27 “Standard Test Method for J-Integral Characterization of Fracture Toughness,” ASTM E 1737, Annual Book of Standards, Vol 03.01, ASTM, 1996 28 J.D Landes and J.A Begley, in Fracture Toughness, ASTM STP 560, 1974, p 170 29 S Hashemi and J.G Williams, Plast Rubber Process Appl., Vol 6, 1986, p 363 30 M.-L Lu and F.-C Chang, Polymer, Vol 36, 1995, p 2541 31 Z Zhou, J.D Landes, and D.D Huang, Polym Eng Sci., Vol 34, 1994, p 128 32 M.-L Lu, C.-B Lee, and F.-C Chang, Polym Eng Sci., Vol 35, 1995, p 1433 33 J.W Hutchinson and P.C Paris, in Elastic-Plastic Fracture, ASTM STP 668, 1979, p 37 34 I Narisawa and M.T Takemori, Polym Eng Sci., Vol 29, 1989, p 671 35 H Swei, B Crist, and S.H Carr, Polymer, Vol 32, 1991, p 1440 36 C.-B Lee, M.-L Lu, and F.-C Chang, J Appl Polym Sci., Vol 47, 1993, p 1867 37 M.-L Lu and F.-C Chang, J Appl Polym Sci., Vol 56, 1995, p 1065 38 B.M Rimnac, T.W Wright, and R.W Klein, Polym Eng Sci., Vol 28, 1988, p 1586 39 B.D Huang, in Toughened Plastics I: Science and Enginering, C.K Riew and A.J Kinloch, Ed., Vol 233, p 39, ACS Advances in Chemistry Series,, American Chemical Society, 1993 40 M.-L Lu, K.-C Chiou, and F.-C Chang, Polymer, Vol 37, 1996, p 4289 41 K.J Pascoe, in Failure of Plastics, W Brostow and R.D Corneliussen, Ed., Hanser Publishers, 1989, p 119 42 M.-L Lu, K.-C Chiou, and F.-C Chang, Polym Eng Sci., Vol 36, 1996, p 2289 Fracture Resistance Testing of Plastics Kevin M Kit and Paul J Phillips, University of Tennessee, Knoxville References N.G McCrum, B.E Read, and G Williams, Anelastic and Dielectric Effects in Polymeric Solids, Wiley, 1967 I.M Ward, Mechanical Properties of Solid Polymers, Wiley, 1983, p 15 E.H Andrews, Cracking and Crazing in Polymeric Glasses, The Physics of Glassy Polymers, R.N Haward, Ed., Wiley, 1973, p 394 R Natarajan and P.E Reed, J Polym Sci A, Polym Chem., Vol (No 10), 1972, p 585 G.A Bernier and R.P Kambour, Macromolecules, Vol 1, 1968, p 393 E.H Andrews, G.M Levy and J Willis, J Mater Sci., Vol 8, 1973, p 1000 L.E Weber, The Chemistry of Rubber Manufacture, Griffin, London, 1926, p 336 K Memmler, The Science of Rubber, R.F Dunbrook and V.N Morris, Ed., Reinhold, 1934, p 523 G.R Irwin, in Encyclopaedia of Physics, Vol 6, Springer Verlag, 1958 10 N.G McCrum, C.P Buckley, and C.B Bucknall, Principles of Polymer Engineering, Oxford University Press, 1997, p 201 11 A.A Griffith, Phil Trans R Soc (London) A, Vol 221, 1921, p 163 12 R.S Rivlin and A.G Thomas, J Polym Sci., Vol 10, 1953, p 291 13 R.P Kambour, Appl Polym Symp., Vol 7, John Wiley & Sons, 1968, p 215 14 J.P Berry, J Polym Sci A, Polym Chem., Vol 2, 1964, p 4069 15 E.H Andrews, J Mater Sci., Vol 9, 1974, p 887 16 J.R Rice, J Appl Mech (Trans ASME), Vol 35, 1968, p 379 17 J.R Rice, Fracture, Vol 2, 1968, p 191 18 J.A Begley and J.D Landes, in Fracture Toughness, ASTM STP 514, 1972, p 19 J.D Landes and J.E Begley, in Fracture Toughness, ASTM STP 514, 1972, p 24 20 J.M Hodgkinson and J.G Williams, J Mater Sci., Vol 16, 1981, p 50 21 S Hashemi and J.D Williams, Polym Eng Sci., Vol 26, 1986, p 760 22 Y.W Mai and P Powell, J Polym Sci B, Polym Phys., Vol 29, 1991, p 785 23 M Ouederni and P.J Phillips, J Polym Sci B., Polym Phys., Vol 33, 1995, p 1313 24 “Standard Test Methods for Plane Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials,” ASTM D 5045, Annual Book of Standards, Vol 08.03, ASTM, 1996 25 “Standard Test Method for Determining J-R Curves of Plastic Materials,” ASTM D 6068, Annual Book of Standards, Vol 08.03, ASTM, 1996 26 “Standard Test Method for JIc, A Measure of Fracture Toughness,” ASTM E 813, Annual Book of Standards, Vol 03.01, ASTM, 1989 27 “Standard Test Method for J-Integral Characterization of Fracture Toughness,” ASTM E 1737, Annual Book of Standards, Vol 03.01, ASTM, 1996 28 J.D Landes and J.A Begley, in Fracture Toughness, ASTM STP 560, 1974, p 170 29 S Hashemi and J.G Williams, Plast Rubber Process Appl., Vol 6, 1986, p 363 30 M.-L Lu and F.-C Chang, Polymer, Vol 36, 1995, p 2541 31 Z Zhou, J.D Landes, and D.D Huang, Polym Eng Sci., Vol 34, 1994, p 128 32 M.-L Lu, C.-B Lee, and F.-C Chang, Polym Eng Sci., Vol 35, 1995, p 1433 33 J.W Hutchinson and P.C Paris, in Elastic-Plastic Fracture, ASTM STP 668, 1979, p 37 34 I Narisawa and M.T Takemori, Polym Eng Sci., Vol 29, 1989, p 671 35 H Swei, B Crist, and S.H Carr, Polymer, Vol 32, 1991, p 1440 36 C.-B Lee, M.-L Lu, and F.-C Chang, J Appl Polym Sci., Vol 47, 1993, p 1867 37 M.-L Lu and F.-C Chang, J Appl Polym Sci., Vol 56, 1995, p 1065 38 B.M Rimnac, T.W Wright, and R.W Klein, Polym Eng Sci., Vol 28, 1988, p 1586 39 B.D Huang, in Toughened Plastics I: Science and Enginering, C.K Riew and A.J Kinloch, Ed., Vol 233, p 39, ACS Advances in Chemistry Series,, American Chemical Society, 1993 40 M.-L Lu, K.-C Chiou, and F.-C Chang, Polymer, Vol 37, 1996, p 4289 41 K.J Pascoe, in Failure of Plastics, W Brostow and R.D Corneliussen, Ed., Hanser Publishers, 1989, p 119 42 M.-L Lu, K.-C Chiou, and F.-C Chang, Polym Eng Sci., Vol 36, 1996, p 2289 Fracture Toughness of Ceramics and Ceramic Matrix Composites J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville Introduction CERAMICS are lightweight structural materials with much higher resistance to high temperatures and aggressive environments than other conventional engineering materials These characteristics of ceramics hold promise in various applications for gas turbines, heat exchangers, combustors and boiler components in the power generation systems, first-wall and high-heat-flux surfaces in fusion reactors, and structural components in the aerospace industry (Ref 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, and 25) However, most of these engineering applications require high reliability and the improvement of ceramic fracture toughness Monolithic ceramics are inherently brittle, making them highly sensitive to process- and service-related flaws Due to their low toughness, monolithic ceramics are prone to catastrophic failure and, thus, may be unsuitable for engineering applications that require high reliability Ceramic matrix composites (CMCs), however, can provide significant improvement in fracture toughness and the avoidance of catastrophic failure (Ref 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, and 41) The fracture mechanisms in CMCs are identical to those found in monolithic ceramics (brittle), but “plastic-like” behavior occurs in CMCs because of the toughening mechanisms of crack bridging, branching, and deflection The reinforcing particles, whiskers, or fibers that are present in the ceramic matrix allow the bulk composite material to avoid unstable crack growth and the resulting catastrophic failure The toughness of CMCs comes from the fact that the reinforcement can provide crack bridges and cause cracks to branch, deflect, or arrest These issues are quite complicated, and they demonstrate the critical need for the understanding of the fracture properties of ceramics and CMCs Much work has been done to develop methods for evaluating the fracture toughness of ceramic materials (Ref 42, 43, 44, 45, 46, 47, 48, 49, and 50) The concepts of both linear-elastic fracture mechanics (LEFM) and elastic-plastic fracture mechanics (EPFM) are both of interest in regard to ceramic materials Monolithic ceramics, due to their brittle nature, behave in a linear-elastic manner This fact has lead to the successful use of LEFM methods for monolithic ceramics Many CMCs, on the other hand, have an elastic-plastic fracture behavior This fact has lead researchers to attempt to use EPFM methods to evaluate the fracture toughness of CMCs This article briefly introduces LEFM and EPFM concepts and methods that have been developed or adapted for the evaluation of the fracture behavior of monolithic ceramics and CMCs The general concepts of LEFM and EPFM are briefly reviewed, and test methods are described for fracture toughness testing of monolithic ceramics and CMCs More detailed information on the fracture resistance testing of monolithic ceramics is also contained in the article “Fracture Resistance Testing of Brittle Solids” in this Volume, while this article places emphasis on the fracture toughness testing of cmcs Measuring the fracture toughness of CMCs is not as developed as toughness testing of monolithic ceramics The toughening mechanisms of microcracking, crack bridging, and crack branching cause CMCs to behave in an elastic-plastic-like manner, which makes EPFM methods attractive LEFM and EPFM methods have both been used to evaluate the toughness of CMCs, but because the level of understanding of the complex fracture mechanisms present in CMCs is not well developed, no connection has been made between the macroscopic toughness, either elastic or elastic-plastic, and the fracture mechanisms As a result, evaluation of the fracture toughness of CMCs has been limited However, as the cracking mechanisms become better understood, LEFM and EPFM methods will become better adapted for use in the evaluation of CMC fracture toughness behavior References cited in this section T.M Besmann, B.W Sheldon, R.A Lowden, and D.P Stinton, Vapor Phase Fabrication and Properties of Continuous-Filament Ceramic Composites, Science, Vol 253, 1991, p 1104 M Bouquet, J.M Bribis, and J.M Quenisset, Toughness Assessment of Ceramic Matrix Composites, Compos Sci Technol., Vol 37, 1990, p 223–248 C.H Hsueh, P.F Becher, and P Angelini, Effects of Interfacial Films on Thermal Stresses in WhiskerReinforced Ceramics, J Am Ceram Soc., Vol 71 (No 11), 1988, p 929–933 D.P Stinton, A.J Caputo, and R.A Lowden, Synthesis of Fiber-Reinforced SiC Composites by Chemical Vapor Infiltration, Am Ceram Soc Bull., Vol 65 (No 2), 1986, p 347–350 D.P Stinton, W.J Lackey, R.J Lauf, and T.M Besmann, Fabrication of Ceramic-Ceramic Composites by Chemical Vapor Deposition, Ceram Eng Sci Proc., Vol 5, 1984, p 668–676 J.H Miller, R.A Lowden, and P.K Liaw, Fiber Coatings and the Fracture Behavior of a Continuous Fiber Ceramic Composite, Symposium on Ceramic Matrix Composites—Advanced High-Temperature Structural Materials, R.A Lowden, M.K Ferber, J.R Hellmann, K.K Chawla, and S.G DiPietro, Ed., Vol 365, Materials Research Society, 1995, p 403–410 M.A Borst, W.Y Lee, Y Zhang, and P.K Liaw, Preparation and Characterization of Chemically Vapor Deposited ZrO2 Coating on Nickel and Ceramic Fiber Substrates, J Am Ceram Soc., Vol 80 (No 6), 1997, p 1591–1594 N Miriyala, P.K Liaw, C.J McHargue, L.L Snead, and J.A Morrison, The Monotonic and Fatigue Behavior of a Nicalon/Alumina Composite at Ambient and Elevated Temperatures, American Ceramic Society Meeting, Ceram Eng Sci Proc., Vol 18 (No 3), 1997, p 747–756 W Zhao, P.K Liaw, and N Yu, Effects of Lamina Stacking Sequence on the In-Plane Elastic Stress Distribution of a Plain-Weave Nicalon Fiber-Reinforced SiC Laminated Composite with a Lay-Up of [0/30/60], American Ceramic Society Meeting, Ceram Eng Sci Proc., Vol 18 (No 3), 1997, p 401– 408 10 W Zhao, P.K Liaw, and D.C Joy, Microstructural Characterization of a 2-D Woven Nicalon/SiC Ceramic Composite by Scanning Electron Microscopy Line-Scan Technique, American Ceramic Society Meeting, Ceram Eng Sci Proc., Vol 18 (No 3), 1997, p 295–302 11 J.G Kim, P.K Liaw, D.K Hsu, and D.J McGuire, Nondestructive Evaluation of Continuous Nicalon Fiber Reinforced SiC Composites, American Ceramic Society Meeting, Ceram Eng Sci Proc., Vol 18 (No 4), 1997, p 287–296 12 N Miriyala, P.K Liaw, C.J McHargue, and L.L Snead, The Monotonic and Fatigue Behavior of a Nicalon/Alumina Composite at Ambient and Elevated Temperatures, Ceram Eng Sci Proc., Vol 18 (No 3), 1997, p 747–756 13 W Zhao, P.K Liaw, N Yu, E.R Kupp, D.P Stinton, and T.M Besmann, Computation of the Lamina Stacking Sequence Effect on the Elastic Moduli of a Plain-Weave Nicalon Fiber Reinforced SiC Laminated Composite with a Lay-Up of [0/30/60], J Nucl Mater., Vol 253, 1998, p 10–19 14 N Miriyala, P.K Liaw, C.J McHargue, and L.L Snead, “The Mechanical Behavior of A Nicalon/SiC Composite at Ambient Temperature and 1000 °C”, J Nucl Mater., Vol 253, 1998, p 1–9 15 W.Y Lee, Y Zhang, I.G Wright, B.A Pint, and P.K Liaw, Effects of Sulfur Impurity on the Scale Adhesion Behavior of a Desulfurized Ni-Based Superalloy Aluminized by Chemical Vapor Deposition, Metall Mater Trans A, Vol 29, 1998, p 833 16 P.K Liaw, Understanding Fatigue Failure in Structural Materials, JOM, Vol 49 (No 7), 1997, p 42 17 N Miriyala and P.K Liaw, CFCC (Continuous-Fiber-Reinforced Ceramic Matrix Composites) Fatigue: A Literature Review, JOM, Vol 49 (No 7), 1997, p 59–66, 82 18 N Miriyala and P.K Liaw, Specimen Size Effects on the Flexural Strength of CFCCs, American Ceramic Society Meeting, Ceram Eng Sci Proc., Vol 19, 1998 19 W Zhao, P.K Liaw, and N Yu, Computer-Aided Prediction of the First Matrix Cracking Stress for a Plain-Weave Nicalon/SiC Composite with Lay-Ups of [0/20/60] and [0/40/60], Ceram Eng Sci Proc., Vol 19, 1998, p 20 W Zhao, P.K Liaw, and N Yu, Computer-Aided Prediction of the Effective Moduli for a Plain-Weave Nicalon/SiC Composite with Lay-Ups of [0/20/60] and [0/40/60], Ceram Eng Sci Proc., Vol 19, 1998 21 N Miriyala, P.K Liaw, C.J McHargue, A Selvarathinam, and L.L Snead, The Effect of Fabric Orientation on the Flexural Behavior of CFCCs: Experiment and Theory, The 100th Annual American Ceramic Society Meeting, 3–6 May 1998 (Cincinnati), in press 22 N Miriyala, P.K Liaw, C.J McHargue, and L.L Snead, Fatigue Behavior of Continuous FiberReinforced Ceramic-Matrix Composites (CFCCs) at Ambient and Elevated Temperatures, invited paper presented at symposium proceedings in honor of Professor Paul C Paris, High Cycle Fatigue of Structural Materials, W.O Soboyejo and T.S Srivatsan, Ed., The Minerals, Metals, and Materials Society, 1997, p 533–552 23 W Zhao, P.K Liaw, and N Yu, The Reliability of Evaluating the Mechanical Performance of Continuous Fiber-Reinforced Ceramic Composites by Flexural Testing, Int Conf on Maintenance and Reliability, 1997, p 6-1 to 6-15 24 P.K Liaw, J Kim, N Miriyala, D.K Hsu, N Yu, D.J McGuire, and W.A Simpson, Jr., Nondestructive Evaluation of Woven Fabric Reinforced Ceramic Composites, Symposium on Nondestructive Evaluation of Ceramics, C Schilling, J.N Gray, R Gerhardt, and T Watkins, Ed., Vol 89, 1998, p 121– 135 25 M.E Fine and P.K Liaw, Commentary on the Paris Equation, invited paper presented at symposium proceedings in honor of Professor Paul C Paris, High Cycle Fatigue of Structural Materials, High Cycle Fatigue of Structural Materials, W.O Soboyejo and T.S Srivatsan, Ed., The Minerals, Metals, and Materials Society, 1997, p 25–40 26 W Zhao, P.K Liaw, D.C Joy, and C.R Brooks, Effects of Oxidation, Porosity and Fabric Stacking Sequence on Flexural Strength of a SiC/SiC Ceramic Composite, Processing and Properties of Advanced Materials: Modeling, Design and Properties, B.Q Li, Ed., The Minerals, Metals, and Materials Society, 1998, p 283–294 27 W Zhao, P.K Liaw, and N Yu, Computer Modeling of the Fabric Stacking Sequence Effects on Mechanical Properties of a Plain-Weave SiC/SiC Ceramic Composite, Proc on Processing and Properties of Advanced Materials: Modeling, Design and Properties, B.Q Li, Ed., The Minerals, Metals, and Materials Society, 1998, p 149–160 28 J Kim and P.K Liaw, The Nondestructive Evaluation of Advanced Ceramics and Ceramic-Matrix Composites, JOM, Vol 50 (No 11), 1998 29 N Yu and P.K Liaw, Ceramic-Matrix Composites: An Integrated Interdisciplinary Curriculum, J Eng Ed., supplement, 1998, p 539–544 30 P.K Liaw, Continuous Fiber Reinforced Ceramic Composites, J Chin Inst Eng., Vol 21 (No 6), 1998, p 701–718 31 N Yu and P.K Liaw, “Ceramic-Matrix Composites: Web-Based Courseware and More,” paper presented at the 1998 ASEE annual conference and exposition, June 28–July 1, 1998 (Seattle) 32 N Yu and P.K Liaw, “Ceramic-Matrix Composites,” http://www.engr.utk.edu/~cmc 33 P.K Liaw O Buck, R.J Arsenault, and R.E Green, Jr., Ed., Nondestructive Evaluation and Materials Properties III, The Minerals, Metals, and Materials Society, 1997 34 W.M Matlin, T.M Besmann, and P.K Liaw, Optimization of Bundle Infiltration in the Forced Chemical Vapor Infiltration (FCVI) Process, Symposium on Ceramic Matrix Composites—Advanced High-Temperature Structural Materials, R.A Lowden, M.K Ferber, J.R Hellmann, K.K Chawla, and S.G DiPietro, Ed., Vol 365, Materials Research Society, 1995, p 309–315 35 P.K Liaw, D.K Hsu, N Yu, N Miriyala, V Saini, and H Jeong, Measurement and Prediction of Composite Stiffness Moduli, Symposium on High Performance Composites: Commonalty of Phenomena, K.K Chawla, P.K Liaw, and S.G Fishman, Ed., The Minerals, Metals, and Materials Society, 1994, p 377–395 36 N Chawla, P.K Liaw, E Lara-Curzio, R.A Lowden, and M.K Ferber, Effect of Fiber Fabric Orientation on the Monotonic and Fatigue Behavior of a Continuous Fiber Ceramic Composite, Symposium on High Performance Composites, K.K Chawla, P.K Liaw, and S.G Fishman, Ed., The Minerals, Metals and Materials Society, 1994, p 291–304 37 P.K Liaw, D.K Hsu, N Yu, N Miriyala, V Saini, and H Jeong, Modulus Investigation of Metal and Ceramic Matrix Composites: Experiment and Theory, Acta Metall Mater., Vol 44 (No 5), 1996, p 2101–2113 38 P.K Liaw, N Yu, D.K Hsu, N Miriyala, V Saini, L.L Snead, C.J McHargue, and R.A Lowden, Moduli Determination of Continuous Fiber Ceramic Composites (CFCCs), J Nucl Mater., Vol 219, 1995, p 93–100 39 P.K Liaw, book review on Ceramic Matrix Composites by K.K Chawla, MRS Bull., Vol 19, 1994, p 78 40 D.K Hsu, P.K Liaw, N Yu, V Saini, N Miriyala, L.L Snead, R.A Lowden, and C.J McHargue, Nondestructive Characterization of Woven Fabric Ceramic Composites, Symposium on Ceramic Matrix Composites—Advanced High-Temperature Structural Materials, R.A Lowden, M.K Ferber, J.R Hellmann, K.K Chawla, and S.G DiPietro, Ed., Vol 365, Materials Research Society, 1995, 203–208 41 S Shanmugham, D.P Stinton, F Rebillat, A Bleier, E Lara-Curzio, T.M Besmann, and P.K Liaw, Oxidation-Resistant Interfacial Coatings for Continuous Fiber Ceramic Composites, S Shanmugham, D.P Stinton, F Rebillat, A Bleier, T.M Besmann, E Lara-Curzio, and P.K Liaw, Ceram Eng Sci Proc., Vol 16 (No 4), 1995, p 389–399 42 C.B Thomas, “Processing, Mechanical Behavior, and Microstructural Characterization of Liquid Phase Sintered Intermetallic-Bonded Ceramic Composites,” M.S Thesis, The University of Tennessee, Knoxville, 1996 43 J.H Miller, “Fiber Coatings and The Fracture Behavior of a Woven Continuous Fiber FabricReinforced Ceramic Composite,” M.S Thesis, The University of Tennessee, Knoxville, 1995 44 I.E Reimonds, A Review of Issues in the Fracture of Interfacial Ceramics and Ceramic Composites, Materials Science and Engineering A, Vol 237 (No 2), 1997, p 159–167 45 D.L Davidson, Ceramic Matrix Composites Fatigue and Fracture, JOM, Vol 47 (No 10), 1995, p 46– 50, 81, 82 46 J.C McNulty and F.W Zok, Application of Weakest-Link Fracture Statistics to Fiber-Reinforced Ceramic-Matrix Composites, J Am Ceram Soc., Vol 80 (No 6), 1997, p 1535–1543 47 Z.G Li, M Taya, M.L Dunn, and R Watanbe, Experimental-Study of the Fracture-Toughness of a Ceramic/Ceramic-Matrix Composite Sandwich Structure, J Am Ceram Soc., Vol 78 (No 6), 1995, p 1633–1639 48 A Ishida, M Miyayama, and H Yanagida, Prediction of Fracture and Detection of Fatigue in Ceramic Composites from Electrical-Resistivity Measurements, J Am Ceram Soc., Vol 77 (No 4), 1994, p 1057–1061 49 M Sakai and H Ichikawa, Work of Fracture of Brittle Materials with Microcracking and Crack Bridging, Int J Fract., Vol 55 (No 1), 1992, p 65–79 50 J.B Quinn and G.D Quinn, “Indentation Brittleness of Ceramics: A Fresh Approach,” J Mater Sci., Vol 32 (No 16), 1997, p 4331–4346 Fracture Toughness of Ceramics and Ceramic Matrix Composites J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville An Overview of Fracture Mechanics Fracture mechanics involves the stress analysis of cracking in structures or bodies with cracks or flaws Most of the work in this field has concentrated on the cracking behavior of metals, so this brief overview introduces the concepts and ideas of LEFM and EPFM for metals (Ref 51, 52, and 53) This is followed by a description of the use of LEFM and EPFM methods in the evaluation of monolithic ceramic and CMCs, respectively Linear-Elastic Fracture Mechanics The use of LEFM is applicable under two conditions: • • The applied load deforms a cracked body in a linear-elastic manner The flaw or crack is assumed to be a sharp crack with a tip radius near zero The stresses required for cracking under these two conditions can be analyzed according to LEFM by two parameters: the energy release rate and the stress intensity factor The energy release rate, G, is the amount of stored energy that is available for an increment of crack extension: (Eq 1) where Π is the stored potential energy and A is the crack surface area that is created as the crack grows In other words, G is the amount of store elastic energy that is converted to surface energy as the crack grows Because the body behaves in an elastic manner, all of the energy available is used to create the crack surfaces (Ref 51, 52, and 53) Expressions for the energy release rate can be derived based on the geometry of the crack and the loading conditions Two basic types of configurations are shown in Fig and for an edge crack and a central throughthickness crack, respectively, for Mode I (tensile opening) loads In this case, crack length is defined by typical convention as a for an edge crack (Fig 1) and as a 2a for a central through-thickness crack (Fig 2) With this convention, then the value of G for a wide plate (plate width >> a) in plane stress is as follows (Ref 51, 52, and 53): (Eq 2) where σ is the applied stress, E is Young's modulus, and a is either the total length of an edge crack (Fig 1) or half the length of center crack (2a in Fig 2) Equation thus applies to both of these basic configurations in Fig and with the appropriate definition for a as shown Fig Schematic illustration of an edge-notched specimen (a) Crack length, a, and general coordinate system for crack tip stresses in Mode I loading Fig Schematic illustration stress distributions near the tip of a through-thickness crack an infinitely wide plate (plate width >> than the crack length, 2a) The stress intensity factor, K, is a measure of stress intensity in the entire elastic stress field around the crack tip It is derived based on the analysis of the stress field near the tip of a sharp crack, rather than an energy consideration, as in the case of the energy release rate The stress intensity factor can be related to the local stress at the crack tip as: (Eq 3) where σYY is the local stress near the tip of the crack, KI is the stress intensity factor with a Mode I (tensile opening) load, and r is the distance in front of the crack tip (with θ = 0) (Fig 1) The stress intensity factor in Mode I loading can also be related to the applied or nominal stress as (Ref 51, 52, 53): KI = σnomY (Eq 4) where σnom is the nominal or applied stress and Y is a geometrical factor that is specific to a particular loading condition and crack configuration As in the case of Eq 2, the crack length, a, in Eq is defined either as the length of an edge crack (a in Fig 1) or as one-half the length of a through-thickness crack (2a in Fig 2) With these definitions for a, Eq applies for both an edge crack and a center crack configuration Figure shows a schematic plot of the stress normal to the crack plane as a function of the distance, r, from the crack tip for both σYY and σnom (Ref 51, 52, and 53) According to Eq and Fig 3, there is a singularity in the stress field at the tip of the crack This fact is the reason why elastic action is an important assumption in LEFM If significant plasticity occurred, the crack would be blunted by the plastic flow, and the stress intensity solution would no longer be valid Fatigue, Creep Fatigue, and Thermomechanical Fatigue Life Testing Gary R Halford and Bradley A Lerch, Glenn Research Center at Lewis Field, National Aeronautics and Space Administration; Michael A McGaw, McGaw Technology, Inc Thermomechanical Fatigue Thermal fatigue is a structural failure mode in many high-temperature components Thermal fatigue loading is induced by temperature gradients during transient heating or cooling from one high temperature of operation to another Thermal fatigue loading can also occur when heating and cooling are present simultaneously and thermal gradients are maintained during steady-state operation Internally air-cooled high-temperature turbine blades are examples Thermal gradients produce differential expansion as the hottest material wants to expand more than the cooler, but is constrained from doing so by the cooler and stronger material The constraint is perceived by the hottest material as a compressive thermal strain that is no different in its effect on the material than would be a mechanically induced strain of equal magnitude Similarly, the coldest material is forced by the hottest to expand more than normal The thermally induced strain in the colder material is tensile Conditions of strain compatibility will be maintained The corresponding thermal stresses result directly from the thermal strains according to the current stress-strain relation and the necessity to obey the laws of equilibrium The integrated sum of the internal stresses into forces must always equal zero Because of the gradients of the primary variables, it is impossible to measure the thermal fatigue properties of a material in the same way that isothermal fatigue or creep-fatigue properties are measured, that is, in terms of holding certain variables constant while the response of the others are measured To overcome this basic difficulty, TMF tests have been devised Thermomechanical Fatigue Testing The testing machine and specimen set up for TMF testing are essentially the same as used for creep-fatigue testing or baseline high-temperature isothermal fatigue testing The major distinction is that the temperature of the specimen, instead of remaining constant, must be programmed to vary in a precisely defined manner Furthermore, the cycling rate must, at times, be rather high, requiring the ability to heat and cool the test specimen as rapidly as possible without creating undue thermal gradients This requirement virtually rules out the use of conventional clamshell radiation furnaces because of their large thermal inertia Most commonly, induction heating is used This is because of the reasonably high rates of heating possible, and because the temperature gradient along the specimen gage length can be controlled better with a three-zone induction heating coil arrangement, as shown in Fig 11 Induction coils are also more conducive for use of extensometers Direct resistance heating, although not commonly used, has the capability of heating a sample so rapidly that it could be melted in a matter of seconds Heating is usually not the limiting factor in governing the cycling rate, rather, cooling is Forced air cooling has been used successfully Jets of air are impinged on the specimen surface along the gage length and around the circumference Excessive cooling induces thermal gradients and, hence, unwanted thermal stress and strains A balance must be achieved between cooling (as well as heating) rate and the extent of undesired thermally induced stresses and strains Thermal cycling rates as fast as minutes per cycle are employed on a routine basis A test run to 12,000 cycles requires 36,000 minutes or 600 hours This is without consideration of a hold period at the peak temperature A testing program involving dozens of specimens could thus become extremely expensive and time consuming Cycling rates as high as 20 seconds per cycle have been achieved through diligence However, the thermal gradients are quite high and control of the temperature and strain is poor, although reproducible Raising the minimum temperature in the laboratory TMF cycle is a commonly used approach to help speed up TMF testing frequency This can considerably reduce the time needed to cool because cooling follows an exponential decay curve Removing the last portion of that curve can significantly decrease the cooling time per cycle However, the range of temperature is reduced in the process, and the measured TMF characteristics are removed further from what occurs in most applications For most industrial equipment, the minimum temperature in a thermal fatigue cycle is ambient, and is considerably below the minimum temperature usually selected for TMF testing Normally, the testing conditions of temperature range, minimum temperature, and cycling rate are determined by compromise Regardless of the minimum temperature selected for testing, there remains the desire to shorten the time per cycle; this leads to higher thermal gradients throughout the test specimen Of course, one of the purposes of TMF testing is to intentionally keep thermal gradients negligibly small while the overall temperature of the test volume of the specimen is raised and lowered cyclically Simultaneously, the magnitude of the uniformly distributed strains (stresses) in the specimen is controlled independently of the temperature change, although a fixed phasing is usually maintained between them As a consequence, the test specimen could be programmed to experience cyclic thermal and mechanical strains just as the material might at a critical point were it undergoing thermal fatigue in a structural element In this way, the resistance of a material to thermal fatigue can be experimentally evaluated for a range of phasings and amplitudes of strain (stress) and temperature Figure 31 illustrates a series of basic TMF strain cycles for the most rudimentary of TMF situations in which mechanical strain and temperature vary in lock step with one another A triangular waveform is used for the example cycles, although sinusoidal, is also in vogue When the same waveform is used for both strain and temperature, their time phase shift can be described by a single parameter, the phase angle In-phase cycling (0 ° phase shift) is defined as having the maximum algebraic strain occur at the same instant as the maximum temperature and having the minimum algebraic strain occur at the minimum temperature Out-of-phase TMF cycling (180 ° phase shift) is just the reverse of in-phase cycling A phase angle of 90 ° or 270 ° corresponds to a diamond-shaped (sometimes referred to as baseball) pattern of mechanical strain versus temperature The resultant stress-strain hysteresis loop for a diamond cycle will appear as unusual because the maximum and minimum temperatures not occur at the maximum or minimum mechanical strain These and other basic cycles (bithermal) to be introduced later serve as excellent uniform types of cycles for characterizing the TMF fatigue resistance of materials Fig 31 Basic thermomechanical fatigue strain cycles Rarely, however, are the simple cycles discussed above encountered exactly in service Because TMF fatigue life is generally wave-shape dependent, means are required to generalize laboratory characterizations so they may be applied to any unique thermal fatigue cycle encountered in service This is usually accomplished with a life prediction model Again, physically based models will have the greatest potential for proper interpolation and extrapolation of results generated There are spectra of TMF tests of any given type of cycle that could be conducted in a laboratory: phasings could cover the range from in phase to out of phase and all points between, as well as for TMF cycles that are not describable, by quoting a simple measure of phasing; temperature ranges could be very narrow or very wide; the maximum and minimum temperatures could also cover a broad range, as could the mechanical strain range The frequency (or other measure of the cycling rate and hold periods) is yet another critical variable to be investigated if one is to document the broad range of the thermal fatigue resistance of a material A complete test matrix that could capture all of the pertinent variables is too large to be practical Judicious selection of the variables and their combinations and ranges is usually required based on the potential application of the results ASTM committee E-08 on fatigue is currently crafting a standard for basic TMF fatigue testing (Ref 74) involving simple waveforms (e.g., triangular, sinusoidal) of phased strain and temperature cycling Once approved and published, the standard will be a valuable document to consult before conducting TMF tests Table lists in-test and post-test information that should be documented for each TMF test conducted As discussed in the reviews of Ref 75, 76, and 77, the thermal fatigue resistance of a material is not necessarily derivable from isothermal fatigue resistance, and it is frequently lower than isothermal fatigue resistance This is generally observed despite comparisons made to isothermal fatigue resistance measured at the maximum TMF test temperature (i.e., usually thought to be the lowest isothermal fatigue resistance within the span of the TMF temperature range) The basis for comparison of isothermal and TMF fatigue resistance of a material is also important For example, the TMF resistance may be poorer if the inelastic strain range is used as the basis of comparison, but could be better if the total strain range is used This apparent dichotomy is a direct result of the differences in the cyclic stress-strain behavior between isothermal and TMF cycling Comparisons of isothermal and TMF fatigue resistance to inelastic strain for two example alloys (Ref 78, 79) are shown in Fig 32 and 33 Fig 32 Comparison of isothermal and thermomechanical fatigue resistance of A 286 precipitationhardening stainless steel Source: Ref 76, 77, 78 Fig 33 Comparison of isothermal and thermomechanical fatigue resistance of AISI 1010 carbon steel Source: Ref 76, 77, 79 Thermomechanical Fatigue-Life Modeling Because of the large number of variables and the inherent problem of not being able to afford to test for all possible combinations of variables, alternate approaches are desirable One attractive approach is to adopt a TMF life prediction method By calibrating the constants in equations representing the model, the means are available to calculate behavior under other conditions by interpolation and extrapolation A variety of TMF life prediction models are discussed in Ref 67, 73, 76, and 77 Among the more frequently used models are the ASME time- and cycle-fraction rule (Ref 68), the continuum damage model of ONERA (the French space agency) (Ref 71), the University of Illinois creep-fatigue-oxidation model (Ref 80, 81), and the NASA Glenn (formerly Lewis) method of strain-range partitioning (SRP) (Ref 82) The SRP approach for creep-fatigue and TMF life prediction takes advantage of bithermal fatigue testing (Ref 83) As the name implies, bithermal cycling is conducted using two isothermal temperatures within each cycle The high isothermal temperature represents the maximum temperature of a more complex TMF cycle, while the low isothermal temperature represents the minimum The impetus for developing bithermal testing was to permit direct measurement of both thermal expansion strain and mechanical strain without them being intermixed Visual observation of a bithermal hysteresis loop unequivocally identifies these two types of strain During conventional TMF cycling, thermal and mechanical strains are applied simultaneously and can only be separated by calculation During bithermal cycling, mechanical straining (and stress) is applied only during the two isothermal halves and not when the temperature is being changed The stress on the specimen is controlled at zero during any change in temperature, thus providing a clear separation of thermal expansion and mechanical strains A schematic bithermal hysteresis loop is shown in Fig 34 An out-of-phase cycle is shown All tensile mechanical straining is done at the low temperature, and compressive mechanical straining is done at the high temperature The loading sequence in traversing a cycle is noted in the table to Fig 34 The tensile loading from point A to B and unloading from B to C is done at the cold temperature where the elastic modulus is Ecold It is presumed the temperature is low enough and the straining rate is high enough that time-dependent creep is precluded and only plasticity occurs Hence, the tensile inelastic (plastic) strain is AC and the corresponding elastic strain is CB′, that is, stress at B divided by Ecold At point C the load is held at zero and the specimen temperature raised to the hottest temperature where the elastic modulus is Ehot The specimen expands freely from C to D, a direct measure of the thermal expansion strain over the temperature range Once thermal stability has been attained, the specimen is strained rapidly into compression until a predetermined stress is reached at point E The inelastic strain DE″ is time-independent plastic strain Under the stress at E, compressive creep occurs until the strain limit at point F is reached and the specimen is rapidly unloaded to point G The amount of compressive creep strain is EF, and the compressive inelastic strain is DG = DE″ + EF (or E″G) The corresponding compressive elastic strain is the creep stress (along EF) divided by Ehot Cooling from point G to point A completes the bithermal loop The thermal contraction GA should be equal to the expansion CD Strain AB BC CD DE EF FG GA Type of strain Elastic + plastic Elastic unloading Thermal expansion Elastic + plastic Creep Elastic unloading Thermal constraction Temperature Low Low Low-high High High High High-low Action Rapid straining Rapid straining Zero stress Rapid straining Constant stress Rapid straining Zero stress Fig 34 Schematic bithermal hysteresis loop (out-of-phase cycle) It is simple to interpret directly from the hysteresis loop of Fig 31 the magnitudes of the elastic strains, the inelastic strains, the total strains, and the thermal expansion strains It is much more difficult to determine these parameters from a continuously varying TMF hysteresis loop The elastic strain range for the bithermal loop is the sum of the absolute values of the tensile and compressive elastic strains The corresponding inelastic strain range is the width of the hysteresis loop at zero stress There are two measures of this strain range, AC or DG Theoretically, they must be equal; otherwise, cyclic ratcheting takes place However, the fixed strain limits prevent ratcheting Since every experimental measurement has some scatter, it is recommended that AC and DG be averaged to determine the value of the inelastic strain range The total strain range of the bithermal loop is the sum of the elastic and inelastic strain ranges The loop also reveals the partitioning of the inelastic strains into its creep and plasticity components for use in the strain-range partitioning method for life prediction An in-phase bithermal hysteresis loop would look just like the out-of-phase loop, except that the loop would be mirror imaged about the strain axis Thermal fatigue cycles experienced in service rarely have high enough temperatures in both the tensile and compressive halves to suffer creep strains in both directions Even the 90° or 270° diamond-type cycles tend to experience creep strains predominately in tension or compression only If, however, the total strain range is very large, all TMF cycles will experience reversed creep Such cycles rarely, if ever, occur in service situations and are an artifact of TMF testing in the laboratory By contrast, bithermal tests, for any magnitude of strain range, can be devised that not experience reversed creep Commercially available software is available to conduct bithermal tests on a routine basis using computer control Laboratory TMF testing is comparatively expensive Obtaining data from tests of more than a couple of weeks duration (~10,000 cycles) is prohibitively expensive Accelerated TMF testing is generally not feasible Hence, application of TMF life prediction methods to long-life structures requires considerable extrapolation of laboratory results Three primary variables in the laboratory results must be extrapolated: cycles to failure, time to failure, and the mechanical component of the total strain range Because of the complexity of TMF cycling, it is essential to capitalize on calibrated models for both the failure and the flow (cyclic stress-strain) behavior Failure behavior can only be calibrated with the longest-life data available, but the flow behavior can be calibrated without carrying tests to the point of failure Affordable yet realistically long hold times per cycle and small mechanical strain ranges can be applied for just a few cycles to capture the desired flow behavior under anticipated service conditions Measured flow behavior can then be used to calibrate sophisticated cyclic viscoplastic models (see, for example, Ref 76, 77, and 84) or simpler empirical relations (Ref 82) The latter have been utilized recently for the development of life prediction modeling for long-life automotive exhaust systems (Ref 85) Because cyclic response behavior is so highly dependent on the two major variables of time and temperature, it is imperative that modeling play a vital role in describing practical thermal fatigue cycles and, hence, in extending the direct usefulness of failure data generated at shorter and more affordable lifetimes References cited in this section 67 G.R Halford, Creep-Fatigue Interaction, Heat Resistant Materials, ASM International, 1997, p 499–517 68 Code Case N-47-23, American Society of Mechanical Engineers, 1986 71 J.-L Chaboche, Continuous Damage Mechanics: A Tool to Describe Phenomena before Crack Initiation, Nucl Eng Des., Vol 64, 1981, p 233–247 73 S.S Manson, “The Challenge to Unify Treatment of High Temperature Fatigue— A Partisan Proposal Based on Strain-Range Partitioning,” ASTM STP 520, Fatigue at Elevated Temperature, American Society for Testing and Materials, 1973, p 744–782 74 “Proposed Standard Test Method for Strain Controlled Thermomechanical Fatigue Testing,” draft/working document prepared by the ASTM Thermomechanical Fatigue Task Group, E08.05.07, American Society for Testing and Materials, 1999 75 G.R Halford, Low-Cycle Thermal Fatigue, Thermal Stresses II, R.B Hetnarski, Ed., Elsevier Science Publishers, Amsterdam, 1987, p 329–428 76 H Sehitoglu, Thermal and Thermomechanical Fatigue of Structural Alloys, Fatigue and Fracture, Vol 19, ASM Handbook, 1996, p 527–556 77 Heat-Resistant Materials, ASM International, 1997, p 454–485 78 K.D Sheffler, “Vacuum Thermal-Mechanical Fatigue Testing of Two Iron-Base High Temperature Alloys,” ASTM STP 612, Thermal Fatigue Resistance of Materials and Components, D.A Spera and D.F Mowbray, Ed., American Society for Testing and Materials, 1976, p 214–226 79 C.E Jaske, “Thermal-Mechanical, Low-Cycle Fatigue of AISI 1010 Steel,” ASTM STP 612, Thermal Fatigue Resistance of Materials and Components, D.A Spera and D.F Mowbray, Ed., American Society for Testing and Materials, 1976, p 170–198 80 R Neu and H Sehitoglu, Thermo-Mechanical Fatigue Oxidation, Creep, Part I: Experiments, Metall Trans A, Vol 20, 1989, p 1755–1767 81 R Neu and H Sehitoglu, Thermo-Mechanical Fatigue Oxidation, Creep, Part II: Life Prediction, Metall Trans A, Vol 20, 1989, p 1769–1783 82 J.F Saltsman and G.R Halford, “Life Prediction of Thermomechanical Fatigue Using The Total Strain Version of Strain-Range Partitioning (SRP)—A Proposal,” NASA TP-2779, Feb 1988 83 G.R Halford, M.A McGaw, R.C Bill, and P.D Fanti, “Bithermal Fatigue: A Link Between Isothermal and Thermomechanical Fatigue,” ASTM STP 942, Low Cycle Fatigue, H.D Solomon, G.R Halford, L.R Kaisand, and B.N Leis, Ed., American Society for Testing and Materials, 1988, p 625–637 84 D.N Robinson and R.W Swindeman, Unified Creep-Plasticity Constitutive Equations for Cr-1Mo Steel at Elevated Temperature, ORNL/TM-8444, 1982 85 G.-Y Lui, M.B Behling, and G.R Halford, “Bithermal Low-Cycle Fatigue Characterization of the High Temperature Exhaust System Alloy SS409 Using the Strain-Range Partitioning (SRP) Approach,” paper presented at The Complete Metals & Materials Experience, ASM International, Cincinnati, Nov 1999 Fatigue, Creep Fatigue, and Thermomechanical Fatigue Life Testing Gary R Halford and Bradley A Lerch, Glenn Research Center at Lewis Field, National Aeronautics and Space Administration; Michael A McGaw, McGaw Technology, Inc Helpful Guidelines for Fatigue Testing Both novice and experienced fatigue test engineers should find the following operational guidelines valuable It should also be pointed out that there are a considerable number of commercial fatigue testing laboratories located throughout the world These laboratories may be equipped to perform certain tests more economically and in a more timely fashion than could be done in a smaller, less-equipped laboratory Overall laboratory operation, safety, and training guidelines include the following considerations: • • • • • • Operation of modern fatigue testing laboratories has become sophisticated Hardware and software are complex and require considerable training for safe, accurate, and reliable operation Carelessness is intolerable because serious, maiming accidents can occur in split seconds with fastresponding, high-pressure hydraulic equipment Noise from hydraulic pumps, valves, and vibrating lines must be attenuated to prevent hearing damage to operators High-temperature testing also poses a potential burn hazard Shields, guards, and hazard warning signs are helpful in preventing accidents to laboratory visitors OSHA regulations, along with other related safety regulations and procedures, should be observed Cleanliness of hydraulic fluid is crucial, and systematic replacement of micron-level filters should be scheduled Room air cleanliness is also important for reliable operation of all computers and electronic equipment Calibration of all measuring devices, electronics, and computer software should be checked on a regular basis, and a frequency of calibration policy should be established See ASTM and ISO 9000 standards for maintaining quality systems Basic and advanced training courses for use of testing machines and ancillary equipment are generally available through the respective manufacturers Skills may be required in several areas, including mechanical and hydraulic systems, electronics and instrumentation, computers and software, thermal management, and environmental control In addition, it is necessary to keep abreast of the latest developments in fatigue behavior and fatigue-life prediction technologies Short courses are offered by a variety of educational institutions Overall Control of Materials to be Tested A record-keeping system should be set up to keep track of all of the materials being tested Information on each might include: • • • • • • • • • • • • Commercial name or designation Nominal (and actual) chemical composition Commercial source and dates of production and acquisition Product form (e.g., billet, plate, sheet, or bar) Method of production (e.g., casting, forging, rolling, or heat treatment) AMS, ASM, ASTM, or other specifications X-rays and/or NDE results Representative micrographs and documentation of anisotropy on material stock Proper storage of material stock to avoid any possible contamination Reference to mechanical and pertinent physical, thermal, and electrical properties Tensile test properties (elastic modulus, Poisson's ratio, yield and ultimate strength, ductility as percent reduction of area and percent elongation) Clear designation of material stock (e.g., stamped identification number and color coding) Overall Control of Specimens A record-keeping system should be set up to track all specimens made of the above materials Specimen information might include: • • • • • • • • • • • • • Diagram of specimen location and orientation relative to material stock Specimen drawing(s), dimensions, and specifications for machining Specimen final preparation (e.g., heat treatment or surface treatment) Specimen dimensions and means of measurement Specimen material and individual identification scheme (stamped alphanumeric in visible area near both ends and visible once installed in machine) Accessible yet protective specimen storage to prevent damage prior to test Document thermocouple attachment techniques and calibration (temp gradients) Care exercised in gripping specimens in testing machine Orientation of specimen in grips in fatigue machine Care to not damage fracture surface prior to machine automatic shut-down Care exercised in removing fatigued specimens from testing machine Accessible storage system for tested specimens (do not store with fracture surfaces of mating pieces touching) Maintain records of metallographic mounts taken from broken specimens Laboratory Documentation of Set-Ups, Procedures, Calibrations, and Maintenance One should maintain continuous laboratory documentation books for recording particulars of each new set-up and each new program Books should be kept, along with fatigued specimens and raw data records, for as long as is practical (then a little longer) Resurrecting old data is far less costly than having to generate new data, and old data are invaluable if untested material specimens are no longer available at a much later date Data books should be signed and dated by the test engineer(s) and technician(s) Pretest Checklist Maintain a checklist to go over prior to the start of each new test Checklists may consider the following: • • • Always predict the cyclic and clock lifetime of each specimen prior to testing All pertinent test information is entered onto any data sheets, paper recorders, computerized data taking and manipulating systems This information includes fatigue machine number, material, specimen identification number, type of test, temperature, frequency, hold periods, control parameter(s), parameters to be recorded, equipment being used, test engineer, extensometer and load cell ranges of scales employed, ranges of analog recorders, strip chart speeds, computer control programs and data processors utilized, date, time, and any other unique test information An analog X-Y recorder for load cell and extensometer output (stress and strain) is highly recommended even though results can also be recorded electronically In case of a mishap, the X-Y recording provides • • • • a better vision of what might have gone wrong and how to correct it than individual load or extensometer signals as a function of time Ensure that each piece of equipment is turned on and functioning properly (e.g., pens of recorders are ready to write and timers and cycle counters are working) Ensure that safety limits are set to prevent overload of the specimen and damage of equipment in case of an accident Before actually starting a test, trace a low-amplitude stress-strain hysteresis loop on the X-Y recorder as a check that the recorder is functioning and to check that the modulus of elasticity is close to its expected value If not, one or more bits of information may be erroneous (e.g., load or extensometer scales, X-Y recorder scales, or specimen dimensions) Decide, up front, how to abort a test that is not following the expected response (e.g., abrupt shut down or gradual shut down) During the early stages of a test, be prepared to switch scales of recorders or signal conditioners to better record response signals For example, large amounts of cyclic strain hardening under strain control may require a switch to a coarser load scale in order to avoid missing measurement of off-scale signals Do not switch ranges of the control signal during the test During the fatigue test the following should be considered: • • • • • • • • As a test progresses, make note of any changes in specimen response (e.g., cyclic strain hardening, softening, relaxation of initial mean stresses under strain control, any strain ratcheting occurring under load control, or any changes in specimen) Pay particularly close attention to the progression of failure of the test specimen, marking notes of anything out of the ordinary After specimen failure, and after the machine has been stopped, record the orientation (relative to the specimen and its mounting in the grips and machine) of the initiation location(s) of cracking Shut down and rezero all equipment that will not be needed immediately for the next test Record observations of the fracture surface (e.g., single or multiple cracks, multiple planes of cracking, secondary cracking, or angular orientation of cracks to specimen axis) Ascertain cyclic lifetime (and, hence, half-life values) at various points along the process of cracking and final fracture using criteria contained in the next of this Section Reduce and tabulate the figure characterization data (e.g., half-life values of total, elastic, and inelastic strain ranges; stress range or amplitude; and mean stress), and compare observed lives with lives predicted prior to testing Add each fatigue data point to the evolving fatigue curve to maintain a current view of the extent of the figure curve This knowledge may dictate the conditions to be imposed on the next fatigue test Fatigue, Creep Fatigue, and Thermomechanical Fatigue Life Testing Gary R Halford and Bradley A Lerch, Glenn Research Center at Lewis Field, National Aeronautics and Space Administration; Michael A McGaw, McGaw Technology, Inc Acknowledgments The authors gratefully acknowledge the help of Peter J Bonacuse, Army's Vehicle Technology Center, NASA Glenn Research Center, for his valuable technical peer review of the manuscript Fatigue, Creep Fatigue, and Thermomechanical Fatigue Life Testing Gary R Halford and Bradley A Lerch, Glenn Research Center at Lewis Field, National Aeronautics and Space Administration; Michael A McGaw, McGaw Technology, Inc References W.J Putnam and J.W Harsch, “Rise of Temperature” Method of Determining Endurance Limit, An Investigation of the Fatigue of Metals, H.F Moore and J.B Kommers, Ed., Engineering Experiment Station Bulletin 124, University of Illinois, Oct 1921, p 119–127 Strain Gage Based Transducers, Their Design and Construction, Measurements Group, Inc., Raleigh, NC, 1988 M.F Day and G.F Harrison, Design and Calibration of Extensometers and Transducers, Measurement of High Temperature Mechanical Properties, M.S Loveday et al., Ed., National Physical Laboratory, London, 1982, p 225–240 G.B Thomas, Axial Extensometry for Ridged Specimens, Techniques for High Temperature Fatigue Testing, G Sumner and V.B Livesey, Ed., Elsevier Applied Science, 1985, p 45–56 J.W Dally and W.F Riley, Experimental Stress Analysis, McGraw-Hill, 1978, p 179–179 R.L Hannah and S.E Reed, Ed., Strain Gage Users' Handbook, Elsevier Applied Science, New York, 1992 J.-F Lei and W.D Williams, PdCr Based High Temperature Static Strain Gage, AIAA 2nd Int National Aerospace Planes Conf Publication, AIAA-90-5236, 1990 J.-F Lei, M.G Castelli, D Androjna, C Blue, R Blue, and R.Y Lin, Comparison Testings Between Two High-Temperature Strain Measurement Systems, Exp Mech., Vol 36 (No 4), 1996, p 430–435 E.G Ellison, Thermal-Mechanical Strain Cycling and Testing at Higher Temperatures, Measurement of High Temperature Mechanical Properties, M.S Loveday et al., Ed., National Physical Laboratory, London, 1982, p 204–224 10 E.G Ellison and R.D Lohr, The Extensometer-Specimen Interface, Techniques for High Temperature Fatigue Testing, G Sumner and V.B Livesey, Ed., Elsevier Applied Science, 1985, p 1–28 11 Creep, Stress-Rupture, and Stress-Relaxation Testing, Mechanical Testing, Vol 8, Metals Handbook, ASM International, 1985, p 313 12 J.Z Gyekenyesi and P.A Bartolotta, “An Evaluation of Strain Measuring Devices for Ceramic Composites,” NASA TM 105337, National Aeronautics and Space Administration, Nov 1991 13 R Hales and D.J Walters, Measurement of Strain in High Temperature Fatigue, Measurement of High Temperature Mechanical Properties, M.S Loveday et al., Ed., National Physical Laboratory, London, 1982, p 241–254 14 ASTM STP 465, Manual of Low Cycle Fatigue Testing, R.M Wetzel and L.F Coffin, Ed., American Society for Testing and Materials, 1969 15 M.G Castelli and J.R Ellis, “Improved Techniques for Thermomechanical Testing in Support of Deformation Modeling,” ASTM STP 1186, Thermomechanical Fatigue Behavior of Materials, H Sehitoglu, Ed., American Society for Testing and Materials, 1993, p 195–211 16 S.S Manson, G.R Halford, and M.H Hirschberg, Creep-Fatigue Analysis by Strain-Range Partitioning, Design for Elevated Temperature Environment, American Society of Mechanical Engineers, 1971, p 12–28 17 K.D Sheffler and G.S Doble, “Influence of Creep Damage on the Low-Cycle Thermal-Mechanical Fatigue Behavior of Two Tantalum Base Alloys,” NASA CR-121001, National Aeronautics and Space Administration, 1972 18 M.H Hirschberg, D.A Spera, and S.J Klima, “Cyclic Creep and Fatigue of TD-NiCr (ThoriaDispersion-Strengthened Nickel-Chromium), TD-Ni, and NiCr Sheet at 1200 °C,” NASA TN D-6649, National Aeronautics and Space Administration, 1972 19 P.R Breakwell, J.R Boxall and G.A Webster, Specimen Manufacture, Measurement of High Temperature Mechanical Properties, M.S Loveday et al., Ed., National Physical Laboratory, London, 1982, p 322–340 20 E.T Camponeschi, Jr., “Compression of Composite Materials: A Review,” ASTM STP 1110, Composite Materials: Fatigue and Fracture (Third Volume), T.K O'Brien, Ed., American Society for Testing and Materials, 1991, p 550–578 21 F.A Kandil and B.F Dyson, Influence of Load Misalignment During Fatigue Testing I and II, Fatigue and Fracture of Engineering Materials and Structures, Vol 16 (No 5), 1993, p 509–537 22 J Bressers, Axiality of Loading, Measurement of High Temperature Mechanical Properties, M.S Loveday et al., Ed., National Physical Laboratory, London, 1982, p 278–295 23 J Bressers, Ed., A Code of Practice for the Measurement of Misalignment Induced Bending in Uniaxially Loaded Tension-Compression Test Pieces (Institute for Advanced Materials, Joint Research Centre, Netherlands, and the High Temperature Mechanical Testing Committee), the DirectorateGeneral of the European Commission, Luxembourg, 1995, 52 pages 24 F.A Kandil, Measurement of Bending in Uniaxial Low Cycle Fatigue Testing, National Physical Laboratory, Teddington, England, 1998 25 A.K Schmieder, “Measuring the Apparatus Contribution to Bending in Tension Specimens,” ASTM STP 488, Elevated Temperature Testing Problem Areas, American Society for Testing and Materials, 1971, p 15–42 26 A.A Braun, “A Historical Overview and Discussion of Computer-Aided Materials Testing,” ASTM STP 1231, Automation in Fatigue and Fracture: Testing and Analysis, C Amzallag, Ed., American Society for Testing and Materials, 1994, p 5–17 27 S Dharmavasan, D.R Broome, M.C Lugg, and W.D Dover, FLAPS—A Fatigue Laboratory Applications Package, Proc 4th Int Conf on Engineering Software, R.A Adey, Ed., Springer-Verlag, London, 1985 28 A.A Braun, The Development of a Digital Control System Architecture for Materials Testing Applications, Proc 17th Int Symposium for Testing and Failure Analysis, ASM International, 1991, p 437–444 29 S Dharmavasan and S.M.C Peers, “General Purpose Software for Fatigue Testing,” ASTM STP 1231, Automation in Fatigue and Fracture: Testing and Analysis, C Amzallag, Ed., American Society for Testing and Materials, 1994, p 18–35 30 M.A McGaw and P.J Bonacuse, Automation Software for a Materials Testing Laboratory, Proc Turbine Engine Hot Section Technology (HOST), NASA CP-2444, National Aeronautics and Space Administration, 1986, p 399–406 31 M.A McGaw and P.J Bonacuse, “Automation Software for a Materials Testing Laboratory,” ASTM STP 1092, Applications of Automation Technology to Fatigue and Fracture Testing, A.A Braun et al., Ed., American Society for Testing and Materials, 1990, p 211–231 32 M.A McGaw and P.A Bartolotta, The NASA Lewis Research Center High Temperature Fatigue and Structures Laboratory, Proc 4th Annual Hostile Environments and High Temperature Measurement Conf., Society for Experimental Mechanics, 1987, p 12–29 33 M.A McGaw, materials testing software LEW-16160, COSMIC, 1995 34 J Christiansen, R.L.T Oehmke, and E.A Schwarzkopf, “Materials Characterization Using Calculated Control,” ASTM STP 1303, Applications of Automation Technology to Fatigue and Fracture Testing, A.A Brown and L.N Gilbertson, Ed., American Society for Testing and Materials, 1997 35 S.S Manson, Fatigue—A Complex Subject, Exp Mech., Vol (No 7), 1965, p 193–226 36 J Morrow, “Cyclic Plastic Strain Energy and Fatigue of Metals,” ASTM STP 378, Internal Friction, Damping, and Cyclic Plasticity, American Society for Testing and Materials, 1965, p 45–84 37 J.F Newell, A Note of Appreciation for the MUS, Material Durability/Life Prediction Modeling: Materials for the 21st Century, S.Y Zamrik and G.R Halford, Ed., Pressure Vessel and Piping Conference, PVP Vol 290, American Society of Mechanical Engineers, 1994, p 57–58 38 R.W Landgraf, “The Resistance of Metals to Cyclic Deformation,” ASTM STP 467, Achievement of High Fatigue Resistance in Metals and Alloys, American Society for Testing and Materials, 1970, p 3– 36 39 Parameters for Estimating Fatigue Life, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996, p 963–979 40 S.S Manson, Predictive Analysis of Metal Fatigue in the High Cyclic Life Range, Methods for Predicting Material Life in Fatigue, W.J Ostergren and J.R Whitehead, Ed., American Society of Mechanical Engineers, 1979, p 145–183 41 Characterization of Low Cycle High Temperature Fatigue by the Strain-Range Partitioning Method, AGARD Conf Proc., No 243, NATO, 1978 42 J.B Conway, R.H Stentz, and J.T Berling, Fatigue, Tensile, and Relaxation Behavior of Stainless Steels, United States Atomic Energy Commission, 1975, p 11 43 O.H Basquin, The Exponential Law of Endurance Tests, Proc ASTM, Vol 10 (Part II), 1910, p 625– 630 44 L.F Coffin, Jr., Thermal Stress Fatigue, Prod Eng., June 1957 45 B.F Langer, Design of Pressure Vessels for Low Cycle Fatigue, J Basic Eng (Trans ASME), Vol 84 (No 4), 1962, p 389 46 S.S Manson, discussion of ASME paper 61-WA-199 by J.F Tavernelli and L.F Coffin, Jr., J Basic Eng (Trans ASME), Vol 85 (No 4), 1962, p 537–541 47 D.F Socie, N.E Dowling, and P Kurath, “Fatigue Life Estimation of Notched Members,” ASTM STP 833, Fracture Mechanics: Fifteenth Symposium, R.J Sanford, Ed., American Society for Testing and Materials, 1984, p 284–299 48 S.M Tipton and D.V Nelson, Developments in Life Prediction of Notched Components Experiencing Multiaxial Fatigue, Material Durability/Life Prediction Modeling—Materials for the 21st Century, S.Y Zamrik and G.R Halford, Ed., Pressure Vessel and Piping Conference, PVP Vol 290, American Society of Mechanical Engineers, 1994, p 35–48 49 H Neuber, Theory of Stress Concentration for Shear Strained Prismatical Bodies with Arbitrary Nonlinear Stress-Strain Law, J Appl Mech (Trans ASME), Vol 28, 1961, p 544–550 50 G Glinka, Energy Density Approach to Calculation of Inelastic Stress-Strain near Notches and Cracks, Eng Fract Mech, Vol 22, 1985, p 485–508 51 W.Z Gerber, Bestimmung der Zulossigne Sannugen in Eisen Construction, Bayer Arch Ing Ver., Vol 6, 1974, p 101 (in German) 52 J.B Conway and L.H Sjodahl, Analysis and Representation of Fatigue Data, ASM International, 1991, p 21, 145–178 53 G.R Halford and A.J Nachtigall, The Strain-Range Partitioning Behavior of an Advanced Gas Turbine Disk Alloy, AF2-1DA, J Aircr., Vol 17, 1980, p 598–604 54 M Doner, K.R Bain, and J.H Adams, Evaluation of Methods for Treatment of Mean Stress Effects on Low-Cycle Fatigue, J Eng Power (Trans ASME), Vol 104, 1982, p 403–411 55 Y Murakami, Ed., The Rainflow Method in Fatigue, Butterworth Heinemann Ltd., Oxford, 1992 56 M.R Mitchell, Fundamentals of Modern Fatigue Analysis for Design, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996, p 227–249 57 S.S Manson and G.R Halford, Re-Examination of Cumulative Fatigue Damage Analysis—An Engineering Perspective, Eng Fract Mech., Vol 25, 1986, p 539–571 58 G.R Halford, Cumulative Fatigue Damage Modeling—Crack Nucleation and Early Growth, Int J Fatigue, Vol 19 (No 1) supplement, 1997, p S253–S260 59 M.A Miner, Cumulative Damage in Fatigue, J Appl Mech., Vol 12 (No 3), 1945, p A159–A164 60 P.T Bizon, D.J Thoma, and G.R Halford, Interaction of High Cycle and Low Cycle Fatigue of Haynes 188 at 1400 °F, Structural Integrity and Durability of Reusable Space Propulsion Systems, NASA CP2381, 1985, p 129–138 61 S Kalluri and P.J Bonacuse, “Cumulative Axial and Torsional Fatigue: An Investigation of Load-Type Sequencing Effects,” ASTM STP 1387, Symposium on Multiaxial Fatigue and Deformation: Testing and Prediction, S Kalluri and P.J Bonacuse, Ed., American Society for Testing and Materials, 2000 (in press) 62 R.M Curran and B.M Wundt, Continuation of a Study of Low-Cycle Fatigue and Creep Interaction in Steels at Elevated Temperatures, 1976 ASME-MPC Symposium on Creep-Fatigue Interaction, Materials Property Council MPC-3, American Society of Mechanical Engineers, 1976, p 203–282 63 S.S Manson, Critical Review of Predictive Methods for Treatment of Time-Dependent Metal Fatigue at High Temperatures, Pressure Vessels and Piping: Design Technology—1982—A Decade of Progress, American Society of Mechanical Engineers, 1982, p 203–225 64 D.A Miller, R.H Priest, and E.G Ellison, A Review of Material Response and Life Prediction Techniques under Fatigue-Creep Loading Conditions, High Temp Mater Process., Vol 6, 1984, p 155– 194 65 V.M Radhakrishnan, Life Prediction in Time Dependent Fatigue, Advances in Life Prediction Methods, American Society of Mechanical Engineers, 1983, p 143–150 66 G.R Halford, Evolution of Creep-Fatigue Life Prediction Models, Creep-Fatigue Interaction at High Temperature, G.K Haritos and O.O Ochoa, Ed., Vol 21, American Society of Mechanical Engineers, 1991, p 43–57 67 G.R Halford, Creep-Fatigue Interaction, Heat Resistant Materials, ASM International, 1997, p 499–517 68 Code Case N-47-23, American Society of Mechanical Engineers, 1986 69 S.S Manson, G.R Halford, and M.H Hirschberg, Creep-Fatigue Analysis by Strain-Range Partitioning, Symposium on Design for Elevated Temperature Environment, American Society of Mechanical Engineers, 1971, p 12–28 70 J.F Saltsman and G.R Halford, “An Update on the Total Strain Version of SRP,” ASTM STP 942, Low Cycle Fatigue—Directions for the Future, H.D Solomon, G.R Halford, L.R Kaisand, and B.N Leis, Ed., American Society for Testing and Materials, 1988, p 329–341 71 J.-L Chaboche, Continuous Damage Mechanics: A Tool to Describe Phenomena before Crack Initiation, Nucl Eng Des., Vol 64, 1981, p 233–247 72 C.E Jaske, H Mindlin, and J.S Perrin, “Combined Low-Cycle Fatigue and Stress Relaxation Behavior of Alloy 800 and Type 304 Stainless Steel at Elevated Temperatures,” ASTM STP 520, Fatigue at Elevated Temperature, American Society for Testing and Materials, 1973, p 365–376 73 S.S Manson, “The Challenge to Unify Treatment of High Temperature Fatigue— A Partisan Proposal Based on Strain-Range Partitioning,” ASTM STP 520, Fatigue at Elevated Temperature, American Society for Testing and Materials, 1973, p 744–782 74 “Proposed Standard Test Method for Strain Controlled Thermomechanical Fatigue Testing,” draft/working document prepared by the ASTM Thermomechanical Fatigue Task Group, E08.05.07, American Society for Testing and Materials, 1999 75 G.R Halford, Low-Cycle Thermal Fatigue, Thermal Stresses II, R.B Hetnarski, Ed., Elsevier Science Publishers, Amsterdam, 1987, p 329–428 76 H Sehitoglu, Thermal and Thermomechanical Fatigue of Structural Alloys, Fatigue and Fracture, Vol 19, ASM Handbook, 1996, p 527–556 77 Heat-Resistant Materials, ASM International, 1997, p 454–485 78 K.D Sheffler, “Vacuum Thermal-Mechanical Fatigue Testing of Two Iron-Base High Temperature Alloys,” ASTM STP 612, Thermal Fatigue Resistance of Materials and Components, D.A Spera and D.F Mowbray, Ed., American Society for Testing and Materials, 1976, p 214–226 79 C.E Jaske, “Thermal-Mechanical, Low-Cycle Fatigue of AISI 1010 Steel,” ASTM STP 612, Thermal Fatigue Resistance of Materials and Components, D.A Spera and D.F Mowbray, Ed., American Society for Testing and Materials, 1976, p 170–198 80 R Neu and H Sehitoglu, Thermo-Mechanical Fatigue Oxidation, Creep, Part I: Experiments, Metall Trans A, Vol 20, 1989, p 1755–1767 81 R Neu and H Sehitoglu, Thermo-Mechanical Fatigue Oxidation, Creep, Part II: Life Prediction, Metall Trans A, Vol 20, 1989, p 1769–1783 82 J.F Saltsman and G.R Halford, “Life Prediction of Thermomechanical Fatigue Using The Total Strain Version of Strain-Range Partitioning (SRP)—A Proposal,” NASA TP-2779, Feb 1988 83 G.R Halford, M.A McGaw, R.C Bill, and P.D Fanti, “Bithermal Fatigue: A Link Between Isothermal and Thermomechanical Fatigue,” ASTM STP 942, Low Cycle Fatigue, H.D Solomon, G.R Halford, L.R Kaisand, and B.N Leis, Ed., American Society for Testing and Materials, 1988, p 625–637 84 D.N Robinson and R.W Swindeman, Unified Creep-Plasticity Constitutive Equations for Cr-1Mo Steel at Elevated Temperature, ORNL/TM-8444, 1982 85 G.-Y Lui, M.B Behling, and G.R Halford, “Bithermal Low-Cycle Fatigue Characterization of the High Temperature Exhaust System Alloy SS409 Using the Strain-Range Partitioning (SRP) Approach,” paper presented at The Complete Metals & Materials Experience, ASM International, Cincinnati, Nov 1999 Ultrasonic Fatigue Testing Introduction ULTRASONIC FATIGUE TESTING involves cyclic stressing of material at frequencies typically in the range of 15 to 25 kHz The major advantage of using ultrasonic fatigue is its ability to provide fatigue-limit and nearthreshold data within a reasonable length of time High-frequency testing provides rapid evaluation of the highcycle fatigue limit of engineering materials Fatigue crack growth at extremely slow crack propagation rates is also possible with ultrasonic frequency testing Ultrasonic fatigue testing is applicable to most engineering materials, including metals, ceramics, glasses, plastics, and composites Test data can be used for screening of high-cycle fatigue properties or extending the fatigue data already available from conventional frequency fatigue testing This article reviews underlying concepts and basic techniques for performing ultrasonic fatigue tests It describes test equipment design, specimen design, and effective control over test variables Results obtained with ultrasonic fatigue test methods are discussed with respect to strain-rate-dependent material behavior Standardized procedures and test machinery for performing ultrasonic fatigue tests currently are not available ... 6, 1986, p 363 30 M.-L Lu and F.-C Chang, Polymer, Vol 36, 1995, p 2541 31 Z Zhou, J.D Landes, and D.D Huang, Polym Eng Sci., Vol 34, 1994, p 128 32 M.-L Lu, C.-B Lee, and F.-C Chang, Polym Eng... p 1440 36 C.-B Lee, M.-L Lu, and F.-C Chang, J Appl Polym Sci., Vol 47, 1993, p 1867 37 M.-L Lu and F.-C Chang, J Appl Polym Sci., Vol 56, 1995, p 1065 38 B.M Rimnac, T.W Wright, and R.W Klein,... three- and four-point flexure are allowed in certain outer and inner support spans, again, as contained in both the ASTM and JIS standards (Fig 8) Also, as contained in the ASTM and JIS standards,