Ratio Of Crack Length Research Articles

Determination of the Resonance Frequencies in the Course of Sounding of Impedance Defects on the Boundary of the Rigid Joint of a Plate and a Half Space by Elastic SH-Waves

We study the problem of diffraction of elastic SH-waves on the striplike impedance surface of the rigidly fastened edge of an infinite elastic layer. The problem is solved by the Wiener–Hopf method. We analyze the eigenvalues of operator of the problem corresponding to resonance vibration of the dynamical system in the main mode. We also construct the dependences of the first branch of roots of the characteristic equation on the ratio of crack length to the thickness of the plate for various values of the impedance of defects.

Size and crack length effects on fracture toughness of polycrystalline graphite

In this paper, the effects of specimen size and crack length on the fracture toughness of polycrystalline graphite are studied. The experimental results reported in the previous studies showed that the fracture toughness of graphite increase in bigger specimen. It has been also demonstrated that the fracture toughness of graphite is nearly identical in specimens with crack length ratio less than 0.7 but decreases for grater crack length ratios. To justify the size and crack length dependency of fracture toughness, the modified form of maximum tangential stress (MMTS) criterion, which makes the use of higher order terms in calculating the stress field around the crack tip is employed. It is shown that the MMTS criterion can provide good estimates for the fracture toughness of graphite obtained from specimen with different sizes. It is also indicated that the MMTS criterion can predict very good the reported experimental fracture toughness data for samples with the crack length ratios less than 0.7.

Structural Integrity Assessment of Thermal Power Plant Superheater Collector

Thermal power plants (TPPs) belong to the important objects, the failure of which can cause accidents with severe consequences. A large portion of Ukrainian TPP has exceeded its design life, which is determined by the main elements of steam power systems. Therefore, the main task is to assess correctly the superheaters collectors limit state using modern approaches and taking into account the service degradation of material.TPP superheater collectors operate in the steamy environment under the pressure of 15.5MPa at temperature 545°C. As a result of combined action of prolonged thermo-mechanical stresses, corrosive and hydrogen environment and slow deformation, fatigue cracks emerge in these components on the inner collector surface.The limit state of boiler steam superheater collector model was assessed using failure assessment diagram (FAD). The FADs were built for Kmat = KIc and Kmat = Kfc taking into account safety factors for plastic collapse and for brittle fracture mechanisms for the collector model with part circumferential internal surface crack for various ratio of crack length l to depth a.The critical sizes of the inner surface defect, that is perpendicular to the axis of the cylinder, considering fracture toughness of 12Cr1MoV steel for static and cyclic loading, were assessed.It was found out, that the increase of l/a ratio decreases the minimum crack depth that is critical for structural element.

A Fully Parametric Weight Function for Inclined Kinked Edge Cracks

A general method for evaluating the Stress Intensity Factors (SIFs) of an inclined kinked edge crack in a semi-plane is presented. An analytical Weight Function (WF) with a matrix structure is derived by extending a method developed for a straight inclined edge crack. The effects of the principal geometrical parameters governing the problem were studied through a parametric Finite Element (FE) analysis, carried out for different reference loading conditions. The proposed WF can be used to produce efficient and accurate evaluations of the SIFs for cracks with initial inclination angle in the range [–60°,60°], kink angle in the range [- 90°,90°], and kinked crack to initial crack length ratios in the range [0,1/4].

Size effects in mode II brittle fracture of rocks

In this paper, a stress-based criterion is suggested for predicting the mode II fracture resistance of rock materials by considering the effects of specimen size. This criterion is a modified form of the maximum tangential stress criterion which takes into account the second and third terms of Williams series expansion in addition to the singular terms. In order to assess the proposed criterion, a number of modes I and II fracture tests are conducted on the semi-circular bend specimens manufactured from marble. For using the proposed criterion, the constant coefficients of higher order terms are determined for the semi-circular bend specimen with different crack length ratios and various loading span to radius ratios. Finally, it is shown that the proposed criterion can provide good estimates for the mode II fracture resistance of marble from its mode I fracture results while the effects of specimen size are taken into account.

Modified NASGRO equation for physically short cracks

A typical fatigue crack growth curve consists of the threshold region, the Paris region (linear in a logarithmically scaled diagram) and the transition region from the Paris region to unstable crack growth. For cracks exceeding a certain material-dependent length, this curve depends only on the load ratio R and is well described by commonly accepted crack growth models such as the Forman/Mettu (NASGRO) equation. However, cracks below this length typically grow significantly faster due to the absence of crack-closure effects, leading to an additional dependence of the crack growth curve on the crack extension Δa. In this paper, a simple analytical model for describing the crack growth behavior for any crack length and load ratio R is presented. For the QT steel 25CrMo4, the model is applied to describe the crack growth behavior for different crack length and load ratios between −3 and 0.5.

Modeling of debonding and fracture process of FRP-strengthened concrete beams via fracture mechanics approach

Fiber-reinforced polymer (FRP) composite materials have been widely used in the field of retrofitting. To estimate their service reliability, it is necessary to conduct a theoretical analysis of FRP-strengthened concrete beams. In this paper, a fracture mechanics approach is presented to model the cracking behavior of and interfacial debonding process in FRP-strengthened concrete beams. The K-superposition method is adopted to calculate the net stress intensity factor at the crack tip. After the validity of the proposed approach is verified with experimental results obtained from the literature, the effects of various factors on the load-bearing capacity and crack growth resistance of FRP-reinforced concrete beams are quantitatively evaluated. It is found that the first peak load increases as the beam height and compressive strength of concrete increase or the ratio of the initial crack length to beam height decreases, whereas the second peak load is an increasing function of the FRP sheet thickness and width. It is also found that the crack growth resistance increases with an increase in ratio of the initial crack length to beam height and FRP sheet thickness and width but is seldom influenced by the beam height and compressive strength of concrete.

Effect of Specimen Geometry on Stress Intensity Factors of Inclined Crack by Finite Element Method

A rectangular plate with inclined cracks of different crack lengths at different crack inclination angles under biaxial loading condition are being analyzed in mixed mode condition using finite element method (FEM) for the determination of stress intensity factors (SIFs). With increases of the width of the plate and the crack length ratio, SIF increases up to 45° of crack inclination angle and then decreases; maximum value is obtained at 45° of crack inclination angle. With the increasing value of size factor, the value of SIF starts decreasing. The accuracy of the results of the proposed method is validated by comparing with the previously obtained results by theoretical and experimental methods. The FEM results give significant result for the two-dimensional mixed mode loading conditions.

Influence of test method used to evaluate resistance of C‐Mn steel to hydrogen induced cracking

AbstractThe presented paper deals with a comparison of test methods for evaluating the resistance of API grade X65 steel to hydrogen induced cracking (HIC). It concerned particularly the ultrasonic immersion method using an AGFA non‐destructive testing device by Krautkrämer and metallographic evaluation of the results of ultrasonic tests according to the directive NACE TM 0284. Comparison of test methods was made on the basis of established parameters of cracks, i. e. crack length ratio (CLR), crack thickness ratio (CTR) and crack sensitivity ratio (CSR). The determination of parameters in case of ultrasonic examination was performed using the pulse reflection method. Metallographic evaluations were performed always at hundred‐fold magnification on a light microscope ZEISS NEOPHOT 32. The obtained results showed that all the test methods used had very small differences between the investigated parameters.

비 이상화된 원주방향 관통균열이 존재하는 두꺼운 배관의 균열 성장 매개변수 계산

The present paper provides the elastic stress intensity factors(SIFs) of thick-walled cylinder with non-idealized circumferential through-wall cracks. For estimating these elastic SIFs, the systematic three-dimensional(3D) elastic finite element(FE) analyses were performed. In order to consider practical shape of thick-walled cylinder and non-idealized circumferential through-wall crack, the values of thickness of cylinder, reference crack length and crack length ratio were systematically varied. As for loading conditions, axial tension, global bending and internal pressure were considered. In particular, in order to calculate the SIFs of thick-walled cylinder with non-idealized circumferential through-wall crack from those of thick-walled cylinder with idealized circumferential through-wall crack, the correction factor representing the effect of non-idealized crack on the SIFs were proposed in this paper. The present results can be applied to accurately evaluate the rupture probabilities of nuclear piping considering actual crack growth behaviors.

3D effects on crack front core regions, stress intensity factors and crack initiation angles

Results pertaining to three dimensional finite element analysis of a mixed mode edge crack in a tension specimen are presented. Considering three values for the crack inclination angle, the effect of thickness is investigated on the predicted crack tip plastic zone size, stress intensity factors and crack initiation angles at the surface and the mid plane. The crack initiation angles are calculated using two crack initiation criteria: MTS and R-criterion. In general, the effect of thickness is noted for low values of thickness over crack length ratio at the surface. The finite element results are optimized through mesh convergence and validated by experiments. The experimental set up is designed and used to measure the crack initiation angle in mixed mode SENT specimen and estimate the stress intensity factors for different crack inclination angles and specimen thicknesses.

Investigation of UT Procedure for Crack Depth Sizing by Phased Array UT in Ni-Based Alloy Weld

Recently, it has been reported that the primary water stress corrosion cracking (PWSCC) has occurred in nickel based alloy weld components such as steam generator safe end weld, reactor vessel safe end weld, and so on, in PWR. Defect detection and sizing are important in order to ensure the reliable operation and life extension of nuclear power plants. In the reactor vessel safe end weld, it was impossible to measure crack depth of PWSCC. The cracks have occurred in the axial direction of the safe end weld. Furthermore, the cracks had some features such as deep, large aspect ratio (ratio of crack depth and length), sharp geometry of crack tip, and so on. Therefore, development and improvement of defect depth sizing capabilities by ultrasonic testing (UT) have been required. Phased array UT technique was applied with regard to defect depth sizing at the inside inspection in Ni-based alloy welds. Phased array UT was examined a standard block specimen with side drilled holes (SDHs). From the experimental results, the performance of linear array probes and dual matrix array probe were investigated. In the basis of the results, UT procedure for defect depth sizing was investigated and proposed. The UT procedure was applied to the defect depth measurement in Ni-based alloy weld specimen with electric discharge machine (EDM) notches. From these results, good accuracy of defect depth sizing by phased array UT for the inside inspection was shown. Therefore, it was clarified the effectiveness of the UT procedure for defect depth sizing in Ni-based alloy weld.

두꺼운 배관에 존재하는 축방향 경사관통균열의 탄성파괴역학 매개변수 계산

본 논문에서는 두꺼운 배관에 존재하는 축방향 경사관통균열의 탄성응력확대계수 및 탄성 균열열림변위 해를 제시하였다. 이를 위해 배관의 두께, 기준균열길이, 경사관통균열 길이비를 체계적으로 변화시키며 3차원 탄성 유한요소해석을 수행하였다. 하중조건으로는 균열 성장에 영향을 미치는 내압을 고려 하였다. 유한요소해석 결과를 바탕으로 두꺼운 배관에 존재하는 이상적인 축방향 관통균열과 경사관통균열에 대한 탄성응력확대계수와 탄성 균열열림변위를 균열선단 및 두께를 따라 제시하였다. 특히 응력확대 계수의 경우에는 이상적인 축방향 관통균열 결과로부터 쉽게 경사관통균열의 응력확대계수를 구할 수 있는 경사관통균열 보정계수를 제시하였다.

The effect of thermally grown oxide on multiple surface cracking in air plasma sprayed thermal barrier coating system

The objective of this paper is to understand the effect of thermally grown oxide (TGO) on the multiple surface cracking behaviors in an air plasma sprayed (APS) thermal barrier coating system (TBCs). The extended finite element method (XFEM) and periodic boundary conditions are used to investigate the TGO dependences of periodic surface crack driving force and crack propagation path. It is seen that the effect of TGO thickness on the strain energy release rate (SERR) is negligible while ignoring the thickening and elongation strains of the TGO layer. However, the effect of elastic modulus of TGO layer is significant. In particular, for relatively stiff TGO layer the SERR drops to zero as the ratio of surface crack length to coating thickness approximates to one. And vice versa, for a severely damaged TGO layer with relatively compliant modulus, the SERR approaches infinity as surface cracks propagate to the interface. This kind of fracture mechanism is mainly governed by the elastic mismatch across the bimaterial interfaces, which can be used as a guide for the design of good strain-tolerant coating film in APS-TBCs.

Three-dimensional vibrations of cracked rectangular parallelepipeds of functionally graded material

A novel examination of the three-dimensional (3-D) vibrations of rectangular parallelepipeds of functionally graded material (FGM) having side cracks is summarized. Employing 3-D theory of elasticity and a variational Ritz methodology, new hybrid series of mathematically complete orthogonal polynomials and crack functions as the assumed displacement fields are proposed to enhance the convergence modeling of the stress singular behavior of the crack terminus edge front in a rectangular FGM parallelepiped. The proposed admissible hybrid series properly describe the ϑ(1/r)3-D stress singularities at the terminus edge front of the crack, allowing for displacement discontinuities across the crack sufficient to explain the most general 3-D “mixed modes” of local crack-edge deformation and stress fields typically seen in fracture mechanics. The correctness and validity of the vibration analysis are confirmed through comprehensive convergence studies and comparisons with published results for cracked rectangular FGM parallelepipeds modeled as homogeneous rectangular plates with side cracks and FGM rectangular plates with no cracks based on various plate theories. Two types of FGM parallelepipeds, Al/Al2O3 and Al/ZrO2, are included in the study. The locally effective material properties are estimated by a simple power law and the effects of the volume fraction on the frequencies are investigated. For the first time in the published literature, this work reports frequency data and nodal patterns for FGM rectangular parallelepipeds modeled as moderately thick plates with several combinations of hinged, clamped, and completely free kinematic and stress conditions along the four side faces, and having side cracks with varying crack size effects implying flaw-size influence in FGM parallelepiped vibration and fracture, including crack length ratios (d/a and d/b), crack positions (cx/a and cy/b), and crack inclination angles (α).

Bulging factors and geometrically nonlinear responses of cracked shell structures under internal pressure

An approach based on the transverse or out-of-plane nonlinear dynamic responses at the centers of edges of cracks is being proposed as a viable alternative to bulging factors for damage tolerance design and characterization of cracked cylindrical shell structures under applied internal pressure. This approach circumvents the problems of mesh selection at the crack tip in the finite element analysis for bulging factors and provides information about the influence of crack lengths as well as crack widths on responses. The influence of crack widths on responses has been found to be significant but it is not available in bulging factors. Furthermore, existing individual bulging factor only applies to a different range of ratios of crack length to radius of shell. It is concluded that (i) the proposed approach has no limit on the range of ratios of crack length to radius of shell; (ii) conceptually, the proposed approach is simple, and (iii) computationally, the nonlinear responses at the centers of edges of cracks are relatively easy to obtain accurately and efficiently by using the mixed formulation-based shell finite elements since the present dynamic approach converges quickly at very coarse meshes.

Analysis of Mode III Collinear Periodic Cracks-Tip Stress Field of an Infinite Orthotropic Plate

The cracks-tip field on collinear periodic cracks of infinite orthotropic fiber reinforcement composite plate subjected to anti-plane shear force is studied in this paper. With the introduction of the Westergaard stress function and application of complex function theory and undetermined coefficients method, mechanical problem is changed into partial differential boundary value problem. The undetermined coefficients and the stress function are obtained with the help of boundary conditions. Due to the distribution of periodic cracks, stress intensity factor depends on the shape factor. The results show that interaction happens between the collinear periodic cracks. When the ratio of crack length and crack spacing is less than 1/3, the interaction between the cracks is very small. When the ratio gradually increases to 1, strong interaction between the cracks will be found. Cracks-tip field has scale effect. When the ratio of crack length and the given reference crack length decreases, the displacement field is significantly smaller.

Analysis of Mode III Collinear Periodic Cracks-Tip Stress Field of an Infinite Orthotropic Plate

The cracks-tip field on collinear periodic cracks of infinite orthotropic fiber reinforcement composite plate subjected to anti-plane shear force is studied in this paper. With the introduction of the Westergaard stress function and application of complex function theory and undetermined coefficients method, mechanical problem is changed into partial differential boundary value problem. The undetermined coefficients and the stress function are obtained with the help of boundary conditions. Due to the distribution of periodic cracks, stress intensity factor depends on the shape factor. The results show that interaction happens between the collinear periodic cracks. When the ratio of crack length and crack spacing is less than 1/3, the interaction between the cracks is very small. When the ratio gradually increases to 1, strong interaction between the cracks will be found. Cracks-tip field has scale effect. When the ratio of crack length and the given reference crack length decreases, the displacement field is significantly smaller.

Thermal Shock damage and Residual Strength Behavior of a Functionally Graded Plate with Surface Cracks of Alternating Lengths

Multiple surface cracking greatly influences the thermal shock behavior of ceramics and ceramic composites. This work aims to investigate the effects of surface crack morphology coupled with material gradation on the thermal shock damage and residual strength behavior of functionally graded ceramics. We consider a functionally graded plate with an array of periodically spaced surface cracks of alternating lengths subjected to thermal shocks. The coupled strongly singular integral equations for the opening displacements along the long and short cracks are derived using the Fourier transform and a superposition technique. Thermal shock damages (arrested lengths of the long and short cracks) in the specimen and the residual strength are determined using the stress intensity factor criterion. Numerical results for an Al2O3/Si3N4 graded material are presented to examine the effects of initial crack length ratio, crack spacing, and material gradation on the thermal shock damage and residual strength behavior. It is found that surface crack morphology in combination with thermal property gradation significantly influences the thermal shock damage and residual strength behavior of functionally graded ceramics. The specimens with smaller initial crack length ratios suffer severer damages and strength degradation at moderately intense thermal shocks.

A Global Limit Load Solution for Plates With Embedded Off-Set Elliptical Cracks Under Combined Tension and Bending

A global limit load solution is derived in this paper for embedded off-set elliptical cracks in a plate under combined tension and bending, based on the net-section collapse principle. The new limit load solution is validated using 3D elastic-perfectly plastic finite element (FE) limit analyses. The results show that the limit load solution developed in this paper is conservative and close to the elastic-perfectly-plastic FE results. The global limit load solution is then compared with the limit load solution based on the rectangular crack assumption, showing that the difference between the two solutions is negligible as the ratio of crack length to the plate width is less than 0.25. However, the difference may become significant when the ratio approaches one.