July 1997 High-Temperature Transverse fracture Toughness l813 limited plasticity, materials like ceramics and glasses The theoretical analysis of the dt technique assu atisfy the plar ditions as long as the thickness of the crack front is straight and orthogonal to the plane of the tative of the material 23 ough to be microstructurally represen the specimen is specimen. However, in most materials the crack front profile is significantly curved, with the furthest advance along the bot tom face of the specimen. 4 Because of this, Evans2suggests I. Test Technique rather than analytically. It is important that a constant-K(stress intensity factor The consensus among most researchers, 32 has been specimen be used so that continuous crack length measure crack velocity and crack length of interest is that of the ments are not required for data reduction, since high dge of the crack, i.e the furthest advanced bottom temperature tests will take place within a furnace. the doubl location transverse fracture toughness in this study, satisfies the con- specimen dimensions are approximately as follows: wit um Tait Fry and Garrett 3 have suggested that the opti stant-K requirement. The utility of the dt technique has been demonstrated in both ceramic and in composites. 20, 2It thicknesses complicate the analysis because of the significant has been shown that it gives results similar to those of other test contact stresses generated by the interaction of the torsion arms The original DT technique was suggested by Outwater and Another area of contention for the dt test configuration is Gerry and developed by Kies and Clark. 27 As illustrated in Fig. the length of crack over which the stress intensity may be I, the test specimen is a rectangular plate with a narrow notch considered to be independent of crack length(constant-K re or crack started in one end. The specimen is loaded in four- point bending across the notch, i. e, in"double torsion. " Thus lengths greater than 0. 55w, and ligaments(uncracked portion) the crack propagates axially along the specimen The crack is greater than 0. 65W. Tait et al found a consensus over severa researchers which indicated that at least the central one-third t one-half of the specimen (for L/w =3) should offer shear deformation for the crack to develop modes Il and III constant-K conditions Shetty and Virkar4 stated that the valid failure vanishes because of the symmetric double torsion"of region decreases as the en length-to-width ratio de- 山 pecimen with respect to the crac2 creases First, the pecimen complia ance, c (inverse of the against displacement, d, curve), is linearly related to the spec Il. Experimental Procedure men crack length, a. Second, the critical load, Pc, at which crack propagation is initiated, is independent of crack length, a The materials used in this study were unidirectional ([0]16) (constant-K specimen). Therefore, the fracture toughness, GIe Nicalon fiber/CAS-Il matrix composites. They were supplied ed from the compliance by Corning, Inc in the form of square plates, approximately I UsIn cm by 15 cm and about 3 mm thick. dt tests were conducted on an instron model 8562 servo- P? dc electric universal testing machine. Tests were performed with a Gle=2 da (1) 500 lb Le Bow load cell mounted below the standard 20 000 lb Instron load cell. This lower capacity load cell was used be where t is the specimen thickness. Both Pc and dida can be cause of its better resolution in the load range of interest. An accurately determined from the test results, as will be discussed Inconel rod was attached to the load cell for load application in the Experimental Section A flat compression table was mounted to the bottom grip to The compliance relationship with respect to the crack length, hold the DT fixture base. a photograph of the loading section dClda, can also be expressed analytically by 28 of the dt test system is shown in Fig. 2 The test fixture used for the dt test was similar to the one designed by Professor Leon Chuck from the University of Day ton. A close-up of the fixture, with a composite specime mounted, appears in Fig. 3. The fore-and-aft, and side-to-side modifying the lengt由 the two pivot rollers:0m如b w(r=1-0.6302(2t/W)+1.20(2 /W)e m/ww (3) the top portion plays no role during loading. The fixture, the base plate, and the loading rod were all made from Inconel, a nickel-based superalloy, for use at ter mperatures up to 1000C. The testing machine was equipped with a slot type, 2 Zone Model"D", fumace, mounted on rails, supplied by Instron Corp This furmace which was originally designed for tensile sts was enlarged axially by plates to create a box-shaped furnace positioned over the slot furnace. Internal dimensions of the box were 15 cm x 15 cm For those tests performed at high temperatures using the en larged furnace, the temperature was read by inserting a ther mocouple wire into the furnace next to the dt specimen DT test specimen blanks of 2. 18 cm x 6.70 cm were cut from the composite plates using a diamond saw and a diamond coated grinding wheel. Initial notches were cut into one side of the specimens using the 1 mm thick diamond saw. To deter mine the compliance vs crack length calibration, dc/da, six to mens were prepared and a different notch length was machined into each specimen. The introduced notch length Fig. 1. Double torsion test configuration ranged from 1. 80 to 5.08 cm.July 1997 High-Temperature Transverse Fracture Toughness 1813 limited plasticity, brittle materials like ceramics and glasses satisfy the plane-strain conditions as long as the thickness of the specimen is large enough to be microstructurally represen￾tative of the material.23 11. Test Technique It is important that a constant-K (stress intensity factor) specimen be used so that continuous crack length measure￾ments are not required for data reduction, since high￾temperature tests will take place within a furnace. The double torsion (DT) test method, which was utilized to measure the transverse fracture toughness in this study, satisfies the con￾stant-K requirement. The utility of the DT technique has been demonstrated in both ceramics2626 and in composites.20.21 It has been shown that it gives results similar to those of other test technique^.^^.^^ The original DT technique was suggested by Outwater and Gerry and developed by Kies and Clark.27 As illustrated in Fig. 1, the test specimen is a rectangular plate with a narrow notch or crack started in one end. The specimen is loaded in four￾point bending across the notch, i.e., in “double torsion.” Thus the crack propagates axially along the specimen. The crack is more open at the bottom face and less open at the top face of the specimen, defining Mode I fra~t~re.~~.~~.~~*~~ The necessary shear deformation for the crack to develop Modes 11 and 111 failure vanishes because of the symmetric “double torsion” of the specimen with respect to the crack plane.2’.28 The DT test has two major features.20.21,2627,29.30 First, the specimen compliance, C (inverse of the initial slope of load, P, against displacement, d, curve), is linearly related to the speci￾men crack length, a. Second, the critical load, P,, at which crack propagation is initiated, is independent of crack length, a (constant-K specimen). Therefore, the fracture toughness, GI,, can be computed from the compliance calibration method by using.20.21 25.283 I dC G --- IC- 2t da where t is the specimen thickness. Both P, and dClda can be accurately determined from the test results, as will be discussed in the Experimental Section. The compliance relationship with respect to the crack length, dClda, can also be expressed analytically by28 dC 3x2 da - G Wr3 +( t) -- where G is the elastic shear modulus of the material, x, W, and t are specimen dimensions shown in Fig. 1, and +(t) is the thickness correction factor, which may be expressed by28 $(t) = 1 - 0.6302(2t/W) + 1.20(2t1W)e-“’(2‘w (3) v2 t Fig. 1. Double torsion test configuration. The theoretical analysis of the DT technique assumes that the crack front is straight and orthogonal to the plane of the specimen. However, in most materials the crack front profile is significantly curved, with the furthest advance along the bot￾tom face of the specimen.24 Because of this, Evansz3 suggests that the compliance calibration be obtained experimentally rather than analytically. The consensus among most re~earchers~~.~~ has been that the crack velocity and crack length of interest is that of the leading edge of the crack, i.e., the furthest advanced bottom surface location. Tait, Fry, and Garrett33 have suggested that the optimum specimen dimensions are approximately as follows: width = W; length, L = 3W; and thickness = W16 to W/15. Greater thicknesses complicate the analysis because of the significant contact stresses generated by the interaction of the torsion arms (the two sides of the specimen separated by the crack). Another area of contention for the DT test configuration is the length of crack over which the stress intensity may be considered to be independent of crack length (constant-K re￾gion). Trantina30 showed that this assumption is valid for crack lengths greater than 0.55 W, and ligaments (uncracked portion) greater than 0.65W. Tait et found a consensus over several researchers which indicated that at least the central one-third to one-half of the specimen length (for UW = 3) should offer constant-K conditions. Shetty and Virkar34 stated that the valid region decreases as the specimen length-to-width ratio de￾creases. In. Experimental Procedure The materials used in this study were unidirectional ([O],,) Nicalon fiberlCAS-11 matrix composites. They were supplied by Coming, Inc. in the form of square plates, approximately 15 cm by 15 cm and about 3 mm thick. DT tests were conducted on an Instron Model 8562 servo￾electric universal testing machine. Tests were performed with a 500 lb LeBow load cell mounted below the standard 20 OOO lb Instron load cell. This lower capacity load cell was used be￾cause of its better resolution in the load range of interest. An Inconel rod was attached to the load cell for load application. A flat compression table was mounted to the bottom grip to hold the DT fixture base. A photograph of the loading section of the DT test system is shown in Fig. 2. The test fixture used for the DT test was similar to the one designed by Professor Leon Chuck from the University of Day￾ton.35 A close-up of the fixture, with a composite specimen mounted, appears in Fig. 3. The fore-and-aft, and side-to-side alignment of the base and the upper fixture is adjusted by modifying the length of the two pivot rollers. Once the speci￾men and fixture are aligned during setup, the support fixture for the top portion plays no role during loading. The fixture, the base plate, and the loading rod were all made from Inconel, a nickel-based superalloy, for use at temperatures up to 1000°C. The testing machine was equipped with a slot type, 2 Zone Model “D”, furnace, mounted on rails, supplied by Instron Corp. This furnace which was originally designed for tensile tests was enlarged axially by attaching alumina insulation plates to create a box-shaped furnace positioned over the slot furnace. Internal dimensions of the box were 15 cm x 15 cm. For those tests performed at high temperatures using the en￾larged furnace, the temperature was read by inserting a ther￾mocouple wire into the furnace next to the DT specimen. DT test specimen blanks of 2.18 cm x 6.70 cm were cut from the composite plates using a diamond saw and a diamond￾coated grinding wheel. Initial notches were cut into one side of the specimens using the 1 mm thick diamond saw. To deter￾mine the compliance vs crack length calibration, dClda, six to eight specimens were prepared and a different notch length was machined into each specimen. The introduced notch length ranged from 1.80 to 5.08 cm