Fracture damage prediction in fissured red sandstone under uniaxial compression: acoustic emission b‐value analysis

In this paper, uniaxial compression tests are conducted on fissured red sandstone specimens to predict fracture damage (large‐scale events). The acoustic mission (AE) coupled with digital image correlation (DIC) technologies are used to monitor and record the real‐time cracking process of tested specimens. The AE characteristics are analysed during the cracking process. Moreover, three types of b‐value methods based on the AE parameters are adopted to predict the occurrence of large‐scale events (macro‐cracking). The results show that every macro‐cracking leads to a rapid decrease in three types of b value. When the fissured specimens reach to ultimate failure, all three types of b value reach to the minimum. The b value based on the AE parameters can be used as a predictor of large‐scale events during the cracking process of fissured rocks.     

Simulation of cracking behaviours in interlayered rocks with flaws subjected to tension using a phase‐field method

A phase‐field method (PFM) is used to investigate cracking behaviours, including crack initiation and propagation, in interlayered rocks with preexisting flaws subjected to tension. An example with a bi‐material plate with a centre flaw is used to validate the PFM. Then, numerical simulations of cracking behaviours in interlayered rocks with a single flaw and a cross‐flaw are carried out using PFM. Moreover, the load‐displacement responses are numerically investigated. The PFM numerical results show that the crack propagation trajectories and peak loads of rock specimens depend on the preexisting flaw configuration and the mechanical properties of the interlayers.     

The influence of different fluids on the static fatigue of a porous rock: Poro-mechanical coupling versus chemical effects

Characterization of time-dependent brittle deformation is important for estimating the long-term stability of rock structures in shallow environments such as underground mines which are exposed to water or in a water vapor environment. The poro-mechanical (pore pressure) and chemical (stress corrosion reactions) effects of fluids at crack tips are responsible for the subcritical propagation of microcracks. This brittle creep results in the weakening of porous rocks over time (i.e., static fatigue). The focus of this work was to characterize using very long duration uniaxial multi-step creep tests, both the fluids effects on subcritical stress corrosion cracking in a porous rock (oolithic iron ore). Different fluids with increasing levels of chemical influence (oil, ethanol and water) were tested and both acoustic and mechanical properties were investigated. The evolution of the cumulative number of AE (Acoustic Emission) events, which reproduces the shape of the creep curves very efficiently, and static elastic properties indicate that micro-cracking plays the main role in the creep process. The poro-mechanical effect, which is predominant under partially saturated (water or ethanol) conditions, decreases the rate of subcritical cracking through capillary attraction forces. These forces harden porous rocks by modifying the effective stress state, increasing the activation energy barrier of the stress corrosion process and the fracture toughness and decreasing the stress intensity factor. The chemical effect of fluids is related to minerals developing stress corrosion reactions at crack tips which enhance subcritical cracking. Immersion in water/ethanol annihilates capillary forces and decreases the activation energy of the chemical reactions, thus increasing dilatancy, the rate of stress corrosion cracking, AE activity and rock weakening. Under saturated conditions, the time-dependent strength and time to failure increase as the chemical influence of the interstitial fluid decreases but the cumulative number and energy of AE at failure do not seem to be influenced by the chemistry of fluids. The short-term strength and deformability are also influenced by the level of chemical influence of the interstitial fluid but to a less remarkable extent because of the slow rate of chemical reactions. Water is therefore the most effective chemical agent promoting stress corrosion of iron ore among the fluids tested in our study.     

Bruchmechanik und zerstörungsfreie Werkstoffprüfung

Requirements by Fracture Mechanics on Nondestructive Testing Methods Fracture mechanics is a tool in evaluating the magnitude of critical flaws in structures. By means of Material properties such as fracture toughness, subcritical flaw growth, and existing primary and secondary stress it becomes possible to evaluate critical values for given flaw configurations. In Section XI, Appendix A of the ASME-Nuclear Pressure Vessel Code allowable flaw dephts are usually determined as a function of flaw configuration and localisation and wall thickness. Thus one wants to enable a fracture mechanical assessment of detected defects and of the safety of a component against brittle and tough fracture. Besides, it shall be possible to get an idea about the subcritical flaw growth. Therefore Practical application of fracture mechanics is based on progress in nondestructive surveillance methods. In the presented work the guidelines for integrity assessment of flawed structures based on Appendix A are described and the problems relating with fracture mechanical approaches are outlined. Up to this day it is not possible to get quantitative statements about the configuration, localisation and magnitude of flaws in structures by means of non destructive testing. Therefore factors of safety are introduced with the goal of assuring the integrity of flawed structures.     

An examination of the role of flaw size and material toughness in the brittle fracture of polyethylene pipes

At low temperatures and hoop stresses, polyethylene pipes fail by the time-dependent propagation of a crack. These brittle, fissure-like failures have been observed to initiate from adventitious flaws, and the concepts and methods of fracture mechanics indicate that flaw size should determine stress rupture lifetime. A number of controlled model experiments have therefore been undertaken to assess the influence of flaw size and material toughness on the stress rupture lifetimes of polyethylene pipes. To two different pipe grade polyethylene resins (one shorter, one longer lifetime resin) flaws of varying sizes have been added. For the shorter lifetime resin small flaws were, in addition, purposely excluded by the use of fine melt filtration techniques. Pipes containing added flaws or pipes where flaws were excluded were then stress rupture tested under those conditions designed to induce brittle failure by slow crack growth. The stress rupture lifetimes of the various pipes are then correlated with flaw size. The results of the tests using the shorter lifetime resin show that flaw size does have a significant influence. It is particularly interesting to note that melt filtration, which removes large inherent flaws, substantially improved the stress rupture lifetime. With respect to material toughness, the longer lifetime pipe grade polyethylene resin showed a healthy tolerance to included flaws. In respect of the stress rupture test preferred resins can therefore be identified in terms of their tolerance to included flaws.     

Cracking process of a granite specimen that contains multiple pre‐existing holes under uniaxial compression

The pre‐existence of openings, which play an important role in the mechanical properties and cracking behaviours of rock, is prevalent in rock mass. The interaction among pre‐existing openings (or holes) complicates the instability problems when rock contains multiple holes. Studying the strength failure behaviour of rock that contains multiple pre‐existing holes contributes to the fundamental knowledge of the excavation and stability of underground rock engineering. In this study, first, a series of uniaxial compression tests were performed on granite specimens that contain multiple small holes to investigate the effect of the geometry of pre‐existing holes on the strength and fracture behaviours of rock. The crack initiation, propagation and coalescence process, and acoustic emission (AE) characteristics were investigated using photographic and AE monitoring. Three failure modes were identified, ie, splitting failure, stepped path failure, and planar failure modes. Second, a set of micromechanical parameters in the PFC3D model were calibrated by comparison with the experimental results of an intact granite specimen. The numerically simulated peak strength, peak strain, and failure mode of preholed specimens were consistent with the experimental results. In accordance with the numerical results, the failure modes of the preholed specimens were dependent on the bridge angle and number of holes. Last, the internal fracture characteristics of numerical specimens were revealed by analyzing the horizontal and vertical cross sections at different positions.     

Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression

Uniaxial compression experiments were carried out for the marble samples (located in the eastern ground of China) with different pre-existing flaws in non-overlapping geometry by the rock mechanics servo-controlled testing system. Based on the experimental results of complete axial stress-axial strain curves, the effect of flaw geometry on the strength and deformation behavior of marble samples is made a detailed analysis. Compared with the intact marble sample, the marble samples with different pre-existing flaws show the localization deformation failure. The uniaxial compressive strength (UCS), elastic modulus and peak axial strain of marble samples with pre-existing flaws are all lower than that of intact marble sample, and the reduction extent is closely related to the geometry of pre-existing flaws. The crack coalescence were observed and characterized from internal tips of different pre-existing flaws in brittle marble sample. Eight different crack types were identified based on their geometry and crack propagation mechanism (tensile, shear and compressive) for two pre-existing flaws, which can be used to analyze the failure mode and cracking process of marble sample containing different flaws in uniaxial compression. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle marble sample is analyzed under uniaxial compression. The present research provides increased understanding of the fundamental nature of rock failure under uniaxial compression.     

Combined continuum damage‐embedded discontinuity model for explicit dynamic fracture analyses of quasi‐brittle materials

In this paper, a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi‐brittle failure phenomena. The model is capable of describing the rate‐dependent behavior in dynamics and the three phases in failure of quasi‐brittle materials. The first phase is always linear elastic, followed by the second phase corresponding to fracture‐process zone creation, represented with rate‐dependent continuum damage with isotropic hardening formulated by utilizing consistency approach. The third and final phase, involving nonlinear softening, is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions. The proposed model is capable of describing the rate‐dependent ductile to brittle transition typical of cohesive materials (e.g., rocks and ice). The model is implemented in the finite element setting by using the CST elements. The displacement jump vector is solved for implicitly at the local (finite element) level along with a viscoplastic return mapping algorithm, whereas the global equations of motion are solved with explicit time‐stepping scheme. The model performance is illustrated by several numerical simulations, including both material point and structural tests. The final validation example concerns the dynamic Brazilian disc test on rock material under plane stress assumption. Copyright © 2014 John Wiley & Sons, Ltd.     

Quasi-static fracturing in double-flawed specimens under uniaxial loading: the role of strain rate

Mechanical properties and cracking behaviors of flaw-weakened rock mass are distinguishably influenced by the quasi-static strain rate. Such advanced knowledge is mainly obtained through the numerical simulations, which are rarely verified experimentally. This paper carries out a coupled experimental-numerical investigation on double-flawed rock-like specimens at different quasi-static strain rates, with consideration given to the macro-mechanical properties, the quasi-static cracking behaviors and the underlying fracture mechanism. Three ordinary arrays of double pre-existing flaws, namely, the coplanar array, the vertical non-overlapping array and the vertical aligning array, are analyzed experimentally. The obtained results show that the crack initiation stress and the peak stress of double flaw-contained specimens generally increase with increasing the strain rate. The extension length of the first macroscopic crack, the crack initiation mode, the amount of far-field cracks, and the degree of ultimate fragmentation in double flaw-contained specimens are closely related to the strain rate. Furthermore, the vertical non-overlapping array of double pre-existing flaws is studied numerically by using peridynamics. The quasi-static fracture behaviors obtained by peridynamics are in good agreement with the experimental observations. The stress concentrates around the tips of flaws when the strain rate is relatively low, while apart from around the tips of flaws, the stress concentration also occurs in the interior of specimens when the strain rate is relatively high. This study provides the better understanding of the quasi-static strain rate effects on mechanical properties and fracture behaviors of rock mass, in particular those containing natural flaws that appear in sets or groups with similar orientation and characteristics.     

Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

A coupled model resulting from the boundary element method and eigen‐analysis is proposed in this paper to analyse the stress field at crack tip. This new combine method can yield several terms of the non‐singular stress in the Williams asymptotic expansion. Then the maximum circumferential stress (MCS) criterion taken the non‐singular stress into account is introduced to predict the brittle fracture of cracked structures. Two earlier experiments are re‐examined by the present numerical method and the role of the non‐singular stress in the brittle fracture is investigated. Results show that if more terms of non‐singular stress are taken into account, the predicted crack propagation direction and the critical loading by MCS criterion are much closer to the existing experimental results, especially for dominating mode II loading conditions. Moreover, numerical results manifest that Williams series expansion can describe the stress field further from the crack tip if more non‐singular stress terms are adopted.     

Experimental study on fracture behaviour of three‐flawed sandstone specimens after high‐temperature treatments

The crack coalescence of rocks significantly affects the stability of rock engineering, and extensive studies have been performed on preflawed rock specimens without thermal treatment. However, the fracturing behaviour of preflawed specimens after thermal treatment has not been investigated comprehensively. In this study, three‐flawed sandstone specimens with different flaw inclinations after high‐temperature treatments were tested under uniaxial compression. Photographic, acoustic emission and digital image correlation techniques were used to investigate the crack initiation, propagation and coalescence behaviour. Experimental results show that the peak strength, elastic modulus and peak strain of the three‐flawed specimens were lower than those of intact specimens and that they gradually recovered with increasing flaw angle. The peak strength and elastic modulus first increased and then decreased, whereas the peak strain increased with temperature. Noncoalescence, indirect coalescence and direct coalescence were three patterns observed between the two adjacent pre‐existing flaws. Finally, the mechanism of high temperature in alteration of the mechanical properties of sandstone was revealed through microobservations.     

The effect of fatigue pre‐cracking forces on fracture toughness

Testing procedures for the determination of the fracture toughness of a material by monotonic loading of fatigue pre‐cracked specimens are well established in standards such as BS 7448, BS EN ISO 15653, ISO 12135, ASTM E1820 and ASTM E1921. However, a review of these standards indicates a wide range of permitted fatigue pre‐cracking forces, whilst the underlying assumption in each standard is that the pre‐cracking conditions do not affect the fracture toughness determined. In order to establish the influence of different fatigue pre‐cracking forces on the fracture toughness, tests were carried out on specimens from an API 5L X70 pipeline steel. Single‐edge notch bend specimens of Bx2B geometry were notched through thickness and tested at temperatures of +20 °C, ?80 °C and ?140 °C to show the fracture behaviour in different regions of the fracture toughness ductile‐to‐brittle transition curve. Fatigue pre‐cracking was conducted on a high‐frequency resonance fatigue test machine over a range of pre‐cracking forces permissible within the various standards and beyond. The results showed that an excessively high pre‐cracking force can result in a significant overestimation of the value of fracture toughness for material exhibiting brittle behaviour, whilst very low fatigue pre‐cracking forces appeared to result in an increase in scatter of fracture toughness. A review of standards indicated that there was a possibility to misinterpret the intention of the ISO 12135 standard and potentially use excessively high pre‐cracking forces. Suggested clarifications to this standard have therefore been proposed to avoid the risk of overestimating fracture toughness.     

Study on Failure Characteristic of Rock‐Like Materials With an Open‐Hole Under Uniaxial Compression

Abstract: The failure strength model of brittle materials with a pre‐existing open‐hole defect is proposed in this paper. A modified Sammis–Ashby model is deduced, in which it can be used to calculate the peak strength of brittle materials. It shows the law between peak strength σ_p and independent variable μ, which is the ratio of open‐hole radius (a) to half‐width of the specimen (t). Moreover, numerical and experimental investigations on failure process of rock‐like materials with an open‐hole imperfection were carried out. In the experiments, 3D‐digital image correlation method, an optical technique which utilises the full‐field and non‐contact measurement, was employed. A progressive elastic damage method realistic failure process analysis (RFPA) was used in the numerical investigation to inspect and verify the modified model and simulate the failure process. The investigation finds that there are good correlations between the experimental, numerical and theoretical results. Moreover, because of the influences of boundary conditions, shear failure type was obtained both experimentally and numerically.     

Deformation localization and cracking processes of sandstone containing two flaws of different geometric arrangements

We present deformation localization and cracking process of sandstone with two flaws of different geometric configurations in uniaxial compression. The full field strain and progressive cracking processes are quantitatively monitored using three‐dimensional digital image correlation and acoustic emission techniques. The results show that peak strength and elastic modulus show a first decrease and then increase trend with regard to ligament angle under the same flaw geometry, achieving the minimum at the ligament angle 60°. The tensile strain develops at low stress level and then increases significantly. However, the shear strain only tends to be obvious while approaching peak stress. With the ligament angle increasing, the crack coalescence mode transfers from indirect to direct coalescence. In addition, the complete cracking processes of sandstone can be divided into six stages, together with six crack coalescence modes.     

The surface cracking of glassy polymers under a sliding spherical indenter

Glassy polymers crack under a sliding hard spherical indenter in a way that is observed in other brittle materials. A series of curved cracks concave to the wake of the indenter are formed and these can penetrate to a depth of a few hundredths of a millimetre. With polystyrene the additional stress imposed by sliding reduces the critical load to fracture under normal loading conditions by 95% and the presence of an active environment, methanol, reduced the critical fracture load for sliding by 83%. Other glassy polymers which are generally considered tough, cracked in the presence of agents which could promote environmental stress cracking. The stress necessary to cause cracking and the crack size obeyed laws pertaining to fracture under elastic stress conditions. Although the flaws observed are referred to as cracks it is recognized that they could possibly be crazes. The introduction of surface damage in the form of cracks or crazes is important practically, since the inadvertent scratching or abrasion of the polymer surfaces may introduce flaws which under normally acceptable stress-environmental conditions could lead to failure. It is also noted that the flaws are detrimental to the polymer's optical properties.     

Monitoring the fracture of wood in torsion using acoustic emission

Acoustic emission (AE) was used to monitor the failure process of hardwood and softwood test-pieces under static and fatigue torsional loading. In static torsional-loading tests, acoustic activity indicated some microcrack initiation before the visible cracking in both hardwood and softwood test-pieces. Hardwood produced more AE counts than softwood during testing, and the grain angle of test-pieces influenced the total AE counts. During torsional fatigue fracture, increased acoustic activity indicated the onset of microcrack formation. Fatigued test-pieces produced more total AE counts during fracture than static test-pieces, provided the angle of twist exceeded a minimum value. The results show that it is possible to monitor and analyze the failure process in wood when under torsional loading using acoustic emission techniques.     

A continuum damage mechanics method for fracture simulation of quasi‐brittle materials

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh.     

聚乙烯自增强复合材料损伤过程的声发射特征

复合材料在承受外载时, 声发射可产生于基体破裂、纤维-基体界面脱粘和纤维断裂等。测定了U HMWPE/ HDPE 复合材料在拉伸载荷作用下的声发射(AE) 振幅信号。对特殊试样, 即预测到断裂有明确方式, 如纤维-基体界面脱粘、基体破裂、纤维断裂和分层等的试样, 实施加载直至破坏。用扫描电子显微镜(SEM) 观测试样的断裂表面, 对产生于若干特殊损伤类型的AE 信号进行了鉴别。在相同加载条件下, 完成了不同种类的U HMWPE/ HDPE 准各向同性层合板声发射检测。结果在特殊试样损伤类型与声发射信号事件振幅之间建立了对应关系, 揭示了上述各种准各向同性层合板损伤扩展过程的AE 特征与损伤破坏机制。各种准各向同性层合板试样的声发射事件累计数对拉伸应力关系曲线相异, 其相同损伤类型发生时所对应的拉伸载荷水平不等, 表明它们的铺设角度和铺设顺序对损伤演变过程有显著的影响。结果证实了它们的最终破坏由严重层间分层造成。      

The effect of a residual stress field on fracture initiation in RPV steel

Whether flaws in structures containing residual (secondary) stresses will extend under particular operational (primary) loads depends on the extent to which the residual stress field affects: (a) the nature and distribution of initiators; (b) the combined (primary + secondary) stresses and strains experienced by potential initiators. This paper compares fractographic data from specimens loaded by only a primary stress with data from specimens also containing a tensile residual stress field. Three‐dimensional elastic–plastic finite element calculations are used to characterize the stress–strain conditions at the initiation sites at the onset of brittle fracture. The introduction of a residual stress changes the dominant stage in fracture nucleation from microcrack extension to particle cracking. This offsets some of the decrease in fracture toughness expected when the residual stress field increases specimen constraint.