Measurement of interfacial strength of a composite material
BACKGROUND OF THE INVENTION 
     This invention relates to a method of evaluating the interfacial strength of a composite material at a boundary between its fiber and matrix. This invention relates also to an apparatus for using such a method. 
     Composite materials with reinforcing fibers dispersed within matrix are widely in use in various fields of industrial applications such as automobiles, airplanes, tanks and concrete. For evaluating the interfacial strength between the fibers and the matrix of such a material, it is necessary to apply a force on a fiber in order to cause a separation. Since the fibers in such materials are usually very thin with a diameter on the order of 10˜150 microns, however, use must be made of an indentator with a sharp tip. Since such an indentator penetrates the fiber while pushing it, what is actually being measured is the total displacement of the indentator, including the distance by which the fiber is penetrated by the sharp tip of the indentator. In order to obtain only that portion of the displacement of the indentator at the interface between the fibers and the matrix, therefore, the distance of penetration by the indentator must be subtracted from the measured total displacement. 
     In order to determine the distance of penetration by an indentator, it has been known to preliminarily provide a correction curve by using a test sample with a very large interfacial strength between its fibers and matrix and to make use of such a curve to make corrections on measured values. It is cumbersome, however, to keep making reference to such a correction curve in order to obtain a desired displacement value at the interfacial boundary. Moreover, there are situations where a sample cannot be manufactured with a satisfactorily large interfacial strength. In such a situation, it is impossible to prepare a correction curve needed for the method. Furthermore, there has not been available any apparatus designed specifically for the measurement of interfacial strength of composite materials. It seems to have been a common practice among some researchers to make changes on a commercially available instrument for measuring hardness, but such a make-shift instrument is not easy to operate, and use was commonly made of an average value of fiber diameters rather than the diameter of the selected fiber which is actually tested. As a result, fluctuations were large, and the conclusions obtained by such prior art methods were not highly reliable. 
     In view of the above, it is a general object of the present invention to provide an improved method of measuring interfacial strength of a composite material accurately. 
     It is a more specific object of the present invention to provide such a method which does not requite a sample to be manufactured with a large interfacial strength for preparing a correction curve but is able by a single test to determine the critical value of load at which separation of fibers starts at the interfacial boundary. 
     It is still another object of the present invention to provide an apparatus which makes use of such a method for the measurement of interfacial strength of a composite material. 
     SUMMARY OF THE INVENTION 
     A method embodying the present invention, with which the above and other objects can be accomplished, may be characterized as comprising the steps of applying a load on a selected one of reinforcing fibers by means of an indentator, measuring the displacement of the indentator while increasing the load thereon to thereby obtain a characteristic curve representing the relationship between the square root of the load and the displacement. Since the penetration of the indentator into the fiber should be proportional to the square root of the load from the definition of its hardness, the deviation from a straight line of the curve representing this measured relationship represents the portion of the indentator displacement at the interfacial boundary between the fibers and the matrix of the material being tested. The value of the load at which this deviation starts is the critical load at which the separation of fibers is considered to have started. 
     An apparatus embodying the present invention, with which the method described above can be used, may be characterized as comprising a selecting means for selecting one of the reinforcing fibers from a sample of composite material, a diameter-measuring means for measuring the diameter of the selected fiber, an indentator for pressing the fiber, a loading means for applying a load on the indentator, a load-measuring means for measuring the magnitude of the load being applied to the fiber by the indentator, a displacement-measuring means for measuring the displacement of the indentator as the selected fiber is pressed thereby, and a calculating means for calculating the surface shear strength of the fibers from measured data. This apparatus is adapted to calculate the interfacial shear strength of fibers while applying a load on the indentator and measuring the corresponding displacement of the indentator. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. In the drawings: 
     FIG. 1 is a schematic front view of an apparatus embodying the present invention to show its general structure; 
     FIG. 2 is a schematic sectional front view of the loading unit, showing also its functional connection to the control unit; 
     FIG. 3 is a sketch of the field of vision of the microscope; 
     FIGS. 4, 5 and 6 are graphs for schematically showing the basic principle and actual method of obtaining data from which the interfacial shear strengths can be calculated according to the present invention; 
     FIG. 7 is a schematic sectional front view of another loading unit embodying the present invention, having an electromagnetic indentator-driving means controlled by a control unit; and 
     FIG. 8 is a schematic sectional front view of still another loading unit embodying the present invention, having a piezoelectric indentator-driving means controlled by a control unit. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     As shown schematically in FIGS. 1 and 2 which illustrate an apparatus embodying the present invention, a base 1 supports a support column 2 for vertically moving its loading unit 10 upward and downward and a sample table 3 with as so-called X-Y stage (not shown) one side of the support column 2. The X-Y stage may be of a known kind comprising a pair of plates which can be moved with respect to each other by rotating micrometer heads 3a and 3b such that one can slide in one direction and the other in a perpendicular direction, enabling the user to move two-dimensionally a sample placed thereon. A sample 4 of a composite material with reinforcing fibers 4a dispersed in a matrix 4b is placed on top of the X-Y stage. A microscope 6 has its objective lens 5 disposed above the sample table 3 such that the sample can be observed through its eye piece 7. As shown in FIG. 3, indicators 7a and 7b are adapted to appear in the field of vision of the microscope 6. Knobs 8 shown in FIG. 1 are for moving these indicators 7a and 7b. 
     The microscope 6 and the loading unit 10 are attached to a support table 9 which can be moved vertically upward and downward along the support column 2. The loading unit 10 includes a vertically extending rod 11 with an indentator 12 attached at the bottom, and is functionally connected to a control unit 13 for the control of measurements. The control unit 13 is of a known kind generally adapted to carry out many functions including transmitting signals to apparatus, receiving signals from various sensors and detectors, performing analog-to-digital conversion of such received signals and carrying out various numerical calculations. As shown in FIG. 2, the loading unit 10 contains within its frame 20 a motor 21 for moving the indentator 12 up and down, a micrometer 22 adapted to have its spindle move linearly downward without rotating it, a position sensor 23 of a known kind with a core rod 24 for detecting vertical displacement of the indentator 12, and a load sensor (such as a load cell) 25 for measuring the load on the indentator 12. The sample table 3 can slide between a left-hand position (with reference to FIG. 1 and shown in solid lines therein) below the microscope 6 and a right-hand position (shown by broken lines in FIG. 1) below the indentator 12. The sliding mechanism for the sample table 3 is adapted such that the point on the sample table 3 which is positioned at the center of the field of vision of the microscope 6 by the user as described below when the sample table 3 is at the left-hand position will automatically come to the position directly below the indentator 12 when the sample table 3 is moved to the right-hand position. 
     For the measurement by this apparatus, the sample 4 on the X-Y stage is observed first through the microscope 6, and a fiber to be pushed for testing is selected by the user and moved to the center of the field of vision of the microscope 6. The diameter of the selected fiber is measured by rotating the knobs 8 to move the indicators 7a and 7b so as to sandwich it exactly therebetween as shown in FIG. 3. Thereafter, the sample table 3 is caused to slide to the right-hand position below the indentator 12. Since the selected fiber 4a, of which the diameter has been measured as described above, is directly below the indentator 12, a command signal is outputted from the control unit 13 to activate the motor 21, causing the micrometer 22 to move downward. The indentator 12 is thereby lowered and pushes the selected fiber 4a downward. The load L on the fiber 4a and the displacement of the indentator 12 are measured by the sensors 23 and 25. The load L will be constant, representing the weight of the indentator 12 itself before the indentator 12 comes into contact with the sample 4, increasing suddenly when the indentator 12 touches the sample 4. Displacement D of the indentator 12 will be herein measured from this point. In other words, the zero-point of the displacement D is taken at the point where the load L increases suddenly as the indentator 12 touches the sample 4. 
     The relationship between the load L and the indentator displacement D, as defined above, is as shown in FIG. 4 by Curve A for a typical composite material. If its interfacial strength were extremely strong, the relationship between the load L and the indentator displacement D for such an idealized material would be as shown by Curve B, with Curves A and B coinciding where the load L is smaller than a certain critical value hereinafter referred to as the &#34;debonding load L d  &#34;. For a load such as L u  greater than L d , the difference in indentator displacement between Curve A and B will be herein referred to as the differential displacement and denoted by u, as shown in FIG. 4. FIG. 5 is a graph, derived from Curves A and B in FIG. 4, between the load L and the differential displacement u. Curves A and B in FIG. 4 show that indentator displacement D is essentially due to the penetration of the indentator 12 into the fiber 4a before the value of the load L reaches L d  at which the fiber 4a begins to separate from the matrix 4b. Since the distance D by which the indentator 12 with a load of L penetrates the fiber 4a is related to the hardness H of the fiber 4a according to the formula H=αL/D 2  where a is a constant depending on the indentator, one obtains: 
     
         D=(αL/H).sup.1/2.                                    Formula (1) 
    
     In other words, the indentator displacement D due only to its penetration into the fiber 4a should be proportional to the square root of load, and this relationship should appear as a straight line in a graph between D and square root of L (that is, √L). 
     FIG. 6 is such a graph showing the relationship between D and √L corresponding to Curves A and B of FIG. 4. In FIG. 6, Curves A and B are nearly straight for load value less than L d . Irregularities near the origin of the graph may be interpreted as representing the surface roughness of the sample 4. As explained above with reference to FIG. 4, the vertical separation between the two curves in FIG. 6, or the differential displacement u, represents the portion of the indentator displacement D at the interfacial boundary, that is, the difference between the total indentator displacement and the distance of penetration by the indentator 12 into the fiber 4a when the load L u  is greater than the debonding load L d . 
     According to a method of measurement embodying the present invention, the apparatus of FIGS. 1 and 2 is used to measure and record mutually corresponding values of the load L and the indentator displacement D. If the results are plotted as a relationship between the square root of load (√L) and D, the graph thus obtained will generally look like Curve A in FIG. 6 with a substantially straight portion extending to a certain point, deviating therefrom for loads and displacements beyond this point. This point is identified as the debonding point and the value of the load corresponding to this point (=L d ) is identified. A value of differential displacement u corresponding to a certain load (=L u ) greater than L d  is also obtained. The debonding shear strength τ d  and the sliding shear strength τ s  are calculated (say, by the control unit 13) from these values as follows: 
     
         τ.sub.d =αL.sub.d /2πR.sup.2, and             Formula (2) 
    
     
         τ.sub.s =L.sub.u.sup.2 /(4π.sup.2 R.sup.3 E.sub.f u) Formula (3) 
    
     where 
     
         α.sup.2 =2E.sub.m /{E.sub.f (1+ν.sub.m).sup.2 1n(1/√B)}, Formula (4) 
    
     E is the elastic modulus, ν is the Poisson&#39;s ratio, R is the radius of the fiber, B is the bulk modulus of the fiber, and the subscripts m and f respectively refer to the matrix and the fibers. 
     As can be understood from the formulas given above, shear strength depends heavily on the radius of the fiber. Since an actually measured value of the diameter, rather than an average value, is used in the calculation according to the present invention, the result obtained by the method of the present invention is expected to be far more reliable. The present invention, furthermore, eliminates the need to go through the trouble of manufacturing a test sample with high surface strength and makes it possible to carry out evaluation of different kinds of composite materials easily and accurately. 
     Although the present invention has been described above by way of only one embodiment, it was intended to be illustrative, and not as limiting the scope of the invention. The indentator 12, for example, need not be raised or lowered by means of a motor as described above with reference to FIG. 2. FIG. 7 shows another indentator-driving mechanism for another loading unit 10&#39;, characterized by electro magnetic means for controlling the motion of the indentator (not shown), including a combination of a permanent magnet 31 and a coil 32 serving together as a driving unit, the coil 32 being placed within the magnetic field of the permanent magnet 31. The coil 32 is attached to one end of a lever 33, and the current therethrough is controlled by a control unit 13&#39;. The other end of the lever 33, opposite the coil 32 across its fulcrum 34, is attached to a rod 11&#39; through a plate spring 35 such that the vertical motion of the rod 11&#39;, and hence also that of the indentator, can be controlled by the control unit 13&#39;. FIG. 8 shows still another indentator-driving mechanism for still another loading unit 10&#39;, characterized by the use of a piezoelectric element 41 attached to a supporting bracket 42. A control unit 13&#34; is adapted to control the current supplied to the piezoelectric element 41 to thereby control the vertical motion of a rod 11&#34;. In FIGS. 7 and 8, other components which are substantially the same as those shown in, and explained with reference to, FIG. 1 are indicated by the same numerals. 
     In summary, all such modifications of variations of the disclosures given above, that may be apparent to persons skilled in the art, are intended to be included within the scope of the invention.