1486 M. Drissi-Habti, K. Nakano and Vm=0 49 and that of the fibers(Er=250 GPa and Vr=0-48)into the rule of mixtures E=EV+ emv the as-calculated longitudinal Youngs modulus of the 一Es3N4(m) omposite is 215 GPa, Such a value would be expected a 一日 Ecomp tional Hi-Nicalon/BN/Silicon-nitride composite. How- ever, the value of E calculated from eqn (5)is greater than that measured in the three-point bend test. Since the reverse would be expected. such a difference may be due to a loss in stiffness of the hi-Nicalon fibers during the bn coating process at 1500C, or when hot 100200300400500600 pressing during the sintering stage. This will be partially elucidated by micro-indentation tests and Fig. 6. Illustration of the parameters used when interpreting atomic force microscope observations. indentation tests (after Puttock and Thwaite) 3.2.3 Micro-indentation tests Micro-indentation tests were performed on the fibers Analysis of the partial unload data provides for the and the matrix(both on monolithic Si3 N4 and on extraction of Eat each step. The longitudinal Young's matrix-rich regions in the composite), to evaluate the modulus of the material is then determined if the local Youngs modulus of the matrix and the fibers longitudinal Youngs modulus and poissons ratio of This was accomplished by a multiple partial unloading the indenter(v; and Ei) and the poissons ratio of the procedure. Such tests are particularly suitable for a aterial (vm) are known, according to the earlier spherical indentation and give reliable measures of the analysis of Ref. 6: hardness and the longitudinal Young s modulus as a 1/E′=(1-v)E+(1-vm)E function of the depth of elastic/plastic penetration for An important parameter to control is the contact materials whose properties vary with distance from the force. To prevent impact damage, the contact force surface. To determine the hardness from an indenta must be properly chosen. The above relationships have tion test, it is necessary to determine the penetration already been integrated into a computer program and of the indenter below the perimeter of contact, the this makes the exploitation of experimental results remainder of the total measured depth being elastic straightforward. However, the procedure described depression of the surrounding material. The elastic above implies that no damage appears when loading contribution obtained from unloading data is required In this case the test must be rejected, since measured to make these calculations. In the multiple partial valucs are dependent on the amount of damage unloading(20 in our case), a single indentation is Figure 7 shows micro-indentation curves recorded partially unloaded in one increment at each step by an for the monolithic matrix and the matrix-rich region amount of 50% of the total step. Each force step in the composite, using 250 mN maximum appl provides two pieces of information: the total depth of elastic/plastic penetration and a measure of the recovery from that load. For a spherical indenter, the elastic recovery, d, and the longitudinal Youngs modulus of both the material and the indenter e, are given by the following relationships, derived from the work of Puttock and Thwaite(Fig. 6) E′=F(98)(D-1Dn)2d-32 where D(=2R)is the diameter of the spherical indenter, D is the diameter of the residual spherical 鲁鲁鲁鲁一你 depression and F the total load. If h,, ho and h, are the total(corresponding to the total force, F), plastic and residual depths, the elastic recovery may be obtained neration be low depth(nm) Fig. 7. Variation of the mean longitudinal Youngs modulus values with the penetration below contact when indenting he monolithic silicon nitride [ESi,N,(m) and the matrix rich regions in the Hi-Nicalon/BN/silicon-nitride compo (Ecomp). The maximum applied force is 250 mN1486 M. Drissi-Habti, K. Nakano and V, = 0.491 and that of the fibers (E, = 2.50 GPa and V, = 0.48) into the rule of mixtures: 225 1 E = EfVf + E,V, (5) the as-calculated longitudinal Young’s modulus of the composite is 215 GPa. Such a value would be expected when testing uniaxial tensile specimens of unidirec￾tional Hi-Nicalon/BN/silicon-nitride composite. How￾ever, the value of E calculated from eqn (5) is greater than that measured in the three-point bend test. Since the reverse would be expected, such a difference may be due to a loss in stiffness of the Hi-Nicalon fibers during the BN coating process at 15OO”C, or when hot pressing during the sintering stage. This will be partially elucidated by micro-indentation tests and atomic force microscope observations. 220 I 7 215 '\ i i L 0 210 ~. % I '\ iG 205 -: + 200 t i ‘; ‘1\ 195 4 \ b-_- i-, ---I)---------o ,go -., : ;.-~-~-~-._+__, 0 100 200 300 400 500 600 Penetration below depth (nm) Fig. 6. Illustration of the parameters used when interpreting indentation tests (after Puttock and Thwaite)‘. ----)- E33N4(m) -*-komp 3.2.3 Micro-indentation tests Micro-indentation tests were performed on the fibers and the matrix (both on monolithic S&N, and on matrix-rich regions in the composite), to evaluate the local Young’s modulus of the matrix and the fibers. This was accomplished by a multiple partial unloading procedure. Such tests are particularly suitable for a spherical indentation and give reliable measures of the hardness and the longitudinal Young’s modulus as a function of the depth of elastic/plastic penetration for materials whose properties vary with distance from the surface. To determine the hardness from an indenta￾tion test, it is necessary to determine the penetration of the indenter below the perimeter of contact, the remainder of the total measured depth being elastic depression of the surrounding material. The elastic contribution obtained from unloading data is required to make these calculations. In the multiple partial unloading (20 in our case), a single indentation is partially unloaded in one increment at each step by an amount of 50% of the total step. Each force step provides two pieces of information: the total depth of elastic/plastic penetration and a measure of the recovery from that load. For a spherical indenter, the elastic recovery, d, and the longitudinal Young’s modulus of both the material and the indenter, E’, are given by the following relationships, derived from the work of Puttock and Thwaite’ (Fig. 6): Analysis of the partial unload data provides for the extraction of E’ at each step. The longitudinal Young’s modulus of the material is then determined if the longitudinal Young’s modulus and Poisson’s ratio of the indenter (Yi and Ei) and the Poisson’s ratio of the material (Y,) are known, according to the earlier analysis of Ref. 6: l/E ’ = (1 - v;)lE + (1 - I&/E,,, (10) An important parameter to control is the contact force. To prevent impact damage, the contact force must be properly chosen. The above relationships have already been integrated into a computer program and this makes the exploitation of experimental results straightforward. However, the procedure described above implies that no damage appears when loading. In this case the test must be rejected, since measured values are dependent on the amount of damage.’ Figure 7 shows micro-indentation curves recorded for the monolithic matrix and the matrix-rich regions in the composite, using 250 mN maximum applied d = (9/8)1’3(1/E’)2’3(1/D - 1/D,)“3F2’3 (6) E’ = F(9/8)1’2(1/D - 1/D,)“2d-3’2 (7) where D (=2R) is the diameter of the spherical indenter, D, is the diameter of the residual spherical depression and F the total load. If h,, h, and h, are the total (corresponding to the total force, F), plastic and residual depths, the elastic recovery may be obtained from: d = h, - h, (8) ,o(J ,/,,i,iiLtLY,i ,,,, l.iAl 0 100 200 300 400 500 Penetration below depth (nm) where Fig. 7. Variation of the mean longitudinal Young’s modulus values with the penetration below contact when indenting the monolithic silicon nitride [ES&N,(m)] and the matrix￾rich regions in the Hi-NicalorUBNMicon-nitride composite h, = h, - d/2 (9) (Ecomp). The maximum applied force is 250 mN