Energy Release Rate Method Research Articles

Comparison of mode II delamination behaviours in multidirectional and unidirectional composite laminates

Multidirectional (MD) composite laminates are extensively employed in structural applications owing to their superior mechanical characteristics. Nevertheless, the evaluation of the fracture toughness of composite laminates primarily relies on tests using unidirectional (UD) specimens. This study evaluates the reliability of characterizing mode II delamination behaviour in MD laminates by using UD specimens. The quantification of delamination area through Digital Image Correlation (DIC) analysis is integrated with a physical Energy Release Rate (ERR) method to ascertain the fracture resistance, which is compared with the ERR derived via a modified J-integral method and the standardized compliance methods. Fractographic analysis reveals similar fracture mechanisms in specimens with identical interfaces. The physical ERR increases notably due to large-scale fibre bridging induced by fibre nesting at 0∘//0∘ interfaces. Conversely, in 0∘//90∘ interfaces, large-area matrix cracking enhances the intrinsic fracture resistance, excluding the extrinsic toughening provided by fibre bridging.

Fatigue failure analysis of U75V rail material under Ⅰ+Ⅱ mixed-mode loading: Characterization using peridynamics and experimental verification

Fatigue failure behavior of U75V rail material under Ⅰ+Ⅱ mixed-mode loading is analyzed and characterized in this work. A fatigue crack propagation experiment was carried out on U75V rail material under mixed-mode loading for R = 0.1. Then, based on the Ordinary State-Based Peridynamic (OSB PD) theory, bond strain rate and bond energy release rate methods were used to characterize the fatigue failure behavior of the rail material. Finally, the simulation results were compared with experimental results in terms of crack propagation length, path and angle to evaluate the characterization effects of both methods. The conclusions were as follows: under single mode I loading, both methods could accurately characterize the fatigue failure behavior of the rail material. However, compared with the bond strain rate method, the bond energy release rate method could provide a more accurate characterization under I + II mixed-mode loading.

Programmatic model updating of damaged structures using modified SERR method

Vision inspection information of damages in civil engineering structures is hard to be transformed into an analysis-available resistance model to conduct in-service condition assessment. This paper proposes an updating crack-embedded finite element modeling framework using periodical vision inspection information, which offers a convenient crack embedding approach for safety assessment of cracked reinforced concrete (RC) frame structures. For this purpose, a modified stain energy release rate (SERR) method is proposed to enable the method for solid element with high accuracy. Consequently, an algorithm is proposed to map the crack information obtained by vision method in the FE model. The combination of modified SERR method and proposed mapping algorithm could achieve flexibility matrix updating of cracked element. In addition, the effectiveness and generality of the proposed framework are validated using three cracking configurations. This research can provide a feasible framework for the rapid condition assessment of in-service civil engineering structures, showing a great prospect of intelligent disaster prevention.

Study on the developmental characteristics and mechanism of shale FPZs

The fracture process and behavior of shale play a key role in the success of hydraulic fracturing stimulation in shale reservoirs. In this study, the central straight cracked Brazilian disc (CSCBD) splitting test in three fracture directions (arrester, divider, and short transverse) is conducted to reveal the propagation behavior and mechanism of closed symmetric fractures in laminated shales, with a focus on the fracture process zone (FPZ). The developmental characteristics and anisotropy of the FPZ near the crack tip of Mode I fracture of shale are identified and quantified based on the digital image correlation (DIC) method. By monitoring the crack tip opening displacement (CTOD) during the whole process, the critical CTOD, as one of the pivotal cohesive parameters, is obtained, and the development of the FPZ can be phased into three stages by CTOD evolution patterns. Based on double-K fracture criterion, the initiation fracture toughness and unstable fracture toughness of shale fractures at different laminar configurations are also analyzed. Additionally, the cohesive fracture model in the shale FPZ is derived based on the power function form using the energy release rate method.

Evaluation of Hydraulic Jacking Mechanism during In Situ Rock Grouting Using a Strain Energy Release Rate Method

Evaluation of Hydraulic Jacking Mechanism during In Situ Rock Grouting Using a Strain Energy Release Rate Method

Nonlinear dynamic behavior of rotating blade with breathing crack

This study aims at investigating the nonlinear dynamic behavior of rotating blade with transverse crack. A novel nonlinear rotating cracked blade model (NRCBM), which contains the spinning softening, centrifugal stiffening, Coriolis force, and crack closing effects, is developed based on continuous beam theory and strain energy release rate method. The rotating blade is considered as a cantilever beam fixed on the rigid hub with high rotating speed, and the crack is deemed to be open and close continuously in a trigonometric function way with the blade vibration. It is verified by the comparison with a finite element-based contact crack model and bilinear model that the proposed NRCBM can well capture the dynamic characteristics of the rotating blade with breathing crack. The dynamic behavior of rotating cracked blade is then investigated with NRCBM, and the nonlinear damage indicator (NDI) is introduced to characterize the non-linearity caused by blade crack. The results show that NDI is a distinguishable indicator for the severity level estimation of the crack in rotating blade. It is found that severe crack (i.e., a closer crack position to blade root as well as larger crack depth) is expected to heavily reduce the stiffness of rotating blade and apparently result in a lower resonant frequency. Meanwhile, the super-harmonic resonances are verified to be distinguishable indicators for diagnosing the crack existence, and the third-order super-harmonic resonances can serve as an indicator for the presence of severe crack since it only distinctly appears when the crack is severe.

Experimental and computational analyses on fatigue fracture and microstructure in dissimilar metal weldments with circular sharp stress raiser

Fatigue strengths of dissimilar metal weldments with a circular sharp stress raiser, which were the inner peripheral side welded joints of flange pipes with tungsten inert gas (TIG) or metal inert gas (MIG) welding process, were defined through bending fatigue experiments. Fatigue strengths decreased according to stress concentration factors in some cases but not in samples with a different welding process, and stress intensity factors at the sharp weld notch were applied for analyses using the energy release rate method. The crack states corresponded to the fact that the fatigue cracks propagated at nearly right angles to the maximum stress direction, and it is possible to predict their propagation direction. The local fatigue resistance of the martensite-ferrite structure with the TIG welding was higher than that of the austenite-ferrite structure with the MIG welding which has a largely different penetration rate. In the samples which have similar weld metal microstructure, the nominal fatigue strength declines according to the increase in the stress concentration factor. The TIG samples and the MIG samples reach their fatigue failure in the same level of stress intensity factors, except for a MIG sample which has a large excess metal shape and a different fracture mode. The stress intensity factors can be used as the fatigue fracture threshold criterion in the weldments with a circular sharp stress raiser, where have the complex stress effects.

Investigation of the elastoplastic and fracture behavior of solid materials considering microstructural anisotropy: A discrete element modeling study

The discrete element method (DEM) has great advantages in expressing the deformation and fracture of materials at large scale compared to the molecular dynamics (MD) and the finite element method (FEM). However, its application is constrained by the fact that most of the existing models are limited to elastic-brittle homogeneous materials. In this paper, a spring connected DEM model is proposed to describe the elastoplastic and fracture behavior of materials under quasi-static and dynamic loading conditions. In contrast to many other DEM models, the central element is connected to the surrounding double-layer elements with both short-range and long-range interactions. The elastic parameters of the connecting components are derived from the conservation of strain energy density, and the distortion energy is expressed uniquely by the defined distortion coefficients. Based on the von-Mises yield criterion and isotropic hardening effect, the plastic behavior of the connecting component is derived. Furthermore, the energy release rate and Voronoi tessellation method are used to characterize the failure process and the microstructures generation, respectively. The bilinear elastoplastic response under quasi-static cyclic loading as well as the elastic and plastic stress wave propagating in a one-dimensional bar and a two-dimensional plate subjected to impact loading are analyzed successfully with the proposed approach. In addition, the simulations of mode-I and mode-II crack propagation are conducted and validated by the theoretical prediction and dynamic shearing impact experiment, respectively. The effects of short-range and long-range interactions on material quasi-static and dynamic behavior are also discussed, and it is concluded that their impact on the material dynamic behavior (e.g. wave speed and crack propagation) is greater than that on the quasi-static response (e.g. elastoplastic deformation).

Bonded composite repair of metallic pipeline using energy release rate method

A methodology of repair in pipes involving bonded joints, manufactured through the wrappage of a composite around the pipe, is becoming a common practice in the industry for a series of associated advantages. The prediction of failure pressure in bonded repaired pipes is vital to guarantee a good quality of adhesion in this type of repair. Nowadays, the failure pressure is usually evaluated using hydrostatic tests that demand complex preparation to pressurize a section of the pipe and that are also dangerous for possible debris during rupture. With this fact in mind, this research purpose is to verify a simpler and more efficient methodology to predict the failure pressure applying energy release rate concepts. Double Cantilever Beam (DCB) and Width Tapered Double Cantilever Beam (WTDCB) tests were used to obtain the energy release rate of dissimilar specimens constituted with the same material as the most common repairs (steel/glass fiber reinforced polymer). Through a design equation that relates the energy release rate and the failure pressure presented in Standards ISO/PDTS 24817 and ASME PCC-2, it is possible to predict a value of failure pressure using DCB and WTDCB energy release rate results. The failure pressure predicted value was compared with the experimental hydrostatic tests results and analyzed. Results showed a good agreement between these two values, indicating that the methodology developed in this research might be used, in the future, to predict the failure pressure in bonded repaired pipes.

Innovative theory for the compliance computation in rotors

The conventional energy release rate approach to the computation of the crack compliance in rotors is critically reviewed and its shortcoming is highlighted. The state functions and the generic compliance are introduced, de ned, and veri ed. The proposed functions are de ned based on the end states' conditions and are exact. The crack compliance of the shaft in torsion is explicitly de ned as the function of the crack depth ratio and recommended as a good alternative to the classical procedure of the energy release rate method. The accuracy and eciency of the work are veri ed by concise mathematical formulation and comparison of the results of the work with the others in four examples.

Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors (SIFs) of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.

Crack modeling of rotating blades with cracked hexahedral finite element method

Dynamic analysis is the basis in investigating vibration features of cracked blades, where the features can be applied to monitor health state of blades, detect cracks in an early stage and prevent failures. This work presents a cracked hexahedral finite element method for dynamic analysis of cracked blades, with the purpose of addressing the contradiction between accuracy and efficiency in crack modeling of blades in rotor system. The cracked hexahedral element is first derived with strain energy release rate method, where correction of stress intensity factors of crack front and formulation of load distribution of crack surface are carried out to improve the modeling accuracy. To consider nonlinear characteristics of time-varying opening and closure effects caused by alternating loads, breathing function is proposed for the cracked hexahedral element. Second, finite element method with contact element is analyzed and used for comparison. Finally, validation of the cracked hexahedral element is carried out in terms of breathing effects of cracked blades and natural frequency in different crack depths. Good consistency is acquired between the results with developed cracked hexahedral element and contact element, while the computation time is significantly reduced in the previous one. Therefore, the developed cracked hexahedral element achieves good accuracy and high efficiency in crack modeling of rotating blades.

Stiffness Characteristics of a Rotor Shaft with Slant Crack Including Elliptical Front Edge

The stiffness characteristics of a rotating cracked shaft including elliptical front edge between transverse crack and 45° slant crack have been studied here. The strain energy release rate (SERR) method has been used to calculate the stiffness matrix of two types of the crack element. Time-varying characteristics of stiffness of the straight front edge and elliptical front edge of the cracked shaft were studied in a stable rotation cycle. The analytical result of this paper shows that change of the cracked shaft stiffness raises during the increase of the crack depth. The stiffness characteristics of the rotor with slant crack having elliptical front edge vary differently from those of the rotor with transverse crack having elliptical front edge.

Parametric instability of a Jeffcott rotor with rotationally asymmetric inertia and transverse crack

Both the rotationally asymmetric inertia and transverse crack frequently appear in the rotor system. The parametric excitations induced by this two features cause instability and severe vibration under certain operating conditions. Thus, the parametric instability of a Jeffcott rotor with asymmetric disk and open transverse crack is studied analytically. The vibration equations of four degrees-of-freedom of the system are established, and the stiffness coefficients of cracked rotor shaft are derived based upon the compliance method and strain energy release rate method. Then, utilizing the harmonic balance method and Taylor expansion technique, the unstable widths of simple and combination instability regions (SIR and CIR) are solved approximately. For a practical rotor system, the approximate unstable widths are verified by the Floquet numerical analysis. The effects of crack depth and position upon the unstable widths are discussed, and the conditions for zero unstable points (ZUPs) are given: Besides the asymmetric angle should be π/2 (for SIR) or 0 (for CIR), the relationships between the inertia asymmetry and crack parameters (depth and position) are also presented analytically. These results would be useful for crack detection and instability control of the asymmetric rotor-bearing system.

An efficient BEM formulation for analysis of bond-line cracks in thin walled aircraft structures

In this paper bond-line cracks in assembled plate structures are investigated. A multi-region boundary element formulation is used to model the assembly and to perform the analysis. Once the solution at the boundary has been obtained, energy methods are used to extract relevant fracture parameters from the boundary values. The energy release rate (G) method and a new J-integral formulation are implemented for interlaminar cracks in shear deformable plates. The energy release rate and the J-integral are then decomposed into stress intensity factors and their value along the bond-line is computed by means of a displacement discontinuity method.

얇은 막재에서 컷의 진전방향에 주름이 미치는 영향

본 논문에서는 기하학적 비선형 후좌굴 유한요소 해석을 통하여 얇은 멤브레인에서 주름 발생이 컷의 진전방향에 미치는 영향을 연구하였다. 해석에는 양단에 인장을 받고 있고 중앙에 기울어진 컷을 가진 직사각형 멤브레인을 고려하였다. 주름이 발생한 경우와 주름이 발생하지 않은 경우에 대해 각각 해석을 수행하여 컷의 진전각도 및 <TEX>$J$</TEX>-적분값을 비교하였다. 컷의 진전각도는 에너지 방출률이 최대인 방향, <TEX>$K_{II}$</TEX>의 값이 0이 되는 방향을 구하는 방법 및 접선응력이 최대인 방향을 구하는 방법을 사용하여 계산하였다. 또한 다양한 컷의 초기방향각을 고려하여 각도에 따른 주름의 영향을 조사하였으며 가상의 미소크기의 컷을 반복적으로 진전시켜 컷이 전파되는 경향도 알아보았다. In this paper, the effect of wrinkling on the cut propagation direction of thin membrane was studied using geometrically nonlinear shell element post-buckling analysis. In the analysis, rectangular tensile membrane configuration with a slanted center cut was considered. The cut propagation direction was predicted by maximum energy release rate method, <TEX>$K_{II}$</TEX>-zero method, and maximum tangential stress method. The cut propagation angle and the <TEX>$J$</TEX>-integral values were calculated for the wrinkled and unwrinkled cases and the results were compared. Various initial cut orientation angles were considered and the effect on the propagation direction was studied. The cut propagation paths were also predicted by virtual cut extension approach.

Nonlinear Field Theory of Fracture Mechanics for Paramagnetic and Ferromagnetic Materials

A nonlinear field theory of fracture mechanics is developed for crack propagation in paramagnetic and ferromagnetic materials from the global energy balance equation and the non-negative global dissipation requirement. The crack-front generalized J̃-integral is equivalent to the generalized energy release rate serving as the thermodynamic driving force for crack propagation and also related to the generalized energy-momentum tensor in a way similar to the material force method. On the basis of the developed theory, the generalized energy release rate method, the generalized J̃-integral method, and the extended essential work of fracture method are proposed for quasistatic and dynamic fracture characterization of magnetosensitive materials in the presence of magnetothermomechanical coupling and dissipative effects. The present work overcomes the drawbacks and limitations of conventional fracture mechanics and resolves the controversial issues on magnetoelastic fracture criterion. Especially, the crack-front generalized J̃-integral has an odd dependence on the magnetic induction intensity factor for a Griffith-type crack in a magnetoelastic solid.

Coupled hygro-thermo-viscoelastic fracture theory

A coupled hygro-thermo-viscoelastic fracture theory is developed for quasi-static and dynamic crack propagation in viscoelastic materials subject to combined mechanical loading and hygrothermal environmental exposure based on fundamental principles of thermodynamics. The Helmholtz free energy is taken to be a functional of the histories of strain, temperature and fluid concentration with the crack parameter being introduced as an internal state variable. A thermodynamically consistent time-dependent fracture criterion for crack propagation in the presence of thermally and mechanically assisted fluid transport is obtained from the global energy balance equation and the requirement of non-negativity of the global energy dissipation rate, which is generally applicable to both quasi-static and dynamic loading and both isothermal/isohumidity and non-isothermal/non-isohumidity conditions with classic fracture criteria as special cases. On the basis of the developed theory, the generalized energy release rate method, the generalized contour integral method and the extended essential work of fracture method are proposed for fracture characterization of load-carrying viscoelastic materials in hygrothermal environments, and the interrelation of these methods and their correlation with conventional methods and existing models, simulations and experiments are discussed.

Computation of Stress Intensity Factors in Fatigue Crack Closure

Extensive work for fatigue crack closure using the finite element method has been conducted. It was concerned with the estimation of the K parameter as a forcing function in roughness-induced crack closure, assessment of methods for evaluating the closure stress intensity factors, and numerical modeling of crack closure. From the analyses, K parameter appears to be valid for representing the change of stress distribution due to crack closure. Also, it was shown that the strain energy release rate method, using the nodal release technique and work done by applied loads for strain energy, was clearly superior for calculating the closure stress intensity factor. In addition, a review for the characterization of crack tip stress fields has been made in terms of roughness dimension on the crack surface.

Matrix cracking behavior of K3B/IM7 composite laminates subject to static and fatigue loading

The matrix cracking behavior of a new high-performance thermoplastic composite material, K3B/IM7, was systematically investigated. Laminates in various grouped thickness and ply stacking sequences, [0 2/90 2/0 2], [0 2/90 4/0 2], and a quasi-isotropic laminate [+45/0/−45/90] s were tested under static and tension–tension fatigue loading. Depending on the stacking sequence of the laminates and the type of loading, various matrix cracking behavior were found. Under static loading, the matrix cracks were mainly close to the specimen edges. A few cracks were found to penetrate the specimen width, even when the load was large enough to break the specimen. However, under fatigue cyclic load, the edge initiated cracks propagated fully across the specimen width. Combined with the fatigue Paris Rule and considering the ply thickness and stacking sequence, the energy release rate method was applied to predict the relations between the loading strain amplitude and fatigue cycles for matrix cracking failure.