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A mixed-mode geometry has been chosen to investigate a crack propagation using the multi-parameter fracture mechanics concept. The so-called Williams series expansion is used for the crack-tip stress field approximation. It has been shown that application of the generalized fracture mechanics concept can be crucial for materials with specific fracture behaviour, such as elastic-plastic or quasi-brittle one, when fracture occurs not only in the very vicinity of the crack tip, but also in a more distant surrounding. Then, considering the higher-order terms of the Williams expansion in fracture criteria (describing the crack stability and/or crack propagation direction) can bring more precise results. The coefficients of the Williams expansion must be calculated numerically (for instance by means of the over-deterministic method in this work) for each cracked configuration, which is very time-consuming, and the analysis is very extensive even for a few basic cracked specimen configurations. On the other hand, a suitable choice of the geometrical configuration of the cracked disc enables performing experiments only on the specimens that could prove the theory about the importance of using the higher-order terms.

PurposeSoil cracking is a common natural phenomenon. The existence of soil cracks has significant effects on the engineering properties of clayey soil, and can cause significant problems in geotechnical, geological, and environmental aspects. Understanding of the potential mechanisms of soil cracking is essential in assessments of potential damages to earthen infrastructures.Materials and methodWe review the past research efforts devoted to the experimental investigations and applications of fracture mechanics in soil cracking, attempting to provide a better understanding of the formation mechanism of desiccation cracking with a perspective of fracture mechanics.Results and discussionThis review analyzes the influence of soil cracking on soil engineering properties and the significance of soil cracking phenomena. Past and current formulations of soil fracture criteria and their experimental investigation are discussed. This review reveals the factors that affect the mechanisms of soil fracture can be divided into two groups, namely soil intrinsic properties and test-related factors. The applications of fracture mechanics in soil cracking are also discussed with particular focus on soil fracture models that are separately based on linear elastic fracture mechanics (LEFM), elastic plastic fracture mechanics (EPFM), and numerical simulations of soil cracking based on fracture mechanics. Some challenges and prospects of the applications of fracture mechanics in soil cracking are presented.ConclusionsFracture mechanics is a significant method to explain soil crack initiation and propagation. It is expected that researchers can gain better understanding of the range of fracture mechanics applications in soil cracking, and seek improvements and extensions of existing models through this review.

Cracking in fibrous composites is inevitable, and the fracture pattern is influenced by its fiber distribution. Bamboo fibrous composites have a distinct fiber distribution, which makes them an excellent material for studng the relationship between fiber distribution and fracture mode. Glued laminated bamboo is a bi-directional bamboo fibrous composite, which is called glubam for short. Its vertical thickness is about 28 mm, and the ratio of the number of longitudinal fiber layers to the number of transverse fiber layers is 4:1. This study conducted three-point bending fracture tests on single-edge notched specimens of glubam to investigate its mode-I fracture characteristics in the transverse vertical direction. The deformation curves show that the specimens still have the load-carrying capacity after reaching the maximum load, and the load shows a trend of step-like decrease, exhibiting a quasi-ductile fracture behavior. Overall, the fracture process can be divided into four stages, including linear, softening, quasi-ductile, and failure stages. In this study, based on certain assumptions, the prefabricated notch length a0 was adjusted according to the position of the transverse fibers. Subsequently, the non-linear elastic fracture mechanics method was employed to calculate the fracture parameters of glubam during the softening and quasi-ductile stages, including the fracture toughness KIC* and fiber tensile strength ft. The deviation of the fracture parameters between the two stages is within 10%, indicating that the correction of the a0 is correct. This indirectly proves that the staggered structure formed by longitudinal and transverse fibers is responsible for the quasi-toughness fracture of glubam. Finally, this study summarized and analyzed the quasi-ductile fracture behavior and found that materials or structures exhibiting quasi-ductile fracture behavior often possess a staggered structure. This staggered structure makes the crack in the form of semi-stable propagation, while the load decreases in a step-like manner.

Several studies have been conducted on the fatigue behavior of copper and 7-3, and 6-4 brasses. However, there have been fewer studies on the fatigue behavior and fatigue crack growth (FCG) properties of free-cutting brass, primarily because emphasis has been placed on the development of lead-free free-cutting brass. In this study, fatigue experiments were performed in the atmosphere at room temperature using three types of free-cutting, two types of bismuth (Bi)-based (with different grain sizes), and lead (Pb)-based brasses. It was found that lead-free Bi-based free-cutting brass had approximately the same fatigue performance as that of Pb-based free-cutting brass. It was also clarified that the addition of Bi or Pb initiated fatigue cracks, and that the crack growth period occupied most of the fatigue life. Differences in the FCG behavior of the three free-cutting brasses were observed in the low ΔK range. The modified linear fracture mechanics parameter M was used to quantitatively analyze the fatigue life and FCG behavior (short surface cracks). A comparison between the calculated and experimental results showed that M was useful.

Anisotropy is ubiquitous in the Earth's crust, which causes the elastic characteristics of seismic waves to change with direction. The study of seismic wave anisotropy is of great significance to seismic exploration, prediction and geodynamics. As one of the sources of seismic anisotropy, in situ stress belongs to secondary anisotropy as common as the intrinsic and fracture-induced anisotropy, but it is often ignored among the sources of seismic anisotropy. Therefore, we focus on the study of seismic anisotropy under the influence of in situ stress using the nonlinear acoustoelasticity theory. Based on a horizontal transversely isotropic (HTI) model and the linear slip theory, the characteristics of azimuthal seismic reflection response in anisotropic media under horizontal in situ stress are discussed in this paper. Firstly, by using the quasi-linear relationship between stress and Tsvankin’s anisotropic parameters and the transformation relationship between anisotropic and fracture parameters in HTI medium, the elastic stiffness matrix of an HTI medium with the effect of horizontal in situ stress is established. Secondly, the reflection coefficient of PP-wave seismic data for a planar weak-contrast interface separating two weak-anisotropy and small-stress HTI half-spaces is derived using both the seismic scattering theory and the stiffness matrix under horizontal in situ stress, building the quantitative relationship between azimuthal seismic reflection characteristics and the model parameters, such as the background elastic parameters, the fracture parameters and the horizontal-stress-induced anisotropic parameters. Finally, the variation rules of azimuthal seismic reflection response characteristics of four elastic interfaces under different in situ stress conditions are analyzed. The results demonstrate that the seismic inversion for fracture parameters and horizontal-stress-induced anisotropic parameters is more favorable under the condition of large incident angle. In addition, the effect of horizontal in situ stress on the reflection coefficient depends on the second- and third-order elastic properties of the rock itself. Also, the established seismic PP-wave reflection coefficient equation has provided an alternative approach to calculate the magnitude of horizontal in situ stress.Article HighlightsA novel linearized PP-wave reflection coefficient is presented for HTI media with the effect of horizontal in situ stressThe response law of azimuthal seismic reflection characteristics induced by horizontal in situ stress is demonstratedA simple inversion method is provided to calculate the magnitude of horizontal in situ stress

The fracture mechanism and macro-properties of SVSAC were studied using a novel test system combined with numerical simulations, which included three-point bending beam tests, the digital image correlation (DIC) technique, scanning electron microscopy (SEM), and ABAQUS analyses. In total, 9 groups and 36 specimens were fabricated by considering two critical parameters: initial notch-to-depth ratios (a0/h) and concrete mix components (seawater and volcanic scoria coarse aggregate (VSCA)). Changes in fracture parameters, such as the load-crack mouth opening displacement curve (P-CMOD), load-crack tip opening displacement curve (P-CTOD), and fracture energy (Gf), were obtained. The typical double-K fracture parameters (i.e., initial fracture toughness (KICini) and unstable fracture toughness (KICun)) and tension-softening (σ-CTOD) curve were analyzed. The test results showed that the initial cracking load (Pini), Gf, and characteristic length (Lch) of the SVSAC increased with decreasing a0/h. Compared with the ordinary concrete (OC) specimen, the P-CMOD and P-CTOD curves of the specimen changed after using seawater and VSCA. The evolution of the crack propagation length was obtained through the DIC technique, indicating cracks appeared earlier and the fracture properties of specimen decreased after using VSCA. Generally, the KICun and KICini of SVSAC were 36.17% and 8.55% lower than those of the OC specimen, respectively, whereas the effects of a0/h were negligible. The reductions in Pini, Gf, and Lch of the specimen using VSCA were 10.94%, 32.66%, and 60.39%, respectively; however, seawater efficiently decreased the negative effect of VSCA on the fracture before the cracking width approached 0.1 mm. Furthermore, the effects of specimen characteristics on the fracture mechanism were also studied through numerical simulations, indicating the size of the beam changed the fracture toughness. Finally, theoretical models of the double-K fracture toughness and the σ-CTOD relations were proposed, which could prompt their application in marine structures.

As a commonly used surface structure for airport runways, concrete slabs are subjected to various complex and random loads for a long time, and it is necessary to investigate their fracture performance at different strain rates. In this study, three-point bending fracture tests were conducted using ordinary performance concrete (OPC) and basalt fiber-reinforced airport pavement concrete (BFAPC) with fiber volume contents of 0.2, 0.4, and 0.6%, at five strain rates (10−6 s−1, 10−5 s−1, 10−4 s−1, 10−3 s−1, and 10−2 s−1). Considering parameters such as the peak load, initial cracking load, double K fracture toughness, fracture energy, and critical crack expansion rate, the effects of the fiber volume content and strain rate on the fracture performance of concrete were systematically studied. The results indicate that these fracture parameters of OPC and BFAPC have an obvious strain rate dependence; in particular, the strain rate has a positive linear relationship with peak load and fracture energy, and a positive exponential relationship with the critical crack growth rate. Compared with OPC, the addition of basalt fiber (BF) can improve the fracture performance of airport pavement concrete, to a certain extent, where 0.4% and 0.6% fiber content were the most effective in enhancing the fracture properties of concrete under strain rates of 10−6–10−5 s−1 and 10−4–10−2 s−1, respectively. From the point of view of the critical crack growth rate, it is shown that the addition of BF can inhibit the crack growth of concrete. In this study, the fracture properties of BFAPC were evaluated at different strain rates, providing an important basis for the application of BFAPC in airport pavement.

A correct understanding of the fracture mechanism of Recycled Aggregate Concrete (RAC) plays an important role in the design of RAC structure and also in gaining a better understanding of the behavior of structures made from it. On the other hand, one of the most important parameters that affects cracking behavior and the fracture parameters of concrete is the water to cement ratio. The main objective of this study is to investigate the effect of different water to cement ratios on the fracture behavior of RAC. To achieve this objective, 125 notched concrete beams were subjected to three-point bending experiments, with W ranging 0.35 to 0.7. Specific fracture energy ( G F ) and characteristic length ( L ch ) from work-of-fracture method and initial fracture energy ( G f ), brittleness number, fracture toughness, effective length of fracture process zone ( C f ), and the critical crack-tip opening displacement from size effect method were evaluated. The results illustrate that G F and G f increase by 34 and 64% when W reduces from 0.7 to 0.35, respectively. Moreover, L ch and C f reduce from 378 to 208 mm and from 32.5 to 17.2 mm by decreasing W from 0.7 to 0.35, respectively. On average, G F /G f ratio for various W s attains 2.48 with the variation coefficient of 10.9%. Eventually, multivariate prediction models were developed for RACs with various W s. A comparison was made between prediction and experimental values of the present and previous research works.

The geometric parameters and stress conditions of fractures are the main factors that determine the strength and deformation characteristics of fractured rock masses, and the ultimate instability and failure of fractured rock masses are caused by the extension and penetration of the structural plane. In this study, a series of Φ50 × 100 mm standard cylinder specimens were prepared to simulate brittle rock masses. The uniaxial compressive strength and tensile strength of the specimens were 33 and 2.8 MPa, respectively. Non-persistent fractures with different inclination angles, connectivity rates, openings, spacings, groups, and roughness were prefabricated in the specimens, and the fractures were filled with plasticine. Furthermore, the crack propagation and failure mechanisms of filled fractured rock masses under uniaxial compression (the loading rate is 0.2 MPa/s) were analyzed by a 3D video image correlation system. Comparing the results of this research with those of previous researches, and combining with relevant theoretical analysis, the following conclusions are drawn: (1) the curve of the peak strength reduction coefficient kσ of the specimen with the fracture inclination angle α is roughly V-shaped, and being the smallest when the fracture inclination angle α is 45°; the reduction coefficient k is monotonically decreasing with the three groups of fracture geometric parameters of spacing b, connectivity rate μ, and opening d, and the peak strength reduction coefficient kσ of the specimen is typically smaller than the elastic modulus reduction coefficient kE. (2) The post-peak stress–strain curve of the specimen with filled fractures is relatively slow, and the plasticity is obviously enhanced. The geometric parameters of the fractures are important factors affecting the change of the mechanical properties of the specimen. The influence degree of different fractures geometric parameters on rock masses mechanical properties is as follows: fracture sets > spacing > connectivity rate > inclination angle > opening > roughness. (3) Due to the concentration of stress, cracks first initiate from the fracture tips, then propagate parallel to the loading direction, and ultimately coalesce between the fractures and the specimen surface. During the failure process of the specimens, four types of cracks were observed: tensile cracks, shear cracks, wing cracks, and reverse wing cracks, with wing cracks dominating crack propagation. (4) Compared with the specimens with unfilled fractures, the stress concentration at the filled fractures was reduced, and more microcracks with higher dispersion developed around the filled fracture.HighlightsThe variation mechanism of the mechanical parameter reduction coefficient of a filled fractured rock mass is studied;The influence of different joint geometric parameters on the mechanical properties of a filled fractured rock mass is investigated;The crack propagation of a filled fractured rock mass is observed under different joint geometric parameters and the failure mechanism is analyzed.

The chemical structure, polymer mobility and mechanical properties are studied for a cross-linked amorphous poly(ether urethane) (PU) from glass transition to rubber elasticity for juvenile dry samples and for water-saturated states after exposure to humid air (r.h. = 29, 67, 95, 100%) at 60∘C during 1 y of ageing. For saturated samples, network chain cleavage is the chemical ageing mechanism, but it is too weak and slow to affect on the physical properties significantly within 1 y. Water acts primarily in a physical manner. Within 1 d, H2O molecules replace part of the weak urethane H-bonds by H2O–urethane H-bonds and reduce all other physical interactions between network chains by solvating hydrophilic segments. Thus, the cooperative polymer mobility strongly amplifies: The gain of specific conformational entropy doubles across the caloric glass transition, which shifts by −17 K. A H2O concentration of only cH2O≈(0.4…0.5)cH2O,max suffices for the major part of these fast rearrangements. Some part of the water slowly forms (during 3–4 months) a finely dispersed water-rich mixed phase with the PU chains. Except the new phase, these molecular processes of physical ageing strongly affect the mechanical properties at damage-free deformation. For dry PU in the glass transition, the shear modulus, μrelaxed(T), after viscoelastic stress relaxation only depends on the deformation-induced entropy change—like in the rubber elastic state. Within one month, water drastically decreases the viscoelastic response, as expected for plasticisation. However, μrelaxed(T) slightly grows in wet PU. H2O molecules cause these opposite trends by boosting the cooperative mobility (i.e. extension of the accessible conformational space and entropy by reduction in energy barriers) and by occupation of free volume compartments. Water quickly reduces the fracture parameters by about 50%. We explain that embrittlement by the H2O-induced facilitation of cooperative network chain motions, which let fracture proceed with less energy. In summary, our findings provide a detailed conception of the molecular effects the H2O molecules have on the PU network, and they explain the consequences for the mechanical properties.