Local and global instabilities in ductile failure

• Autorzy: Wnuk M. P.
• Języki publikacji: EN

Abstrakty

EN

Catastrophic fracture in ductile solids is usually preceded by a certain amount of quasistatic crack growth that occurs as a result of void expansion and coalescence process associated with large deformations localized in the narrow zone adjacent to the crack leading edge. This zone is subject to a tri-axial state of stress, and its local properties may vary from those of the bulk material. To describe this condition a modified cohesive crack model is suggested based on the mesomechanical law of the S-stress distribution and equipped with the "fine structure" feature that is lacking in the standard model. Subcritical crack growth may be likened to the phenomenon of "preliminary displacements" known in the studies encountered in the physics of tribology. Microscopic sliding of a solid block placed on an elastic-plastic substrate located on the inclined plane is observed to begin at angles somewhat smaller than the critical angle q = tan-1(m), where m denotes the coefficient of friction. With careful observational techniques these displacements can indeed be measured. Likewise, in the course of the early stages of ductile fracture, quasistatic crack growth is detected between the lower bound KI = Kini' , tantamount to the onset of stable growth, and the upper bound KI = Kf. equivalent to occurrence of the catastrophic failure. While Kini' is believed to be a material constant, the other quantity, Kf is determined not only by the material properties, but it also depends on specimen geometry, crack configuration and type of the external loading. The exact shape of the terminal instability locus represented in the plane (load, crack length) must be established by employment of the R-curve technique, in which the second variations of the energy terms are involved. When the Liapunov criterion is invoked, then it appears that the propagation of a stable crack should be viewed as a sequence of local instability states, while transition to an unstable propagation becomes equivalent to the loss of global stability, as then the entire component breaks up. A moving quasistatic crack is described on the basis of the Wnuk criterion of final stretch, which leads to the nonlinear differential equations governing the resistance curves for various materials. Both the ductile and brittle limits of material response are discussed. One of the essential results of this study is the partition of energy available for fracture within the end zone, accomplished by means of considerations of the pre-fracture states developed at the mesa-level. This, in turn, leads to a discovery of the energy screening effect, which manifests itself by a significant enhancement of material fracture toughness prior to the catastrophic failure state. Such phenomena are being confirmed by the brilliant experimental work of the Panin group in Tomsk, and Popov's team in Berlin.

Słowa kluczowe

EN

ductile; brittle; deformation; fracture; non-elastic response; energy of fracture; quasistatic crack; resistance curves

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2004
• Tom: nr 3
• Strony: 40--51
• Opis fizyczny: bibliogr. 20 poz.

Twórcy

autor

Wnuk M. P.

• College of Engineering and Applied Science University of Wisconsin - Milwaukee

Bibliografia

• [1] Wnuk M. P.: Accelerating Crack in a Viscoelastic Solid Subject to Subcritical Stress Intensity, in Proceedings of the International Conference on Dynamic Crack Propagation, pp. 273 – 280, Lehigh University, Editor George C. Sih, publ. by Noordhoff, Leiden, 1972.
• [2] Wnuk M. P.: Quasi-Static Extension of a Tensile Crack Contained in a Viscoelastic-Plastic Solid, J. Appl. Mechanics 1974, Vol. 41, No. 1, pp. 234 – 242.
• [3] Wnuk M. P.: Criterion of Final Stretch for a Quasistatic Crack in Non-Elastic Medium, in Proceedings of ICM3 Conference, Cambridge, England 1979, Vol.3, pp. 549-561.
• [4] Wnuk M. P.: Mathematical Modeling of Nonlinear Phenomena in Fracture Mechanics, in Nonlinear Fracture Mechanics, Editor M. P. Wnuk, published by Springer-Verlag, Wien – New York, CISM Course and Lecture No. 314, International Centre for Mechanical Sciences, Udine, Italy 1990.
• [5] Wnuk M. P.: Effect of Cohesive Stress Distributions on the Specific Work of Fracture. Triaxiality Dependent Cohesive Zone Model, plenary lecture presented at the 2001 MESOMECHANICS and CADAMT Int. Conference, Tomsk, March 2001, Russian Federation.
• [6] Wnuk M. P., Legat J.: Work of Fracture and Cohesive Stress Distributions Resulting From Triaxiality Dependent Cohesive Zone Model, Int. J. Fracture, 2002, Vol. 114, pp. 29 - 46.
• [7] Rice J. R., Sorensen E. P.: Continuing Crack-Tip Deformation and Fracture for Plane Strain Crack Growth in Elastic-Plastic Solids, J. Mech. Phys. Solids 1978, Vol. 26, pp. 263-286.
• [8] Rice J. R., Drugan W. J., Sham T. L.: Elastic-Plastic Analysis of Growing Cracks, ASTM STP 700, ASTM, Philadelphia 1980, pp. 189 – 221.
• [9] Wnuk M. P., Mura T.: Effect of Microstructure on the Upper and Lower Limit of Material Toughness in Elastic-Plastic Fracture, J. Mech. of Materials 1983, Vol. 2, No. 1, pp. 33 – 46.
• [10] Wnuk M. P., Omidvar B.: Local and Global Instabilities Associated with Continuing Crack Extension in Dissipative Solids, International Journal of Fracture 1997, Vol. 84, 1997, pp. 237-260.
• [11] Xia L., Shih C. F., Hutchinson J. W.: A Computational Approach to Ductile Crack Growth under Large Scale Yielding, J. Mech. Phys. Solids 1995, Vol. 42, pp. 21 – 40.
• [12] Budiansky B.: Resistance Curves for Finite Specimen Geometries, 1996, a seminar at Harvard University.
• [13] Read D. T., Petrovski B.: Elastic-Plastic Fracture at Surface Flaws in HSLA Weldments, The Proceedings of the 9th International Conference on Offshore Mechanics and Arctic Engineering, Houston, TX, Vol. III, Materials Engineering, Part B, pp. 461 – 471; publ. In Transactions of ASME, J. of Offshore Mechanics and Arctic Engineering 1990, Vol 114, No. 4, pp. 264 – 271.
• [14] Read D., McHenry H. I., Petrovski B.: Elastic-Plastic Models of Surface Cracks in Tensile Panels, J. Experimental Mechanics, June 1989, pp. 226-230.
• [15] Petrovski B., Kocak M.: Fracture of Surface Cracked Undermatched Weld Joint in High Strength Steel, IIW Document X-1284-93 presented at the 46th Annual Assembly of International Institute of Welding, August 28 – September 4, 1993, Glasgow, UK.
• [16] Petrovski B.: Evaluation of Fracture Behaviour of Mismatched Steel Weld Joints in Cracked Tensile Panels, invited lecture at First Slovenian – Japanese Seminar on “Fracture of Welded Structures under Static and Dynamic Loading”, Maribor, July 2001.
• [17] Ungsuwarungsri T., Knauss W. G.: The Role of Delayed-Softened Material Behavior in the Fracture of Composites and Adhesives, Int. J. of Solids and Structures 1987, Vol. 35, pp.221-241.
• [18] Ungsuwarungsri T., Knauss W. G.: A Nonlinear Analysis of Equilibrium Craze, Part I: Problem Formulation and Solution, J Appl. Mechanics 1987, Vol. 110, pp.44-51.
• [19] Ungsuwarungsri T., Knauss W. G.: Part II: Simulation of Craze and Crack Growth, J. Appl. Mechanics 1987, Vol. 110, pp. 52-58.
• [20] Wnuk M. P. : Enhancement of Fracture Toughness Due to Energy Screening Effect in the Early Stages of Non-Elastic Failure, Fatigue and Fracture of Engineering Materials Structures (FFEMS )Journal 2003, UK, Vol.26, pp. 741-753.