respect to linkage 10 will produce a range of ratios between 
the horizontal and vertical components of the stress tensor. This will 
allow all four quadrants of the biaxial stress tensor to be defined. 
FIG. 2 is a plan view of a flat plate test specimen 28 showing an example 
set of grips 30 and 32 for attaching load transfer members to test 
specimen 28. Grips 30 and 32 each comprise a pair of grip sides on top and 
bottom sides of test specimen 28 to sandwich test specimen 28 and hold it 
in place with multiple staggered pins 34. The stress concentrations caused 
by pins 34 will be small far from the pin locations, most importantly in 
the center of specimen 28. Grips 30 and 32 are but one means for attaching 
load transfer members to a test specimen. One alternative method would be 
to use a scissors-type gripping mechanism to produce a more uniformly 
strained specimen. 
The load transfer members do not need to be in pairs, but may be made as 
single units or as multi-arm units, both as functional equivalents to the 
described paired load transfer members. For example, the described load 
transfer member pairs may, depending on the exact manner in which they 
connect to the grips, need to comprise four arms, two each for the top and 
bottom of a test specimen, so that they do not impart a twist to the test 
specimen. The use of multi-arm load transfer members, however, is 
preferred because it allows for relative angular movement among the load 
transfer member arms. The use of a single unit load transfer member may be 
expected to be limited to precise positioning of the connection points of 
each load transfer member so that relative angular movement will not 
occur. Using multi-arm load transfer members permits a greater variety of 
configurations. Those of ordinary skill in the art will readily see other 
methods for attaching load transfer members to the grips. The term load 
transfer member as used in the claims, therefore, includes load transfer 
members of one or more arms and load transfer members of other 
configurations as might occur to one of skill in the art. 
The disclosed biaxial testing apparatus and method successfully demonstrate 
the advantages of using a straightforward four-bar linkage as the 
actuating mechanism for applying a biaxial load to a test specimen. 
Although the disclosed invention is specialized, its teachings will find 
application in other areas where overly complex mechanisms are currently 
used for movement and force application. 
Those with skill in the art of the invention will readily see other 
possible embodiments for the described invention. For example, the load 
transfer members may be connected directly to a test specimen. Although 
not recommended, such an arrangement will still take advantage of the 
teachings of the present invention. As used in the claims, therefore, any 
attachment to the sides of a test specimen is understood to include 
attachment by grips, as related in this description, by grips other than 
as described, by means for attaching other than grips, or by direct 
attachment to a test specimen. It is further understood, therefore, that 
modifications to the invention may be made, as might occur to one with 
skill in the field of this invention, within the scope of the appended 
claims. All embodiments contemplated have not been shown in complete 
detail. Other embodiments may be developed without departing from the 
spirit of this invention or from the scope of the claims.