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Photoelastic investigation of bolted joints in composites
Photoelastic investigation of bolted joints in composites R. PRABHAKARAN In this paper, the methods of photo-orthotropic elasticity are applied to the study of bolted joints in composites. The photoelastic models are E-glass fibre-reinforced epoxy strips loaded through a cylindrical pin, simulating bolt loading without lateral pressure. A special loading arrangement is devised so that the photoelastic response around the hole is not obscured. Quasi-isotropic and unidirectionallyreinforced specimens are tested, with ratios of end distance to hole diameter varying from 2 to 6. Photoelastic isochromatic fringe patterns are presented along with the shear stress distribution for the quasi-isotropic models.
Key words: composite materials; mechanically fastened joints; photoelastic analysis; glass fibre-reinforced epoxy
Mechanical fastening is a common joining method for composite laminates used in structural applications. Fastener holes degrade the laminate strength and the degradation may be amplified by material anisotropy, brittleness and heterogeneity. The prediction of the strength of bolted joints requires the determination of the stress distribution around the joint and the application of a suitable failure criterion. Theoretical, closed-form, solutions for the stresses around a hole loaded by a rigid inclusion are scarce. Finite element 1'2 and approximate elasticity solutions a,4 are available. Experimental methods have a clear advantage but only a limited amount of work appears to have been done. Strain gauges s and Moir~ analysis 6 have been employed to complement results from finite element analyses of finite width composite panels loaded through a cylindrical pin.
TEST PROCEDURE The test specimen configuration and the loading arrangement are shown in Fig. 1. All the specimens were 50 mm wide and were glued to aluminium tabs at one end. Holes of
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specirr~
T
F
I
The extension of transmission photoelastic techniques to birefringent composites offers a very useful method of studying the stresses and failure modes in composite joints. The birefringent composites consist of continuous glass fibres in an epoxy or polyester matrix and exhibit a considerable degree of transparency if the refractive indices of the glass and the polymer are closely matched. The composite exhibits an over-all photoelastic response which can be related to the stresses in the composite on a macroscopic level. The interpretation of the isochromatics and the isoclinics in birefringent composite models has been developed in recent years and many of these developments have been reviewed by the author. 7 In this paper, preliminary photoelastic tests of pin-loaded composite models are described. Quasi-isotropic and unidirectionally-reinforced models have been tested and for each material the end distance (distance from the hole to the end of the specimen) is varied. The resulting isochromatic fringe patterns are presented and the influence of the end distance on the maximum in-plane shear stress for the quasi-isotropic models is shown.
1
1
Fig. 1 Schematic diagram of specimen and loading arrangement
0010-4361/82/030253-04 $03.00 © 1982 Butterworth & Co (Publishers) Ltd COMPOSITES . JULY 1982
253
most of the region around the hole was clear. Two different materials were used to fabricate the specimens, a quasiisotropic lay-up consisting of [04 / + 454 / - 4 5 4 / 9 0 4 ] s plies and a unidirectional lay-up. The nominal thickness of all the specimens was 4 mm. Three values of end distance, designated as AB in Fig. 1, namely 25 mm, 50 mm and 75 mm, were employed for each material. The isochromatic fringe patterns were photographed at successively increasing loads. EXPERIMENTAL RESULTS
Fig. 2 Light-field isochromatic fringe pattern for quasi-isotropic model (load = 3560 N, end distance = 25 mm)
Light field isochromatic fringe patterns for the quasiisotropic material, corresponding to end distances of 25 mm, 50 mm and 75 mm are shown in Figs 2, 3 and 4, respectively. While the over-all features of the three fringe patterns are similar, the isochromatics for the shortest end distance differ from the other two. All the photographs correspond to a tensile load of 3560 N; the fringe pattern for 25 mm end distance shows the influence of the end. All the fringes are flattened and the half-order fringe is bent towards the hole on the line of symmetry. None of the specimens showed any damage due to the pin bearing stress; in addition, there was no residual birefringence on unloading. The in-plane maximum shear stress was computed from the dark field and light field isochromatic fringe patterns for the quasi-isotropic specimens. A typical shear stress distribution is shown in Fig. 5. In this figure the shear stress is normalized with respect to the tensile stress over the net section across the hole diameter. The variation of the shear stress along the line AB represents the shear-out failure 1.0
0.9 Fig. 3 Light-field isochromatic fringe pattern for quasi-isotropic model (load = 3560 N, end distance = 50 mm)
0.8
m
0.7
0-6 (I)
e n g t h - -
AB=25mm
5mm
0.5 E •( 0.4 E 0-:5 Z
Fig. 4 Light-field isochromatic fringe pattern for quasi-isotropic model (load = 3560 N, end distance = 75 mm)
12.5 mm diameter were drilled in the specimens by ultrasonic machining and the hole boundaries were sharp and stress-free. A slightly undersized steel pin, giving a ratio of pin diameter to hole diameter of 0.990, was used to load the specimens. To load the specimen without obscuring the neighbourhood of the hole, a special loading fixture was devised, as shown in Fig. 1. With this loading arrangement,
254
0.2
01 t O
I
I
I
I
I
I
5
IO
15
20
25
50
Distance along AB from A (ram) Fig. 5 Variation of maximum in-plane shear stress for quasiisotropic model along line AB (load = 2560 N)
COMPOSITES.
JULY 1982
stress, which is critical for short end distances. It is seen that the stress levels are higher for the shortest end distance and there is no difference between the 50 mm and 70 mm end distances. The general nature of these results agree with finite element results reported in Reference [5]. Light field isochromatic fringe patterns for the unidirectionally-reinforced models, corresponding to end distances
of 25 mm, 50 mm and 75 ram, are shown in Figs 6,7 and 8, respectively. The reinforcement was along the loading direction in all the models. While the effect of the specimen end is a maximum in Fig. 6, a small influence of the end can be seen in Fig. 7, mainly on the half order fringe, when compared to Fig. 8. Though the ratio of the pin diameter to hole diameter was the same as in the case of the quasiisotropic models, the material anisotropy results in two distinct sets of fringe loops. All these fringe patterns correspond to a tensile load of 3560 N. On unloading, none of the specimens showed any sign of damage due to the pin bearing stress; there was no residual birefringence. The shear-out mode of failure can be expected to be favoured for these specimens. However, the maximum in-plane shear stress cannot be directly computed from the isochromatic fringe order for the unidirectionally-reinforced models. Additional information is required for this determination. Two promising methods are drilling small holes at selected points 8 and bonding a photoelastic coating on one side of the model. 9 Work is in progress in employing the second method. SUMMA R Y AND CONCLUSIONS
Fig. 6 Light-field isochromatic fringe pattern for unidirectionallyreinforced model (load = 3 5 6 0 N, end distance = 25 ram)
A transmission photoelastic method has been employed in the study of pin-loaded birefringent composite models which simulate bolted joints in composites. A special loading arrangement has been devised to obtain the photoelastic response around most of the neighbourhood of the hole. Quasi-isotropic and unidirectionally-reinforced E-glass epoxy models have been tested, with varying distances from the hole to the model end. For both materials, the influence of the end distance was appreciable for the shortest end distance employed. The effect of the material anisotropy was clearly evident from the isochromatic fringe patterns. These preliminary results indicate that photo-orthotropicelastic techniques can be usefully employed in the investigation of bolted joints in composites. Further work is in progress to obtain the additional results from photoelastic coatings which are necessary for a complete stress analysis and also to study the effect of pin diameter, bolt tightening torque, etc. ACKNOWLEDGEMENT
Fig. 7 Light-field isochromatic fringe pattern for unidirectionallyreinforced model (load = 3 5 6 0 N, end distance = 50 ram)
The research work was performed with photoelastic equipment purchased under an equipment grant No CDP-8016606 from NSF and was supported by NSF research grant No CME-8012956. The author would like to thank Dr Clifford J. Astill and Dr Howard H. Hines of NSF for their support and encouragement. REFERENCES
1 2
3 4 Fig. 8 Light-field isochromatic fringe pattern for unidirectionallyreinforced model (load = 3 5 6 0 N, end distance = 75 mm)
C O M P O S I T E S . J U L Y 1982
Waszczak,J.P. and Cruse, T.A. 'Failure mode and strength predictions of anisotropic bolt bearing specimens' J Composite Mater 5 No 3 (July 1971) pp 421--434 Crews,J.H., Jr. 'Bolt-bearing fatigue of a graphite/epoxy laminate' Joining o f Composite Materials, A S T M STP 749 (American Society for Testing and Materials, 1981) pp 131-144 Jong, T.D. 'Stresses around pin-loaded holes in elastically orthotropic or isotropic plates' J Composite Mater 11 No 3 (July 1977) pp 313-325 Oplinger,D.W. and Gandhi, R.R. 'Stresses in mechanically fastened orthotropic laminates' Proe 2nd Conference on Fibrous Composites in Flight Vehicle Design (Dayton, Ohio, May 1974)
255
5
6 7
8
256
Wilson, D.W. and Pipes, R.B. 'Analysis of the shearout failure mode in composite bolted joints' Proc 1st Int Conf on Composite Structures (Paisley, Scotland, September 1981) pp 34--49 Wilkinson, T.L. and Rowlands, R.E. 'Analysis of mechanical joints in wood'ExperimentalMech 21 No 11 (November 1981) pp 408--414 Prabhakaxan, R. 'Applications of transmission photoelasticity to composite materials' Developments in Composite Materials, Volume 2 (Applied Science Publishers, 1981) pp 75-99 Prabhakaran, R. 'Extension of the hole-drilling method to birefringent composites' Polymer Composites 3 No 1 (January 1982) pp 40--43
Prabhakaran, R. 'Separation of principal stresses in photo-orthotropic-elasticity' Fibre Sci and Tech 13 No 3 (July 1980) pp 245-253 AUTHOR
R. Prabhakaran is Associate Professor with the Old Dominion University's Department of Mechanical Engineering and Mechanics. Inquiries should be addressed to: Professor R. Prabhakaran, Department of Mechanical Engineering and Mechanics, Old Dominion University, Norfolk, VA 23508, USA.
COMPOSITES. JULY 1982
Key words: composite materials; mechanically fastened joints; photoelastic analysis; glass fibre-reinforced epoxy
Mechanical fastening is a common joining method for composite laminates used in structural applications. Fastener holes degrade the laminate strength and the degradation may be amplified by material anisotropy, brittleness and heterogeneity. The prediction of the strength of bolted joints requires the determination of the stress distribution around the joint and the application of a suitable failure criterion. Theoretical, closed-form, solutions for the stresses around a hole loaded by a rigid inclusion are scarce. Finite element 1'2 and approximate elasticity solutions a,4 are available. Experimental methods have a clear advantage but only a limited amount of work appears to have been done. Strain gauges s and Moir~ analysis 6 have been employed to complement results from finite element analyses of finite width composite panels loaded through a cylindrical pin.
TEST PROCEDURE The test specimen configuration and the loading arrangement are shown in Fig. 1. All the specimens were 50 mm wide and were glued to aluminium tabs at one end. Holes of
T
o ho.os, l ~
specirr~
T
F
I
The extension of transmission photoelastic techniques to birefringent composites offers a very useful method of studying the stresses and failure modes in composite joints. The birefringent composites consist of continuous glass fibres in an epoxy or polyester matrix and exhibit a considerable degree of transparency if the refractive indices of the glass and the polymer are closely matched. The composite exhibits an over-all photoelastic response which can be related to the stresses in the composite on a macroscopic level. The interpretation of the isochromatics and the isoclinics in birefringent composite models has been developed in recent years and many of these developments have been reviewed by the author. 7 In this paper, preliminary photoelastic tests of pin-loaded composite models are described. Quasi-isotropic and unidirectionally-reinforced models have been tested and for each material the end distance (distance from the hole to the end of the specimen) is varied. The resulting isochromatic fringe patterns are presented and the influence of the end distance on the maximum in-plane shear stress for the quasi-isotropic models is shown.
1
1
Fig. 1 Schematic diagram of specimen and loading arrangement
0010-4361/82/030253-04 $03.00 © 1982 Butterworth & Co (Publishers) Ltd COMPOSITES . JULY 1982
253
most of the region around the hole was clear. Two different materials were used to fabricate the specimens, a quasiisotropic lay-up consisting of [04 / + 454 / - 4 5 4 / 9 0 4 ] s plies and a unidirectional lay-up. The nominal thickness of all the specimens was 4 mm. Three values of end distance, designated as AB in Fig. 1, namely 25 mm, 50 mm and 75 mm, were employed for each material. The isochromatic fringe patterns were photographed at successively increasing loads. EXPERIMENTAL RESULTS
Fig. 2 Light-field isochromatic fringe pattern for quasi-isotropic model (load = 3560 N, end distance = 25 mm)
Light field isochromatic fringe patterns for the quasiisotropic material, corresponding to end distances of 25 mm, 50 mm and 75 mm are shown in Figs 2, 3 and 4, respectively. While the over-all features of the three fringe patterns are similar, the isochromatics for the shortest end distance differ from the other two. All the photographs correspond to a tensile load of 3560 N; the fringe pattern for 25 mm end distance shows the influence of the end. All the fringes are flattened and the half-order fringe is bent towards the hole on the line of symmetry. None of the specimens showed any damage due to the pin bearing stress; in addition, there was no residual birefringence on unloading. The in-plane maximum shear stress was computed from the dark field and light field isochromatic fringe patterns for the quasi-isotropic specimens. A typical shear stress distribution is shown in Fig. 5. In this figure the shear stress is normalized with respect to the tensile stress over the net section across the hole diameter. The variation of the shear stress along the line AB represents the shear-out failure 1.0
0.9 Fig. 3 Light-field isochromatic fringe pattern for quasi-isotropic model (load = 3560 N, end distance = 50 mm)
0.8
m
0.7
0-6 (I)
e n g t h - -
AB=25mm
5mm
0.5 E •( 0.4 E 0-:5 Z
Fig. 4 Light-field isochromatic fringe pattern for quasi-isotropic model (load = 3560 N, end distance = 75 mm)
12.5 mm diameter were drilled in the specimens by ultrasonic machining and the hole boundaries were sharp and stress-free. A slightly undersized steel pin, giving a ratio of pin diameter to hole diameter of 0.990, was used to load the specimens. To load the specimen without obscuring the neighbourhood of the hole, a special loading fixture was devised, as shown in Fig. 1. With this loading arrangement,
254
0.2
01 t O
I
I
I
I
I
I
5
IO
15
20
25
50
Distance along AB from A (ram) Fig. 5 Variation of maximum in-plane shear stress for quasiisotropic model along line AB (load = 2560 N)
COMPOSITES.
JULY 1982
stress, which is critical for short end distances. It is seen that the stress levels are higher for the shortest end distance and there is no difference between the 50 mm and 70 mm end distances. The general nature of these results agree with finite element results reported in Reference [5]. Light field isochromatic fringe patterns for the unidirectionally-reinforced models, corresponding to end distances
of 25 mm, 50 mm and 75 ram, are shown in Figs 6,7 and 8, respectively. The reinforcement was along the loading direction in all the models. While the effect of the specimen end is a maximum in Fig. 6, a small influence of the end can be seen in Fig. 7, mainly on the half order fringe, when compared to Fig. 8. Though the ratio of the pin diameter to hole diameter was the same as in the case of the quasiisotropic models, the material anisotropy results in two distinct sets of fringe loops. All these fringe patterns correspond to a tensile load of 3560 N. On unloading, none of the specimens showed any sign of damage due to the pin bearing stress; there was no residual birefringence. The shear-out mode of failure can be expected to be favoured for these specimens. However, the maximum in-plane shear stress cannot be directly computed from the isochromatic fringe order for the unidirectionally-reinforced models. Additional information is required for this determination. Two promising methods are drilling small holes at selected points 8 and bonding a photoelastic coating on one side of the model. 9 Work is in progress in employing the second method. SUMMA R Y AND CONCLUSIONS
Fig. 6 Light-field isochromatic fringe pattern for unidirectionallyreinforced model (load = 3 5 6 0 N, end distance = 25 ram)
A transmission photoelastic method has been employed in the study of pin-loaded birefringent composite models which simulate bolted joints in composites. A special loading arrangement has been devised to obtain the photoelastic response around most of the neighbourhood of the hole. Quasi-isotropic and unidirectionally-reinforced E-glass epoxy models have been tested, with varying distances from the hole to the model end. For both materials, the influence of the end distance was appreciable for the shortest end distance employed. The effect of the material anisotropy was clearly evident from the isochromatic fringe patterns. These preliminary results indicate that photo-orthotropicelastic techniques can be usefully employed in the investigation of bolted joints in composites. Further work is in progress to obtain the additional results from photoelastic coatings which are necessary for a complete stress analysis and also to study the effect of pin diameter, bolt tightening torque, etc. ACKNOWLEDGEMENT
Fig. 7 Light-field isochromatic fringe pattern for unidirectionallyreinforced model (load = 3 5 6 0 N, end distance = 50 ram)
The research work was performed with photoelastic equipment purchased under an equipment grant No CDP-8016606 from NSF and was supported by NSF research grant No CME-8012956. The author would like to thank Dr Clifford J. Astill and Dr Howard H. Hines of NSF for their support and encouragement. REFERENCES
1 2
3 4 Fig. 8 Light-field isochromatic fringe pattern for unidirectionallyreinforced model (load = 3 5 6 0 N, end distance = 75 mm)
C O M P O S I T E S . J U L Y 1982
Waszczak,J.P. and Cruse, T.A. 'Failure mode and strength predictions of anisotropic bolt bearing specimens' J Composite Mater 5 No 3 (July 1971) pp 421--434 Crews,J.H., Jr. 'Bolt-bearing fatigue of a graphite/epoxy laminate' Joining o f Composite Materials, A S T M STP 749 (American Society for Testing and Materials, 1981) pp 131-144 Jong, T.D. 'Stresses around pin-loaded holes in elastically orthotropic or isotropic plates' J Composite Mater 11 No 3 (July 1977) pp 313-325 Oplinger,D.W. and Gandhi, R.R. 'Stresses in mechanically fastened orthotropic laminates' Proe 2nd Conference on Fibrous Composites in Flight Vehicle Design (Dayton, Ohio, May 1974)
255
5
6 7
8
256
Wilson, D.W. and Pipes, R.B. 'Analysis of the shearout failure mode in composite bolted joints' Proc 1st Int Conf on Composite Structures (Paisley, Scotland, September 1981) pp 34--49 Wilkinson, T.L. and Rowlands, R.E. 'Analysis of mechanical joints in wood'ExperimentalMech 21 No 11 (November 1981) pp 408--414 Prabhakaxan, R. 'Applications of transmission photoelasticity to composite materials' Developments in Composite Materials, Volume 2 (Applied Science Publishers, 1981) pp 75-99 Prabhakaran, R. 'Extension of the hole-drilling method to birefringent composites' Polymer Composites 3 No 1 (January 1982) pp 40--43
Prabhakaran, R. 'Separation of principal stresses in photo-orthotropic-elasticity' Fibre Sci and Tech 13 No 3 (July 1980) pp 245-253 AUTHOR
R. Prabhakaran is Associate Professor with the Old Dominion University's Department of Mechanical Engineering and Mechanics. Inquiries should be addressed to: Professor R. Prabhakaran, Department of Mechanical Engineering and Mechanics, Old Dominion University, Norfolk, VA 23508, USA.
COMPOSITES. JULY 1982