Hopkinson Bar Loaded Fracture Experimental Technique: A Critical Review of Dynamic Fracture Toughness Tests

Hopkinson bar experimental techniques have been extensively employed to investigate the mechanical response and fracture behavior of engineering materials under high rate loading. Among these applications, the study of the dynamic fracture behavior of materials at stress-wave loading conditions (corresponding stress-intensity factor rate ∼106 MPam/s) has been an active research area in recent years. Various Hopkinson bar loading configurations and corresponding experimental methods have been proposed to date for measuring dynamic fracture toughness and investigating fracture mechanisms of engineering materials. In this paper, advances in Hopkinson bar loaded dynamic fracture techniques over the past 30 years, focused on dynamic fracture toughness measurement, are presented. Various aspects of Hopkinson bar fracture testing are reviewed, including (a) the analysis of advantages and disadvantages of loading systems and sample configurations; (b) a discussion of operating principles for determining dynamic load and sample displacement in different loading configurations; (c) a comparison of various methods used for determining dynamic fracture parameters (load, displacement, fracture time, and fracture toughness), such as theoretical formula, optical gauges, and strain gauges; and (d) an update of modeling and simulation of loading configurations. Fundamental issues associated with stress-wave loading, such as stress-wave propagation along the elastic bars and in the sample, stress-state equilibrium validation, incident pulse-shaping effect, and the “loss-of-contact” phenomenon are also addressed in this review.

[1]  D. Hui,et al.  Dynamic mode II delamination fracture of unidirectional graphite/epoxy composites , 2003 .

[2]  Aashish Rohatgi,et al.  Analysis of the dynamic responses for a pre-cracked three-point bend specimen , 2004 .

[3]  T. Nicholas.  Tensile testing of materials at high rates of strain , 1981 .

[4]  A. Rosakis,et al.  Comparison of three real time techniques for the measurement of dynamic fracture initiation toughness in metals , 2005 .

[5]  A. Ghoul,et al.  Initiation and arrest of cracks on two pipeline steels at low temperature , 1998 .

[6]  Daniel Rittel,et al.  A hybrid experimental–numerical investigation of dynamic shear fracture , 2005 .

[7]  R. Davies.  A critical study of the Hopkinson pressure bar , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  David E. Lambert,et al.  Strain rate effects on dynamic fracture and strength , 2000 .

[9]  Y. Dzenis,et al.  Determination of dynamic delamination toughness of a graphite‐fiber/epoxy composite using Hopkinson pressure bar , 2005 .

[10]  Yang Wang,et al.  Mode-I fracture toughness of PMMA at high loading rates , 2006 .

[11]  V. Parameswaran,et al.  An experimental investigation of dynamic crack propagation in a brittle material reinforced with a ductile layer , 2003 .

[12]  Huajian Gao,et al.  Modern topics and challenges in dynamic fracture , 2005 .

[13]  J. Kalthoff.  Fracture behavior under high rates of loading , 1986 .

[14]  Daniel Casem,et al.  A Four-Point Bend Technique to Determine Dynamic Fracture Toughness of Ceramics , 2006 .

[15]  Anna Pandolfi,et al.  Numerical investigation on the dynamic behavior of advanced ceramics , 2004 .

[16]  H. Kolsky.  An Investigation of the Mechanical Properties of Materials at very High Rates of Loading , 1949 .

[18]  L. Yulong,et al.  EFFECT OF LOADING RATE ON MODE I DYNAMIC FRACTURE TOUGHNESS OF HIGH STRENGTH STEELS 40Cr AND 30CrMnSiNi2A , 2006 .

[19]  Sia Nemat-Nasser,et al.  Hopkinson techniques for dynamic recovery experiments , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[20]  L. Freund,et al.  Analysis of a dynamically loaded three-point-bend ductile fracture specimen , 1986 .

[21]  A. Rosakis,et al.  Dynamic fracture of berylium-bearing bulk metallic glass systems: A cross-technique comparison , 2005 .

[22]  Aashish Rohatgi,et al.  Analysis of modified split Hopkinson pressure bar dynamic fracture test using an inertia model , 2004 .

[23]  S. Rizal,et al.  Experimental approach to dimple fracture mechanisms under short pulse loading , 2002 .

[24]  Christophe Bacon.  Numerical prediction of the propagation of elastic waves in longitudinally impacted rods: Applications to Hopkinson testing , 1993 .

[25]  J. F. Kalthoff,et al.  On the measurement of dynamic fracture toughnesses — a review of recent work , 1985 .

[26]  A. Lomunov,et al.  Methodological aspects of studying dynamic material properties using the Kolsky method , 1995 .

[27]  I. Rokach.  On the influence of one-point-bend impact test parameters on dynamic stress intensity factor variation , 1997 .

[28]  Hubert Maigre,et al.  A NEW METHOD FOR DYNAMIC FRACTURE TOUGHNESS TESTING , 1992 .

[29]  K. Kussmaul,et al.  Investigation of Dynamic Crack Propagation and Arrest for Pulse Loaded specimens Made from a Modified MoV-Steel (KS22) by Means of a Hopkinson-Pressure-Bar , 1997 .

[30]  James W. Dally,et al.  Dynamic measurements of initiation toughness at high loading rates , 1988 .

[31]  P. R. Marur,et al.  Dynamic analysis of three point bend specimens under impact , 1994 .

[32]  D J Parry,et al.  Materials testing at high constant strain rates , 1982 .

[33]  J. Färm,et al.  Dynamic fracture toughness determined from load-point displacement , 1994 .

[34]  R. Clos,et al.  Determination of the dynamic fracture toughness using a new stress pulse loading method , 1992 .

[35]  S. Aoki,et al.  SIMPLE FORMULAS FOR DYNAMIC FRACTURE MECHANICS PARAMETERS OF ELASTIC AND VISCOELASTIC THREE-POINT BEND SPECIMENS BASED ON TIMOSHENKO'S BEAM THEORY , 2013 .

[36]  T. Hsu,et al.  Fracture toughness of coal under quasi-static and impact loading , 1984 .

[37]  Hubert Maigre,et al.  Mixed-mode quantification for dynamic fracture initiation: Application to the compact compression specimen , 1993 .

[38]  K. Vecchio,et al.  Dynamic fracture of bovine bone , 2006 .

[39]  Francisco Gálvez,et al.  Numerical modelling of SHPB splitting tests , 2003 .

[40]  K. Vecchio,et al.  Dynamic-compression fatigue of hot-pressed silicon-nitride , 1994 .

[41]  A. Shukla,et al.  Fabrication, characterization, and dynamic behavior of polyester/TiO2 nanocomposites , 2003 .

[42]  Yang Wang,et al.  A finite element analysis for using Brazilian disk in split Hopkinson pressure bar to investigate dynamic fracture behavior of brittle polymer materials , 2006 .

[43]  Per-Arne Lindqvist,et al.  Effects of loading rate on rock fracture , 1999 .

[44]  Takashi Yokoyama,et al.  Determination of Dynamic Fracture-Initiation Toughness Using a Novel Impact Bend Test Procedure , 1993 .

[45]  Yulong Li,et al.  Analytical and experimental determination of dynamic impact stress intensity factor for 40 Cr steel , 1997 .

[46]  Joseph W. Tedesco,et al.  Numerical simulation of high strain rate concrete compression tests , 1994 .

[47]  T. Nishida,et al.  Fracture strength of fiber-bonded ceramic composite subjected to static and impact bending , 1998 .

[49]  Anindya Ghoshal,et al.  Damage Detection Testing on a Helicopter Flexbeam , 2001 .

[50]  T. Kusaka,et al.  Low-velocity impact fracture behaviour of impact-resistant polymer matrix composite laminates under mixed mode loading , 2000 .

[51]  I. V. Rokach.  MODAL APPROACH FOR PROCESSING ONE‐ AND THREE‐POINT BEND TEST DATA FOR DSIF–TIME DIAGRAM DETERMINATION. PART II—CALCULATIONS AND RESULTS , 1998 .

[52]  O. L. Bowie,et al.  The weight function for various boundary condition problems , 1983 .

[53]  L. Guillaumat,et al.  Influence of some test parameters on specimen loading determination methods in instrumented Charpy impact tests , 2001 .

[54]  D. Rittel,et al.  Dynamic fracture detection using the force-displacement reciprocity: application to the compact compression specimen , 1995 .

[55]  J. A. Loya,et al.  Three-dimensional effects on the dynamic fracture determination of Al 7075-T651 using TPB specimens , 2008 .

[56]  J. Klepaczko.  Discussion of a New Experimental Method in Measuring Fracture Toughness Initiation at High Loading Rates by Stress Waves , 1982 .

[57]  S. W. Park,et al.  Time-Resolved Impact Response and Damage of Fiber-Reinforced Composite Laminates , 2000 .

[58]  G. Ravichandran,et al.  Effect of Loading Rate on Fracture Morphology in a High Strength Ductile Steel , 2001 .

[59]  Francisco Gálvez,et al.  Tensile Strength Measurements of Ceramic Materials at High Rates of Strain , 1997 .

[60]  V.P.W. Shim,et al.  An analysis of stress uniformity in split Hopkinson bar test specimens , 2005 .

[61]  M. Hojo,et al.  RATE-DEPENDENT MODE II INTERLAMINAR FRACTURE BEHAVIOR OF CARBON-FIBER/EPOXY COMPOSITE LAMINATES , 1999 .

[62]  C. H. Popelar,et al.  An experimental method for determining dynamic fracture toughness , 2000 .

[63]  John Lambros,et al.  Dynamic fiber debonding and frictional push-out in model composite systems: Experimental observations , 2002 .

[64]  Kenneth S. Vecchio,et al.  Dynamic Effects in Hopkinson Bar Four-Point Bend Fracture , 2007 .

[65]  Min Zhou,et al.  Separation of elastic waves in split Hopkinson bars using one-point strain measurements , 1999 .

[66]  Peter K. Kaiser,et al.  A study on the dynamic behavior of the Meuse/Haute-Marne argillite , 2007 .

[67]  J. Buchar,et al.  Photoelasticity Studies of a New Method of Fracture Toughness Evaluation at High Loading Rates , 1985 .

[68]  Satya N. Atluri,et al.  A method for determining dynamic stress intensity factors from cod measurement at the notch mouth in dynamic tear testing , 1982 .

[69]  Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA , 1997 .

[70]  V. Sánchez-Gálvez,et al.  Splitting tests : an alternative to determine the dynamic tensile strength of ceramic materials , 1994 .

[71]  G. Mesmacque,et al.  Dynamic fracture toughness of pre-fatigued materials , 2008 .

[72]  Q. Wang,et al.  A Method for Testing Dynamic Tensile Strength and Elastic Modulus of Rock Materials Using SHPB , 2006 .

[73]  Wl Server,et al.  Impact Three-Point Bend Testing for Notched and Precracked Specimens , 1978 .

[74]  Daniel Rittel,et al.  A method for dynamic fracture toughness determination using short beams , 2000 .

[75]  G. Nash.  An analysis of the forces and bending moments generated during the notched beam impact test , 1969 .

[76]  T. Kusaka.  Experimental Characterization of Interlaminar Fracture Behavior in Polymer Matrix Composites under Low-Velocity Impact Loading , 2003 .

[77]  An experimental cum numerical technique to determine dynamic interlaminar fracture toughness , 1998 .

[78]  L. M. Yeakley,et al.  High strain-rate testing: Tension and compression , 1968 .

[79]  Ares J. Rosakis,et al.  Experimental Determination of Dynamic Crack Initiation and Propagation Fracture Toughness in Thin Aluminum Sheets , 1998 .

[80]  C. Rousseau.  Critical Examination of the Use of Coherent Gradient Sensing in Measuring Fracture Parameters in Functionally Graded Materials , 2006 .

[81]  Ares J. Rosakis,et al.  Effect of loading and geometry on the subsonic/intersonic transition of a bimaterial interface crack , 2003 .

[82]  Hiroshi Tada,et al.  The stress analysis of cracks handbook , 2000 .

[83]  J. Molinari,et al.  Three-dimensional numerical simulations of dynamic fracture in silicon carbide reinforced aluminum , 2004 .

[84]  Arun Shukla,et al.  On the use of strain gages in dynamic fracture mechanics , 1995 .

[85]  J. Duffy,et al.  Dynamic Fracture Toughness Measurement Methods for Brittle and Ductile Materials , 1989 .

[86]  J. Fernández-Sáez,et al.  General expressions for the stress intensity factor of a one-point bend beam , 2007 .

[87]  R. Chona,et al.  A Review of Dynamic Fracture Studies in Functionally Graded Materials , 2007 .

[88]  S. Aoki,et al.  Measurement of Dynamic Fracture Toughness of Ceramic Materials at Elevated Temperature by One-point-bend Impact Test , 1989 .

[89]  Per-Arne Lindqvist,et al.  Effects of high temperatures on dynamic rock fracture , 2001 .

[90]  A. Bakker,et al.  COMPATIBLE COMPLIANCE AND STRESS INTENSITY EXPRESSIONS FOR THE STANDARD THREE-POINT BEND SPECIMEN , 1990 .

[91]  K. Vecchio,et al.  Aging and loading rate effects on the mechanical behavior of equine bone , 2008 .

[92]  H. Homma,et al.  Viscoelastic Effect on the Fracture Toughness of GFRP: Experimental Approach , 2006 .

[93]  S. Rizal,et al.  Effects of Loading Rate and Stress-State on Dimple Fracture , 2000 .

[94]  John Lambros,et al.  Dynamic fiber debonding and frictional push-out in model composite systems: numerical simulations , 2002 .

[95]  Hubert Maigre,et al.  An investigation of dynamic crack initiation in PMMA , 1996 .

[96]  D. Shockey,et al.  Short-pulse fracture mechanics , 1986 .

[97]  Franz-Josef Ulm,et al.  A tribute to Fernando L. L. B. Carneiro (1913–2001) engineer and scientist who invented the Brazilian test , 2002 .

[98]  Arun Shukla,et al.  Subsonic and intersonic crack growth along a bimaterial interface , 1996 .

[99]  J. Duffy,et al.  Dynamic fracture behavior of SiC whisker-reinforced aluminum alloys , 1991 .

[100]  Hi-Seak Yoon,et al.  Dynamic Fracture Toughness of Chevron-notch Ceramic Specimens measured in Split Hopkinson Pressure Bar , 2002 .

[101]  Wada Hitoshi.  Determination of dynamic fracture toughness for PMMA , 1992 .

[102]  W. Böhme,et al.  The behavior of notched bend specimens in impact testing , 1982 .

[103]  A. Shukla,et al.  Development of stress field equations and determination of stress intensity factor during dynamic fracture of orthotropic composite materials , 1994 .

[104]  Arun Shukla,et al.  Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[105]  Weinong W Chen,et al.  Pulse shaping techniques for testing brittle materials with a split hopkinson pressure bar , 2002 .

[106]  Yoshiaki Yamauchi,et al.  Dynamic fracture initiation in brittle materials under combined mode I/II loading , 1994 .

[107]  V. D. Chuban,et al.  Numerical simulation of flutter validated by flight-test data for TU-204 aircraft , 2002 .

[108]  J. Williams,et al.  The analysis of instrumented impact tests using a mass-spring model , 1987 .

[109]  C. Sun,et al.  A method for testing interlaminar dynamic fracture toughness of polymeric composites , 2004 .

[110]  Subra Suresh,et al.  Tensile Fracture Toughness of Ceramic Materials: Effects of Dynamic Loading and Elevated Temperatures , 1990 .

[111]  J. Fitoussi,et al.  Damage Evolution in Quasi-Isotropic SCS-6/Timetal 21S under Quasi-Static and Dynamic Bending , 2002 .

[112]  A. Shukla,et al.  Using strain gages to investigate subsonic dynamic interfacial fracture in an isotropic–isotropic bimaterial , 2003 .

[113]  J. Duffy,et al.  A Method for Dynamic Fracture Initiation Testing of Ceramics , 1988 .

[114]  Bayoumi,et al.  Determination of Fracture Toughness JIc Under Quasi-Static and Dynamic Loading Conditions Using Wedge Loaded Specimens , 1984 .

[115]  R. Mines.  Characterization and measurement of the mode 1 dynamic initiation of cracks in metals at intermediate strain rates—A review , 1990 .

[116]  W Böhme,et al.  Dynamic Key-Curves for Brittle Fracture Impact Tests and Establishment of a Transition Time , 1990 .

[117]  M. Bassim.  Use of the stretch zone for the characterization of ductile fracture , 1995 .

[118]  M. M. Al-Mousawi,et al.  The use of the split Hopkinson pressure bar techniques in high strain rate materials testing , 1997 .

[119]  V. Srivastava,et al.  Measurement of critical stress intensity factor in C/C–SiC composites under dynamic and static loading conditions , 2004 .

[120]  T. Kurokawa,et al.  Effects of strain rate on mode II interlaminar fracture toughness in carbon-fibre/epoxy laminated composites , 1994 .

[121]  Arun Shukla,et al.  Photoelastic Evaluation of Stress Fields and Fracture During Dynamic Splitting Experiments , 2002 .

[122]  G. Sinha,et al.  Transient Dynamic Response of Arbitrary Stiffened Shells by the Finite Element Method , 1995 .

[123]  Taketoshi Nojima,et al.  Rate dependence of mode I fracture behaviour in carbon-fibre/epoxy composite laminates , 1998 .

[124]  John W. Gillespie,et al.  Hopkinson bar experimental technique: A critical review , 2004 .

[125]  Effect of specimen shape on the behavior of brittle materials using probabilistic and deterministic methods , 2006 .

[126]  L. Freund,et al.  Fracture initiation in metals under stress wave loading conditions , 1977 .

[127]  Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites , 2005 .

[128]  G. Ravichandran,et al.  Dynamic fracture under plane wave loading , 1989 .

[129]  J. Duffy,et al.  The effect of loading rate and temperature on fracture initiation in 1020 hot-rolled steel , 1980 .

[130]  Eric Martin,et al.  Dynamic analysis of instrumented CHARPY impact tests using specimen deflection measurement and mass-spring models , 1998 .

[131]  P. Roudier,et al.  DYNAMIC FRACTURE TOUGHNESS MEASUREMENTS AND LOCAL APPROACH MODELLING OF TITANIUM ALLOYS , 1996 .

[132]  Estimation of Dynamic Stress Intensity for One-Point Bend Specimen by Inverse Analysis , 2002 .

[133]  W. G. Proud,et al.  High-strain rate Brazilian testing of an explosive simulant using speckle metrology , 2004 .

[134]  D. Rittel.  The influence of temperature on dynamic failure mode transitions , 1998 .

[135]  Joseph W. Tedesco,et al.  Strain-rate-dependent constitutive equations for concrete , 1998 .

[136]  Arun Shukla,et al.  Comparison of the techniques of transmitted caustics and photoelasticity as applied to fracture , 1988 .

[137]  S. Rizal,et al.  Dimple fracture under short pulse loading , 2000 .

[138]  K. Vecchio,et al.  Fracture of Nitinol under Quasistatic and Dynamic Loading , 2007 .

[139]  K. Vecchio,et al.  Evaluation of dynamic fracture toughness KId by Hopkinson pressure bar loaded instrumented Charpy impact test , 2004 .

[140]  V. Prakash,et al.  Dynamic fracture of linear medium density polyethylene under impact loading conditions , 2007 .

[141]  J. A. Kapp,et al.  More on compliance of the three-point bend specimen , 1985 .

[142]  F. Benitez,et al.  Towards the Development of a Dynamic Fracture Initiation Test , 1984 .

[143]  P. Marur,et al.  Dynamic response of bimaterial and graded interface cracks under impact loading , 2000 .

[144]  Hubert Maigre,et al.  Dynamic crack propagation under mixed-mode loading – Comparison between experiments and X-FEM simulations , 2007 .

[145]  Tensile strength of the brittle materials, probabilistic or deterministic approach? , 2006 .

[146]  Arun Shukla,et al.  Photoelastic investigation of interfacial fracture between orthotropic and isotropic materials , 2003 .

[147]  I. V. Rokach.  Comparison of simplified methods of dynamic stress intensity factor evaluation , 1994 .

[148]  T. Kurokawa,et al.  Evaluation of Mode II Interlaminar Fracture Toughness of Composite Laminates under Impact Loading , 1997 .

[149]  B. D. Agarwal,et al.  Determination of stress intensity factor in orthotropic composite materials using strain gages , 1989 .

[150]  Stephen M. Walley,et al.  Review of experimental techniques for high rate deformation and shock studies , 2004 .

[151]  Hubert Maigre,et al.  A study of mixed-mode dynamic crack initiation in PMMA , 1996 .

[152]  D. Rittel,et al.  Dynamic mechanical and fracture properties of an infiltrated TiC-1080 steel cermet , 2005 .

[153]  The Influence of Mode-Mixity on Dynamic Failure Mode Transitions in Polycarbonate , 1997 .

[154]  James W. Dally,et al.  Strain-gage methods for measuring the opening-mode stress-intensity factor,KI , 1987 .

[155]  D. Hoy,et al.  Digital Imaging and Fractographical Analyzes of Perforation-induced Delamination of Laminated Graphite-Epoxy Composite , 2006 .

[156]  D. Hui,et al.  Dynamic mixed-mode I/II delamination fracture and energy release rate of unidirectional graphite/epoxy composites , 2005 .

[157]  A. S. Eremenko,et al.  Determination of fracture toughness and fracture energy of brittle materials under impact wedging , 1996 .

[158]  G. Y. Sha.  AN EXPERIMENTAL-NUMERICAL METHOD FOR MEASURING CRACK PROPAGATING VELOCITIES UNDER STRESS WAVE LOADING , 2009 .

[159]  Jonathan M. Huntley,et al.  Experimental methods at high rates of strain , 1994 .

[160]  Meng Zhang,et al.  Micromechanisms of fatigue crack nucleation and short crack growth in a low carbon steel under low cycle impact fatigue loading , 1999 .

[161]  Kichinosuke Tanaka,et al.  Dynamic Strength Research by Hopkinson Bar Technique , 1973 .

[162]  M. Elices,et al.  Stress Intensity factor, compliance and CMOD for a General Three-Point-Bend Beam , 1998 .

[163]  S. Aoki,et al.  Simple formula for dynamic stress intensity factor of pre-cracked Charpy specimen , 1980 .

[164]  J. G. Williams,et al.  Fracture of Polymers, Composites and Adhesives , 2000 .

[165]  Ares J. Rosakis,et al.  A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results , 1991 .

[166]  M. Bassim,et al.  Evaluation of fracture toughness of HSLA80 steel at high loading rates using stretch zone measurements , 1992 .

[167]  I. V. Rokach.  MODAL APPROACH FOR PROCESSING ONE‐ AND THREE‐POINT BEND TEST DATA FOR DSIF‐TIME DIAGRAM DETERMINATION PART I—THEORY , 1998 .

[168]  I. V. Rokach,et al.  On the numerical evaluation of the anvil force for accurate dynamic stress intensity factor determination , 2003 .

[169]  Kenneth S. Vecchio,et al.  Improved Pulse Shaping to Achieve Constant Strain Rate and Stress Equilibrium in Split-Hopkinson Pressure Bar Testing , 2007 .

[170]  K. Ogawa,et al.  Impact three-point bending tests on FRP by split-Hopkinson bar technique. , 1990 .

[171]  Karl-Gustaf Sundin,et al.  Analysis of elastic waves in non-uniform rods from two-point strain measurement , 1990 .

[172]  Kichinosuke Tanaka,et al.  Impact Bending Test on Steel at Low Temperatures Using a Split Hopkinson Bar , 1980 .

[173]  Joseph W. Tedesco,et al.  Numerical analysis of dynamic split cylinder tests , 1989 .

[174]  J. Fernández-Sáez,et al.  Determination of dynamic fracture-initiation toughness using three-point bending tests in a modified Hopkinson pressure bar , 2003 .

[175]  J. S. Epstein,et al.  Long wavelength impact of izod fracture specimens: An experimental/numerical investigation , 1991 .

[176]  Vesta I. Bateman,et al.  Certification of 200,000 g Shock Calibration Technique for Sensors , 2002 .

[177]  K. Ogawa.  Impact friction test method by applying stress wave , 1997 .

[178]  Yu Long Li,et al.  Determination of the Dynamic Fracture Initiation Toughness of Metal-Ceramic Composites , 2003 .

[179]  Daniel Rittel,et al.  On testing of charpy specimens using the one-point bend impact technique , 2002 .

[180]  John Lambros,et al.  An experimental study of dynamic delamination of thick fiber reinforced polymeric matrix composites , 1997 .

[181]  Toshio Nakamura,et al.  Elastic-plastic analysis of a dynamically loaded circumferentially notched round bar , 1985 .

[182]  M. Nakano,et al.  Measurement of dynamic fracture toughness by longitudinal impact of precracked round bar , 1990 .

[183]  B. Hopkinson.  A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets , 1914 .

[184]  A. Pineau,et al.  Impact fracture of a ferritic steel in the lower shelf regime , 2002 .

[185]  Michael Ortiz,et al.  Three‐dimensional finite‐element simulation of the dynamic Brazilian tests on concrete cylinders , 2000 .

[186]  C. Ruiz,et al.  Dynamic testing of ceramics under tensile stress , 1995 .

[187]  R.A.W. Mines,et al.  Analysis of the Hopkinson Pressure Bar loaded Instrumented Charpy Test using an inertial modelling technique , 1991, International Journal of Fracture.

[188]  Joseph W. Tedesco,et al.  Numerical analysis of high strain rate splitting-tensile tests , 1993 .

[189]  V. Prakash,et al.  Dynamic deformation and fracture behavior of novel damage tolerant discontinuously reinforced aluminum composites , 2000 .

[190]  D. Shockey,et al.  Response of cracks in structural materials to short pulse loads , 1983 .

[191]  P. R. Marur.  Charpy specimen—a simply supported beam or a constrained free-free beam? , 1998 .

[192]  Hubert Maigre,et al.  A new approach to the experimental determination of the dynamic stress intensity factor , 1992 .

[193]  R. Asaro,et al.  Correlations of microstructure with dynamic and quasi-static fracture in a plain carbon steel , 1988 .

[194]  H. Couque,et al.  Effect of planar size and dynamic loading rate on initiation and propagation toughness of a moderate-toughness steel , 1994 .

[195]  D. Koss,et al.  Damage development in carbon/epoxy laminates under quasi-static and dynamic loading , 1999 .

[196]  Jia-Lin Tsai,et al.  Use of split Hopkinson pressure bar for testing off-axis composites , 2001 .

[197]  B. A. Crouch.  Finite element modeling of the three-point bend impact test , 1993 .

[198]  Shigeru Aoki,et al.  One-Point-Bend Impact Testing of Ceramic Material , 1990 .

[199]  Per-Arne Lindqvist,et al.  The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks; analytical and numerical results , 2004 .

[200]  Arun Shukla,et al.  Intersonic crack propagation in bimaterial systems , 1998 .

[201]  R.A.W. Mines,et al.  The Hopkinson pressure bar: an alternative to the instrumented pendulum for Charpy tests , 1985 .

[202]  C. Ruíz,et al.  The Mechanical Behaviour of Composite Materials under Impact Loading , 1997 .

[203]  Takashi Yokoyama,et al.  A novel impact three-point bend test method for determining dynamic fracture-initiation toughness , 1989 .

[204]  Wang Qi-zhi.  Method for determination of dynamic fracture toughness of rock using holed-cracked flattened disk specimen , 2006 .

[205]  M. Seika,et al.  Measurement of impact fracture toughness for PMMA with single-point bending test using an air gun , 1993 .

[206]  A. Bertram,et al.  Crack Propagation Toughness of Rock for the Range of Low to Very High Crack Speeds , 2003 .

[207]  On dynamic crack initiation in polycarbonate under mixed-mode loading , 1997 .

[208]  Aashish Rohatgi,et al.  Crack length calculation for bend specimens under static and dynamic loading , 2004 .

[209]  Lin Jing,et al.  Hopkinson bar acceptance testing for shock accelerometers , 1999 .

[210]  Fengchun Jiang,et al.  Experimental investigation of dynamic effects in a two-bar/three-point bend fracture test. , 2007, The Review of scientific instruments.

[211]  Bayoumi,et al.  Investigation of Dynamic JId for Alloy Steel Weldments Using the Split Hopkinson Bar , 1986 .

[212]  Ömer G. Bilir,et al.  Strain gage methods for measurement of opening mode stress intensity factor , 1996 .

[213]  Ares J. Rosakis,et al.  Dynamic fracture initiation and propagation in 4340 steel under impact loading , 1990 .

[214]  Xibing Li,et al.  TESTING AND RESPONSE OF LARGE DIAMETER BRITTLE MATERIALS SUBJECTED TO HIGH STRAIN RATE , 2002 .

[215]  J. Duffy,et al.  The Effect of Loading Rate and Temperature on the Initiation of Fracture in a Mild, Rate-Sensitive Steel , 1979 .

[216]  T. Nishida,et al.  Impact Strength of Continuous-Carbon-Fiber-Reinforced Silicon Nitride Measured by Using the Split Hopkinson Pressure Bar , 2005 .

[217]  Joseph W. Tedesco,et al.  Numerical analysis of high strain rate concrete direct tension tests , 1991 .

[218]  G. Pluvinage,et al.  Fracture criterion for glass under impact loading , 2001 .

[219]  F. Delvare,et al.  Modified split Hopkinson pressure bars for dynamic bending and shear tests , 2006 .

[220]  Y. Huang,et al.  Measurement of the fracture toughness of a fiber-reinforced composite using the Brazilian disk geometry , 1997 .

[221]  H. Couque,et al.  ON THE USE OF COUPLED PRESSURE BARS TO MEASURE THE DYNAMIC FRACTURE INITIATION AND CRACK PROPAGATION TOUGHNESS OF PRESSURE VESSEL STEELS , 1988 .

[222]  L. Freund,et al.  Stress Wave Radiation From a Crack Tip During Dynamic Initiation , 1992 .