Investigation of residual stress around cold expanded holes using thermoelastic stress analysis Part 2

EXPERIMENTAL PROCEDURE

The plate specimens used in this work have been chosen to be representative of in-service applications, whilst at the same time realising the limitations associated with the load capacity of test machines and loading jigs (shown in Fig. 3 and Table 1). Aluminium plate specimens were manufactured with dimensions of 300 mm by 150 mm by 10 mm containing holes of nominal diameter 5/8" (15.875 mm). These dimensions were chosen for two reasons: firstly, the distance from the edge of the plate relative to the diameter of the hole (e/D ratio) is sufficiently large (i.e. greater than 3) for edge effects to not cause any unusual variation of the residual stress distribution during the cold expansion process. Secondly, it was shown in [14] that infinite plate conditions (i.e. no edge effects during cyclic loading for TSA) can be assumed if the distance from the hole to the plate edges (d1 and d2) are greater than 3.3D and 6.7D in the x and y directions respectively. It has been noted on several occasions that the level of strain hardening a material experiences may affect the change in thermoelastic constant that can be expected from plastic deformation. Subsequently, two grades of aluminium are investigated; one which experiences a high level of strain hardening (2024-T351) and one which does not strain harden significantly (7085-T7651). Finally, since the optimum level of cold expansion is 4% using the split sleeve method, four plates of each material have been manufactured containing holes with 0%, 2% and 4% cold expansion. Typically holes are reamed to a final dimension after expansion, for this reason one plate contains a 4% cold expanded hole that has not been reamed. It should also be noted that the mandrel split was aligned with the top of the hole, and that prior to cold expansion, the plates had been cold-rolled (in the 300 mm direction). In total, 8 plates were manufactured from each aluminium alloy; 4 containing cold expanded holes, and 4 additional plates from which the dog-bone type specimens were manufactured. Specimens had a nominal cross sectional area of 15 mm by 5 mm and were cut at 0°, 45° and 90° to the rolling direction; these were used to obtain the material properties, to assess the effect of material directionality, to obtain the baseline thermoelastic constant, and to determine the effect of plastic deformation on the thermoelastic constant for the two grades of aluminium.

A Cedip Silver 480M infra-red detector was used to obtain thermoelastic data. A thin layer of RS matt black paint was applied to the surface of all specimens to provide a high emissivity surface in accordance with established preparation guidelines [15]. An Instron 8500 servo-hydraulic test machine was used to statically apply load to induce plastic deformation in the tensile specimens, as well as cyclically load both the tensile and plate specimens for TSA.

To assess the effect of plastic deformation, dog-bone type specimens were strained quasi-statically in three loading steps: (i) 0.5 mm min-1 extension until yield, (ii) 0.5 mm min-1 until an additional 2% strain (or 4%), (iii) -0.5 mm min-1 until initial load (i.e. the pre-load when gripping the specimen) prior to applying the cyclic load for TSA. Linear strain gauges were applied to one side and an Imetrum video-extensometer was used on the opposite side of the specimen to measure the strain during the plastic deformation procedure. A calibration specimen was used to obtain the thermoelastic constant, K0, for 0% strain for each material. Specimens were cyclically loaded at a mean load of 8 kN (107 MPa), with a load amplitude of 4 kN (54 MPa) to obtain AT and T, allowing KP for each level of plastic strain to be calculated. Tests were conducted at 5 Hz, 7.5 Hz and 10 Hz to assess the effect of any non-adiabatic behaviour caused by the paint coating.

Plate specimens were cyclically loaded (in the rolling direction) at a mean load of 30 kN, with a load amplitude of 25 kN. The loading jig shown in Fig. 3 was used to facilitate loading of the specimens and to minimise bending during each test. Thermoelastic data was recorded from both the entry and exit faces of the plate, at two viewing distances: (i) at a stand off distance of 385 mm, showing the hole as well as areas of uniform stress away from the hole, and (ii) at a stand off distance of 200_mm, showing the areas immediately adjacent to the hole. Once again to assess any possible non adiabatic behaviour resulting from the paint coating, tests were conducted at 5 Hz, 7.5 Hz and 10 Hz.

Fig. 3 Plate specimen dimensions and loading mechanism

Table. 1 Plate Dimensions

A	Plate length	300 mm
B	Plate width	150 mm
C	Attachment holes	6 mm
D	Hole diameter	15.875 mm (5/8")
d1	Edge distance (x)	9.4 D
d2	Edge distance (y)	4.7 D
h	Plate thickness	10 mm

RESULTS AND DISCUSSION

Table 2 shows the relevant mechanical and thermoelastic properties of the two aluminium alloys obtained from tensile specimens. Five specimens of each alloy were used to obtain the data, and the values shown are the average over all five specimens; numbers in brackets represent the largest variation seen within each set of tests. AA2024 strain hardened by 32% and AA7085 by approximately 9%, confirming the different strain hardening characteristics of the two alloys (where the ability to strain harden is defined by the percentage increase of the ultimate tensile strength in comparison to the yield strength).

Table. 2 Mechanical and thermoelastic properties of AA2024-T351 and AA7085-T7651

Material	Yield Stress	Ultimate Tensile	% Strain	Thermoelastic
	[MPa]	Stress [MPa]	Hardening	Constant, K [Pa-1]
AA2024-T351	352 (± 5)	464 (± 3)	31.8 (± 1.8)	9.8 x 10-12 (± 0.05)
AA7085-T7651	494 (± 6)	538 (± 9)	8.9 (± 1.2)	9.4 x 10-12 (± 0.06)

Fig. 4 and Fig. 5 show the variation of KP/K0 for AA2024 and AA7085 specimens aligned with the 0°, 90° and 45° rolling directions. It can be seen that the change in KP/K0 is different for each alignment direction, and that the effect of plastic strain is greatest for the 45° specimen; the smallest change was measured for the 0° direction. While the temperature changes associated with this effect are very small (approximately 5 – 15 mK for the data shown), it can be seen that KP/K0 increases with increasing levels of plastic strain for each material. For specimens aligned with the 0° direction there was no visible effect of strain hardening on the change in KP/K0 which is in contrast to previous work [6], however the material directionality was not previously considered. It was seen that for the 90° and 45° specimens, the change in KP/K0 is larger for the AA2024 material, which does exhibit more strain hardening.

Fig. 4 Variation of KP/K0 for different specimen orientations for AA2024 at 10 Hz

Fig. 5 Variation of KP/K0 for different specimen orientations for AA7085 at 10 Hz

Some analysis of the microstructure is required to understand the physical processes causing the change in KP/K0 due to the introduction of plastic strain and how material directionality influences this change. Finally, due to the differences in KP/K0 for different alignment directions, it is now apparent that knowledge of material directionality would be required to enable an evaluation of plastic strain based on a change in thermoelastic constant from a reference specimen. While the plates containing cold expanded holes have been cold rolled and the direction is known, the stress distribution is more complex such that a simple calculation of KP is not necessarily possible; however, the fact that plastic deformation has occurred is likely to change the measured thermoelastic response, even though for cold expansion the relaxation is constrained, and thus residual stress is present.

The 0% cold expanded hole should contain no significant residual stress, since it has not been cold expanded, and any residual stress present due to cold rolling would be somewhat relieved during the subsequent hole drilling and reaming. In comparison, the 2% and 4% cold expanded holes would contain large compressive residual stress very close to the hole (within a few mm) reducing to small tensile residual stress further from the hole. Therefore any differences in thermoelastic response due to residual stress should be identifiable from comparison of the thermoelastic data recorded from the specimens. Every effort was made to ensure the infra-red detector was positioned such that the location of the hole remained the same in each test, thus allowing a pixel by pixel comparison of the thermoelastic data to be performed for each plate. However, due to the high dynamic loading, motion was noticeable in the TSA video data and this was particularly apparent at the specimen edges. Motion compensation was performed on the TSA data to remove this motion and the resulting errors than can be associated with it. It was achieved by identifying two significant and contrasting features in the first frame of the recorded data, which are then tracked through subsequent frames allowing them to be rotated, distorted or translated such that any motion appears stationary. Fig. 6 shows TSA data observed from around 0%, 2% and 4% cold expanded holes on the entry side of AA7085 plates; the stress distribution that would normally be expected around a hole is clearly identifiable.

Fig. 6 Thermoelastic response around cold expanded holes in AA7085-T7651 plates, Entry side loaded at 10 Hz; (Top) 4%, (Middle) 2%, (Bottom) 0%.

The circular area (1) was applied to each image to check the hole was in the same position and that motion compensation was successful; during each test, the hole itself was filled with Blue-Tac, and therefore shows little or no thermoelastic response. Two line plots have been taken from the data; the first (2) shows the thermoelastic response directly across the hole, the second (3) shows the response further from the hole, in a region of more uniform stress. It can be seen that the background temperature change is approximately 0.10°C and the maximum temperature occurring at the hole is approximately 0.25°C. Using Eqn. 1 and the thermoelastic constant for AA7085 from Table 2, the applied stresses can be approximated as 35 MPa in the plate and 90 MPa at the hole. In an ideal situation, increasing the applied load would increase the stress, and thus increase the differences in the temperature changes that are of interest, however, further increasing the applied load could result in some areas containing tensile residual stress entering plasticity, as well as approaching the load capacity of the test machine and other deleterious effects arising from bending or distortion of the loading rig. To examine differences in thermoelastic response, the AT data around the 0% cold expanded holes was subtracted from the data around the corresponding 4% cold expanded holes on a pixel by pixel basis; this formed new data sets revealing areas with a different thermoelastic response (Fig. 7); note, the data from within the holes has been removed, along with the immediate the edge data that may be erroneous.

Fig. 7(a) shows clear differences in the thermoelastic response from around the 4% and 0% cold expanded holes can be seen in the new data sets; however, the data is relatively noisy. The marks seen in the top left and top right corners of each image correspond to paint that was scratched from the surface to provide a reference point for motion compensation. In an attempt to remove the noise, a line of data from an area of uniform stress in each 0% plate was subtracted from the same area on the corresponding 4% plate; this provided an estimation of the background noise variation caused by the subtraction process. A threshold filter was then applied to each new data set to remove any data that fell within the calculated noise limits, providing an image where departures in the thermoelastic response between identically loaded plates of the same material can be clearly identified. Fig. 7(b) shows the AT4% – ATm data sets for the entry and exit sides of the AA2024 and AA7085 plates with the threshold noise filter applied. The variations in AT are small, but it is encouraging that measurable differences exist that are larger than the proposed noise levels, and far enough from the hole edge to be a result of erroneous measurement or edge effects.

Fig. 7 Difference in thermoelastic response around the 4% and 0% cold expanded holes, (a) Without threshold noise filter applied, (b) With threshold noise filter applied.(Top left) AA7085 entry side, (Bottom left) AA7085 exit side, (Top right) AA2045 entry side, (Bottom right) AA2024 exit side.

Since the loading conditions are the same for each plate, the difference in the thermoelastic response between the specimens must be a result of the residual stress around the hole caused by the cold expansion process. The expected residual stress profile (Fig. 2) would take the form of a ring of compressive residual stress close to the hole, with a very small region of tensile residual stress directly above the hole corresponding to the location of the split in the sleeve. The data for the AA7085 entry side and the AA2024 exit side show variations in AT all around the hole which correlates with the expected areas of residual stress; however a different distribution is seen for the AA7085 exit side and the AA2024 entry side. At this point, it is not clear what the causes of the differences are, and since there is no consistency between the shape and magnitude of the variation, it is difficult to ascertain if this is a result of the mean stress effect, plastic deformation causing a change in K or a combination of the two.

CONCLUSIONS

The residual stress distribution around cold expanded holes presented an opportunity to investigate changes in thermoelastic response that occur as a result of residual stress, and assess the feasibility of using TSA as a potential residual stress assessment tool. It was known that the presence of residual stress may influence the effective mean stress, possibly providing an additional component of the thermoelastic signal; it was also shown that the occurrence of plastic strain can modify the thermoelastic constant K, for some materials, again possibly resulting in a change in thermoelastic response. The loading conditions were rigorously maintained during experimental work and the position and settings of the infra-red detector remained constant. Differences in the thermoelastic response were observed from around the cold expanded holes in regions that would be expected to contain residual stress, and a basic noise filter applied to identify areas where significant departures in thermoelastic response were measured.

Experimental work using tensile specimens (utilised to eliminate the mean stress effect) revealed that plastic deformation did affect the thermoelastic constant for both materials analysed in this work, confirming that the changes in thermoelastic response around the holes could be attributed to the deformation experienced during cold expansion. However, since the purpose of cold expansion is to create compressive residual stress around the hole, the 4% hole contained residual stress from cold expansion, and had experienced plastic deformation, whereas the 0% hole did not contain residual stress from cold expansion and had not experienced plastic deformation; therefore there is also the possibility that the change in response or part of, was a result of an increase in effective mean stress due to the residual stress. Nevertheless, small but measurable differences in the thermoelastic response from areas that were known to contain different levels of residual stress were detected, suggesting that there may be potential for TSA to be used for assessing residual stress at some point. Currently, the extent of its practical application is limited and significant further work is required to identify the cause of the change in thermoelastic response, and to develop procedures that could possibly relate this change to residual stress.