Page 69 - Handbook of Properties of Textile and Technical Fibres

50 Handbook of Properties of Textile and Technical Fibres

where d is the fiber diameter and R m is the minimum radius of curvature at the location
where the first kink band is seen. R m can be obtained either graphically from the
minimum radius of the circle drawn into the loop or from equations of elastica;

2
R m ¼ Y=4; Y ¼ 4EI=T (2.20)
where Y is the distance from the arm to the bottom of the loop, E the elastic modulus, I
the moment of inertia, and T the tension in the fiber.

2.5 High temperature characterization

2.5.1 Loop test for high temperature evaluation
A variation of the above loop test has been developed and used, above all, for evalu-
ating the time-dependent properties of ceramic fibers at very high temperatures.

Although such fibers are elastic and brittle at temperatures, usually up to 1000 C,
they are candidates as reinforcements in composite structures, which will experience
much higher temperatures and creep has been shown to be a major factor to be consid-
ered (Di Carlo, 1977; Morscher and Di Carlo, 1992). An evaluation of the resistance to
creep is given by the bend stress relaxation observed when the fibers are bent into a loop
and then heated to high temperatures. If the fiber remains elastic it returns to its original
straight form after such a test, whereas if relaxation occurs a residual curvature is seen.
The curvature allows the creep resistance of different fibers to be classed.
An initial elastic bend strain is imposed on the fiber by forming it into a loop or by
placing it between cylindrical male and female ceramic forms, as shown in Fig. 2.20.
The initial stress s o and strain ε o vary within the fiber by the relations s o ¼ Eε o and
ε o ¼ z/R o , where E is the Young’s modulus of the fiber, z is the distance from the fiber
axis in the plane of the loop (0 z d/2), and R o is the loop radius. The fiber is then
heated, usually in an inert atmosphere and if relaxation occurs, on cooling back to
room temperature a residual curvature, R a , will be observed that will decrease with
time. If no relaxation has occurred and the fiber has behaved in a purely elastic fashion,
R a will be infinity. A relaxation factor, m, has been defined as:

mðt; TÞ¼ 1 R o =R a (2.21)
where m ¼ 0, if the fiber is completely relaxed and m ¼ 1, if no relaxation occurs and
the fiber has remained perfectly elastic during the test.
This technique has proved to be a valuable method for classifying the creep resis-
tance of many ceramic fibers from whiskers of only 1-mm diameter to large diameter
ceramic fibers.

2.5.2 High-temperature tensile and creep tests

The universal fiber tester, with a furnace positioned between the jaws, described above
for tensile and fatigue tests, can also be used for evaluating high-performance fibers at