Biaxial Tensile Strength Test for Brittle Rectangular Plates

Abstract

Fig. 1. Schematic sketches of the situation in a B3B test of a rectangular plate: a section of the system and b sketch of the top view. 1: specimen, 2: supporting balls, 3: loading ball, 4: die and 5: manifold guide. The dotted circle connects the contact points between supporting balls and specimen and represents the support radius R a . Note that the size of the balls is only a little smaller than the width of the plate. A new biaxial tensile strength test ball on three balls test, B3B-test for brittle materials has been proposed by some of the authors several years ago. A disc-shaped plate is symmetrically supported by three balls at one plane and loaded by a fourth ball in the centre of the opposite plane. This new test has several advantages compared to conventional bending tests or other biaxial strength tests, especially the well defined load transfer geometry and a high tolerance against measurement uncertainties. This makes the testing of as-sintered slightly buckled specimens possible. In the past years the test has proved to be very practicable to test as-sintered disc specimens as well as as-sintered specimens which are shaped like a disc. Although discs areâin principleâeasy to produce, in some cases it is more convenient to produce specimens having the shape of rectangular plates. Also many components have the shape of rectangular plates. Therefore, in this paper, the B3B-test is extended to test specimens which are that shape. An FE analysis of the stress fields in the specimens is performed and the maximum tensile stress amplitude and the effective volume in the specimens are determined. Specimens of different size and of several advanced ceramic materials were tested. It is shown that there exists a size effect on strength which can be explained in the framework of the Weibull theory. The B3B strength data determined on rectangular plate specimens fit to tests results determined on disc specimens and to conventional bending test results. The smallest tested specimen had a volume of some tenth of a cubic millimetre. To demonstrate the practicability of the method a strength distribution of an electroceramic component is determined by testing 494 individual rectangular B3B test specimens.

Fracture of Ceramics

“…The data are nicely arranged around a straight line, which indicates the Weibull behaviour of the material (for details of the data evaluation see Ref. [62] …”

“…Details can be found in the literature. [62] For example, as shown in the noteworthy paper of Jayatilaka et al [67] the Weibull modulus only depends on the slope of the crack size frequency distribution: m = 2 (p-1).…”

“…19 and Figure 11 it can be seen that several 1000 strength tests would be needed to experimentally detect a difference between a Weibull and a Gaussian distribution curve. [62,95] This effort exceeds the possibilities of any research laboratory. But the theoretical arguments given at the beginning of Section 5 tell us that a Weibull distribution is more appropriate to describe the strength data of brittle materials than a Gaussian distribution.…”

Influence of the geometry of ceramic specimens on biaxial flexural strength: experimental testing and finite element analysis

“…A good agreement between biaxial strength values has been reported for circular-and square-shaped specimens tested in different configurations, such as ball-on-threeballs [8,14] and ball-on-ring-of-balls [15]. In these studies, to calculate the strength of plate specimens, mathematical adaptations were performed in the formulations standardized for disc specimens.…”

“…Therefore, it is not recommended comparison between different specimen geometries in the same study. Future studies should focus on adaptations on the ISO 6872:2008 formula to calculate the biaxial strength of square and rectangular plate specimens, such as the formula existing for ball-on-three-balls test [14].…”