PSI - Issue 50

Andrey Yu. Fedorov et al. / Procedia Structural Integrity 50 (2023) 83–90 A.Yu. Fedorov et al. / Structural Integrity Procedia 00 (2023) 000–000

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Since γ 1 + γ 2 = 2 π , it follows from equation (1) that the eigenvalues depend on the magnitude of one of the angles and the mechanical characteristics of materials ν 1 , ν 2 , G 2 / G 1 . In the space of these parameters (angle and mechanical characteristics of materials) the boundary between the solutions with and without stress singularity can be found using equation (1). The boundary values of the Poisson’s ratios of the filling material determined for a symmetrical stress state with respect to the bisector of the closed wedge angle define the boundary between singular and non-singular solutions. The study was conducted for the values of the opening angle of the part of the wedge simulating the filling material in the range from 5 ◦ to15 ◦ at ratios of elastic moduli E 2 / E 1 of 10, 100, 1000 and Poisson’s ratio ν 2 ranging from 0 to 0.5. The boundary values of Poisson’s ratio ν 1 found for all considered cases are listed in Table 1.

Table 1. Boundary values of Poisson’s ratio ν 1 of filling material. Ratios of elastic moduli

Poisson’s ratio ν 2 of base material

E 2 / E 1

0.0

0.1

0.2

0.3

0.4

0.45

0.5

10

0.4659 0.4967 0.4996

0.4701 0.4971 0.4997

0.4757 0.4976 0.4997

0.4825 0.4983 0.4998

0.4907 0.4991 0.4999

0.4952 0.4996 0.4999

0.4999 0.4999 0.4999

100

1000

Note that in the case when Poisson’s ratio of the base material is equal to 0.3, and the elastic modulus of the filling material of the V-shaped notch is two orders of magnitude lower than the elastic modulus of the base material ( E 2 / E 1 = 100), singular solutions do not exist if Poisson’s ratio ν 1 is greater than or equal to 0.4983.

3. Experimental study

A series of destructive tensile tests was carried out to evaluate the e ff ectiveness of reducing the stress concentration near the V-shaped notch by filling it with another material. The evaluation criterion is the maximum force causing the destruction of the specimens. The results are obtained for specimens with unfilled V-notch and specimens with a V-notch filled with a certain material. The computational scheme for tested specimens is shown in Fig. 1. Thee ff ectiveness of ”healing” is strongly influenced by the strength of adhesion between the specimen material and the filling material. Therefore, it was first decided to conduct preliminary tests to determine the strength of adhesive bonding of materials and then to determine experimentally the elastic moduli of materials with the highest adhesive strength. The main samples (Fig. 1) were cut from ebonite sheet in an oil medium. The V-notch was made on a hand operated milling machine using a special tool with the angle of cutting edge of 12 . 5 ◦ . As candidate materials for filling the cavity of the V-shaped notch we chose the materials with a Poisson’s ratio close to 0.5 such as: ”Moment BL-1” rubber adhesive, Kim Tec Silicon 101E silicone sealant, material obtained in the laboratory of the Institute of Technical Chemistry of UB RAS (P1000 material), and ”Artline Crystal Monolith Epoxy 5” epoxy. Before applying any of the above materials, the surface of ebonite specimens was cleaned, degreased and dried. Epoxy resin consisted of two components - epoxy resin and amine hardener. For the preparation of the composition, two components were mixed in the proportion of 3 to 1. The composition was mixed until a homogeneous mixture was obtained and then applied to the surface of ebonite, or poured into a silicone mold to obtain blades, which were used in the elasticity modulus tests. Curing time was 7 days at 25 ◦ C. The P1000 material was composed of two components. To obtain the composition, it is necessary to mix two components in the proportion of 7 to 1. Curing time was 48 hours at 80 ◦ C. The composition was applied to the surface of an ebonite sample or poured into flat molds, and then, after polymerization, blades for tensile testing were cut with a stamp. Silicone sealant and rubber adhesive were applied to the cleaned ebonite surface. The curing time was 24 hours at a temperature of 25 ◦ C. 3.1. Preparation of samples and materials