USOII7S4481B2 «2 United States Patent (10) Patent No: US 11,754,481 B2 Fahem et al. 4s) Date of Patent: ‘ep. 12, 2023 ($4) METHOD FOR DETERMINING MIXED 60) References Cited MODE DYNAMIC FRACTURE. TOUGH SINEERING MATERIALS INVOLVING US. PATENT DOCUMENTS. CAROLINA, Columbia, SC (US) - ‘TONAL (72) Inventors: All F: Fahem, Columbiv, SC (US) Addis Kidane, Columbi, SC (US) Michuel A. Sutton, Columbia, § (OTHER PUBLICATIONS (US) Abagus Fea. “SIMULIAM™: Abagus Unifiod FEA Simulate Real ‘ni Performance with Advanced MuliphysicsSokaions” Dessau Systemes Corp. 2017) pp. 16. Comtinved) (73) Assignee: University of South Caroling Columbia, SC (US) Notice: Subject wo any diselaimer, the tem of this patent is extended or adjusted under 35 Primary Examiner —Pirandi N Hopkins USC. 15405) by $28 days (74) Attorney, Agent, o” Firm — Dority & Manning, PA. (21) Appl. No. 167899,023, 7) ABSTRACT A hybrid experimental-numerical approach is disclosed 1 Getermine the Mixed Mode (UI) dynam facture initiation (5) Prior Publication Duta toughness of engineering materials, Cylindrical Aluaioum 5 . alloy specimens with a V-notch spiral crack on the surface ‘US 202010408657 AL Dee. 31, 2020 at spiral angles of O°, 11.28°, 228°, 33.75 and 48° are Related US. Application Data subjected to dynamic torsion load using torsional Hopkinson bar apparatus. The torque applied t the specimen at the onset of factre is measured throwgh stein gages attached to the incident and transmitter bars. stereo digital image correlation is performed to measure the fllield deforms tion, and the crack mouth opening displacement asa fune- tion of Fong time and is used to estimate te time at which the erack initiation is started. The dynamic stress intensity factors are extracted numerically based on the dynamic {nteroetion iteural method using Abagus. The Mode-l (K,,) Moves (Kya and Mixed Mode (Kyun) dynamic tic tiation toughness is presented as a function of spiral angles and Toaing rte (22) Filed: Jun, 11, 2020 (60) Provisional application No, 63/010,879, filed on Ape 16, 2020, provisional application No. 62/868,015, filed on Jun, 28, 2019. (1) Incr. GIN 322 (2006.01) u oe GOIN 322 (2013.01); GOIN 2203/027 01301) (68) Field of Classification Search crc ‘GOIN 3/313: GOIN 3/30; GOIN 3/00; GOIN 1/36: GOIN 320; GOIN 302: (Continaed) 38 Claims, 15 Drawing SheetsUS 11,754,481 B2 Page 2 (58) Fleld of Classitication Search CPC in. GOIN 33/24; GOIN 3/44; GOIN 21/8851; GOIN 3/22; GOIN 308; GOIN 3/068; GOIN 3/066; GOIN 3/307: GOIN 29/14; GOIN 2208/027; CO3C 28/0025: GOL 1724; GOOB 2/30 See application file for complete search history: 66) References Cited (OTHER PUBLICATIONS amet, ct al. “The Fracture Mechanics of Silke Cracks in Anisotropic Ehstic Mein” J. Mech. Phys. Sol. 20-1972) pp. 3s.306 ‘Chao cal “Relationship BetacenCrck-TipConsint and Dynanic Fracture lotto Toughnes” J. Pres. Hesse Techn, 132021404 (2010) pp. 19. ‘Chao, ea. “Oa the Faire of Cracks Under Mine Mod Loa” Ian 1. Pract. 81 (1997) pp. 201-22 ‘Chea, eal. “Spit Hopkiton (Kolsky) Bar= Design, Testing and Application” Springer (2011) pp. 1-80. ‘Chong, etal. "Now Speimns for Mixod Mode Fracture lnvesti- ations of Geomaterials” Eng. Fract. Mec 30 (1988) pp 701-712. Deng. X. The Asymptotic Stneture of Transient Eastedynamic Fels a the Tip of Stationary Crack” Pro Roy. Soe Lond 4-46 1999 pp. et Doak, eal. “Numerical Evaluation of Domin and Contour Interas for Nonlinear Fractre Mechanics: Formulation an Inp= reataton Asposts” €-of Mods UILU-ENG-206 (1588) pp 2 Duly et al. "A Method for Dynamic Fracture Initiation Testing of| (Ceramics Eng Mater Tech 110 1987) pp. 3253531 Fahem, eal "Misol Mode (Mode Il) Dynamic Fracture Inia tion Toughness of Aluminum Alloy” Challemes in Mechanics of Time Dependent Matera: Fracture, Fagus, Petre and Damage Evolution vo: 2 Springer (2020) pp. 59-64, Fahem, otal. “Mode-l Dyoamie' Fracture Ination Toughness Using Torsion Load” Eng. Fract Mech, 213 2019) yp. 3-71 ahem, etal. "iomelry Factors for Me | Ses Intensity Factor ‘ofa Cyiniial Specimen with Spiral Crack Subjected te Torsion” {Bng, Pract. Mech 244 2019) pp. 79-94 dm. tal. "Ch,L0-Moifston of Benthem Solution for Made [I Fractare of Cinder with Spiral Crk Subjected {0 Torsion” -ractare, Fetige, Fallre and Damage Evolution sl. 6 Springer (2019) pp. 57-03, Fahem, ca. “Ch, 15—A Progsesion on the Defemination of| Dynamic Fracture Initiation Toughness Using Spiral Crack" Frac fare, Fatigue, eile and Damage Bvalton vol 6 Spinger(2019) pp 098 Fahem, AE. “Using a Nondisprsive Wave Propagation for Mex suing Dyaarnie Fracture nition Toughness of Mails: Exper ‘meatal and Numerical Based Stay" U.S. Coralna (2019) pp. rat, Fahem, etal. "Ch. 24 Hybvid Computational and Experimental Approach o [deny dhe Dynamic Initiation Fracture Toughness at Nigh Loading Rate” Dynamic Behaviw of Mata vol. 1 Spinget (2018) pp. 141-14. Fahen, et al "Ch. 26—A General Approach to Evaluate the Dynamic Fracture Toughness of Materials” Dynamic Behovor of Matrials vl. 1 Springer 2017) pp, 185-194 Freund, LB. “Dynami Frastre Mechanics" Cambridge Universiy ress (1990) pp. 1-563 ‘Gos al. "An interaction energy integral metho for computation of mixed-mode tres intensity Tctors along non-panar rack rots in thre dimensions” Eng Fact. Mech. 69 (2002) pp. 299319. ‘Goal, KE "Wave Motion late Solids” Dover (975) pp. 1-689, Jiang eal. “Hopkinson Bar Loaded Fracture Experimental Teck- nigh A Citical Review of Dynami Face Toughness Tots” ‘Aopl Mech Rev. 62 (2008) pp. 1-3 altho etal. Tnstablity of Cracks Under Impulse Lows" J ppt Phys. 48 1977) pp. 986993, Klang etal “Ch. 37 A New Method for Dynamic Fractre ‘Toushness Determination Using Torsion Hophinsoa Pressure Bat” Dynamic Behavior of Material 3.1 Springer QD14) pp. 307312. ‘Kane, eta "ThermosMechanical Stes lds and Stain Energy Associated with a MixedMose Propagating Crack" Acta Mech 218, (2010) pp. $7.60, ‘Ridaney ta. "Mixed-Mode Dynamic Crack Proptgtion in Grad ‘Materials Under Thermo Mechanical Loading” Eng Frat. Meh 77 2010) pp 2864-2890, ‘lepaczko, JR. "Ch. Dynamic CackIntation, Some Exper rental Methods and. Modeling" Crack Dynanis tn Metalic Matrials Springer-Verlag (1990) pp. 285-483 ‘Kung M, “Fat Elements in Fracture Mechanic Theory Numerics Aplications” Springer O13) pp. 1-447 ‘ih etal “Tensile Shear Tranton in Mised Mode VI Factre™ In. Sole Sirct. 2008) pp. 6147-6172. Maigi, sal. “Mised-Mede Quantification for Dynamic Fracture Iniation” Application to the Compact Compresion Specimen” Int 1S. Solids Sct. 0 (1993) pp. 3233-3248, Mallon, etal “On the Huet af Microsiuetue onthe Torsion Response of AATOSO-TT5S1 at Elevated Sin Ras” Mater Si Eng 659 (2015) pp. 280-287 Nala, A “Thooy Of Flow and Fracture of Solis” MeGraw- #1 (4980) pp. 1-572. Naik etal “Intrtaninar Shear Propeies of Polymer Matix Composites: Stn rate elles” Mach, Maer 39 (2007) pp. 1043- ws? ‘Nakamura. “Analysis of Dynamically Loaded Three-Point ‘Bend Ductile Fracture Specimen” Bg, Fact. Mech. 25 (1986) 9. 323399, Nakamura, cal. “lastc-lastic Analysis ofa Dynamically Loaded CCircunftetally ‘Notched Round Bar” Eng. Frac. Meh, 22 (1985) pp 487-482, Nisha. eal. “Path-Independent Integrals, Energy Release ates, and Goncrl Solutions of Nea-Tip ies in Mixed-Mode Dynamic Fracture Mechanics" Eg Pract Mech. 18 (1983) pp. 122 (Owen, et al. “Experimenal Determination of Dynamic Crick Initiation apd PropogationFrsctore Toughness Thin Akin Sets" In J. Frac. 90 (1998) pp. 153-174 Pato ea. "On the Modeling of Fracture of Bit Mech. 61 1984) pp. 710-712 Peyia, etal. "Comutaton of Dynamic Siess Intensity Factors forCracksin Trce-Dinesional Functionally Graded Solus” Pr, Inst Meth. Eng. Pe Ll Mater Des. appt. 2017) pp. -12 ‘Prasad tal. lnhtene of Med Mode UH Loading on Dynamic Fracture Toughness of Mild Ste at Room sad Low Temperatures” Marr Sol Eng. $90 (2014) pp. 54-9. av-Chanda, K. “Dynamic Facute” Elvever Led. (2004) pp, 1st Rav-Chanar, K. “Oa the Fale Mode Tesnitions in Polyarbon- se Unter Dynamic Mixes Londing” In 1. Solid Suc? 32 (1995) pp. 925-938. Tice, J. "A Path ImlopendeatInestal aad the Approximate Analysis of Stain Concentration by Notches and Cracks" J Ap Mech. 38 (1968) pp. 379.386, Shih, cal. "Flasic-Plasic Anaysis of Cracks on Bimteil Inrfaes: Pst I~ Shall Sale Yielding” Jp Mech. 88 (1088) pp 9.6. Sih, GC. “Stsin-Fnergy-Densty Factor Applic to Mixed Mode (Crack Problems” Inv 11. Frat. 10 (1974) pp 305320, Sik etal. “Wave Propagation in an Haste Solid wih a Line of Discontinty of Finite Crack” Qi Appl Math. 27 (1989) pp. 198-213 Sih, GC. *Some Hlastodynanie Problems of Cracks" In 1 Frac Mech. 4 (1968) pp. 31-8 Sundaram, etal) “Dynamic mixed-mode facture behaviors of PMMA and polyeatbonae™ fing Frac Mech. 176 (2017) pp. 186-212 ‘Sutton, ct al. "Image Correlation for Shape, Motion and Dsfrm- tion Measurements Basic Conceps, Theory and Applications” Springer 2009) pp. 1-321 Sole” J ApUS 11,754,481 B2 Page 3 66) References Cited (OTHER PUBLICATIONS, Suton, ea, “The Est of Out-fplane Motion on 20 and SD Digital Image Comelaion Metsiments™ Opt avers Eng 46 (2008) pp 746.75. Suton, M.A. Theeimensonl tl image conebation gue tty deformation and rck-openingpncement nda run ander mixed-mode 1 fondig” Ope Ee 46081003 (2007) he Seen, J "Analysis ofa Proposed Method fo Toughaes Mea srements Using Torsion Testing” Sian Anal ng Ds 201985) pets “hist al. “The Fate Toughnes of Poyshynes by a Novel High ese Tecaigue™ J Marr So 19 0984) pp be? Vrs tal. “Tvee-Dimensional incase Response of Single ge Noch Bend Specimens Sujet nget Lowlig” Noel Suef. Warfare Cr CARDIVNS 1. Wales, tal. “Computation of Mined-Mode Suoss Intensity Fac tors for Cracks in Tree Dimensional Functionally Gra Sols” hg Meh 132 (2006) pp 5 Wang otal. “Using torsional bar testing to detenine facture toughness” Fatigue Fract. Eng. Mater. Strut. 23 (2000) pp. O17 327 Willams, ML. “On the Stress Distibution at the Base of = Satonary Crack" Japp. Mech. 24 (1987) pp. 109-114 ‘Ya, eal "A Mixed Mode Crack Analysis of aoropie Sod Using Conservation Laws of Flatt”. ppl Mech 47 (1980) pp. asl ‘Yu, etal. “An interaction intepral method for 3D curved cracks in ‘nonhomogeneous material with comple intsices™ In. Soles Siruct. 47 (2010) pp- 2178-2199 wi TRI-CR9802 (1993) pp. * cited by examinerU.S. Patent Sep. 12, 2023 Sheet 1 of 15 US 11,754,481 B2 >I ‘crack Front {vvolume Segmentintegral crack lgament area crack front Figure 1U.S. Patent Sep. 12, 2023 Sheet 2 of 15 US 11,754,481 B2 MODEL MODE (I/II1) bo MODEL IIT t 1 f 1 fC 1 1 f oy Bsp=0" Bsp=11.25° Bsp=22.5 Bsp=33.75° Bsp=45° FIG. 2A Bap = 225° FIG. 2BU.S. Patent Sep. 12, 2023 Sheet 3 of 15 US 11,754,481 B2 Niwa Gri Gent 105 S1200T 79 NI10G1 Z0.0F50 NI15G1Z.05 Fa 12061 x60.¢360 niasat za 19061 x0. co Figure 3U.S. Patent Sep. 12, 2023 Sheet 4 of 15 US 11,754,481 B2 bs. sew Sanne 0 eet jose Incident Bar Champ Transmitter Bar! etl FrrSmeesiciaGages | ete | Sheae Strnin ages | Spesimen Figure 4U.S. Patent Sep. 12, 2023 Sheet 5 of 15 US 11,754,481 B2 PHOTRON HIGH-SPEED CAMERAS UGHTS ‘ALU. 2024-13 SPECIMEN AG. 5A {LOCAL coorU.S. Patent Sep. 12, 2023 Sheet 6 of 15 US 11,754,481 B2 250 200 150 3 100 50 9 %6 192 PIXEL INTENSITY Fig. 5D STEREO-DIC SETUP (D0V=8mm, FOV=15mm SPECIMEN ‘STEREO ANGLE 6 =14'U.S. Patent Sep. 12, 2023 Sheet 7 of 15 US 11,754,481 B2 Voltage (VI 2 oe ¢9 ot te S Figure 6A & o 30 09 900 4200 1500 Figure 6B Voltage (V) 666 a 8 0 = 300 600 90012001500 Figure 6C ° 500 1000 1500 Time (uSec.)US 11,754,481 B2 Sheet 8 of 1s Sep. 12, 2023 U.S. Patent a 125° =e MIXED MODE (I/ a S 3375) > 5° ‘AIXED MODE (1 » «QW RR Ze FIG. 7A s° > Bap = MODEU.S. Patent Sep. 12, 2023 Sheet 9 of 15 US 11,754,481 B2 Figure 7B Figure 7C Figure 7D 8 a Normalized Stress, (0,/a;;) ° Ss 0 02 04 06 O08 1 12 Normatized Distanse From The Crack Tip , 8 = 0, (t/a)US 11,754,481 B2 Sheet 10 of 15, Sep. 12, 2023 U.S. Patent (ui) weuareldsig 200 160 s (urn) anbsoy e¢e¢°e 8 Time (wSec.) Figure 8 {ww ) dowd 200 300 400 100 Time (uSec.) Figure 9U.S. Patent 200 i= a 3 120 % 8 Effective Torque (N.m)} B 3 DSIF (MPams~1) Sep. 12,2023 Sheet 11 of 15 US 11,754,481 B2 ~ ay 5 wv ” Bl "Ae ! at tl MH rls ei 4 \ \ a) Re oa. peo 100 200 300 400 Time (uSec.) Figure 10 26 a Crack initiation 16 > 0 200 400 600 Time (pSec.) Figure 11AU.S. Patent Sep. 12, 2023 Sheet 12 of 15 US 11,754,481 B2 m6 pe > Crack initiation o lE 16 _I 3 omni a KIL = 6 wen KHL et Re ammean K w . a 4 0 200 400 600 Time (Sec.) Figure 11B 30 pres Crack initiation nN So —{K! sommes KE women KAT oS oman K J DSIF (MPaVms™) Ss ney ° 0 200 400 600 Time (jtSec.) Figure 11CU.S. Patent Sep. 12, 2023 Sheet 13 of 15 US 11,754,481 B2 penn Crack initiation 40 . ie 25 & = 10 & GB a 5 0 200 400 600 Time (uSec.) Figure 11D ae r= Crack initiation 4 ‘E 25 —_ K} Se seen & Kil = 10 seme KT ty oom KJ =~ a aQ 0 200 400 600 Time (j1Sec.) Figure 11EU.S. Patent Fracture Toughness (MPayii) Fracture Toughness (MPayiii) 40 35, 30 Bw Sep. 12,2023 Sheet 14 of 15 US 11,754,481 B2 Rie > Kua! Kie < Kia Translation zone oo Kua 10 2» 30 40 Crack Spiral Angle (Oegree) Figure 12A 10 20 30 40 Crack Spiral Angle (Degree) Figure 12BU.S. Patent Sep. 12, 2023 Sheet 15 of 15 US 11,754,481 B2 120 Translation “ ® 100 a gs zone @_ oem zZlE 80 + © eee R; EE 60 wre gS fe & : mE 40 FO Rin 20 F 0 1 20 40 60 Spiral angle (Degree) Figure 13 60 - Dynamic conditions = -~-~--~— > Intecmediate High and very high so (Medium tzeing Pate 4 Loading Rate 30 (Owen et al. 1998) 20 & 2 Quasistatic Loading Rete (Less than 0.002) 200 Loading Rate, Ry (GPayi/s) Figure 14US 11,754,481 B2 1 METHOD FOR DETERMINING MIXED MODE DYNAMIC FRACTURE TOUGHNESS (OF ENGINEERING MATERIALS INVOLVING FORMING SURFACE CRACKS IN ‘SPECIMENS CROSS REFERENCE TO RELATED 'APPLICATIONS| ‘This application claims filing benefit of U.S. Provisional Patent Application Ser. No, 62/868,015, having a fing date ‘of Jun, 28, 2019, and claims filing benefit of U.S. Provie sional Patent Application Ser, No, 63/010,879 having a filing date of Apr 16,2020, boll of which are eailed "METHOD TO. DETERMINE MIXED-MODE (Ill), DYNAMIC FRACTURE TOUGHNESS,” and both of which are fully Incomporated herein by reference, and forall purposes BACKGROUND OF THE PRESENTLY DISCLOSED SUBJECT MATTER Dynamic fracture has been @ topic of interest in the scchanies and material science communities in the last for decades (Freund 1990; Ravi-Chandar 2004), Generally speaking, fracture mechanics isan available tool for address- ing the tsk of improving the performance of mechanical ‘components. In such context, racture events ar classified ‘shaving specific determined Mode ehiracteristcs, In par ticular, Mode relates to opening mode (tensile stress nor malt te plane of the crack). Mode-ITs called sliding mode (shear stress aeting parallel t the plane of the crak and perpendicular to the erck front insplane shear). Mode] Folate ta tearing mode (a shear stress acting parallel to the plane of the erack and parallel to the ersek froat; out-of plane shear), ‘Mixed Mode fracture (Mode I and Mode 11) are seen in thin-walled stroctares and structures that are subjected 0 axialtorsion loading, such as pipes, airraft wings, shafts, and rotor blades, as well as to biomedical applications ‘Understanding the dyaamie Iracture peopentes of materials under the Mixed Mode condition i essential for the integrity and safety of structures. Though there is lot of progres in the gener! understanding of Iracture (Owen etal. 1998), Timited data is availabe in Mixed Mode dynamic fracture of materials. There are few experimental methods available to measure the dynamic fracture properties of materials under Mode-I or Mode-II conditions (liamg and Vecchio 2009) However, there is no standard experimental method measure the dynamic Mixed) Mode fracture properties of materials, especially for the Mode VMode Ill condition (ahem 2019), Some of the early work on a static and dynamic Mixed Mode ffacture are summarized below. In 1974, Sib devel- ‘oped a theoretical solution of the Mixed Mode fracture is disclosed to determine the Mixed Mode (VID) dynamic ‘ractute initiation toughness of engineering materials. Cylin- drical Aluminum alloy specimens with a V-noteh spiral crack on the surface at spiral angles of 0°, 11.28%, 22.5, 53.75", and 45° are subjected to dynamic torsion load using torsional Hopkinson bar apparsts. The tue applied to the specimen atthe onset of fracture is measured through stain _2nges attached tothe incident and transmitter bars. A stereo ‘digital image correlation is performed to measure the full. field deformation, and the enick mouth opening displace- ment as a fonction of loading time and used to estimate the time at which the erick initiation is stated, The dynamic sine intensity factors are extracted numerically based on the dynamic interaction integral method using Abaqus. The Moder (K,,), Mode-TIl (Kj) and Mixed-mode (Ky) dynamic initiation toughness is presented as a function af spiral angles and loading rate. For some presetly disclosed subject mater, the dynamic Jacture initiation toughness of Al. 2024-T3 under Mode, Mode IL, and Mixed-mode (VII) are measured experimen- tally and numerically. The experimental method and numeri- ‘cal method may both be used, as discussed herein, with reference to exemplary results ‘One exemplary embodiment of presently disclosed subs Jeet matter relates in pertinent part to a method for deter mining Mixed Mode dynamic fricture toughness of engi- hering materials. Such method preferably comprises providing a least wo specimens ofthe subject engineering ‘materials to be rated; forming a surface rack in each of the specimens at a respective selected angle representative of slfferent fracture Modes; respectively subjecting the speci mens to dynamic torsion load; respectively: measuring torque applied to each of the specimens at the onset of facture therein; respectively measuring the ful fiekdl defor- mation and the erack mouth opening displacement of each such facture as a fonetion of loading time; respectively ‘estimating the time at which each erack initiation is started, ‘and respectively determining dynamie stress intensity foc: tors for the specimens, based on such measurements and determinations “Another exemplary embodiment of presently disclosed subject matter relates in pertinent part to a methodology for o 4 determining dysamie Mixed-mode (VII) of materials by investigating. plurality of spiral erack specimens from pure ‘Mode up to pure Mode- throughout the dynamie Mixed- sede (VII) of fracture under pure impulse torsional load Such methodology preferably comprises using « torsional Hopkinson Bar to generate a torsional impulse load foreach specimen: using one-dimension wave propagation theory to ensure a fatfield maximum fracture load for each speci- ‘men; determining under pure torsional foad dynamic stwss intensity fectors of plural specimen spiral eracks with di erent crack angles: and using dynamic intersction integral ‘numerical calculation to idealfy dynamic fracture initiation propertios Ky Kirn aid Kygy of Mode-l, Modell and Mixed-mode (ill, respectively ‘Yet another exemplary embodiment of presently disclosed subject matter relates in pertinent part 0 methodology 10 estimate dynamic facture properties for Mode I, Mode Il, fand Mixed-mode Vil fratare conkitions for engineering ‘materials subjected to critical load with different loading rte without inertia elect. Such methodology preferably comprises applying loading to a plurality of specimens of ‘engineering materials suficent to induce Iracture therein in plural Modes of fractire conditions; measuring initiation {ime (oF fracture event; measuring ineident tongue during 4 fracture event, inputting measured incident torque to 3 finite element model; calculating the interaction integral of ‘unit virtual advance ofa finite crack front segment for a Specific mode at a particular point as a function of times and using the components of dynamie interaction integral t0 calculate the dynamic stress imensiy factor for each mode Additional objects and advantages of the presently dis closed subject matter are set forth in or will Be apparent t0 those of ordinary sil inthe art from the detailed description hherein. Also, it should be further appreciated that modiica- tions and variations to the specifically illustrated, relerred and discussed features, elements, and seps hereof may be practiced in varios embodiments, uses, and practices ofthe presently disclosed subject matter without departing from the sprit and scope of the subject matter. Variations may inchide, bt are not Kinited to, the substitution of equivalent means, features, or steps for those illustrate, referenced or discussed, and the functional, operational, or positional reversal of various pats, feature, steps, or the like SUill further, it is to be understood that different embodi- ments, as well as different presently profered embodiments, of the presently disclosed subject matter might inelude various combinations or configumtions of presently dis closed features, steps, or elements, or their equivalents (Gncluding combinations of features, parts, or steps or con- figurations thereof not expressly shown in the Figures or stated in the detailed description of such Figures). Addi- ‘ional embodiments of the presently disclosed subject mat- ter, not necessarily expressed in the summarized section, ‘may inchule and. incorporate various combinations of aspects of features, componeats, or steps relerenced in the ‘summarized objects above, andor other features, compo- fens, oF steps as ctierwise discussed in thi application. Those of ordinary skill in the aet will better appreciate the ‘features and aspects of such embodiments, and others, upon review of the renainder ofthe specification, and will appre- ciate that the presently disclosed subject matter applies equally to coresponding methodologies as associated with the practice of any of the present exemplary devices, and BRIPP DESCRIPTION OP THE FIGURES. A fall and enabling disclosure of the presealy disclosed subject matter, including the best mode thereof, directed toUS 11,754,481 B2 5 ‘one of ordinary skill inthe artis se forth inthe ypecifia tion, which makes reference to the appended Figures, ia whieh FIG, 1 isa throe-imensional schematic of a partition of 42 spiral erick, pointwise volume integral domain, and ‘q-Function (per Fabiem etal, 20198): FIG. 2A illustrates specimens of Aluminum 2024-13 with {ull spiral v-notches of Mode-IIl, Mixed-mode (I+IH}) and Mode, respectively; FIG. 2B illusrates one close up an example from FIG. 2A, regarding a eylindrical specimen with spiral v-noteh at ‘an angle of 22.5° prepared from Aluminum 2024-73, and showing overprinted dotied-lines identiying the subject spiral angle IG. 3 illustrates a schematic of various examples ofthe subject exemplary spiral path dimensions, for the subject ‘examples of FIG. 24; FIG. 4illistrates a schematic of @ Torsional Spit Hop= kinson Bar (TSHP) and the respective subject Specimens of 2 FIG, 2A (with certain dimensions ia mm): FIG. 8A illustrates an exemplary representative Stereo Image Correlation Setup: ‘51 illustrates an exemplary typical speckle pattem: Di Tl FIG. 5C illustrates a Tocal coordinate system and Crack > Mouth Opening Displacement (CMOD) for an exemplary specimen of FIG. 5B: FIG, $D illustrate « graph of gry cae intensity, FIG. SE illustrates a schematic of stereo cameras posi- tions (se also with reference to Table 2) TIGS. 1A theoagh 6C illest respostve typical wave signal graphs for respective crack angle examples of: (A) 0". (B) Py l125°, and (C) P45" “1G 6D represents the numerical sul ofa stress contour stsibtion sound a crack tp FIG. 6E graphically ilustates normaliod stress (von Mises stress Far-Field Stess) versus nomalized distance from a erck tip along the evack Higament; TIG. 7 ilustates reapetive 2fnite clement models of spiel cracks and siess profiles around crack tips forthe spective spa crock angular examples coc ilstatd oe referenced in FIGS. 2A, 3, and 4, HIG. 8 graphically llsirats typical Digital Image Core ‘elation (DIC) and stein gages data versus iitation times Tor a representative 48° let speci: IG. 9 graphically ilustates Crack Mouth Opening Dis- placement (CMOD) data Verss time, for respective spiral ‘rack angular examples each ilostated of refereed in FIGS, 28, 3, and 4 FIG. 10 graphically illustrates Effective Fracture Tox sional Load data versus time, lor respective spn erick angular examples each strated or referenced in FIGS. 28, Sand 4 FIGS, 11 though ILE respectively graphically ilstate Dynaonie Stes Intensity Factors fr respective spiral era angle examples of (A) Pure Mode-Il(f.,,~0.0", (B) Mixed Mode Vil (he -1123% (©) Mino Mode 1 fu22 5) (©) Mixed Mode UIT (hy-38.75°), and (FE) Modest Bar45 FIG. 124 graphically ilustates variations of Dynamic Mode-, Model, Mode-I, and Mixed Mode (M) of frac: ture toughness versus respective spiral crack. angular ‘examples each ilstated or ference in FIGS, 2A, 3, and © FIG. 128 is a repeat ofthe graphical illustrations of FIG. 124, with added grap lines t interconnect respectively related data pos o 6 FIG, 13 graphically ustrates variations of loading rate celfects versus respective spiral eaek angular examples each illustrated or referenced in FIGS. 2A, 3, and 4; and FIG. 14 graphically illustrates variations of loading rate clfocts versus respective initiation facture toughness data {orrespective spiral erack angular examples, each illustrated or referenced in FIGS. 24, 3, and Repeat use of relerenee characters in the present spociti- cation and drawings is intended to represent the same oF ‘analogous features or elements or steps of the presently closed subject mater, DETAILED DESCRIPTION OF THE. PRESENTLY DISCLOSED SUBJECT MATTER Itisto be understood by one of ordinary sill inthe at dat the present disclosure isa description of exemplary emboat als only, and is not intended as limiting the broader aspects of the disclosed subject matter, Each example is provided by way of explanation of the presently disclosed Subject matter, not limitation of the presently disclosed subject matter. In fat, twill be apparent to those skilled in the art that variows modifications and variations ean be made in the presently disclosed subject matter without departing from the scope or spirit of the presently disclosed subject ‘matter. For instance, features illustrated or described as part ‘fone embodiment can be used with another embod yield sil futher embodiment. Thus, ii iatended presently disclosed subject mater covers such modifications fad variations as come within the scope of the appended claims and thei equivalents "The present disclosure is generally ditted to measuring the fictire toughness of material with a different loading rate and differnt fracture mode without inertia effet |. THEORETICAL FORMULATION 1.1 Elastodynamic Analysis of Stationary Dynamic Crick ‘ora stationary crack in an isotropic linear elastic mate- rial, the Wiliam’ quasi-static stress profile around the rack tip is held under dynamic loading conditions. As the dynamic initiation fracture toughness is the goal of this work, itis essential to demonstrate thatthe dynamic stress around the crack tip as a similar form ofa static ease (he, the fist four terms in William's series expansion solution can be used for the static and dynamic problem as wel) (Williams 1957b; Sih and Loeber 1969: Deng 1994; Chao et al 2010). In general, when all three modes exist, the linear elastodymami¢ asymptotic crack stress field solution of ‘material close to the crack tip can be writen as Eq, (1) (round 1990, RavicChandar 2008). When the rack tip velocity is equal to zero, v-0 (ams), then Eq. (1). can represent the stress field for a stationary erick under dynamic loading, cuir ene ocmanfensaueigianermingions © where: 6, Dynamite stress tensor (Cavey stress) 1.6, Polar coordinate system located at the erack ime of leadingUS 11,754,481 B2 1 vensionless funetion of 8, and erac tip velocity + full details in (Freund 1990; Ravi-Chandar 2004) K(0) The dynamic stress intensity factor IL [0] Refers to diferent three modes Opening, ln-plane seas, and Out-oFplane shear ‘The total dynamic energy release rate criteria J,(), Grif fith energetic fracture criterion is used to extract the fracture parameter (Williams 1957%; Freund 1990). For 2 Mixed ‘Mode dynamie fracture, the dynamie energy release rate ean be written, as shown in Fg. 2): na b= SE aonGio s Auton] Ate ew is crack tip velocity, ¢y and ¢, ate the elastic dilatational wave speed, and elastic shear wave speed of the material respectively: iy and are seal factors of dilatational wave and shear wave speed, respectively (Freund 1990), "The properties of Fa. (2.1) do not depend on the load applies or the erek geometry, and as v-+0" (mv) (stationary ‘dynamic erack), all values become a unity, Appeal (r= und 1990; Ravi-Chandar 2004). As a result, fora stationary ‘rack, the dynamic energy release rate eritera, Eg. (2) can, ‘8 shown in Eq. 3), ° (On the other hand, for linear elastic materials and in a plane strain condition, the erack tip area is autonomous, the ‘rack tip is completely surounded by a very small plastic ‘area compared to other dimensions (small-scale-vielding (SSY) condition) (Rice 1968; Freund 1990). "Thus, the ‘integral can be related tothe toa stress intensity factor K,, through the properties of the material as shown in Eq. (4 sn “Thus, the total dynamic energy’release rates representing the contribution of all modes, Ky=AK,, Ky, Ky,)- Subst- tating equation Eq, (4) into Eq. (3), the relation hetween the total Mixedmode stress intensity factor K,, with the indir vidual modes can be written as show in Bq. (5) where #. B, and v are the shear modulus, modulus of ‘elasticity, and Poisson's ratio of the material, respectively. 0 o 8 The dyamic interaction integral method was used to cal= culate the individual J-integral related to the stress intensity ‘actor, as briefly discussed in the following section. 1.2 Dynamic Ineraction Integral Method The J-integral i a scalar quantity and t does not have any rection related to the fracture mode, The interaction ine- aral method is a technique used to exirct the amount of ‘integral that relates to each mode of fracture separately. For a general dynamic condition, the J-integral fon for non-growing crack is extended by adding the kinetic energy density (T) to the stain energy density (W) ofthe material as shown in Bg. (6) (Nakamura etal 1985, 1986), sayin (erm oon er ® 162) In dynamic fracture mechanics, the inertia force terms can be developed by quick erick propagation or by rapidly applying 2 dynamic load (Freund 1990; Ravi-Chandar 2004). In this work, the erack was analyzed in a stationary condition, ic. means no crack propagation oF inertia Toad {rom the erack propagation was considered. Also, the (or sional impulse Toad does not have axial inertia force as the ‘wave propagates from the incident bar to the trnsmited bar through the specimen (Dufly et al. 1987; Klepaczko 1990) ‘Thus, Fq, (62) can be eliminate. FIG. 1 is threeimensional schematic of a partition of 4 spiral crack, pointwise volume integral domain, and «gefumetion (per Fahem et al. 2019b). Thus, for a3-D curve (like spiral crack), the divergence theorem was applied t0 Fg. (6)to conver it from the line integral o area and volume intra, as shown in FIG. 1. A schematic ofthe segment of the volume inteyel domain at specie point on the rack ‘ron is extended from point a to point through the volume center point b. The general solution of J-integral of the volume sezment on a spiral erack front without thermal sin und neglected Kinetic energy is cleulated ws shown ia previous studies (Vargas and Reber, H1. Dodds 1993; Gosz and Moran 2002; Walters eta 2006; Yuet al. 2010; Peyman etal. 2017), Eq. (7). Sle ‘The mean value of the integral at point b (he middle of | the volume segment) can be written as Fa. (8) Funsa= [gestUS 11,754,481 B2 9 where: ‘s): The energy release rate at point (9) corresponding (0 the weighted fhnetion qs) Ts: A dynamic weighted average of J-integral over the volume segment, FIG. 1 V- As illustrated in FIG. 1, the volume enclosed by surlaees $°, S), Sa Sy Sy S*,S,.34° The crack face surfaces, an upper surface, an ‘outer surface, an inner surface, and bortom surface respectively, of the volume domain shown in FIG. 1, (3: Contour path around (6) point and perpendicular on ‘the spiral erack front that swept along to gonerate a volume integral domain (V). 4g¢: The smooth continuous weight funetion (unity atthe ‘surface close to the erack tp S, and vanish atthe outer surface S,, Sa, Sy) FIG. 1B ty: Cauchy stress tensor and strain tensor Position along the erack front (6 The material density, whieh is eonstant ‘A,: The project area of the q-finetion KT Rn Kal ac Da Bal Be [Eneantscon On the basis of the dynamic J-intepral formula, an x= iiary load field was added to the spirals erack fro. The suuiliany loading field was added to the actual field load. “Ths, the superposition J-integral around the crack front was calculated. Then, sccording to the definition, the dynamic Jmeraction integral J, ean be writen as Fq, (9), (Shih and Asaro 1988), Frac Pe POI In general, Fg. (9) can be written in thee different modes that depend on the auxiliary loading field as Eg. (10), ae an, § Larue cgreresin et Snir oF. 7 a) he esl of (1038s slong a 3-D segment by using a weighted function, q() as shown in Eq. (11), 0 o a a where: Jer (Oren OD Toner", Fe 001 “The Tn, (b.) is the interaction integral of unit vital advance Ota finite crack front segment fora specie mode fata particular point as a function of time. The diseretizd orm of interaction integral for a three-dimensional domain ‘is used in a finite element solution. As discussed inthe next section, the components of dynamic interationinteyral ill be used to calculate the dynamic stress intensity factor for each mode. 13 Extraction of Stess Intensity Factors In the ease of iotropic linear elastic materials and inlai- ‘esimal deformation, the actual J-intepral J, coresponding testes intensity factors can be written, os shown in Eq, (12) (Bamott and Asaro 1973: Shih and Asaro 1988; Simulia 2017). where: ee Se eee ere eee eee 08 Ba = ge and ‘he J-integral defined in Bg, (12) isa peneral relationship that can be used for static and dynamic initiation conditions since it epresens the total energy release rate on a crack. ‘The integral intersetion method, as introduced by Asaro and Shih (38.40), was used again to separate the J-integral into the comesponcding SIFS associated with diferent fractre modes, Following a similar procedure, the interaction-intogral, Bq, (9), in addition to using an auxiliary stress intensi ctr, nthe dynamic interatioa inteyeal- asshownin 1-68 5 prscis a pure Mover. The rise time ofthe incident ‘eave iv about (495 se, The factre i nite at about {)2170 yee shown inte ronan signal. Right afer Crick ition. Tange portion of the incident wave is reflected a shown in the reflected wave, FIG, 6D shows a Sypial signal of Mined Mods fracture forthe spl crack ile fiy11.25. There time ofthe incident wave rains tthnoa fe same compare withthe Py? However, the fracture ination time has increased 1 about a5 pce FIG. 6C shows a specimen with a spiral cnc angle Is ve fp AS! and it reprosetsa pure Modo face. There {ie ofthe incident wave remains about te same at, 9525 tse, however, the fractreintiaton Time increases 10 {Ua375 sce. I should he noted here that sine the effective Jeng of the specimen is inresing, the stored potion of the cident ba has fo be Ke longer to incre the pod Of the inekent wave without alerng the ampli. As Shown in FIG. 6, the period ofthe nsident wave i higher ty about 100 jsce compared withthe By, and 11" nll experimental works, the dynanie facture initiation acre at he time pont Below the maximum vale ofthe transmitted wave, about 99% of the peak vale. Further thors, the eansmted wave signals are changing according {othe specimens” size andthe spiral erick pitch length 3. NUMERICAL SOLUTION ‘The dynamic interaction integral equation developed above was solved numerically by using commercial so Cover) Pee aoa ons ona Cover Pcs 086 china? gaers Fecal Legh x Sita 130802 raao10 Fecal Lent y S009 oma ies Saenz toot cone en TABLE 4 Digital age cota ave partes Insp Parsntes vines ‘Sis aie Px Pe we Averae Speke se (Pel Pt) Sis ineprlaion pias 9 cages) 1 degeee 24 Experimental Stnin Gauge Data FIGS. 34 theough 6C ilstrate respective typical wave sianal graphs for respective erack ange examples of (A) By, (B) Pyrl1.28, and (C) B85" elie pxion a) 1883 (am) ua dep) 000 ware Abas SIMULTA 2017. The numerical version of {he sami iteraction integral is shown in Fa (20) Vargas find Robert, 1 Dove 19%, Wolters etal. 2006). The Stes, tins, and displacement were cxkulted and Sssemblod witha standard Gaus quadrature procedure tall the integration points in each element inside the volume Ye if as HONEA teeming e In Bg. 20), G.Q.P is 4 Gassian quadrature integration pinta cack clement, wis repectve weight Sinsion at Exch inegration point [7], i evaluated at Gass points (Kuna 2013), and det Fis determinant of Jacobian for 3D Coordinates. ihe FE commercial software Abas Sona ‘Dynamic-Implicit 2017 was used to salve Fq. (20). Addi- ‘ona dt forthe numeral solution meted aeailable athe open irate for exam, se (Dos a Vara 18; Watters etl. 2006; Kuna 2013) 0 eo oUS 11,754,481 B2 15 3.1 Finite Element Model A numerical method is performed to calculate the ‘dynamic stress intensity eto, as presented in Fg. (14), Due to the nature othe torsional load, which is uniform slong the spiral length, modeling a quarter section of the specimen is suficient (Kidane and Wang 2013: Fahem and Kidane 2018). A commercial finite element software Abagus-Dy- amie was used to solve a finite element model of a quarter spiral erack spocimen and with the ineident and tansaitted Hopkinson torsional bars (SIMULIA™ 2017). The typical finite element model for the different spiral crack angles is shown in FIG. 7. In particular, FIG. 7. illustrates respec- tive finite element models of spiral eracks and stress profiles ‘around erick tips for the respective spiral erick angular ‘examples each illustrated of referenced in FIGS. 2A, 3, and ‘4. For the specimen's model, a circular tube with 19 mm. ‘extemal and 12.7 mm intemal diameters are considered. The tube cross-section extruded fora suitable let, as sho in Table (5), TABLE Soin nah ued a ae Pe eres seas ao esa : Face Mole Mode (Ul) Mode (UI) Mode) Malet A shell revolve was used to make # spiral seam crack slong the specimen length with all models. Since the Jin- teas the base of the integral interaction method, the very refine mesh around the crack tp is not required since the ‘integral is path independent (Kuna 2013), The middle volume of the solid eylinder was divided into a sufficient numberof elements that generated a robust mesh around the ‘rack tp, as shown in FIG. 7A. The model was built with 3 3D solid structure quadratic hexahedral C3D20R element. The incident tnqve measured experimentally Was used as ‘input tothe finite element model. The boundary conditions x applied inthe specimen in FIG. 7B as follows: First, one ‘end ofthe bar (Front surface) was fixed in three dimensions (,y, and 7). Socond, the impulse torsional load was applied ‘on the other end (back surface) a a moment load (Fahem. tnd Kidane 2017, 2018). The dynamic stress profile tthe fracture initiation time, tp atound the crack tip fom pure Mode-III to pure Mode-1 throughout the transition Mixed Mode are shown in FIG. 7A. FIG. 7A shows clearly the gradual change of stress profile fom pure Mode-I, though Mixed Mode (UII), up to pure Mod ‘The typical numerical result ofa stress contour distribu tion around the crack tip is shown in FIG. 7C. FIG. 7C shows a fll field of the stress result atthe time of erack initiation, whichis similar to the static stress profile under plane stain condition. The normalized stess, (von Mises sires, o/Far-Field Stress, 0), versus normalized distance Jom the erack tip along the érack ligament, a is ilusrated in FIG. 7D, 4, RESULTS AND DISCUSSION ‘The dynamic interaction integra, dyna sts itesity fect, and numerical solutions tha were discus i the ous selon ar sed lo estsae the dyoanie nition Ferave toughness of materials ith differen spiral erck 16 inclined angles, In this work, the temperature effect is ‘neglected, and the crack assumes tobe a stress-free surface and a linear elastic isotropic material. Furthermore, the <éynamie interaction integral-dynamic stress intensity factor 5 terms are presented at each efaek point on the crack front ‘and assuming the zxial ineria foree is too small and is Siscarded inside the integral domain. The results ane pre- sented in three subsections: 1) fracture initiation time mea- ‘ing: 2) dynamic stress imensity fietor and dynamic initiation fracture toughness; and 3) the effect of bath Fading rate ad pra ale othe xed Mode tre 4.1 Time of Fracture Initition ‘The first main parameter to measure is the initiation ime of the facture The fractured time was measured By {0 experimental methods: stain gage signal and 3D-DIC. With the sirain gages signals, the fracture initiation time was ‘dentifed t the location where sudden change inthe tans- sited and reflected signals are occuring, The stereo digital mage correlation was used to measure the Crack Month (Opening Displacement (CMOD) as given by Eqs. (19.1- 193). Using the DIC dat, the displacement of the crack ‘edge at wo poiats (upper (ECD,) and lower edge (ECD, ) ‘cross the erack line was measured to calculate the CMOD. PIG. & griphicaly illustrates typical Digital Image Cor. relation (DIC) and strain gages data versus initiation times fora representative 45° test specimen, In particular, typical ‘ransmitted strain gage data (items of applied torque), the edge crack displacements, and the CMOD forthe specimen ‘with the spiral angle of 43° are plotted in FIG. &. As shown in FIG. 8, there isa distinct future in all the plots around 395 jsee indicating the fractre initiation time. The frac- ‘ure ination time was proved to be very’ consiste based ‘on a mimber of repeated experiments FIG. 9 graphically illustrates Crack Mouth Opening Di placement (CMOD) data versus time for respective spiral rack angular examples, each illustrated or referenced FIGS. 2A,3, and 4 FIG. 10 graphically lustraws Effective Fracture Tor. sional Load data versus time for respective spiral crack angular examples, each illustrated or referenced in FIGS. 2A, 3, and 4 ‘Typical CMOD and effective torque fo all spiral erack angles c.-0", 11,25", 22.5, 38.75", and 45° are shown in FIG, 9 and FIO. 10, respectively. As show in FIG, 9, a all the cases, there isa distinet change and 2 the slope of the CMOD at the time of facture ini js also apparent from the plots shown in FIG, 9 and FIG. 10 ‘that the erack initiation time (incubation rime) inereases as the spiral angle increases from 0° 10 48°. The resus of lgctire time for Aluminum 2024-T3 related to @ range of spiral angle and fracture modes are shown in Table 6. Daring the incubation time, for fracture subjected to & constant sttain rat, the microcrack developed, and finaly, unstable crack initiation and propagation happened. The effective torque plot shossn in FIG. 10, indicates that, 28 the angle changes from 0F to 45° degree, the influence of Mode-1 0 TABLE 6 o esion Frcure Te Rela Spal Anse fe ass sows wm) Sa ms an Frcure Mle Mode (UI). Mode QH)Mode (i) Modes NieUS 11,754,481 B2 7 ‘42. Dynamic Stress Intensity Factor and Fracture Toughness TIGS. 114 dough HE respectively graphically tate Dynamie Stes Intensity Factors for fespectve spl erck fe examples of (A) Pare, Modell (fy) 00, (2) ined Mode Vill (Py11.28"), (C) Mined Made Wil (G25, (D) Mined Mode VI (f-33.75"), and (E) Moc (Bg 48" In prtica, the dynamic stess intensity factor of Ale tminum 2024-13 sea finction of ime forall the spiral angles considered obtained from the finite element analysis ate tiven in FIGS, ILA through ILE, respectively. As shown in the Figures, as expected, Modell ts lst ero for all cites, wh 2 maximum eror of 0.17% of the ot facture Joad At 0° spiral angle the Fracture is gover by Mode- i, wih almost no contribution from Mode As the angle changes fo Oo 45%, th contibution of Mode-1 Becomes ‘apparent. Finally, at 45°, the fracture becomes dominated by Mode-1 Since the fracture initiation time is known, as discussed above, the dynamic fracture initiation toughness snd the stress intensity corresponding othe initiation instant the dynamic fracture toughness results obtained in this study, ‘TABLE 7 Sind cure ge ___Druanskision Tugs av Mole _Dewee) Ky Kur Kms Konanetuun % BK gs For pure Mode-II facture wilh circumferential cack ‘with 0 the dynamic facture intron onghness i 13 Mnf wich ie lene than the quar tate factor tough. ness Kye Theater ean fi with ering (Mode) vader ‘yma loading condiions aa value of lees tan 33% of the quasi-static ature toughness value. "AS the spiral crack angle increased 10 iy-I1.28 the Mode contribution stared 10 appear quickly and Mode 1 tecome higher than Modell” KyI8.10 (Pav) Kin 1289 (MPaVin, and the tual Mixed-mode facture nd Kymd-2053 (MPavin). At this angle, the total frac- {ure toughness iy stil lower than the Mode-T quasistatic fracture toughness value HIG. 124 graphically ilstates variations of Dynami Mode, Model Mode und Mixed-ode (M) of fue: ture touginess versus respective spiral crack angular ‘xamples each iistated or referenced in FIGS, 24,3, and 4.116.128 sa repeat ofthe graphical ilusrations of FIG, 12, with added graph Finest interconnect Rapectively related datapoints. ‘As showa ia FIG, 12A, when the spiral angle inreases further from 11.28° w 225°, the contibuion of Mode] becomes doatiuat, aod the coatibution of Model become wenker. However the dynamic Mixed-mode fae- ture toughness is stil fower tha the quasistatic Modest fracture toughness unl the spiral ange s more than 22-5 The specimen with a spiral angle Between 22° 9 38.78" cat be considered ava translton zone. In this range, the ‘ontibution of Mode-T becomes above 50%, In ation, at 0 o 18 the spiral ange of 38.75", the dynamic Mixedsmoe facture toughens become higher than the quasistatic Mode-T frac: ture toughness, As spiral erick angle Ther nereses, the contribution of Mode inreane from 96% a -33.75° to 99.8% at B45" ‘The spirtl crack angles show a erica effect om the nani intation fracture toughness behavior. With spiral angle between 10"<),220°, the Mixedsmodeo fracture ean te measured esly For the spiral erack at an angle less than BS, the results ales coset pore Mode-IL, When the spiral crack angle 22, Modest has the most significant effet on the toa fracture driving foes: even Modest Shows a light elo that came from the numerical solution ron whic cannot be avoids. The loading rate of fracture {hot develops with a spiral erack angle shows more signifi cant results as shown in the next section. 43 Loading Rate and Dynami Fracture Toughness ‘A lading rate parameter is used in dymamie fractore necanics stead of sean ate de to the singularity field athe crack tip The Toaing ate, provides the measure of loading applied pe tine around the rack tip, and it has a similar mit of sess intensity factor , where (ys a facture initiation time, In dynamic fracture smechanis, the loading rate can be divided into two eatezo- Fes: intermediate loading rate at 1.0 (MPaviis), andthe factre loading increases exponentially with a spi crc ale ‘Wit spiral crack angle more than 33.75%, the fracture ination times almost the sate: however, the facture oad is diferet, ‘The dynamic Hacture intiion toughness of Mode increases asa pial crack increases, while Mode decrees. The maximum dynam factre toughness ‘of Mode-III is Kyyy13 (MPavm) at the loading rate KgaSO (GPaNai while Model is K38 (MPa) at the loading rate K/-105 (GPavims). Atte midile point between the Mode-1 and Mode angles, ie, fy-225%, the maximum Mixed-node is Kemmedial” (avin) atthe loadin Kenge (GPa), while Ky o2249 (MPa Keats 0 o -a/n). Dyndtmc fracture initiation toughness of Mode-1is larger ‘than the static fracture toughness, ie, Kal 31K, at 2 high loading rate K,-105 (GPav'ns). 20 Fora spiral crack specimen, the loading rate i a fonction ‘of the dynamic stress intensity fector (DSIF), initiation time ty and spiral angles. Furthermore, the loading rte can be develope around the crack front, starting {fom intermediate to high loading levels. The dynamic initiation toughness of Aluminum 2024-T3 is nonlinear and increased exponentially with the loading ‘The enor from Mode-II of fracture mechanies is less than 1.7%. The eror may develop from the physical experi- ‘mental issues and finite element boundary conti ‘effect, However, that error is too smal, and it ean be neglected. ‘The spiral crack with different inclined angles ca be see to lest a fracture of materials behavior with a different loading rate an a higher loading rate can be achieved ‘with more equipment. The spiral crack specimen ‘opened a new window to test the dynamic fracture of material with diferent loading rates and Mixed Mode This written description uses examples to disclose the presently disclosed subject matte, including the best mode, ‘nd also to enable any person skilled inthe art to practice the presently disclosed subject matter, including making and ting any devices or systems and performing any incorpo- rated methods, The patentable scope of the presently dis closed subject matter is defined By the claims and may ‘nclude other examples that oecur o those skilled inthe ar. Such other examples are intended to be within the seope of the claims if they include structural elements that do not diller from the literal language of the claims, or if they include equivalent structural elements with insubstantial ferences from the literal language of the claims. REFERENCES Barnett D M, Asaro R J (1972) The Fracture Mechanies of Slitlike Crcks in Anisotropic Elastic Media, J Mech Phys Solids 20°353-366, Chao Y J, Lin'S (1997) On the Failure of Cracks Under ‘Mixed Mode Loads. Int} Froet 87:201-223, (Chao Y J, Wang C, Kim Y, Chien C-11 2010) Relationship Between Crack-Tip Constraint and Dynamie Fracture Initiation Toughness. J Press Vessel Technol 132021404 ‘Chen W, Bo S 2011) Split Hopkinson (Kolsky) Bar Design, “Testing and Application. Springer ‘Chong K P, Kunipp MD (1988) New Specimens for Mixed ‘Mode Fracture Investigations of Geomaterials Eng Fract ‘Mech 30:701-712, Deng X (1994) The Asymprotie Structure of Transient Elastodynamic Fields at the Tip of a Stationary Crack 46:14 Dodds RH, Vargas P M (1988) Numerical Evaluation of ‘Domain and Contour Integrals for Nonlinear Fracture ‘Mechanies: Formulation and Implementation Aspects. Urhana-Champaign Day J, Suresh 8, Cho K, Bopp E R (1987) A Method for Dynamic Fractire Initiation Testing of Ceramics, J Eng ‘Mater Technol 110:325-331. doi: 10.1115/1.3226087 ahem A, Addis Kidane (2019) Modification of Benth Solution for Mode | Fracture of Cylinder with Spiral Crack Subjected to Torsion. Fact Fatigue, Fail Damage Evol Proe Soe Fxp Mech Ser 6:57-63, doi: htps/dai org 10,1007978-3-819-95879-8_10 Pahem A, Kidane A (2017) A General Approach to Pvaluate the Dynamic Fracture Toughness of Materials. Dyn Behav Mater Conf Proc Soe Exp App! Mech 1185-194. do Inps:do.ony/10.1007/978.3-319-41132-3.26US 11,754,481 B2 2 Fabem A, Kidane A (2019) A Progression on the Detemni- ‘ation of Dynamic Fracture Initiation Toughness Using Spiral Crack. Fract Fatigue, Fail Damage Evol Conf Proc ‘Soe Exp Mech Ser 689-95, doi htps:/doi.rg/ 10.1007) 978-3-319-95879-8_15 Fahem A, Kidane A’ (2020) Mixed Mode (Mode VII) ‘Dynamic Fracture Initiation Toughness of Alun Alloy. Pract Fatigue, Fail Damage Evol Conf Proc Soc Exp Appl Mech. do: Accepted Fabem A, Kidane A (2018) Hybrid Computational and "Experimental Approach to [deny the Dynamic Initiation Fracture Toughness at High Looding Rate. Dyn Behav ‘Mater Conf Proe Soe Fxp Mech 1:141-146, doi: tps! Kinson Presse Bar, Klepaczko JR (1990) Dynamie Crack Initiation, Some Experimental Methods and Modelling. Crack Dyn Met ‘Mater Springer, Vienna 310:255-153, Kuna M2013) Finite Elements in Fracture Mechanies ‘Theory-Numeries-Applications. Springer Dordrecht Heidelberg New York London Liu, Chao Y J, Zhu X (2004) Tensile-Shear Transition in ‘Mixed Mode VIII Fracture lat J Solids Struct 41:6147~ orn, Maigre H, Rittel D (1993) Mixed Mode Quantification for ‘Dynamic Fracture Initiation: Applicaton tothe Compact Compression Specimen, Int J Solids Struct 30:3233-3244 Nakamura T, Shih C F, Freund L B (1986) Analysis of ‘Dynamically Loaded ‘Three-Point-Bend Duetile Fracture ‘Specimen, Fng. Fract. Mech. 25:323-339. Nakamura T, Shik C P, Freund 1 B (1985) Elaste-Plastie "Analysis of a Dynamically Loaded Circumfemtilly NNotehed Round Bar. Eng Frat 22:4379452. 2 Nishioka T; Aduri $ N (1983) Path-Independent Integrals, Energy Release Rates, and General Solutions of Near-Tip| Fields in Mixed Mode Dynamic Fracture Mechanics. Eng Pract Mec 18:1-22, ‘Owen D, Zhuang 8, Rosakis A, Ravichandran G (1998) ‘Experimental Determination of Dynamic Crack Initiation and Propagation Fracture Toughness in Tin Aluminum Shoots. ln J ract 90:153-174 Petrov Y V,, Morozov N F (1994) On the Modeling of Fracture of Brittle Solids. J Appl Mech 61:710, doi: 10.1115/1.2901518, Peyman S, Ghajar R, Irani S$ (2017) Computation of Dynamic Stress Intensity Factors for Cracks in Three- Dimensional Functionally Graded Solids, Proc Inst Mech Eng Part LJ Mater Des Appl 01-12. dai: 10.1177) 1464420717711467 Prasad K, Srinivas M, Kamat S V (2014) Influence of Mixed ‘Mode VIII Loading on Dynamic Fracture Toughness of ‘Mild Steel st Room and Low Temperatures, Mater Sei Eng A 590:54-59. doi: 10.1016)j.msea.2013,09,099 Ravi-Chandar K (2004) Dynamie Prature, First eit. Ese- vier Ltd, Netherlands avi-Chandar K (1995) On the Failure Mode Transitions in PPolyeathonate Under Dynamic Mixed Mode Loading. Int I Solids Siret 32:925.938, Rice JR (1968) A Path Independent Integral and the Approximate Analysis of Strain Concentration by [Nofehes and Cracks. J Appl Mech 35:379-386, Shih C F, Asaro RJ (1988) Flasie-Plastic Analysis of Cracks ‘on Bimteial Interfaces: Part [Small Seale Yielding. J Appl Mech $5:299-316, doi. 10.1115) 13173676 Sib G C (1974) Stain-Fneruy-Density Factor Applied t0 ‘Mixed Mode Crack Problems, Int Fract 10:305-320. Sih G C (1968) Some Elasiodynamic Problems of Cracks TInt J Fract Mech 4:51-68. doi: 10.1007/BFO0189147 Sih GC, Loeber JF (1969) Wave Propagation in an Flastic Solid With a Line of Diseontinity of Finite Crack, Simulia, D'S 2017) ABAQUS FEA. Dassault Systemes Simulia Comp, USA ‘Sundaram Bt M, Tippur HV. (2017) Dynamic Mixed Mode facture behaviors of PMMA and polycarbonate. Eng Fract Mech 176:186-212, Sutton M A (2007) Three-Dimensional Digital Image Cor- relation t Quantify Deformation and Crack-Opening Displacement in Ductile Aluminum Under Mixed Mode ‘VI Loading, Opt Eng 46:051008. Sutton MA, Orten J J, Sebreier 1 W (2008) Image Corre: Jation for Shape, Motion and Deformation Measure smeatsBasic Concepts, Theory and Applications. Image Rochester N-Y. 341 Sutton MA, Yan JH, Tiwari Vet al (2008) The Elfeet of ‘Out-of plane Motion on 2D and 30) Digital Image Cor- relation Measurements. Opt Lasers Fag 46:746-757, ‘Vargas P, Robert, H. Dodds J (1993) Threo-Dimensional, Inelastic Response of Single-Fdge Noteh Tend Speci ‘meas Subjected 1 Impact Loading. Univ Hlinois Urbana- Champsign 208. Walters M C, Paulino G H, Dodds R H (2006) Computation of Mixed Mode Stress’ Intensity Factors for Cracks in ‘Three-Dimensional Functionally Graded Solids. J Png Mech 1321-15, Williams M (19S7a) On The Stress Distribution at The Base of a Stationary Crack J Appl Mech 24:109-114 Williams MI_(1957) On the Stress Distribution at the Base of A Stationary Crack. Appl Mech 24:109-114US 11,754,481 B2 23 ‘Yau JF, Wang $ 8, Corten HT (1980) A Mixed Mode Crack “Analysis of Isotropic Solids Using Conservation Laws of Elasticity, J Appl Mech 47:335-341, Yu H, War L, Guo L, et al. 010) An Interetion Integral ‘Method for 3D Curved eracks in Nonhomogeneous Mate= fials With Complex Interfaces. Int J. Solids Struct, 4:2178-2180. ‘What is claimed is: 1. A method for determining Mixed Mode dynamic frve- ture toughness of engineering: materials 19 be rated, com prising: Providing a least wo specimens ofthe engineering mate tals to be rated; forming a surface crack in each of the at least two specimens ata respective selected angle representative of different Frctare Modes respoctively subjecting the at Jeast two specimens t0 dynamic torsion loads respectively measuring torque applied to each of the Teast two specimens at set of fracture therein respectively measuring full-field deformation and crack ‘mouth opening displacement of each such fracture as & function of loading time: respectively estimating time at which each erack initiation is started: and respectively determining dynamic stress intensity factors for the specimens, based on measurements and deter- 2A method asin claim 1, wherein forming each surface ‘rack in each of the at least wo specimens ata selected angle, comprises forming a surface V-notch spina crack ia ‘each respective specimen at a selected angle. 3. A method as in claim 2, further comprising performing ‘a stereo digital image correlation for respectively measuring the fullfield deformation and the erick mouth opening displacement for each of the at lest two specimens 38 funetion of loeding time, and using soch determinations for ‘estimating the respective time at which each erack initiation js started. 4. Amethod as in claim 3, wherein determining dynamic stress intensity factors for the specimens, comprises extrac ing said dynamie sess intensity factors numerically based ‘on.a dynamic interaction integral method, '5, Amethod as in claim 4, further eomprising conducting such method for a plurlity of at least three specimens having respective surface V-notch spiral eracks in each of the atleast three specimens ata corresponding plurality of respective selected inclined angles. ‘6. A method asin claim 8, wherein sid plurality of atleast thee specimens exch comprise cylindrical aluminum alloy specimens with respective V-notch spiral surface eacks a at Jeast one of spiral angles of O°, 11.25°, 22.5%, 33.75, and 45°, respectively 7A method as in claim §, wherein the at least three specimens are respectively subjected to dynamic torsion Joa using the Torsional Hopkinson Bar apparatus. '8. Amethod asin clams 7, wherein the torsional Hopkinson bar apparatus includes incident ‘and transaster bars: and messuring torque comprises respectively, measuring Torque applied on each respective of the at Teast three specimens at suid onset of facture by measurements from strain gages attached to the respective incident and transmitter bars of the torsional Hopkinson bar apparats, 9, Nmethod asin claim 5, wherein sid plurality of at least, three specimens each comprise specimens with respective 2 ‘Votch spiral sure cracks at spiral angles selected to include at least 2 pure Modell fracture, a pure Mode-1 ‘racture, and a least one Mixed Mode fracture combining Modes [and TI. 10, 8 method as in claim 9, wherein said plurality of at Jeast three specimens each comprise specimens with respec- tive V-notch spiral surface cracks at spiral angles selected to jnclude one pare Mode-IIl facture a a fracture angle of 0°, pure Mode-I fracture at a fracture angle of 43°, and plurality of Mixed Mode fractures having fracture angles of 11.28", 22.507, 33.75° combining Modes I and II U1, A method as in claim 9, wherein suid plrality of at Jeast three specimens each comprise specimens with respec tive Venotch spiral surface cracks at spiral angles selected to include one pure Mode-IIL fracture at a facture ange of 4 pure Mode-I facture at a fracture angle of 43°, and plurality of Mixed Mode fractures having fracture angles of {rom $° to 28° for combining Modes I and IIL 12. A method asin claim 9, further including determining or said at least ree specimens the Mode (K,,), Mode-II (Ra) and Mixed Mode (K,yn,) dynamic initiation tough- ess ratings 13. A method as in claim 12, further including determin- ing sich Mixed Mode fracture values asa unetion of spiral angles 14, A method asin clan 13, further including determi ing such Mixed Mode fracture values as a function of Joaadng rate 1S, Methodology for determining dynamie Mixed Mode (UIT) of ductile materials by investigating a plurality of spiral crack specimens from pure ModelIl up to pure Mode-I throughout the dynamic Mixed Mode (VII) of facture under pre impulse torsional load, comprising using a torsional Hopkinson Bar to generate a torsional impulse loo for eseh specimen: using one-dimension wave propagation theory fo measure ‘far-field maximum fracture load for each specimen; detemnining under pure torsional Toad! dynamic stress intensity factors of plral specimen spiral cracks with diffrent crack angles; and ‘using dynamic interaction integral numerical ealeuation ‘to determine dynamic fracture initiation properties Ky Kyo and Kyyy of Mede-1, Mode], and Mixed Mode il, respectively 16, Methodology asin claims 18, funher comprising using 4 three-dimensional Digital Image Correlation (DIC) ‘method to measure Crack Mouth Opening Displacement (CMOD) for each specimen and to monitor fracture iita- 17. Methodology as in claim 16, further comprising eternining dynamic sites intensity fator of said materials as 8 funetion of specimen erack angles and as a function of Tacture initiation time. 18, Methodology as in claim 16, further comprising determining dynamic sites intensity Factor of said materials fa 8 function of specimen erack angles and as a function of Jong rates. 19, Methodology as in claim 16, wherein said specimens comprised Aluminum and said method futher comprises termining the average Mode-l, Mode-Ill, and Mixed Mode (VIM) of dynamie fracture’ initiation toughness of Auminum as fuetion of loading rate 20, Methodology to estimate dynamic fracture properties for Mode-I, Mode-Ill, and Mixed Mode V/ll fracture con- Aitions for engineering materials subjected to eritcal load ‘witha different loading rate without inertia effect, compris- ing:US 11,754,481 B2 25 applying loading toa plurality of specimens of engineer- ing materials sulficient to induce fracture therein in plural Modes of fracture conditions smcssuring inition time t, ofa fracture event ‘measuring incident torque during a fracture event ‘inputting measured incident torque to a finite clement ‘model: csleulating the interaction integral of @ unit vitwal advance of # finite erack front segment for a specific ‘mode at particular point as a function of time: and ‘wing the eomponents of dynamie interation integral 10 calculate the dynamic sires intensity factor for each mode. 21, Methodology as in claim 20, furher including mea suring the fmeture time by two experimental methods, Including strain gage signal and stereo Digital Image Cor relation (@D-DIC). 22, Methodology as in claim 21, wherein for stain gages anal, said initiation ime t/oFa fracture event is identified ‘at the Tocation where sudden change in tansmsitted and reflected signals occurred, 23, Methodology as in claim 22, wherein said stereo Digital Image Correlation is used to measure a Crack Month ‘Opening Displacement (CMOD), by measuring, with diss placement of the erack edge, at two points (upper (FCD,) ‘and ower edge (ECD, ) across the crak line to calculate the CMOD, 24, Methodology as in claim 24, futher including using such methodology for determining dynamic initiation fue- ture toughness Mixed Mode fracture (Mode-I and Mode-I) for engineering materials sirctures that are subjected t0 axialtorsion loading 25, Methodology asin clsim 24, wherein said engineering materials structures comprise one of pipes, aicralt wings, shall, and rotor blades. 26. Methodology 38 in claim 21, wherein applying load ing to such plurality of specimens comprising using tor- sional Hopkinson bar apparatus for applying to Toad, and Wherein measuring said initiation time i, of a fracture event Includes. measuring through strain gages attached to an ‘incident bar and a transmitter bar of the lorsional Hopkinson bar apparatus 27, Metheslology 3 in claim 26, wherein during loading, further including using a hydraule-driven rotary actuator to ‘apply’ and store shea stain in w portion of sad incident ba between a rotary actuator and a clamp system, and then 26 stddenly releasing the stored shear sta 10 cause bal of Said stored. shear strvin to propagate towards a specimen ‘rough the incident bar "28: Methodology as in claim 27, wherein when an inci= dent wave reaches 2 specimen, with some of said incident ‘wave transmitted to an output bar through the specimen, and the remainder of said incident wave reflected back to said incident bar, acquiring. the incident, transmitted, and reflected shear strain data by using pairs of two-element ‘Ondogree shear strain gauges attached to the bars at respec- tive positions thereof 29. Methodology as in claim 20, further including using such methodology for determining dynamic initiation fne- ture toughness Mixed Mode frature (Mode-1 and Mode-II} as seen ia thin-walled strnetures 30. Methodology 3s in claim 20, wherein the plurality of specimens, respectively, comprise cylindrical aluminam Alloy specimens, each having 2 V-notch spiral erack at spiral angles of 0", 11 25°, 22.5% 33.75", and 45" respectively. ‘31, Methodology as in claim 30, Turter including using a shell revolve 10 make a spiral seam crack along the specimen length for all specimens. '32. Methodology asin claim 20, wherein the plurality of specimens, respectively, comprise specimens eacis having a ‘notch spital erack at spiral angles of 0, 45°, and an angle therebetween, respectively 3. Methodology as in claim 32, further including deter- ining Dynamic Stress Intensity Factors for respective spiral crack angle examples of pure Mode-II (et a spiral angle of O°), pure Mode-I (ata spiral angle of 45°), and ‘Mixed Mode VII (an angle therebetween). 34. Methodology asin elaim 33, further including deter- mining loading rate effects versus respective spiral cack angular specimens, where the loading rate provides the measure of loading applied per time around a rack tip, with the unit of stress intensity factor K, and where {pis sud initiation time of a fracture event 35. Methodology ss in claim 34, wherein the plurality of specimens, respectively, comprise specimens each having a Vnotch spiral erack at spiral angles of O°, 11.25", 225°, 32.75, and 45°, respectively.