INVESTIGATION OF ELASTIC STRESS SHIELDING DAMAGE INTERACTION BASED ON FITNESS FOR SERVICE (FFS) CODES Pauh, Perlis, Malaysia

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1 International Conference on Mechanical Engineering Research (ICMER03), -3 uly 03 Bukit Gambang Resort City, Kuantan, Pahang, Malaysia Organized By Faculty of Mechanical Engineering, Universiti Malaysia Pahang Paper ID: P86 INVESTIGATION OF ELASTIC STRESS SHIELDING DAMAGE INTERACTION BASED ON FITNESS FOR SERVICE (FFS) CODES R. Daud *, M.S. Abdul Majid, M. Afendi, A.K. Ariffin, S. Abdullah School of Mechatronic Engineering, Universiti Malaysia Perlis, Pauh Putra Campus 0600 Pauh, Perlis, Malaysia * ruslizam@unimap.edu.my Phone: ; Fax: Faculty of Engineering and Built Environment, Universiti Kebangsan Malaysia, Bangi, Sangor, Malaysia ABSTRACT Fitness-for-service (FFS) codes that used for combination and re-characterization of crack interaction from multiple cracks to single crack are encountered some limitations and may provide incorrect and overestimated prediction of failure. This paper presents a numerical investigation of astic stress shiding damage interaction between parall cracks based on the FFS codes using -integral analysis. In present study, the stress shiding damage (SSD) mod was introduced to define the combination and recharacterization of crack interaction from two parall edge cracks to single edge crack in weak and strong interaction state. The stress shiding fracture parameters were compared to single edge crack to define the crack unification limit (CUL), crack interaction limit (CIL) and the effective FFS codes range based on CUL and CIL. The results show good corration with Griffith strain energy theory and wl agreed with analytical formulation in literature Keywords: Stress shiding damage; Crack interaction; Stress intensity factor INTRODUCTION Fitness-for-service (FFS) codes proposed combination and re-characterization of multiple interacting cracks into single cracks or single combined cracks with satisfying certain rules and conditions that used in safety assessment for in-service plants. The FFS codes outlined by ASME Boiler and Pressure Vess Code Section XI (ASME, 998, 004, 007; ASTM, 0) defines that the multiple cracks are assumed to be independent until or unless the certain conditions are satisfied. The similar assumption is made by UK Engineering Critical Assessment, where the potential or actual defects in engineering structures is codified into BSI PD6495 (99), BS790 (997; 005) and Nuclear Electric CEGB R6 (006). In apanese Society of Mechanical Engineers (SME, 008), by considering the example of parall offset cracks, the cracks are replaced by an equivalent single crack based on the stage of detected cracks with satisfy the certain condition. In summary, the combination and re-characterization of multiple cracks in non-coplanar orientation and arrangement were assumed as combined single crack if the crack interval b is satisfied with FFS codes ASME,BSI,SME FFS b.7mm, b ( a a ) /, b 0mm ()

2 FFS guidine provides structural assessment guidine for multiple cracked bodies. The combination rule of multiple cracks-to-single crack in FFS codes are reported to be unrealistic, i.e. (Kamaya, Miyokawa, & Kikuchi, 00; Kamaya & Miyoshi, 0). The FFS states that the multiple cracks characterized as one larger crack regards to certain rules and conditions. In some cases that involve different geometrical parameters, these codes may results with inaccurate and unriable prediction of failure and service life. This statements need extension of validation and verification works. The re-characterizing rule of multiple interacting cracks used in safety assessment of in-service plants. The current FFS codes addressed the statement that multiple cracks are combined and treated as single crack if the distance between two cracks satisfies a prescribed criterion (Kamaya, 003, 008a, 008b; Kamaya et al., 00; Kobayashi & Kashima, 000; Moussa, Bl, & Tan, 999; O'donoghue, Nishioka, & Atluri, 984; Xuan, Si, & Tu, 009). The argument is the simple combination will introduce the unrealistic prediction of cracking behavior due to interacting effect is neglected (Kamaya et al., 00). The ASME pressure vess codes (ASME, 998) and British Standard PD6495 (BSI, 99) do not quantify the interaction between cracks especially in two close proximity cracks. The exclusion of crack interaction may result with unrealistic SIF. In this paper, the FFS codes used for combination and re-characterization of crack interaction from multiple is re-evaluated using devoped stress shiding damage (SSD) mod. In specific case study, the combination and re-characterization of crack interaction from two parall edge cracks to single edge crack in weak and strong interaction state is investigated for the determination of crack interaction limit (CIL) and crack unification limit (CUL) using finite ement method. STRESS SHIELDING DAMAGE MODEL Based on energy damage of phase fid mod that used to mod the interaction between grains under loading, the total astic strain energy E of a linear astic body with stiffness tensor C and crack resistance G depends on the displacement fid u and the crack indicator s is given by E( u, s), s c, and expressed as E( u, s) s u : C u Gc s / 4ò ò s dv () The cracks are represented by a fid variable s, where s if the material is undamaged and s 0if there is a crack. For present case, the variable s is considered as damage parameter I astic damage mods. The infinitesimal strain tensor is rated to the displacement fid u by T ( u) / u u and the astic stress are derived from the energy density by / s C,where the factor s mods the stiffness loss between an undamaged s and broken material s 0. In undamaged finite body that divided into two sections N,, the total energy density can be

3 expressed as, where. Figure shows the increase and decrease pattern of subjected to transition of undamaged and damaged body 0 based on single crack basis of potential energy concept. s 0 ξ Ψ ξ Figure Energy pattern of undamaged and damaged body 0 The two edge cracks with no interaction between them contain the energy at and it equivalent to single independent crack. This is the stage where the crack interaction limit (CIL) can be determined. Figure also shows the example of single and two cracks equivalent based on damage value of damage amplification factor. As the cracks are interacting each other in starts by weak interaction at and keep decrease 0 until reach 0. Here, the two cracks are proposed by FFS codes to be considered as single crack and the strong interaction is occurred. This is the stage where the crack unification limit (CUL) can be observed. Theoretically, the energy density of two edge cracks at CIL should be equivalent to single edge crack at certain length of crack interval b with no crack interaction. As the crack interval decrease to zero, the energy density of two edge cracks at CIL should be equivalent to single edge crack at lower value to define the CUL. Based on phase fid formulation, the damage parameter of s by E( u, s) which derived from energy density to govern the evolution of damage parameter of s for two cracks, the generalization of the Eshby tensor is considered. The generalization of u T / s s and decomposed Eshby tensor is given by into astic part and surface part surf of energy density by T u with s : C (3) s s Gc s s surf surf / with surf ò / 4ò (4) surf In non-crack propagation phase, the cracks fid s, therefore the surface part of the energy density is generally vanished and the astic part coincide with astic energy of Hooke material. Based on configuration of body force g, the force acting on the crack tips can be computed as an integral body force g over a sufficiently large domain of 0 around the crack tips as depicted in Fig. (a). 3

4 The integral expression can be re-written as the integral of divergence of as a contour integral over the boundary 0 0, 0 A B B A of the domain 0 with n being the outer normal vector. surf gdv div dv nds nds n ds (5) Based on Figure, under mode I loading, the astic energy and stresses, on 0 B A is vanished. Thus, the integral astic Eshby tensor can be written as nds n n (6) AB As cracks fid s, coincides with (Rice, 968) -integral that equal to energy rease rate of mode I crack (Hakim & Karma, 009; Kuhn & Muller, 00). ds u dy T / i ui x ds n n (7) 0 0 The interpretation of 0 of s and for value can be defined further for detail investigation of CIL and CUL. Figure (b) illustrates the formation of path integral of 0 B A of s and for -integral. (a) (σ ) (b) (σ ) C B A 0 n ct Path C ds dx dy ct T u n Path 0 = C B A 0 ct n Path C ds dx dy ct Path 0 (σ ) Figure Schematic contour of s and (σ ) integration domain The agreement of Griffith (Griffith 9) classical energy definition G with energy density and astic energy corresponds to damage parameter of s by partial energy parameter at sections ( ) have proven wl equivalent to -integral value. Fig. (b) shows the graphical summary and representation of CIL and CUL definition regards to s which define the G. 4

5 FINITE ELEMENT ANALYSIS In the context of LEFM analysis, (Rice, 968) has demonstrated that the total strain energy rease rate, G is equal to path independent integral called or G. The - integral has the following expression i i / u dy T u x ds (8) where u is the displacement vector components and ds is the length increment along i the (any path beginning at the bottom crack face and ending at the top crack face), is strain energy density, while traction vector T n is defined as ij stress tensors and i ij j n is the component of the unit vector normal to, respectivy. Figure ij 3(a) - (c) shows the assigned line integral to both crack tips. The line integrals denote as PATH and PATH. These two paths will get close as the crack interval reduces. Figure 3(d) displays the final meshing of line integral formation surround the crack tips including assigned PATH and PATH. (a) ELEMENTS PATH (b) η 6 5 (d) UN 3 : h Global mesh ξ c a Sub-mod mesh Ct 4 PATH Ct Front free surface c a Ct b Local mesh Sub-mod mesh Ct H Back free surface (c) ds dx dy y T u n h Global mesh Crack tip x 6 PATH SC PSTRAIN L F Figure 3 (a) Two parall edge cracks in finite body, (b) 8-node quadrilateral ement, (c) line integral contour path and (d) complete meshing of mix ements Y 3 5 Z X 5

6 A series of ANSYS subroutine for executed to determine e e contour formulation are constructed and value,. A number of contour radii are set to obtain the convergence value. According to (Ismail et al., 0), the astic -integral can be determined by ' (,, ) K / E (9) By defining a mean value of interval b/a is determined by e I II III e e at each execution, mode I SIF magnitude for all crack K E. For starting of weak interaction I ' / ' ' I K CIL / E and for starting of strong interaction I CUL / E' E under plain stress and K E where E' E/ ( ) under plain strain, with E and designating the Young s Modulus and Poisson s ratio, respectivy. RESULTS AND DISCUSSION In different perspective, the FFS codes provide a correct interaction margin for any interacting cracks analysis as being benefited in present study. The codes proposed the combination and re-characterization of multiple interacting cracks into single cracks or single combined cracks with satisfying certain rules and conditions that used in safety assessment for in-service plants. All the proposed solutions is unable to schematically show the SIF K or normalized SIF is equivalent to single edge crack SIF K I, ref, BS by intersection. The intersection point will determine the equivalent of combination rules to rate with FFS codes. The CIL and CUL results of present study have successfully proved the correctness lev of FFS combination rules is fairly depend on geometrical parameter of cracked finite body. Figure 4 shows that CIL and CUL point are identified by intersection point to single edge crack and provided with FFS codes recommendation rules. The CIL is not mentioned directly in FFS codes but rather based on the two cracks to single crack combination since the two parall cracks will be considered as coplanar if the distance between cracks is b.7 mm. It is assumed that the CIL might be exist at b.7 mm. The same assumption is made for BSI codes where the astic CUL will be somewhere at b ( a a ). It also observed that the SIF of two edge cracks is equivalent to single crack SIF of crack at a/ 0.05 and a/ 0.5. Similarly, SME codes for parall offset cracks defines that multiple cracks are replaced by an equivalent single crack based on the stage of detected cracks, while satisfying the condition of b 0 mm. Thus, the interaction starts to weaken at b 0 mm and possibly the limit of interaction is beyond that. 6

7 b b 0.75,,.5,.5 b.5,,.5,3.5,3,3.75,4.5 b b b b b b b 3,4,5,6 Stress intensity factor, K I,in, (MPa mm) 3.75,5,6.5, ,6,7.5,9 5.5,7,8.75,0.5 6,8,0, 6.75,9,.5, ,0,.5, Present (b/a = 3.0) Present (b/a =.5) Present (b/a =.0) Present (b/a =.5) Brown & Strawley (966) CUL.7 ( ASME, BSI ) ( SME ) CIL CUL a a b K I, in, CIL a K I, ref, BS Crack -to-width ratio, a/ Figure 4 FFS codes (ASME, BSI, SME) rationship with variation of K single edge crack K for different a/ and b I, ref and Figure 5 shows exact location and range of FFS codes in present investigation results for weak interaction. It can be seen, theoretically crack interval of crack interaction limit at b/ a 3.0 and based on crack to width ratio a/, the intersection point is observed to occur a/ 0. which defined as crack unification limit (CUL) and at a/ 0.5 which noted as crack interaction limit (CIL). Figure 6 show the FFS codes rationship for strong interaction. It can be seen that in strong interaction, the CIL is impossible to achieve due to no tendency of K prediction to intersect with Brown & Strawley (966) prediction for single edge crack. However, CUL is possible to achieve since both prediction have shown the tendency to converge and intersect at smaller a/. The present investigation has provided comprehensive understanding of FFS codes on interacting cracks and provides more facts why FFS codes may underestimate the failure prediction. The translation of CUL and CIL from FFS codes is significant for interacting cracks evaluation. 7

8 Stress intensity factor, K I (MPa mm) b/a = 3.0 Brown & Strawley (966) Present iang et al. (990) CUL.7 ( ASME, BSI ) Crack interaction factor, γ I Intersectio n point CUL 0 ( SME ) CIL 0 CIL Crack to width ratio, a/ Figure 5 Variation of against a/ for b/ a 3.0 pertinent to FFS codes (ASME, BSI and SME) Present (b/a =.0) Present (b/a = 0.5) Brown & Strawley (966) CUL.7 ( ASME, BSI ) 700 ( SME ) 600 CUL 0 CIL P (σ ) 400 a K I, ref, BS 300 a a b K I, in, P (σ ) CIL Crack -to-width ratio, a/ Figure 6 FFS codes (ASME, BSI, SME) rationship with variation of K different a/ for 8

9 CONCLUSION The present devoped stress shiding damage (SSD) mod has successfully shown the significant effects on stress intensity factors and crack interaction factor due to interacting cracks for weak and strong interaction condition. The recommendation of the ASME boiler and pressure vess code (Section XI, Articles IA-3330), SME fitnessfor-service code and BSI PD6493 have also been investigated and it maybe concluded that they tend to underestimate the design life of flawed structure. At the same time, based on the proposed FE algorithm of CUL and CIL, they actually can be moderaty applied for weak interaction but not for strong interaction. The outlined FFS codes may provide inaccurate prediction since the recommended combination rules is too general and not able to define the CUL and CIL for weak and strong interaction. REFERENCES ASME ASME Boiler and Pressure Vess Code, Section XI. New York, USA. ASME ASME Boiler and Pressure Vess Code, Section XI. New York, USA. ASME / FFS- Fitness-for-service, Section 9, American Society of Mechanical Engineers. New York, USA. ASTM. 0. ASTM E90--08e. Standard test method for crack tip opening displacement fracture toughness measurement, American Society of Testing and Materials. New York, USA. BSI. 99. British Standard Institute, PD 6493, Section 8. Guidance on methods for assessing the acceptability of flaws in fusion wded structures. BSI British Standard Institute, BS790. Guidance on methods for assessing the acceptability of flaws in metallic structures. Hakim, V., & Karma, A Laws of crack motion and phase-fid mods of fracture. ournal of the Mechanics and Physics of Solids, 57: Ismail, A. E., Ariffin, A. K., Abdullah, S., Ghazali, M.., AbdulRazzaq, M., & Daud, R. 0. Stress intensity factor under combined bending and torsion moments. ournal of Zhejiang University-SCIENCE A, 3(): -8. SME SME Fitness-for-Service Code S NA-008. Kamaya, M A crack growth evaluation method for interacting multiple cracks. SME International ournal, 46(): 5-3. Kamaya, M. 008a. Growth evaluation of multiple interacting surface cracks. Part II: Growth evaluation of parall cracks. Engineering Fracture Mechanics, 75: Kamaya, M. 008b. Growth evaluation of multiple interacting surface cracks.part I: Experiments and simulation of coalesced crack. Engineering Fracture Mechanics, 75, Kamaya, M., Miyokawa, E., & Kikuchi, M. 00. Growth prediction of two interacting surface cracks of dissimilar sizes. Engineering Fracture Mechanics, 77: Kamaya, M., & Miyoshi, K. 0. Monitoring of inside surface cracks growth by strain measurement of the outside surface: A feasibility study. Nuclear Engineering and Design, 4:-. 9

10 Kobayashi, H., & Kashima, K Overview of SME flaw evaluation code for nuclear power plants. International ournal of Pressure Vesss and Piping, 77: Kuhn, C., & Muller, R. 00. A continuum phase fid mod for fracture. Enginering Fracture Mechanics, 77: Moussa,. A., Bl, R., & Tan, C. L The interaction of two parall noncoplanar identical surface cracks under tension and bending. International ournal of Pressure Vesss and Piping, 76: O'donoghue, P. E., Nishioka, T., & Atluri, S. N Multiple surface cracks in pressure vess. Engineering Fracture Mechanics, 0(3): Rice,. R. (968). A path independant integral and the approximate analysis of strain concentration by notches and cracks. ournal of Applied Mechanics, 35: Xuan, F.-Z., Si,., & Tu, S. T Evaluation of C* integral for interacting cracks in plates under tension. Engineering Fracture Mechanics, 76: 9-0. iang Z. D., Zeghloul A., Bezine G. and Petit Stress intensity factor of parall cracks in a finite width sheet. Engineering Fracture Mechanics, 35: pp