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Gradients in composite materials
Materials Science and Engineering American Society for Metals. Metals Park, Ohio, and ElsevierSequoia S.A., Lausanne
Printed in the Netherlands
Invited Review Gradients in Composite Materials M. B. BEVER Department of Metallurgy and Materials Science, Massachusetts Institute oJ Technology, Cambridge, Mass. 02139 i (J.S.A.)
and P. E. D U W E Z W. M. Keck Laboratory ql Engineerin9 Materials, CaliJornia Institute of Technology, Pasadena, Cal(ll 91109 (U.S.A.) (Received February 7, 1972)
Summary Composite materials may have gradients in their compositional and structural characteristics. In such materials properties sensitive to these characteristics also exhibit gradients. These gradients occur in the local properties and aJJect the global properties of the composite. Gradient composites, thereJore, are o[ interest Jor engineering applications. In this paper we analyze various types of gradient composites and consider some of their properties. WE"also review reported and potential applications of gradient composites.
1. INTRODUCTION
Composite materials may have gradients in their compositional and structural characteristics; such materials may be designated as "gradient composites". Because of the large number of features which characterize a composite 1. a variety of gradients is possible. Since these gradients cause changes in properties, gradient composites are of interest for engineering applications. Several applications of composite materials possessing gradients have been reported, but no systematic survey appears to have been published. In this paper we shall analyze possible types of gradient composites and shall consider some of their properties. We shall then review reported applications and discuss potential applications of Mater. Sci. Eng., 10 (1972)
gradient composites. In general, we shall not be concerned with questions of how the gradients can be produced.
2. THE NATURE OF GRADIENTS IN COMPOSITES
The dependence on position of a characteristic feature c of a body can be expressed as c = f(x) where x is a vector originating at a referenFe point (Fig. la). A reference line or reference plane may be used in cases in which the variation of the feature c and the geometry and symmetry of the body make this desirable (Fig. lb and c). The characteristic feature c may involve the composition or the structure. Each shaded surface in Fig. 1 represents a uniform value of the feature c ; differences in shading indicate different values and suggest the direction of the associated gradient. The function f(x) may be continuous or discontinuous. A continuous function f(x) may be analytical, in particular, linear, or nonanalytical. Composites for which f(x) is continuous are "gradient composites" in the strict sense. If f(x) is discontinuous, specifically a step function, the associated singularity represents an interface or graded joint. Such composites could be designated as "graded composites"; we shall include them here as a special case of gradient composites. The geometry and symmetry of a compositional or structural gradient are frequently related to the geometry and symmetry of the body in which the
2
M . B . BEVER, P. E. D U W E Z
(o) j
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~i ~
J j j
~. ~.
1
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J
J
I
j J
---T~J
J J
i
~
j
f 11-
J
f
Fig. 1. Schematic representation of a characteristic feature referred to (a) a point, (b) a line and (c) a plane, Shaded surfaces indicate uniform values of the characteristic feature and suggest directions of gradients.
G R A D I E N T S IN C O M P O S I T E MATERIALS
3
T~-
.Jr
~-
Fig. 2. Schematic representation of gradients of a characteristic feature (a) in the plane of a plate and (b) normal to the plane of a plate. If the characteristic feature is the concentration of filaments, the direction of the shading may represent their direction. j f
-.
(a) (b) Fig. 3. Gradients in filament concentration in (a) the radial direction and (b) the radial and longitudinal directions in a rod. In (b) only filaments near the facing cylindrical surface are shown.
gradient exists. For example, a unidirectional gradient can lie in the plane of a plate (Fig. 2a) or be normal to it (Fig. 2b). As in Fig. 1, we may interpret the shaded surfaces in Fig. 2 as representing equal values of any characteristic feature c; we may consider them now as specifically representing the concentration of filamentary reinforcements in composites. In a rod or tube a gradient of the filament concentration may be radial or longitudinal (Fig. 3). The relations between the gradient and the shape of the body may be more complex than these examples or such relations may be absent. The compositional or structural gradients in a composite may be due to changes with location of the characteristics or arrangement of the particles of the dispersed phase or phases. The type of gradient depends in some respects on the type of the dispersed phase : certain gradients can occur with such shapes Mater. Sci. Eng., 10 (1972)
as filaments, ribbons, plates and particulate shapes, while other gradients are possible only with some of these shapes. The steepness of a gradient is to some extent determined by the fineness of the particles of the dispersed phase. We shall discuss gradients involving the dispersed phase or phases in Section 3. The matrix may also have various gradients, which will be discussed in Section 4. The gradient of a characteristic compositional or structural feature must be considered on an appropriate scale. Local discontinuities due to the differences between the dispersed phase and the matrix of a composite material should not be resolved. Also, in considering gradient composites we are not concerned with composition gradients caused by diffusion across the interface between the dispersed phase and the matrix.
3. G R A D I E N T S I N V O L V I N G THE DISPERSED PHASE
Gradients involving the dispersed phase are a unique feature of composite materials. We shall first consider gradients typical of filamentary dispersed phases and shall then proceed to other shapes. 3.1. Onefilamentary phase We assume that the dispersed phase consists of unidarectionally arranged filaments o f a species A. The filaments may be homogeneous or heterogeneous as in the case of boron deposited on tungsten wires. The most frequently encountered gradient involves the local concentration (or density) of filaments in terms of their number per unit volume. Other gradients may involve the orientation of the filaments and in the case of discontinuous fibers also their length l, their diameter d and the aspect ratio
t/d. The concentration of filaments may vary continuously in a regular or irregular manner. Alternatively, it may change discontinuously and, in particular, may fall discontinuously to zero; the resulting structure is characteristic of a "graded" composite according to the strict definition given in Section 2 above. The concentration gradient of filaments may be normal to the filament direction. In a plate such a gradient can lie in the plane of the plate (Fig. 4a) or be normal to it (Fig. 4b) ; simultaneous gradients in both directions are also possible. In a rod the concentration of filaments may change in a radial direction (Fig. 3a).
4
M . B . BEVER, P. E. D U W E Z
3.2. Several filamentary phases A composite may contain more than one type of filament. For example, boron and glass filaments may reinforce an epoxy matrix. We shall assume that the matrix contains filaments of type A and B ; their volume concentrations will be designated as (A) and (B), respectively. The following cases may be distinguished : (a) grad grad (b) grad grad (c) grad grad (d) grad grad
Fig. 4. Gradients in filament concentration in a direction (a) in the plane of a plate and (b) normal to the plane of a plate.
(a)
(A) ¢ grad (B) = 0; (A)/(B) va const ; [(A)+(B)] -~ 0 (A)= grad (B)~ 0; (A)/(B)= const ; [(A)+(B)] # 0 (A) ~ grad (B) # 0; (A)/(B) ~ const ; [(A)+(B)] # 0 (A) = - g r a d (B) ¢ 0; (A)/(B) # const ; [(A)+(B)] = 0
In case (a) the gradient of phase A is similar to the gradient considered in Subsection 3.1 but a second phase B with a constant concentration is present; this case is shown schematically in Fig. 7a. Case (b) of equal gradients of (A) and (B) is equivalent to a non zero gradient of [(A) + (B)] at a constant ratio of(A)/(B) ;it is shown in Fig. 7b. In case (c), shown
Y
2
Y
(b)
Fig. 5. Gradients in filament concentration in a rod in the longitudinal direction in (a) a constant cross section and (b) a changing cross section. (a)
The concentration of filaments can also change in a direction parallel to the filament axis. In a rod this can be in the longitudinal direction within a constant or a changing cross section (Fig. 5a and b); in the former case the filfiment must be discontinuous. The concentration of discontinuous filaments can also change simultaneously in the longitudinal and radial directions (Fig. 3b). The orientation of aligned filaments may change with position. This can be accomplished by the gradual change in the orientation of stacked multiple plies. By adopting an appropriate stacking sequence a gradient of orientation can be established across the thickness of a plate ; for example, the orientation of the filaments can be changed from an angle q5 of 0 ° with a certain direction to one with an angle of 90 ° (Fig. 6). Short filaments also can have an orientation gradient. Gradients of volume concentration and orientation of the filaments may occur simultaneously. Mater. Sci. Eng., lO (1972)
///. T 9C
50" (b)
Angle
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I 5 Number
I 4
I
Fig. 6 Change of the orientation of unidirectional plies. (a) Projection of filament directions in plies and angle qS. {b) Values of the angle 4~ in successive plies.
GRADIENTS IN COMPOSITE MATERIALS
0
0
0
0
0
0
0
0
5
0
0
of one phase is the mirror image of that of the other, as shown in Fig. 7d.
0
(o) O
0
0
0
0
0
0
0
O
O
0
0
0
0
0
3.3. Dispersed particles with shapes other than o
o
0
0
0
0
0
o
o
o
cylindrical lilaments
o
(bl O
0
o
O
0
O
0
O
0
0
o
0
0
o
0
o
0
0
0
0
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(c) D O
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O
[]
O
O
0
O 0
0
0
0
0
0
o
O
O
(dl 0
D
O
O
D
O
Fig. 7. Gradients in composites containing the dispersed phases A (circles) and B (squares). The symbols may represent the concentrations of these phases or the locations of filaments A and B. The following gradients are shown: (a) grad (AW: grad (B)=0 (b) grad (A)-grad (B)#0 (c) grad (A):~ grad (B)¢0 (d) grad (A)= - g r a d (B):#0.
(a)
/
A dispersed phase in a composite may have shapes other than filaments of circular cross section. Flat ribbons constitute a simple variant. In a composite containing such ribbons the gradients discussed in Subsections 3.1 and 3.2 can be present. In addition the orientation of the plane of the ribbon may change with position, as illustrated in Fig. 8a for a plate. In a rod such orientation gradients are possible in the radial and longitudinal directions: see, for example, Fig. 8b. Additional possibilities exist for discontinuous ribbons: in particular, their orientation may change in the direction of their long axis. Twisted continuous ribbons are also possible. Gradients in a dispersed phase consisting of plates or flakes may involve their concentration, size, shape and orientation. Since particulate phases with equiaxed shapes have no morphologically distinguishing features on which an orientation gradient could be based, gradients involving them are restricted to concentration and particle size ; if the particles are single crystals or polycrystalline aggregates with preferred orientation, gradients in crystallographic orientation are also possible. A composite may contain particles of more than one dispersed phase of a nonfilamentary shape. The particles may differ in size. They may have the same shape and different compositions, they may have different shapes and the same composition or they may differ in both shape and composition. Combinations of filamentary and nonfilamentary dispersed phases are also possible. The number of possible combinations and gradients is obviously large.
4. GRADIENTS IN THE MATRIX
(b)
Fig. 8. Change of the orientation of ribbon-shaped reinforcements in (a) the plane of a plate and (b) a radial direction in a rod.
in Fig. 7c, the gradients of(A ) and (B)are independent of each other; the ratio (A)/(B) changes and the gradient of [(A )+(B)] has a nonzero value. In case (d) a constant sum of the concentrations of A and B implies that grad (A) = - grad (B), that is the gradient Mater. Sci. Eng., 10 (1972)
In the matrix of a composite the same gradients may be present as in the matrix material in the absence of a dispersed phase 2. These gradients may involve the composition or various structural features. In particular, if the matrix is a metal or ceramic, gradients may occur in the grain size, grain shape or grain orientation. Porosity gradients are another example. Polymer matrices also can have gradients 3'4. Gradients in the matrix are not as uniquely characteristic of composites as gradients involving
6
M.B. BEVER, P. E. DUWEZ
the dispersed phase. In general, gradients in the matrix are also less likely to be important for engineering applications. Possible applications of composites with a gradient in the matrix will be mentioned in Subsection 6.3. 5. THE EFFECTS OF GRADIENTS ON PROPERTIES The properties at a given location in a composite and the properties of the composite as a whole depend on all pertinent characteristics and their gradients. Compositional and structural gradients, therefore, affect the properties of a composite on both a local and a global scale. 5.1. Local properties We shall take as an example the elastic modulus of a composite with unidirectional continuous filaments and a gradient in the concentration of the filaments in a plane normal to their direction. We shall consider the modulus in the direction of the filaments. If the modulus obeys the mixture rule, its value at any given location in the composite depends linearly on the local concentration of the filaments ; if the concentration gradient is not too steep, no second-order effects occur. The local modulus in the direction of the filaments, therefore, can be found by linear interpolation. In a case in which the mixture rule is applicable, a property Pc of a filamentary composite is given by the following equation in which the volume fraction of the filaments V is linear in the distance x, the subscripts c, f and m designate the composite, filaments and matrix respectively, and k is a constant : Pc = Pf Vf "-~P m( 1 - Vf ) Vf = kx
Pc(local) = Pfkx + Pro(1 -- k x ) . Other relations hold for a property which depends in a nonlinear analytical manner on the concentration of the filaments. Different types of gradients such as gradients involving the orientation or the aspect ratio of filaments lead to more complicated relations. The local properties of nonfilamentary composites with a gradient, for example, a composite reinforced by a particulate dispersed phase having a concentration gradient, behave also in a manner which in principle can be analyzed. 5.2. Global properties The global properties of a composite represent Mater. Sci. Eng., 10 (1972)
the integral effects of the local properties. For some properties such as the specific gravity simple averaging gives the correct value. Other cases are more complicated. For example, the directional properties of a gradient composite depend on the angle between the direction considered and the direction of the gradient. Detailed analyses of various possible cases should be carried out. If the unidirectional filaments in a composite have a concentration gradient normal to their axes, a global property in the direction of the filaments in general behaves in a manner analogous to a parallel circuit. In directions normal to the filaments and parallel to the filament concentration gradient a series relation holds and the smallest local value is the critical value; for example, in a conduction process this value is rate controlling. Filaments may be oriented parallel to the axis of a rod and concentrated preferentially near its surface. With respect to properties that depend primarily on the filaments, such a configuration results in a behavior approximating that of a tube.
6. APPLICATIONS OF GRADIENT COMPOSITES 6.1. General considerations In Section 5 we have discussed effects of gradients on some properties of composites. We shall now consider applications which are based on such effects. Gradients in composites can contribute to the solution of design and fabrication problems. For example, in one type of application they make it possible to avoid sharp interfaces. A composite can be designed to oppose a gradient in an external variable or a gradient in an internal characteristic of the composite. In principle it is possible to choose a gradient of a property which will match the gradient of an applied force; in a composite this can be done by establishing the appropriate gradient in the reinforcing phase. Similarly if a property of the matrix of a composite has a certain gradient, it is in principle possible to compensate for this gradient by adjusting the dispersed phase in such a way that the property in question has an equal but opposite gradient. As a result the global property of the composite is uniform. In another type of gradient composite the surface and core properties are different. This difference may be achieved by omitting the dispersed phase from the surface layer or by a suitable gradient in the matrix. Possible applications for composites with
GRADIENTS IN COM POSITE MATERIALS
special surface properties may relate to the chemical conditions of service or some other required compatibility with the environment. A suitable surface can facilitate the joining of composite materials : this is important for the welding or brazing of metal matrix composites. 6.2. Reported applications The literature reports examples of gradients in composite materials 5. Designs incorporating gradients are found in various mechanical and structural applications. For example, one type involves variable winding patterns on pressure vessels. An interesting use of the gradient principle was made in reinforcing stringers for an aerospace structure 6;. In order to permit bending required in fabrication, the stringers were produced from unidirectional aluminum boron composite sheets with selectively placed filaments. Filaments were omitted from regions requiring bends with a sharp radius. Selectively placed filaments in regions of sharp-bend radii are becoming the accepted solution to this secondary fabrication problem of aluminum boron composites 8. Gradient composites with preferentially positioned filaments have been made by casting a magnesium matrix around boron filaments 9. In one case the filaments were placed in an annular space close to the cylindrical surface of a rod. Experimental blades for jet engines were produced from a cermet in which titanium carbide was the hard ceramic phase and a nickel alloy served as the metallic binder 10 12. The concentration of titanium carbide was a maximum in the interior of the air foil body, where large stresses had to be resisted at high operating temperatures. The composition of the cermet graded to the essentially pure alloy in the rool and tip of the air foil, for which the main requirements were ductility and toughness. The surface layers of the blades consisted also of the essentially pure alloy for improved impact resistance and oxidation protection. The blades were produced by infiltration of the alloy into a titanium carbide skeleton of properly adjusted porosity. This application illustrates the importance of both local and global properties in gradient composites. A composite characterized by a gradient in the volume fraction of one phase dispersed in another has been proposed as gradient armor ~3. Experimental work was carried out with a graded composite which consisted of an aluminum oxide matrix containing up to 5 volume percent of molybdenum Mater. Sei. Eng., 10 (1972)
7 particles 14. Standard powder metallurgy techniques were used. Other combinations of refractory compounds as matrix materials and dispersed metal particles have also been investigated in experimental work which was based on an original analysis begun in 1968 of the mechanical behavior of such combinations 15. A thermal protection system uses a composile consisting of a polymer matrix and two kinds of filaments: carbonaceous filaments are present in a surface layer and silica fibers in a lower layer. The surface layer is intended to be sacrificed by ablation and the lower layer contributes mechanical strength. It has been reported that "'no interface" separates the two layers. The continuity of the matrix and perhaps the two kinds of filaments may be effective in this regard. 6.3. Potential applications Finally we shall consider applications of gradient composites which are speculative at present but to varying degrees hold promise for the future. Composites with matched gradients are of interest for potential applications. As a simple illustration a beam intended for elastic bending loads would have an increasing concentration of unidirectional filaments on {he side subjected to tensile stress; the resulting gradient in the stiffness of the beam tends to compensate for the stress gradient. In another application of the idea of matched gradients of a property and an imposed conjugate force, a plate can be so designed that there will be no gradient in its thermal expansion in spite of an applied temperature gradient. In a similar manner the thermal flux can be made uniform in the presence of a gradient in the temperature difference in a plane normal to the direction of conduction. An analogue for electrical conduction in a nonuniform field can readily be conceived. Composites have been suggested as damping materials 16. If the dispersed phase in such a composite has a gradient, the damping capacity also has a gradient and in the limit falls to the value characteristic of the matrix material. Such a gradient can be parallel or normal to the plane of a plate. In a rod the gradient of the damping capacity can be parallel to the axis. Gradient composites may find an interesting application in ablation heat shields. Since the heat flux and the process of material remowfl change continuously during re-entry, it may be possible to vary the properties of the material through its
8
thickness in such a manner that optimum conditions are achieved at any time during ablation. In fact, a uniform composite such as a glass fiber reinforced epoxy becomes a gradient composite as the epoxy is progressively charred during re-entry. A composite may be designed to have special friction or wear properties. To this end a surface layer of the matrix may be kept free from reinforcing particles or filaments; in other applications an especially high concentration may be introduced in the surface layer. The choice depends on the service requirements and the characteristics of the matrix and dispersed particles. A composite of an aluminum alloy and a reinforcing phase such as boron filan:lents will be more corrosion resistant 'if the matrix in the surface layer consists of unalloyed aluminum. The same approach could be applied to other metal-matrix composites ; for example, a surface layer of a corrosion-resistant metal or alloy could be used as cladding over a composite susceptible to corrosion which is specified because of other requirements such as strength. It has also been suggested that a composite with blood compatibility can perhaps be made by combining a compatible matrix with a reinforcing phase which is restricted to the interior of the composite 16. ACKNOWLEDGEMENT
This study was supported by the Advanced Research Projects Agency of the Department of Defense under Contract No. DAHC15-71-C-0253.
Mater. Sci. Eng., 10 (1972)
M.B. BEVER, P. E. DUWE'Z REFERENCES 1 M. B. Bever, A general scheme for the characterization of composite materials, in Preliminary Rept., Memoranda and Tech. Notes of the ARPA Materials Summer Conj., July, 1968. 2 M. B. Bever, On gradient materials, in Preliminary Repts., Memoranda and Tech. Notes of the ARPA Materials Summer ConJl, July, 1971. 3 J. D. Ferry, Control of mechanical properties of swollen hydrophilic network polymers; layer and gradient structures, in Preliminary Repts., Memoranda and Tech. Notes oJ the ARPA Materials Summer Con/i, July, 1970. 4 M. Shen and M. B. Bever, J. Mater. Sci., to be published. 5 See for example: Composite materials: testing and design, A S T M Special Tech. Publ. 460, Am. Soc. Testing Mater., 1969. 6 J. L. Christian, J. D. Forest and M. D. Weisinger, Metal Progr, 97 No. 5 (1970) 113. 7 J.D. Forest and J. L. Christian, Development and application of aluminum-boron composite material, J. Aircraft, 7 (1970) 145. 8 M. D. Weisinger, Metals Eng. Quart., 11 No. 3 (1971) 17. 9 A. Alexander, in Metal matrix composites, Proc. Syrup., Pittsburgh, Pa., May 12-13, 1969, DMIC Mere., 243, May, 1969, p. 68. 10 C. G. Goetzel and J. B. Adamec, Metal Progr., 70 No. 6 (1956) 101. 11 H. W. Lavendel and C. G. Goetzel, in R. F. Hehemann and (3. M. Ault (eds.), High Temperature Materials, Wiley, New York, 1959, p. 140. 12 C.G. Goetzel and H. W. Lavendel, Infiltrated powder components for power plant and propulsion systems, in F. Benesovsky (ed.), Plansee Proc., 1964, p. 149. 13 J. J. Stiglich, Jr., New materials and processes for ceramic armor, DCIC Rept. 69-1, Part 1, 1969. 14 J. J. Stiglich, Jr., D. T. Rankin, D. R. Petrak and R. Ruh, Characterization of hot-pressed A1203 with a Mo-dispersed phase, A M M R C TR 70-35, 1970. 15 M. L. Wilkins, Lawrence Radiation Laboratory, Livermore, Calif., personal communication. 16 M. B. Bever, P. E. Duwez and W. A. Tiller, Mater. Sci. Eng., 6 (1970) 149.
Printed in the Netherlands
Invited Review Gradients in Composite Materials M. B. BEVER Department of Metallurgy and Materials Science, Massachusetts Institute oJ Technology, Cambridge, Mass. 02139 i (J.S.A.)
and P. E. D U W E Z W. M. Keck Laboratory ql Engineerin9 Materials, CaliJornia Institute of Technology, Pasadena, Cal(ll 91109 (U.S.A.) (Received February 7, 1972)
Summary Composite materials may have gradients in their compositional and structural characteristics. In such materials properties sensitive to these characteristics also exhibit gradients. These gradients occur in the local properties and aJJect the global properties of the composite. Gradient composites, thereJore, are o[ interest Jor engineering applications. In this paper we analyze various types of gradient composites and consider some of their properties. WE"also review reported and potential applications of gradient composites.
1. INTRODUCTION
Composite materials may have gradients in their compositional and structural characteristics; such materials may be designated as "gradient composites". Because of the large number of features which characterize a composite 1. a variety of gradients is possible. Since these gradients cause changes in properties, gradient composites are of interest for engineering applications. Several applications of composite materials possessing gradients have been reported, but no systematic survey appears to have been published. In this paper we shall analyze possible types of gradient composites and shall consider some of their properties. We shall then review reported applications and discuss potential applications of Mater. Sci. Eng., 10 (1972)
gradient composites. In general, we shall not be concerned with questions of how the gradients can be produced.
2. THE NATURE OF GRADIENTS IN COMPOSITES
The dependence on position of a characteristic feature c of a body can be expressed as c = f(x) where x is a vector originating at a referenFe point (Fig. la). A reference line or reference plane may be used in cases in which the variation of the feature c and the geometry and symmetry of the body make this desirable (Fig. lb and c). The characteristic feature c may involve the composition or the structure. Each shaded surface in Fig. 1 represents a uniform value of the feature c ; differences in shading indicate different values and suggest the direction of the associated gradient. The function f(x) may be continuous or discontinuous. A continuous function f(x) may be analytical, in particular, linear, or nonanalytical. Composites for which f(x) is continuous are "gradient composites" in the strict sense. If f(x) is discontinuous, specifically a step function, the associated singularity represents an interface or graded joint. Such composites could be designated as "graded composites"; we shall include them here as a special case of gradient composites. The geometry and symmetry of a compositional or structural gradient are frequently related to the geometry and symmetry of the body in which the
2
M . B . BEVER, P. E. D U W E Z
(o) j
J'["-
~i ~
J j j
~. ~.
1
"~
J
J
I
j J
---T~J
J J
i
~
j
f 11-
J
f
Fig. 1. Schematic representation of a characteristic feature referred to (a) a point, (b) a line and (c) a plane, Shaded surfaces indicate uniform values of the characteristic feature and suggest directions of gradients.
G R A D I E N T S IN C O M P O S I T E MATERIALS
3
T~-
.Jr
~-
Fig. 2. Schematic representation of gradients of a characteristic feature (a) in the plane of a plate and (b) normal to the plane of a plate. If the characteristic feature is the concentration of filaments, the direction of the shading may represent their direction. j f
-.
(a) (b) Fig. 3. Gradients in filament concentration in (a) the radial direction and (b) the radial and longitudinal directions in a rod. In (b) only filaments near the facing cylindrical surface are shown.
gradient exists. For example, a unidirectional gradient can lie in the plane of a plate (Fig. 2a) or be normal to it (Fig. 2b). As in Fig. 1, we may interpret the shaded surfaces in Fig. 2 as representing equal values of any characteristic feature c; we may consider them now as specifically representing the concentration of filamentary reinforcements in composites. In a rod or tube a gradient of the filament concentration may be radial or longitudinal (Fig. 3). The relations between the gradient and the shape of the body may be more complex than these examples or such relations may be absent. The compositional or structural gradients in a composite may be due to changes with location of the characteristics or arrangement of the particles of the dispersed phase or phases. The type of gradient depends in some respects on the type of the dispersed phase : certain gradients can occur with such shapes Mater. Sci. Eng., 10 (1972)
as filaments, ribbons, plates and particulate shapes, while other gradients are possible only with some of these shapes. The steepness of a gradient is to some extent determined by the fineness of the particles of the dispersed phase. We shall discuss gradients involving the dispersed phase or phases in Section 3. The matrix may also have various gradients, which will be discussed in Section 4. The gradient of a characteristic compositional or structural feature must be considered on an appropriate scale. Local discontinuities due to the differences between the dispersed phase and the matrix of a composite material should not be resolved. Also, in considering gradient composites we are not concerned with composition gradients caused by diffusion across the interface between the dispersed phase and the matrix.
3. G R A D I E N T S I N V O L V I N G THE DISPERSED PHASE
Gradients involving the dispersed phase are a unique feature of composite materials. We shall first consider gradients typical of filamentary dispersed phases and shall then proceed to other shapes. 3.1. Onefilamentary phase We assume that the dispersed phase consists of unidarectionally arranged filaments o f a species A. The filaments may be homogeneous or heterogeneous as in the case of boron deposited on tungsten wires. The most frequently encountered gradient involves the local concentration (or density) of filaments in terms of their number per unit volume. Other gradients may involve the orientation of the filaments and in the case of discontinuous fibers also their length l, their diameter d and the aspect ratio
t/d. The concentration of filaments may vary continuously in a regular or irregular manner. Alternatively, it may change discontinuously and, in particular, may fall discontinuously to zero; the resulting structure is characteristic of a "graded" composite according to the strict definition given in Section 2 above. The concentration gradient of filaments may be normal to the filament direction. In a plate such a gradient can lie in the plane of the plate (Fig. 4a) or be normal to it (Fig. 4b) ; simultaneous gradients in both directions are also possible. In a rod the concentration of filaments may change in a radial direction (Fig. 3a).
4
M . B . BEVER, P. E. D U W E Z
3.2. Several filamentary phases A composite may contain more than one type of filament. For example, boron and glass filaments may reinforce an epoxy matrix. We shall assume that the matrix contains filaments of type A and B ; their volume concentrations will be designated as (A) and (B), respectively. The following cases may be distinguished : (a) grad grad (b) grad grad (c) grad grad (d) grad grad
Fig. 4. Gradients in filament concentration in a direction (a) in the plane of a plate and (b) normal to the plane of a plate.
(a)
(A) ¢ grad (B) = 0; (A)/(B) va const ; [(A)+(B)] -~ 0 (A)= grad (B)~ 0; (A)/(B)= const ; [(A)+(B)] # 0 (A) ~ grad (B) # 0; (A)/(B) ~ const ; [(A)+(B)] # 0 (A) = - g r a d (B) ¢ 0; (A)/(B) # const ; [(A)+(B)] = 0
In case (a) the gradient of phase A is similar to the gradient considered in Subsection 3.1 but a second phase B with a constant concentration is present; this case is shown schematically in Fig. 7a. Case (b) of equal gradients of (A) and (B) is equivalent to a non zero gradient of [(A) + (B)] at a constant ratio of(A)/(B) ;it is shown in Fig. 7b. In case (c), shown
Y
2
Y
(b)
Fig. 5. Gradients in filament concentration in a rod in the longitudinal direction in (a) a constant cross section and (b) a changing cross section. (a)
The concentration of filaments can also change in a direction parallel to the filament axis. In a rod this can be in the longitudinal direction within a constant or a changing cross section (Fig. 5a and b); in the former case the filfiment must be discontinuous. The concentration of discontinuous filaments can also change simultaneously in the longitudinal and radial directions (Fig. 3b). The orientation of aligned filaments may change with position. This can be accomplished by the gradual change in the orientation of stacked multiple plies. By adopting an appropriate stacking sequence a gradient of orientation can be established across the thickness of a plate ; for example, the orientation of the filaments can be changed from an angle q5 of 0 ° with a certain direction to one with an angle of 90 ° (Fig. 6). Short filaments also can have an orientation gradient. Gradients of volume concentration and orientation of the filaments may occur simultaneously. Mater. Sci. Eng., lO (1972)
///. T 9C
50" (b)
Angle
so~
Co
I 2 Ply
I 5 Number
I 4
I
Fig. 6 Change of the orientation of unidirectional plies. (a) Projection of filament directions in plies and angle qS. {b) Values of the angle 4~ in successive plies.
GRADIENTS IN COMPOSITE MATERIALS
0
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of one phase is the mirror image of that of the other, as shown in Fig. 7d.
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3.3. Dispersed particles with shapes other than o
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cylindrical lilaments
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Fig. 7. Gradients in composites containing the dispersed phases A (circles) and B (squares). The symbols may represent the concentrations of these phases or the locations of filaments A and B. The following gradients are shown: (a) grad (AW: grad (B)=0 (b) grad (A)-grad (B)#0 (c) grad (A):~ grad (B)¢0 (d) grad (A)= - g r a d (B):#0.
(a)
/
A dispersed phase in a composite may have shapes other than filaments of circular cross section. Flat ribbons constitute a simple variant. In a composite containing such ribbons the gradients discussed in Subsections 3.1 and 3.2 can be present. In addition the orientation of the plane of the ribbon may change with position, as illustrated in Fig. 8a for a plate. In a rod such orientation gradients are possible in the radial and longitudinal directions: see, for example, Fig. 8b. Additional possibilities exist for discontinuous ribbons: in particular, their orientation may change in the direction of their long axis. Twisted continuous ribbons are also possible. Gradients in a dispersed phase consisting of plates or flakes may involve their concentration, size, shape and orientation. Since particulate phases with equiaxed shapes have no morphologically distinguishing features on which an orientation gradient could be based, gradients involving them are restricted to concentration and particle size ; if the particles are single crystals or polycrystalline aggregates with preferred orientation, gradients in crystallographic orientation are also possible. A composite may contain particles of more than one dispersed phase of a nonfilamentary shape. The particles may differ in size. They may have the same shape and different compositions, they may have different shapes and the same composition or they may differ in both shape and composition. Combinations of filamentary and nonfilamentary dispersed phases are also possible. The number of possible combinations and gradients is obviously large.
4. GRADIENTS IN THE MATRIX
(b)
Fig. 8. Change of the orientation of ribbon-shaped reinforcements in (a) the plane of a plate and (b) a radial direction in a rod.
in Fig. 7c, the gradients of(A ) and (B)are independent of each other; the ratio (A)/(B) changes and the gradient of [(A )+(B)] has a nonzero value. In case (d) a constant sum of the concentrations of A and B implies that grad (A) = - grad (B), that is the gradient Mater. Sci. Eng., 10 (1972)
In the matrix of a composite the same gradients may be present as in the matrix material in the absence of a dispersed phase 2. These gradients may involve the composition or various structural features. In particular, if the matrix is a metal or ceramic, gradients may occur in the grain size, grain shape or grain orientation. Porosity gradients are another example. Polymer matrices also can have gradients 3'4. Gradients in the matrix are not as uniquely characteristic of composites as gradients involving
6
M.B. BEVER, P. E. DUWEZ
the dispersed phase. In general, gradients in the matrix are also less likely to be important for engineering applications. Possible applications of composites with a gradient in the matrix will be mentioned in Subsection 6.3. 5. THE EFFECTS OF GRADIENTS ON PROPERTIES The properties at a given location in a composite and the properties of the composite as a whole depend on all pertinent characteristics and their gradients. Compositional and structural gradients, therefore, affect the properties of a composite on both a local and a global scale. 5.1. Local properties We shall take as an example the elastic modulus of a composite with unidirectional continuous filaments and a gradient in the concentration of the filaments in a plane normal to their direction. We shall consider the modulus in the direction of the filaments. If the modulus obeys the mixture rule, its value at any given location in the composite depends linearly on the local concentration of the filaments ; if the concentration gradient is not too steep, no second-order effects occur. The local modulus in the direction of the filaments, therefore, can be found by linear interpolation. In a case in which the mixture rule is applicable, a property Pc of a filamentary composite is given by the following equation in which the volume fraction of the filaments V is linear in the distance x, the subscripts c, f and m designate the composite, filaments and matrix respectively, and k is a constant : Pc = Pf Vf "-~P m( 1 - Vf ) Vf = kx
Pc(local) = Pfkx + Pro(1 -- k x ) . Other relations hold for a property which depends in a nonlinear analytical manner on the concentration of the filaments. Different types of gradients such as gradients involving the orientation or the aspect ratio of filaments lead to more complicated relations. The local properties of nonfilamentary composites with a gradient, for example, a composite reinforced by a particulate dispersed phase having a concentration gradient, behave also in a manner which in principle can be analyzed. 5.2. Global properties The global properties of a composite represent Mater. Sci. Eng., 10 (1972)
the integral effects of the local properties. For some properties such as the specific gravity simple averaging gives the correct value. Other cases are more complicated. For example, the directional properties of a gradient composite depend on the angle between the direction considered and the direction of the gradient. Detailed analyses of various possible cases should be carried out. If the unidirectional filaments in a composite have a concentration gradient normal to their axes, a global property in the direction of the filaments in general behaves in a manner analogous to a parallel circuit. In directions normal to the filaments and parallel to the filament concentration gradient a series relation holds and the smallest local value is the critical value; for example, in a conduction process this value is rate controlling. Filaments may be oriented parallel to the axis of a rod and concentrated preferentially near its surface. With respect to properties that depend primarily on the filaments, such a configuration results in a behavior approximating that of a tube.
6. APPLICATIONS OF GRADIENT COMPOSITES 6.1. General considerations In Section 5 we have discussed effects of gradients on some properties of composites. We shall now consider applications which are based on such effects. Gradients in composites can contribute to the solution of design and fabrication problems. For example, in one type of application they make it possible to avoid sharp interfaces. A composite can be designed to oppose a gradient in an external variable or a gradient in an internal characteristic of the composite. In principle it is possible to choose a gradient of a property which will match the gradient of an applied force; in a composite this can be done by establishing the appropriate gradient in the reinforcing phase. Similarly if a property of the matrix of a composite has a certain gradient, it is in principle possible to compensate for this gradient by adjusting the dispersed phase in such a way that the property in question has an equal but opposite gradient. As a result the global property of the composite is uniform. In another type of gradient composite the surface and core properties are different. This difference may be achieved by omitting the dispersed phase from the surface layer or by a suitable gradient in the matrix. Possible applications for composites with
GRADIENTS IN COM POSITE MATERIALS
special surface properties may relate to the chemical conditions of service or some other required compatibility with the environment. A suitable surface can facilitate the joining of composite materials : this is important for the welding or brazing of metal matrix composites. 6.2. Reported applications The literature reports examples of gradients in composite materials 5. Designs incorporating gradients are found in various mechanical and structural applications. For example, one type involves variable winding patterns on pressure vessels. An interesting use of the gradient principle was made in reinforcing stringers for an aerospace structure 6;. In order to permit bending required in fabrication, the stringers were produced from unidirectional aluminum boron composite sheets with selectively placed filaments. Filaments were omitted from regions requiring bends with a sharp radius. Selectively placed filaments in regions of sharp-bend radii are becoming the accepted solution to this secondary fabrication problem of aluminum boron composites 8. Gradient composites with preferentially positioned filaments have been made by casting a magnesium matrix around boron filaments 9. In one case the filaments were placed in an annular space close to the cylindrical surface of a rod. Experimental blades for jet engines were produced from a cermet in which titanium carbide was the hard ceramic phase and a nickel alloy served as the metallic binder 10 12. The concentration of titanium carbide was a maximum in the interior of the air foil body, where large stresses had to be resisted at high operating temperatures. The composition of the cermet graded to the essentially pure alloy in the rool and tip of the air foil, for which the main requirements were ductility and toughness. The surface layers of the blades consisted also of the essentially pure alloy for improved impact resistance and oxidation protection. The blades were produced by infiltration of the alloy into a titanium carbide skeleton of properly adjusted porosity. This application illustrates the importance of both local and global properties in gradient composites. A composite characterized by a gradient in the volume fraction of one phase dispersed in another has been proposed as gradient armor ~3. Experimental work was carried out with a graded composite which consisted of an aluminum oxide matrix containing up to 5 volume percent of molybdenum Mater. Sei. Eng., 10 (1972)
7 particles 14. Standard powder metallurgy techniques were used. Other combinations of refractory compounds as matrix materials and dispersed metal particles have also been investigated in experimental work which was based on an original analysis begun in 1968 of the mechanical behavior of such combinations 15. A thermal protection system uses a composile consisting of a polymer matrix and two kinds of filaments: carbonaceous filaments are present in a surface layer and silica fibers in a lower layer. The surface layer is intended to be sacrificed by ablation and the lower layer contributes mechanical strength. It has been reported that "'no interface" separates the two layers. The continuity of the matrix and perhaps the two kinds of filaments may be effective in this regard. 6.3. Potential applications Finally we shall consider applications of gradient composites which are speculative at present but to varying degrees hold promise for the future. Composites with matched gradients are of interest for potential applications. As a simple illustration a beam intended for elastic bending loads would have an increasing concentration of unidirectional filaments on {he side subjected to tensile stress; the resulting gradient in the stiffness of the beam tends to compensate for the stress gradient. In another application of the idea of matched gradients of a property and an imposed conjugate force, a plate can be so designed that there will be no gradient in its thermal expansion in spite of an applied temperature gradient. In a similar manner the thermal flux can be made uniform in the presence of a gradient in the temperature difference in a plane normal to the direction of conduction. An analogue for electrical conduction in a nonuniform field can readily be conceived. Composites have been suggested as damping materials 16. If the dispersed phase in such a composite has a gradient, the damping capacity also has a gradient and in the limit falls to the value characteristic of the matrix material. Such a gradient can be parallel or normal to the plane of a plate. In a rod the gradient of the damping capacity can be parallel to the axis. Gradient composites may find an interesting application in ablation heat shields. Since the heat flux and the process of material remowfl change continuously during re-entry, it may be possible to vary the properties of the material through its
8
thickness in such a manner that optimum conditions are achieved at any time during ablation. In fact, a uniform composite such as a glass fiber reinforced epoxy becomes a gradient composite as the epoxy is progressively charred during re-entry. A composite may be designed to have special friction or wear properties. To this end a surface layer of the matrix may be kept free from reinforcing particles or filaments; in other applications an especially high concentration may be introduced in the surface layer. The choice depends on the service requirements and the characteristics of the matrix and dispersed particles. A composite of an aluminum alloy and a reinforcing phase such as boron filan:lents will be more corrosion resistant 'if the matrix in the surface layer consists of unalloyed aluminum. The same approach could be applied to other metal-matrix composites ; for example, a surface layer of a corrosion-resistant metal or alloy could be used as cladding over a composite susceptible to corrosion which is specified because of other requirements such as strength. It has also been suggested that a composite with blood compatibility can perhaps be made by combining a compatible matrix with a reinforcing phase which is restricted to the interior of the composite 16. ACKNOWLEDGEMENT
This study was supported by the Advanced Research Projects Agency of the Department of Defense under Contract No. DAHC15-71-C-0253.
Mater. Sci. Eng., 10 (1972)
M.B. BEVER, P. E. DUWE'Z REFERENCES 1 M. B. Bever, A general scheme for the characterization of composite materials, in Preliminary Rept., Memoranda and Tech. Notes of the ARPA Materials Summer Conj., July, 1968. 2 M. B. Bever, On gradient materials, in Preliminary Repts., Memoranda and Tech. Notes of the ARPA Materials Summer ConJl, July, 1971. 3 J. D. Ferry, Control of mechanical properties of swollen hydrophilic network polymers; layer and gradient structures, in Preliminary Repts., Memoranda and Tech. Notes oJ the ARPA Materials Summer Con/i, July, 1970. 4 M. Shen and M. B. Bever, J. Mater. Sci., to be published. 5 See for example: Composite materials: testing and design, A S T M Special Tech. Publ. 460, Am. Soc. Testing Mater., 1969. 6 J. L. Christian, J. D. Forest and M. D. Weisinger, Metal Progr, 97 No. 5 (1970) 113. 7 J.D. Forest and J. L. Christian, Development and application of aluminum-boron composite material, J. Aircraft, 7 (1970) 145. 8 M. D. Weisinger, Metals Eng. Quart., 11 No. 3 (1971) 17. 9 A. Alexander, in Metal matrix composites, Proc. Syrup., Pittsburgh, Pa., May 12-13, 1969, DMIC Mere., 243, May, 1969, p. 68. 10 C. G. Goetzel and J. B. Adamec, Metal Progr., 70 No. 6 (1956) 101. 11 H. W. Lavendel and C. G. Goetzel, in R. F. Hehemann and (3. M. Ault (eds.), High Temperature Materials, Wiley, New York, 1959, p. 140. 12 C.G. Goetzel and H. W. Lavendel, Infiltrated powder components for power plant and propulsion systems, in F. Benesovsky (ed.), Plansee Proc., 1964, p. 149. 13 J. J. Stiglich, Jr., New materials and processes for ceramic armor, DCIC Rept. 69-1, Part 1, 1969. 14 J. J. Stiglich, Jr., D. T. Rankin, D. R. Petrak and R. Ruh, Characterization of hot-pressed A1203 with a Mo-dispersed phase, A M M R C TR 70-35, 1970. 15 M. L. Wilkins, Lawrence Radiation Laboratory, Livermore, Calif., personal communication. 16 M. B. Bever, P. E. Duwez and W. A. Tiller, Mater. Sci. Eng., 6 (1970) 149.