Abstract: Thermoelectric thin film/substrate structures have many practical applications such as in heat recovery systems. The general problem of thermally induced delamination between a thermoelectric thin film and a substrate is investigated. The temperature varies along the length direction but is constant along the thickness direction of the film. Analytical solutions of the temperature field in the film and the stress intensity factors (SIFs) at the delamination crack tips are obtained. The combined heat convection and heat radiation between the film surfaces and the surrounding medium (i.e., the air) are taken into account. Numerical results show that the SIFs sharply increase as the tips of the delamination crack approach the ends of the film. The combined heat convection and heat radiation can increase or decrease the SIFs. The mechanism for the delamination propagation in the thermoelectric film/substrate system is examined. The critical (permissible) temperature difference across the film governing the delamination propagation is identified. PubDate: 2018-11-12

Authors:Xin Sun; Jian Yao; Guozhong Chai; Yumei Bao Abstract: The integrity of reactor pressure vessel (RPV) is greatly affected by pressurized thermal shock (PTS). Once crack appears in the nozzle region, the stress concentration around the crack tips may lead to crack propagation, and finally cause a serious security problem. When the transient temperature is above the nil-ductility reference temperature, elastic–plastic constitutive relations are considered in the fracture mechanics analysis. The temperature-related properties of the materials are introduced into a 3-D finite element model to establish the temperature field and stress field of a real RPV. Since the test and safety inspection for RPV with defects under PTS loads are quite difficult and dangerous, the process of the ductile crack propagation is simulated by the extended finite element method (XFEM), and the critical crack sizes for different base wall thicknesses are determined. Then, the quantitative analysis of the effect of the crack position on the ultimate bearing capacity is carried out. For the crack tips with different shapes, the crack propagation law and the shape effect on the ultimate bearing capacity of the whole structure are also analyzed. According to their crack propagation paths and damage degrees, a good agreement is obtained. PubDate: 2018-11-08 DOI: 10.1007/s10704-018-0326-3

Authors:Weijie Huang; Zhiping Li Abstract: A numerical study on a new bifurcation phenomenon in multi-void growth is carried out for a 2-D problem in nonlinear elasticity, where the reference configuration is y-axisymmetric with two pre-existing small voids. The numerical experiments show that, under large radially-symmetric displacement boundary conditions, other than the y-axisymmetric equilibrium solution one would normally expect, there are two energetically more favorable non-y-axisymmetric equilibrium solutions in which the growth of one void is overwhelmingly dominant. The relationships between the critical bifurcation boundary displacement and the compressibility of the material as well as some geometric parameters are illustrated by numerical results. The numerical experiments also show that the existence of the secondary bifurcation will effectively expedite the onset of fractures. PubDate: 2018-11-02 DOI: 10.1007/s10704-018-0323-6

Authors:Shengwen Tu; Xiaobo Ren; Jianying He; Zhiliang Zhang Abstract: The increasing demand of energy prompts the petroleum industry exploitation activities to the Arctic region where the low temperature is a strong challenge, both for structural design and material selection. For structural materials exhibiting the Lüders plateau, it has been reported that lowering the temperature will increase the Lüders plateau length. In order to obtain a deep understanding of the Lüders plateau effect on ductile crack growth resistance, we performed numerical analyses with SENT specimens and the Gurson damage model. The Lüders plateau was simplified by keeping the flow stress constant and varying the plateau length. The results show that the existence of the Lüders plateau does not influence the initiation toughness, however, will alter the material’s fracture resistance significantly. It is found that the Lüders plateau effect is in general controlled by the stress triaxiality level in front of the crack tip. Both the strain hardening and the crack depth effects on resistance curves are alleviated due to the Lüders plateau. For materials with very small initial void volume fraction, the Lüders plateau effect is more pronounced. Since the Lüders plateau intensifies the crack driving force and may lower down crack resistance curve, special attention should be paid to the application of materials with the Lüders plateau in the Arctic. PubDate: 2018-11-02 DOI: 10.1007/s10704-018-0327-2

Authors:Ying Zhen; Hongjun Tian; Haijiao Yi; Yuguang Cao; Shihua Zhang Abstract: In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value. PubDate: 2018-11-01 DOI: 10.1007/s10704-018-0322-7

Authors:Eric B. Chin; Joseph E. Bishop; Rao V. Garimella; N. Sukumar Abstract: We introduce a framework for modeling dynamic fracture problems using cohesive polygonal finite elements. Random polygonal meshes provide a robust, efficient method for generating an unbiased network of fracture surfaces. Further, these meshes have more facets per element than standard triangle or quadrilateral meshes, providing more possible facets per element to insert cohesive surfaces. This property of polygonal meshes is advantageous for the modeling of pervasive fracture. We use both Wachspress and maximum entropy shape functions to form a finite element basis over the polygons. Fracture surfaces are captured through dynamically inserted cohesive zone elements at facets between the polygons in the mesh. Contact is enforced through a penalty method that is applied to both closed cohesive surfaces and general interpenetration of two polygonal elements. Several numerical examples are presented that illustrate the capabilities of the method and demonstrate convergence of solutions. PubDate: 2018-11-01 DOI: 10.1007/s10704-018-0325-4

Authors:Lufan Long; Zhiping Li Abstract: A dynamic cavity growth problem in an isotropic compressible nonlinear hyper-elastic material subject to a gradually applied traction is numerically studied. The effects of three parameters, namely the material mass density, the maximum traction, and the loading rate, on the evolution of the cavity radius, especially the maximum cavity radius, are investigated. The numerical results show that, while both the inertia and loading rate have only marginal effect on the onset of cavitation, they do significantly affect the maximum cavity radius. Furthermore, the applied traction eventually leads to a periodic oscillatory cavity growth, and a square root power law for the vibration period as a function of the material mass density is found to hold. PubDate: 2018-10-19 DOI: 10.1007/s10704-018-0321-8

Authors:D. V. Bachurin Abstract: Atomistic simulations of tensile straining of three-dimensional nanocrystalline palladium samples at room temperature and at a constant strain rate of \(10^{8}\,\hbox {s}^{-1}\) were performed. Potential understating surface energies and therefore facilitating intergranular fracture was applied for modeling of interatomic interactions. Palladium samples subjected to uniaxial straining have demonstrated initiation of intergranular cracks which have occurred preferably at the high-angle grain boundaries oriented perpendicular to the direction of applied strain and independently of their tilt/twist character. Further propagation of cracks took place along the adjacent grain boundaries. No cases of intergranular fracture at low-angle grain boundaries, of both the general and special character, were found. Intergranular fracture was observed only in an insignificant number of special high-angle grain boundaries. PubDate: 2018-10-10 DOI: 10.1007/s10704-018-0319-2

Authors:Minghao Zhao; Huayang Dang; Cuiying Fan; Zengtao Chen Abstract: The potential theory method is utilized to derive the steady-state, general solution for three-dimensional (3D) transversely isotropic, hygrothermopiezoelectric media in the present paper. Two displacement functions are introduced to simplify the governing equations. Employing the differential operator theory and superposition principle, all physical quantities can be expressed in terms of two functions, one satisfies a quasi-harmonic equation and the other satisfies a tenth-order partial differential equation. The obtained general solutions are in a very simple form and convenient to use in boundary value problems. As one example, the 3D fundamental solutions are presented for a steady point moisture source combined with a steady point heat source in the interior of an infinite, transversely isotropic, hygrothermopiezoelectric body. As another example, a flat crack embedded in an infinite, hygrothermopiezoelectric medium is investigated subjected to symmetric mechanical, electric, moisture and temperature loads on the crack faces. Specifically, for a penny-shaped crack under uniform combined loads, complete and exact solutions are given in terms of elementary functions, which serve as a benchmark for different kinds of numerical codes and approximate solutions. PubDate: 2018-10-10 DOI: 10.1007/s10704-018-0320-9

Authors:A. Sapora; P. Cornetti Abstract: The brittle crack initiation from a circular hole in an infinite slab subjected to remote biaxial loading is investigated by means of the coupled finite fracture mechanics criterion, focussing on the behaviour of the average energy release rate. The work then analyzes the stability/instability of crack growth, following the terminology put forward by Weißgraeber et al. (Eng Fract Mech 168:93–104, 2016). Depending on the loading biaxiality and on the ratio between the crack advance and the hole radius, the crack propagation could reveal to be either unstable (positive geometries), or stable (negative geometries). Furthermore, it is shown that stable paths could follow unstable paths and vice-versa, leading to locally positive/globally negative or locally negative/globally positive configurations, which are discussed in detail case by case. PubDate: 2018-10-09 DOI: 10.1007/s10704-018-0315-6

Authors:Bo Ren; C. T. Wu; Pablo Seleson; Danielle Zeng; Dandan Lyu Abstract: This paper presents a discontinuous Galerkin weak form for bond-based peridynamic models to predict the damage of fiber-reinforced composite laminates. To represent the anisotropy of a laminate in a peridynamic model, a lamina is simplified as a transversely isotropic medium under a plane stress condition. The laminated structure is modeled by stacking the surface mesh layers along the thickness direction according to the laminate sequence. To avoid a mesh dependence on either the fiber orientation or the discretization, the spherical harmonic expansion theory is employed to construct a function for the micro-elastic modulus in terms of the bond-fiber angle. The laminate material is decomposed into an isotropic matrix material part and a transversely isotropic material part. The bond stiffness can be evaluated using the engineering material constants, based on the equivalence between the elastic energy density in the peridynamic theory and the elastic energy density in the classic continuum mechanics theory. Benchmark tests are conducted to verify the proposed model. Numerical results illustrate that the convergence of simulations with different horizon sizes and meshes can be achieved. In terms of damage analysis, the proposed model can capture the dynamic process of the complex coupling of the inner-layer and delamination damage modes. PubDate: 2018-10-04 DOI: 10.1007/s10704-018-0317-4

Authors:Weian Yao; Xiang Li; Xiaofei Hu Abstract: In this study, the crack problem in linear viscoelastic material is investigated numerically. The time dependent two-dimensional (2D) viscoelastic crack problem is treated by the precise time-domain expanding algorithm (PTDEA), such that the original problem is transformed into a series of quasi-elastic crack problems. The relationships among these quasi-elastic problems are expressed in terms of the time-domain expanding coefficients of displacement and stress in an improved recursive manner. Then a symplectic analytical singular element (SASE) which has been demonstrated to be effective and efficient for 2D elastic fracture problem is applied to solve the quasi-elastic crack problems obtained above. The SASE is constructed by using the symplectic eigen solutions with higher order expanding terms. An improved convergence criterion employing both displacement and stress for PTDEA is proposed. Taking advantage of the SASE, the stress intensity factors, crack opening and sliding displacements (COD and CSD) and strain energy release rate of the studied problem can be solved directly without any post-processing. Numerical examples show that the results of the present method can be solved accurately and effectively. PubDate: 2018-09-26 DOI: 10.1007/s10704-018-0316-5

Authors:N. A. Giang; A. Seupel; M. Kuna; G. Hütter Abstract: Micro-cracks in ferritic steel often originate from broken or debonded carbide particles, or from cleavage of the ferrite matrix. Experiments in literature show that dislocation pile-ups at grain boundaries or particles predominantly induce micro-cracks in ferritic steel. On the other hand, the ferrite can also arrest nucleated micro-cracks owing to local plastic deformations which reduce the stresses at the crack tip. In the present study, the competition between these mechanisms is investigated by cell model simulations using effective gradient plasticity (scalar gradient plasticity) for the ferrite. This theory allows to model the dislocation pile-up by suitable interface conditions. Potential cleavage of the ferrite or failure of the carbide is modelled by a cohesive zone. Parameter studies are performed with respect to the size of the particle and the strengths of ferrite and carbide. PubDate: 2018-09-21 DOI: 10.1007/s10704-018-0313-8

Authors:Arthur Coré; Jean-Benoît Kopp; Jérémie Girardot; Philippe Viot Abstract: A numerical procedure for estimating the critical dynamic energy release rate ( \(G_{IDc}\) ), based on experimental data is proposed. A generation phase simulation is conducted where fracture parameters can be determined using an experimentally measured crack propagation history (position of the crack tip as a function of time). The discrete element method is used to simulate the dynamic fracture by implementing a node release technique at the crack tip. The results are compared with analytical data on the dynamic propagation of a crack in a semi infinite plate. It reveals that the node release technique causes dynamic instabilities that can only be corrected by adding numerical damping on the edges of the crack or in the entire sample. On the other hand, the progressive node release technique, based on an elasto-damage zone model does not generate dynamic instabilities. It is shown that for a linear relaxation scheme and a damage zone length equal to the mean radius of the discrete elements, results comparable to finite element or analytical methods are obtained in plate structure. The present model offers an alternative to the finite element method to simulate self-similar or more complex crack growth. It also gives a first proper analysis of the evaluation of the critical dynamic energy release rate in a lattice-discrete model. PubDate: 2018-09-21 DOI: 10.1007/s10704-018-0314-7

Authors:Ruijie Liu; Ahmed Mostafa; Zhijun Liu Abstract: Zirconium alloys have been serving as primary structural materials for nuclear fuel claddings. Structural failure analysis under extreme conditions is critical to the assessment of the performance and safety of nuclear fuel claddings. This work focuses on simulating structural failure of Zircaloy tubes with multiple hydride defects through modeling explicit crack propagation in ductile media. First, we developed an integrated cladding failure model by taking into account both crack initiation induced by hydride/matrix interface separation and ligament tearing-off between activated hydride cracks. Second, to accommodate the initiation, propagation, and coalescence of multiple cracks in finite plastic media we incorporated this structural failure model into a coupled continuous/discontinuous Galerkin (DG) based finite element code, a traditionally preferred implicit numerical framework. Third, to improve the adaptive placement of DG interface elements for crack propagation and to identify potential coalescence of cracks due to the interaction between adjacent hydride cracks, we defined a special failure index for the assessment of potential failure zones using both true plastic strain developed and predicted failure strain based on the Johnson–Cook material failure criterion. Finally, by calibrating the proposed material failure model using a cluster of Zircaloy material experimental tests, we successfully simulated a complete failure process of a fuel cladding tube with multiple hydride cracks. PubDate: 2018-09-06 DOI: 10.1007/s10704-018-0312-9

Authors:R. J. Kashinga; L. G. Zhao; V. V. Silberschmidt; R. Jiang; P. A. S. Reed Abstract: Modelling of crack tip behaviour was carried out for a nickel-based superalloy subjected to high temperature fatigue in a vacuum and air. In a vacuum, crack growth was entirely due to mechanical deformation and thus it was sufficient to use accumulated plastic strain as a criterion. To study the strong effect of oxidation in air, a diffusion-based approach was applied to investigate the full interaction between fatigue and oxygen penetration at a crack tip. Penetration of oxygen into the crack tip induced a local compressive stress due to dilatation effect. An increase in stress intensity factor range or dwell times imposed at peak loads resulted in enhanced accumulation of oxygen at the crack tip. A crack growth criterion based on accumulated levels of oxygen and plastic strain at the crack tip was subsequently developed to predict the crack growth rate under fatigue-oxidation conditions. The predicted crack-growth behaviour compared well with experimental results. PubDate: 2018-09-06 DOI: 10.1007/s10704-018-0311-x

Authors:Shushant Singh; Debashis Khan Abstract: In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range ( \(\Delta \hbox {K})\) , load ratio (R), number of cycles (N), plastic compressibility ( \({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\) , R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study. PubDate: 2018-09-01 DOI: 10.1007/s10704-018-0310-y

Authors:Ali Taghichian; Hamid Hashemalhoseini; Musharraf Zaman; Zon-Yee Yang Abstract: Unconventional drilling and completion architecture includes drilling multilateral horizontal wells in the direction of minimum horizontal stress and simultaneous multistage fracturing treatments perpendicular to the wellbore. This drilling and stimulation strategy is utilized in order to raise the connectivity of the reservoir to the wellbore, thereby remedying the low permeability problem, increasing reserve per well, enhancing well productivity, and improving project economics in this type of reservoir. However, in order to have the highest production with the least cost, an optimization technique should be used for the fracturing treatment. According to the fact that aperture, propagation direction, and propagation potential of hydraulic fractures are of paramount importance in optimization of the fracking treatment, in this research paper, these three major factors are studied in detail, the control variables on these three factors are examined, and the effect of each factor is quantified by proposing a complete set of equations. Using the proposed set of equations, one can make a good estimate about the fracture aperture (directly controlling the fracture conductivity), the stress shadow size (directly controlling the fracture path), and the change of stress intensity factor (directly controlling the fracture propagation potential). A geomechanical optimization procedure is then presented for toughness-dominated and viscosity-dominated regimes based on the proposed equations that can be used for estimation of different optimal fracturing patterns. The most efficient fracturing pattern can be determined afterward via considering the cumulative production using a reservoir simulator e.g. ECLIPSE, Schlumberger. This procedure is likely to offer an optimal simultaneous multistage hydraulic fracture treatment without deviation or collapse, with no fracture trapping, with the highest possible propagation potential in the hydrocarbon producing shale layer, and a predicted aperture for proppant type/size decision and conductivity of the fractures. PubDate: 2018-08-24 DOI: 10.1007/s10704-018-0309-4

Authors:Motomichi Koyama; Takahiro Kaneko; Takahiro Sawaguchi; Kaneaki Tsuzaki Abstract: We investigated the damage evolution behaviors of binary Fe–28–40Mn alloys (mass%) from 93 to 393 K by tensile testing. The underlying mechanisms of the microstructure-dependent damage evolution behavior were uncovered by damage quantification coupled with in situ strain mapping and post-mortem microstructure characterization. The damage growth behaviors could be classified into three types. In type I, the Fe–28Mn alloy at 93 K showed premature fracture associated with ductile damage initiation and subsequent quasi-cleavage damage growth associated with the \(\upvarepsilon \) -martensitic transformation. In type II, the Fe–28Mn alloy at 293 K and the Fe–32Mn alloy at 93 K showed delayed damage growth but did not stop growing. In type III, when the stacking fault energy was \(>\,\) 19 \(\hbox {mJ/m}^{2}\) , the damage was strongly arrested until final ductile failure. PubDate: 2018-08-24 DOI: 10.1007/s10704-018-0307-6