1916 Journal of the American Ceramic Sociery-Choi and bansal Vol. 87, No. 10 100 SIC/BSAS Tension (DNS/1100 C) SIC /CAS 200 800400 n=11.4 SIC/MAS 90 0000 SIC/BSAS 10 10410310210110010102103 102101100101102 Applied stress rate, o [MPa/s Applies shear stress rate, t [MPa/s Fig. 7. Examples of ultimate tensile strength as a function of applied Fig. 8. Shear strength as a function of applied shear stress rate ess rate at elevated temperatures in air for CFCCs. including SiC /MAS (2-D, 1100 C), SIC CAS (1-D. 1100 C), SiC,/SiC (2-D woven 1200C). and SiC/BSAS (2-D, 1100C) where T is(remote) shear stress, and t is applied shear stress rate A test methodology based on Eq(3)or(4) is called constant he applied shear stress rate T in displacement control can be stress-rate(dynamic fatigue")testing and has been established as determined from the slope(AP/Ar) of each recorded force versus ASTM test methods C136814 and C1465 5 to determine sCG time curve(such as in Fig. 5)including the portion at or near the parameters of advanced monolithic ceramics at ambient and oint of fracture but excluding the initial nonlinear portion, if any, elevated temperatures. As mentioned before. the data fit to Eq (4) using the following relat tion was shown to be very reasonable even for CFCCs including SiC/CAS (1-D), SIC, /MAS (1-, 2-D), SiC /SiC (2-D), C/SiC (2-D), and SiC/BSAS (2-D)in tension at 1 100 to 1200C in air. accumulation or delayed failure of those composites would be In case of force control. the applied shear stress rate can be dequately described by the power-law formulation, Eq. ( 2). The obtained, without determining the slope, directly from the follow SCG parameter n is the most important life prediction paramet g relation: since it represents a measure of susceptibility to slow crack growth. For monolithic ceramics, glasses, or glass-ceramics, the sceptibility to slow crack growth is typically categorized such that significant slow crack growth lies in the range "< 30, where P is the applied force rate used within a test frame. Hence insignificant slow crack growth in the range n a 50. For the mining t in terms of accuracy and convenience, as also suggested in ASTM dynamic fatigue test standards in flexure. The hence the composites exhibited significant susceptibility to slow generalized expression of stress intensity factor in shear for the crack growth. Examples of some CFCCs showing invariably case of an infinite body with a circular or semicircular crack takes significant strength degradation and consequently significant slow crack growth susceptibility in constant stress-rate testing in ten- the following form sion" are presented in Fig. 7. which show the dependency of shear strength on test rate, the where Y, is a crack geometry factor in shear. Using Eqs. (5).(6). reasonable data fit to log(shear strength) vs log(test rate)relation. and following a similar procedure as used to derive Eq. (3 and the indication of slow crack growth from the force versus time le I, one can obtain shear strength (T,) as a function of curves, the governing failure mechanism in shear can be assumed shear stress rate as follows to be the one associated with slow crack growth, similar in expression to the power-law relation of Eq.(2). Therefore, the =D[ (10) following empirical slow crack velocity formulation for shear is proposed her where da D,=[B(n1+1rx-2]m v,dr-a, (K/Kne)" where B,= 2Kne/a, Y,(n,-2)] and, T, is the inert shear "a,a, 4, Ku, and Kue are the crack velocity in shear, the crack test rate whereby little or no slow crack growth occurs. Equ toughness, respectively. a, and n, are SCG parameters in (10) can be expressed in a more convenient form by takin shear In monotonic shear testing, a constant displacement rate or logarithms of both sides constant force rate is applied to a test specimen until the test specimen fails, so that the shear stress applied to the test specimen is a linear function of test time: T are inevitable from specimen to specimen in the case of T= t() dr=tr are entered as logarithmic numbers when SCG strength and t,1916 Journal of the American Ceramic SocieTy^Choi and Bansal Vol. 87. No. 10 CL S tT xT c 09 lest ensil a> *.• I•E 500 400 300 200 80 70 60 50 Tension SiC/MAS . SiC^BSAS (n=7) SiC/SiC SiC/CAS 10-3 10"' 10"' 10" 10^ 10^ 10^ Applied stress rate, d [MPa/s] Fig. 7. Examples of ultimate tensile strength as a function of applied stress rate at elevated tetnperatures in air for CFCCs**'' including SiC/MAS (2-D, 1 lOO'-C). SiC,/CAS (I-D. 11(K)"C). SiC,/SiC (2-D woven, I2OO''C), and SiC,/BSAS (2'D. llOO^C). 0. E sz a> (A <u V) 100 ?8 60 50 40 30 20 10 SiC/BSAS - (DNS/1100°C) In-plane Interlamtnar 10-3 10-2 10^ 10" 10' 10' 10^ 10^ Applies shear stress rate, r [MPa/s] Fig. 8. Shear strength as a function of applied shear stress rate for SiC/BSAS composite at 1 lW C in air, reconstrucled from the data in Fig. 3 using E(|. (12). A test methodology based on Eq. (3) or (4) is called constant stress-rate ("dynamic fatigue") testing and has been established as ASTM test methods C1368''^ and C1465'^ to determine SCG parameters of advanced monolithic ceramics at ambient and elevated temperatures. As mentioned before, the data fit to Eq. (4) was .shown to be very reasonable even for CECCs including SiC/CAS (1-D), SiC|/MAS (1-. 2-D), SiC,/SiC (2-D), C/SiC (2'D), and SiC/BSAS (2-D) in tension at 1100° to 1200°C in air. This indicates that slow crack growth or damage evolution/ accumulation or delayed failure of those composites would be adequately described by the power-law formulation. Eq. (2). The SCG parameter n is the most important life prediction parameter since it represents a measure of susceptibilily to slow crack growth. For monolithic ceramics, glasses, or glass-ceramics, the susceptibility to slow crack growth is typically categorized such that significant slow crack growth lies in the range n < 30, intermediate slow crack growth in the range n — 30--40, and insignificant slow crack growth in the range n ^ 50. For the aforementioned composites, the values of n were all less than 20; hence the composites exhibited significant susceptibility to slow crack growth. Examples of some CFCCs showing invariably significant strength degradation and consequently significant slow crack growth susceptibility in constant stress-rate testing in ten￾sion^"'' are presented in Fig. 7. Based on the experimental results of the SiC,/BSAS composite. which show the dependency of shear strength on test rate, the reasonable data fit to log (shear strength) vs log (test rate) relation. and the indication of slow crack growth from the force versus time curves, the governing failure mechanism in shear can be assumed to be the one associated with slow crack growth, similar in expression to the power-law relation of Eq. (2). Therefore, the following empirical slow crack velocity formulation for shear is proposed here: da — (5) where v^. a. l. A",,, and A!",,^. are the crack velocity in shear, the crack size, the time, the Mode II stress intensity factor, and the Mode II fracture toughness, respectively, o:^ and JI, are SCG parameters in shear. In monotonic shear testing, a constant displacement rate or constant force rate is applied to a test specimen until the test specimen fails, so that the shear stress applied to the test specimen is a linear function of test time: fit) d/ - fr where T is (remote) shear stress, and t is applied shear stress rate. The applied shear stress rate t in displacement control can be determined from the slope (A.P/^1} of each recorded force versus time curve (such as in Fig. 5) including the portion at or near the point of fracture but excluding the initial nonlinear portion, if any. using the following relation:* (7) In case of force control, the applied shear stress rate can be obtained, without determining the slof)e, directly from the follow￾ing relation: (8) where P is the applied force rate used within a test frame. Hence. force control is much better than displacement control in deter￾mining t in terms of accuracy and convenience, as also suggested in ASTM dynamic fatigue test standards in flexure.''*•'''' The generalized expression of stress intensity factor in shear for the case of an infinite body with a circular or semicircular crack takes the following form:"' where Y^ is a crack geometry factor in shear. Using Eqs. (5). (6), and (9) and following a similar procedure as used to derive Eq. (3) in Mode 1, one can obtain shear strength (T,) as a function of applied shear stress rate as follows: where (10) (II) where B^ — 2K^fJ[oi^Y^^^(n^ — 2)] and. T, is the inert shear strength that is determined in an appropriate inert environment or at a fast test rate whereby little or no slow crack growth occurs. Equation (10) can be expressed in a more convenient form by taking logarithms of both sides: *Sonie variations in t are inevitable from specimen to speeimen in the case of siighlly nonlinear force-vs-time curves. However, such small variations in t will not affect SCG parameters ii, and D^ significanily since both shear strength and t, according to Eq, (12), are entered as logarithmic ntimbers when SCG parameters are determined via regression analysis