DOI 10.1007/s11003-017-0050-6 Materials Science, Vol. 53, No. 1, July, 2017 (Ukrainian Original Vol. 53, No. 1, January–February, 2017) EVALUATION OF DAMAGE TO THE MATERIAL BY THE RESULTS OF STRAIN MEASUREMENTS AND COMPUTER ANALYSIS OF THE STATE OF SURFACE DEFORMATION TOPOGRAPHY P. О. Мarushchak,1,2 І. V. Konovalenko,1 М. H. Chausov,3 R. Т. Bishchak,4 and А. P. Pylypenko3 We reveal the physicomechanical regularities of the accumulation of surface defects on the basis of the computer analysis of photographic images of the surfaces of deformed specimens. The main laws of the pore formation in D16cht alloy are established by the method of strain measurements. We also demonstrate the existence of a physicomechanical relationship between the deformation of loosening and the accumulation of defects on the surface of the material. Keywords: degradation, damage, diagnostics, optical-and-digital control. It is known that the surface layers of the metals are especially sensitive to the deformation influence, which creates favorable conditions for their application in the diagnostics of the accumulation of dispersed defects. There are numerous approaches proposed for the analysis of the images of the surfaces with defects of different physicomechanical nature . The methodical aspects of the identification of dispersed and localized defects including, in particular, the images with great numbers of disturbances were substantiated in [1, 2]. On this basis, the methodology of determination of the state of transport aircrafts according to the parameters of deformation topography of the surfaces of structural elements and reference specimens was analyzed in . The theoretical aspects of self-organization of the surfaces of fatigue sensors in the course of long-term operation were adjusted and extended and the technological approaches to the problem of fastening of these sensors on the surfaces were substantiated in [1, 2]. To estimate the accumulation of internal microdefects in materials, it is customary to use the method of complete diagrams , which gives information on the kinetics of damage to the material not only in the ascending part of the static tensile stress–strain diagram but also on its descending part. There are two principles used for the estimation of the engineering state of materials and structures: on the basis of the designed service life or according to the actual service life [1–3]. The evaluation of serviceability on the basis of the designed service life is based on the principle of guaranteed safety, whereas the procedure based on the actual state includes solely the analysis of admissible defects and the prediction of the “safe” duration of operation . However, it is important to predict the initiation and kinetics of propagation of fatigue cracks by using both approaches. Combining the advantages of the methods of optical-and-digital monitoring and complete diagrams, it is possible to establish the relationship between the internal and surface dispersed defects . 1 2 3 4 Pulyui Ternopil’ National Technical University, Ternopil’, Ukraine. Corresponding author; e-mail: email@example.com. Ukrainian National University of Bioresources and Nature Management, Kyiv, Ukraine. Іvano-Frankivs’k National Technical University of Oil and Gas, Іvano-Frankivs’k, Ukraine. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 53, No. 1, pp. 96–101, January–February, 2017. Original article submitted July 3, 2014. 1068-820X/17/5301–0109 © 2017 Springer Science+Business Media New York 109 110 P. О. МARUSHCHAK, І. V. KONOVALENKO, М. H. CHAUSOV, R. Т. BISHCHAK, AND А. P. PYLYPENKO The aim of the present work is to study the relationship between the parameters of surface and internal defects of D16cht aluminum alloy. Procedure The choice of D16cht aluminum alloy is explained by the necessity of investigation of the kinetics of damage accumulation in aircraft materials under static tension. These studies are of high importance because the analyzed alloy can be used as a sensor of fatigue accumulation in flying vehicles. It is susceptible to surface wave processes in the course of plastic deformation and, hence, one can clearly record damages to the object of diagnostics. We studied plane specimens with working part 10 × 50 mm in size and a thickness of 5 mm. The tests were performed in a ZD-100Pu modernized hydraulic installation in which the principle of regulated stiffness of the loading system was realized in the course of the tests. Moreover, the installation was equipped with a computer-based measuring system aimed at processing of the results and a special device for the realization of abrupt changes in the load. In the course of the tests, the strain sensors were used to record the transverse and longitudinal narrowing of the specimens. The specimen surface was photographed with the use of a Canon-D550 camera and an MBS-10 optical microscope. The total strains were found as follows : ε = εl + ε p , (1) where ε l is the loosening strain and ε p is the plastic strain. The kinetics of the accumulation of dispersed defect was found by using the loosening strain  by the formula ε l = ( 1 − 2µ ( ε ) ) ε , (2) where µ(ε) is the coefficient of transverse strains measured at any time, and ε is the relative strain: µ = − εt . ε (3) Here, ε t is the transverse strain. Results of Deformation We plotted the curves of static tension of the specimens up to different values of the total strain by the method of strain measurements (Fig. 1а). To estimate the kinetics of dispersed defects in different stages of deformation, we used the model of their accumulation in metallic materials under static loading developed at the Pysarenko Institute for Problems of Strength of the Ukrainian National Academy of Sciences. In this model, the role of the main parameter of state of the material is played by the coefficient of transverse strains corresponding to the loosening strain . We revealed the relationship between the values of total (ε) and loosening (ε l ) strains and determined more precisely the kinetics of accumulation of dispersed defects in the material (Fig. 1b). EVALUATION OF DAMAGE TO THE MATERIAL BY THE RESULTS OF STRAIN MEASUREMENTS AND COMPUTER ANALYSIS 111 Fig. 1. Curves of static deformation of D16cht alloy (а) and the dependence of the loosening strain on the total strain in the specimens (b); (I–IV) damaged domains. Table 1. ε l – ε Dependences at the Points of Unloading of the Complete Diagram for D16cht Alloy Value, % Longitudinal ε 2.6 13.0 14.6 15.5 Loosening ε l 0.8 4.8 5.6 6.2 The ε l – ε dependence is practically linear up to a strain ε = 11%, which confirms the “homogeneity” of the process of accumulation of defects in the material and, hence, the increase in the relative elongation of the specimens. However, if ε < 11%, then the plot contains wavelike oscillations with an amplitude of 2–3%, which corresponds to the coalescence of defects with the formation of micropores. Thus, the dissipative structure is formed mainly in the final stage of the indicated specific oscillations of the values of ε l . It was discovered that, in this region, the density of the material changes (due to the accumulation of structural defects). Hence, the degree of loosening of the material increases due to significant changes in its structure (as compared with tension at lower strains [4, 5]). These features of deformation of the aluminum alloy can be explained by the results of evaluation of the accumulated current damage (Table 1). To estimate the state of the surface according to its photographic images, we used the algorithm proposed in [5, 6], which has the following stages: equalization of illuminance, binary transformation, and evaluation of the area of surface formations. It was proved that the plastic strains in the alloy are concentrated in local zones covering the surface by a system of adjacent strips of localized deformation. The cause of their formation is the structural inhomogeneity of material and, first of all, internal boundaries between the grains and their conglomerates . Automated Analysis of the Surface Defects There exists a relationship between the structural parameters of the material and the response of its surface layers to the deformation influence [4, 5]. This fact is a physical ground for the analysis of the mechanical behavior of materials and interpretation of the physical mechanisms of deformation. Moreover, the parameters of 112 P. О. МARUSHCHAK, І. V. KONOVALENKO, М. H. CHAUSOV, R. Т. BISHCHAK, AND А. P. PYLYPENKO Fig. 2. Original images of the investigated surface at the points of unloading of the complete diagram (see Fig. 1a) (a–e) and the images illustrating the results of clustering (f–j) (white pixels correspond to the background; black pixels correspond to the deformation topography). surface deformation topography serve as a source of information about the state of the entire material. Therefore, it is necessary to clarify the principal regularities of changes in the kinetics of deformation processes and to establish in advance the relationship between the structural state of the alloy and the strain-induced defects accumulated on the surface. It is assumed that the main act of plastic yield of metal surface is realized by the “shear + rotation” mechanism , which leads to the formation of dissipative mesostructures and plastic shears. Hence, the assumption about the mutual correlation between the parameters of loosening strains characterizing the accumulation of defects in the material and the area of the surface defects is the condition required for the investigations aimed at establishing the relationship between these characteristics. The main cause of degradation of the material surface is connected with high internal stresses induced in thin subsurface layers in the course of plastic deformation [2, 8]. We proposed an algorithm for the estimation of the degree of damage to the surface of the plastically deformed material as a function of the accumulated plastic shears, where the area of the surface defects ( F ) serves as the parameter for its evaluation. In the original images of the surface (Figs. 2а–е), due to the unequal intensity of illumination of different zones, the picture of distribution of the surface formations is distorted. To remove this shortcoming, the intensity of illumination was equalized. For this purpose, we performed the convolution of the image with a lowfrequency filter, thus removing the low-frequency component from the original image. To obtain an approximate picture of the intensity of illumination l ′(x, y) , we used a Gaussian filter with large size of the kernel. The picture with equalized intensity of illumination is described by the formula [6, 8] I L ( x, y ) = K L I 0 ( x, y ) , l ′ ( x, y ) where I 0 is the original image, x is the index of a column, x ∈(1,…, m) ; y is the index of a row of the image I 0 , y ∈(1,…, n) , (4) EVALUATION OF DAMAGE TO THE MATERIAL BY THE RESULTS OF STRAIN MEASUREMENTS AND COMPUTER ANALYSIS 113 and K L = max ( l ′(x, y) ) is the coefficient of equalization of the intensity of illumination. The next step of our algorithm, i.e., the binary transformation is intended for the preliminary partition of the image into two clusters: the background and the required objects. Each point of the binary image I B was obtained from the condition IB ( ⎧ 1 ⎪ j, i ) = ⎨ ⎪ 0 ⎩ for I 0 ( j, i ) < Bmin , for I 0 ( j, i ) ≥ Bmin , (5) where Bmin is the limiting value of binary transformation. In the image I B , white pixels correspond to the background and black pixels correspond to the recognized surface formations (Figs. 2f–j). As the integral parameter used for the estimation of the state of the analyzed surface, we used the coefficient of surface damage: F = Nb N ⋅100% = b ⋅100% , N mn (6) where N b is the number of pixels in the image that belong to the cluster of recognized objects and N is the total number of pixels. In the approaches of physical mesomechanics, the surface layer is regarded as an independent part of the material, which plays an important role in the mechanical behavior of deformed solid bodies . In view of the weakened intermolecular bonds [5, 6], the structure with the maximum number of defects is formed in the surface layers. Hence, the shear strength of the surface layer is lower than for the internal layers and, therefore, the process of plastic deformation is more intense in the surface layer. We regarded the deformation of D16cht alloy as a process running in a two-layer system: “surface layer–volume of the material.” The limiting state of the material is attained under the condition of saturation of the surface with strain formations [2, 9, 10]. According to the results of automated analysis of the images of the surfaces of deformed specimens, we can compare the kinetics of accumulation of damage with the relative strains in the specimen (Fig. 3). For a more comprehensive investigation of the behavior of materials in the prefracture state, we analyzed the deformation processes in the internal layers (Fig. 3b). In this case, a section of the stress–strain curve locally descends if ε = 11% (point A ) and the stresses increase (point B ), which corresponds to changes in the micromechanisms of fracture and a high sensitivity of the material to these processes (Fig. 3b). Further, we observe the formation of the neck (point C ) and the appearance of the fracture front on the lateral surface of the specimen (point D ) by the low-energy method of “rapid shear,” which is confirmed by the geometry of the descending section of the diagram (Fig. 3b). 114 P. О. МARUSHCHAK, І. V. KONOVALENKO, М. H. CHAUSOV, R. Т. BISHCHAK, AND А. P. PYLYPENKO Fig. 3. Dependence of the area of surface topography on the relative strains (a) and the deformation processes in domains III and IV (b). In view of the sufficiently high rigidity of the loading system , we recorded oscillations of the deformation process in the material in the prefracture stage. Hence, the process of coalescence of dispersed defects into a macrocrack terminates in the material. The same “oscillating” processes were also detected on the specimen surface, which is an indication of a similar evolution of the surface state, its adaptation to the external influence, and self-organization of its microstructural components [5, 9–11]. The process of deformation causes the coalescence of small microdefects, growth of their sizes, and the formation of macrodefects [8, 9]. The accumulated results are in good agreement with the data from , where it was discovered that grains located near the surface have lower shear strength than in the bulk of the material and the nonlinearity of this process increases with the level of plastic strains. 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