A Parametric Study of Ridge-cut Explosive Bolts using
Paper Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) http://dx.doi.org/10.5139/IJASS.2015.16.1.50 A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes Juho Lee* and Jae-Hung Han** Department of Aerospace Engineering, KAIST, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea YeungJo Lee*** The 4th R&D Institute, Agency for Defense Development, Daejeon 305-600, Republic of Korea Hyoungjin Lee**** PGM R&D Lab., LIG NEX1 Co. Ltd., Seongnam 463-400, Republic of Korea Abstract Explosive bolts are one of pyrotechnic release devices, which are highly reliable and efficient for a built-in release. Among them, ridge-cut explosive bolts which utilize shock wave generated by detonation to separate bolt body produce minimal fragments, little swelling and clean breaks. In this study, separation phenomena of ridge-cut explosive bolts or ridge-cut mechanism are computationally analyzed using Hydrocodes. To analyze separation mechanism of ridge-cut explosive bolts, fluid-structure interactions with complex material modeling are essential. For modeling of high explosives (RDX and PETN), Euler elements with Jones-Wilkins-Lee E.O.S. are utilized. For Lagrange elements of bolt body structures, shock E.O.S., Johnson-Cook strength model, and principal stress failure criteria are used. From the computational analysis of the author’s explosive bolt model, computational analysis framework is verified and perfected with tuned failure criteria. Practical design improvements are also suggested based on a parametric study. Some design parameters, such as explosive weights, ridge angle, and ridge position, are chosen that might affect the separation reliability; and analysis is carried out for several designs. The results of this study provide useful information to avoid unnecessary separation experiments related with design parameters. Key words: Pyrotechnics, Ridge-Cut Explosive Bolts, Hydrocodes, Separation Behavior Analysis. 1. Introduction one of the high-explosive types, utilize shock wave generated by detonation to separate bolt bodies. Furthermore, it is well known that the ridge-cut explosive bolt produces minimal shrapnel, little swelling, and a clean break [3]. While the usage of explosive bolts is quite prevalent, designing procedures still rely on heritage with repetitive experiments. To overcome this limitation, the computational analysis method for the explosive bolts is needed. Based on the computational analysis, separation reliability of the explosive bolts can be evaluated without time-consuming and costly experiments. Furthermore, complex separation phenomena and characteristics can be studied. In many Explosive bolts are reliable and efficient pyrotechnic release devices that can be used for diverse applications including launcher operation, stage separation, release of external tanks, and thrust termination [1, 2]. The explosive bolt, which has a form of a bolt body with the cavity filled with a removable cartridge or an explosive charge, is more reliable and robust than other types of release devices, due to its simplicity. Most of the explosive bolts can be categorized as high-explosive type and pressure type, based on their separation mechanism. Ridge-cut explosive bolts, which are * Ph. D Student Professor, Corresponding author: [email protected] ** ***Principal Researcher ****Principal Researcher This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Received: January 21, 2015 Revised: March 5, 2015 Accepted: March 5, 2015 Copyright ⓒ The Korean Society for Aeronautical & Space Sciences (50~63)15-012.indd 50 50 http://ijass.org pISSN: 2093-274x eISSN: 2093-2480 2015-03-31 오후 1:53:57 Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes A 17-4PH stainless steel is used for the bolt body and the fixtures of the ridge-cut explosive bolts. A removable initiator and the priming material (Lead Azide, LA) are utilized to initiate the high explosives. For the high explosives, PETN and RDX are utilized. The separation reliability of the ridge-cut explosive bolts is verified by repetitive separation experiments. The separation plane observed by separation experiments is shown in Fig. 1. However, the pyroshock generated by the exploding bolts exceeded 10,000 g above 4,000 Hz at near field. If the explosive weight can be reduced without compromising the separation reliability, the probability of malfunctions in nearby electrical components can be significantly reduced. Unlike other types of explosive bolts, the separation mechanism of ridge-cut explosive bolts cannot be understood by classical fracture mechanics, but it can be explained by ridge-cut mechanism (Fig. 2). Ridge-cut technique or mechanism can be explainable by the fracture mechanism, when a metal structure has ridge on one side and high explosives detonate on the other side. At first, shock waves generated by detonation of high explosives are emitted cases, complex separation characteristics cannot be fully understood based on simple theories and experimental results. Based on the computational method regarding the blast loading on structures [4-10], the authors proposed the computational analysis method for the separation behaviors of the ridge-cut explosive bolts [11]. Previous study clearly showed the separation mechanism of the ridge-cut explosive bolts from the computation analysis, and the computation scheme was verified by comparing with the experimental results. From the separation characteristics study regarding the confinement conditions, design improvements were proposed [11]. However, previous study focused only on the specific confinement condition. To widely apply the computation analysis method for the designing procedures, it still requires further studies by applying computation analysis method to general design parameters of explosive bolts. In this study, computational analysis methodology for ridge-cut explosive bolts separation behavior is revised and improved in some aspects. By utilizing this numerical analysis framework, a parametric study with design parameters of ridge-cut explosive bolts is performed, and meaningful analysis results are obtained to apply design procedures. 2. Separation mechanism of ridge-cut explosive bolts In this study, the ridge-cut explosive bolts as depicted in Fig. 1, which are designed by the author’s previous experience [12, 13], are computationally analyzed to understand the separation characteristics. The ridge-cut explosive bolts are designed based on the theory of ridge-cut mechanism [11]. Fig. 2. Ridge-cut mechanism Fig. 2. Ridge-cut mechanism Fig. 1. Cross-sectional diagram of ridge-cut explosive bolts Fig. 1. Cross-sectional diagram of ridge-cut explosive bolts http://ijass.org 51 2 (50~63)15-012.indd 51 2015-03-31 오후 1:53:58 Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) 3.1 Summary of computational analysis method the connections between the bolt body and the fixtures are modeled as mesh connections, allowing the joining of the meshes of topologically disconnected bodies. In ANSYS AUTODYN, the mesh connections are recognized as bonded connections. The remaining modeling steps, including Eulerian modeling and materials modeling, are performed in ANSYS AUTODYN. Materials modeling, definition of initial conditions, Euler parts, Euler boundary conditions, structural boundary condition, Euler-Lagrange interaction, detonation, and solution controls are necessary in AUTODYN. In the ridge-cut explosive bolts, the removable initiator and the priming material are utilized merely to initiate detonation of PETN and RDX. Therefore, initiator and LA that generate negligible blast loading on bolt body are neglected in computational analysis. For high explosives, RDX and PETN, Jones-Wilkins-Lee (JWL) E.O.S. are used. For 17-4PH stainless steel (material of the bolt body and the fixtures), the Shock E.O.S., the Johnson-Cook strength model, and the principal stress failure model are used. Surrounding air is defined as the ideal gas with material properties at 1 atmosphere. Initial density and internal energy of each material are defined as initial conditions. The air, PETN, and RDX are constructed as the Euler parts. The size of Euler elements for air and high explosives is 0.1 mm, which is half of Lagrange elements (Fig. 4). To model the spread-out of detonation products, flow out Euler boundary condition is applied to Due to geometric complexity of ridge-cut explosive bolts, geometric modeling including structure meshing, the connections and body interaction are performed in ANSYS Workbench Explicit Dynamics. The structural mesh is constructed via a quadrilateral dominant method with Lagrange elements 0.2 mm in size, as shown in Fig. 3. Smaller element sizes generally induce accurate analysis results, but they require high computational costs. Therefore, optimal mesh size is determined to guarantee converged numerical results and fast computation time. In this study, Fig. 4. Elements size comparison between Lagrange and Euler. Fig. 4. Elements size comparison between Lagrange and Euler. into the metal structure. When the shock waves encounter the free surface of metal structure, they reflect back as the rarefaction waves (or release waves). When the rarefaction waves collide at the meeting site of rarefaction waves, particles at the meeting site move in opposite directions. These movements create high tensile stress at the meeting site, resulting in the separation. 3. Improvements of computational analysis methodology Ridge-cut explosive bolts and their separation mechanism can be computationally analyzed in AUTODYN (one of commercial Hydrocodes), due to necessity of Euler-Lagrange interactions and complex material models. Computational analysis of ridge-cut explosive bolts are performed in 2-D axisymmetric to minimize computational costs. The computational analysis method for the ridge-cut explosive bolts was well developed in previous study [11]. The analysis method is summarized and the improvements are introduced here. The improvements include the structural boundary condition and the parameter values of the Shock E.O.S. (the Gruneisen constant and the U-u Hugoniot). The estimation method for the material properties of the high explosives with slightly different density is also proposed. Fig. 3. Structure geometric modeling and meshing of the ridge-cut explosive bolts. Fig. 3. Structure geometric modeling and meshing of the ridge-cut explosive bolts. DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50 (50~63)15-012.indd 52 52 2015-03-31 오후 1:53:58 strength model, and the principal stress failure model are used. Surrounding air is defined as the ideal gas with material properties at 1 atmosphere. Initial density and internal energy of each material are defined as initial conditions. The air, PETN, and RDX are constructed as the Euler parts. The size of Euler elements for air and high explosives is Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes 0.1 mm, which is half of Lagrange elements (Fig. 4). To model the spread-out of detonation products, flow out Euler boundary condition is applied to the boundary of the Euler parts, excluding the the boundary of the Euler parts, excluding the axisymmetric Here, V is the relative volume ν/ν0; E is the internal energy; axis. In this study, a transmit utilized is utilized and A, R1, R2, ωboundary are empirical parameters determined axisymmetric axis. In this study,boundary a transmitcondition boundaryiscondition as aB,structural as a structural boundary condition, as shown in Fig. 5. The by detonation experiments. The detonation velocity and condition, shown in condition Fig. 5. The ensures transmit boundary condition the stress waves to transmit transmit as boundary the stress wavesensuresinformation regarding the Chapman-Jouguet (C-J) point as to transmit out without reflection at the boundary. It is the reference state of JWL out without reflection at the boundary. It is modeled as infinite structures are attached at the boundaryE.O.S. are also required. The C-J modeled as infinite structures are attached at the boundary point is the position where the reaction (or detonation) is with value (the(the density multiplied by the velocity). It is defined that with identical identicalimpedance impedance value density multiplied by soundcomplete. the sound velocity). It is defined that detonation is initiated Material properties of RDX and PETN for computational detonation is initiated at the left bottom point of PETN in 2-D model. A single time step is determined at the left bottom point of PETN in 2-D model. A single analysis are given in Table 1. The density of RDX and PETN for 3 3 by CFL (Courant-Friedrichs-Lewy) which guarantees stabilityof and accuracy of the solution. time step is determined by CFL condition (Courant-Friedrichs-Lewy) reference isfor1.65 g/cm3 model and 1.50 g/cm , respectively. RDX andmodel PETN reference is 1.65 g/cm and 1.50 g/cm3, respectively. Material condition which guarantees stability and accuracy of the Material properties of COMP A-3 and PETN 1.50 supplied by The computational analysis is performed up to 0.01 ms. of COMP A-3 and PETN for 1.50RDX supplied by AUTODYN solution. The computational analysis is performed up to 0.01 AUTODYN are utilized 1.65 and PETN 1.50.are utilized for RDX 1.65 and PETN ms. Inthis thisstudy, study, material properties of explosive high explosive In thethe material properties of high for different explosive density ar for different explosive density are needed. The estimation 3.2 Modeling of high explosives The estimation method derived for the material with properties with slightly different densit method is derived foristhe material properties slightly 3.2 Modeling of high explosives different density of up to 10%. The linear dependence of For from E.O.S. Formodeling modelingofofdetonation detonationproducts products fromhigh highexplosives, explosives,the Jones-Wilkins-Lee 10%. The linear(JWL) dependence of detonation velocity D upon initial density 0 can b detonation velocity D upon initial density ρ0 can be used to the Jones-Wilkins-Lee (JWL) E.O.S. [14] are widely used. [14] are widely used. It can evaluate experimental geometries of detonation products from initiationvelocity. to estimate thedetonation detonation explosives, the estimate the velocity. For For mostmost explosives, the following relationships are quit It can evaluate experimental geometries of detonation following relationships are quite accurate for a broad range large expansions. products from initiation to large expansions. for a broad [15]: range of density [15]: of density P A(1 R1V )e R1V B (1 R2V )e R2V E D j k 0 (1) V (1) (2) (2 For RDX, j is 2.56 and k is 3.47. For PETN, j is 1.82 and k is 3.7 when the Here, V is the relative volume v / v0 ; E is the internal energy; and A , B , R1 , R2 , are between 0.37 g/cm3 and 1.65 g/cm3. empirical parameters determined by detonation experiments. The detonation velocity and information Also, accurate estimation of the C-J pressure from the detonation velocity and the initial regarding the Chapman-Jouguet (C-J) point as the reference state of JWL E.O.S. are also required. as follows [15]: The C-J point is the position where the reaction (or detonation) is complete. P D 2 (1 0.7215 0.04 ) (3 0 0 CJ in Table Material properties of RDX and PETN for computational analysis are given 1. The density Fig. 5. Euler parts including air, RDX, PETNItand transmit boundary is not unreasonable tocondition. assume that the C-J energy per unit volume E0 is proportional Fig. 5. Euler parts including air, RDX, PETN and transmit 7 boundary condition. [14]. Within 10% variation of density, parameters R1 , R2 , can be retained [14]. To Table 1. Revised Material Properties Explosive with different density Tableof1.High Revised Material Properties of High Explosive with different density Parameter of JWL E.O.S. Density 0 (g/cm3) PETN 1.77 A andRDX B , following system of equations should be solved [14]. Even though PETN 1.50parameters PETN 1.26 1.815 RDX 1.65 RDX 1.485 1.77 1.50 8 it is not necessary modeling. C will 1.26be calculated, 1.815 1.65 for our Hydrocodes 1.485 8 Parameter A (kPa) 6.1705×10 6.253×10 Parameter B (kPa) 1.6926×107 2.329×107 Parameter R1 (none) 4.4 5.25 Parameter R2 (none) 1.2 1.6 Parameter (none) 0.25 0.28 3 3 8 5.731×108 7.826×108 6.113×10 1 PCJ Ae R17VCJ Be R2VCJ 7 C 1 7 2.016×10 1.335×10 V1.065×10 CJ 4.634×108 6.0 4.4 4.4 R2VCJ 4.4 1 e R1VCJ e 1 E0 PCJ (1 VCJ ) A B C R1 1.2 R2 VCJ 1.8 2 1.2 1.2 (5 0.28 0.32 0.32 0.32 PCJ 1 3AR1e R1VCJ BR23e R2VCJ C ( 3 1) ( 2) 3 8.858×10 8.3×10 V7.713×10 VCJ 16.54×10 CJ (6 Detonation velocity D (m/s) 8.30×10 7.45×10 C-J Energy volume E0 (kJ/m3) 1.01×107 8.56×106 VCJ 6 is the9.79×10 v / v06 at C-J8.01×10 Here, relative 6volume point: 6 7.19×10 8.9×10 (kPa) 3.35×107 2.2×107 7 P 7 CJ 3.718×10 V1.4×10 ) CJ (1 2 D C-J Pressure per unit 53 (50~63)15-012.indd 53 (4 8.049×106 3×107 2.359×107 (7 8http://ijass.org 2015-03-31 오후 1:53:59 can be used to the Shock E.O.S. are utilized, which is the Mie-Gruneise 10%. The linear dependence of detonation velocity D upon initial density For 17-4PH stainless steel, D upon 0000 can upon initial initial density density can be be used used to to 10%. 10%. The The linear linear dependence dependence of of detonation detonation velocity velocity D E.O.S. [16] that shock Hugoniot as reference. estimate the detonation velocity. For most explosives, the following relationships are uses quitethe accurate estimate estimate the the detonation detonation velocity. velocity. For For most most explosives, explosives, the the following following relationships relationships are are quite quite accurate accurate for a broad range of density [15]: for for aa broad broad range range of of density density [15]: [15]: P PH D j k 0 D D jj kk000 v (e eH ) (8 (2) (2) (2) Here, P is the pressure, is the Gruneisen constant, is the specific volume, and Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) For RDX, j is 2.56 and k is 3.47. For PETN, j is 1.82 and k is 3.7 when the density is For For RDX, RDX, jj is is 2.56 2.56 and and kk is is 3.47. 3.47. For For PETN, PETN, jj is is 1.82 1.82 and and kk is is 3.7 3.7 when when the the density density is is specific internal energy. Subscript H denotes the shock Hugoniot, which is defined as th between 0.37 jg/cm3 and 1.65 g/cm3. Subscript H denotes the shock Hugoniot, which is defined For RDX, is 2.56and and k isg/cm3. 3.47. For PETN, j is 1.82 and k is between between 0.37 0.37 g/cm3 g/cm3 and 1.65 1.65 g/cm3. all shocked states each material. Here, we need the P v Hugoniot for the Shock E. 3 3 as the locus allfor shocked 3.7Also, when the density is between 0.37pressure g/cm and 1.65 . accurate estimation of the C-J from theg/cm detonation velocity and theof initial density isstates for each material. Here, we Also, Also, accurate estimation estimation of of the the C-J pressure from from the the detonation detonation velocity and the the initial initial density density is isthe Shock E.O.S.. This Hugoniot need and the P-ν Hugoniot Also,accurate accurate estimation of C-J thepressure C-J pressure from the velocity Hugoniot can be obtained for from the U u Hugoniot or the relationship between shock an as follows [15]: can be obtained from the U-u Hugoniot or the relationship detonation velocity and the initial density is as follows [15]: as as follows follows [15]: [15]: velocities. between shock and particle velocities. 0.04 (3) PCJ 0 D2222(1 0.7215 00.04 (3) 0.04 0.04) (3) (3) PPCJ D D (1 (1 0.7215 0.7215 ) ) CJ 000 000 CJ (9) U C0 su (9 notunreasonable unreasonable to assume thatC-J theenergy C-J energy ItItisisnot to assume that the per unitper volume E0 is proportional to density It is not unreasonable to assume that the C-J energy per unit volume E000 is proportional to density Here, C C0 and s are empirical parameters obtained from unit volume E0 is proportional to density [14]. Within 10% Here, 0 and s are empirical parameters obtained from the least-square fits to the exp theretained least-square fitscalculate to the experimental results [17, 18]. For variation of 10% density, parameters R1, parameters R1, ω can be R1 ,retained R2 , can be [14]. Within variation of density, [14]. To R111,, RR222 ,, can [14]. [14]. Within Within 10% 10% variation variation of of density, density, parameters parameters R can be be retained retained [14]. [14]. To To calculate calculate results [17, 18]. For the shockstainless E.O.S. ofsteel, 17-4PH the shock E.O.S. of 17-4PH the stainless density, steel, the the density, the specific [14]. To calculate parameters A and B, following system of A B parameters and , following system of equations should be solved [14]. Even though parameter specific heat, the Gruneisen constant, and the U-u Hugoniot equations should solved [14]. Even AA and BB,, following parameters parameters and be following system system of of though equations equationsparameter should should be be solved solved [14]. [14]. Even Even though though parameter parameter C0 and s ) are Hugoniot (empirical Gruneisen and C the and U s)u are (empiricalconstant, parameters necessary. Only parameters the C will be calculated, it is not necessary for our Hydrocodes 0 C will be calculated, it is not necessary for our Hydrocodes modeling. will be be calculated, calculated, itit is is not not necessary necessary for for our our Hydrocodes Hydrocodes modeling. modeling. density and the specific heat are known [19]. C C will modeling. Only the density and the specific heat are known [19]. In this study, the Gruneisen constant is theoretically 1 R1VCJ R2VCJ (4) 1 1 P Ae Be C R V R V CJ CJ CJ AeRR111VVCJ CJ BeRR222VVCJ CJ C 1 (4)Gruneisen PCJ estimated [16] the from the volumetric expansion In this study, constant is thermal theoretically estimated [16] from the volumetr (4) CJ V CJ 111 CJ VCJ CJ CJ coefficient, the specific heat Cν, and the bulk modulus: expansion coefficient, the specific heat Cv , and the bulk modulus: 1 eRRRR1VVVVCJ eRRRR2VVVVCJ 1 PP E0 11 PCJ (1 VCJ ) A ee 111 CJCJCJ B ee 222 CJCJCJ C 11 ((VV //VV )) 11 (5) (1 EE000 2 PPCJ (1VVCJ )) AA R1 BB R2 1C C VCJP (5) (1 (10) 1 (( (5) P )()( (V / V000 )))PP00 CJ CJ CJ (1 CJ (5) (V / V0 ) (1 ( )( C V V ( / ) 22 RR111 R R V V 298 C V V ( / ) TT )TTP298 0 KK CJ (10) ( CJ )( ) 222 CJ 00 vv 00 P 0 T 0Cv (V / V0 ) T 298 K T 0Cv (V / V0 ) T 298 K PCJ 1 R1VCJ R2VCJ The volumetric thermal expansion coefficient three times of of the the linear linear thermal thermal The thermal expansion coefficient isis three times The volumetric volumetric thermal expansion coefficient is three (6) PPCJ 11 C CJ CJ 9 is three (6) AR1111eeRRR111VVVCJCJCJ BR2222eeRRR222VVVCJCJCJ C (( AR BR The volumetric 1) 1) V ((((2)2)2)2)thermal (6) The volumetric thermal coefficient times of the linear thermal 11 expansion coefficient is three timesexpansion of the linear thermal expansion CJ CJ VCJ V V times of the linear thermal expansion coefficient. All the CJ CJ CJ CJ CJ coefficient.All All the the parameters parameters for for the the theoretical theoretical calculation calculation are are known known [19]. [19]. coefficient. coefficient. forcalculation the theoretical are known [19]. forthe theparameters theoretical are calculation known [19]. coefficient. All parameters for theparameters theoretical All calculation are known [19]. Here, VCJ is the relative volume v / v0 at C-J the point: v /0vat Here, therelative relative volume volume ν/ν at C-J point: C-J point: Here, V VCJ CJ isisthe Becausethe theU of17-4PH 17-4PHstainless stainless steel is CJ Because the Hugoniot of of 17-4PH stainless steel unknown, the relationship relationship per pe UU-u CJ 000 Because Hugoniot steel isis unknown, the uu Hugoniot Because the Usteel ofthe 17-4PH stainless steel is unknown, the relationship pe u isHugoniot Because the U u Hugoniot of 17-4PH stainless unknown, relationship pertaining to unknown, the relationship pertaining to PH13-8MO stainless PCJ PH13-8MO stainless stainless steel [20], [20], which which isis the the material material most most similar similar in in terms terms of of this this relati relat PH13-8MO steel (7)the VCJ (1 PCJ CJ (7) CJ ) steel [20], which is material most similar in terms of this PH13-8MO stainless steel [20], in which thethis material most similar in terms of this relat (7) (7) VVCJ (1 (1 CJ D2222 )) CJ PH13-8MO stainless steel [20], which is the material most similar termsis of relationship, is D D relationship, utilized in thisstainless study. PH13-8MO utilized in this this is study. PH13-8MO stainless steel isis also also astainless a precipitation-hardening precipitation-hardening martensitic martensiti utilized in study. PH13-8MO steel utilized in this study. PH13-8MO stainlessmartensitic steel is also stainless astainless precipitation-hardening martensiti in this study. PH13-8MO stainless isaalso a precipitation-hardening martensitic steel issteel also precipitation-hardening Obviously, if we apply thisutilized calculation for reference steel, like 17-4PH stainless steel. steel, like steel. 8 steel, like17-4PH 17-4PHstainless stainless steel. density, for which the parameters of JWL E.O.S. known, 88 are steel, like 17-4PH stainless steel. steel, like for 17-4PH stainless steel.for which Obviously, if we apply this calculation reference density, the parameters of JWL For modeling of the high-strain-rate plastic deformation the calculated parameters A and B are exactly the same as For modeling modeling of of the the high-strain-rate high-strain-rate plastic plastic deformation or flow flow stress, stress, Johnson-Cook Johnson-Coo For deformation or For modeling of the high-strain-rate plastic deformation or flow stress, Johnson-Coo or flow stress, Johnson-Cook strength model is used. The the known values. For modeling of the high-strain-rate plastic deformation or flow stress, Johnson-Cook strength E.O.S. are known, the calculated parameters A and B are exactly the same as the known values. model used. The The Johnson-Cook equation [21] isis constitutive an empirical empirical constitutive constitutive equation equation rega reg model isis used. Johnson-Cook [21] an Johnson-Cook equation [21] is equation an empirical For the material properties of PETN with different model is[21] used. The Johnson-Cook equation [21] isregarding an empirical constitutive equation reg model is used. The Johnson-Cook equation is an empirical constitutive equation the For the material properties of PETN with different material regarding properties of equation thePETN plastic deformation of metals with explosive densities, material properties of PETNexplosive 1.26 anddensities, plastic deformation deformation of of metals metals with with large large strains, strains, high high strain strain rates, rates, and and high high temperatures. temperatures. plastic plastic deformation of metals with large strains, high strain rates, and high temperatures. large strains, high strain rates, and high temperatures. PETN 1.77 are utilized, which plastic is supplied by AUTODYN. metals with However, large strains, strainproperties rates, and high temperatures. 1.26 and PETN 1.77 are utilized, which isdeformation supplied byofAUTODYN. thehigh material However, the material properties of RDX with different TT TT n (1 T )(1CCln ln )[1 )[1(( T Trrr ))mmm]] (1 ((00 BBnn)(1 T n m properties (1 of RDX withdensities different explosive are not available. Therefore, the material of RDX )(1 ln )[1 ( B C r ( T T ) ] explosive are notdensities available. Therefore, the (11) T 0 (11) ( 0 B )(1 C ln )[1 ( ) ] 00 mm Trr 0 Tm Tr 0 Tm Tr material properties of RDX with 10% variations in density with 10% variations in density are estimated. Material properties of high explosives with different B isis the Here, isis the the yield yield stress stress or or flow flow stress, stress, 00 isis the the static static yield yield stress, stress, B the Here, are estimated. Material properties of high explosives the Here, yield stress or flow stress, ishardening theyield static yield stress, B is the Here, σisis thethe yield stress oryield flow stress, σB0 isisthe 0 static Here, is the yield stress or flow stress, is the static stress, 0 with different explosive are in explosive densities are also densities summarized inalso Tablesummarized 1. stress, B is hardening ε is the strain, n isCCtheisis the the the strain, nnconstant, the hardening hardening exponent, the strain strain rate rate constant, constant, constant, isis the strain, isis the exponent, constant, Table 1. is the strain, isstrain the hardening exponent, constant, C isisnthe rate hardening exponent, exponent, the strain rate constant, constant, theis the strain rate constant, constant, is the strain, n is thehardening isisCthe T the strain rate, thereference referencestrain strainrate, rate,T T the temperature, temperature, TTrr isis the the reference reference tem tem strainrate, rate, 00 isisisthe is strain the reference strain rate, isis temperature, the strain rate, the reference Tstrain rate, T is the temperature, Tr is the reference te 3.3 of17-4PH 17-4PH stainless steel 0 is the reference strain 3.3Modeling Modeling of stainless steelrate, strain rate, is0theis temperature, temperature, T is the T reference temperature,Tr isis the the reference melting point, and m r m Tmmthe m isis the the melting melting point, and and the thermal thermal softening softening exponent. exponent. m isis the point, is thermal softening exponent. For 17-4PH 17-4PH stainless stainlesssteel, steel,the theShock Shock E.O.S.are areutilized, utilized,which T For is form Tmthe is Mie-Gruneisen the melting point, andofm is the thermal softening exponent. T is theE.O.S. melting point, and m is the thermal softening exponent. For 17-4PH stainless steel (H1025, HRC38), only the which is the Mie-Gruneisen formmof E.O.S. [16] that uses the For 17-4PH 17-4PH stainless stainless steel steel (H1025, (H1025, HRC38), HRC38), only only the the static static yield yield stress isis known known [1 [1 For E.O.S. [16] that uses the shock Hugoniot as reference. static 17-4PH yield stress is known [19]. Other parameters are yield stress stainless steelyield (H1025, only theOther static stress is known [1 shock Hugoniot as reference. For 17-4PH stainless steel (H1025,For HRC38), only the static stressHRC38), is known [19]. assumed by of 4340 andsteel S-7 and toolS-7 parameters are averaging assumed by bythose averaging thosesteel of 4340 4340 steel and S-7 tool tool steel, steel, which which have have parameters are assumed averaging those of parameters arehave assumed byS-7 averaging those ofspecific 4340 and parameters are assumed by(8) averaging those of 4340 steel tool steel, which havesteel the same P PH (e eH ) (8) steel, which the and same density and the heat asS-7 tool steel, which have v density and the specific specific heat as 17-4PH 17-4PHthe stainless steel. In addition, the the static static yield yield stres stre density and the as stainless In addition, 17-4PH stainless steel.heat In addition, static steel. yield stress density and thesteel. specific heat as 17-4PH steel.and In addition, the static yield stre density and the specific heat as 17-4PH stainless In addition, the staticstainless yield stress the and thevolume, Rockwell of 17-4PH stainless are Here, P P isisthe e17-4PH Here, the pressure, pressure, γ isisthe theGruneisen Gruneisen constant, constant, ν isis the specific and is thestainless Rockwell hardness ofhardness stainless steel are are similar similarsteel with the the average average values values of of 4340 4340 ste ste Rockwell hardness of 17-4PH steel with Rockwell hardness of 17-4PH stainless steelofsteel are similar with the similar with the average of 4340 and the specific volume, and e is the specific internal energy. stainless Rockwell hardness of 17-4PH steel are similar with the values average values 4340 steelS-7 andtool S-7 average values of 4340 ste tool steel. steel. tool specific internal energy. Subscript H denotes the shock Hugoniot, which is defined as the locus of tool steel. tool steel. To model ridge-cut mechanism, the principal principal stress stress failure failure criteria criteria are are utilized. utilized. With With the the ridge-cut mechanism, the all shocked states for each material. Here, we need the P v HugoniotTo formodel the Shock E.O.S.. This modelstress ridge-cut mechanism, principal stress criteria are utilized. With the DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50 To model ridge-cut mechanism, principal failure criteria aretheutilized. With the failure principal 54 the To stress failureshock model, failure of each each element element isis initiated initiated ifif the the maximum maximum principal principal ten ten stress failure model, Hugoniot can be obtained from the U u Hugoniot or the relationship between andfailure particleof failure model, failure each element is initiated if the maximum principal ten stress failure model, failure of eachstress element is initiated if the of maximum principal tensile stress exceeds aa critical critical value value of of normal normal tensile tensile stress. stress. The The appropriate appropriate failure failure criteria criteria for for the the exceeds velocities. exceedsstress. a critical of normal tensile stress. appropriate failure criteria for the exceeds a critical value of normal tensile The value appropriate failure criteria for The the ridge-cut U C0 su (50~63)15-012.indd 54 explosive bolts bolts are are determined determined from previous previous study study [11]. [11]. Revised Revised material material properties properties oo explosive (9)determined from previous studyof[11]. Revised material properties o explosive bolts are determined fromexplosive previousbolts studyare[11]. Revised from material properties 17-4PH 2015-03-31 오후 1:53:59 stainless steel steel for for computational computational analysis analysis are are summarized summarized in in Table Table 2. 2. stainless Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes waves from detonation are emitted into the bolt body and encounter the free surface near the ridge around 2.1 μs (Fig. 6(b)). At the free surface, shock waves reflect back as rarefaction waves, and these reflected rarefaction waves collide at the meeting site of rarefaction waves at around 2.5 μs (Fig. 6(c)). From this computational analysis, the ridge-cut explosive bolts are expected to be separated at around 2.5 μs. From the previous study [11], the appropriate principal stress failure criteria are determined as 2.8 GPa critical value of normal tensile stress. For comparison, material statuses at 5.0 μs are given in Fig. 7, which use different critical values of normal tensile stress ranging from 2.4 GPa to 3.2 GPa. If low failure criteria are used, widespread failures are observable as shown in Fig. 7(a) and (b), and these are unlike the separation experiments. In the experiments, clean ridge breaks were observed. Furthermore, this makes the separation analysis results insensitive to parameter variations. If high failure criteria are applied, localized failures will be observed as shown in Fig. 7(d) and (e), which imply no separation of the explosive bolts. This makes it difficult to evaluate the separation reliability. steel. To model ridge-cut mechanism, the principal stress failure criteria are utilized. With the principal stress failure model, failure of each element is initiated if the maximum principal tensile stress exceeds a critical value of normal tensile stress. The appropriate failure criteria for the ridge-cut explosive bolts are determined from previous study [11]. Revised material properties of 17-4PH stainless steel for computational analysis are summarized in Table 2. 4. Computational analysis results of ridgecut explosive bolts By utilizing developed numerical analysis framework, separation behavior of the ridge-cut explosive bolts is computationally analyzed. At first, the principal stress failure model is not used to clearly observe propagation, reflection of shock waves, and collision of reflected rarefaction waves. Detonation is initiated at the left bottom point of PETN as analysis starts (0 ms). Detonation of PETN and RDX is finished at around 1.7 μs (Fig. 6(a)). Shock Table 2. Revised Material Properties Table of 17-4PH 2. Stainless RevisedSteel Material Properties of 17-4PH Stainless Steel Parameter of Shock E.O.S. Density 0 17-4PH Stainless Steel 7.81 g/cm3 Gruneisen coefficient Empirical parameter C0 1.36 4550 m/s Empirical parameter s Reference temperature Tr 1.41 Specific Heat Cv 460 J/kgK Parameter of Johnson Cook strength model Shear modulus Static yield stress 0 7.7437×107 kPa 1.172×106 kPa 300 K Hardening constant B Hardening exponent n Strain rate constant C Thermal softening exponent m Melting point Tm 4.935×105 kPa 0.22 0.013 1.015 Reference strain rate 0 1.0 Parameter of principal stress failure model Critical value of normal tensile stress c 2.8×106 kPa Parameter of geometric strain erosion model Erosion strain Type of geometric strain 1.5 Instantaneous 1778 K 55 http://ijass.org 2 (50~63)15-012.indd 55 2015-03-31 오후 1:53:59 Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) for various ridge-cut explosive bolt designs. Some design parameters are chosen that might affect the separation reliability, and behavior analysis is carried out for several designs. From the computational analysis results of ridge-cut explosive bolts, separation reliability can be estimated. Number, position, direction, and density of failed Lagrangian elements can be considered for the evaluation. Through comparison with computational results of the reference ridge-cut explosive bolts, the separation reliability can be evaluated for diverse designs of ridge-cut explosive bolts. 5.1 Explosive weight In the reference ridge-cut explosive bolts, 47 mg of PETN and 50 mg of RDX are used to break the bolt body. When the explosive weight is increased or decreased, shock propagation and the separation reliability are affected. In this study, to observe the effect of the explosive weight on the separation reliability, only the densities of explosives are varied, and the dimensions of the ridge and the fixture are unchanged. Here, four cases are considered as follows: 5. Parametric study of ridge-cut explosive bolts In this study, a separation-behavior analysis method is developed for ridge-cut explosive bolts, and this method allows evaluation of the separation reliability (a) (b) (c) Fig. 6. Pressure contours without failure modeling: (a) at 1.7 μs; (b) at 2.1 μs; (c) at 2.5 μs. Fig. 6. Pressure contours without failure modeling: (a) at 1.7 μs; (b) at 2.1 μs; (c) at 2.5 μs. DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50 56 6 (50~63)15-012.indd 56 2015-03-31 오후 1:54:00 Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes (a) (b) (c) 7 (d) (e) Fig. 7. Material statuses at 5.0 μs for different principal stress failure criteria: (a) 2.4 GPa; (b) 2.6 GPa; (c) 2.8 GPa;criteria: (d) 3.0 GPa; (e) 3.2 GPa. Fig. 7. Material statuses at 5.0 μs for different principal stress failure (a) 2.4 GPa; (b) 2.6 GPa; (c) 2.8 GPa; (d) 3.0 GPa; (e) 3.2 GPa. 57 (50~63)15-012.indd 57 http://ijass.org 2015-03-31 오후 1:54:02 Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) status at 5.0 μs is shown in Fig. 8. According to the comparison with the results for the reference model (Fig. 7 (c)), it is easily inferred that the separation reliability increases as the explosive weight increases. However, this inference is not always correct, due to the side effects of excess explosive. Furthermore, it is quite clear that the separation reliability is affected by the explosive weight 1) the explosive densities of RDX and PETN are increased (RDX 1.815 and PETN 1.77), 2) the explosive density of RDX is increased (RDX 1.815 and PETN 1.50), 3) the explosive densities of RDX and PETN are decreased (RDX 1.485 and PETN 1.26), and 4) the explosive density of PETN is decreased (RDX 1.65 and PETN 1.26). To demonstrate the separation reliability, the material (a) (b) (c) 9 (d) Fig. 8. Material statuses at 5.0 μs for different explosive weight (a) High density RDX and PETN; (b) High density RDX;weight (c) Low (a) density RDX and PETN; Low density Fig. 8. Material statuses at 5.0 μs for different explosive High density RDX(d) and PETN; (b)RDX. High density RDX; (c) Low density RDX and PETN; (d) Low density RDX. DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50 (50~63)15-012.indd 58 58 2015-03-31 오후 1:54:03 Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes elements (i.e., a smaller portion of the bolt) must fail to induce bolt separation, which implies higher separation reliability for the same explosive weight. On the other hand, in the decreased ridge-angle model, the bisection line of the ridge rotates clockwise with respect to the vertex of the ridge, which implies a length increment of the line, as shown in Fig. 9(b). Therefore, more elements (i.e., a larger portion of the bolt) must fail to induce bolt separation, which implies lower separation reliability for the same explosive weight. of RDX, rather than the explosive weight of PETN. This is because PETN is utilized to initiate RDX, and the shock waves mainly generated by the RDX break the bolt body. 5.2 Ridge angle For the reference ridge-cut explosive bolts, the ridge angle of the bolt body is 120°. When the ridge angle is increased or decreased, the reflection of shock waves, the superposition of release waves, and the separation reliability are affected. In this study, the ridge angle (which affects the reflection of shock waves) is increased and decreased by 10°. The meshes used for the increased and decreased ridge angle models are shown in Fig. 9(a) and Fig. 9(b), respectively, with a dashed outline of the reference model. The bisection line of the ridge is indicated by a dotted red line in the reference model and by a dashed black line in the models, with increased and decreased ridge angles. To determine the separation reliability, the material status at 5.0 μs is shown in Fig. 10. Even though the increased ridge-angle model has a larger volume around the ridge of the explosive bolt, it has higher separation reliability than either the decreased ridge angle model or the reference model. These phenomena can be explained by the rotation of the bisection line of the ridge. In the increased ridge-angle model, this line rotates counterclockwise with respect to the vertex of the ridge, which implies a length decrement of the line, as shown in Fig. 9(a). Therefore, fewer 5.3 Ridge position As with the other parameters, ridge position can be adjusted. When the ridge position is shifted to the left or right, the reflection of shock waves, the superposition of release waves, and the separation reliability are affected. In this study, the ridge position is shifted to the left and to the right by 5 mm. To observe the effect of ridge position on the separation reliability, the dimensions of the ridge and the fixture are uniformly varied, as shown in Fig. 11(a) and Fig. 11(b). To illustrate the separation reliability, the material status at 5.0 μs is shown in Fig. 12. Even though the left-shifted ridge-position model has a smaller volume around the ridge of the explosive bolt, it has lower separation reliability than either the rightshifted ridge-position model or the reference model. These phenomena can be explained by the cancellation of the propagating shock waves and reflected release (a) (b) Fig. 9. Mesh with dashed reference outline for different ridge angle (a) Increased ridge angle model; Fig. 9. Mesh with dashed reference outline for different ridge angle (a) Increased angle model; (b) Decreased ridge angle model. (b) Decreased ridge angleridge model. 59 (50~63)15-012.indd 59 http://ijass.org 2015-03-31 오후 1:54:03 Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) encounter trailing shock waves that are not sufficiently dissipated. Therefore, the tensile stress induced by the superposition of release waves is inadequate for failure, waves. In the left-shifted ridge-position model, the distance from the RDX to the free surface of the ridge is reduced, which implies that the reflected release waves (a) (b) Fig. 10. Material statuses at 5.0 μs for different ridge angle (a) Increased ridge angle model; (b) Decreased ridge angle model. Fig. 10. Material statuses at 5.0 μs for different ridge angle (a) Increased ridge angle model; (b) Decreased ridge angle model. (a) 12 (b) Fig. 11. Mesh with dashed reference outline for different ridge position (a) Left-shifted ridge-position model; (b) Right-shifted model. Fig. 11. Mesh with dashed reference outline for different ridge position ridge-position (a) Left-shifted ridge-position model; (b) Right-shifted ridge-position model. DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50 (50~63)15-012.indd 60 60 2015-03-31 오후 1:54:04 Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes 5.4 Summary of parametric study and design improvements which implies lower separation reliability. On the other hand, in the right-shifted ridge-position model, the distance from the RDX to the free surface of the ridge is increased, which implies that the reflected release waves encounter trailing shock waves that are already dissipated. Therefore, the tensile stress induced by the superposition of release waves is greater than that for the reference model. However, the right-shifted ridgeposition model has a larger volume around the ridge of the explosive bolt; and more elements (i.e., a larger portion of the bolt) must fail to induce bolt separation. Due to both effects, the separation reliability will be similar to the reference model. Based on this parametric study, practical design improvements are suggested for the reference explosive bolts. When the explosive weights of the high explosives are increased, the ridge angle is increased; and the separation reliability is increased. Therefore, with an increased ridge angle, the explosive weight can be reduced so that the side effects, such as pyroshock, are reduced even as the separation reliability similar to that of the reference model is maintained. To determine the separation reliability of the increased (a) (b) Fig. 12. Material statuses at 5.0 μs for different ridge angle (a) Left-shifted ridge-position model; (b) ridge-position model. Fig. 12. Material statuses at 5.0 μs for different ridge angleRight-shifted (a) Left-shifted ridge-position model; (b) Right-shifted ridge-position model. Fig. 13. Material statuses at 5.0 μs of increased ridge angle with decreased explosive weight model. Fig. 13. Material statuses at 5.0 μs of increased ridge angle with decreased explosive weight model. 14 61 (50~63)15-012.indd 61 http://ijass.org 2015-03-31 오후 1:54:05 Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015) Meeting of the Pyrotechnics and Explosives Applications Section on the American Defense Preparedness Association, 1983. [4] Balden, V. H. and Nurick, G. N., “Numerical simulation of the post-failure motion of steel plates subjected to blast loading”, International Journal of Impact Engineering, Vol. 32, 2005, pp. 14-34. [5] Bonorchis, D. and Nurick, G. N., “The influence of boundary conditions on the loading of rectangular plates subjected to localised blast loading - Importance in numerical simulations”, International Journal of Impact Engineering, Vol. 36, No. 1, 2009, pp. 40-52. [6] Bonorchis, D. and Nurick, G. N., “The analysis and simulation of welded stiffener plates subjected to localised blast loading”, International Journal of Impact Engineering, Vol. 37, No. 3, 2010, pp. 260-273. [7] Katayama, M. and Kibe, S., “Numerical study of the conical shaped charge for space debris impact”, International Journal of Impact Engineering, Vol. 26, 2001, pp. 357-368. [8] Katayama, M., Itoh, M., Tamura, S., Beppu, M. and Ohno, T., “Numerical analysis method for the RC and geological structures subjected to extreme loading by energetic materials”, International Journal of Impact Engineering, Vol. 34, No. 9, 2007, pp. 1546-1561. [9] Trelat, S., Sochet, I., Autrusson, B., Cheval, K. and Loiseau, O., “Impact of a shock wave on a structure on explosion at altitude”, Journal of Loss Prevention in the Process Industries, Vol. 20, 2007, pp. 509-516. [10] Trelat, S., Sochet, I., Autrusson, B., Loiseau, O. and Cheval, K., “Strong explosion near a parallelepipedic structure”, Shock Waves, Vol. 16, 2007, pp. 349-357. [11] Lee, J., Han, J.-H., Lee, Y. and Lee, H., “Separation characteristics study of ridge-cut explosive bolts”, Aerospace Science and Technology, Vol. 39, 2014, pp. 153-168. [12] Lee, Y. J., The Study of Development of Ridge-Cut Explosive Bolt (I), Agency for Defense Development, 2000. [13] Lee, Y. J., The Study of Devlopment of Ridge-Cut Explosive Bolt (II), Agency for Defense Development, 2001. [14] Lee, E. L., Hornig, H. C. and Kury, J. W., Adiabatic Expansion of High Explosive Detonation Products, Lawrence Radiation Laboratory, UCRL-50422, 1968. [15] Zukas, J. A. and Walters, W. P., Explosive effects and applications, Springer, New York, 1998. [16] Meyers, M. A., Dynamic behavior of materials, Wiley, New York, 1994. [17] Cooper, P. W., Explosives engineering, VCH, New York, N.Y., 1996. [18] Zukas, J. A., Introduction to hydrocodes, Elsevier, Amsterdam, 2004. ridge angle with decreased explosive weight model, the material status at 5.0 μs is shown in Fig. 13. Comparison between the results for the decreased explosive weight model (Fig. 8(c)), and the increased ridge angle with decreased explosive weight model (Fig. 13) shows that the separation reliability is slightly increased due to the effect of ridge angle increment. However, the separation reliability is lower than the reference model (Fig. 7(c)). From this observation, it is easily inferred that the separation reliability are mainly influenced by the explosive weight, rather than by the slight modification of ridge shape. However, the parametric study with design parameters of explosive bolts clearly shows that the separation reliability of ridge-cut explosive bolts are affected by the slight changes in ridge angle and position. 6. Conclusion This study established the separation behavior analysis environments for ridge-cut explosive bolts, based on the ridge-cut mechanism. By using this analysis scheme, a parametric study of ridge-cut explosive bolts was carried out. Some design parameters were chosen that might affect the separation reliability, and the behavior analysis was carried out for several designs. Based on this parametric study, practical design improvements were suggested for the reference explosive bolts. When the explosive weights of the high explosives were increased, followed by an increase in the ridge angle the separation reliability was increased. Especially, the separation reliability was mainly influenced by the explosive weight, rather than by the slight modification of ridge shape. Acknowledgement This work was supported by the LIG Nex1 under the contract YD11-3242. References [1] Brauer, K. O., Handbook of pyrotechnics, Chemical Publishing Co., New York, 1974. [2] Bement, L. J. and Schimmel, M. L., A Manual for Pyrotechnic Design, Development and Qualification, NASA, NASA Technical Memorandum 110172, 1995. [3] Kafadar, C. B., “The Mathematical Foundation for the “Ridge-Cut” Technique Used in Explosive Bolts”, Annual DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50 (50~63)15-012.indd 62 62 2015-03-31 오후 1:54:05 Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes C360 Brass and PZT 65/35 Ferro-Electric Ceramic, Sandia National Laboratories, SAND93-3919, 1994. [21] Johnson, G. R. and Cook, W. H., “A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures”, Proceedings of the Seventh International Symposium on Ballistics, The Hague, Netherlands, 1983. [19] AK_Steel_Corporation, Product Data Bulletin : 17-4PH Stainless Steel, AK Steel Corporation, http:// www.aksteel.com/pdf/markets_products/stainless/ precipitation/17-4_PH_Stainless_Steel_PDB_201404.pdf, 2014. [20] Weirick, L. J., Plane Shock Generator Explosive Lens: Shock Characterization of 4340 and PH13-8Mo Steels, 63 (50~63)15-012.indd 63 http://ijass.org 2015-03-31 오후 1:54:05
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