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This paper describes progress on the development of theoretical models required for studying failure mechanism, crack initiation and growth around the boreholes driven by hydrofracturing processes in Hot Dry Rock (HDR) reservoirs of geothermal energy. Due to the importance of the stress intensity factor concept (K) in Fracture Mechanics, some advanced modeling techniques for accurate and fast determination of K for relevant problems are proposed. Alternative tools to deal with stress intensity factor determination are developed and assessed from the points of view of accuracy and computational cost. We concentrate on residual strength, crack initiation and crack growth as a means to model and understand experimentally observed behaviors. Several modeling methods such as compounding and weight function techniques, and boundary and finite element modeling for stress intensity factor calculation are discussed. Further to reviews of those techniques, work performed included (i) developing alternative solutions to deal with boundary‐to‐boundary interaction when using the compounding technique, (ii) relating the precision of K calculations with the level of precision of the crack opening displacement of a reference solution, in order to assess the precision of weight function technique, (iii) modeling relevant geometries using the finite element method (FEM), (iv) working on the implementation of direct stress intensity factor K determination in the Higher Order Displacement Discontinuity Method (HODDM), and (v) developing tools to deal with residual stress fields around the boundary of the hydraulically pressurized boreholes.

Fracture tests carried out on bimaterial Brazilian disk specimens have been reported elsewhere. Two material pairs are tested in which each of the constituents is linearly elastic, isotropic, and homogeneous. For this material type, the crack fields decouple into in‐plane and out‐of‐plane deformation. Hence, a two‐dimensional approach is taken to analyse the tests. The purpose of this paper is to examine the necessity of using a three‐dimensional approach to predict interface fracture when in‐plane loading is applied.

To this end, the specimens are analysed by means of two‐ and three‐dimensional finite elements. The interaction energy or M‐integral is used to calculate the stress intensity factors.

The paper shows that the Mode III stress intensity factor K_III is not negligible near the specimen outer surfaces. Nevertheless, a two‐dimensional analysis will be seen to be sufficient to analyse these tests. This has implications for the practical engineer.

The paper offers a comparison between two‐ and three‐dimensional fracture criteria for a crack along the interface between two homogeneous, isotropic, linear elastic materials when in‐plane loading is applied to the body, and assesses the importance of the out‐of‐plane deformation.

The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The anticipated unified propagation function describes the infinitesimal crack-length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification functions with different number of fitting parameters are proposed. On one hand, the closed-form analytical solutions facilitate the universal fitting of the constants of the fatigue law over all stages of fatigue. On the other hand, the closed-form solution eases the application of the fatigue law, because the solution of nonlinear differential equation turns out to be dispensable. The main advantage of the proposed functions is the possibility of having closed-form analytical solutions for the unified crack growth law. Moreover, the mean stress dependence is the immediate consequence of the proposed law. The corresponding formulas for crack length over the number of cycles are derived.

In this paper, the method of representation of crack propagation functions through appropriate elementary functions is employed. The choice of the elementary functions is motivated by the phenomenological data and covers a broad region of possible parameters. With the introduced crack propagation functions, differential equations describing the crack propagation are solved rigorously.

The resulting closed-form solutions allow the evaluation of crack propagation histories on one hand, and the effects of stress ratio on crack propagation on the other hand. The explicit formulas for crack length over the number of cycles are derived.

In this paper, linear fracture mechanics approach is assumed.

Shortening of evaluation time for fatigue crack growth. Simplification of the computer codes due to the elimination of solution of differential equation. Standardization of experiments for crack growth.

This paper introduces the closed-form analytical expression for crack length over number of cycles. The new function that expresses the damage growth per cycle is also introduced. This function allows closed-form analytical solution for crack length. The solution expresses the number of cycles to failure as the function of the initial size of the crack and eliminates the solution of the nonlinear ordinary differential equation of the first order. The different common expressions, which account for the influence of the stress ratio, are immediately applicable.

The purpose of this paper is to study the effect of the material inhomogeneity on crack behavior initiated both axially and circumferentially in or near the butt weld and to discuss consequences on residual lifetime of the welded structure.

A three‐dimensional numerical model of pipe weld with smooth and continuous change of material properties has been used to study the fracture behavior of the cracked pipe structure. The stress intensity factor was considered as a parameter controlling the fracture behavior. The semi‐elliptical shape of the crack front was estimated under assumption of constant stress intensity factor along the crack front.

According to the results obtained in the paper the following conclusions were deduced. First, the most critical location of the crack is in the middle of the inhomogeneous region (weld center) regardless of the crack orientation. The stress intensity factor is substantially higher than in the case of a crack located in the homogenous pipe. Second, with regard to crack shapes, the circumferentially oriented cracks are practically identical regardless to the crack location if compared with the axial cracks. Third, the stress intensity factors of axially‐oriented cracks are approximately twice higher than in the case of circumferential cracks. This implies that the cracks are more likely to grow in an axial direction.

The results described in the paper can be used for estimation of critical crack length or for estimation of the critical applied inner pressure of medium transported in the pipe and are of paramount importance for service life estimations of polymer welded pipes in actual use.

The purpose of this paper is to study the effects of overload on the threshold stress intensity factor range (ΔK_th) in SUS316.

The fatigue tests are carried out to determine the resultant threshold stress intensity factor range (ΔK_th). The mechanism of the improvement of ΔK_th by the tensile overloading is analyzed using the Dugdale model.

It is clarified that the value of ΔK_th increases as increasing the overloading.

The apparent value of ΔK_th of stainless steel can be improved by a tensile overload, the fatigue strength of structural members that have a surface crack can be increased by a tensile overload.

As a result, the reliability and safety of structures, such as energy plants, can also be improved.

In this paper, the problem of two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials subjected to an anti‐plane shear loading is investigated by use the Schmidt method. To make the analysis tractable, it is assumed that the material properties varied exponentially with coordinate vertical to the crack. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effect of the geometry of the interacting crack and the functionally graded parameter upon the stress intensity factors. The relations among the electric filed, the magnetic flux field and the stress field are obtained. The shielding effect of two parallel cracks has been discussed.

The purpose of this paper is to develop basic principles of deterministic structural integrity assessment of a component with a crack- or notch-like defect by including safety factors against fracture and plastic collapse in criteria equations of linear and nonlinear fracture mechanics.

The safety factors against fracture are calculated by demanding that the applied critical stress should not be less than the yield stress of the material for a component with a crack or a notch of the acceptable size. Structural integrity assessment of the engineering components damaged by crack- or notch-like defects is discussed from view point of the failure assessment diagram (FAD). The methodology of the FAD has been employed for the structural integrity analysis and assessment of acceptable sizes of throw-thickness notch in a plate under tension and surface longitudinal notch-like defects in a pressure vessel.

Basic equations have been presented to calculate the safety factor against fracture for critical values of the stress intensity factor, crack tip opening displacement (CTOD), the J-integral and the FAD as well as to estimate an acceptable (safe) region for an engineering component with a crack- or notch-like defect of the acceptable size. It was shown that safety factors against fracture depend on both the safety factor against plastic collapse and employed fracture mechanics criterion. The effect of crack/notch tip constraint is incorporated into criteria equations for the calculation of safety factors against fracture.

The deterministic method of fracture mechanics is recommended for structural integrity assessment of a component with a crack- or notch-like defect by including safety factors against fracture and plastic collapse in criteria equations of linear and nonlinear fracture mechanics.

A survey of the literature will undoubtedly show that the last two decades have witnessed a proliferation of research studies on occupational stress among educational personnel, and that interest in this area has not abated. Unfortunately, little is known about occupational stress in many developing societies because a preponderance of these studies have been carried out in industrialized and developed societies where conditions may be dissimilar to those obtaining in developing societies. Therefore, the current study sought to contribute to a better understanding of occupational stress in teaching by investigating the sources, incidence and intensity of administrative stress among headteachers in Zimbabwe. The results of a survey of a sample of 95 headteachers showed that the sample experienced relatively high levels of administrative stress compared with previous findings. In addition, the study revealed several demographic characteristics and school variables which influenced the respondents’ perceptions of situations which cause stress. Finally, implications of the study were discussed in terms of policy, preparation of school administrators, school management and future research.

The purpose of this study is to clarify the influence of stress ratio (R) on the effects of shot peening (SP) on the fatigue limit of high-strength steel containing an artificial small defect.

SP was subjected on the specimens with a semi-circular slit with a depth of a=0.1, 0.2 and 0.3 mm. Then, bending fatigue tests were carried out under R=0.4.

The fatigue limits of specimens with a semi-circular slit were improved by SP under R=0.4. The fatigue limits of the SP specimens with a semi-circular slit under a=0.2 mm fractured outside the slit, and they had considerably high fatigue limits equal to specimens without a slit. Therefore, a semi-circular slit with a depth of under a=0.2 mm could be rendered harmless by SP under R=0.4. Compared to the results of R=0, the increasing ratios of fatigue limits under R=0.4 were lower than those under R=0. However, the size of semi-circular slit that could be rendered harmless by SP was same. In addition, it was found that whether the semi-circular slit is rendered harmless or not is decided by the relationship between the stress intensity factor range of semi-circular cracks and the threshold stress intensity factor regardless of stress ratio.

The proposed method can be applied to mechanical parts used in vehicles, aircraft and trains.

This is the first paper to investigate the fatigue limits after SP in materials containing a surface defect under positive stress ratio. In this study, the authors investigated the influence of stress ratio on the effects of SP on the fatigue limit containing a surface defects.

In this study composite and sandwich beams with homogeneous core and homogeneous or Functional Graded Materials (FGM) faces under three point bending have been confronted. The purpose of this paper is to study numerically sandwich beams with homogeneous core and homogeneous or FGM faces under three point bending and to compare the results for the stress and displacement fields with those resulted of coating – substrate and homogeneous beams. Considering a crack in the lower face sheet to study the influence of the material gradation on the stress intensity factors.

At first a static finite element analysis is performed throughout the composite and sandwich beams, which is taking into account the graded character or not of the faces. For this reason five plane models are considered in order to have a comparable study for the stress and displacement fields of composite beams, which are subjected to three point bending. Second a crack in the lower face is considered parallel to the axis of gradation. When subjected to three point bending, this crack will propagate slowly perpendicular to the lower face.

Computed distributions of the stress fields across the core material and near the interfaces are given for different materials gradation of the faces; and possible crack-initiation positions have been identified. Stress intensity factors are calculated using finite element method, and assuming linear fracture mechanics and plane strain conditions.

The originality of the proposed analysis is to investigate for the first time numerically the influence of the FGMs or homogeneous faces in the core material of sandwich beams under three point bending relative to the coating – substrate and to the homogeneous beams. Second to study the influence of a crack in the lower graded face sheet on the overall behavior of the composite beam and to investigate the influence of the material gradation on the values of stress intensity factors.