Three-dimensional finite-element simulation of the dynamic Brazilian tests on concrete cylinders
Gonzalo Ruiz
Departamento de Ciencia de Materiales, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Search for more papers by this authorCorresponding Author
Michael Ortiz
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, U.S.A.
Graduate Aeronautical Laboratories, California Institute of Technology, Firestone Flight Sciences Laboratory, Pasadena, CA 91125, U.S.A.Search for more papers by this authorAnna Pandolfi
Dipartimento di Ingegneria Strutturale, Politecnico di Milano, 20133 Milano, Italy
Search for more papers by this authorGonzalo Ruiz
Departamento de Ciencia de Materiales, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Search for more papers by this authorCorresponding Author
Michael Ortiz
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, U.S.A.
Graduate Aeronautical Laboratories, California Institute of Technology, Firestone Flight Sciences Laboratory, Pasadena, CA 91125, U.S.A.Search for more papers by this authorAnna Pandolfi
Dipartimento di Ingegneria Strutturale, Politecnico di Milano, 20133 Milano, Italy
Search for more papers by this authorAbstract
We investigate the feasibility of using cohesive theories of fracture, in conjunction with the direct simulation of fracture and fragmentation, in order to describe processes of tensile damage and compressive crushing in concrete specimens subjected to dynamic loading. We account explicitly for microcracking, the development of macroscopic cracks and inertia, and the effective dynamic behaviour of the material is predicted as an outcome of the calculations. The cohesive properties of the material are assumed to be rate-independent and are therefore determined by static properties such as the static tensile strength. The ability of model to predict the dynamic behaviour of concrete may be traced to the fact that cohesive theories endow the material with an intrinsic time scale. The particular configuration contemplated in this study is the Brazilian cylinder test performed in a Hopkinson bar. Our simulations capture closely the experimentally observed rate sensitivity of the dynamic strength of concrete in the form of a nearly linear increase in dynamic strength with strain rate. More generally, our simulations give accurate transmitted loads over a range of strain rates, which attests to the fidelity of the model where rate effects are concerned. The model also predicts key features of the fracture pattern such as the primary lens-shaped cracks parallel to the load plane, as well as the secondary profuse cracking near the supports. The primary cracks are predicted to be nucleated at the centre of the circular bases of the cylinder and to subsequently propagate towards the interior, in accordance with experimental observations. The primary and secondary cracks are responsible for two peaks in the load history, also in keeping with experiment. The results of the simulations also exhibit a size effect. These results validate the theory as it bears on mixed-mode fracture and fragmentation processes in concrete over a range of strain rates. Copyright © 2000 John Wiley & Sons, Ltd.
REFERENCES
- 1 Ravichandar K, Knauss WG. An experimental investigation into dynamic fracture, Part 1. Crack initiation and arrest. International Journal of Fracture 1984; 25(4): 247–262.
- 2 Liu C, Knauss WG, Rosakis AJ. Loading rates and the dynamic initiation toughness in brittle solids. International Journal of Fracture 2000; to appear.
- 3 Braides A, Chiado'Piat V. Integral representation results for functionals defined on sbv. SISSA ISAS 1994; 198(M): 1–31.
- 4 Fonseca I, Francfort GA. Relaxation in BV versus quasiconvexification in W1,p; a model for the interaction between fracture and damage. Calculus of Variations 1995; 3: 407–446.
- 5 Dugdale DS. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 1960; 8: 100–104.
- 6 Barrenblatt GI. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics 1962; 7: 55–129.
10.1016/S0065-2156(08)70121-2 Google Scholar
- 7 Rice JR. Mathematical analysis in the mechanics of fracture. In Fracture, H Liebowitz (ed.). Academic Press:New York, 1968; 191–311.
- 8 Hillerborg A, Modeer M, Petersson PE, Needleman A. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Research 1976; 6: 773–782.
10.1016/0008-8846(76)90007-7 Google Scholar
- 9 Rose JH, Ferrante J, Smith JR. Universal binding energy curves for metals and bimetallic interfaces. Physical Review Letters 1981; 47(9): 675–678.
- 10 Carpinteri A. Mechanical Damage and Crack Growth in Concrete. Martinus Nijhoff: Dordrecht, The Netherlands, 1986.
- 11 Needleman A. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 1987; 54: 525–531.
- 12 Ortiz M. Microcrack coalescence and macroscopic crack growth initiation in brittle solids. International Journal of Solids and Structures 1988; 24: 231–250.
- 13 Willam K. Simulation issues of distributed and localized failure computations. In Cracking and Damage, J Mazars, ZP Bazant (eds). Elsevier Science: New York, 1989; 363–378.
- 14 Needleman A. An analysis of decohesion along an imperfect interface. International Journal of Fracture 1990; 42: 21–40.
- 15 Needleman A. Micromechanical modeling of interfacial decohesion. Ultramicroscopy 1992; 40: 203–214.
- 16 Xu XP, Needleman A. Void nucleation by inclusion debonding in a crystal matrix. Modelling and Simulation in Materials Science and Engineering 1993; 1: 111–132.
- 17 Xu XP, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42: 1397–1434.
- 18 Tvergaard V, Hutchinson JW. The influence of plasticity on mixed-mode interface toughness. Journal of the Mechanics and Physics of Solids 1993; 41: 1119–1135.
- 19 Ortiz M, Suresh S. Statistical properties of residual stresses and intergranular fracture in ceramic materials. Journal of Applied Mechanics 1993; 60: 77–84.
- 20 Planas J, Elices M, Guinea GV. Book chapter: cohesive cracks as a solution of a class of nonlocal problems. In Fracture and Damage in Quasibrittle Structures. Experiment, Modelling and Computer Analysis, ZP Bazant (ed.). E & FN SPON, 1994.
- 21 Xu XP, Needleman A. Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line. International Journal of Fracture 1995; 74: 253–275.
- 22 Ortiz M. Computational micromechanics. Computational Mechanics 1996; 18: 321–338.
- 23 Camacho GT, Ortiz M. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 1996; 33(20–22): 2899–2938.
- 24 Tvergaard V, Hutchinson JW. Effect of strain dependent cohesive zone model on predictions of interface crack growth. Journal de Physique IV 1996; 6: 165–172.
- 25 Tvergaard V, Hutchinson JW. Effect of strain dependent cohesive zone model on predictions of crack growth resistance. International Journal of Solids and Structures 1996; 33: 3297–3308.
- 26 Xu XP, Needleman A. Numerical simulations of dynamic crack growth along an interface. International Journal of Fracture 1996; 74: 289–324.
10.1007/BF00035845 Google Scholar
- 27 De-Andrés A, Pérez JL, Ortiz M. Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. International Journal of Solids and Structures 1999; 36: 2231–2258.
- 28 Ortiz M, Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 1999; 44: 1267–1282.
- 29 Pandolfi A, Ortiz M. Solid modeling aspects of three-dimensional fragmentation. Engineering with Computers 1998; 14: 287–308.
- 30 Pandolfi A, Krysl P, Ortiz M. Finite element simulation of ring expansion and fragmentation the capturing of length and time scales through cohesive models of fracture. International Journal of Fracture 1999; 95: 279–297.
- 31 Pandolfi A, Guduru PR, Ortiz M, Rosakis AJ. Finite element analysis of experiments of dynamic fracture ini c.300 steel. International Journal of Solids and Structures 2000; to appear.
- 32 Repetto EA, Radovitzky R, Ortiz M. Finite element simulation of dynamic fracture and fragmentation of glass rods. Computer Methods in Applied Mechanics and Engineering 2000; to appear.
- 33 Yon JH, Hawkins NM, Kobayashi AS. Strain-rate sensitivity of concrete mechanical properties. ACI Materials Journal 1992; 89(2): 146–153.
- 34 Yu C-T, Kobayashi AS, Hawkins NM. Energy-dissipation mechanisms associated with rapid fracture of concrete. Experimental Mechanics 1993; 33(3): 205–211.
- 35 Du J, Yon JH, Hawkins NM, Arakawa K, Kobayashi AS. Fracture process zone for concrete for dynamic loading. ACI Materials Journal 1992; 89(3): 252–258.
- 36 Ross A, Tedesco JW, Kuennen ST. Effects of strain rate on concrete strength. ACI Materials Journal 1995; 92: 37–47.
- 37 Hughes ML, Tedesco JW, Ross A. Numerical analysis of high strain rate splitting-tensile tests. Computers and Structures 1993; 47: 653–671.
- 38 Guo ZK, Kobayashi AS, Hawkins NM. Dynamic mixed mode fracture of concrete. International Journal of Solids and Structures 1995; 32(17/18): 2591–2607.
- 39 Reinhardt HW, Weerheijm J. Tensile fracture of concrete at high loading rates taking account of inertia and crack velocity effects. International Journal of Fracture 1991; 51: 31–42.
- 40 Tedesco JW, Ross CA, McGill PB O'Neil BP. Numerical Analysis of high strain rate concrete direct tension tests. Computers and Structures 1991; 40(2): 313–327.
- 41 Tedesco JW, Ross CA, Kuennen ST. Experimental and numerical-analysis of high-strain rate splitting tensile tests. ACI Materials Journal 1993; 90(2): 162–169.
- 42 Yon JH, Hawkins NM, Kobayashi AS. Numerical simulation of mode I dynamic fracture concrete. Journal of Engineering Mechanics ASCE 1991; 117(7): 1595–1610.
- 43 Yon JH, Hawkins NM, Kobayashi AS. Fracture process zone in dynamically loaded crack-line wedge-loaded, double-cantilever beam concrete specimens. ACI Materials Journal 1991; 88(5): 470–479.
- 44 van Doormaal JCAM, Weerheijm J, Sluys LJ. Experimental and numerical determination of the dynamic fracture energy of concrete. Journal de Physique IV 1994; C8: 501–506.
- 45 Rodríguez J, Navarro C, Sánchez-Gálvez V. Splitting tests: an alternative to determine the dynamic tensile strength of ceramic materials. Journal de Physique IV 1997; 4(C8): 101–106.
- 46 Johnstone C, Ruiz C. Dynamic testing of ceramics under tensile stress. International Journal of Solids and Structures 1995; 32(17/18): 2647–2656.
- 47 Gálvez F, Rodríguez J, Sánchez V. Tensile measurements of ceramic materials at high rates of strain. Journal de Physique IV 1997; C3: 151–156.
- 48 Bažant ZP, Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press: Boca Raton, FL, 1998.
- 49 Guinea GV. Medida de la Energía de Fractura del Hormigón. Ph.D Thesis, Departamento de Ciencia de Materials, Universidad Politécnica de Madrid, ETS de Ingenieros de Caminos, Ciudad Universitaria, 28040 Madrid, Spain, 1990. (Measurement of the fracture energy of concrete in Spanish.)
- 50 Guinea GV, Planas J, Elices M. Measurement of the fracture energy using three-point bend tests: 1. Influence of experimental procedures. Materials and Structures 1992; 25: 212–218.
- 51 Field JE, Walley SM, Bourne NK, Huntley JM. Experimental methods at high rates of strain. Journal de Physique IV 1994; C8: 3–22.
- 52 Rocco CG. Influencia del Tamaño y Mecanismos de Rotura en el Ensayo de Compresión diametral. Ph.D. Thesis, Departamento de Ciencia de Materiales, Universidad Politécnica de Madrid, ETS de Ingenieros de Caminos, Ciudad Universitaria, 28040 Madrid, Spain, 1996. (Size-dependence and fracture mechanisms in the diagonal compression splitting test, in Spanish.)
- 53 Marsden JE, Hughes TJR. Mathematical foundations of elasticity. Prentice-Hall: Englewood Cliffs, NJ, 1983.
- 54 Lubliner J. On the thermodynamic foundations of non-linear solid mechanics. International Journal of Non-Linear Mechanics 1972; 7: 237–254.
10.1016/0020-7462(72)90048-0 Google Scholar
- 55 Lubliner J. On the structure of the rate equations of materials with internal variables. Acta Mechanica 1973; 17: 109–119.
- 56 Chen G, Ravichandran WN. Dynamic compressive behavior of ceramics under lateral confinement. Journal de Physique IV 1994; 4: 177–182.
- 57 Chen G, Ravichandran WN. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. Journal of the American Ceramic Society 1996; 79: 579–584.
- 58 Petersson PE. Crack growth and development of fracture zones in plain concrete and similar materials. Technical Report TVBM-1006, Division of Building Materials, Lund Institute of Technology, University of Lund, Sweden, 1981.
- 59 Belytschko T. An overview of semidiscretization and time integration procedures. In Computational Methods for Transient Analysis, T Belytschko, TJR Hughes (eds). North-Holland: Amsterdam, 1983; 1–65.
- 60 Hughes TJR. Analysis of transient algorithms with particular reference to stability behavior. In Computational Methods for Transient Analysis, T Belytschko, TJR Hughes (eds). North-Holland: Amsterdam, 1983; 67–155.
- 61 Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
- 62 Mathur KK, Needleman A, Tvergaard V. Three dimensional analysis of dynamic ductile crack growth in a thin plate. Journal of the Mechanics and Physics of Solids 1996; 44: 439–464.
- 63 Carneiro FLL, Barcellos A. Tensile strength of concrete. RILEM Bulletin 1953; 13: 97–123.
- 64CEB-FIP Model Code 1990, Final Draft. Bulletin D'Information N. 203, 204 and 205, EEP Lausanne.
- 65 ASTM C 39. Annual Book of ASTM Standards. vol. 04.02. Chapter Standard test method for compressive strength of cylindrical concrete specimens. ASTM: Philadelphia, 1991; 20–24.
- 66 Cuitiño AM, Ortiz M. A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Engineering Computations 1992; 9: 437–451.
10.1108/eb023876 Google Scholar
- 67 Jia Z, Castro-Montero A, Shah SP. Observation of mixed mode fracture with center notched disk specimens. Concrete and Cement Research 1996; 26(1) 125–137.
- 68 Swartz SE, Taha NM. Crack-propagation and fracture of plain concrete beams subjected to shear and compression. ACI Structural Journal 1991; 88(2) 169–177.
- 69 Subrumaniam KV, Popovics JS, Shah SP. Testing concrete in torsion: Instability analysis and experiments. Journal of Engineering Mechanics ASCE 1998; 124(11): 1258–1268.
- 70 Gustafsson PJ, Hillerborg A. Sensitivity in the shear strength of longitudinally reinforced beams to fracture energy of concrete. ACI Structural Journal 1988; 85(3): 286–294.
- 71 Carpinteri A, Valente S, Ferrara G, Melchiorri G. Is mode II fracture energy a real material property? Computers and Structures 1993; 48: 397–413.
- 72 Gálvez JC, Cendón D, Planas J, Guinea GV, Elices M. Fracture of concrete under mixed loading. Experimental results and numerical prediction. Fracture Mechanics of Concrete Structures, Proceedings FRAMCOS-3, D-79104, AEDIFICATIO Publishers, Freiburg, Germany, 1998.
- 73 Planas J, Elices M. Nonlinear fracture of cohesive materials. International Journal of Fracture 1991; 3: 139–157.
- 74 Nicholas T, Recht RF. Introduction to impact phenomena. In High Velocity Impact Dynamics, JA Zukas (ed.). Wiley: New York, 1990; 1–63.
- 75 Radovitzky R, Ortiz M. Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering 2000; in press.
- 76 Wu XJ, Gorhan DA. Stress equilibrium in the split Hopkinson pressure bar test. Journal de Physique IV 1997; 7(C3): 91–96.
- 77 Albertini C, Cadoni E, Labibes K. Impact fracture process and mechanical properties of plain concrete by means of an Hopkinson bar bundle. Journal de Physique IV 1997; C3: 915–920.
- 78 Fandrich RG, Clout JMF, Bourgeois FS. The CSIRO Hopkinson bar facility for large diameter particle breakage. Minerals Engineering 1998; 11(9): 861–869.
- 79 Planas J, Elices M, Guinea GV. Measurement of the fracture energy using three-point bend tests: 2. Influence of bulk energy dissipation. Materials and Structures 1992; 25: 305–312.
- 80 Rocco CG, Guinea GV, Planas J, Elices M. The effect of the boundary conditions on the cylinder splitting strength. In Fracture Mechanics of Concrete Structures, FH Wittmann (ed.). Aedificatio Publishers: Freiburg, Germany, 1995; 75–84.