PSI - Issue 42

Christos F. Markides et al. / Procedia Structural Integrity 42 (2022) 202–209 Stavros K. Kourkoulis and Christos F. Markides et al. / Structural Integrity Procedia 00 (2022) 000 – 000

207

6

As a next step, and taking advantage of the expressions for the components of the displacement field, the de formed shape of the CTBD is plotted in Fig.5c. In order for the deformed CTBD to be clearly visible, it was as sumed that E 1 =3.2 GPa, ν 1 =0.36, and P frame =40 kN. 3.2 Comparative results with other tests For the same numerical data adopted to plot Figs.5(a, b), the magnitudes of the highest contact stresses on the loaded rim, and the hoop stresses at the center of the disc, are shown in next Fig.6 for the BD test, according to the ASTM (Fig.6a) and the ISRM standards (Fig.6b), the FBD test under non-uniformly distributed boundary stresses (Markides and Kourkoulis 2022) (Fig.6c) and for the CTBD introduced here (Fig.6d). As it is seen from the compar ative consideration of Fig.6, the CTBD causes the weakest stress severity along the contact rim, because of the longest contact length. Most important is the fact that the CTBD test provides a value for the tensile strength, σ t , of the material tested (represented by the hoop stress σ x at the disc’s center for the assumed fracture load P frame =15 kN) equal to 9.47 MPa, very close to the respective value provided by Hondros’ familiar formula σ t = P frame /( π Rt)=9.55 MPa.

766.93MPa

442.79MPa

ISRM

ASTM

o 5.82

o 3.36

BD

BD

9.53MPa

9.54MPa

(a)

(b)

86.47MPa

Indenter

2 R

318.15MPa ( 15) n =

117.07MPa

o 149.77

o 22.26

o 22.26

o 1.40

CTBD

FBD

15.00MPa

(c)

(d)

9.47MPa

Fig. 6. The BD test according to: (a) ASTM, (b) ISRM; (c) The FBD test under non-uniform distribution of pressure; (d) The CTBD test.

3.3 The role of the materials’ stiffness and of the geometry Using again numerical data from section 3.1 for the stresses, the dependence of the CTBD test results on the stiff ness of the material and the geometry is revealed by considering Tables 1(a, b, c). More specifically in Table 1a, six fictitious materials with Young’s moduli E 1 varying in the range from 10 to 110 GPa are considered. It is definitely concluded that the test results are more or less insensitive to the material ’ s stiffness. This behaviour is attributed to the fact that the contact length in case of CTBD is constant and predefined (contrary to the contact length in case of other indirect tests in which the contact length is an increasing function of the externally applied load). Regarding the role of the cavity’s radius R 1 , it is seen from Table 1b that it can be always fixed to reasonable val ues in the range between R/5 and R/6, so that the value provided by the CTBD test for the tensile strength to be close enough to that provided by Hondros’ solution, for relatively low values of P c . The latter is quite important since it prevents premature fracture of the disc in the immediate vicinity of the disc-loading device contact region. Similar conclusions are drawn from Table 1c, with regard to the distance h of the cavity from the disc’s center. It is clearly concluded tha t the “reference” configuration, i.e., the one with E 1 =50 GPa, R 1 = R /5, h =5 R /6 (shown in red