Fields of Residual Stresses near Open Assemblage Holes of Aircraft Wing Panel

Abstract

The results of fatigue tests of two geometrically identical and similar in design models of the lower wing panel of a commercial aircraft were analyzed. The panels differed in the way of installing mounting bolts, which connect the skin and stringers. Cold expansion of holes drilled both in the skin and stringer was performed for the first panel before joining. The second panel included no additional treatment after drilling pilot holes and final reaming. The bolts were mounted with an interference fit varying from 1.3 to 2.1% and from 2.9 to 3.2% for the first and the second panel, respectively. Changes in the interference fit were the consequence of a scatter attributed to the presence of a tolerance zone for the diameters of both bolts and mounting holes. A two-step comparison of both technologies was based on the experimental study of residual stress fields. The first stage, being a subject of the present study, included the analysis of residual stress fields arising after removal of the bolts and separation of the skin from stringers. Hole drilling and gradual crack growth were used to determine the components of residual stresses. The deformation response was measured by electronic speckle pattern interferometry. High quality interferograms, which provided a reliable resolution of the interference fringes of ultimate density over the hole edge or directly along the notch borders, were obtained for both ways of local removal of the material. The first (pointwise) method, based on drilling a probe hole, provided a quantitative determination of the residual stress components, starting from 1.4 mm distance from the assemblage hole edge. The second technique implements the crack compliance method of subsequent lengthening of the notch, starting directly from the mounting hole edge. This approach provided for a quantitative analysis of residual stress fields, related to different bolt mounting technologies, proceeding from the comparison of SIF values. A high level of compressive residual stresses near open holes was characteristic for both types of panels. Both experimental approaches showed the benefits of joints, where bolts are mounted into cold-expanded (reinforced) holes. For this case, the estimation of the relaxation parameters of the principal component of residual stresses in the direction of the external load is presented.

INTRODUCTION

Traditional fatigue tests of large-sized elements of aircraft structures under cyclic loading are carried out using strain gauge sensors of controlling the stress-strain state [1–3]. One of the important objects of such tests are structurally similar samples that simulate longitudinal fragments of metal aircraft wing panels, which contain numerous bolted or riveted joints. The main interest is in uniformly loaded joint zones, in which the fastening elements are hardly loaded with shear forces. The main technological means of ensuring an increased service life of a bolted joint is strengthening the immediate vicinity of the mounting holes by plastic deformation. This is achieved mainly by button-rifling the holes, compressing the transition edges of the countersunk holes for countersunk bolts, and installing the bolts with interference [4]. In such cases, of greatest interest are the residual stresses and deformations that arise in the vicinity of the individual fastening element, which, depending on the magnitude and sign, affect the durability of the joint.

However, reliable determination of the local stress-strain state, both on the basis of strain gauge measurements and using numerical modeling, is a very difficult task, especially under cyclic loading [5]. The main problem is the need to take into account the residual stresses that arise when installing bolts with interference using various technologies or a combination of interference, button-rifling, and compression of the transition edges of the hole. An effective means of the quantitative analysis of residual stresses can be both destructive and nondestructive experimental methods [6]. Destructive methods, which are based on point measurements of various relaxation parameters caused by local removal of material, have become widespread. However, to obtain the final result, this approach requires a complex procedure for processing the initial experimental data [7]. The use of interference-optical methods for measuring the deformation response to local removal of material significantly increases the accuracy and reliability of determining the components of residual stresses [8–16]. The obtained experimental information can be effectively used to create and verify numerical calculation models, as well as for comparative analysis in order to optimize bolt installation technology.

The primary objects of the study were two structurally similar models, designated as ZA and ZB, which relate to the elements of the lower wing panel of a commercial aircraft. Both models, made of 1163T aluminum alloy, have the same geometric dimensions—3700 × 560 mm. The test program, the same for both samples, includes cyclic stretching of each panel with the following parameters of the pulsating loading cycle: the range of gross normal stresses in the uniformly loaded area of the panel is Δσ = 140 MPa; cycle asymmetry coefficient R = 0.01; loading frequency is 3 Hz. The design of the panels is shown in Fig. 1. The material of the skin is aluminum alloy 1163T (80 TR1-92-161-90 plate), of stringers is 1163T (pressed profile 400930 according to OST1 90113-86), and of bolts is VT16. The thickness of the skin is 10 mm, and the stringer flange is 16 mm.

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Fig. 1.

General view of design-similar models of wing lower panels: from the skin side (a); from the stringer side (b).

In both panels, bolts of the same diameter, made using the same technology, were used to connect the skin and stringer. The diameter of the bolts was 10.096–10.123 mm. The diameter of the mounting holes in both cases was 9.8 mm with a tolerance range of H9 (). The difference between the panels was in the technology for installing the mounting bolts. In the panel ZB, after drilling and reaming, no additional processing of the edges of the holes was carried out. The bolts were installed with an interference fit that varied from 2.9 to 3.2% owing to the scatter caused by the tolerance zone for the diameters of both bolts and mounting holes. Before installing the skin and stringer in the ZA panel, the transition edges were crimped, and button-rifling of the holes in the casing and the holes in the stringer was performed. The diameter of the working part of the mandrel was 10.05_–0.02. After cold hardening process, the diameter of the mounting holes increased owing to plastic deformation and amounted to 9.91–9.99 mm. Thus, for the ZA panel, the amount of interference varied from 1.3 to 2.1%.

Estimation of the dimensions of the uniformly loaded zone of joint between the stringer and the skin is based on numerical modeling of the stressed state of the panel using the finite element method without taking into account the presence of residual stresses. The calculation results are shown in Fig. 2, in which the boundaries of the panel area are visible, where the stresses are distributed evenly in both the stringer and the skin.

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Fig. 2.

Stress state of a panel in the zone of stringer and skin connection by bolts.

Both panels withstood the assigned resource of N = 125 000 cycles without visible external damage; the difference in the two technologies for installing mounting bolts did not affect the results. The traditional approach used to assess the impact of technology on the fatigue strength of joints was as follows. After testing, the tail parts were separated from both panels to obtain only uniformly loaded zones. Then the joints of the stringers with the skin were dismantled for subsequent flaw detection of the hole walls for the presence of small fatigue cracks. During the flaw detection process, a number of holes were identified, in the walls of which the presence of fatigue cracks was most likely. To confirm this, laboratory rectangular samples were cut out from the supposed locations in the stringer and casing (Fig. 3).

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Fig. 3.

Specimens cut from stringer (a) and skin (b) for defect detection.

In the cross section of the sample, passing along the diameter of the controlled hole, through cuts 1 mm wide and 5 mm deep were made on both sides of the outer contour (Fig. 3a). Next, each sample was subjected to destruction under the influence of increasing tensile load. The plane of destruction coincided with the section of the sample in which the presence of a fatigue crack was assumed (Fig. 3b). Static fractures of laboratory samples were examined using an SMZ-168 microscope (Motic) with a magnification of 5–50 for the presence of fatigue cracks. The amount of obtained data made it possible to perform a probabilistic-statistical assessment of the influence of button-rifling and compression of the transition edges of holes for fasteners on fatigue life. Thus, the ratio of operating hours at which identical fatigue damage is formed in a single bolt hole in panels with and without button-rifling, which corresponds to the probability level of ρ = 0.001323, is 1.28. This means that the fatigue life of a single bolt hole in the panels with hole reinforcement should be approximately 28% greater than in the panels without hole reinforcement.

The resulting probabilistic assessment needed additional justification. For this purpose, studies were carried out to compare the fields of residual stresses that remain in the elements of a high-life bolted joint of the skin and stringer after testing for fatigue strength. This paper presents the results of determining the residual stress fields that arise in the wing skin after completion of fatigue tests and removal of mounting bolts. This approach made it possible to fairly accurately estimate the values of local stresses, which during cyclic loading act in the vicinity of the elements of bolt joints.

OBJECTS OF EXPERIMENTAL STUDY OF RESIDUAL STRESSES

Experimental determination of residual stresses by drilling a hole was carried out for four samples cut from uniformly loaded zones of connection of the panels ZA and ZB after dismantling the bolt joints. Figure 4 shows the locations of cutting samples that were used to study residual stresses in the skin and stringer.

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Fig. 4.

Skin and stringer after disassembling.

Samples with odd and even numbers refer to the panels ZA and ZB, respectively. Samples Z1 and Z2 with dimensions of 217 × 122 × 16 mm in plan contained a stringer fragment and had a T-shaped cross section. The height of the stringer flange measured from the inner surface of the skin was 45 mm. Flat samples Z3 and Z4 had dimensions of 215 × 280 × 10 mm and the same geometry of the mounting holes, as shown in Fig. 5 for the sample Z3. Mounting holes were made with and without reinforcement for samples Z3 and Z4, respectively. Fragments of the flat surface of samples with a grid of probing holes are shown in Fig. 6. The direction of load during fatigue testing coincides with the y axis. The same grids of probing holes were used to determine residual stresses in the samples Z1 and Z2. The results of determining the residual stress components in the samples Z1 and Z3 are very similar in nature, as in the samples Z2 and Z4. Therefore, in this work, detailed results are presented for the samples Z3 and Z4. The characteristic features of the distribution of residual stresses in the samples Z1 and Z2 will be discussed below.

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Fig. 5.

Geometrical dimensions (a) and general view (b) of plane specimens.

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Fig. 6.

Assemblage hole grid in specimen Z3 (a) and Z4 (b).

INITIAL DATA FOR THE HOLE DRILLING METHOD

Experimental information takes the form of patterns of interference fringes that appear when drilling a probing hole in a field of residual stresses. These interferograms quantitatively describe the distributions of the tangential components of displacements u and v in the direction of the x and y coordinate axes, respectively. A detailed description of the experimental approach is given in [11, 17]. Most probing holes made with a carbide drill have a diameter of 2r₀ = 1.9 mm. In all cases, the depth of blind holes is h ≥ 3r₀. Typical patterns of interference fringes obtained for the sample Z3 are shown in Fig. 7. The direction of the pulsating load during fatigue tests coincides with the coordinate y axis.

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Fig. 7.

Specimen Z3 interference fringe patterns obtained in terms of in-plane displacement component u and v as the result of hole drilling at points 1 (a), 2 (b), and 10 (c).

Typical patterns of interference fringes obtained for the sample Z4 are shown in Fig. 8.

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Fig. 8.

Specimen Z4 interference fringe patterns obtained in terms of in-plane displacement component u and v as the result of hole drilling at points 2 (a), 6 (b), and 7 (c).

The main task is to determine residual stresses in irregular zones of the structures, namely, in the immediate vicinity of mounting holes. Until now, this problem has not had a reliable experimental solution, including using the method of drilling a hole. This is due to the fact that it is technically quite problematic to drill a deep probing hole at the minimum possible distance from the contour of the mounting hole and obtain high-quality fringe patterns. Patterns of fringes in Fig. 7a (point 1) and Fig. 8b (point 6) clearly indicate that this problem has been successfully solved. Interferograms of the same high quality were obtained for the points 6, 8, 9, and 13 (sample Z3) and the points 5, 1, 05, and 06 (sample Z4), which are not shown in the work. The presented patterns of interference fringes were obtained for the first time and clearly indicate the almost ideal quality of the performed experiment. One of its most important features is the ability to reliably resolve fringes along the contour of a small hole with a diameter of 2r₀ = 1.9 mm. All obtained interference patterns provide reliable resolution of fringes directly on the hole contour.

In addition, the configuration of the patterns of interference fringes clearly shows that the directions of the coordinate axes x and y practically coincide with the directions of the main residual stresses σ₁ and σ₂, respectively. This means that to determine the components of residual stresses in thin plates, the following formulas can be used [11]:

1

where r₀ is the radius of the hole; E is modulus of elasticity of the material; Δu and Δv are increments in the diameter of the probing hole in the direction of the principal stresses σ₁ and σ₂; a = (α₁ – 1), b = (σ₂ – μ), α₁ and α₂ are coefficients of stress concentration during uniaxial tension of a plate with a hole; and μ is the Poisson ratio of an isotropic material.

The first condition for the possibility of using formulas (1) is the coincidence of the directions of measuring increments in the diameters of the probing hole with the directions of the main residual stresses. This condition is satisfied for all obtained patterns of interference fringes, regardless of the location of the probing holes. It is important that relations (1) represent the only solution of a correctly formulated inverse problem [11]. In other words, this approach provides the minimum possible error in determining the main components of residual stresses on the basis of the hole drilling method. Any attempts to improve the accuracy by adding additional measurement points lead to the need to obtain an approximate solution to an ill-posed inverse problem based on a numerical solution to an ill-conditioned system of linear algebraic equations. Such a process rarely leads to reliable results, as discussed in detail in the paper [7]. An approach based on measuring increments in the diameters of the probing hole in the direction of the main residual strains provides the highest possible sensitivity with respect to the components of residual stresses. In addition, the method based on the use of formulas (1) makes it possible to quantify the errors in determining the main components of residual stresses.

The second condition for the applicability of formulas (1) is the elastic nature of the deformation of the contour of the probing hole, since the coefficients α₁ and α₂ are determined as a result of solving the elastic problem of stress concentration. All obtained interferograms confirm the fulfillment of this condition. The values of the stress concentration coefficients α₁ and α₂ do not affect the correctness of the formulation of the inverse problem, which is used to move from experimentally measured parameters to the values of the principal components of residual stresses. Numerical modeling was used to determine α₁ and α₂. The problem of uniaxial tension of a thick-walled square plate with a deep dead hole that meets the condition h ≥ 3r₀ (h is the plate thickness) is solved using the finite element method (FEM). It has been established that α₁ = 3 and α₂ = 1. This approach is suitable without restrictions for probing holes located at a noticeable distance from the mounting hole, for example, for the points 2 and 10 (sample Z3), as well as the points 2 and 7 (sample Z4). For probing holes located in the immediate vicinity of the mounting hole, the exact values of the coefficients α₁ and α₂ can also be determined using FEM modeling. In this work, where residual stresses are compared in two different samples, this issue is not of fundamental importance. Therefore, for all probing holes, α₁ = 3 and α₂ = 1 were taken, which naturally led to a slight increase in the error of determining residual stresses in the nearest vicinity of the mounting holes. In any case, there is no more reliable method for quantifying residual stresses in irregular zones.

The increments in the diameter of the probing hole in the direction of the main stresses (Δu and Δv), which are necessary to apply formulas (1), were determined from the patterns of the interference fringes obtained using the method of electronic speckle pattern interferometry [11]. They were calculated on the basis of the following relations [11–13]:

2

where λ = 532 nm is the wavelength of laser radiation; Ψ = π/4 is the angle between the direction of illumination and the direction of observation, normal to the surface of the object; and ΔN^u and ΔN^v are the differences in the absolute orders of the fringes. The latter are defined as differences in the orders of the fringes, calculated from one pattern of fringes between two basic points corresponding to the directions of the main stresses σ₁ (ΔN^u) and σ₂ (ΔN^v).

The base point on each of the two interferograms shown in Fig. 9 is located at the intersection of the considered direction of the main stress and the hole contour. The patterns of the fringes are obtained by drilling a hole in the sample Z4 and serve to illustrate the concept of a “base point.” A probing hole with a diameter of 2r₀ = 2.5 mm is located in the direction of the x axis between two adjacent mounting holes, into which tension bolts are inserted, at an equal distance from them Δb = 15 mm. Base points (Fig. 9) 1 and 2 are for component u, and 3 and 4 are for component v. As a result of the calculations, the following values are obtained: ΔN^u = +7 bands; ΔN^v = –14 bands. Consistent substitution of these values into formula (2) and formula (1) leads to an intermediate result—Δu = 2.66 μm, Δv = –5.32 μm, and then to the desired values of residual stresses: σ₁ = –67.2; σ₂ = +16.7 MPa.

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Fig. 9.

General scheme of counting fringe order differences.

When determining the values of residual stresses using formulas (1), it is important to correctly identify the physical sign (increase or decrease) of the increments in the diameters of the probing hole Δu and Δv. The patterns of interference fringes given above do not allow one to judge the physical signs of the tangential components of displacements. Additional information for identifying the signs of displacement components can be obtained by recording interferograms with an additional phase shift [11]. The sign of this phase shift is known in advance for each specific interferometer design. The patterns of interference fringes corresponding to Fig. 9, but recorded with an additional phase shift, are shown in Fig. 10. For the optical design of the interferometer used in this work, the hyperbolic configuration of the interference pattern determines the positive sign of the u component (Fig. 10a), and the elliptical shape of the compositional interferogram corresponds to the negative sign of the v component (Fig. 10b).

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Fig. 10.

Specimen Z4 interference fringe patterns obtained with additional phase shift for in-plane displacement component u (a) and v (b) as the result of blind hole drilling.

RESULTS OF DETERMINING RESIDUAL STRESSES IN FLAT SAMPLES

The grids of probing holes in the samples Z3 and Z4 are shown in Fig. 6. The measurement points are grouped in the direction of the x axis (line A) and in the direction of the y axis (line B) in order to increase the reliability of the results of determining the residual stress components by using the data related to geometrically similar areas of the samples. The obtained results are given in Tables 1 and 2 and Tables 3 and 4 for the sample Z3 and the sample Z4, respectively.

Table 1. . Components of residual stresses along line A in specimen Z3

	Point number					Hole contour
	9	10	11	12	13
x, mm	1.91	7.75	15.59	23.45	28.07	30.02
σ1, MPa	–127.0	–101.0	–88.0	–126.0	–74.0
σ2, MPa	–111.3	–4.0	–29.0	–24.0	–54.0

Table 2.  . Components of residual stresses along line B in specimen Z3

	Point number
	1	01	(2 + 02)/2	3
y, mm	2.32	3.05	9.23	18.90
σ1, MPa	–111.0	–13.0	–29.0	–54.0
σ2, MPa	–133.0	–82.0	–105.7	–63.0

Table 3.  . Components of residual stresses along line A in specimen Z4

	Point number						Hole contour
	5	05	4	3	2	1
x, mm	1.91	2.62	7.82	15.73	23.71	29.18	31.63
σ1, MPa	–75.0	–95.0	–72.0	–83.0	–96.0	–93.0
σ2, MPa	–58.0	–50.0	–17.0	–50.0	–43.0	–68.0

Table 4.  . Components of residual stresses along line B in specimen Z4

	Hole contour
	6	06	7	07	8	9
y, mm	1.39	2.50	7.21	8.80	13.12	18.48
σ1, MPa	–172.0	–32.0	–27.0	–15.0	–28.0	–53.0
σ2, MPa	–139.0	–96.0	–101.0	–79.0	–61.0	–70.0

The experimental dependences of the residual stress components obtained for the sample Z3 and sample Z4 are presented in Fig. 11 and Fig. 12, respectively. The origin of each axis is located on the contour of the mounting hole closest to the contour of the first probe hole.

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Fig. 11.

Distributions of principal residual stress components along line A (a) and line B (b) in specimen Z3.

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Fig. 12.

Distributions of principal residual stress components along line A (a) and line B (b) in specimen Z4.

For both samples, in the horizontal direction A, the negative component σ₁ exceeds component σ₂ in absolute value (Figs. 11a and 12a), and the situation is the opposite in the vertical direction B (Figs. 11b and 12b). This fact shows the relaxation of the residual stress component σ₂ between the mounting holes caused by cyclic loading. The presence of a real bolt in the hole during fatigue tests reduces the relaxation of the component σ₂ in the direction of application of cyclic load that coincides with the y axis (Figs. 11b and 12b).

Comparison of the data shown in Figs. 11a and 12a indicates that, for the sample Z3, the direction of the cyclic load hardly affects the values of the negative components of residual stresses in the vicinity of the mounting hole. Note that cold hardening of the hole provides a very high level of negative values of both components of residual stresses in the nearest vicinity of the mounting hole after reaching a given resource, namely, –100 ≤ σ_i ≤ –140 MPa (i = 1, 2).

The sample Z4 (Fig. 12b) is characterized by the presence of high level of negative residual stresses in the vertical direction, namely, σ₁ = –172 MPa, σ₂ = ‒139 MPa. These results are slightly higher than the level of residual stresses for the sample Z3 (Fig. 11b). However, one should take into account the difference in distances y from the contour of the mounting hole to the center of the probing hole: y^Z3 = 2.32 mm (Fig. 6a, point 1); y^Z4 = 1.39 mm (Fig. 6b, point 6). This difference is obviously caused by a high gradient of residual stress components in the vicinity of the mounting holes. It should also be noted that the contours of the mounting holes after life tests are subject to plastic deformation. Thus, the shape of these contours is not a perfect circle. Very good condition of the vicinity of the mounting hole in the sample Z4 made it possible to drill a probing hole at point 6 at the minimum technically possible distance from the contour of the hole.

The distributions of residual stress components coinciding in direction, which were obtained for the samples Z3 and Z4, are presented in Fig. 13 and Fig. 14. These dependences make it possible to obtain additional information for the comparative analysis of the influence of the technology for preparing initial mounting holes on the residual stress fields.

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Fig. 13.

Distributions of principal residual stress component σ₁ (a) and σ₂ (b) along line A in specimen Z3 and specimen Z4.

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Fig. 14.

Distributions of principal residual stress component σ₁ (a) and σ₂ (b) along line B in specimen Z3 and specimen Z4.

Analysis of the differences in the residual stress components that relate to line B is presented above and further illustrated in Figs. 14a and 14b. The greatest differences in the values of both components of residual stresses are observed in the vicinity of the left mounting hole for line A in Figs. 13a and 13b. The values of the residual stress components for the samples Z3 and Z4 were = –127.0 MPa (Fig. 6a, point 9) and = –75.0 MPa (Fig. 6b, point 5). Of greatest interest are the differences in the values of the residual stress component σ₂, which relaxes the most under the influence of an external load, since it coincides with the direction of this load: = –111.3 MPa; = ‒58.0 MPa. A twofold difference in the maximum values of the absolute values of σ₂ is observed. This fact may mean a reduction in the probability of the appearance of the most dangerous fatigue crack in the direction of the x axis for the sample Z3 compared to the sample Z4 (the x axis is directed perpendicular to the acting load).

The results presented above for determining the components of residual stresses are obtained on the basis of a discrete method of drilling probing holes. For technical reasons, not all holes are made at the same distances from the test contour of the mounting hole, where gradients of residual stresses are highest. Note that the adjacent mounting holes, between which probing holes were drilled along line A, in both samples had a slight shift in the direction of the y axis (Fig. 5b). This fact may be caused by deformation of the panels during fatigue tests. Therefore, to clarify the obtained information and the conclusions drawn on its basis, it is desirable to use a method that is capable of characterizing the discontinuous distribution of the residual stress component σ₂ along line A.

APPLICATION OF THE METHOD OF SEQUENTIAL INCREASE IN THE CRACK LENGTH

The results of determining the residual stresses presented above are obtained on the basis of the discrete method of drilling a hole. Their comparison with the data established by another method is of considerable interest, especially in the vicinity of mounting holes, where distributions of residual stresses are characterized by significant gradients. In the paper, a method based on sequentially increasing the length of an artificial notch (SILAN method) is used. The artificial notch starts directly from the contour of the mounting hole in the direction of the x axis. This approach provides a comparative analysis of the residual stress fields related to two bolt installation technologies by comparing the SIF values obtained for notches of different lengths. In this case, it is natural to assume that the SIF values are proportional to the values of the residual stress component σ₂. As a criterion of preference for the technology of installing fastening bolts into mounting holes, the value of compressive residual stresses at the points closest to the contour of the mounting hole is considered. The higher the absolute value of the negative component of residual stresses σ₂, which relaxes most under the influence of an external load, since it coincides with the direction of this load, the better the technology for installing bolts in terms of fatigue strength.

Experimental information has the form of patterns of interference fringes that appear when a narrow notch is made in the field of residual stresses. The resulting interferograms quantitatively describe the distributions of the tangential components of the displacements u and v in the direction of the coordinate axes x and y, respectively. In the work, for a comparative analysis of the values of the σ₂ components, the displacement components v were used, directed perpendicular to the notch along the y axis. A detailed description of the experimental approach is given in [13, 18–23]. All artificial cuts were made with a jeweler’s saw with a width of Δb = 0.24 mm in the direction of the x axis, as shown in Fig. 5b. Typical patterns of interference fringes obtained for the samples Z3 and Z4 are presented in Figs. 15 and 16. The direction of the pulsating load during fatigue tests coincides with the coordinate axis y, perpendicular to the notch line. Let us note high quality of all interferograms, which were first obtained by making a narrow notch in a plate 10 mm thick.

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Fig. 15.

Specimen Z3 interference fringe patterns obtained in terms of in-plane displacement component v as the result of insertion of narrow notch: (a) initial notch length a₀ = 0 with increment Δa₁ = 1.48 mm; (b) initial notch length a₃ = 6.43 mm with increment Δa₄ = 2.78 mm.

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Fig. 16.

Specimen Z4 interference fringe patterns obtained in terms of in-plane displacement component u and v as the result of insertion of narrow notch: (a) initial notch length a₁ = 1.22 with increment Δa₂ = 1.52 mm; (b) initial notch length a₂ = 2.74 mm with increment Δa₃ = 2.37 mm.

COMPARATIVE ANALYSIS OF SIF VALUES

The results of processing the patterns of interference fringes obtained by successively increasing the length of the notch in terms of crack opening and stress intensity coefficients are given in Tables 5 and 6 for the samples Z3 and Z4.

Table 5.  . Notch opening and SIF values for specimen Z3

	Notch number
	1	2	3	4	5	6
Δan, mm	1.48	1.92	3.03	2.78	3.81	2.78
an, mm	1.48	3.40	6.43	9.21	13.02	15.80
, fringes	–42.0	–51.0	–50.0	–22.0	–4.0	–4.5
, μm	–15.96	–19.38	–19.0	–8.36	–1.52	–1.71
, fringes	–28.0	–37.0	–37.0	–17.0	–8.0	0.0
, μm	–10.64	–14.06	–14.06	–6.46	–3.04	0
, MPa m1/2	–8.5	–10.8	–8.8	–4.4	–2.7	0.8

Table 6.  . Notch opening and SIF values for specimen Z4

	Notch number
	1	2	3	4	5	6
Δan, mm	1.22	1.52	2.37	3.74	2.89	5.30
an, mm	1.22	2.74	5.11	8.85	11.74	17.04
, fringes	–31.0	–39.0	–34.0	–15.5	–6.0	–1.0
, μm	–11.78	–14.82	–10.64	–6.08	–3.8	–0.76
, fringes	–21.0	–38.0	–28.0	–16.0	–10.0	–2.0
, μm	–7.98	–14.44	–10.64	–6.08	–3.8	–0.76
, MPa m1/2	–7.2	–15.5	–8.2	–4.3	–3.7	–0.6

The distributions of SIF values along the length of the notches obtained for the samples Z3 and Z4 according to the data in Tables 5 and 6 are shown in Fig. 17. Note that the SIF values refer to the extreme point of each notch, but reflect the influence of the distribution of residual stress components along the entire length of the notch.

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Fig. 17.

Dependence of SIF on the notch length.

In Fig. 17, first of all, we draw attention to the sharp increase in the value of = –15.5 MPa m^1/2 for the sample Z4 in relation to the SIF of the sample Z3 when the total notch length a² = 2.74 mm is reached. When the total length of the notch reaches a² = 3.40 mm for the sample Z3, the analogous value is = –10.8 MPa m^1/2. This fact may indicate the presence of a significant gradient of the field of negative residual stresses in the vicinity of the mounting hole in the sample Z4, which was not detected by the method of drilling probing holes. The second circumstance in favor of this statement can be a comparison of the values of residual stresses obtained upon drilling probing holes in the vertical and horizontal directions (Tables 5 and 6). Residual stresses determined in the horizontal direction (line A) for the distance between the contour of the mounting hole and the center of the nearest probing hole x = 1.91 mm were σ₁ = –75.0 MPa and σ₂ = –58.0 MPa. Let us present the analogous values obtained in the vertical direction (line B) for the distance between the contour of the mounting hole and the center of the nearest probing hole y = 1.39 mm: σ₁ = –172.0 MPa; σ₂ = –139.0 MPa.

ANALYSIS OF RESULTS

On the basis of the method of drilling probing holes and measuring the deformation response using electron speckle pattern interferometry, quantitative data describing two-dimensional fields of residual stresses in the samples of two types were obtained. For all samples, when drilling probing holes, an extensive set of high-quality interference fringe patterns were recorded. According to the results of processing interferograms, it has been established that all samples, even after their separation from a large-sized panel, retain a high level of compressive residual stresses in the vicinity of the mounting holes. For the samples Z3 and Z4, their limiting values were as follows: = ‒127 MPa (x = 1.9 mm); = –133 MPa (y = 2.3 mm) and = –172 MPa (y = 1.4 mm); = –139 MPa (y = 1.4 mm). The x and y coordinates are measured horizontally and vertically from the contour of the nearest mounting hole. The similar values for the samples Z1 and Z2 were as follows: = –158 MPa (x = 3.7 mm); = –143 MPa (y = 3.3 mm) and = ‒114 MPa (x = 8.6 mm); = –105 MPa (y = 3.9 mm). In all samples, the residual stresses are practically zero at half the distance between the mounting holes (x = 0). In addition, drilling probing holes in the end surfaces of all samples reveals the absence of residual stresses away from the line of the bolt joint.

The fact that there are compressive residual stresses in the vicinity of the mounting holes in both the skin and the stringer after disassembling the ZB panel is a rather unexpected circumstance. The fact is that installing tension bolts leads to the appearance of tensile stresses in the vicinity of the filled hole. The validity of this fact will be confirmed in the next publication of the authors. In addition, during the fatigue tests, the ZB panel was subjected to only tensile stresses. Nevertheless, in all samples, to one degree or another, relaxation of the residual stress component σ₂ coinciding with the line of application of the external load was observed.

As a criterion of preference for the technology of installing mounting bolts in mounting holes, one can consider the magnitude of compressive residual stresses at the points closest to the contour of the mounting hole. The main interest is the differences in the values of the residual stress component σ₂ in the vicinity of the mounting hole, which relaxes the most under the influence of an external load, since it coincides with the direction of this load. For all the considered cases, in the vicinity of the hardened hole, greater absolute values of the compressive component of residual stresses σ₂ are preserved than near the unstrengthened hole. This fact means a decrease in the probability of the most dangerous fatigue crack occurring in the horizontal direction between the mounting holes for the sample Z1 compared to the sample Z2 and for the sample Z3 compared to the sample Z4. The quantitative characteristics of this process are as follows:

The results of determining the components of residual stresses obtained on the basis of the discrete method of drilling probing holes are characterized by some scatter. The fact is that, for technical reasons, not all probing holes are made at the same distances from the studied contour of the mounting hole, where the gradients of residual stresses are highest. In addition, as indicated earlier, the values of the main components of residual stresses in the nearest vicinity of the mounting holes are determined on the basis of approximate stress concentration factors. Therefore, to clarify the obtained information and the conclusions drawn on its basis, a method was used that is capable of characterizing the continuous distribution of the residual stress component σ₂ along the horizontal line A. It is assumed that the SIF values are proportional to the values of the residual stress component σ₂. This circumstance makes it possible to avoid the complex procedure of quantitative determination of residual stress components using the SILAN method. By successively increasing the length of the notch, the dependences of the SIF values on the length of the artificial notch were constructed. It has been established that the value of SIF (Z3) = –8.5 MPa m^1/2 obtained for the first notch of the length a₁ = 1.48 mm in the sample Z3 exceeds in absolute value the value of SIF (Z4) = –7.2 MPa m^1/2 obtained for the first notch of the length a₁ = 1.22 mm in the sample Z4:

This fact can be interpreted as a 15 percent reduction in the probability of the most dangerous fatigue crack appearing on the contour of the mounting hole in the horizontal direction for the sample Z3 compared to the sample Z4. A similar trend was identified earlier on the basis of the comparison of negative values of the σ₂ component directed along line A.

Let us note one of the important reasons that prompted us to study the evolution of residual stresses in the samples cut from a real model of the wing panel after fatigue tests and dismantling of bolted joints. Thus, previously, the results of studying the evolution of residual stresses by the method of sequentially increasing the length of a crack during high-cycle fatigue in flat samples (200 × 70 × 10 mm) were obtained with a central through hole with a diameter of 10 mm, strengthened by the cold deformation method (button-rifling method) [24]. The samples designated as Z0_k (k = 1, 2, 3, 4, 5) were made from the same 1163T alloy as the panels studied in this work. In addition, the hole hardening technologies were completely identical, and the loading cycle parameters were very close. The control sample failed upon reaching N_F = 110 000 cycles for a stress range Δσ = 160 MPa and an asymmetry coefficient R = 0.01. It is important that the values of the parameters of fracture mechanics when applying a sequence of artificial notches were determined for the sample in the initial state (N = 0, sample Z0₁) when N reached 20 000, 40 000, 60 000, and 80 000 (sample Z0₅) cycles. The distributions of SIF values obtained for the samples Z0₁ (N = 0) and Z0₅ (N = 80 000) are shown in Fig. 18 by curves 1 and 2 respectively.

[See PDF for image]

Fig. 18.

Dependence of SIF on the notch length: (1) specimen Z0₁; (2) specimen Z0₅; (3) specimen Z3.

For comparison, Fig. 18 shows the distribution of SIF values for a notch in the sample Z3 (curve 3). Curves 2 and 3 coincide to a sufficient degree. It is necessary to take into account that the control sample was subjected to cyclic loading with a free hardened hole, and the hardened holes in the sample Z3 during the loading process were filled with bolts installed with interference. A comparison of curve 2, reflecting the evolution of the SIF values in sample Z0₅, and curve 3, obtained for the sample Z3 after reaching N = 125 000 cycles, provides a quantitative assessment of the relaxation of the residual stress component σ₂ in a real structurally similar sample. Let us recall that testing of the Z3 sample was stopped after reaching N = 125 000 cycles.

CONCLUSIONS

Fatigue strength tests of two geometrically identical structurally similar models of the lower wing panel of a commercial aircraft were performed. The panels differ in the way of installation of the mounting bolts connecting the skin and the stringer. Both panels ensured the achievement of the specified resource without revealing the advantage of one of the technologies. Therefore, a two-stage comparison of both technologies was carried out on the basis of the study of residual stress fields. The first stage presented in this paper includes analysis of the magnitudes of the residual stress components in the vicinity of the mounting holes after removing the bolts and separating the skin from the stringer. To determine the components of residual stresses, two approaches were used to measure the deformation response to local removal of the material using the speckle interferometry method. The first, a discrete method based on drilling a probing hole, provides quantitative determination of residual stress components starting from a distance of 1.4 mm from the contour of the mounting hole. The second, a continuous method, is based on a sequential increase in the length of the artificial notch, starting directly from the contour of the mounting hole. This approach provides analysis of the residual stress fields characteristic of two bolt installation technologies by comparing the SIF values. As a criterion of preference for the technology of installing fastening bolts into mounting holes, the value of compressive residual stresses at the points closest to the contour of the mounting hole is considered. The higher the absolute value of the negative component of residual stress σ₂, which relaxes the most under the influence of an external load, since it coincides with the direction of this load, the better the technology for installing bolts from the viewpoint of fatigue strength. Both experimental approaches reveal the advantages of connecting with bolts installed in a reinforced hole. For this case, quantitative parameters of relaxation of the residual stress component in the direction of panel loading are determined. The next paper will present similar data that relates to the results of determining residual stresses in the vicinity of the holes filled with bolts.

FUNDING

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

CONFLICT OF INTEREST

The authors of this work declare that they have no conflicts of interest.

ABBREVIATIONS AND NOTATION

SIF

stress intensity factor

ZA and ZB

two structurally similar models

Δσ

the range of gross normal stresses

R

cycle asymmetry coefficient

H9

tolerance range

N

the assigned resource

ρ

probability level

u and v

distributions of the tangential components of displacements

h ≥ 3r₀

the depth of blind holes

2r₀

diameter

σ₁, σ₂

main residual stresses

FEM

finite element method

r₀

radius of the hole

E

modulus of elasticity of the material

Δu and Δv

increments in the diameter of the probing hole in the direction of the main stresses

σ₁ and σ₂

direction of the main stresses

a = (α₁ – 1), b = (σ₂ – μ), α₁ and α₂

coefficients of stress concentration during uniaxial tension of a plate with a hole

μ

Poisson ratio of an isotropic material

α₁, α₂

stress concentration coefficients

λ

wavelength of laser radiation

Ψ = π/4

angle between the direction of illumination and the direction of observation, normal to the surface of the object

ΔN^u, ΔN^v

differences in the absolute orders of the fringes

SILAN

sequentially increasing the length of an artificial notch

a₂

total notch length

value of SIF

Translated by Sh. Galyatdinov

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