The method of diagnosing glued joints subjected to static loads

The article presents a new type of sample developed for the purpose of assessing the strength of glued joints. The construction and the idea of testing glued joints were described in detail. In the article put a question: what geometric features of the sample significantly affect the change in the stress values at the measuring points S1, S2 and S3 under the influence of the acting bending moment? Analysis of the results of numerical calculations allowed to state that the width of the glued joint h, spacing of connectors L3 and the thickness of the upper beam g1 significantly affect the value of stresses in points S1, S2 and S3.

On beam M1 and beam M2 measuring points were determined (S), in which the measurement of deformations is carried out at the moment of testing. Measurement points S they are symmetrically oriented with respect to the axis of the sample in the width range H1 and H2, as well as length L1. In the symmetry axis of the sample, measuring points are located: S2 on a beam M1 and S3 on a beam M2. The axis of the sample is distant from the edge of the beam M1 by value 0.5L1. Position of the measuring point S1 in relation to the axis of symmetry determines the dimension F. Its value should be within the range L4 < 2F < Y. At each measuring point S1, S2 and S3 two strain gauges were mounted (T()), located on both sides of the beam. The task of strain gauges T() is the measurement of deformations on the surface of the sample elements, i.e. the upper beam M1 and bottom beam M2. This sample is designed to assess the strength of adhesive joints in conditions of controlled deformation of machine construction elements. The most advantageous form of loading the sample is a four-point bending with a monotonically increasing value of the bending moment. The structure of the sample also allows the implementation of tests in cyclic loading conditions with cycle asymmetry coefficient R ≥ 0. The method of applying the load is shown on the Figure 1c.
During the tests, the sample rests on supports A remote from each other by value X. Forces loading the sample are applied in points B, remote from each other by value Y. Points of load application B they are symmetrical with respect to supports A. Position of the symmetry axis of the sample relative to the supports A defines the dimension X/2. The value of the bending moment loading the sample depends on the value of forces acting, as well as on the ratio of dimensions X/Y.

The idea of testing glued joints
Examination of a sample of an innovative shape in four-point bending conditions with a monotonically increasing torque value consists in measuring the deformation values at the measuring points: S1 (S1'), S2 and S3. On the basis of strain measurements, the value of stresses is determined using prawa Hooke'a. Measurement points S1 and S2 they are in places where the value of bending moment has a constant value. Point S1 it is located outside the glued joints, and the point S2 between glued joints. The change in the stress value at S1 is proportional to the change in the bending moment value (Fig. 3). Relationship between stresses in points S1 and S2 should be considered in three intervals (Fig. 3): -section I -proportionally changing values of stresses S1 and S2 against the monotonically increasing value of the bending moment; this dependence indicates the lack of joint damage and work in the area of elastic stresses, -section II -progressive increase of stresses S2 against stress values S1; This indicates the loss of load bearing capacity through the glued joint together with the increase of the bending moment, in the final stage the total failure of the joint, -section III -equalization of stress values S1 and S2; applies to the situation of total damage to the glued joint. The boundary between section I and section II should be considered as the value of allowable stresses, which do not damage the glued joint. Stress value S1 = S2 indicates that the joint is completely damaged. Stresses at S3 refer to load changes in the lower beam M2, which change in opposition to the value S2.

Numerical calculations
The purpose of calculations is to get the answer to the question: which geometrical features of the sample significantly affect the change in stress values at the measuring points S1, S2 and S3 under the influence of the acting bending moment?

Calculation results
The results of numerical calculations allowed to determine the values of stresses in points S1, S2 and S3, which are presented in the tables 1-3.

Selection of most important attributes
A set of attributes undergoes (in the form of parameter columns) initial data processing to enable their comparison and further analysis. Due to the type of processed data, standardization was used, in result of which, the variable mean expected value assumes zero and the mean variance is equal to one. The most commonly used standardization method can be expressed as: (1) where: x -value of parameter, µ -mean value of parameter, σ -standard deviation of parameter. There can be many parameters from one or more measurement but most of them are significantly interfered or independent of the monitored phenomenon. The proposed method involves choosing parameters with the use of rough set theory. This technique provides methods for determination of the most important attributes of a computer system without losing classification ability [12]. The rough set theory was developed by Zdzisław Pawlak [13,14,15] and is based on the concept of upper and lower approximation of the set, approximating space and models of sets. Measurement data is presented in the form of a table, whose columns correspond to the attributes and rows corresponds to particular objects or states. Such a record is called an information system [16]. Based on rough set theory is a reduct, which is the main part of the information system. As a result of this, it is possible to distinguish all the distinguishable objects from the original set of attributes, hence, reducts are minimal subsets of attributes maintaining characteristics of the whole set of attributes. Literature studies provides many algorithms for determination of sets  Table 4. Parameters ordered according to significance are presented in Table 5.  The set of reducts for S1 is presented in Table 6. Parameters ordered according to significance are presented in Table 7. The set of reducts for S2 is presented in Table 8. Parameters ordered according to significance are presented in Table 9. The set of reducts for S3 is presented in Table 10. Parameters ordered according to significance are presented in Table 11. Conclusions Diagnostic possibilities of glued joints are related to the analysis of stress values at points S1, S2 and S3. The analysis of the results of numerical calculations shows that all indicated geometric parameters, i.e. h, L3, g1, g2 and g3 they affect the value of stresses in points S1, S2 and S3. Considering the set of results S1, S2 and S3 as a whole, the most important parameters are: g2 and g3. Analyzing the results of stresses at individual measurement points, it can be indicated that the most significant impact on the value: -S1 have dimensions:h, L3, g1, -S2 have dimensions:h, L3, g3, g1, g2,