Brittle Planes Research Articles

On the determination of the quasi-static evolution of brittle plane cracks via stationarity principle

The crack front evolution in brittle solids is commonly modelled by defining some crack increment criterion, which can be derived from considerations on the stress singularity, from the definition of a dissipative potential, from the introduction of phenomenological concepts such as the crack mobility, and so on. In this work, we faced the problem with no allowance for any crack increment criterion, but using only the elastic properties, the fracture energy, and a stationarity principle. We will show that these ingredients are enough for determining the equilibrium and the quasi-static evolution of generally shaped three-dimensional brittle plane cracks. In doing this, we pointed out some new insight on the crack front motion, a set of new, generalised, domain integrals for measuring the pointwise crack ‘tension’, and a rigorous calculation of the intersection angle between the crack front and the free surface.

A novel fracture behavior of the 304L stainless steel with heterogeneous lamella structure

The tensile fracture behavior of a 304L stainless steel with heterogeneous lamella structure (HLS) is studied by observation of its fracture appearance and analysis of its microstructure evolution. The HLS steel has two disparate fracture appearances of ductile clusters and brittle planes while the conventional steel with homogenous structure (HS) has a uniform fracture only consisting of ductile clusters. It is proposed that the fracture initiation is originated from boundaries between ultra-fine grains (UFGs) and recrystallized micro-grains (Micro-RGs) in the HLS steel while that is from some dislocation migration barriers in the HS steel.

Post-forming Room Temperature Brittle Fracture in a High-Strength Low-Alloy Steel Sheet After Various Forming Modes

The effects of various sheet forming modes on the post-forming room temperature fracture behavior of a 550-MPa yield strength high-strength low-alloy (HSLA) steel are investigated. In-plane biaxial stretching, plane strain (cold rolling), uniaxial tension, cylindrical cup drawing, and in-plane compression (IPC) are examined up to a von Mises effective prestrain eeff = 0.7. Most of the results pertain to sub-size Charpy-type impact specimens prepared from the prestrained material. After sufficiently large prestrains, the fracture behavior is highly anisotropic. Low-energy fracture modes, namely cleavage and intergranular fracture, occur after all modes of prestraining along plane directions that are perpendicular to the principal compressive prestrain. These planes are parallel to the sheet surface after biaxial stretching and cold rolling and correspond to brittle splits extending into the primary, ductile fracture surface. After cup drawing, the brittle planes are oriented perpendicular to the circumferential compressive prestrain. This results in very low energy fractures propagating in the length direction of a fully drawn cup. After in-plane compression, brittle fracture occurs along planes that are perpendicular to the compression direction. The fracture toughness for a crack propagating along such a plane after IPC to eeff = 0.38 was very low (12.7 MPa √m), much lower than in the undeformed condition (247 MPa√m). Changes in grain shape and in crystallographic texture caused by the various prestraining modes, as well as the microstructural damage at non-metallic inclusions and carbides, are examined to try to understand the fracture behavior.

Brittle Shear Tectonics in a Narrow Continental Rift: Asymmetric Nonvolcanic Barmer Basin (Rajasthan, India)

Our field studies emphasizing brittle shear P- and Y-planes along the margins of the Barmer basin (Rajasthan, India) support its two-phase (NW-SE, followed by NE-SW) extension during Early Cretaceous and Late Cretaceous–Paleocene periods. We also document nearly NE-trending megascale transfer zones along the northern margin of the Barmer basin. Preexisting brittle planes in the Malani basement rocks guided the relay structures here. Structures at the western basin shoulder margin indicate NE-SW extension, and the crosscut relation connotes the relative timing of the two extension phases. The crosscutting conjugate fault sets are non-Andersonian. The NW-trending faults produced by the second-phase extension and the inherited NNW-trending brittle features are dominantly dip-slip. Prior fractures of the Malani rocks at ≥45° to the NE-SW principal extension direction extended the Barmer basin obliquely during the Late Cretaceous–Paleocene period. The asymmetric nature of the rift, too, connotes its oblique rifting. The extension direction of the first phase probably rotated clockwise. This is derived mainly from WSW-trending faults cutting NE-trending faults. Brittle planes of shear and fracture significantly promoted fluid flow, as understood from secondary hydrothermal mineral deposits (Barmer hill area) and pre-Deccan basalts (Sarnoo area). Reverse slip detected along subvertical faults on the western and eastern rift shoulders are probably due to isostatic flexure–related contraction or might be related to the far-field effect of ridge-push forces. The Mesozoic subsurface stratigraphy there and elsewhere within the Barmer basin requires more study to substantiate the potential for structural entrapment of hydrocarbon.

Structural characterization of Turtle Mountain anticline (Alberta, Canada) and impact on rock slope failure

This paper proposes a structural investigation of the Turtle Mountain anticline (Alberta, Canada) to better understand the role of the different tectonic features on the development of both local and large scale rock slope instabilities occurring in Turtle Mountain. The study area is investigated by combining remote methods with detailed field surveys. In particular, the benefit of Terrestrial Laser Scanning for ductile and brittle tectonic structure interpretations is illustrated. The proposed tectonic interpretation allows the characterization of the fracturing pattern, the fold geometry and the role of these tectonic features in rock slope instability development. Ten discontinuity sets are identified in the study area, their local variations permitting the differentiation of the study zone into 20 homogenous structural domains. The anticline is described as an eastern verging fold that displays considerable geometry differences along its axis and developed by both flexural slip and tangential longitudinal strain folding mechanisms. Moreover, the origins of the discontinuity sets are determined according to the tectonic phases affecting the region (pre-folding, folding, post-folding). The localization and interpretation of kinematics of the different instabilities revealed the importance of considering the discrete brittle planes of weakness, which largely control the kinematic release of the local instabilities, and also the rock mass damage induced by large tectonic structures (fold hinge, thrust). • Remote methods such as TLS and ALS are powerful tools for detailed structural analyses. • Five sets of fractures occurred during folding event, three are post-folding. • Fold geometry variation along axis induces variation of the fractures properties. • Small-scale instabilities mainly controlled by fold geometry and related fracturing • Large rock slope failure allowed by tectonic induced rock mass strength reduction

The M-Integral Description for a Brittle Plane Strip With Two Cracks Before and After Coalescence

In this paper we extend the M-integral concept (Eshelby, J. D., 1956, The Continuum Theory of Lattice Defects, Solid State Physics, F. Seitz and D. Turnbull, eds., Academic, New York, pp. 79–141; Eshelby, J. D., 1970, The Energy Momentum Tensor in Continuum Mechanics, Inelastic Behavior of Solids, M. F. Kanninen, ed., McGraw-Hill, New York, pp. 77–115; Eshelby, J. D., 1975, “The Elastic Energy-Momentum Tensor,” J. Elast., 5, pp. 321–335; Knowles, J. K., and Sternberg, E., 1972, “On a Class of Conservation Laws in Linearized and Finite Elastostatics,” Arch. Ration. Mech. Anal., 44, pp. 187–211; Budiansky, B., and Rice, J. R., 1973, “Conservation Laws and Energy Release Rates,” ASME J. Appl. Mech., 40, pp. 201–203; Freund, L. B., 1978, “Stress Intensity Factor Calculations Based on a Conservation Integral,” Int. J. Solids Struct., 14, pp. 241–250; Herrmann, G. A., and Herrmann, G., 1981, “On Energy Release Rates for a Plane Cracks,” ASME J. Appl. Mech., 48, pp. 525–530; King, R. B., and Herrmann, G., 1981, “Nondestructive Evaluation of the J- and M-Integrals,” ASME J. Appl. Mech., 48, pp. 83–87) to study the degradation of a brittle plan strip caused by irreversible evolution: the cracks coalescence under monotonically increasing loading. Attention is focused on the change of the M-integral before and after coalescence of two neighborly located cracks inclined each other. The influences of different orientations of the two cracks and different coalescence paths connecting the two cracks on the M-integral are studied in detail. Finite element analyses reveal that different orientations of the two cracks lead to different critical values of the M-integral at which the coalescence occurs. It is concluded that the M-integral does play an important role in the description of the damage extent and damage evolution. However, it only provides some outside variable features. This means that the complete failure mechanism due to damage evolution cannot be governed by a single parameter MC as proposed by Chang and Peng, 2004, “Use of M integral for Rubbery Material Problems Containing Multiple Defects,” J. Eng. Mech., 130(5), pp. 589–598. It is found that there is an inherent relation between the M-integral and the reduction of the effective elastic moduli as the orientation of one crack varies, i.e., the larger the M-integral is, the larger the reduction is. Of great significance is that the M-integral is inherently related to the change of the total potential energy for a damaged brittle material regardless of the detailed damage features or damage evolution. Therefore, this provides a useful and convenient experimental technique to measure the values of M-integral for a damaged brittle material from initial damage to final failure without use of many stain gages (King, R. B., and Herrmann, G., 1981, “Nondestructive Evaluation of the J- and M-Integrals,” ASME J. Appl. Mech., 48, pp. 83–87).

The M-integral description for a brittle plane strip with two holes before and after coalescence

This paper extends the M-integral concept (Eshelby in The continuum theory of lattice defects, solid state physics, Academic Press, New York, 1956; The energy momentum tensor in continuum mechanics, inelastic behavior of solids, McGraw-Hill, New York; and J Elast 5:321–335, 1975; Knowles and Sternberg in Arch Rat Mech Anal 44:187–211, 1972; Budiansky and Rice in ASME J Appl Mech 40:201–203, 1973; Freund in Int J Solids Struct 14:241–250, 1978; Herrmann and Herrmann in ASME J Appl Mech 48:525–530, 1981; King and Herrmann in ASME J Appl Mech 48:83–87, 1981) to study the degradation of a brittle plane strip caused by irreversible evolution: the coalescence between two holes under monotonically increasing loading. Attention is focused on the change of the M-integral before and after coalescence of two neighborly located holes. Different orientations of the two holes and different coalescence path curves connecting the rims of the two holes are studied in detail. Finite element analyses reveal that different orientations of the two holes lead to different critical values of the M-integral, at which the maximum hoop stress (i.e., the stress along the rim of a hole) reaches the material strength and coalescence occurs, and that the minimum critical value of the M-integral approximately corresponds to the minimum critical tensile loading as the orientation varies. It is concluded that the M-integral as a configurational force does play an important role in description of the damage extent and damage evolution. However, it only provides some outside variable features. This means that the complete failure mechanism due to damage evolution cannot be governed by a single parameter M C as proposed by Chang and Peng [ASCE J Eng Mech 130(5):589–598, 2004]. It is found that there is an inherent relation between the M-integral and the reduction of the effective elastic moduli as the orientation varies. The larger the M-integral is, the larger the reduction is. Of great significance is that the M-integral is inherently related to the change of the total potential energy (CTPE) for a damaged brittle material regardless of the detailed damage features or damage evolution. Therefore, this provides a convenient and useful experimental technique to measure the values of the M-integral for a damaged brittle material from initial damage to final failure without use of many strain gages (King and Herrmann in ASME J Appl Mech 48:83–87, 1981).

Structural evolution of Andros (Cyclades, Greece): a key to the behaviour of a (flat) detachment within an extending continental crust

Abstract The continental crust extends in a brittle manner in its upper part and in more distributed (ductile) manner in its lower part. During exhumation of HP metamorphic rocks, brittle features superimpose on earlier ductile ones as a result of the progressive localization of deformation. The islands of Tinos and Andros are part of the numerous metamorphic core complexes exhumed in the Aegean domain. They illustrate two steps of a gradient of finite extension along a transect between Mt. Olympos and Naxos. This study confirms the main role of boudinage as an initial localizing factor at the brittle–ductile transition and emphasizes the continuum of strain from ductile to brittle during exhumation. Early low-angle semi-brittle shear planes superimpose onto precursory ductile shear bands, whereas steeply dipping late brittle planes develop by progressive steepening of structures or sliding across en echelon arrays of veins. The comparison between Tinos and Andros allows us to propose a complete dynamic section of the Aegean extending continental crust and emphasizes that the strain localization process depends on both its rheological stratification and its compositional heterogeneity.

A novel technique for measuring the impact properties of a tough polyethylene

AbstractA novel technique is described which enables reliable fracture toughness measurements to be made in impact test on relatively small specimens of a tough polyethylene. Composite specimens have been made in which a tough polyethylene is sandwiched between two layers of a more brittle polyethylene. The overall fracture toughness is interpreted on the basis of simple additivity of the strain energy release rate associated with each of the component layers. Brittle plane strain failures were obtained for specimens in which the relative thickness of the layers was varied over a substantial range and the fracture toughness of each layer determined by suitable extrapolation. The fracture toughness of the brittle layer obtained in this way agreed well with direct measurements on that material.