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Deformation in adhesive joints using moiré interferometry
Deformation in adhesive joints using moir interferometry A. Asundi (University of Hong Kong, Hong Kong)
A wholefield optical method, moir~ interferometry, is shown to be capable of measuring deformations in adhesive joints with very high sensitivity. A high frequency phase grating attached to the specimen is interrogated with an optically generated reference grating to reveal in-plane isothetics with a sensitivity of 0.83 i~m/fringe. This technique thus enables local deformations within the adhesive bond to be investigated, as well as giving an overall deformation contour map.
Kay words: adhesive-bonded joints; deformation; u-isothetics; shear strain distribution; Moir6 interferometry It is well known that the properties of adhesives when used as thin films in bonded joints can be significantly different from their bulk properties. It is therefore necessary to study these adhesives in specimen configurations similar to their use in actual structures, and the thick-adherend symmetric lap joint has been proposed = as a suitable test specimen. However, it is still difficult to perform experiments to study deformation within the thin adhesive layer of interest. In this paper, a new optical technique is proposed which has the capability of measuring minute displacements over any part of the bonded joint, even within the thin adhesive layer and its interface with the adherend. Moir6 interferometry 2 is an extension of the classical moir6 method. Using the experimental set-up outlined in this paper, in-plane displacement components can be measured with a maximt~m sensitivity approaching the theoretical limit (ff half a wavelength per fringeL Thus the method is suitable for studying deformations within a thin adhesive layer in a bonded joint.
Experimental details As with the classical moir6 method, moir6 interferometry can be superficially explained as the interference produced between a deformed specimen grating and a fLxed reference grating. Since the gratings used in this method have a frequency of 600 l/mm, the method is more rigorously explained in terms of diffraction and interference. However, it has been shown 4 that the resulting fringe pattern still provides contours of constant displacement components (isothetics) as in the classical moir6 approach, but with a much higher sensitivity. The adhesive joint investigated comprised aluminium adherends bonded via a thin adhesive layer
to form the symmetric lap joint (see Fig. 1). Selfadhesive tape was applied to the joint boundary to control the length and thickness of joint. The joint thickness was adjusted to 0.3 mm and was checked using a fillet gauge. The adhesive was Ciba-Geigy Araldite resin AWl06 and hardener HV9530, mixed with a resin-to-hardener ratio of 10:8 parts by weight. The joint was clamped in a jig to maintain alignment and cured for 30 min at 100*C, followed by room temperature curing for 24 h. The specimen grating was created by transferring the corrugations of a cross-line phase grating onto a thin layer of epoxy poured on the specimen. The procedure for making the phase grating and its transfer is quite routine, and is explained in greater detail in Reference 2. The lines of the transferred grating were aligned parallel and perpendicular to the line of load application. The adhesive-bonded specimen was mounted in a screw-type loading fixture, which could be rotated through 90 ° to investigate both the in-plane displacement components at the same load. A load cell with a sensitivity of 44 N/division was used to measure the applied load. This assembly was placed in the optical set-up as shown schematically in Fig. 2. A collimated beam of light from a 100 mW He-Ne laser is incident on the specimen and the plane mirror
~,~/
600//mm grating
.qT--( t ~
~1111m /~,I
• 0.3 rnrn
y t~
~] z
~
x
ZOOmrr;, i
Fig. 1
Geometry of test specimen
0 1 4 3 - 7 4 9 6 / 8 7 / 0 1 0 0 3 9 - 0 4 $03.00 © 1987 Butterworth Et Co (Publishers) Ltd INT.J.ADHESlON AND ADHESIVES VOL.7 NO.1 JANUARY 1987
39
Mirror Lens
plane Speci
....
_
SfPlt;iral
Fig. 2
~
/
Parabolic
mirror
Schematicof the moir~ interferometric set-up
at a prescribed angle a, which is determined using the diffraction equation:
V
sina =-2
(1)
where A is the wavelength of laser light a n d f is twice the frequency of the specimen grating. The plane mirror reflects the beam, incident on it, on to the specimen surface. Thus at the specimen plane, two beams of coherent light are incident at _+ a with respect to the normal. They interfere to produce a virtual reference grating of twice the frequency of the specimen grating. This reference grating can now interefere with the deformed specimen grating to
Fig. 3
Moir~ pattern representing the u-isothetics, Sensitivity is 0.83 pro/fringe
40
INT.J.ADHESlON AND ADHESIVES JANUARY 1987
produce the moir6 fringes with a sensitivi~ equal to the pitch of the reference grating (0.83 pm/fringe). The virtual grating lines created with this set-up are perpendicular to the plane of Fig. 2. They will therefore interfere with the corresponding grating lines on the specimen grating to reveal the displacement component in the x-direction (u-isothetics). To obtain the corresponding v-isothetics, the specimen is rotated through 90 ° so that the perpendicular grating lines can be interrogated. Initially, with zero applied load, there should be a null field with no fringes. However, due to imperfection of the grating and low quality optics, a few fringes are seen for the no-load case. On application of the load, fringes due to the deformation are added on to this initial pattern. Hence, to obtain the deformation due to load alone, the initial pattern should be subtracted from the final pattern. This can be achieved by graphical or optical subtraction. Graphical subtraction can be tedious if done manually due to the large number of fringes. The optical subtraction involves addition of a carrier or bias fringe pattern of the same magnitude to both the no-load and loaded fringe patterns. This is accomplished by either changing the angle or by rotating the specimen by small amounts. This is similar to introducing mismatch (linear or rotational) fringes in the classical moir6 method. The mismatch creates a carder pattern of frequency 8 to 10 I/mm, although the exact value is immaterial so long as it is the same in both the no-load and loaded cases. Now, if the no-load plus carder is superimposed on the load
10
i
x
=0K
mI 0.1
0.2
0.3
x L
10
[
I
5
0 y (mm)
mid-plane
I 5
Fig. 5
Fig. 4 Displacement distribution across width of the adhesive joint st a few locations over the bond length; from Fig. 3
plus carrier fringe pattern, the resulting moir6 reveals the difference between the two patterns, ie, the isothetics corresponding to load alone. Having obtained the two fringe patterns representing the u and v displacement components, these components can be calculated according to the moir6 equation:
Fig. 6
Shear strain distribution along the mid-plane of the adhesive layer
lO u = Nxp
v = N~v
(2)
where Nx and Ny are the fringe orders and p is the pitch of the reference grating. Since, in general, we are interested in the strains (ie, the derivatives of the displacement), it is not necessary to know the absolute fringe orders; the relative displacements suffice. Hence a fringe order can be arbitrarily assigned and neighbouring fringes numbered in increasing or decreasing order depending on the sign of fringes.
Moir~ pattern representing the u-isothetics due to load alone. Sensitivity is 0.83 pm/fringe
INT.J.ADHESION A N D ADHESIVES J A N U A R Y 1 9 8 7
41
Results
The adhesive joint of Fig. 1 with the imprinted specimen grating was tested to obtain the in-plane displacement components. It was observed that the displacement component in the y-direction was relatively small and hence only u-isothetics are shown and evaluated. Fig. 3 is a representative isothetic fringe pattern due to a load of 660 N. Due to the limited size of the optical components, only one-third of the total bond length is shown. However, this is the most critical area along the bond area and hence sufficient to provide a good insight to the problem. In addition, this fringe pattern also has the initial (no-load) fringes. Nevertheless, this pattern demonstrates the extremely high sensitivity and the clarity of fringes that moire interferometry provides, as well as the deformation within and around the adhesive layer. The relative displacement along a few lines parallel to the ydirection are plotted in Fig. 4. The slope of these curves at discrete points within the adhesive thickness gives du/dy. Since the other component of the shear strain dv/dx is negligibly small, these derivatives approximate to the shear strain at various locations. Fig. 5 shows the shear strain distribution along the centreline of the adhesive, as well as at the adhesive/adherend interface. Although the shear strain distribution is as expected, the above results may not be accurate since the initial pattern was not subtracted. To reveal the displacement field due to load alone, carrier patterns of the same frequency were added to both the initial (no-load) and the final (load of 440 N) patterns. Superposition of these two fringe patterns thus reveals the displacement due to load alone (see Fig. 6). As before, the displacement distributions along selected vertical lines are plotted in Fig. 7 and their slope at the mid-plane of the adhesive layer gives the shear strain distribution (see Fig. 8). The shear strain distributions in both cases exhibit the phenomenon of differential shear, characteristic of adhesive joints with elastic adherends. Indeed, in the first experiment, the no-load pattern had relatively few fringes and hence its influence within the adhesive layer was small. The displacement distribution (see Fig. 7) shows some unsymmetry about the mid-plane. The reason for this was that the specimen experienced a small rotation during loading which tended to distort the fringe pattern. This is also evident from the fringe pattern (see Fig. 6), where the lack of symmetry is clearly visible close to the end of the adherend. This further substantiates the high sensitivity of the method. The shear strain distribution along any other direction (for example, the adhesive/adherend interface) can also be easily obtained. In fact, the normal strain distribution could also be evaluated along any section.
Conclusion
Moir~ interferometry has been demonstrated to be a useful and highly sensitive method in the study of deformations in bonded adhesive joints. The ability to obtain the wholefleld displacement patterns permits the strains to be measured within the adhesive or at the interface between the adhesive layer and the adherend. These critical areas can also be investigated in more
detail by suitable magnifications during the recording
42
INT.J.ADHESION AND ADHESIVES JANUARY 1987
~"
u
X
•
-c =°2w I =o.2,5 v
N=I tu=0.83 x 103mm
i l
2,0
I 1.0
~
mid-plane
l 0 y (ram)
x
1 1.0
I
2.0
Displacement distribution across the adhesive layer at a few locations over the bond length; from Fig. 6
Fig. 7
m
3 0 x
e ear strain
0.1
0.2
1 0.3
__x L
Shear strain distribution along the mid-plane of the adhesive layer
Fig. 8
process. Further investigation of such detail is under study to provide better experimental insight into this problem. Acknowledgement
The assistance of Dr C.W. Woo, Mr M.T. Cheung and Miss S.C. Wong with the project details and experimentation is gratefully acknowledged. References 1
Renton, W J . "The symmetric lap-shear test - - what good is it?"
2
Post, D. 'Developments in moire inter/erometry' Opt Engng 21 No 3 ( 1 9 8 2 ) pp 4 5 8 - 4 6 7
3
Weismn,
Exptl Mech 16 ( 1 9 7 6 ) pp 4 0 9 - 4 1 5
4
E.M. and Post, D. 'Moire interferometry near the theoretical limit' Appl Opt 21 No 9 (1982) pp 1621-1623
Livnat, A. end Poet, D. "The governing equations for moire
interferometwand their identity to equations of geometrical moire' ExptlMech 25 N o 4 (1985) pp 360-366 Author
Dr Asundi is with the Department of Mechanical Engineering, University of Hong Kong, Hong Kong.
A wholefield optical method, moir~ interferometry, is shown to be capable of measuring deformations in adhesive joints with very high sensitivity. A high frequency phase grating attached to the specimen is interrogated with an optically generated reference grating to reveal in-plane isothetics with a sensitivity of 0.83 i~m/fringe. This technique thus enables local deformations within the adhesive bond to be investigated, as well as giving an overall deformation contour map.
Kay words: adhesive-bonded joints; deformation; u-isothetics; shear strain distribution; Moir6 interferometry It is well known that the properties of adhesives when used as thin films in bonded joints can be significantly different from their bulk properties. It is therefore necessary to study these adhesives in specimen configurations similar to their use in actual structures, and the thick-adherend symmetric lap joint has been proposed = as a suitable test specimen. However, it is still difficult to perform experiments to study deformation within the thin adhesive layer of interest. In this paper, a new optical technique is proposed which has the capability of measuring minute displacements over any part of the bonded joint, even within the thin adhesive layer and its interface with the adherend. Moir6 interferometry 2 is an extension of the classical moir6 method. Using the experimental set-up outlined in this paper, in-plane displacement components can be measured with a maximt~m sensitivity approaching the theoretical limit (ff half a wavelength per fringeL Thus the method is suitable for studying deformations within a thin adhesive layer in a bonded joint.
Experimental details As with the classical moir6 method, moir6 interferometry can be superficially explained as the interference produced between a deformed specimen grating and a fLxed reference grating. Since the gratings used in this method have a frequency of 600 l/mm, the method is more rigorously explained in terms of diffraction and interference. However, it has been shown 4 that the resulting fringe pattern still provides contours of constant displacement components (isothetics) as in the classical moir6 approach, but with a much higher sensitivity. The adhesive joint investigated comprised aluminium adherends bonded via a thin adhesive layer
to form the symmetric lap joint (see Fig. 1). Selfadhesive tape was applied to the joint boundary to control the length and thickness of joint. The joint thickness was adjusted to 0.3 mm and was checked using a fillet gauge. The adhesive was Ciba-Geigy Araldite resin AWl06 and hardener HV9530, mixed with a resin-to-hardener ratio of 10:8 parts by weight. The joint was clamped in a jig to maintain alignment and cured for 30 min at 100*C, followed by room temperature curing for 24 h. The specimen grating was created by transferring the corrugations of a cross-line phase grating onto a thin layer of epoxy poured on the specimen. The procedure for making the phase grating and its transfer is quite routine, and is explained in greater detail in Reference 2. The lines of the transferred grating were aligned parallel and perpendicular to the line of load application. The adhesive-bonded specimen was mounted in a screw-type loading fixture, which could be rotated through 90 ° to investigate both the in-plane displacement components at the same load. A load cell with a sensitivity of 44 N/division was used to measure the applied load. This assembly was placed in the optical set-up as shown schematically in Fig. 2. A collimated beam of light from a 100 mW He-Ne laser is incident on the specimen and the plane mirror
~,~/
600//mm grating
.qT--( t ~
~1111m /~,I
• 0.3 rnrn
y t~
~] z
~
x
ZOOmrr;, i
Fig. 1
Geometry of test specimen
0 1 4 3 - 7 4 9 6 / 8 7 / 0 1 0 0 3 9 - 0 4 $03.00 © 1987 Butterworth Et Co (Publishers) Ltd INT.J.ADHESlON AND ADHESIVES VOL.7 NO.1 JANUARY 1987
39
Mirror Lens
plane Speci
....
_
SfPlt;iral
Fig. 2
~
/
Parabolic
mirror
Schematicof the moir~ interferometric set-up
at a prescribed angle a, which is determined using the diffraction equation:
V
sina =-2
(1)
where A is the wavelength of laser light a n d f is twice the frequency of the specimen grating. The plane mirror reflects the beam, incident on it, on to the specimen surface. Thus at the specimen plane, two beams of coherent light are incident at _+ a with respect to the normal. They interfere to produce a virtual reference grating of twice the frequency of the specimen grating. This reference grating can now interefere with the deformed specimen grating to
Fig. 3
Moir~ pattern representing the u-isothetics, Sensitivity is 0.83 pro/fringe
40
INT.J.ADHESlON AND ADHESIVES JANUARY 1987
produce the moir6 fringes with a sensitivi~ equal to the pitch of the reference grating (0.83 pm/fringe). The virtual grating lines created with this set-up are perpendicular to the plane of Fig. 2. They will therefore interfere with the corresponding grating lines on the specimen grating to reveal the displacement component in the x-direction (u-isothetics). To obtain the corresponding v-isothetics, the specimen is rotated through 90 ° so that the perpendicular grating lines can be interrogated. Initially, with zero applied load, there should be a null field with no fringes. However, due to imperfection of the grating and low quality optics, a few fringes are seen for the no-load case. On application of the load, fringes due to the deformation are added on to this initial pattern. Hence, to obtain the deformation due to load alone, the initial pattern should be subtracted from the final pattern. This can be achieved by graphical or optical subtraction. Graphical subtraction can be tedious if done manually due to the large number of fringes. The optical subtraction involves addition of a carrier or bias fringe pattern of the same magnitude to both the no-load and loaded fringe patterns. This is accomplished by either changing the angle or by rotating the specimen by small amounts. This is similar to introducing mismatch (linear or rotational) fringes in the classical moir6 method. The mismatch creates a carder pattern of frequency 8 to 10 I/mm, although the exact value is immaterial so long as it is the same in both the no-load and loaded cases. Now, if the no-load plus carder is superimposed on the load
10
i
x
=0K
mI 0.1
0.2
0.3
x L
10
[
I
5
0 y (mm)
mid-plane
I 5
Fig. 5
Fig. 4 Displacement distribution across width of the adhesive joint st a few locations over the bond length; from Fig. 3
plus carrier fringe pattern, the resulting moir6 reveals the difference between the two patterns, ie, the isothetics corresponding to load alone. Having obtained the two fringe patterns representing the u and v displacement components, these components can be calculated according to the moir6 equation:
Fig. 6
Shear strain distribution along the mid-plane of the adhesive layer
lO u = Nxp
v = N~v
(2)
where Nx and Ny are the fringe orders and p is the pitch of the reference grating. Since, in general, we are interested in the strains (ie, the derivatives of the displacement), it is not necessary to know the absolute fringe orders; the relative displacements suffice. Hence a fringe order can be arbitrarily assigned and neighbouring fringes numbered in increasing or decreasing order depending on the sign of fringes.
Moir~ pattern representing the u-isothetics due to load alone. Sensitivity is 0.83 pm/fringe
INT.J.ADHESION A N D ADHESIVES J A N U A R Y 1 9 8 7
41
Results
The adhesive joint of Fig. 1 with the imprinted specimen grating was tested to obtain the in-plane displacement components. It was observed that the displacement component in the y-direction was relatively small and hence only u-isothetics are shown and evaluated. Fig. 3 is a representative isothetic fringe pattern due to a load of 660 N. Due to the limited size of the optical components, only one-third of the total bond length is shown. However, this is the most critical area along the bond area and hence sufficient to provide a good insight to the problem. In addition, this fringe pattern also has the initial (no-load) fringes. Nevertheless, this pattern demonstrates the extremely high sensitivity and the clarity of fringes that moire interferometry provides, as well as the deformation within and around the adhesive layer. The relative displacement along a few lines parallel to the ydirection are plotted in Fig. 4. The slope of these curves at discrete points within the adhesive thickness gives du/dy. Since the other component of the shear strain dv/dx is negligibly small, these derivatives approximate to the shear strain at various locations. Fig. 5 shows the shear strain distribution along the centreline of the adhesive, as well as at the adhesive/adherend interface. Although the shear strain distribution is as expected, the above results may not be accurate since the initial pattern was not subtracted. To reveal the displacement field due to load alone, carrier patterns of the same frequency were added to both the initial (no-load) and the final (load of 440 N) patterns. Superposition of these two fringe patterns thus reveals the displacement due to load alone (see Fig. 6). As before, the displacement distributions along selected vertical lines are plotted in Fig. 7 and their slope at the mid-plane of the adhesive layer gives the shear strain distribution (see Fig. 8). The shear strain distributions in both cases exhibit the phenomenon of differential shear, characteristic of adhesive joints with elastic adherends. Indeed, in the first experiment, the no-load pattern had relatively few fringes and hence its influence within the adhesive layer was small. The displacement distribution (see Fig. 7) shows some unsymmetry about the mid-plane. The reason for this was that the specimen experienced a small rotation during loading which tended to distort the fringe pattern. This is also evident from the fringe pattern (see Fig. 6), where the lack of symmetry is clearly visible close to the end of the adherend. This further substantiates the high sensitivity of the method. The shear strain distribution along any other direction (for example, the adhesive/adherend interface) can also be easily obtained. In fact, the normal strain distribution could also be evaluated along any section.
Conclusion
Moir~ interferometry has been demonstrated to be a useful and highly sensitive method in the study of deformations in bonded adhesive joints. The ability to obtain the wholefleld displacement patterns permits the strains to be measured within the adhesive or at the interface between the adhesive layer and the adherend. These critical areas can also be investigated in more
detail by suitable magnifications during the recording
42
INT.J.ADHESION AND ADHESIVES JANUARY 1987
~"
u
X
•
-c =°2w I =o.2,5 v
N=I tu=0.83 x 103mm
i l
2,0
I 1.0
~
mid-plane
l 0 y (ram)
x
1 1.0
I
2.0
Displacement distribution across the adhesive layer at a few locations over the bond length; from Fig. 6
Fig. 7
m
3 0 x
e ear strain
0.1
0.2
1 0.3
__x L
Shear strain distribution along the mid-plane of the adhesive layer
Fig. 8
process. Further investigation of such detail is under study to provide better experimental insight into this problem. Acknowledgement
The assistance of Dr C.W. Woo, Mr M.T. Cheung and Miss S.C. Wong with the project details and experimentation is gratefully acknowledged. References 1
Renton, W J . "The symmetric lap-shear test - - what good is it?"
2
Post, D. 'Developments in moire inter/erometry' Opt Engng 21 No 3 ( 1 9 8 2 ) pp 4 5 8 - 4 6 7
3
Weismn,
Exptl Mech 16 ( 1 9 7 6 ) pp 4 0 9 - 4 1 5
4
E.M. and Post, D. 'Moire interferometry near the theoretical limit' Appl Opt 21 No 9 (1982) pp 1621-1623
Livnat, A. end Poet, D. "The governing equations for moire
interferometwand their identity to equations of geometrical moire' ExptlMech 25 N o 4 (1985) pp 360-366 Author
Dr Asundi is with the Department of Mechanical Engineering, University of Hong Kong, Hong Kong.