Investigating effect of Norton and Liu Murakami creep models in determination of creep fracture mechanic parameter (C*)

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1 mme.modares.ac.ir - (C*) 2 * - -2 snakhodchi@kntu.ac.ir *. C*. (CT) C* - - P IN78 C* - -. C* : : : Investigating effect of Norton and Liu Murakami creep models in determination of creep fracture mechanic parameter (C*) Soheil Nakhodchi *, Ehsan Saberi - Department of Mechanical Engineering, K.N.Toosi University of Technology, Tehran, Iran * P.O.B , snakhodchi@kntu.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received7September25 Accepted2October25 AvailableOnline5December25 Keywords: Creep Fracture Parameter Creep Crack Growth Damage Mechanics Reference Stress Method [6-4] [3-] C* J J.[7]. - Creep fracture mechanic parameter, C*, is an essential tool for creep crack growth rate estimation and so remnant life determination of components operating at high temperature. For determining this parameter experimental works, FE methods, and engineering approaches can be utilized. In this paper, in order to facilitate FE methods in C* determination for a CT specimen, creep behavior models of Norton and Liu-Murakami were developed and related subroutines were created. Each of the aforementioned models has its own temperature dependent material coefficients which were determined and validated based on creep rupture tests on crack free uniaxial specimens of P9 steel and IN78 super alloy, respectively, at temperatures of 65C and 62C. In this study creep fracture mechanic parameter value of a CT specimen made of P9 steel was derived by application of Norton and Liu- Murakami creep behavior models and results were compared with results of the experimental tests and reference stress engineering approach results. The results indicate that Liu-Murakami creep behavior model better estimates creep fracture mechanics parameter with greater accuracy, yet reference stress engineering approach is the most economical way to determine this parameter. () -. ). (A6 R5 BS 79. Pleasecitethisarticleusing: : S. Nakhodchi, E. Saberi, Investigating effect of Norton and Liu Murakami creep models in determination of creep fracture mechanic parameter (C*), Modares Mechanical Engineering, Vol. 5, No. 2, pp , 25 (in Persian)

2 (C*) -.[] C*. - P IN C* P9 C* - C* C* (CT) IN78 P Subroutine 4- ABAQUS 5- FORTARN 6- Quadratic 7- Singularity 8- Collapsed element = ( ) () ui Ti w J C*.[8] C*..[8] (2) = ( ) (2) C* (K) C*.[9] C* [9].[]. C* C*.[,] C* (). ( ). 969 [2] [3] [5,4] 998 [6] C* C*. C*.[7]. - Thumbnail Specimen 2- Compact Tension (CT) Specimen

3 . (C*) - J.[8]. c b C* (2) 2 C*.. (C*) (C(t)) C(t) C* (b) (a) (3). = (3) IN78. n A(3) P9 65. (IN78 ) [2,9] 62 (P9 )... Log n D.[2].. (c) Fig. -a Dimensions of compact tension (CT) specimen for C* calculation. Fig. -b Discretization of FE 2D model. Fig. -c Details of crack tip elements. (Dimensions in millimeter) b-.c* (CT) a- ) c-. Crack Contour 2 Contour Contour 3 ( Fig. 2 Integration contours around crack tip for C* calculation. To enhance figure quality just contours to 3 is shown.c*

4 (C*) - tf (7) =.( ) (7) tf (-Log M) (-X) X M. q2. ( ). q2.[2,9] 3 3 q (-2 (4-2).. C* - 4..[7]..[27]. 3- Notched bar specimen 4[6] -. = exp[ () ( ). ] = )] exp( ).[26-2] (a -4) (b -4) Xq2MmnA D Sij. (5) = + ( ).[5,4] (5) 2.( <<) [2,9] n A. - (b-4) (6) ( <<) = [ exp( )] exp( ) Fig. 3 Geometry, dimensions and discretization details of notched bar specimen for calculation. (Dimensions In millimeter). 3 (6) ) - Rupture stress 2- Multiaxial stress parameter

5 (3) C* (C*) - K.. (8) C* - 5 C* C*. (8) = + ( ) ( ( )) n C*. (8) P.[] a W BN 2. 5 n - 6 A 4 65 P IN78 A IN78. P q2xm 8-6 P9 3 IN78 P9. Creep strain rate (% /hour).. Test data point Fitted curve log=log(.92 ) log Stress (MPa) Fig. 4 Fitting linear curve on creep strain rate vs. stress test data to calculate A, n parameters of P9 at 65C 4 65 P9 n A = PL (8) P.[28].[29,9] C* -J (9) = (9) h. a h [3,3] h(9) () = = (). K G = () () (9) () h = ( ). (2) J (2). (3) J C* = ( ). (3) K (8) (5,4) =.455( ).72( ) = ( 2 ) + ( 4 ) + 2 ( 2 + ).[8] (4) (5). B a W (7,6) K 2 + = ( ).. ( ( ). ) ( ) = ( ) 3.32( ) +4.72( ) 5.6.[] (6) (7)

6 (C*) - Fig. 7 Adjusting q 2 values to agree with experiment data obtained from P9 creep test under 7 MPa stress at 65C 7 q P9 Fig. 8 Adjusting values to agree with experiment data obtained from P9 creep test at 65C 8 65 P9. P9 9 Rupture time (hour) 65 IN78 [2,9] IN78. Creep strain (%) P9 IN q2=3. q2=3. q2=3.2 q2=3.3 q2=3.4 Experiment data Experiment: 7 MPa Experiment: 82 MPa Fig. 5 Fitting nonlinear curve on creep strain rate vs. stress test data to calculate A, n parameters of P9 at 65C A 5 65 P9 n ) 65 P9 ( Table P9 Norton power law constants at 65C (Stress in MPa and time in hour) n A Materialconstants Linearfitting Non-Linearfitting Difference(%) 62 IN78 2 ( ) Table 2 IN78 Norton power law constants at 62C (Stress in MPa and time in hour) n A Materialconstants Linearfitting Non-Linearfitting Difference(%) Fig. 6 Fitting linear curve on rupture time vs. stress test data to calculate M, X parameters of P9 at 65C 6 65 P9 X M Creep strain rate (%/hour) Rupture time (hour) Test data point Fitted curve = Stress (MPa) Test data point Fitted curve Log = Log(2.952 ) Log Stress (MPa)

7 (C*) - Creep strain (%) 7 Experiment: 7 MPa 6 Experiment: 82 MPa Experiment: 87 MPa 5 Experiment: 93 MPa Experiment: MPa 4 FEM, Liu-Murakami: 7 MPa FEM, Liu-Murakami: 82 MPa 3 FEM, Liu-Murakami: 87 MPa FEM, Liu-Murakami: 93 MPa FEM, Liu-Murakami: MPa Fig. 9 Validating Liu-Murakami creep model by comparing FE results to P9 creep test results at 65 C [9] [9] 65 P9-9 8 Experiment: 85 MPa 7 Experiment: 9 MPa Experiment: 95 MPa Creep strain (%) 6 FEM, Liu-Murakami: 85 MPa FEM, Liu-Murakami: 9 MPa 5 FEM, Liu-Murakami: 95 MPa Fig. Validating Liu-Murakami creep model by comparing FE results to IN78 creep test results at 62 C [2] [2] 62 - IN78 7 Experiment: 7 MPa Experiment: 82 MPa 6 Experiment: 87 MPa Creep strain (%) 5 Experiment: 93 MPa Experiment: MPa 4 FEM, Norton: 7 MPa FEM, Norton: 82 MPa 3 FEM, Norton: 87 MPa FEM, Norton: 93 MPa 2 FEM, Norton: MPa Fig. Inability of Norton creep model to fully predict P9 creep test results at 65 C [9] [9] P

8 (C*) - Creep strain (%) Experiment: 85 MPa Experiment: 9 MPa Experiment: 95 MPa FEM, Norton: 85 MPa FEM, Norton: 9 MPa FEM, Norton: 95 MPa Fig. 2 Inability of Norton creep model to fully predict IN78 creep test results at 62C [2] [2] 62 IN C* IN78 P9-3 ) Table 3 P9 and IN78 Liu-Murakami model material onstants respectively at 65C and 62C (stress in MPa and time in hour).25. q X M n A Material constant P9 IN78 65 P (2) C*C(t) C* C(t) integral Contour 2 Contour 2 Contour 3 Contour 3 Contour 4 Contour 4 Contour 5 Contour 5... C*. C* C(t) integral Fig. 4 C(t) integral variation at P9 CT specimen crack tip during FE modeling based on Liu-Murakami creep model at 65C under 3N load P9 C(t) Fig. 3 C(t) integral variation at P9 CT specimen crack tip during FE modeling based on Norton creep model at 65C under 3N load P9 C(t)

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