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Hydraulic fracturing is an essential technology for continuously developing non-renewable energy, such as oil and gas. The erosion of solid-liquid two-phase flow in hydraulic fracturing is a theoretical problem that needs to be solved urgently. In the current computational fluid dynamics-discrete element method (CFD-DEM) research, we present calculation methods for the collision restitution coefficients of quartz particle in Newtonian fluids (1 mPa⋅s) and non-Newtonian fluids (10 mPa⋅s and 20 mPa⋅s). The influence of power-law fluid is considered in the algorithm, and the problem of particle penetration in the CFD-DEM method is optimized. These experimentally obtained collision restitution coefficients are incorporated into the optimized CFD-DEM method to consider the influence of fluid viscous forces on particle collisions. The accuracy of the numerical simulation method in this paper is verified by particle settlement and erosion experiments. The elbow erosion experiment is then used to validate the correctness of the erosion simulation. Finally, the erosion behavior of the fracturing pipe (elbow and tee junction) under different conditions is analyzed. Nanyang Technological University This work was supported by Singapore Center for 3D Printing (SC3DP) [grant numbers 001163–00010], and State Key Laboratory of Robotics and Systems (HIT) [SKLRS-2023-KF-24].

The wetting properties of ALES (Ammonium lauryl ether sulfate), SLES (sodium lauryl ether sulfate), TD (dodecyl triethanolamine salfate) and SDS (sodium dodecyl sulfate) solutions and their adsorption capacities on coal dust surface were evaluated by surface tension, contact angle, sink time, wetting rate, and changes in the micromorphology and functional groups on coal surface. The results showed that the four surfactants share similar adhesion and spreading wettability, while they differ notably in immersion wetting. A water-surfactant-low rank coal (LRC) system was established using Materials Studio software and the Wender coal model; then quantum chemical calculations and molecular dynamics (MD) simulations were conducted. The results showed that ALES is of the widest relative concentration distribution range (25.25–60 Å), the largest overlap range (25 Å) and the largest diffusion coefficient (D = 0.318); NH4+ can easily penetrate the surfactant layer, which proves the strong modification ability of ALES to LRC. ALES/LRC/H2O has the lowest interaction energy and the most H-bonds, indicating that ALES is of a strong adsorption capacity. Based on the experimental data and simulation results, the integrated wettabilities of the four surfactants follow ALES＞SLES＞TD＞SDS, partially contributed by the hydrolytic cations and EO groups. This project was supported by the Key Program of the National Natural Science Foundation of China (Grant No. 52130411), the National Natural Science Foundation of China (Grant No. 51974299), and the Fundamental Research Funds for the Central Universities (2020CXNL10). Jian Gan was supported by the China Scholarship Council (Grant No. 202006420018).

Three-dimensional (3D) particles in composite materials often have sharp corners which cause complex stress singularities. In our current research, the 3D singular stress fields in the corner front vicinity of various revolution-shaped inclusions have been investigated using a specially developed novel singular inclusion corner element SICE. Numerical eigensolutions with both singular and non-singular terms for the 3D singular stress and displacement fields in the curvilinear coordinate system are transformed into the interpolation forms of the SICE. The robustness of the element stiffness matrix is reflected in the fact that it is established based on a local coordinate system attached to the rotation axis with arbitrary inclusion orientation. The singular stresses in the vicinities of revolution-shaped inclusions of various shapes, orientations and material properties are investigated. The benchmark examples show that the proposed SICE has excellent versatility and are very useful for micro-damage analysis of particle-reinforced composites. Agency for Science, Technology and Research (A*STAR) The authors acknowledge the support of the National Natural Science Foundation of China under Grant Nos.51975411 and 51365013, the Tianjin Natural Science Foundation of China under Grant No. 18JCYBJC88500, and the Personnel Training Plan for Young and Middle-aged Innovation Talents in Universities in Tianjin, China. The support of Singapore A*STAR SERC AME Programmatic Fund for the “Structural Metal Alloys Programme” (Project WBS 4070307.051) is acknowledged. Congman Wang acknowledges the support of Tianjin Graduate Research and Innovation Project under grant No. 2020YJSB072.

The high-speed flow of sand-carrying fracturing fluid through tee junctions causes severe erosion and affects the safety of the fracturing operation. This study improves the traditional computational fluid dynamics-discrete element method (CFD-DEM) to avoid the (dense particles) collision-leading abnormal penetration but also considers the influence of fracturing fluid viscosity on particle collisions. Then the tee junction erosion model under fracturing conditions is established and verified by experiments. The simulation analysis shows that with the increase of two-phase flow velocity and Stokes number, the dominant effect of particle motion and collision changes from viscous force to inertial force, and then the tee junction erosion position also changes. Nanyang Technological University This work was supported by Singapore Centre for 3D Printing (SC3DP) under the project “Acquisition and reconstruction of 3D CAD models for repair and re-engineering [grant numbers 001163-00010]; the National Natural Science Foundation of China [grant number 11972114]; and the Natural Science Foundation of Heilongjiang Province in China [grant number LH2020A00].

Based on the virtual crack closure technique for finite element numerical simulation, a new magnetic structural algorithm is proposed to analyze fracture signals from nondestructive testing. As an example of solving engineering problems, this algorithm is employed to investigate the circumferential symmetric double-crack propagation in an X80 oil and gas pipeline welding zone. The material property of the welding zone is treated as bilinear kinematic hardening elastic–plastic, and the fluid pressure load on the inner wall of the pipeline weld is dynamically applied. In our magnetic structural multi-physics field model, every time when the incremental crack propagation is completed, the mesh is reconstructed. As a result, the crack propagation and magnetic field is analyzed cyclically. Six characteristic quantities (P, GI, Lg, CTOA, Bxᴾ, Msᴾ) in the process of crack propagation are computed, forming the magnetic structural algorithm for circumferential symmetric double-crack propagation. The results show that using the algorithm can judge the damage location and damage degree of the pipeline weld by calculating the crack growth process. The algorithm has high sensitivity which can distinguish the double cracks whose circumferential spacing is greater than or equal to 0.05 times of the circumferential arc length of the weld. When the circumferential spacing of double cracks is less than or equal to 0.4 times of the circumferential arc length of the weld seam, the single crack grows faster than the double crack due to the interference effect of double cracks, and the existence of double cracks inhibits the crack growth. Through this practical example, it is proved that the implementation of the proposed algorithm can provide a theoretical basis for guiding the actual safety assessment of engineering materials and structures containing microcracks. Agency for Science, Technology and Research (A*STAR) This work was sponsored by the National Natural Science Foundation of China (51607035, 11502051, 51774091) and China Postdoctoral Science Foundation (2018M641804, 2018T110268) and China Scholarship Council and Heilongjiang Youth Innovation Talents of Ordinary Undergraduate Colleges and Universities (UNPYSCT-2018046) and Heilongjiang Postdoctoral Research Foundation (LBH-Q18029) and Heilongjiang Postdoctoral Foundation (LBH-Z16040) and Science and Technology Project of China Petroleum and Chemical Industry Association (2017-11-04) and Research start-up fund of Northeast Petroleum University (rc201732) and Natural Science Foundation of Heilongjiang province (LH2019E018). The authors acknowledge the support of Singapore A*STAR SERC AME Programmatic Fund for the “Structural Metal Alloys Programme” (Project WBS M4070307.051).

Buckling of rods with cylindrical constraints is an essential problem in engineering and medical fields. Completely different to the buckling of classical Euler rods, the post-buckling modes for rods with cylindrical constraints involve highly complicated deformations and geometric configurations. In this paper, the rods are discretized into beam elements by finite element method, and the constraint relation between the rods and cylinders is described by gap element. A dynamic relaxation method for static buckling of compressed rods in cylinders is introduced. Numerical simulations have been carried out to investigate the effects of damping, element length, initial contact stiffness and penetration on post-buckling, etc. The characteristic buckling modes include deflection curves with single point, two points, three points and point-line-point contact. For the helical buckling, it is found that the transition section consists of two noncontact sections only, while the perturbed-helix section does not exist. Except the critical load and shear force of helical buckling, numerical simulation results are in good agreement with the analytical solution. By using the dynamic relaxation method, stable helical buckling modes can be obtained directly without undergoing sinusoidal buckling deformation under given compressive loads.

Three-dimensional diamond-like defects with circumferential V-shape corner fronts are often contained in engineering materials. In this paper, generalized stress intensity factors are calculated for this type of defect using a modified advanced finite element method. A super corner front element model in the global coordinates is established to capture the stress singularities along the circumferential corner front. Three-dimensional numerical series eigen-solutions in the element have been transformed from asymptotic expressions in the local curvilinear coordinates. The element is suitable for a sharp V-shape corner with arbitrary opening and inclination angle. Singular stress fields near various shapes of diamond-like defects are systematically investigated. The interaction of an embedded defect with free surface or another identical defect is also investigated. The numerical results can be used as stress intensity parameters to predict fatigue strength at circumferential corner front of a diamond-like defect. Agency for Science, Technology and Research (A*STAR) The authors acknowledge the support of National Natu-ral Science Foundation of China under grantno. 51975411 and 51365013, the Natural Foundation of Tianjin, China, under grantno. 18JCYBJC88500, and the Personnel Training Plan forYoung and Middle-aged Innovation Talents in Universi-ties in Tianjin, China. The work was finished when X. CPing visited Prof. Z.M. Xiao at School of Mechanical andAerospace Engineering in Nanyang Technological Uni-versity as a visiting Scholar. The support of SingaporeA*STAR SERC AME Programmatic Fund for the“Struc-tural Metal Alloys Programme”(project WBSM4070307.051) is also acknowledged.

Defects in terms of three-dimensional voids are commonly encountered at bi-material interfaces. In the current study, the singular stress field near the circumferential corner line of a three-dimensional axisymmetric interfacial void is analyzed using our newly established singular interface edge elements. Under the premise that ρ≪ R, the proposed singular element method does not depend on the size of the element; thereby, it is not necessary to use refined elements at the interface corner line. The numerical results reveal the intensity of the stress singularity at the interface line of the three-dimensional axisymmetric voids. The obtained stress intensity parameters can be used to judge the local fatigue crack initiation. The geometry effect of the void on the singular stress field at the circumferential interface corner line is studied and discussed in detail. Agency for Science, Technology and Research (A*STAR) The National Natural Science Foundation of China (Grant Nos. 51975411 and 51365013), the Tianjin Natural Science Foundation of China (Grant No. 18JCYBJC88500), and the Personnel Training Plan for Young and Middle-aged Innovation Talents in Universities in Tianjin, China, are acknowledged. The support of Singapore A*STAR SERC AME Programmatic Fund for the “Structural Metal Alloys Programme” (Project WBS M4070307.051) is also acknowledged.

In polymer composites, inclusions (fillers) are introduced into the glassy polymeric matrices in order to improve the toughness properties as the brittleness is one of the fatal drawbacks for glassy polymers. For the first time, in our current study, the stress analysis has been performed on the interaction between a circular inclusion and a craze with an internal small crack in polymeric composites. A craze can be treated as a crack with fibrils bridging the two crack surfaces. The forces applied by the fibrils to the crack surfaces (pulling the two surfaces closer) depend on the crack opening displacement. However, the crack opening displacement is directly related to the forces applied by the craze fibrils. To solve this dilemma, an iterative procedure is proposed for the first time to solve the formulated singular integral equations. The craze thickness profiles, the cohesive stress distribution, and the fracture toughness of the polymeric composites are investigated thoroughly. Moreover, due to the influence of the inclusion, the uneven craze thickness profiles are observed from the left to the right part of the entire craze zone. Accepted version

The interface effect of a nano-inhomogeneity on the elastic–plastic fracture behavior of a crack with the influence of nearby edge dislocation is studied by applying the surface/interface stress model. When the inhomogeneity and the crack become nano-sized, the bimaterial interface contributes considerable stresses to the crack surfaces, which are usually ignored in the traditional micro/macro crack problems. With the existence of nano-inhomogeneity, an extra dislocation near the crack may be either absorbed into the crack (so the crack grows bigger) or repelled away by the crack and the inhomogeneity. The Zener–Stroh mechanism is employed to model the nano-sized fracture behavior and the generalized Irwin plastic zone correction is taken to improve the fracture analysis at the crack tips. Using the complex potential functions and distributed dislocation method, the stress intensity factor, plastic zone size, and crack tip opening displacement are evaluated by solving the Cauchy singular integral equations. The numerical examples prove that the values of stress intensity factors, plastic zone size and crack tip opening displacement are sensitive to the interface properties of the current nano-scaled problem, especially when the inhomogeneity is small. When the extra edge dislocation is close to the sharp crack tip, the stress intensity factor increases significantly, which indicates the crack has a potential to absorb the nearby dislocation. Further investigations find that mixed mode loading conditions always induce much higher stress intensity factors, plastic zone size, and crack tip opening displacement comparing to pure mode I loading problem.

A nonlinear cohesive stress distribution function is employed by relating the cohesive stress to the cohesive zone size (CZS) and the distance from the crack tip to investigate the elastic-plastic fracture behaviors. A crack-inclusion interaction problem is taken as an example to explore the fracture process in the cohesive zone area. The CZS and crack surface opening displacement are evaluated numerically. It is found that for different cohesive parameter combinations, the normalized CZS and crack surface opening displacements change drastically. By reducing the current model to the famous Dugdale model, the results obtained match well with the existing ones.

The elastic-plastic fracture behavior of a Zener-Stroh crack nucleated by a wedge disclination dipole interacting with a nearby circular inclusion is investigated. It is known that a disclination is a strong source of internal stresses and energy, one possible way for the relaxation of the stresses can be in the form of an initiated crack. In the current work, the nucleated Zener-Stroh crack is simulated by a series of edge dislocations with distributed dislocation method. The influence of the disclination is accounted through crack surface traction free condition. To improve the analysis accuracy, the Irwin plastic zone correction is employed to evaluate the elastic-plastic fracture behavior at the sharp crack tip. Von Mises yielding criterion is applied in the plastic zone area to judge the yielding occurrence. Numerical results are given to study the influence of the disclination strength, disclination dipole arm as well as material properties on the stress intensity factor (SIF), plastic zone size (PZS), and crack tip opening displacement (CTOD). It is found that the property of the wedge disclination dipole has great effect on the stress field and the elastic-plastic fracture behavior of the Zener-Stroh crack. Either disclination strength or dipole arm increases, the SIF, PZS, and CTOD will increase significantly. For the same disclination, if the nucleated Zener-Stroh crack has a longer crack length, the SIF, PZS, and CTOD could be smaller. For a Zener-Stroh crack nucleated between the inclusion and the disclination dipole, the interaction between the disclination and inclusion greatly influences the elastic-plastic fracture behavior. However, this influence highly depends on material combinations of the two phases.

The opening profile and near tip stress fields of an interface crack between a polymeric hydrogel and a rigid substrate in the plane strain case are studied with the finite element method. The constitutive model proposed by Hong et al. (2008) is implemented by using a user subroutine in ABAQUS to simulate the chemo-mechanical coupling behavior of the hydrogel. Two interface models in front of the crack tip are considered, i.e., a perfectly bonded interface (fully pinned) model and a cohesive interface model. Our numerical results show that, when subjected to a tensile load, the solvent molecules in the hydrogel tend to concentrate around the crack tip and introduce extra swelling, which influences the opening profile and near-tip fields of the interface crack. For the fully pinned interface model, an increase of the free swelling stretch may hinder the flipping over of the crack face. The dominant stress component in front of the crack tip is closely related to the opening profile of the interface crack. The effect of interface damage on the opening profile of the interface crack is also studied in this paper with the aid of the cohesive zone model. Our study indicates that the intrinsic properties of the interface have significant influences on the opening profile of the interface crack.

Corrosion is an electrochemical process in offshore pipelines where the material strength begins to decrease as corrosion advances. Numerous studies have been performed to determine the remaining strengths (failure pressure) of corroded pipelines. Currently the axial corrosions of the girth welded pipelines still leave much to be understood. This study attempted to simulate girth welded pipeline with various corroded depths and lengths in order to compare with offshore pipeline design manuals. Based on the numerical results, the influence of corrosion defects parameters on remaining strengths were investigated for girth welded pipelines. The investigation on the effect of strength mismatch revealed that in the cases of under-matched, higher failure pressures are obtained. Comparisons of current results with B31G-2012 and DNV-RP-F101 demonstrated that both codes may produce somewhat conservative predictions on the failure pressure. Furthermore, an equation was proposed to evaluate the corrosion progress across girth welded pipelines.

The investigation on the interaction among a Zener–Stroh crack, a nearby inhomogeneity/inclusion and an extra edge dislocation has been carried out. A Zener–Stroh crack is formed by pileup of net dislocations. With the existence of a nearby inclusion, an extra dislocation near the crack may be either absorbed into the crack (so the crack grows bigger) or repelled away by the crack and the inclusion. The result depends on the force on the dislocation from the crack and inclusion. In our current study, the plastic zone correction at the crack tips is adopted, where the plastic zone size (PZS) is determined by our newly developed generalized Irwin approach since the stress fields around the crack tips are mixed modes. With the distributed dislocation method, the expressions for the stress intensity factor, PZS and crack tip opening displacement (CTOD) are obtained for different sets of geometric and material parameters. Numerical examples show that when the extra single edge dislocation is located near the sharp tip of the Zener–Stroh crack, the normalized PZS and normalized CTOD become very sensitive to the position of the edge dislocation. It is also observed that the mixed mode problem usually has larger PZS and CTOD comparing to the pure mode I loading problem.

Elastic–plastic stress analysis of a Zener–Stroh crack paralleling to the interface of a coating-substrate system has been carried out in this work. The sum of the Burgers vectors of the climb and the glide dislocations along the crack line accounts for the stress field around its blunt tip where dislocation enters, and the sharp tip where crack propagates. Firstly, Gauss–Chebyshev quadrature technique is applied to solve the governing equation of dislocation density functions constrained by load-free crack faces. When taking plasticity into account at both crack tips where stresses are high, the generalized Irwin plastic zone correction is recommended. Plastic zone size (PZS) for both tips, crack tip opening displacement (CTOD) and effective stress intensity factors for the sharp tip are then obtained. The effects of coating thickness, crack depth, material mismatch and displacement loads ratio onto PZSs and CTOD have been analyzed in detail.

The fracture behavior of a Zener–Stroh crack near a bi-material interface is investigated under the small-scale yielding condition. The plastic zone area is thus modeled by a modified Dugdale model, in which the Von Mises yielding criterion is applied in the yielding zone. The initial crack problem is formulated into a set of singular integral equations by dislocation method so that the stress intensity factors can be calculated numerically. The yielding zone size or the plastic zone size (PZS) and the crack tip opening displacements (CTOD) at the blunt and sharp tip are evaluated for the current Zener–Stroh crack. Numerical examples are given to show the effects of material properties and crack-interface distance on the normalized PZS and normalized CTOD of the Zener–Stroh crack. It is found that the Zener–Stroh crack is easier to propagate when it locates in the “softer” phase of the bi-material structures. For a Zener–Stroh crack, the crack propagation always starts from the sharp tip. By carrying out the plastic zone correction, failure analysis becomes more accurate thus able to avoid over-estimation in composite structure design and enhance the service life of the structure.

This article studies the axial buckling of a nanowire (NW) lying on Winkler–Pasternak substrate medium with the Timoshenko beam theory. The surface effect of the NW is accounted for with the Steigmann–Ogden model. An explicit solution of the critical buckling force and its associated buckling mode are obtained analytically. The influences of the surface stress effect, the geometry of the NW, and the elastic foundation moduli on the buckling behavior are fully discussed.

The general solution of an arbitrarily oriented sub-interface Zener–Stroh crack is derived with the aid of distributed dislocation methods. The crack problem is formulated as a set of singular integral equations and solved numerically so that the stress intensity factor can be evaluated for any orientation angle. To make the facture analysis more accurate, the plastic zone size (PZS) and the crack tip opening displacement (CTOD) are examined by the generalized Irwin model. The plastic zone area is assumed to follow the von Mises yielding criterion and can be related to the stress intensity factors at the crack tips. Numerical examples are given to demonstrate the influence of various parameters, such as material properties, crack–interface distance and loading ratios, on the normalized PZS and CTOD for vertical and parallel crack cases. It is found that the Zener–Stroh crack becomes easier to propagate when it is located in the “softer” phase of the bi-material structure and parallel to the material interface. If the crack is perpendicular to the interface, it would be much easier for the crack to propagate into the “softer” side of the structure.

Elastic-plastic stress investigation for a pileup of edge dislocations interacting with a nanoscale inhomogeneity has been carried out in the form of Zener–Stroh crack. The interface and size effects of the inhomogeneity based on the Gurtin–Murdoch model are considered. The fracture behavior of the crack with plastic zone correction is examined by the generalized Irwin model for mixed loading conditions, in which von Mises yielding criterion is fulfilled in the plastic zone area. The stress intensity factor (SIF), the plastic zone size (PZS), and the crack tip opening displacement (CTOD) of the crack are evaluated. For a nanoscale inhomogeneity (inclusion), the size and interface properties have great influence on the fracture behavior of the crack, which is completely different to a classical crack-inclusion interaction problem. Numerical examples are given to show the effects of the inhomogeneity radius, interface properties and crack-inhomogeneity distance, as well as the dislocation loading ratio on the normalized SIFs, PZS, and CTOD of the Zener–Stroh crack. It is found that for different intrinsic lengths, the normalized SIFs, PZS, and CTOD are very different. This influence will be even greater when the crack is closer to the nano-inhomogeneity. For the mixed-mode problem, the dislocation loading ratio does not have too much effect on the normalized SIFs, but does have significant influence on the normalized PZS and CTOD.

Elastic-plastic stress analysis on a radial crack interacting with a coated-circular inclusion in a matrix has been carried out with the aid of a generalized Irwin plastic zone correction. The crack line is assumed to be at the angle of 90° − θ from a remote tensile loading. In the mathematical formulation, the distributed dislocation method is used to simulate the crack. By solving a set of singular integral equations, three quantities, the effective stress intensity factor, the plastic zone size and the crack tip opening displacement (CTOD), are evaluated with the generalized Irwin model proposed. Numerical examples are given to show the influence of the key parameters such as the crack orientation angle θ, the normalized crack distance, the normalized coating phase thickness and the shear modulus ratio ([Formula: see text], coating phase/matrix) on the fracture behavior. The results indicate that the influence of angle θ is the greatest, while the effect of shear modulus ratio [Formula: see text] is relatively small. A validation checking is performed by the finite element method (FEM) for one case. The result obtained from the FEM simulation matches well with that from the current method.

The plastic zone size and crack tip opening displacement have been investigated for a curved interface crack between a circular inclusion and an infinite matrix. The mixed-mode Dugdale model is used to study the plastic deformation where the stresses in the plastic zones satisfy the Von Mises yield criterion. The plastic zone size at the crack tip is calculated by satisfying the condition that the complex stress intensity factors induced by external load and those induced by closure stress cancel off. With the distributed dislocation method, the physical problem is formulated into a set of singular integral equations which are numerically solved by using Jacobi polynomials. The influence of the material properties and other geometric parameters on the stress intensity factors (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) is discussed in detail. The numerical examples show that both the crack debonding angle and the inclusion/matrix shear modulus ratio have significant influence on the normalized values of SIF, PZS and CTOD. The normalized PZS reaches its maximum value when the crack debonding angle is 90°. The effect of shear modulus ratio is very significant when the inclusion is “softer” than the matrix. When the inclusion is much “stiffer” than the matrix, the inclusion plays a dominant role. Changing the shear modulus ratio does not have great influence on the plastic deformation ahead the crack tips.

Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with nearby inclusions (the fibers) in fiber-reinforced composites has been carried out. The Zener-Stroh crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. Plastic zone correction is introduced the first time for such a crack-inclusion interaction problem so that the fracture behavior can be analyzed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode loading problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the near-by fiber has great effect on the fracture behavior of the crack. In our study, the effective stress intensity factor (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fiber) shear modulus, inclusion volume fraction and the crack sharp tip position on the fracture behavior of the crack is discussed. It is found that the shear modulus ratio has great effect on the normalized values of PZS and CTOD, while the effect of fiber volume fraction depends highly on the conditions of the inclusion/matrix properties and the crack sharp tip position.

This paper studies the stress field and crack nucleation behavior in a disclinated nanowire with a continuum model. The surface stress effects of the nanowire is accounted for with the Gurtin-Murdoch model. The Green’s functions for the stress fields of a single wedge disclination and a single edge dislocation in a cylindrical nanowire are solved respectively with the complex variable method. To make the superposition principle valid, the stress field induced by the residual surface tension is properly handled in the Green’s functions. After that, the distributed dislocation method is applied to simulate the crack nucleation behavior. The influences of the surface stress effects on the stress fields of the wedge disclination and edge dislocation as well as on the Griffith crack nucleation behavior are systematically discussed.

A generalized Irwin model is proposed to investigate elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under combined tension and shear loading. The dependence of the stress intensity factors, the plastic zone size, the effective stress intensity factor and the crack tip opening displacement on the crack depth h, the Dundurs’ parameters and the phase angle θ is discussed in detail. Numerical results show that in most cases, if the crack is embedded in a stiffer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will increase. On the contrary, if the crack is embedded in a softer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will decrease.

Stress analysis has been carried out for a curved interfacial Zener–Stroh crack between a circular inclusion and an infinite matrix due to interface debonding in a composite. Using the distributed dislocation technique, the physical problem is formulated into singular integral equations of the 2nd kind. With the Jacobi polynomials and Gauss-Legendre integration methods, the integral equations are discretized and solved numerically. The stress intensity factors and energy release rates of the curved crack are evaluated accordingly. In the numerical examples, the effects of half debonding angle, the Dundurs’ constants, and the loading ratio \({{b_{x}^{T}}/{b_{y}^{T}}}\) on the stress intensity factors and the energy release rates are analyzed in detail. It is found that the stress intensity factors are greatly affected by the half debonding angle, the Dundurs’ constant β and the loading ratio \({{b_{x}^{T}}/{b_{y}^{T}}}\), while the influence of Dundurs’ constant α is relatively small especially when the loading ratio is close to zero.

Offshore pipelines consist of short pipeline segments connected by girth welding method. Surface and embedded elliptical cracks are often observed at welding zone which pose a potential threat to the reliability of the offshore pipelines. In this paper, three-dimensional nonlinear elastic–plastic stress investigation for the fracture responses of such offshore pipeline with surface or embedded elliptical cracks has been carried out. Based on the reference strain method, strain-based estimation formulas for crack tip opening displacement (CTOD) are proposed for the flawed pipelines under pure bending. Furthermore, based on the proposed estimation formulations, two failure assessment diagrams (FADs) for strain-based fracture are established to perform fracture assessment on the specific pipelines.

A generalized Irwin plastic zone model is proposed to investigate the interaction problem for a circular inclusion embedded in an elastic–plastic matrix that contains a radial crack, oriented at an arbitrary angle from a remote load. The distributed dislocation technology is applied to formulate the current problem. The effective stress intensity factors, the plastic zone size, and the crack tip opening displacement are evaluated by solving the formulated singular integral equations. In the numerical examples, the inclusion is taken as a void and a rigid body. The effects of the crack angle and the inclusion–crack distance (the distance from the inclusion center to the crack center) on the effective stress intensity factors, the plastic zone size, and the crack tip opening displacement are discussed in detail. Numerical results show that if the crack angle is not large, the values of the plastic zone size and the crack tip opening displacement are less than the corresponding values in the homogenous case when the inclusion is a rigid body; when the inclusion is a void, these values are larger than the corresponding values in the homogenous case.

The 2D problem of a time-harmonic plane shear horizontal (SH) wave scattered by a finite closed crack in an isotropic material is presented in the paper. The crack is arbitrarily orientated with regard to the incident wave. A spring model based on the assumption that the traction components on the crack surfaces are linearly related to the crack opening displacement (COD) is used to model the closed crack. The problem is formulated in a set of boundary integral equations which contains the CODs as unknowns. Numerical examples are presented for the CODs, elastodynamic stress intensity factors, and the scattered displacement field for various parameters, such as spring stiffness, crack sizes and crack orientations. The results show that both the crack closure and orientation have significant effects on the scattered displacement field for the closed crack.

Offshore pipelines are subjected to large plastic strain conditions, such as bending accompanied by high internal pressure, during the installation and operation processes. These pipelines are usually constructed by the girth welding method and weldments may contain naturally occurring surface and embedded planar and/or volumetric imperfections and/or defects. It is widely recognized that the existing fracture assessment procedures which are based on the load-controlled method, are not explicitly designed for situations with large plastic deformation. The main objective of the current paper is to find a routine to make fracture assessment for a pipeline subjected to plastic bending. In this paper, based on 3D elastic–plastic finite element analyses, the influences of various parameters on the fracture responses (CTOD) of the cracked pipelines are investigated and a CTOD estimation formula is proposed. Furthermore, comparison with fracture assessments made by BS7910:2005 code and finite element analyses indicates that the former gives over-conservative predictions. Based on the proposed formula, a failure assessment diagram (FAD) for strain-based fracture, is presented for the specific geometry and material properties of the particular pipe with semi-elliptical surface cracks under large plastic bending, where the global strain is up to 3%.

Steel pipelines used for oil and gas transportation are joined by girth welding and welds may contain weld imperfections/defects such as lack of fusion, under-cuts, porosity, slag inclusion etc. of certain height and length at certain location along the longitudinal direction of the weld. During the installation and operation, these pipelines are exposed to large plastic deformation. Fracture assessment procedures: BS7910:2005 [1] or R6 [2] , are not suitable for such plastic strains (3%). The evolution of crack tip opening displacement (CTOD) of the pipeline with elliptical embedded crack in a girth weld is investigated under biaxial loading conditions using a three dimensional elastic–plastic finite element method. Based on the results, empirical formulas depicting relationship between the CTOD and the global strain are proposed.

Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs’ parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs’ parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.

The analytical investigation of the plastic zone size of a crack in three-phase cylindrical model composite material was carried out. The physical problem is simulated as a crack near a circular inclusion (a single fiber) in the composite matrix, while the three-phase cylindrical composite model is used to represent the composite matrix. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, a thin strip of yielded plastic zone is introduced at each crack tip. Using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function, the physical problem is formulated into a set of singular integral equations. By employing Erdogan and Gupta’s method, as well as iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements.

An analytical solution is given for plastic yielding of a Zener–Stroh crack near a circular inclusion embedded in an infinite matrix. The crack is orientated along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. Using the Dugdale model of small-scale yielding, plastic zones are introduced at both crack tips. Using the solution of a circular inclusion, interacting with a single dislocation as the Green’s function, the physical problem is formulated into a set of singular integral equations. With the aid of Erdogan’s method and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement. The results obtained in the current work are verified by reduction to simpler cases of the Dugdale model. Various parameters such as the distance, shear modulus ratio, Poisson’s ratio, and loading condition are studied.

The transformation toughening behavior of a finite edge through crack in zirconia ceramics is studied with a three-dimensional finite element model. The continuum-based constitutive law of zirconia ceramics is implemented into a user-defined subroutine in ABAQUS to simulate the loading and unloading mechanical response of zirconia ceramics. We have given up the small-scale transformation assumption. The propagation behavior of a finite edge through crack in a zirconia plate is simulated at the structural level with the cohesive zone model and compared with the case in which the material is purely elastic. The influences of the stress state, the cohesive strength, the shear transformation strain and the activation energy threshold on the size of the transformation zone and the crack propagation behavior are systematically discussed. The numerical method and results presented in this work may be helpful for the design of engineering components made of zirconia ceramics.

The magnetoelectroelastic solution of a generalized screw dislocation interacting with a wedge-shaped magnetoelectroelastic bi-material interface is derived in this paper. The screw dislocation is assumed to be straight and infinitely long in the z-direction and suffers a finite discontinuity in the displacement, electric potential and magnetic potential across the slip plane. The explicit closed-form analytical solution for the generalized stress field is derived by means of the complex variable and conformal mapping methods. The generalized stress intensity factors of the wedge tip induced by the dislocation and the image force acting on the dislocation are formulated and calculated. The influence of the wedge angle and the different bi-material constant combinations on the image force is discussed. Numerical examples for three particular wedge angles are calculated and compared with other available results.

A new framework of non-local model for the strain energy density is proposed in this paper. The global strain energy density of the representative volume element is treated as a non-local variable and can be obtained through a special integral of the local strain energy density. The local strain energy density is assumed to be dependent on both the strain and the rotation-gradient. As a result of the non-local model, a new strain gradient theory is derived directly, in which the first and second strain gradients, as well as the triadic and tetradic stress, are introduced in the context of work conjugate. For power law hardening materials, size effects in thin metallic wire torsion and ultra-thin cantilever beam bend are investigated. It is found that the result predicted by the theoretical model is well consistent with the experimental data for the thin wire torsion. On the other hand, the calculation result for the micro-cantilever beam bend clearly shows the size effect.

The interaction between a screw dislocation and an elliptical nano inhomogeneity embedded in an infinite matrix is investigated. The interface stress effects of the nano inhomogeneity are accounted for with the Gurtin–Murdoch model. The stress fields inside the inhomogeneity and matrix are then solved with the complex variable and conformal mapping method. The solution is of semi-analytical nature and is verified by studying a degenerated case wherein a screw dislocation interacts with a circular nano inhomogeneity. The image force on the screw dislocation is then calculated. The influences of the elastic mismatch between the inhomogeneity and matrix, the interfacial properties, the aspect ratio of the elliptic nano inhomogeneity and the position of the screw dislocation on the image force are systematically discussed.

The stress relaxation of an eccentric (off-center) negative wedge disclination in an isotropic homogeneous cylinder by nucleation of a Zener crack has been investigated with a continuum model. The nucleated Zener crack is simulated with distributed edge dislocations. The stress intensity factor (SIF) at the sharp tip of the Zener crack is computed through solving the singular integral equations formulated. By enforcing the fracture criterion at the sharp tip, the critical disclination power to nucleate a Zener crack is determined. The equilibrium crack lengths of the crack are then calculated when the disclination power is above the critical value. It is found that there is a special position at which the critical disclination power reaches the minimum value. As the disclination deviates from this position, the critical disclination power increases. Two or four equilibrium crack lengths could be found for the Zener crack, dependent upon the power and off-center position of the disclination. The influence of the off-center distance on the equilibrium crack lengths and the dependence of the critical disclination power and stable equilibrium crack lengths on cylinder radius are also discussed.

An analytical investigation on the plastic zone size (PZS) of a crack near a circular inclusion has been carried out. Both the crack and the circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, two stripe plastic zones at both crack tips are introduced. Using the solution of a circular inclusion interacting with a single dislocation as the Green’s function, the physical problem is formulated as a set of singular integral equations. With the aid of Erdogan and Gupta’s method and iterative numerical procedures, the singular integral equations are solved numerically for the PZS and the crack tip opening displacement. The results obtained in the current work can be reduced to those simpler cases of the Dugdale model.

The nucleation of a Mode-I Zener crack from a wedge disclination dipole in the presence of a circular inhomogeneity is investigated. It is assumed that the disclination dipole and the nucleated Zener crack are along the radial direction of the inhomogeneity. Two cases are studied herein, i.e., the positive or negative wedge disclination of the dipole locates nearer to the inhomogeneity respectively. In order to investigate how various factors such as the elastic mismatch between the inhomogeneity and the matrix influence the nucleation of the Zener crack, the Stress Intensity Factor (SIF) at the sharp tip of the Zener crack is determined for different sets of geometric and material parameters with the distributed dislocation technique. The formulated singular integral equations are then solved numerically. Our results indicate that a nearby ‘hard’ inhomogeneity (having a higher shear modulus than the matrix) is beneficial to the crack nucleation for the first case (the positive disclination locates nearer to the inhomogeneity) while it retards the crack nucleation for the second case (the negative disclination locates nearer to the inhomogeneity). A nearby ‘soft’ inhomogeneity is helpful to the crack nucleation for the second case while it has inverse effects on the crack nucleation for the first case. This phenomenon can be explained with the concept of material force. The characteristics of the crack nucleation and the effects of the disclination strength, the distance between the inhomogeneity and the dipole, the disclination dipole arm length and inhomogeneity size on the crack nucleation are also systematically studied. The obtained results are helpful to characterize and enhance the strength of precipitate alloys and particle reinforced composites.

We perform a theoretical analysis on a ceramic plate piezoelectric transformer operating with thickness-twist modes. Mindlin's first order theory of piezoelectric plates is employed. Forced vibration solution is obtained. Transforming ratio and vibration mode shapes are calculated. The effects of plate thickness, electrode dimension and inertia are examined. The results are useful to the understanding of the operating principle and the design optimization of the transformer.

Disclinations are rotational line defects which may be introduced in metal wires during the manufacturing process. In this work, the relaxation of an eccentric (off-center) negative wedge disclination in a cylinder by nucleation of a Griffith crack is investigated. The nucleated crack is simulated with distributed edge dislocations. The stress intensity factors (SIFs) of the crack are evaluated by solving a set of singular integral equations. By enforcing the condition that the SIFs at the two crack tips should keep the same value in the nucleation process, the crack length growth on each side of the wedge disclination is determined. The critical disclination power and equilibrium crack lengths are then numerically determined. Some important characteristics of the Griffith crack nucleation are revealed. (1) The two tips of the nucleated Griffith crack grow asymmetrically when the disclination locates eccentrically. The tip closer to the cylinder edge travels a shorter length. This asymmetry is getting more severe as the normalized off-center distance increases. (2) The critical disclination power increases monotonically with the normalized off-center distance. (3) The normalized stable equilibrium crack length decreases as the normalized off-center distance increases while the normalized unstable equilibrium crack length shows an opposite dependence. The dependence of the critical disclination power and the equilibrium crack lengths on the disclination power and cylinder radius is also discussed in this work. It is believed that this work helps to predict the strength of disclinated metal wires at various length scales.

Based on the complex variable method and perturbation technique, an analytical closed-form solution is derived for the interaction between a screw dislocation and collinear rigid lines along the interface of two dissimilar piezoelectric media under remote anti-plane mechanical and in-plane electrical loading. The rigid lines are either conducting or dielectric. The dislocation core is subjected to a line-force and a line-charge. A square-root singularity of field variables near the tip of an interfacial rigid line is observed. The rigid line extension force acting on the tip is obtained in terms of the strain and electric field intensity factor. The force on the dislocation due to the interfacial rigid line is calculated. The influence of the angular position of the dislocation, material properties and electromechanical coupling factor on the force is studied in detail.

Electro-elastic stress investigation on the interaction between a piezoelectric screw dislocation and collinear rigid lines under anti-plane mechanical and in-plane electrical loading is carried out. The lines are considered, respectively, as dielectrics or conductors. The screw dislocation is subjected to a line charge and a line force at the core. Closed-form analytical solutions are derived by means of complex variable method. Explicit expressions for the field variables, the singularity of the field variables at the line tip and the force on the dislocation are obtained for a single rigid line.

Analytical solutions for the generalized two-dimensional problem of a dislocation interacting with a finite crack in piezoelectric media are formulated via Stroh formalism. Two kinds of electrically boundary conditions along the crack surface, namely, electrically impermeable and electrically permeable are studied in the analysis. Based on the complex variable method and the perturbation technique, the closed form solutions are obtained. The field intensity factors at the crack tip and the image forces on the dislocation due to the crack are computed and discussed.

This paper investigates the interaction problem between a dislocation and a finite crack in piezoelectric media. Analytical solutions for the generalized two-dimensional problem of a dislocation that is interacting with a finite crack in piezoelectric media are formulated via Stroh formalism. The analysis is conducted on the unified electrical crack boundary condition with the introduction of the electric crack condition parameter that can describe all the electric crack boundary conditions. The two ideal crack boundary conditions, namely, the electrically impermeable and permeable crack assumptions are obtained as two special cases for the current solutions. Based on the complex variable method and the perturbation technique, closed form solutions are obtained. The field intensity factors at the crack tip and the image forces on the dislocation due to the crack are computed and discussed.

A Mode III Griffith crack interacting with a coated inclusion in piezoelectric media is investigated. The crack, the coated inclusion are embedded in an infinitely extended piezoelectric matrix media, with the crack being along the radial direction of the inclusion. In the study, three different piezoelectric material phases are involved: the inclusion, the coating layer, and the matrix. A far-field loading condition is considered. During the solution procedure, the crack is simulated as a continuous distribution of screw dislocations. By using the solution of a screw dislocation near a coated inclusion in piezoelectric media as the Green function, the problem is formulated into a set of singular integral equations, which are solved by numerical method. The stress and electric displacement intensity factors are derived in terms of the asymptotic values of the dislocation density functions evaluated from the integral equations. Numerical examples are given for various material constants combinations and geometric parameters.