9.6 Annex to the Brazilian Test
95
Then from formulas (9.30) and (9.32), we find
) = −
1
2πiζ 2
γ
(N − iT )dσ
σ − ζ
−
(ζ )
ζ
+
(ζ )
ζ 2 +
a 0
ζ 2 .
(9.33)
9.6 Annex to the Brazilian Test
Problem Statement Direct uniaxial compression tests of non-metallic brittle
materials are related to the technical problem of application of elongating axial
forces to the specimen. This problem is solved by the termination of specimen
ends in special lugs using epoxy [7] or other adhesive materials, Wood’s alloy [11]
equipping specimen with such devices makes experiments much more expensive
and in fact prevents mass or prompt testing.
For this reasons, an indirect method to determine the material elongation
resistance proposed in 1947 by the Brazilian engineer F. Carneiro [10] is widely
used in materials science and production. The method consists in that the material
elongation strength is determined by a test of a cylindrical specimen for compression along a diametric plane evenly distributed along the generatrix by the load
transmitted by a triangle prism rib. Tests in scientific publications were named
the Brazilian test or Brazilian method. Regulatory documents (state standards,
departmental instructions, etc.) call the Brazilian test as the “cleavage test.”
Hertz Solution Standards for testing specimens of carbonic materials [4], concretes [1], and some other materials define the diametric compression of a cylindrical specimen under the scheme given in Fig. 9.3a. If we assume the specimen
material to be elastic until destruction, for this scheme we have a problem of plane
strain of a cylinder loaded by two diametrically opposite forces P (Fig. 9.4a).
It is known [9] that the solution to this problem was given by H. Hertz in 1883.
Let us write the Muskhelishvili functions representing the solution to this problem
as follows: 1 must be before the third addend in brackets
) = −
p
2πR
1
1 − ζ
+
1
1 + ζ
− 1
,
(ζ ) =
p
2πR
1
1 − ζ
+
1
1 + ζ
+
1
(1 − ζ ) 2 +
1
(1 + ζ ) 2
,
(9.34)
where p = P /l is the loads per unit length l of the generatrix of the compressed
cylindrical specimen with a radius R.
1 There is a misprint in the formula for the function on page 298 of the paper [9] that we used to
obtain formulas (9.34): the sign «+».
95
Then from formulas (9.30) and (9.32), we find
) = −
1
2πiζ 2
γ
(N − iT )dσ
σ − ζ
−
(ζ )
ζ
+
(ζ )
ζ 2 +
a 0
ζ 2 .
(9.33)
9.6 Annex to the Brazilian Test
Problem Statement Direct uniaxial compression tests of non-metallic brittle
materials are related to the technical problem of application of elongating axial
forces to the specimen. This problem is solved by the termination of specimen
ends in special lugs using epoxy [7] or other adhesive materials, Wood’s alloy [11]
equipping specimen with such devices makes experiments much more expensive
and in fact prevents mass or prompt testing.
For this reasons, an indirect method to determine the material elongation
resistance proposed in 1947 by the Brazilian engineer F. Carneiro [10] is widely
used in materials science and production. The method consists in that the material
elongation strength is determined by a test of a cylindrical specimen for compression along a diametric plane evenly distributed along the generatrix by the load
transmitted by a triangle prism rib. Tests in scientific publications were named
the Brazilian test or Brazilian method. Regulatory documents (state standards,
departmental instructions, etc.) call the Brazilian test as the “cleavage test.”
Hertz Solution Standards for testing specimens of carbonic materials [4], concretes [1], and some other materials define the diametric compression of a cylindrical specimen under the scheme given in Fig. 9.3a. If we assume the specimen
material to be elastic until destruction, for this scheme we have a problem of plane
strain of a cylinder loaded by two diametrically opposite forces P (Fig. 9.4a).
It is known [9] that the solution to this problem was given by H. Hertz in 1883.
Let us write the Muskhelishvili functions representing the solution to this problem
as follows: 1 must be before the third addend in brackets
) = −
p
2πR
1
1 − ζ
+
1
1 + ζ
− 1
,
(ζ ) =
p
2πR
1
1 − ζ
+
1
1 + ζ
+
1
(1 − ζ ) 2 +
1
(1 + ζ ) 2
,
(9.34)
where p = P /l is the loads per unit length l of the generatrix of the compressed
cylindrical specimen with a radius R.
1 There is a misprint in the formula for the function on page 298 of the paper [9] that we used to
obtain formulas (9.34): the sign «+».