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Stress concentrations near a discontinuity in fibrous composites
tive properties of fibre-reinforced materials as a function of the properties and proportions of the phases present; (2) the average spacing between fibres as a ftmction of the fibre thickness and volume fraction; (3) the volume fraction of the fibre phase as a function of the fibre separation, fibre thickness and matrix sheet thickness, when the composite material is produced by the compression of alternate layers of fibres and matrix sheets. Some exact results in transverse deformation of fibre reinforced composites Sendeckyj, G. P. and Ing-Wu Yu.
Journal o[ Composite Materials, Vol 5, p 533 (October 1971) An exact solution is derived for the stresses in a composite material in which the shear modulus of the fibres is the same as that of the matrix. Solutions in this case may be derived for both random and regular fibre arrays.
examined in two previous papers. T h e present paper investigates the magnitude of such effects for doubly curved plates and shells.
strengthening of the composite. At high strains, however, the strain hardening of the composite was independent of the matrix strength.
Viscous flow of aligned composites McLean, D. Journal o[ Materials
Directional solidification of an off-eutectic AI-Be alloy
Science, Vol 7(I), pp 98-104 (1972) Considering the case of an aligned composite subjected to tensile creep in the direction of the fibres, a geometrical approach shows that an appreciable degree of amplification of shear stress and strain in the reinforced matrix will be achieved. Consequent on this is the amplification of energy expenditure and tensile flow resistance indicating the enormous potential increase in flow resistance of the composite over the unsupported matrix material. However, the fibre end-stress, which is proportional to fibre diameter, may be large enough to initiate rupture if fibre diameter is greater than approxima,tely 1 ttm.
Stress concentrations near a discontinuity in fibrous composites Barker, R. M. and MacLaughlin, T. 1:.
Wave surfaces due to impact on aniso-
Journal o] Composite Materials, Vol 5, pp 492-503 (October 1971)
Space Administration Technical Note D-6357, 24 pp (September 1971)
Stress concentration factors are defined for the fibre and matrix in an axially loaded unidirectional composite which has a discontinuous fibre. Effects of variations in fibre volume fraction, end-gap size and modulus ratio are studied by using a linearly elastic finite-element analysis. Results show that the fibre stress concentration factors reach a maximum value of 1-3 and then remain relatively unchanged. However, the matrix stress concentration factors increase rapidly with decreasing end-gap size and increasing modulus ratio.
T h e application of advanced fibre composite materials to the fabrication of fan or compressor blade.s depends on their ability to sustain limited damage under impact forces. For small objects such as pebbles or hailstones. the impact times are of the order of microseconds. T h u s the energy transmission to the blade is completed before there are any or many reflections from the boundaries. T h e stress waves induced in anisotropic plates by transverse, short-duration impac,' forces are examined in this report. T h e anisotropy is related to the lay-up angles of the fibres. Using a modification of Mindlin's approximate theo D' of plates, it is shown that both extensional and bending waves are generated by transverse impact. T h e magnitudes of wave velocities in different directions are calculated for graphic ftbre-epoxy matrix plates as well as b o r o n - a l u m i n i u m and glass-epoxy systems for various lay-up angles Finally, the shapes of the wave fronts or wave surfaces due to point impact are also presented for the cases mentioned.
Thermal and infra-red non-destructive testing of composites and ceramics Green, D. R. Materials Evaluation.
Vol 29, No 11, p 24I (November 1971) T h e applicability of thermal techniques to the detection of delamin,~tions~ voids, density variations, thermal conductivity variations and graphitization in carbon-carbon composi,tes is demonstrated. Infra-red detection has been combined with induction heating using a full-width heating coil which traverses the specimen in a single path. A low-cost thermal transducer system has proved equally useful for nonconducting materials such as ceramics. Testing may be carried out using either technique in a few seconds. Vibration and buckling analysis of composite plates and shells McElman, J. A. and Knoell, A. C.
Journal o[ Composite Materials, Vol 5, p 529 (October 1971) In the analysis of laminated composites it is known that coupling exists between extension and b e n d i n g if the plies are not balanced ,in n u m b e r and fibre orientation. This effect for bending, vibration and buckling of two, four and six ply laminates was
tropic fiber composite plates Moon, F. C. National Aeronautics and
METAL MATRICES Deformation of a precipitation-hardenable Cr-Cu sintered powder composite Garmong, G. and Shepard, L. A.
Metallurgical Transactions, Vol 2, No 10, pp 2935-2937 (October 1971) A composi.te was prepared of 57.6 vol% spherical chromium particles in a copper matrix, by a method of liquid-phase sintering. It was subsequently found possible to precipitation harden the copper matrix by suitable heat treatments. Measurement of the stress-strain behaviour of the material showed that the hardening of the matrix caused a considerable
Pepper, R. T. and Wilcox, W. R.
Journal o] Composite Materials, Vol 5, pp 466-476 (October 1971) Aligned fibres of beryllium in a l u m i n i u m were obtained by zonemelting of an a l u m i n i u m / 2 0 wt%beryllium alloy. T h e composite UTS and Young's modulus were limited as a result of restricted fibre length caused by freezing-rate fluctuations but the strong preference of beryllium to grow fibres is seen as encouraging for the growth of oriented composites from this system with proper control of freezing-rate. ln~uence of processing history on the mechanical behavior of a Zn-W composite Edwards, G. R. and Sherby, O. D.
International Journal or Powder Metallurgy, Vol 7, No 4, pp 21-23 (October 1971) A composite of 28 vol% of fine tungsten particles in a matrix of zinc was prepared by mixing the metal powders and sintering. Specimens of the composite were then extruded. In unextruded specimens, the presence of the tungsten caused embrittlement of the zinc. Extrusion resulted in a progressive homogenization of the microstructure, and the composite became more ductile as well as weaker than unalloyed zinc. This effect was attributed to the production of dislocations near the tungsten particles. Initial dislocation distributions in tungsten fibre-copper composites Chawla, K. K. and Metzger, M. Journal
or Materials Science, Vol 7(1), pp 34-39 (1972) Etch-pit studies of composites of Cu containing low (15% or less) volume fractions of tfngsten wires have shown that dislocation densities in the singlecrystal matrix increase with fibre volume fraction and rise to high values toward the fibre-matrix interface. T h e dislocation distributions, which result from strains arising from differential shrinkage, were interpreted in terms of a contribution, independent of fibre fraction, due to transverse strains which fall off with distance from the fibre and a second one due to axial. strain which increases with fibre fraction but does not vary with distance from the fibre. Part of the axial adjustment is accomplished by interface shear. Mechanical behaviour of rapidly solidifled AI-AI~Cu and AI-AIsNi composites Lawson, W. H. S. and Kerr, H. W.
Metallurgical Transactions, Vol 2, No 10, pp 2853-2859 (October 1971) By variation of the rates of unidirectional solidification, eutectic alloys Of A1-AI2Cu and A1-AlsNi were prepared with rod-like microstructures of varying degrees of fineness. For both
COMPOSITES May 1972
]43
Journal o[ Composite Materials, Vol 5, p 533 (October 1971) An exact solution is derived for the stresses in a composite material in which the shear modulus of the fibres is the same as that of the matrix. Solutions in this case may be derived for both random and regular fibre arrays.
examined in two previous papers. T h e present paper investigates the magnitude of such effects for doubly curved plates and shells.
strengthening of the composite. At high strains, however, the strain hardening of the composite was independent of the matrix strength.
Viscous flow of aligned composites McLean, D. Journal o[ Materials
Directional solidification of an off-eutectic AI-Be alloy
Science, Vol 7(I), pp 98-104 (1972) Considering the case of an aligned composite subjected to tensile creep in the direction of the fibres, a geometrical approach shows that an appreciable degree of amplification of shear stress and strain in the reinforced matrix will be achieved. Consequent on this is the amplification of energy expenditure and tensile flow resistance indicating the enormous potential increase in flow resistance of the composite over the unsupported matrix material. However, the fibre end-stress, which is proportional to fibre diameter, may be large enough to initiate rupture if fibre diameter is greater than approxima,tely 1 ttm.
Stress concentrations near a discontinuity in fibrous composites Barker, R. M. and MacLaughlin, T. 1:.
Wave surfaces due to impact on aniso-
Journal o] Composite Materials, Vol 5, pp 492-503 (October 1971)
Space Administration Technical Note D-6357, 24 pp (September 1971)
Stress concentration factors are defined for the fibre and matrix in an axially loaded unidirectional composite which has a discontinuous fibre. Effects of variations in fibre volume fraction, end-gap size and modulus ratio are studied by using a linearly elastic finite-element analysis. Results show that the fibre stress concentration factors reach a maximum value of 1-3 and then remain relatively unchanged. However, the matrix stress concentration factors increase rapidly with decreasing end-gap size and increasing modulus ratio.
T h e application of advanced fibre composite materials to the fabrication of fan or compressor blade.s depends on their ability to sustain limited damage under impact forces. For small objects such as pebbles or hailstones. the impact times are of the order of microseconds. T h u s the energy transmission to the blade is completed before there are any or many reflections from the boundaries. T h e stress waves induced in anisotropic plates by transverse, short-duration impac,' forces are examined in this report. T h e anisotropy is related to the lay-up angles of the fibres. Using a modification of Mindlin's approximate theo D' of plates, it is shown that both extensional and bending waves are generated by transverse impact. T h e magnitudes of wave velocities in different directions are calculated for graphic ftbre-epoxy matrix plates as well as b o r o n - a l u m i n i u m and glass-epoxy systems for various lay-up angles Finally, the shapes of the wave fronts or wave surfaces due to point impact are also presented for the cases mentioned.
Thermal and infra-red non-destructive testing of composites and ceramics Green, D. R. Materials Evaluation.
Vol 29, No 11, p 24I (November 1971) T h e applicability of thermal techniques to the detection of delamin,~tions~ voids, density variations, thermal conductivity variations and graphitization in carbon-carbon composi,tes is demonstrated. Infra-red detection has been combined with induction heating using a full-width heating coil which traverses the specimen in a single path. A low-cost thermal transducer system has proved equally useful for nonconducting materials such as ceramics. Testing may be carried out using either technique in a few seconds. Vibration and buckling analysis of composite plates and shells McElman, J. A. and Knoell, A. C.
Journal o[ Composite Materials, Vol 5, p 529 (October 1971) In the analysis of laminated composites it is known that coupling exists between extension and b e n d i n g if the plies are not balanced ,in n u m b e r and fibre orientation. This effect for bending, vibration and buckling of two, four and six ply laminates was
tropic fiber composite plates Moon, F. C. National Aeronautics and
METAL MATRICES Deformation of a precipitation-hardenable Cr-Cu sintered powder composite Garmong, G. and Shepard, L. A.
Metallurgical Transactions, Vol 2, No 10, pp 2935-2937 (October 1971) A composi.te was prepared of 57.6 vol% spherical chromium particles in a copper matrix, by a method of liquid-phase sintering. It was subsequently found possible to precipitation harden the copper matrix by suitable heat treatments. Measurement of the stress-strain behaviour of the material showed that the hardening of the matrix caused a considerable
Pepper, R. T. and Wilcox, W. R.
Journal o] Composite Materials, Vol 5, pp 466-476 (October 1971) Aligned fibres of beryllium in a l u m i n i u m were obtained by zonemelting of an a l u m i n i u m / 2 0 wt%beryllium alloy. T h e composite UTS and Young's modulus were limited as a result of restricted fibre length caused by freezing-rate fluctuations but the strong preference of beryllium to grow fibres is seen as encouraging for the growth of oriented composites from this system with proper control of freezing-rate. ln~uence of processing history on the mechanical behavior of a Zn-W composite Edwards, G. R. and Sherby, O. D.
International Journal or Powder Metallurgy, Vol 7, No 4, pp 21-23 (October 1971) A composite of 28 vol% of fine tungsten particles in a matrix of zinc was prepared by mixing the metal powders and sintering. Specimens of the composite were then extruded. In unextruded specimens, the presence of the tungsten caused embrittlement of the zinc. Extrusion resulted in a progressive homogenization of the microstructure, and the composite became more ductile as well as weaker than unalloyed zinc. This effect was attributed to the production of dislocations near the tungsten particles. Initial dislocation distributions in tungsten fibre-copper composites Chawla, K. K. and Metzger, M. Journal
or Materials Science, Vol 7(1), pp 34-39 (1972) Etch-pit studies of composites of Cu containing low (15% or less) volume fractions of tfngsten wires have shown that dislocation densities in the singlecrystal matrix increase with fibre volume fraction and rise to high values toward the fibre-matrix interface. T h e dislocation distributions, which result from strains arising from differential shrinkage, were interpreted in terms of a contribution, independent of fibre fraction, due to transverse strains which fall off with distance from the fibre and a second one due to axial. strain which increases with fibre fraction but does not vary with distance from the fibre. Part of the axial adjustment is accomplished by interface shear. Mechanical behaviour of rapidly solidifled AI-AI~Cu and AI-AIsNi composites Lawson, W. H. S. and Kerr, H. W.
Metallurgical Transactions, Vol 2, No 10, pp 2853-2859 (October 1971) By variation of the rates of unidirectional solidification, eutectic alloys Of A1-AI2Cu and A1-AlsNi were prepared with rod-like microstructures of varying degrees of fineness. For both
COMPOSITES May 1972
]43