Tensile Crack Propagation Research Articles

Rock mass strength at depth and implications for pillar design

Construction of infrastructure in deep underground mines depends on an understanding of near wall rock behaviour as well as the ultimate load bearing capacity of confined rock, and thus on a reliable strength criterion for the rock near and far from the excavation. The topic of brittle failing rock i.e. rock failure dominated by tensile crack and fracture propagation even under low overall compressive conditions, is briefly summarised. Recently, it was suggested that the failure envelop for the entire confinement range of brittle rocks and rock masses is distinctly S-shaped. If validated, this impacts engineering problems such as pillar design where both wall instability and confined rock mass stability issues need to be considered. This paper explores the limitations and potential opportunities in pillar design. It is illustrated that current empirical design rules may be flawed and further studies are required to arrive at more economic designs for pillars at depth, or under high stress, and in brittle failing rock masses. When confined in the core of pillars, the rock mass may exhibit superior strength than typically assumed by Mohr–Coulomb or Hoek–Brown failure criteria as it will fail differently than near the wall. As a result, pillar strength may be underestimated based on field observations and if procedures of rock strength back analysis from near wall behaviour are adopted to determine the rock mass strength envelop. This means that the strength of pillars with width to height (W/H) ratios exceeding 1·5 to 2 may be systematically underestimated and may become burst prone, as the core may not yield as anticipated. Consequently, pillar designs based on current empirical rules may be inadvertently conservative and thus not optimal from an economic perspective. This aspect is of particular interest for block cave mines where drawpoint spacing may have a significant impact on cave propagation, recovery performance, and economics.

Upper and lower bounds for structural design of RC members with ductile response

In the present paper, some of the complex phenomena characterizing the flexural behaviour of reinforced concrete beams, such as hyper-strength and snap-back and snap-through instabilities, are interpreted under a unified approach based on nonlinear fracture mechanics concepts. In particular, they are analysed by means of a numerical algorithm adopting the cohesive crack model for concrete in tension and the overlapping crack model for concrete in compression. According to the latter constitutive law, a fictitious interpenetration is assumed to describe the concrete damage, analogously to the fictitious crack opening used for tension. Such an integrated cohesive-overlapping crack model is applied to assess the minimum reinforcement amount necessary to prevent unstable tensile crack propagation and to evaluate the rotational capacity of plastic hinges. The main novelty is given by the capability to predict the size-scale effects evidenced by several experimental programmes available in the literature. According to the numerical results obtained, new practical design formulae and diagrams are proposed, as well as, upper and lower bounds to the reinforcement amount, the material properties and the structural dimensions are defined in order to avoid brittle failures.

A crack-tracking technique for localized damage in quasi-brittle materials

This work presents a procedure to simulate the growth and propagation of localized tensile cracks on quasi-brittle materials. The so-called smeared damage approach, which consists in standard finite elements and local nonlinear constitutive laws, is recovered and improved in order to represent crack localization and avoid spurious mesh-bias dependence in the discrete problem. This is achieved by means of the implementation of a local crack-tracking algorithm which can reproduce individual (discrete) cracks and ensure objectivity of the finite element problem solution. The performance of the localized damage model is stressed by means of the analyses of structural case-studies. Compared to the Smeared Crack Approach in its original form, the presented procedure shows clearly a better capacity to predict realistic collapse mechanisms. The proposed tracking technique is relatively inexpensive.

Nonlinear fracture mechanics investigation on the ductility of reinforced concrete beams

In the present paper, a numerical algorithm based on the finite element method is proposed for the prediction of the mechanical response of reinforced concrete (RC) beams under bending loading. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing. According to this model, the concrete dam- age in compression is represented by means of a fictitious interpenetration. The larger is the interpenetration, the lower are the transferred forces across the damaged zone. The well-known Cohesive Crack Model in tension and an elastic-perfectly plastic stress versus crack opening displacement relationship describing the steel reinforcement behavior are also integrated into the numerical algorithm. The application of the proposed Cohesive-Overlapping Crack Model to the assessment of the minimum reinforcement amount neces- sary to prevent unstable tensile crack propagation and to the evaluation of the rotational capacity of plastic hinges, permits to predict the size-scale effects evidenced by several experimental programs available in the literature. According to the obtained numerical results, new practical design formulae and diagrams are proposed for the improvement of the current code provisions which usually disregard the size effects.

Numerical simulation of geofluid focusing and penetration due to hydraulic fracture

Ore body formation and mineralization are the consequence of transport, focusing and mixing processes of geofluids from the deep earth into the upper crust of the earth. These processes largely depend on geological structures, particularly heterogeneity such as cracks and faults. Both geological stress and geofluid-induced hydraulic pressure can create and alter the heterogeneity, thus changing the transport, focusing and mixing patterns. As a preliminary study, this paper investigates the intrusion and focusing of geofluids through simulation of the hydraulic fracturing process. First, the deformation of porous media and geofluid flow are coupled through the Biot's consolidation theory to consider both the elastoplasticity of porous media and the deformation induced evolution of permeability. Second, the crack induced anisotropy of stiffness and permeability is described, on the basis of a smeared theory and an equivalent anisotropic medium, to establish a criterion for tensile crack initiation and propagation at an element level. Finally, the resulting nonlinear equations are solved by a coupled algorithm of the meshless method and the finite element method (FEM). Numerical examples indicate that the proposed method is able to simulate the stress-induced crack propagation, geofluid intrusion and focusing in fluid-saturated porous media. It thus provides a potential tool for simulating the detailed mineralization process associated with the geological stress and geofluid intrusion.

Practical Estimates of Tensile Strength and Hoek–Brown Strength Parameter m i of Brittle Rocks

By applying the Griffith stress criterion of brittle failure, one can find that the uniaxial compressive strength (σc) of rocks is eight times the value of the uniaxial tensile strength (σt). The Griffith strength ratio is smaller than what is normally measured for rocks, even with the consideration of crack closure. The reason is that Griffith’s theories address only the initiation of failure. Under tensile conditions, the crack propagation is unstable so that the tensile crack propagation stress (σcd)t and the peak tensile strength σt are almost identical to the tensile crack initiation stress (σci)t. On the other hand, the crack growth after crack initiation is stable under a predominantly compressive condition. Additional loading is required in compression to bring the stress from the crack initiation stress σci to the peak strength σc. It is proposed to estimate the tensile strength of strong brittle rocks from the strength ratio of \( R = {\frac{{\sigma_{\text{c}} }}{{\left| {\sigma_{\text{t}} } \right|}}} = 8{\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}}. \) The term \( {\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}} \) accounts for the difference of crack growth or propagation in tension and compression in uniaxial compression tests. \( {\frac{{\sigma_{c} }}{{\sigma_{ci} }}} \) depends on rock heterogeneity and is larger for coarse grained rocks than for fine grained rocks. σci can be obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the strength ratio R determined, the tensile strength can be indirectly obtained from \( \left| {\sigma_{\text{t}} } \right| = {\frac{{\sigma_{\text{c}} }}{R}} = {\frac{{\sigma_{\text{ci}} }}{8}}. \) It is found that the predicted tensile strengths using this method are in good agreement with test data. Finally, a practical estimate of the Hoek–Brown strength parameter mi is presented and a bi-segmental or multi-segmental representation of the Hoek–Brown strength envelope is suggested for some brittle rocks. In this fashion, the rock strength parameters like σt and mi, which require specialty tests such as direct tensile (or Brazilian) and triaxial compression tests for their determination, can be reasonably estimated from uniaxial compression tests.

Tensile performance and crack propagation of coated woven fabrics under multiaxial loads

AbstractThe tensile performance of coated woven fabrics under multiaxial loads is examined in the present study. Two groups of experiments were conducted to investigate the influences of the configuration of the fabric specimen and the loading speed on the multiaxial tensile properties of the fabrics. The configuration of the specimen for the multiaxial tensile tests is identified as gear‐shape with large arm widths. A loading speed of lower than 20 mm/min is suggested to obtain the tensile properties of the coated woven fabrics under multiaxial loads. The tensile performances of coated woven fabrics under uni‐, bi‐, and multiaxial loads were compared. We found that the tensile performances under bi‐ and multiaxial loads are much better than those under uniaxial loads. Therefore, for the application of the coated woven fabrics in lightweight structures, biaxial or multiaxial loading conditions will be necessary. Experiments on the specimens with an initial crack in the center under multiaxial loads show that, by comparison with other loading directions, the tensile properties in warp direction of the coated woven fabrics play an important role in the failure performance and crack propagation under multiaxial loads. To eliminate the dependence on the mechanical properties in warp direction, the balance of the two principle directions of coated woven fabrics should be improved. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Evaluation of Post-Weld Heat Treatments to Restore the Corrosion Resistance of Friction Stir Welded Aluminum Alloy 7075-T73 vs. 7075-T6

Friction stir welding (FSW) is rapidly becoming accepted as a viable manufacturing process for aerospace applications. One potential area of concern, however, is the corrosion resistance of some FSW joints. While the corrosion resistance of friction stir welded 7075 aluminum has been investigated, and attempts made to enhance its corrosion resistance through different combinations of starting temper and post-weld artificial aging (PWAA) treatments, a clear approach for selecting pre-temper conditions and PWAA processing has not emerged. For this investigation, FSW butt-welds in sheets of 0.125-inch 7075-T73 and 7075-T6 were given a variety of PWAA treatments, some of which were developed previously by other authors. Thermal treatments were evaluated using optical microscopy, exfoliation, electrical conductivity, microhardness, tensile, and fatigue crack propagation testing. An important conclusion drawn from this work is that 7075-T73 can be friction stir welded and post-weld aged in a manner that produces superior exfoliation resistance and good mechanical properties without invalidating the bulk parent material temper specified in AMS 2770G.

Characterization of seam weld quality in AA6082 extruded profiles

The performance of the extruded profile in subsequent manufacturing processes such as bending or forming is limited by the strength of the weakest weld. In literature, owing to the great variety of extruded profile shapes, different techniques for testing welds have been proposed: tensile tests, bending tests or wedge insertion among the others. In this paper the production of an I shape extruded profile, suitable for mechanical testing, has been described and analyzed. This profile was produced both with and without material welding, by the use of a bridge before the flat die, thus reproducing the typical welding condition of a hollow profile extrusion. Different preheating temperatures of the billet, production rates and welding chamber heights were used and their influence on the weld quality was analyzed. The welded profiles were characterized by means of both tensile tests (strength, elongation and fracture strain) and crack propagation tests, in order to understand the relationships between process parameters, die design and weld properties. The results were compared with unwelded profiles. Metallographic analyses were also performed in order to explain fracture mechanisms.

Simulation of dynamic response of granite: A numerical approach of shock-induced damage beneath impact craters

The mechanical response of rocks to dynamic loading is complex. It is not well understood because of the difficulty of defining an effective shear and tensile strength model. Recently AUTODYN-2D from Century Dynamics is used to simulate the shock-induced damage in granite targets impacted by projectiles at different velocities. The simulated results are compared with experiment data. Johnson–Holmquist shock damage constitutive model for brittle materials is applied to describe the damage and shear strain achieved in a confined volume of granite. A tensile crack softening model is coupled with the JH model to simulate the propagation of radial tensile cracks generated by the principal tensile stress perpendicular to the shock front. The tensile stress is assumed to be equal to the deviatoric stress at radii that experience less than the Hogoniot elastic limit stress. Instead of traditional grid-based methods, a smooth particle hydrodynamics is used to define damaged regions in brittle media.

Assessment of excavation damaged zone using a micromechanics model

Abstract It is well known that acoustic emission (AE) and microseismic (MS) events are indicators of rock fracturing or damage as the rock is brought to failure at high stress. By capturing the microseismic events, underground excavation induced rock mass degradation or damage can be located. The use of microseismic method has been shown as a valuable tool in a number of nuclear waste repository research programs to monitor the extent of the excavation damaged zone (EDZ), but most of the works are limited to a qualitative assessment. This paper presents a study on the quantification of the degree of damage, in terms of crack density calculated from the crack length, and the extent, in terms of crack density distribution, from microseismic event monitoring data. The approach builds on the finding that a realistic crack size corresponding to a microseismic event can be established by applying a tensile cracking model instead of the traditional shear model, commonly used in earthquake data analysis. It can be shown that brittle rock failure is the result of tensile crack initiation, propagation, accumulation, and interaction. Tensile stress can be generated in a confined rock with heterogeneous material properties. When a crack is formed by tensile cracking in this fashion, its orientation tends to become parallel to the direction of maximum compressive stress. A method is developed to take microseismic event monitoring data as input to determine the damage state and the extent of the EDZ by crack distribution. Based on the crack orientation and crack density information, the rock is modeled by a micro-mechanics based constitutive model which considers the anisotropic material properties. Numerical examples are presented using field monitoring data from a tunnel in granite to demonstrate how microseismicity can be quantitatively linked to dynamic rock mass properties.

Development of Low Carbon and Boron Added 22Mn-13Cr-9Ni-1Mo-0.24N Steel (JK2LB) for Jacket Which Undergoes<tex>$hboxNb_3hboxSn$</tex>Heat Treatment

Japan Atomic Energy Research Institute has developed a low carbon and boron added 0.03C-22Mn-13Cr-9Ni-1Mo-0.24N-0.003B steel (JK2LB) for a conductor jacket of the central solenoid for the International Thermonuclear Experimental Reactor in collaboration with Kobe Steel Ltd. The feature of JK2LB is to have enough ductility and toughness after reaction heat treatment to produce Nb/sub 3/Sn. Tensile properties, fracture toughness, and fatigue crack propagation rate were measured at 4 K by using samples taken from an intermediate billet and the final jacket of JK2LB, which were produced with a mass production line. The average elongation and fracture toughness at 4 K after the heat treatment are 33% and 93 MPa/spl radic/m for the final jacket, and 30% and 121MPa/spl radic/m for the intermediate billet, respectively. The mechanical properties of weld metals were also evaluated and all data satisfied the ITER targets. It was also clarified that improvement of ductility and toughness were caused by reduction of chromium carbide precipitations due to low carbon and boron addition.

Characterisation and Modelling of Brittle Fracture in Two-dimensional Soil Cutting

Brittle fracture by the propagation of tensile cracks accounts for soil failure during many soil cutting and tilth forming operations. However, this mechanism is little understood and cannot be analysed using the classical Mohr–Coulomb failure theory in which soil is characterised by its cohesive strength c and angle of internal shearing resistance φ. Based on previous experimental observations of its deformation characteristics, a theoretical analysis was developed for the mechanism of brittle fracture using linear elastic fracture mechanics methods. The soil was characterised by a fracture strength property namely the critical stress intensity factor K Ic . Using five model plane blades of rake angles 25, 40, 55, 70 and 90°, respectively, soil cutting experiments were carried out in the laboratory on sandy loam and clay loam soils prepared to different soil strength and soil–blade interface conditions. During these experiments, clod sizes and cutting force components were measured. The results showed that in brittle fracture, the cutting force is cyclic in nature and is essentially concentrated in the region of the blade tip. For experiments where brittle fracture occurred, clod size estimates based on critical crack lengths predicted using the present brittle fracture theory were in closer agreement with measured experimental rupture distances than rupture distances predicted using existing shear failure theory. The theoretical analysis, which comprises inter alia two regimes of crack behaviour termed the short and long crack models, covers the complete process of crack initiation and subsequent clod formation. The analysis further shows that there is a transition from short to long crack behaviour and the cutting force attains a maximum during this transition. However, the inability to deduce short crack behaviour under mixed mode loading limits further extraction of this maximum cutting force using the present theoretical analysis.

Mechanical and Fatigue Properties of the SiCp/Al Composites

Mechanical and fatigue properties of the SiCp/Al with three different SiC particle volume fractions: 5%, 7.5% and 10% as well as Al6061 alloy were examined with tensile test, hardness measurement and fatigue crack propagation test. Tensile strengths and hardness of the SiCp/Al increased together with SiC particle volume fraction. It was checked that tensile strengths of the SiCp/Al had a certain relation with the corresponding hardness. On the other hand, fatigue crack propagation behavior (FCPB) of the SiCp/Al was faster than that of the AA6061. Besides, difference of the FCPB among SiC particle volume fractions was not pronounced. However, The FCPB slightly increased together with SiC particle volume fraction. It was noted that fatigue properties of the SiCp/Al was more affected by local volume fraction in front of crack tip than bulk volume fraction. In addition, the presence of SiC particles delayed fatigue crack initiation effectively because the percentage of fatigue crack initiation life to the whole fatigue life was a maximum of 38%, larger than that of ordinary structural materials.

Crack propagation from 3-d surface fractures in pmma and marble specimens under uniaxial compression

To understand deeply the fracture mechanism of brittle rock material, the rock specimen containing combined flaws (two square holes and one pre-existing fissure) with seven different fissure angles is carried out the numerical simulation by RFPA2D. Numerically simulated results show a good agreement with the experimental results. The crack coalescence behavior of specimen containing combined flaws under uniaxial compression is summarized, which is closely dependent to fissure angle. The stable propagation of original cracks does not lead to a larger AE event, but the coalescence of new cracks causes a larger AE event. The peak strength of specimen containing combined flaws increases with the confining pressure. According to the linear Mohr–Coulomb criterion, the cohesion and internal friction angle of specimen containing combined flaws are obtained, which is found to take on a distinct nonlinear relation with the fissure angle. The accumulated AE events decreases as the confining pressure increases from 0 to 30 MPa, which results mainly from the restraining of higher confining pressures on the initiation and propagation of tensile cracks at the fissure tips and nearby double squares.

Fatigue characteristics of AC4CH aluminium cast alloys fabricated by inclined cooling plate technique

Semi-solid metal casting influences not only the primary α size but also the size of grains, eutectic Si and intermetallic compound particles, as well as their spheroidization. To examine the effects of microstructure on mechanical properties, cast aluminium alloys having three different primary α sizes (i.e. 38 μm, 82 μm and 160 μm) were prepared by the means of the inclined cooling plate technique. Tensile, fatigue and short fatigue crack propagation tests are performed. In-situ tensile tests are also carried out with a scanning electron microscope to quantify the difference in damage accumulation behaviors during tensile loading. The material with the smallest primary a size (i.e. 38 μm) showed the maximum improvement in almost all of the investigated mechanical properties. However, the improvements were at most around 10% as compared to the squeeze cast material. Moreover, in-situ studies revealed that damage accumulation during tensile loading did not have a discernible effect on fatigue properties. This unexpected lack of improvement can not be attributed to the difference in grain structure according to the quantitative investigation of misorientation angles between neighboring grains by the SEM-EBSP technique.

Mechanical performance of acrylic bone cements containing different radiopacifying agents

The effect that three different radiopacifying agents, two of them inorganic (BaSO4, ZrO2) and one organic (an iodine containing monomer, IHQM) have on the static and dynamic mechanical properties of acrylic bone cements was studied. Compressive and tensile strength, fracture toughness and fatigue crack propagation were evaluated. The effect of the inorganic fillers depends on their size and morphology. In relation to the radiolucent cement, the addition of zirconium dioxide improved significantly the tensile strength, the fracture toughness and the fatigue crack propagation resistance. In contrast, the addition of barium sulphate produced a decrease of the tensile strength, but did not affect the fracture toughness and improved the crack propagation resistance. When the iodine containing monomer was used, although the tensile strength and the fracture toughness increased, the fatigue crack propagation resistance remained as low as it was for the radiolucent cement.

Roller-Compacted Fiber Concrete Pavement Foundation with Recycled Aggregate and Waste Plastics

A laboratory investigation was conducted to evaluate the performance of a moderate-strength roller-compacted concrete (RCC) made from reclaimed crushed concrete used as aggregate, Class C fly ash, and wasteplastic fibrous reinforcement. The motivation for evaluating this primarily waste composite is to develop a high-quality foundation layer for a conventional flexible or rigid pavement while attempting to address such crucial issues as the ever-increasing solid waste disposal problem, rapidly depleting landfill spaces, and conservation of natural resources. A summary is given of the findings of materials characterization studies with the following objectives: ( a) to evaluate the effectiveness of recycled high-density polyethylene strips in stabilizing the tensile crack propagation through the brittle cementitious matrix; ( b) to determine the strength and toughness characteristics of the composite; and ( c) to suggest performance-based mixture design proportions for recycled aggregate, fly ash, cement, and recycled plastic fibers. Because an RCC pavement slab will be subjected to repeated tensile stresses under traffic loads, the study focused on instrumented split tensile and flexural tests to evaluate the performance of the foundation material. Results indicate that a mix containing only 8 percent cement and 92 percent recycled materials can achieve 28-day compressive strengths of up to 14 MPa and split tension strength of 1.5 MPa. It is found that the plastic fibers can improve the toughness characteristics significantly in split tension and moderately in flexure. Therefore, the new cement-bound composite made primarily from recycled products offers promise as an alternative material for construction and rehabilitation of highway pavements.

岩盤 つくばでの最近の研究 （３） 砂岩のサブクリティカルなクラック成長とそれに基づく引張強度のひずみ速度依存性推定の試み

Double torsion tests in ambient air and liquid water have been used to establish stress intensity factor (KI )-crack velocity (V ) diagrams for propagation of single tensile crack in dry or water-saturated sandstones, Kimachi sandstone and Shirahama sandstone. The following main results were obtained: 1) All the experimental data for dry specimens in ambient air and water-saturated specimens in water pertain to region I of the typical KI-V curve, while even region II was clearly observed in KI-V curve of dry specimens tested in water. The appearance of region was particularly clear in Shirahama sandstone. 2) No stress corrosion limit was encountered in the specimens tested in water even at nearly 20 % of critical stress intensity factor (KIC ). But, dry Kimachi sandstone specimen tested in ambient air possibly exhibits the stress corrosion limit at nearly 50 % of critical stress intensity factor (KIC ). 3) The KI-V data of Kimachi sandstone were used to generate a diagram predicting the influence of strain rate on tensile strength. These predictions were in good agreement with the tensile strength determined by Brazilian experiments in ambient air and liquid water. Both the predictions and the experimental results are consistent with a monotonic reduction in tensile strength as strain rate is reduced from nearly 10-2 s-1 to nearly 10-8 s-1.

Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone

Discontinuous fatigue disturbances are common in rock mass engineering, but the corresponding mechanical behaviour of rock is unclear. In this study, discontinuous multilevel constant-amplitude fatigue tests of sandstone containing pre-existing cracks with different angles were performed, and the fatigue characteristics and fracture behaviour were analysed using acoustic emission (AE) and digital image correlation (DIC) techniques. The results showed that the peak strength and strain, fatigue life and modulus decreased with increasing crack angle. The dissipated energy first decreased and subsequently increased during loading, and the relationship between the three strain energy density parameters and the stress level was a quadratic polynomial. Meanwhile, there was a significant accelerating energy release (AER) phenomenon in the AE energy, and the AE energy release of the 0° and 30° samples was more rapid. A fatigue damage model considering the initial damage was established based on the strain energy density, and the initial damage and cumulative rate of fatigue damage were proportional to the crack angle. In terms of fracture behaviour, the samples developed wing cracks, anti-wing cracks, secondary shear cracks, and out-of-plane shear or tensile crack propagation in sequence. The change in b-value indicated that the load holding at a higher stress level would increase the propagation scale of rock fatigue cracks. The AF and RA values indicated that the 0° and 30° samples were dominated by tensile fracture, while the 60° and 90° samples were dominated by shear fracture. The shear cracks were concentrated in the unstable fracture stage, and the ratio was proportional to the crack angle.