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Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code.

Low-cycle strain-controlled fatigue tests were carried out to determine the influence of porosity, binder volume and binder type used within a calcium carbonate based composite. Fatigue lifetime, degree of plastic strain, maximum cyclic stress and hysteresis loops were analysed. Porosity influenced by binder volume was identified as the main factor to effect a change in fatigue lifetime. Increasing polymer content by ten times led to a similar lifetime at 30 times the amplitude. Lower Tg polymer binder improved lifetime for high percentage volume binder by 2–5 times, but its effects were not noticeable in lower amounts. There was little degradation in compressive strength as a function of number of cycles but tensile load bearing resistance depreciated noticeably throughout testing due to areas of low binder leading to widespread areas of crack propagation. Hysteresis loops show that for lower polymer concentrations little plastic damage occurs within the compressive portion of the fatigue cycles. This was due to the hard pigment particles dominating compressive behaviour.

Airshafts are commonly used in manufacturing processes for fitting to a reel that is used for winding rolls of material such as paper, card and plastic film. An airshaft is designed so that, on fitting into a reel, it can be readily expanded, thereby achieving a firm attachment: it may also be easily contracted prior to dismantling to facilitate removal. Their efficient design makes them ideal for quick and firm attachment onto a reel and then mounting onto bearing housings to enable the winding or unwinding of rolls of stock material with the minimum of equipment down time. The inherent shape and functionality of an airshaft means that failure by fatigue and fracture is a major concern. The airshaft, for example, has a cross-section which changes along its length and it is subjected to significant bending stresses, which alternate with rotation. The weight of the roll of material will also change appreciably during operation and, in addition, the inflated inner tube pressure further increases stress levels at critical locations. This paper analyses the service failure of a specific airshaft, from both fatigue crack initiation and crack propagation considerations, and discusses how the failure might have easily been avoided.

Mechanical behaviour of SiC ceramics synthesized from two artificial precursors from plants – coir fibreboard and bamboo pulp fibreboard – was studied and the mechanical properties – flexural strength, Young's modulus, fracture toughness and hardness – of the ceramics synthesized from the two kinds of artificial precursors were compared. The effect of processing of the artificial precursors, as reflected in the microstructure of the ceramics synthesized from them, was taken into consideration in the analysis of the mechanical property data; these data could also be possible to be explained by the empirical models of fracture mechanics. The results of the study established the possibility of application of the investigated SiC materials as structural ceramics.

The science of fracture mechanics was born and came to maturity in the 20th century. Its literature is now vast. Perhaps the most successful application of fracture mechanics is to fatigue. However, this short paper is limited to a core topic of fracture, the initiation and propagation of fracture under monotonic loading at low strain rates. As the author was invited to present this paper on the occasion of his 65th birthday, it is a somewhat personal view of the development and future of fracture mechanics, but it is hoped that it will interest many, especially the young researchers at the beginning of their careers.

This short paper summarises the curren status of reseach initiated by the European Group on Fracture (EGF) Polymers and Composites Task Group on the standardisation of K c and G c methods for polymers. The work is based on ASTM Standard E399 for metals and has led to a testing protocol which takes account of the major difficulties imposed by polymers. The special features of the current testing protocol are described.

Crack measurement after thermal shock is usually considered as a replacement because real-time observation of thermal shock experiments is difficult to achieve. This paper presents an experimental approach for real-time displaying thermal shock cracking using oxygen-acetylene flame and high-speed imaging of translucent ceramic. We capture the crack propagation process, calculate the crack propagation speed, discuss the effect of sample size and flame heat flux on the crack propagation, and analyze the difference between the crack propagation under cold shock and hot shock. This paper further improves the mechanism of thermal shock damage of ceramic materials.

Author's accepted manuscript The rain-induced fatigue damage in the wind turbine blade coating has attracted increasing attention owing to significant repair and maintenance costs. The present paper develops an improved computational framework for analyzing the wind turbine blade coating fatigue induced by rain erosion. The paper first presents an extended stochastic rain field simulation model that considers different raindrop shapes (spherical, flat, and spindle), raindrop sizes, impact angles, and impact speeds. The influence of these raindrop characteristics on the impact stress of the blade coating is investigated by a smoothed particle hydrodynamics approach. To address the expensive computational time, a stress interpolation method is proposed to calculate the impact stress of all raindrops in a random rain event. Furthermore, coating fatigue analysis is performed by including the fatigue crack initiation in the incubation period and the fatigue crack propagation in the mass-loss-rate increasing period due to raindrop impact. Finally, the proposed computational framework is verified by comparing the estimated fatigue life with those obtained in literature. The results from the study show that by incorporating the statistics of rainfall data, the proposed framework could be used to calculate the expected fatigue life of the blade coating due to rain erosion.

Masonry arch bridges have furnished railway networks as important infrastructures. The evaluation of the behavior of masonry arch bridges has drawn a great deal of attention over the past years due to the increase in the speed of railway fleet, need for augmentation of trains axle loads, and increase in the number of vehicles. These critical structures have been designed for service loads demanded at past times and since service loads are different in the present time, their behavior crucially needs to be assessed. Various analytical, experimental, approximate, and numerical methods have been proposed so far to estimate the residual capacity of masonry arch bridges. The present paper aims to predict the maximum service load of railway plain concrete arch bridges using a new approach with the aid of stress intensity factor in the fracture mechanics. Since stress intensity factor is solved analytically only for highly simple problems, a numerical approach and the finite element method were used in the present paper to calculate this parameter. Finally, given the stress intensity factor and proposing a relation for concrete toughness based on a statistical study, the maximum service load of these vital structures is obtained. To validate the results, two plain concrete arch bridges —located at kilometer 23 and 24 of Tehran-Qom Old Railway— were used. The results revealed that the proposed method has agreed well with the field observations.

In the previous paper (Kobayashi, 2019) based on the proposed micro-crack evolution equation, a solitary pulse wave radiated by crack propagation as the shock wave was analyzed and the solitary character of the solitary pulse wave was examined due to its energy and acceleration. Subsequently, in this viewpoint, the solitary pulse wave was concluded to be a soliton. In this paper, the lattice vibration at the crack tip excited by the crack propagation as a shock wave is examined by considering the shock wave velocity at the crack tip, and then the lattice vibration excited at the crack tip is concluded to be optical branch (mode). Therefore, optical and/or electrical phenomena may be exited at the crack tip due to the crack propagation as shock waves. Based on the optical branch, the mechanism, that causes discontinuity, singularity, the non-locality and also the entanglement in the fracture progress process, is discussed. The correlation of parameters introduced in the previous paper with number and energy of phonons is examined in the viewpoint of quantizing a soliton-like phonon pulse. As a result, it is clarified that the amplitude of the soliton-like phonon pulse cannot be determined arbitrarily and, hence, is a discrete value. Here, the proposed soliton-like phonon pulse may be recognized as a topological soliton of the strain induced by a kink of the displacement occurred by explicit or spontaneous symmetry breaking in the (1+1) dimensional space due to the crack propagation. Therefore, it is suggested that fracture induces phase transformation. The long-period pulse waves that were observed in the seismograms of the 2016 Kumamoto Earthquake and the 2018 Hokkaido Eastern Iburi Earthquake at the neighborhood of the seismic centers are examined in detail in the viewpoint of the proposed quantization of a soliton-like phonon pulse. Then the long-period pulse waves observed in earthquakes are simulated using the value of the proposed parameter λIc determined by the earthquake energy calculated by its magnitude, and its fault area is estimated using the relation between the fracture area and the fracture energy derived in the previous paper (Kobayashi, 2017b). In this paper, the author suggests some examples in which micro-scale properties such as quantum character visibly reflect in macro-scale phenomena.

The present paper analyzes the effects of the beam cross-section on the lengthwise fracture behaviour of inhomogeneous beam configurations in terms of the strain energy release rate by applying linear-elastic fracture mechanics. The material is continuously inhomogeneous along height and length of the beams. A methodology for calculation of the strain energy release rate is developed and used for analyzing lengthwise fracture of a simply supported inhomogeneous beam loaded by one vertical force applied at the lower crack arm. The solutions to the strain energy release rate are verified by using the compliance method. Four beam cross-section geometries (isosceles triangle, antiparallelogram, T-shape and circle) and their effects on the lengthwise fracture behaviour are considered in detail. The lengthwise fracture behaviour of the inhomogeneous beam is analyzed also for the case when material has different moduli of elasticity in tension and compression. The results reported in the present paper can be applied in fracture mechanics based design of inhomogeneous structural members and components.

There is an increased usage of advanced composite structures due to several inherent benefits that they offer in comparison with the monolithic materials. But the application of these materials is being limited by the fact that the knowledge about the crack propagation and strength behaviour under application of loads and environmental conditions is not extensive. So, undertaking research in this direction is still very much important. In this paper, a circular crack which is present in the middle of a composite laminate was modelled and then subjected to combined (temperature + pressure) loading conditions where the temperature was considered to be falling and pressure remaining constant to study the fracture behaviour. The fracture behaviour of the composite laminate was studied using the strain energy release rate (SERR) value calculated using Virtual crack closure technique (VCCT). The effect of temperature fall, fiber angle and the combined thermo-mechanical loading conditions on the SERR value in the 3 different modes of fracture with a circular crack located in the middle of the composite laminate was studied and the influence of these parameter was discussed in this paper

There is an increased usage of advanced composite structures due to several inherent benefits that they offer in comparison with the monolithic materials. But the application of these materials is being limited by the fact that the knowledge about the crack propagation and strength behaviour under application of loads and environmental conditions is not extensive. So, undertaking research in this direction is still very much important. In this paper, a circular crack which is present in the middle of a composite laminate made up with a cross-ply (0/90) and Angle-ply (-45/+45) was modelled and then subjected to thermal loading conditions where the temperature was considered to be rising to study the fracture behaviour. The fracture behaviour of the composite laminate was studied using the strain energy release rate (SERR) value calculated using Virtual crack closure technique (VCCT). Comparison of fracture behaviour between the cross-ply and angle-ply layups the thermal loading conditions on the SERR value in the 3 different modes of fracture with a circular crack located in the middle of the composite laminate was studied and the influence of these parameter was discussed in this paper

The paper deals with an experimental study of shear resistance of reinforced concrete beams without shear reinforcement. A concrete specimen is reinforced besides the steel reinforcing bars also with straight, short fibers with dosing 40, 75 and 110 kg/m3. The research is focused on determining the effect of fibers dosing on the load capacity of the reinforced concrete beams. The research is complemented with numerical modeling of experiments, where one of the possible approaches to the advanced design of structures respecting the actual behavior and failure of fiber reinforced concrete is illustrated, using non-linear analysis and finite element method. A fracture-plastic material model and 3D computational model are chosen for modeling reinforced concrete beams with fibers. Besides common material testing, fracture mechanical tests are performed within the experimental program, specifically a three-point bending test with a notch. In the paper the results of types of tests and the determined fracture energy are compared.

In this paper, three-point bending tests on precast notched beam and multiscale numerical simulation were used to evaluate and predict the effect of different Basalt Fiber (BF) dosages on the fracture resistance performance for Basalt Fiber Reinforced Concrete (BFRC). The three-point bending test was performed on a series of the notched beams in different sizes and volumetric fiber dosage to obtain the Load-Crack Mouth Opening Displacement (P-CMOD) curves during the loading process. The fracture energy and the double-K fracture parameters were calculated from P-CMOD curves to investigate the influences of fiber volume fraction and beam size on fracture parameters of BFRC. The results indicate that the numerical simulation results are in good coherence with the experimental results. The increase of BF dosage could markedly increase the peak load and the fracture energy of concrete. There was no size effect on fracture energy. Based on the two-parameter fracture theory, the initiation toughness had size effect and increased with the rise of specimen height, while size effect was not significant for unstable toughness. With the augment of fiber dosage, the initiation toughness increased linearly. The unstable toughness varied irregularly with the alteration of fiber dosage but higher than that of ordinary concrete. In addition, this paper developed a homogenization algorithm based on Mori-Tanaka and a multi-scale finite element simulation based on continuum progressive damage theory to evaluate and predict the fracture behavior of BFRC with different sizes and fiber volumetric dosages. The calculated P-CMOD curves from this algorithm were in good agreement with those from experiments and revealed the effects of fiber dosage and size effect on fracture behavior for BFRC.

The compaction of asphalt mixtures creates different tensile strengths throughout the asphalt mixture and is thus of importance to ensure durable pavement performance. Asphalt mixtures are composite materials. Therefore, it is necessary to analyse the relationship between the microstructural characteristics and the mechanical performance of asphalt mixtures at different DoCs. In this paper, the 3D microstructures of the asphalt specimens were reconstructed by means of Digital Image Processing (DIP) techniques based on X-ray Computed Tomography (X-ray CT) scanning. Results from the Indirect Tensile Test (ITT) were used to determine the tensile strength of the asphalt specimens. The results show that the relationships between the DoC and the tensile strength as well as the fracture energy are not linear for asphalt specimens at the same testing temperature. This indicates the occurrence of over-compaction during the compaction process. In order to reveal the mechanism of the over compaction at the microscale, the 3D fractal dimension of air voids and aggregates were derived. The 3D fractal dimension of the air voids is variable and constant at first and then becomes smaller during the compaction process. The complexity of the air void morphology is related to the tensile strengths and a hypothesis based on the evolution of 3D fractal dimension of the air voids is proposed in this paper to explain this phenomenon. The results of this research help to increase the understanding regarding the mechanism of over compaction based on the microstructure of the asphalt specimens.

Caustics method has been widely used in dynamic stress intensity factors (DSIFs) measurements in PMMA by the size of caustics patterns. However, caustics geometry may be different between low and high loading rate conditions. To make data interpretation of caustics method as precise as possible, in this paper, mode I crack propagation under drop weight and blast stress wave loadings were investigated by caustics method with high-speed photography. It was found that approximate circle caustics patterns occurred under drop weight loading, while ellipse caustics patterns appeared under blast stress wave loading. These caustics patterns with different geometry were recreated by mathematical simulation, and then a new relationship between DSIFs and diameters of caustics patterns was built for precise DSIFs measurements. Finally, optical microscopic view of fracture surfaces shown that circle and ellipse caustics patterns corresponded to smooth and rough fracture surfaces, respectively. This paper indicates that caustics geometry and fracture surface roughness are important considerations when measuring DSIFs by caustics method in high loading rate conditions, otherwise large errors may occur.

Auxetic cellular structures are advanced materials with negative Poisson’s ratios, which exhibit some unique features which are useful for various applications. The objective of this paper is the numerical simulation and experimental analysis of evolution propagation under quasi-static loading conditions in selected auxetic cellular structures with different geometries and orientations of unit cells that is: (i) honeycomb structure, (ii) re-entrant structure, and (iii) rotated re-entrant structure. The failure modeling capability of Simulia Abaqus code for ductile materials is used for the numerical simulation. The paper presents in detail the calculation methodology for determination of ductile damage material parameters that, are used for further numerical simulations of the damage initiation and evolution. Standard Compact Tension (CT) specimens are selected for the numerical simulation and experimental testing. Here, the specimens are made from 7075-T651 aluminum plate, cut using water jet cutting technology. Using a numerical approach, the fracture behavior of the selected auxetic structures is estimated first. Experimental testing is also carried out to validate the numerical results. The comparison between computational and experimental results regarding crack propagation path and force-displacement diagrams showed a reasonable agreement.

Steel shear studs in bridges are subjected to rapidly fluctuating stresses causing fatigue failure. Research on fatigue of shear studs mainly focused on tests. Both AASHTO and Canadian design curve for fatigue resistance of shear studs are based on the tests conducted in the mid1960s by Slutter and Fisher. This paper presents a finite element based approach using push-out specimen for fatigue life estimation of headed shear stud connectors. Both crack initiation and crack propagation life are estimated and an excellent correlation is found when compared against test results. In addition, since a significant amount of push-out tests data on headed shear studs are now available, this paper evaluates the fatigue design curves of different standards, with special focus given to evaluation of the value of constant amplitude fatigue limit (CAFL) given in the current AASHTO and Canadian code (CSA S6-14). The regression analysis also shows that the current fatigue curves in different codes can be used for shear studs as large as 31.8 mm. Thus, restriction of use of studs larger than 25 mm (1 in.) in different bridge codes (CSA S6, Eurocode 4, and AASHTO) can be waived.

Piezoelectrical solid with nano-holes under time-harmonic anti-plane load is studied in the paper. The model is defined by the system of two partial differential equations and the boundary conditions which define the generalized stress. We reduce the model into an integro-differential boundary value problem and construct Cellular Nanoscale Network (CNN) architecture. Dynamical behavior of the obtained CNN model is studied by means of describing function technique. The simulations are provided which illustrate the theoretical results. The results of this paper are applicable in the field of non-destructive testing and fracture mechanics of multi-functional materials and structural elements based on them.

A finite element-based multiscale model is employed to examine the early-age mechanical behavior of cementitious composites under a mode-I loading condition. The mechanical response of early-age mortar and concrete are influenced by the time-dependent development of mechanical properties of the cement paste as well as the mechanical and morphological properties of the aggregate phase. A competing mechanism exists in the fracture process (i.e., crack propagation) of the aggregate and cement paste phases. This paper investigates the distinct role played by the properties of each phase. This paper addresses the problem through a two-step homogenization approach that first starts at the meso-level of the mortar, where the fine aggregates are embedded within the cement paste. The second step considers the homogenization of concrete composed of the mortar matrix resulting from the first homogenization step, and coarse aggregate particles. For the purpose of computational homogenization, the continuous scheme for bulk modeling combined with the discontinuous scheme for modeling the transition of mesoscopic diffusive damage to macro-crack are employed. Inter- and intra- phase cohesive zone elements are utilized to represent the fracture process. The results indicate the relative significance of elastic and cohesive properties of composite constituents for the development of tensile stiffness and strength, damage evolution, and macro-crack patterns. A competing mechanism was observed for early-age cracking of the cementitious composites. When the tensile strength of the cement paste is lower than the tensile strength of aggregate phase, the crack propagates across the paste. When the tensile strength of the cement paste exceeds that of the aggregate, the cracks begin to deflect and propagate through the aggregates. As such, a critical degree of hydration (associated with a certain time) exists below which the cement paste phase is weaker than aggregate phase at the onset of hydration. This has implications on the inference of kinetic based parameters from mechanical testing (e.g., activation energy). Our results show a promising quantitative agreement with experimental observations.

The author proposed the criterion of micro-crack nucleation, which was deduced theoretically from shock wave theory, and derived the micro-crack evolution equation (Kobayashi, 2012). In the previous paper (Kobayashi, 2017a, 2017b), the crack opening criterion was deduced from the proposed micro-crack evolution equation. The dynamics of crack-front propagation in heterogeneous media was theoretically studied and the crack-front stability conditions was discussed based on the fluctuation of crack fronts induced by small heterogeneities (asperities) in fracture energy; the existence of a propagating mode called crack front waves along the crack front with a velocity slightly less than the Rayleigh wave velocity was found (Ramanathan and Fishe, 1997; Morrissey and Rice, 1998, 2000). The crack front waves (CFW) propagating in soda-lime glass and PMMA were experimentally studied and similar in many aspects to the CFW theoretically predicted above (Sharon et al., 2001; Fineberg et al., 2003). In the present paper, the crack front solitary pulse wave radiated from crack propagated as shock wave is theoretically analyzed based on the proposed micro-crack evolution equation and is verified to be soliton. The long-period pulse waves suggested by the solitary pulse wave analyzed in the present paper were observed in the seismograms of the 2016 Kumamoto Earthquake and the 2018 Hokkaido Eastern Iburi Earthquake at the neighborhood of the seismic centers. The crack propagating in the inhomogeneous media, which is characterized by the crack center strain to be largest and the shock wave velocity at the crack center being smaller than the surrounding velocities, is stably propagating such as the guided wave due to self-focusing just like as the brittle fracture progress. It is suggested based on the proposed micro-crack evolution equation considering the effect of the plastic strain that the numerical simulations and discussions in this paper are available under the plastic deformation.

This paper deals with the definition of an analytical scheme for the evaluation of displacement controlled (secondary) bending moment relaxation in piping systems. After a first presentation of the problematic and the background of the methodology, the paper presents the already existing approach codified in the A16 appendix of the RCC-MRx and the specific improvements performed for the consideration of load history effects. The relevance of the approach is illustrated through comparisons between the analytical scheme and reference Finite Element Modelling solutions specifically developed for validation purpose. It is then shown that the proposed scheme provides an accurate estimation of the secondary bending moment relaxation and, as a consequence, large benefits regarding fracture mechanics assessment.

The static solution of crack propagation problems can be an efficient way to find both the failure load of a structure and the shape of the crack pattern. The paper introduces two new implicit static solution procedures to study crack propagation problems by adopting a Peridynamic-based numerical tool, and compares them with the Sequentially Linear Analysis. We discretize the structures in space by adopting a coupled FEM–PD approach, which exploits the flexibility of FEM to reduce the overall computational cost of the simulation. The results of several numerical examples indicate the main novel conclusions of the paper: when using a PD-based software, controlling the maximum number of bonds broken in each iteration may increase significantly the accuracy of the solution and keep the computational cost to an acceptable level.

This paper develops a new method to select steel grades manufactured to Australian and New Zealand standards. The current materials selection procedure is currently given in the design standards AS 4100, NZS 3404.1 and AS/NZS 5100.6, which is based on test data on the notch toughness characteristics from a previous generation of steel products originally manufactured in Australia or New Zealand. The existing procedure is limited to temperatures down to −40 °C. Moreover, it does not consider the effect of welding, detailing, stress utilisation, seismic loading rates, defects and other important factors. This paper includes a critical review of other international material selection procedures, before preparing a new design method based on fracture mechanics. The method extends the temperature range down to −120 °C, which is much lower than considered in many other international standards. It also includes New Zealand specific requirements for seismic loading rates. In comparison with the new method, it is demonstrated that the current materials selection procedure is much more conservative for plate thickness up to 75 mm for non-seismic design. The paper presents selection tables that can be considered for the development of new brittle fracture provisions for future versions of the Australian and New Zealand steel structures design standards.

A problem in fatigue analysis based on fracture mechanics (FM) is that reliable initial flaw/crack size is generally difficult to obtain. This paper developed a novel corrosion fatigue prediction approach based on equivalent initial flaw size (EIFS). Both crack initiation and propagation life are considered by substituting an EIFS for the initial crack size. Two methods were proposed to derive an EIFS in the presence of corrosion: K-T diagram method and calibrating to test data method. Based on the establishment of relation between fatigue limit and corrosion mass loss, the EIFS derived by K-T diagram method is further extended to suit the corrosion conditions. As test data is available, relation between EIFS and corrosion mass loss was established by calibrating to test data of fatigue life test results of corroded RC beams by this paper and other researchers. The proposed two methods were evaluated in the aspects of crack developing history and validation of corrosion fatigue life prediction. The crack developing history derived by the two methods reflected the same trend as the fatigue test results. The fatigue life predicted by both two proposed methods was in acceptable agreement with the experimental data. The findings of this study can be used for corrosion fatigue life prediction of aging RC beams with different corrosion levels.

Dynamic fracture behavior under impacting loads has been well studied, but for that under blasting loads, less attention has been paid. In order to investigate mode I crack propagation behavior of brittle materials under blasting, a new configuration specimen, i.e. single internal crack circular disc (SICCD) specimen was proposed in this paper, and it was applied in the blasting experiments. Crack propagation gauges (CPGs) were stuck along crack propagation paths to measure crack initiation and propagation time and crack propagation speeds. Green sandstone and PMMA were selected to make the SICCD specimens. Finite difference models were established by using AUTODYN code according to the SICCD specimen dimension and the loading curve measured near the borehole. Generally, the simulation results of crack propagation paths agree with the test results. Finite element code ABAQUS was applied in the calculation of dynamic stress intensity factors (SIFs), and the curves of dynamic SIFs versus time were obtained. By using these curves and the breaking time of the CPG wires, the mode I critical dynamic SIFs in initiation and in propagation were obtained. The results show that the measuring method of the critical dynamic SIFs of brittle materials under blasting presented in this paper is feasible and applicable. During crack propagations, the crack speed is not a constant, and the critical dynamic SIFs in propagation decreases with the increase of crack propagation speeds.

This paper describes fatigue tests performed on 6061-T651 and 5083-H321 aluminum friction stir welded joints with dimensions and loading conditions typical for structural applications. Butt and lap joint details with various defects intentionally introduced were tested under tension-only constant and variable amplitude loading conditions. In this paper, the fatigue test results are presented along with supporting metallurgical and nonlinear fracture mechanics analyses. Based on this work, it is concluded that kissing bond defects on the order of 0.3–1.0 mm can result in a significant fatigue life reduction and a shift in the failure mode to the weld root. The investigated toe-flash defect had less of an effect on fatigue performance. The lap joint did not perform as well as the butt joint detail.

An effective excavation and re-welding process is often needed to correct the installation slope and geometric misalignment in the piping, where significant local plastic strain damage and complex welding residual stresses (WRS) often occur during the repair process. At the same time, it is complex to perform elastic-plastic fracture assessment for combined loads such as the WRS, bending moment and internal pressure. In this paper, three-dimensional (3-D) finite element (FE) analyses of WRS of the repair welding are performed, and the influence of weld bead sequencing as well as the displacement caused by external loads is simulated. In the study, the plastic strain damage is also assessed to prevent void formation. To avoid the complex elastic-plastic fracture assessment, a simplified elastic-plastic fracture study is carried out based on the failure assessment diagram (FAD) method. The results show that the repair process is effective, and the strain damage caused by the weld repair is acceptable. There are clear differences between WRS caused by initial weld and that of the re-weld, and there is palpable influence of the repair process on the WRS for the unrepaired/unexcavated part of the pipe. Based on the simplified elastic-plastic FAD method, the repair process has obviously influence on the margin of safety. The repair process described in this paper is generic and thus can be applied in similar pipe deflection correction applications.

In this paper, a novel elliptical crack problem in magneto-electro-elasticity is studied. Unlike conventional crack problems in which the cracks are usually assumed to be embedded on a horizontal plane parallel to the isotropic plane of a transversely isotropic material, this paper studies a vertical crack with its surface perpendicular to the isotropic plane. The crack is under the action of uniformly distributed shear loads applied on the crack surfaces. The boundary integro-differential equation is derived by the generalized potential theory method. For an elliptical crack, the complete and closed-form coupling field is presented in the integral form, for the first time. Some significant quantities in fracture mechanics are obtained explicitly, in terms of elementary functions. Furthermore, numerical simulations are performed by finite element method to discuss the validity of the present analytical solutions.

This review paper presents the latest research focusing on the crack propagation of the structures under complex dynamic loads. The reviewed publications involve the variable methodologies to study the fracture mechanics of structures under the fatigue stress regime. Besides, the paper discusses the fatigue crack growth under different loads. The paper presents the research about the thermo-mechanical fatigue and fracture of the structure with metal, composite and polymer materials. In the end, the potential challenges and the current research gaps are summarised.

Part I of this series introduced a formulation of phase field fracture in which the inclusion of micro-scale inertia leads to a hyperbolic system of partial differential equations governing the coupled problems of nonlinear elasticity and material damage. This paper applies that formulation to a coupled isogeometric–meshfree discretization of compressible fluid–structure interaction that discretizes the damage field’s governing equation using the reproducing-kernel particle method and the fluid–structure momentum balance equation using isogeometric analysis. The hyperbolic character of the coupled system permits efficient fully-explicit time integration of the entire system (not just the momentum equation, as in previous semi-implicit procedures for phase field analysis of dynamic fracture). Results for dynamic fracture problems match those computed in Part I using implicit time integration and standard finite elements. However, the isogeometric–meshfree discretization of this paper provides greater flexibility in representing structural fragmentation from blast loading. The blast loading computations at the end of this paper demonstrate the model’s ability to represent extreme events involving air-blast–structure interaction.

Prominent characteristics of rock fracturing can be described mainly by crack opening displacement (COD), fracture process zone (FPZ) and fracture energy. In view of lack of real-time and comprehensive measurement techniques for characterizing rock fracturing in field applications, this paper developed a characterizing method of rock fracturing by utilizing and integrating Fiber Bragg Grating (FBG), Digital Imaging Correlation (DIC) and Acoustic Emission (AE). In this paper, mode I fracturing test was performed on sandstone using three-point bending, and the fracturing process was simultaneously detected and recorded by FBG, DIC and AE. The experimental results showed that (1) DIC-based measurement of horizontal displacements across the fracture presented a localized discontinuity, in accordance with FBG-based real-time measurement. At the onset of traction-free zone formation (peak load), the critical COD (δc) was found to be 76 μm as identified by DIC and FBG. (2) Moreover, the dissipated energy distribution and cohesive crack profile in FPZ characterized by the integrated measurement, indicated that 70%–90% of AE energy (dissipated energy) populated in the FPZ, little AE energy concentrated in the traction-free zone, and the position of δc delineated a boundary for specifying FPZ. The length of fully developed FPZ was 20 mm (±2 mm) in length. (3) The integrated measurement delineated the cohesive crack, which was not available previously. The integrated measurement revealed the softening curve followed a straight line; the relationship between FPZ length and crack tip opening displacement (CTOD) was linear, and the relationship between dissipated energy and FPZ length was quadratic. Based on the interrelations of cohesive crack characteristics identified by the integrated measurements, real-time fracturing can be captured by one technique (e.g. FBG) in field application.

A comprehensive model for predicting fatigue failure probability of surface c-shaped cracks in silicon nitride ball bearing elements under rolling contact fatigue (RCF) has been presented in this paper. Firstly, three-dimensional finite element analysis (FEA) is used to determine the stress intensity factors (SIFs) along the front of crack by using fracture mechanics approach. Then the propagation uncertainty of c-crack is evaluated by using surrogate models built upon highly accurate finite element modelling for equivalent stress intensity factors. Finally, the Monte Carlo Simulations combined with surrogate models are used to predict the failure probability of rolling ball bearing element. Simulation results reveal that it is possible to reduce the failure probability of ball bearing element up to 95% by reducing the maximum crack size and enhancing the fracture toughness of the ball material. The modelling results have been verified by experimental studies showing that the current predictions of c-crack fatigue failures were consistent with the experimental results. Fatigues crack initiation and propagation is a significant failure mechanism within ceramic ball bearing elements. It presents design and durability challenges for both manufacturers and users. A three-fold approach, to simulate fatigue propagation of c-shaped crack in rolling contact ceramic bearing element presented in this paper, is novel and will solve major durability issues within ceramic ball bearing elements subject to rolling contact fatigue.

During the latest 20 years, the extended finite element method (XFEM) has been gradually used to investigate the crack growth behaviors of different materials in combination with various mechanics models and became the most popular computational tool in analyzing crack problems. This paper classifies three typical theoretical frameworks of the XFEM, namely the linear elastic fracture mechanics, the cohesive zone model and the elastic-plastic fracture mechanics based XFEM. A review of brittle and ductile crack growth under both monotonic and cyclic loadings using the XFEM was given from both macro-scale and micro-scale after a systematic literature survey. In contrast, the framework of the XFEM for modeling brittle fracture is the most comprehensive and widely used theory, but the theory for the ductile crack growth has still to be developed. Additionally, the XFEM becomes more complicated in microcrack growth simulations than macrocrack by considering the effects of microstructures of materials. The XFEM can introduce an arbitrary discontinuity into the finite element and can be employed to analyze different crack growth problems in engineering materials and structures, this paper is served as a valuable reference for the future study in this field.

Flawed welds often require an Engineering Critical Assessment (ECA) to judge on the necessity for weld repair. ECA is a fracture mechanics based prediction of the integrity of structural components with defects under operating conditions. Adding to the complexity of a weld ECA is the occurrence of local constitutive property variations in the weldment (‘weld heterogeneity’). Their quantification allows for a more accurate assessment compared to common (standardized) practice, which assumes welds to be homogeneous. Hardness measurements allow to quantify weld strength heterogeneity given their theoretical relation with ultimate tensile strength. However, various standards and procedures report a wide variety of relations (‘transfer functions’) between hardness and strength, and recognize substantial scatter in hardness based predictions of strength. Within this context, this paper investigates the suitability of Vickers hardness mapping to perform an accurate weld ECA for high strength low alloy steel. To overcome the scatter associated with standardized transfer functions, this paper suggests an experimental calibration procedure based on all weld metal tensile tests. Finite Element (FE) analysis has been conducted on welds originating from steels to simulate their crack driving force response in Single-Edge notched Tension (SE(T)) specimens. Vickers hardness maps and hardness transfer functions are combined to assign element-specific constitutive properties to the model. The transfer function calibrated by all weld metal tensile tests yields a better agreement with experimental load-CTOD curves than transfer functions mentioned in standards and codes. Finally, a step-by-step procedure facilitates a practical adoption of the methodology.

The reinforcement measures, such as pre-stressed anchor cable and concrete anti-seepage layer covering original dam body, are often used to improve the structural stability, control the crack development and advance the carrying capacity of concrete dam engineering. This paper focuses on the reinforcement effect evaluation problem of gravity dam with cracks. Some mechanical and mathematical methods, such as the J integral and interaction integral methods in fracture mechanics, the support vector machine (SVM) method, are combined. According to the integrated criteria on crack behavior improvement and carrying capacity advancement, the implementation approach for reinforcement effect identification and long-term forecast of gravity dam with cracks is investigated. Firstly, considering the effect of reinforcement practice on structural behavior, stress field and strain field of original crack tip zone in gravity dam, the stress intensity factor (SIF) is taken to represent the combined action response of reinforcement practice and loads. To improve the computation efficiency and accuracy, which are the shortcomings existing in the conventional methods applied to the calculation of stress field with complex crack surface and crack tip, the improved J integral method is combined with the interaction integral method to calculate the SIF of crack tip in gravity dam after the reinforcement implementation. Then, the cracking safety of gravity dam is regarded as a goal, the SIF is regarded as a control index. A SVM method is proposed to determine the critical loads ensuring the cracking safety of gravity dam. An approach using two criteria on SIF and critical load is developed to implement the reinforcement effect evaluation of gravity dam with cracks. Lastly, an actual gravity dam undergoing reinforcement practice is taken as an example. The approach proposed in this paper is used to calculate the SIF of crack tip and the critical loads of cracking safety. The reinforcement effect identification and long-term forecast of gravity dam are fulfilled by analyzing the development of SIF and critical load.

The cyclic J -integral (Δ J -integral) is a crack tip parameter of elastic-plastic fracture mechanics which can be used as governing parameter for the description of fatigue crack growth (FCG) in metallic structures. In this contribution, it is applied for modelling FCG in weldments. The Δ J -integral is determined by means of analytical approximation formulas as well as numerical methods. An analytical solution, which takes into account effects of the local ligament plasticity, was derived. This solution is based on well established methods such as R6, BS7910 and SINTAP which were modified for cyclic loading. It incorporates methods for the description of short crack closure behaviour as well as the well known analytical (long) crack closure function of Newman. A specific code was written to evaluate the Δ J -integral numerically in the course of finite element based crack growth simulations. The code was first validated for an infinite plate with centre crack by applying elastic and elastic-plastic material behaviour. Next, the Δ J -integral was calculated for cracks in various butt and cruciform welded joints. The results were compared with the results of the derived analytical approximation formula. A good accordance was achieved between the results. Note that the work was part of the German research cluster IBESS the aim of which was the development of a method for fracture mechanics based determination of the fatigue strength of weldments. Since the question behind the present paper was restricted to the cyclic elastic plastic crack driving force needed for the short fatigue crack propagation stage, only the geometrical aspects of weldments (i.e. the weld toe notch) are addressed here whilst other characteristics such as material inhomogeneity (HAZ) or residual stresses are discussed by other papers of this special issue.

At meso-scale, Calcium Silicate Hydrate (C-S-H) can be considered as randomly packed globules (about 4.2 nm), which forms the basic unit cell, with water molecules and voids. In this paper, the nanostructures for the globules are developed based on some plausible atomic structures of C-S-H. The mechanical properties for the C-S-H globules are determined through molecular dynamics simulation. Interfaces between the C-S-H globules are also simulated with different amount of water molecules. Key material parameters, e.g., Young’s modulus, strength and fracture energy, are obtained. It has been found that longer mean chain length of silicate tends to increase the strength of C-S-H and change the fracture behavior from brittle to ductile failure, in the chain length direction. In the other direction, however, silicate chains do not play an important role while interlayer structure matters. Moreover, pores in the C-S-H nanostructures can considerably reduce the strength of the globule structures in the normal direction to silicate chain but the weakening effect becomes substantially less in silicate chain direction. Further, it has been found that for all types of the interfaces between C-S-H globules, the interface with no extra water molecules has the greatest tensile/shear strength. The mechanical properties obtained in this paper for C-S-H nanostructures and interfaces could be necessary inputs to the meso-scale modelling of C-S-H via either granular mechanics, i.e., DEM, or continuum mechanics, i.e., FEM.

Any fracture mechanics based determination of the fatigue strength of weldments requires different input information such as the local weld geometry and material data of the areas the crack is passing through during its propagation. The latter is so far not a trivial task as the fatigue crack is usually initiated at the weld toe at the transition from the weld metal to the heat affected zone. Furthermore, the crack propagates through the different microstructures of the weldment even into the base metal and causes final fracture. This paper describes how the material input information has been gained particularly for heat affected zone material by thermo-mechanically simulated material specimens for two steels of quite different static strength. The data comprise the cyclic stress-strain curve, the crack closure effect-corrected crack growth characteristics, fatigue threshold values for long cracks, the dependency of the parameter on the crack length and monotonic fracture resistance. The substantial experimental effort was necessary for the validation exercises of the IBESS approach, however, within the scope of practical application more easily applicable estimating methods are required. For that purpose, the paper provides a number of appropriate proposals in line with its check against the reference data from the elaborate analyses.

A new type of low-stress cropping system based on hydraulic compensation is proposed in this paper. In order to solve the sudden change of critical loading force before and after the crack initiation at the tip of V-shaped notch and improve the quality of cropping section, it is proposed that the fracture process of the bar is divided into two stages. At the crack initiation stage, the calculation formula of the critical loading force is established by means of stress concentration factor and extended finite element method (XFEM). At the crack propagation stage, the calculation formula of the critical loading force is built by stress intensity factor and FRANC3D software. The concept of mutation coefficient Fp0.2/Fci is also put forward. The research results show that the influence of bottom corner radius s of V-shaped notch on Fp0.2/Fci is the largest; when s is between 0.12 mm and 0.3 mm, Fp0.2/Fci decreases sharply; when s is equal to 0.12 mm, there is no force mutation. The cropping results show that the high-quality cross-section is obtained by using the variable frequency-loading curve designed in this paper.

In this paper, the historical context of the development of what is now known as ‘Fracture Mechanics’ is selectively developed. We start from the safety and economic motivations, and review the essential efforts, over the centuries, to develop the ability to predict fracture and those factors leading up to final catastrophic events. The experimental and analytical quantitative aspects, and their interdependence, are emphasized. It is shown how these efforts were integrated to define the field we now know as Fracture Mechanics. The paper concludes with some thoughts on unmet needs and new directions.