- Email: [email protected]
Mechanical properties of fibrous composites
73
Technical Papers The following is a very small selection of the many publications in the field, chosen for their value as introductory literature to the subject. The first two papers comprise a complete issue of Metallurgical Reviews, 10 (37) (1965). The first paper is by A. Kelly and G. L. Davies, "The Principles of the Fibre Reinforcement of Metals". This paper begins with an explanation of the need to reinforce metals; fibre reinforcement is especially important and this is subdivided into the use of whiskers, fibres or metal wires. The advantages and disadvantages are briefly discussed. The main portion of the paper deals with fibre reinforcement. Its particularly clear presentation enables the reader to find easily any particular aspect in which he is particularly interested. The first subdivision deals with composites containing continuous fibres. The stress-strain behaviour and the tensile strength are studied, together with the effect of various parameters. These include fibre volume and elastic or plastic matrix. The same factors are considered for discontinuous fibres, but stress transfer from the matrix to the fibre and the effect of the fibre length are additionally discussed. These two sections are followed by sections on the behaviour at the fibre matrix interface and the stress distribution when non-metallic matrixes are used. The authors explain how three possible failures modes are set up depending on the angle at which the fibre axis is orientated to the axis of the applied load. This is followed by three short sections on statistical analysis of fibre strength, fracture and creep behaviour. The last portion of the paper deals with the various methods for producing fibre-reinforced materials, and how some of these processes can affect the properties of the composites. The authors have compiled an extensive bibliography. The second paper by D. Cratchley, "Experimental Aspects of Fibre Reinforced Metals" also has a brief introduction to the fibre reinforcement of metals, and it includes a brief resum6 of how the elastic constants may be found for the materials. The first main section deals with model metal/metal systems used, purely because of their ease of construction, to study the validity of the proposed basic principles of fibre reinforcement. The author gives several well-known examples. The following section deals with metal systems produced for commercial purposes. The author gives five examples and lists their properties. The use of whiskers (mainly alumina) is discussed. The paper concludes with three sections on glass fibres, silica fibres and reinforcement by intermetallic compounds. An extensive bibliography is given.
Mechanical Properties of Fibrous Composites, B. Rosen, N. F. Dow and Z. Hashin, NASA LR 31, April 1964. The authors use the variational theory of elasticity to obtain expressions for the constants. They have obtained these for three cases; a regular hexagonal array of fibres, a random array of fibres, and hollow fibres. In order that one may fully realise the importance of these expressions, the authors have produced several Fibre Science and Technology, Elsevier Publishing Company Ltd., England--Printed in Great Britain
74
" I E ( ' f I N I C A L PA PI!RS
graphs showing the variation of these expressions with respect to other known parameters. One of the claims of reinforced materials, particularly plastics, is that they have a high strength/density ratio; the authors have tried to increase this still further by obtaining transversely orientated voids in their composite. The analogy they use is that the composite is in the form of a plate with "waffle-like" stiffening. On analysing the composite as such the authors find that the density may be reduced in this way with little or no decrease in the stiffness/density ratio. The second part of this report deals with the tensile strength of composites and is basicallythe same as the chapter written by B. Rosen for Fiber Reit~rcedComposites. R. Hill has published many papers on the theoretical bounding of the elastic constants. These papers are of a highly specialized nature and are obviously intended for applied mathematicians. One of the more recent papers appears in the Journal of the Mechanics and Physics of Solids, 13 (1965). References to Hill's previous papers are given, and it is advisable to read all these papers together for easy cross reference.
Standards in order that the practical measurement of these constants can have some continuity, international codes of practice have been produced. Two sources are the British Standards Institution, and the American Society./or Testing and Materials. Fortunately, these have not stopped people from publishing accounts of methods for measuring these constants. One of the most important constants is the shear modulus and J. M. Hennesay has published "Experimental Methods for Determining Shear Modulus of Fiber Reinforced Materials" (AFML TR-65-42). The author explains the three possible ways of measuring the constants: in-plane shear modulus, shear modulus from four-point loading and shear modulus from the saddle test. The formulas for evaluating the shear modulus from each test is given together with a detailed account of the specimens used and the test procedure. In a series of appendices at the end of the paper, the author derives all the relevant formulas from the basic shear equations for an orthotropic material. Fatigue behaviour is an important aspect of composite behaviour, and the following papers are suggested as a suitable introduction to this subject: A review by R. B. Heywood on the "Fatigue and Creep Strengths of Reinforced Plastics" (R.A.E. Techn. Note Chem. (337)) considers the unsuitability of general fatigue testing machines for testing reinforced plastics. The machines designed for testing them are described. For creep study it was found that general machines would suffice. The author gives a list of fatigue tests that have been carried out using different resins, both push-pull and reversed bending. These results are compared and show that the order of behaviour is not the same for the two types of tests and that the fatigue behaviour of the composite is very much dependent upon the behaviour of the resin matrix. Creep behaviour does not appear to be an important factor. A bibliography of all previous work in the field is given.
TECHNICAL PAPERS
75
A paper, by A. A. Baker and D. Cratchley, appeared in Applied Materials Research, Oct. (1964) 215. This paper describes metallographic observations made by the authors of the fatigue behaviour of silica fibre-reinforced aluminium. Two batches of samples were tested, these being produced under different conditions of pressure and temperature. The results show that the method of preparation has a definite bearing on the results. The surface and sub-surface observations are listed. The authors present an argument for the best possible way of fatigue testing and the possible sources of, and reasons for, fatigue failure. It is of great importance to know when, and under what loading, a fibre-reinforced material sheet (or plate) will fail. Kelly and Davies have presented a theory for fibre-reinforced metals and a general theory of failure has been developed by S. W. Tsai. By assuming that, for most cases, the sheet is in a state of plane stress and orthotropic in the transverse direction, Tsai produces a general equation of failure that is dependent upon the tensile strength normal and parallel to the fibre axis, the shear strength, and also the orientation of the axis of symmetry from the axis of applied load. By considering the loading as uniaxial, Tsai reduces this equation still further. For the case of a single sheet he shows how, for failure strength variation with axis orientation, theoretical values agree with the experimental values. From the results for one sheet Tsai then considers the form in which composites are often used--laminated, cross-ply and single-ply. Tsai describes the procedure for finding which layer will fail first and also the behaviour after initial failure. This work has also been expanded to cover pressure vessel design. Tsai's work has been reported in several publications but the following three are the most important: NASA CR 71 July, 1964. NASA CR 224 April, 1965. NASA CR 620, November, 1966 (with D. F. Adams and D. R. Doner).
Technical Papers The following is a very small selection of the many publications in the field, chosen for their value as introductory literature to the subject. The first two papers comprise a complete issue of Metallurgical Reviews, 10 (37) (1965). The first paper is by A. Kelly and G. L. Davies, "The Principles of the Fibre Reinforcement of Metals". This paper begins with an explanation of the need to reinforce metals; fibre reinforcement is especially important and this is subdivided into the use of whiskers, fibres or metal wires. The advantages and disadvantages are briefly discussed. The main portion of the paper deals with fibre reinforcement. Its particularly clear presentation enables the reader to find easily any particular aspect in which he is particularly interested. The first subdivision deals with composites containing continuous fibres. The stress-strain behaviour and the tensile strength are studied, together with the effect of various parameters. These include fibre volume and elastic or plastic matrix. The same factors are considered for discontinuous fibres, but stress transfer from the matrix to the fibre and the effect of the fibre length are additionally discussed. These two sections are followed by sections on the behaviour at the fibre matrix interface and the stress distribution when non-metallic matrixes are used. The authors explain how three possible failures modes are set up depending on the angle at which the fibre axis is orientated to the axis of the applied load. This is followed by three short sections on statistical analysis of fibre strength, fracture and creep behaviour. The last portion of the paper deals with the various methods for producing fibre-reinforced materials, and how some of these processes can affect the properties of the composites. The authors have compiled an extensive bibliography. The second paper by D. Cratchley, "Experimental Aspects of Fibre Reinforced Metals" also has a brief introduction to the fibre reinforcement of metals, and it includes a brief resum6 of how the elastic constants may be found for the materials. The first main section deals with model metal/metal systems used, purely because of their ease of construction, to study the validity of the proposed basic principles of fibre reinforcement. The author gives several well-known examples. The following section deals with metal systems produced for commercial purposes. The author gives five examples and lists their properties. The use of whiskers (mainly alumina) is discussed. The paper concludes with three sections on glass fibres, silica fibres and reinforcement by intermetallic compounds. An extensive bibliography is given.
Mechanical Properties of Fibrous Composites, B. Rosen, N. F. Dow and Z. Hashin, NASA LR 31, April 1964. The authors use the variational theory of elasticity to obtain expressions for the constants. They have obtained these for three cases; a regular hexagonal array of fibres, a random array of fibres, and hollow fibres. In order that one may fully realise the importance of these expressions, the authors have produced several Fibre Science and Technology, Elsevier Publishing Company Ltd., England--Printed in Great Britain
74
" I E ( ' f I N I C A L PA PI!RS
graphs showing the variation of these expressions with respect to other known parameters. One of the claims of reinforced materials, particularly plastics, is that they have a high strength/density ratio; the authors have tried to increase this still further by obtaining transversely orientated voids in their composite. The analogy they use is that the composite is in the form of a plate with "waffle-like" stiffening. On analysing the composite as such the authors find that the density may be reduced in this way with little or no decrease in the stiffness/density ratio. The second part of this report deals with the tensile strength of composites and is basicallythe same as the chapter written by B. Rosen for Fiber Reit~rcedComposites. R. Hill has published many papers on the theoretical bounding of the elastic constants. These papers are of a highly specialized nature and are obviously intended for applied mathematicians. One of the more recent papers appears in the Journal of the Mechanics and Physics of Solids, 13 (1965). References to Hill's previous papers are given, and it is advisable to read all these papers together for easy cross reference.
Standards in order that the practical measurement of these constants can have some continuity, international codes of practice have been produced. Two sources are the British Standards Institution, and the American Society./or Testing and Materials. Fortunately, these have not stopped people from publishing accounts of methods for measuring these constants. One of the most important constants is the shear modulus and J. M. Hennesay has published "Experimental Methods for Determining Shear Modulus of Fiber Reinforced Materials" (AFML TR-65-42). The author explains the three possible ways of measuring the constants: in-plane shear modulus, shear modulus from four-point loading and shear modulus from the saddle test. The formulas for evaluating the shear modulus from each test is given together with a detailed account of the specimens used and the test procedure. In a series of appendices at the end of the paper, the author derives all the relevant formulas from the basic shear equations for an orthotropic material. Fatigue behaviour is an important aspect of composite behaviour, and the following papers are suggested as a suitable introduction to this subject: A review by R. B. Heywood on the "Fatigue and Creep Strengths of Reinforced Plastics" (R.A.E. Techn. Note Chem. (337)) considers the unsuitability of general fatigue testing machines for testing reinforced plastics. The machines designed for testing them are described. For creep study it was found that general machines would suffice. The author gives a list of fatigue tests that have been carried out using different resins, both push-pull and reversed bending. These results are compared and show that the order of behaviour is not the same for the two types of tests and that the fatigue behaviour of the composite is very much dependent upon the behaviour of the resin matrix. Creep behaviour does not appear to be an important factor. A bibliography of all previous work in the field is given.
TECHNICAL PAPERS
75
A paper, by A. A. Baker and D. Cratchley, appeared in Applied Materials Research, Oct. (1964) 215. This paper describes metallographic observations made by the authors of the fatigue behaviour of silica fibre-reinforced aluminium. Two batches of samples were tested, these being produced under different conditions of pressure and temperature. The results show that the method of preparation has a definite bearing on the results. The surface and sub-surface observations are listed. The authors present an argument for the best possible way of fatigue testing and the possible sources of, and reasons for, fatigue failure. It is of great importance to know when, and under what loading, a fibre-reinforced material sheet (or plate) will fail. Kelly and Davies have presented a theory for fibre-reinforced metals and a general theory of failure has been developed by S. W. Tsai. By assuming that, for most cases, the sheet is in a state of plane stress and orthotropic in the transverse direction, Tsai produces a general equation of failure that is dependent upon the tensile strength normal and parallel to the fibre axis, the shear strength, and also the orientation of the axis of symmetry from the axis of applied load. By considering the loading as uniaxial, Tsai reduces this equation still further. For the case of a single sheet he shows how, for failure strength variation with axis orientation, theoretical values agree with the experimental values. From the results for one sheet Tsai then considers the form in which composites are often used--laminated, cross-ply and single-ply. Tsai describes the procedure for finding which layer will fail first and also the behaviour after initial failure. This work has also been expanded to cover pressure vessel design. Tsai's work has been reported in several publications but the following three are the most important: NASA CR 71 July, 1964. NASA CR 224 April, 1965. NASA CR 620, November, 1966 (with D. F. Adams and D. R. Doner).