A zone of distributed microcracking is often suggested to accompany tensile macrocrack propagation in rocks and ceramics. The microcracking is said to be largely responsible for (1) high values of fracture energy, (2) increasing resistance to fracture with crack extension and (3) the dependence of fracture mechanics data on the experimental setup. In the present paper, the material breakdown processes in imperfectly elastic Westerly granite are investigated using ultrasonic wave probing and in situ microscopy during mode I fracture experiments. These observations are compared with an in situ reflection/transmission microscopy investigation of mode I fracture in a near-ideal elastic polycrystalline alumina (Al2O3). As defined by the spatial distribution of longitudinal and surface wave attenuation in wedge-loaded double-cantilever beam specimens of Westerly granite, the fracture process zone is elongate in the direction of fracture propagation (15–40 mm long by 1–2 grain dimensions wide; grain size 0.75 mm). As revealed by in situ reflection microscopy, the ultrasonic wave energy is partially transmitted through the developing fracture surfaces via two sources of crack interface traction: (1) remnant islands of unfractured material left behind the advancing fracture front and (2) geometrical interlocking of the microstructurally rough fracture surfaces. A similar zone of crack flank tractions is found in the alumina (greater than 2000 μm long; grain size 20–100 μm). No evidence of a diffuse kidney-shaped cloud of microcracking distributed ahead of the main fracture tip (predicted by many fracture models) was found in either material. Instead, interface-localized microcracking was observed to operate at positions where the tractions, or restraining forces, are transmitted across the nascent fracture surfaces. Crack flank tractions shield the main crack tip from high levels of stress and are relieved by friction-induced microcracking and microcrack rupture of intact-material bridges. As a consequence of the crack history dependence of the crack tip shielding, it is proposed that, even under small-scale inelastic deformation conditions appropriate to linear elastic fracture mechanics, neither R-curve behavior nor applied-KI/subcritical crack velocity relationships are intrinsic properties of these and similar materials.
A mechanics model of microcrack toughening is presented. The model predicts the magnitude of microcrack toughening as well as the existence of R-curve effects. The toughening is predicated on both the elastic modulus diminution in the microcrack process zone and the dilatation induced by microcracking. The modulus effect is relatively small and process-zone-size-independent. The dilatational effect is potentially more substantial, as well as being the primary source of the R curve. The dilatatio...
#1Yiu-Wing Mai(NIST: National Institute of Standards and Technology)H-Index: 112
#2Brian R. Lawn(NIST: National Institute of Standards and Technology)H-Index: 101
A fracture mechanics model is developed for nontransforming ceramics that show an increasing toughness with crack extension (R-curve, or T-curve, behavior). The model derives from the observations in Part I, treating the increased crack resistance as the cumulative effect of grain bridging restraints operating behind the advancing tip. An element of discreteness is incorporated into the formal distribution function for the crack-plane restraining stresses, to account for the primary discontinuit...
Modern-day theories of the strength of brittle materials stem from the Griffith energy balance description of fracture processes (1). Griffith regarded a cracked body as a thermodynamic system: a crack exists in a state of equilibrium if, for a virtual incremental extension, the release of mechanical energy in the system balances the work to create the new surface area. In current "fracture mechanics" notation this critical state may be expressed as Ga = Ge or Ka = Ke, where the crack extension ...
#1Victor C. Li(MIT: Massachusetts Institute of Technology)H-Index: 106
#2Erwin Liang(MIT: Massachusetts Institute of Technology)H-Index: 1
This paper discusses the fracture processes of concrete and fiber reinforced cementitious composites with special focus on the development of the fracture process zone with respect to the stress-separation constitutive relation of such materials. The suggestion is that the overall mechanical behavior of a concrete or FRC structure could be strongly influenced by the stress-separation constitutive relation, which in turn could be altered by engineering the microstructure of the material, especial...
Last. R. F. Pabst(MPG: Max Planck Society)H-Index: 5
view all 3 authors...
Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (KIC were then measured as a function of sharp crack length in a fast-fracture, load-controlled test. Crack resistance curves (KIC against crack length) were determined for three commercially pure aluminas of different grain size, a debased alumina containing a glassy phase, and a partially stabilized zirconi...
#1Carolyn J. Fairbanks(NIST: National Institute of Standards and Technology)H-Index: 7
#2Brian R. Lawn(NIST: National Institute of Standards and Technology)H-Index: 101
Last. Yiu-Wing Mai(NIST: National Institute of Standards and Technology)H-Index: 112
view all 4 authors...
Microstructural influences on ceramic strength become significant at small flaw sizes. These influences are readily quantified by strength testing with controlled indentation flaws. Data are presented here for alumina and glassy-ceramic specimens broken under both inert and fatigue conditions. As the flaw size is systematically reduced there is a tendency to a reduction in strength relative to that predicted from macroscopic toughness measurements, reflecting R-curve behavior. This tendency is c...
#1Peter L. Swanson(NIST: National Institute of Standards and Technology)H-Index: 2
Results of subcritical-fracture experiments performed in air on five different rock types are presented. A non-unique relationship between calculated stress-intensity factor and crack velocity suggests violations of the assumptions made when using conventional fracture testing techniques. To obtain a better understanding of fracture propagation in rock without regard to single-parameter characterizations of the fracture process several nondestructive testing techniques were employed in conjuncti...
The resistance of rock to tensile fracture may be measured by its fracture energy GI, which is found to range from 40 to 200 J/m2 in tests on nine types of sedimentary and crystalline rock. Differences in microstructure among the rocks tested are the principal cause of differences in the steady state value of GI, in the distance that a crack must advance before steady state fracturing is attained, and in the amplitude of the fluctuation of GI that accompanies crack advance. When nearly continuou...
#1Robert F. Cook(NIST: National Institute of Standards and Technology)H-Index: 58
#2Brian R. Lawn(NIST: National Institute of Standards and Technology)H-Index: 101
Last. Carolyn J. Fairbanks(NIST: National Institute of Standards and Technology)H-Index: 7
view all 3 authors...
A systematic study of the inert-strength characteristics of ceramics as a function of crack size relative to grain size has been made using controlled indentation flaws. The focus of the test program is on aluminas, with barium titanates and glass-ceramics providing support data in confirmation of general trends. On progressively diminishing the indentation load, the strengths first show a steady increase, but subsequently tend to a plateau, as the contact size begins to approach the characteris...
Last. Anthony G. Evans(University of California, Berkeley)H-Index: 154
view all 3 authors...
Abstract Matrix fracture in brittle-matrix fiber composites is analyzed for composites that exhibit multiple matrix cracking prior to fiber failure and have purely frictional bonding between the fibers and matrix. The stress for matrix cracking is evaluated using a stress intensity approach, in which the influence of the fibers that bridge the matrix crack is represented by closure tractions at the crack surfaces. Long and short cracks are distinguished. Long cracks approach a steady-state confi...
#1Tao Meng(TUT: Taiyuan University of Technology)H-Index: 1
#1Tao Meng(TUT: Taiyuan University of Technology)H-Index: 4
Last. Xue Yongbin(TUT: Taiyuan University of Technology)H-Index: 1
view all 7 authors...
Abstract Subcritical crack growth strongly influences the mechanical behavior of rock and the precursory phase of geohazards and catastrophic failure. In earlier studies, indirect measuring methods were used to investigate the subcritical crack growth behavior of rock materials. However, these methods cannot fully reflect the whole process of subcritical crack growth of geomaterials. Therefore, in this study, a new method (DC voltage fluctuation method) was developed which can monitor the whole ...
This lively introduction to geologic fracture mechanics provides a consistent treatment of all common geologic structural discontinuities. It explores the formation, growth and interpretation of fractures and deformation bands, from theoretical, field and lab-based perspectives, bridging the gap between a general textbook treatment and the more advanced research literature. It allows the reader to acquire basic tools to interpret discontinuity origins, geometries, patterns and implications using...
This chapter lays out a simplified roadmap to the main aspects of fracture mechanics that are important for geologic structural discontinuities. Fracture mechanics is a branch of engineering that nevertheless provides tools, concepts, and a mechanical context for interpreting the major characteristics and patterns of geologic discontinuities that are seen in the field (e.g., Rudnicki, 1980; Pollard and Segall, 1987; Engelder et al., 1993; Pollard and Fletcher, 2005; Segall, 2010; Gudmundsson, 20...
This chapter is devoted to geologic structural discontinuities that accommodate displacements perpendicular to their surfaces, including opening-mode fractures such as cracks, joints, veins, and dikes and closing-mode structures referred to as anticracks (Table 4.1). Opening-mode structures (mode-I, Fig. 1.16) are one of the most common types of geologic structural discontinuity. Cracks are defined as sharp planar to curviplanar surfaces of opening-mode displacement discontinuity (Table 1.1). Du...
#1Tao Meng(TUT: Taiyuan University of Technology)H-Index: 4
#2Donghua Zhang(TUT: Taiyuan University of Technology)H-Index: 2
Last. Li Xiaoming(Taiyuan University of Science and Technology)H-Index: 1
view all 6 authors...
Abstract Based on the project background of salt caverns used for oil and gas storage in laminated salt rock, this study examined the combined mode fracture toughness, the fracture pattern, the morphological evolution of fracture surfaces, and the fracture criterion of gypsum interlayers under confining pressure. Series of laboratory tests, including fracture strength tests and scanning electron microscopy tests, were performed at four confining pressures. The results indicate that the failure l...