The Behavior of Structures Composed of Composite Materials Part 13 ppsx

352 other factors. Even then practical considerations such as hole tolerances, and bolt torque actually applied would limit the usefulness of the results for design. Therefore from a design standpoint it appears that the best approach to use is that of Van Siclen [33], wherein simple easy to use equations can be used, which necessitate that certain tests be performed. For any given structural component, hopefully the material system, and the laminate orientation and number are decided on due to overall loading and environment for the component, rather than letting the joints control such decisions. Thus, material system, laminate orientation and thickness are predetermined before joint decisions are made or considered. For that chosen laminate, tests described by Van Siclen should be performed to determine the net tensile strength, the shear-out strength, and the bearing strength for that particular laminate. In Van Siclen’s [33] excellent paper, he presented the results of tests he performed on a graphite epoxy laminate. The resulting curves are given in Figures 8.12, 8.13, and 8.14. 353 These results then are easily used with Equation (8.40) through (8.42) to design, analyze, and optimize any joint. If the structural component is to be subjected to hygrothermal loads, then these tests should be carried out under those conditions, because Kim and Whitney [34] have shown the deleterious effects of a hygrothermal environment. If there is a normal pressure due to bolt torquing then the tests should be performed with the intended torques applied because Stockdale and Matthews [35] have shown that such pressure can increase bearing strength by 40% to 100%. Also, the actual bolts considered should be used in these tests because Van Siclen [33] points out the differences in strength when countersunk fasteners or protruded head hasteners are used. With those strengths available one can then select a fastener size to transmit the required load. It should be noted that it is generally agreed upon that and = 2 appear to be an optimum value in many cases. However, using the Van Siclen equations one can, to a certain extent, optimize the mechanically fastened joint. 354 If the laminate is too thin to transmit the required load then local stiffening is required. Alternative methods for stiffening have been discussed by Lehman and Hawley [9] and Oplinger and Gandhi [36] and additional testing could be required in the case of the stiffened configuration. If the structure is subjected to fatigue loading it appears that a full cycle set of tests are required, although the preliminary design could be based upon a design for which there is no yielding in tension, shear-out, or bearing at the mean fatigue load. As a data bank on the three strengths is built up for various material systems and ply orientations the amount of testing can be reduced. Since stacking sequence does have a significant effect on joint strength, if the stacking sequence for a structural component could be modified then the optimum design may require a compromise between the stacking sequences best for the component primary purpose, and what is best for the joint strength. Thus, the design of mechanically fastened joints is rather straightforward, and the optimization of joined structural components sufficiently complex that it is a challenge. In any case, simple analyses can be used, but some testing is required. It should also be remembered that Lehman and Hawley [9] found the addition of adhesive bonding to a bolted joint gave strengths that are greater than similar joints using either bonding or bolting only. Hence, in a design this also can be investigated using the Van Siclen approach discussed above. 8.4 Recommended Reading Other recommended reading for adhesive bonded joints includes that of Chamis and Murthy [37], Fujita et al [38], Tong [39], Running, Legon and Miskioglu [40], Mennetyen and Chamis [41], Liu, Raju and Yon [42], Lin and Jen [43], Pierron, Cerisier and Grediac [44], Turaga and Sun [45] and Zeng and Sun [46]. 8.5 References 1. 2. 3. 4. 5. Kuno, James K. (1979) Structural Adhesives Continue to Gain Foothold in Aerospace and Industrial Use, Structural Adhesives and Bonding. Proceedings of the Structural Adhesives Bonding Conference, arranged by Technology Conferences Associates, El Segundo, California. Szepe, F. (1966) Strength of Adhesive-Bonded Lap Joints with Respect to Temperature and Fatigue, Experimental Mechanics, Vol. 6, pp. 280-286. Volkersen, O. (1944) Die Niet Kraft vertelung in Zug bean Spruchten Niet verb bind ungen mit Konstaanten Lasch enguerschnitten, Luftfahrt forschungen, Vol. 15, pp. 41-47. De Bruyne, N.A. (1944) The Strength of Glued Joints, Aircraft Engineering, vol. 16, pp. 115-118. Wang, D.Y. (1963) The Effect of Stress Distribution on the Fatigue Behavior of Adhesive Bonded Joints, ASD-TDR-63-93, AFML, July. 355 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. Goland, M. and Reissner, E. (1947) Stresses in Cemented Joints, ASME Journal of Applied Mechanics, Vol. 11, A-17-A-27. Kutscha, D. (1964) Mechanics of Adhesive-Bonded Lap-Type Joints: Survey and Review, AFML-TDR-64-298, December. Kutscha, D. and Hofer, K.E., Jr. (1969) Feasibility of Joining Advanced Composite Flight Vehicles, AFML-TR-68-391, January. Lehman, G.M. and Hawley, A.V. (1969) Investigation of Joints in Advanced Fibrous Composites for Aircraft Structures, AFFDL-TR-69-43, Vol. 1, June. Dickson, J.N., Hsu, T.M. and McKinney, J.M. (1972) Development of an Understanding of the Fatigue Phenomenon of Bonded and Bolted Joints in Advanced Filamentary composite Materials, Analysis Materials, AFFDL-TR 72- 64 (AD 750 132), Vol. 1, June. Grimes, G.C., et al. (1972) The Development of Nonlinear Analysis Methods for Bonded Joints in Advanced Filamentary Composite Structures, AFFDL-TR-72-97 (AD 905 201), September. Ramberg, W. and Osgood, W.R. (1943) Description of Stress-Strain Curves by Three Parameters, NACA TN 902, July. Hart-Smith, L.J. (1970) The Strength of Adhesive Bonded Single Lap Joints, Douglas Aircraft Company IRAD Technical Report MDC-J0472, April. Hart-Smith, L.J. (1973) Adhesive-Bonded Single Lap Joints, NASA-CR-112236, January. Renton, W.J. and Vinson, J.R. (1973) The Analysis and Design of Composite Material Bonded Joints Under Static and Fatigue Loadings, AFOSR TR 73-1627, August. Renton, W.J. and Vinson, J.R. (1974) Fatigue Response of Anisotropic Adherend Bonded Joints, AMMRC MA-74-8, September. Renton, W.J. and Vinson, J.R. (1974) The Analysis and Design of Anisotropic Bonded Joints, Report No. 2, AFOSR TR-75-0125, August. Renton, W.J. and Vinson, J.R. (1975) On the Behavior of Bonded Joints in Composite Materials Structures, Journal of Engineering Fracture Mechanics, Vol. 7, pp. 41-60. Renton, W.J. and Vinson, J.R. (1975) Fatigue Behavior of Bonded Joints in Composite Materials Structures, AIAA Journal of Aircraft, Vol. 12, No. 5, May, pp. 442-447. Renton, W.J. and Vinson, J.R. (1975) The Efficient Design of Adhesive Bonded Joints, Journal of Adhesion, Vol. 7, pp. 175-193. Renton, W.J., Pajerowski, J. and Vinson, J.R. (1975) On Improvement in Structural Efficiency of Single Lap Bonded Joints, Proceedings of the Fourth Army Materials Technology Conference – Advances in Joining Technology, September. Renton, W.J. and Vinson, J.R. (1977) Analysis of Adhesively Bonded Joints Between Panels of Composite Materials, Journal of Applied Mechanics, April, pp. 101- 106. Renton, W.J., Flaggs, D.L. and Vinson, J.R. (1978) the Analysis and Design of Composite Materials Bonded Joints, Report No. III, AFOSR –TR-78-1512. Sharpe, W.N., Jr. and Muha, T.J., Jr. (1978) Comparison of Theoretical Experimental Shear Stress in the Adhesive Layer of a Lap Joint Model, AMMRC MS 74-8. 356 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. Oplinger, D.W. (1975) Stress Analysis of Composite Joints, Proceedings of the Fourth Army Materials Technology Conference – Advances in Joining Technology, September . Wetherhold , R.C. and Vinson, J.R. (1978) An Analytical Model for Bonded Joint Analysis in Composite Structures Including Hygrothermal Effects, AFOSR TR 78- 1337. Vinson, J.R. (1989) Adhesive Bonding of Polymer Composites, Polymer Engineering and Science, Mid-October, Vol. 29, No. 19, pp. 1325-1332. Flaggs, D.L. and Crossman, F.W. (1979) Viscoelastic Response of a Bonded Joint Due to Hygrothermal Exposure, Modern Developments in Composite Materials and Structures, ASME. Sen, J.K. (1977) Stress Analysis of Double Lap Joints Bonded with a Viscoelastic Adhesive, Ph.D. Dissertation, Southern Methodist University, May. Hart-Smith, L.J. (1980) Further Development in the Design and Analysis of Adhesive Bonded Structural Joints, Douglas Paper 6922 presented at the ASTM Symposium on Joining of Composite Materials. Bickley, W.G. (1928) The Distribution of Stress Round a Circular Hold in a Plate, Royal society of London, Vol. 227A, July 2, pp. 383-415. Murphy, M.M. and Lenoe, E.M. (1974) Stress Analysis of Structural Joints and Interfaces, A Selected Annotated Bibliography, AMMRC MS 74-10. Van Siclen, R.C. (1974) Evaluation of Bolted Joints in Graphite/Epoxy, Proceedings of the Army Symposium on Sold Mechanics (AD 786543 ), September, pp. 120- 138. Kim, R.Y. and Whitney, J.M. (1976) Effect of Temperature and Moisture on Pin Bearing Strength of composite Laminates, Journal of Composite Materials, April, pp. 149-155. Stockdale, J.H. and Matthews, F.L. (1976) The Effect of Clamping Pressure on Bolt Bearing Loads in Glass Fibre-Reinforced Plastics, Composites, January, pp. 34- 38. Oplinger, D.W. and Gandhi, K.R. (1974) Analysis Studies of Structural Performances in Mechanically Fastened Fiber-Reinforced Plates, Proceedings of the Army Symposium on Solid Mechanics (AD 786-543 ), September. Chamis, C.C. and Murthy, P.L. (1991) Simplified Procedures for Designing Adhesively Bonded Composite Joints, Journal of Reinforced Plastics and Composites, Vol. 10, January, pp. 29-41. Fujita, A., Hamada, H., Maekowa, Z., Ohno, E., and Yokoyama, A. (1994) Mechanical Behavior and Fracture Mechanism in Flat Braided Composites, Part 3: Mechanically Fastened Joint in Flat Braided Bar, Journal of Reinforced Plastics and Composites, Vol. 13, August, pp. 740-755. Tong, L. (1998) Failure of Adhesive-Bonded Composite Lap Joints With Embedded Cracks, AIAA Journal, Vol. 36, No. 3, March, pp. 448-456. Running, D.M., Legon, J.B. and Miskioglu, I. (1999) Fastener Design for Transversely Loaded Composite Plates, Journal of Composite Materials, Vol. 33, No. 10, pp. 928-940. 357 41. 42. 43. 44. 45. 46. Minnetyan, L. and Chamis, C.C. (1999) Progressive Fracture of Adhesively Bonded Composite Structures, Theoretical and Applied Fracture Mechanics, Vol. 31, pp. 75-84. Liu, D., Raju, B.B. and Yon, J. (1999) Thickness Effects on Pinned Joints for Composites, Journal of Composite Materials, Vol. 33, No. 1, pp. 2-21. Lin, W.H. and Jen, M.H. (1999) The Strength of Bolted and Bonded Single-Lapped Composite Joints in Tension, Journal of Composite Materials, Vol. 33, No. 7, pp. 640-666. Pierron, F., Cerisier, F. and Grediac, M. (2000) A Numerical and Experimental Study of Woven Composite Pin-Joints, Journal of Composite Materials, Vol. 34, No. 12, pp. 1028-1054. Turaga, U.V.R.S. and Sun, C.T. (2000) Failure Modes and Load Transfer in Sandwich T-Joints, Journal of Sandwich Structures and Materials, Vol. 2, July, pp. 1-21. Zeng, Q.G. and Sun, C.T. (2001) Novel Design of a Bonded Lap Joint, AIAA Journal, Vol. 39, No. 10, October, pp. 1991. 8.6 Problems 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 8.7. 8.8. a. b. a. b. For the laminate discussed by Van Siclen and the results presented in Figures 8.12, 8.13, and 8.14, if each ply is thick, using Figure 8.14 what total load (lbs) per bolt can be carried by a structure using diameter bolt? (i.e. Using Figure 8.13, if the construction has an edge distance, e , of what side distance, s , is required to withstand the same load per bolt as in (a) above? (i.e. For the laminate discussed by Van Siclen in Figures 8.12 and 8.13, namely if each lamina is thick, using Figure 8.14, what total load (lbs) per bolt can be carried by a structure using 5/8 diameter bolts? (what is Using Figure 8.13, if the construction has an edge distance, e , of what side distance, s , is required to withstand the same load per bolt as in Problem 8.1 above? (that is Consider a laminate composed of the composite of Figures 8.12, 8.13, and 8.14, eight plys, hence If a diameter bolt is used, with a side distance and edge distance, e , i n which mode of the three will the panel fail due to the bolt load; what is that failure value? Why is adhesive bonding potentially better for joining composite material components together than using mechanical fasteners? List six different types of adhesively bonded joints. What are three types of failure in mechanically fastened joints? What makes a combination of mechanically fastened and a bonded joint superior to either a mechanically bonded joint or an adhesively bonded joint separately? What are five good design rules for designing a good bonded joint in composite 358 8.9. 8.10. 8.11. 8.12. 8.13. 8.14. 8.15. 8.16. material structures? What are five good rules to follow in designing good mechanically fastened joints in composite material structures? Consider a laminate composed of a composite shown in Figures 8.12, 8.13 and 8.14, i.e., eight plys, hence If a bolt of diameter is used to fasten this laminate to another, where the side distance is and the edge distance is when an in-plane load P is applied, what is the maximum load P that the laminate can withstand, and in what mode will the laminate fail? Consider a laminate composed of a composite shown in Figures 8.12, 8.13 and 8.14, i.e., eight plys, hence If a bolt of diameter is used to fasten this laminate to another, where the side distance is and the edge distance is when an in-plane load P is applied, what is the maximum load P that the laminate can withstand, and in what mode will the laminate fail? For the laminate discussed by Van Siclen in Figures 8.12 and 8.13, namely if each lamina is thick, using Figure 8.14 what total bearing load, per bolt can be carried by this structure using diameter bolts? Using Figure 8.14, if the construction of Problem 8.12 has an edge distance, e, of what side distance, s, is required to withstand the load per bolt found in Problem 8.12 above? (i.e., Consider the laminate described by Figure 8.12, 8.13 and 8.14, composed of eight plies of ply thickness hence laminated thickness totals If a diameter bolt is used, with a side distance of and an edge distance in which mode of the three will the panel fail due to the bolt load? What is that failure value? Given a bolted joint between two graphite/epoxy panels of construction as given in Figures in Chapter 8, if and find the load carrying capacity in a. b. c. Net Tension Shear-out Bearing Consider a single lap joint adhesively bonded in which the adherends are thick, made of E-glass/epoxy whose properties are: 359 What is the ineffective length defined by Oplinger if the adhesive is thick? CHAPTER 9 INTRODUCTION TO COMPOSITE DESIGN 9.1 Introduction Through the first eight chapters, the “trees” of composite structures has been treated, now to discuss the “forest”. Design is so multifaceted, all encompassing and so dependent upon the product, materials, manufacturing processes and the type of end use that it cannot be treated succinctly. However, it is hoped that the following will provide som e insight. WHAT IS DESIGN? WHAT IS THE DESIGN PROCESS? Design is an open ended, sequential iterative procedure with feedback from previous steps required to select the next step. The design process culminates with a set or working drawings, reports and calculations from which a component of a system, a system or a process can be fabricated/constructed. WHAT ARE SOME (EVALUATION OF DESIGN) DESIGN PROCESS MODELS? Four differing models are shown below: 362 WHAT IS THE DIFFERENCE BETWEEN DESIGN AND ANALYSIS? Analysis focuses on quantifying the performance/behavior of a component /system/process as related to a specific need/mission. The design problem is focused on calculating the size, shape and configuration of a component/system/process to meet [...]... Element The RVE represents the smallest reference control volume of material which contains a fiber (or fibers) surrounded by the matrix material The RVE is considered to be both uniform and repetitive over the entire domain of the composite lamina with response characteristics representative of the composite As indicated in the assumption for predicting the micromechanical behavior of composites, the. .. DESIGN? The goals of structural composite material design are the specifications of, The types of constituents and their quantities The ply sequences and orientation of fibers Selection of an appropriate component geometry Selection of a fabrication process 365 WHAT DISCIPLINES MIGHT BE EMPLOYED IN THE DESIGN PROCESS? WHAT IS A FRAMEWORK FOR DESIGNING STRUCTURAL COMPONENTS FROM FIBER COMPOSITES? 366 The. .. information on the modulus of elasticity and the ultimate strength of various composites This can be obtained from the composite design data book Computation: In this example the governing equations are, and, Checking: In this simplistic example a checking of the computations is redundant however, the calculated and could be reintroduced into the equations and a check mode of for example, the load P in... conditions The validity of these simplifications can be measured by comparing the results of the restructured equations with those obtained using the more exact analytical procedures of micromechanics Thus for predicting the four elastic constants for an orthotropic composite in a plan state of stress, the following equations can be used For the unidirectional modulus the rule of mixtures remains a satisfactory... * 376 A number of approaches are available for calculation purposes to establish the material properties of composites Among these are, Analytical approaches Mechanics of Materials approach Theory of Elasticity Self-Consistent Model Variational Principles Exact Solutions Empirical Equations Discussion of these different approaches can be found in a number of references as for example the following:... Based upon the above calculations, since the modulus is high, referencing to the design data bank (see figure below) then a unidirectional boronepoxy composite with a fiber volume ratio of 66% is selected 372 From the figure blow, for a fiber volume fraction of 66%, the corresponding tensile strength in the uniaxial direction is given as, which is greater than the calculated value of 10 ksi Thus the member... constants are generally needed as input into the constitutive equations in order to model the material behavior In order to develop the analytical tools capable of modeling these material response parameters the subject of micromechanics is introduced This topic is based principally upon the determination of overall material properties of lamina in terms of their respective constituent properties and... below 369 370 DESIGN OF A TRUSS/BAR MEMBER As an example of the design process the following truss member is used Returning to the block diagram of the design process Need: Design of a Truss/Bar member to carry tensile loads Specifications: Tensile load requirement of 50 ksi Axial tension limited to 0.05 inches Bar geometry fixed at Concept Formation: The variables for design of the truss member are... introduced/used as proof tests of the selected design Application of Physical Principles/Gathering Data: In this example the physical principles needed are the constitutive (stress-strain-deformation) relations for a structural component loaded uniaxially, that is, and where the subscript i refers to the direction of loading/deformation that is, longitudinal, and the one direction and T refers to tension The data... Optimization: While the member has been adequately designed, the question of optimization for this example is not addressed For example, a cost analysis of this composite system (which works) with that of another candidate system could be examined Also, the current system while adequately designed from a modulus viewpoint is certainly overdesigned (factor of 2.6) from a strength point of view 373 Thus there is . into the design process. WHAT ARE THE GOALS OF A DESIGNER INVOLVED WITH STRUCTURAL COMPOSITE MATERIAL DESIGN? The goals of structural composite material design are the specifications of, The types. distance, e , of what side distance, s , is required to withstand the same load per bolt as in Problem 8.1 above? (that is Consider a laminate composed of the composite of Figures 8.12, 8 .13, and. laminate composed of a composite shown in Figures 8.12, 8 .13 and 8.14, i.e., eight plys, hence If a bolt of diameter is used to fasten this laminate to another, where the side distance is and the