Evaluation Of Stress Intensity Factors Research Articles

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

PurposeThe purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.Design/methodology/approachNumerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.FindingsKnown numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.Originality/valueThis study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

Evaluation of dynamic SIF during crack propagation in layered plates having property variation along the crack front

The present study emphasizes understanding the crack propagation in layered structures under dynamic loading conditions when the property jumps occur across the crack front. Layered plates were made by joining polymethylmethacrylate (PMMA) and epoxy sheets using an epoxy-based adhesive (Araldite). Single edge notched (SEN) specimens were subjected to dynamic loading using a modified Hopkinson bar setup. An array of strain gauges installed on surfaces of specimen was used to record the strain history in the layers during crack propagation from which the dynamic stress intensity factor (SIF) during crack propagation was evaluated. Photographs of the propagating crack front were also simultaneously captured using a high-speed imaging camera to obtain the crack tip location history in each layer.

Plasticity Correction on Stress Intensity Factor Evaluation for Underclad Cracks in Reactor Pressure Vessels

Abstract Structural integrity assessment of reactor pressure vessels (RPVs) is essential for the safe operation of nuclear power plants. For RPVs in pressurized water reactors (PWRs), the assessment should be performed by considering neutron irradiation embrittlement and pressurized thermal shock (PTS) events. To assess the structural integrity of an RPV, a traditional method is usually employed by comparing fracture toughness of the RPV material with the stress intensity factor (KI) of a crack postulated near the RPV inner surface. When an underclad crack (i.e., a crack beneath the cladding of an RPV) is postulated, KI of this crack can be increased owing to the plasticity effect of cladding. This is because the yield stress of cladding is lower than that of base metal and the cladding may yield earlier than base metal. In this paper, detailed three-dimensional (3D) finite element analyses (FEAs) were performed in consideration of the plasticity effect of cladding for underclad cracks postulated in Japanese RPVs. Based on the 3D FEA results, a plasticity correction method was proposed on KI calculations of underclad cracks. In addition, the effects of RPV geometries and loading conditions were investigated using the proposed plasticity correction method. Moreover, the applicability of the proposed method to the case which considers the hardening effect of materials after neutron irradiation was also investigated. All of these results indicate that the proposed plasticity correction method can be used for KI calculations of underclad cracks and is applicable to structural integrity assessment of Japanese RPVs containing underclad cracks.

A displacement-based and explicit non-planar 3D crack propagation model in the generalized/extended finite element method

The displacement-based methods for the extraction of the Stress Intensity Factors (SIFs) were created decades ago and, since them, they have been used in a wide range of numerical analysis, most of them based on standard 2D Finite Element Method (FEM). Although the accuracy of the SIFs computed by the displacement-based methods generally be inferior compared with the energy release methods, the use of the former methods have been motivated by its simplicity, ease of implementation and low computational cost, even though it may yield less accurate SIFs when compared with the latter methods. A major use of the SIFs is the prediction of the crack path direction in crack propagation analysis. The modelling of crack propagation is the most frequent application of the Generalized Finite Element Method (GFEM) and Extended Finite Element Method (XFEM) and a large number of crack propagation models presented in literature uses energy release methods for SIFs evaluation. Very few works using displacement-based methods for the computation of the SIFs have been published in literature in the context of the GFEM and XFEM. This paper presents a propagation model for an explicit non-planar 3D crack in a GFEM/XFEM background. The proposed model uses the Displacement Correlation Method (DCM) for the SIFs extraction. Some crack propagation problems are investigated and the resultant crack paths are compared with reported results from literature. This work demonstrates that the model here proposed generates very reasonable crack paths even for relatively coarse meshes using linear elements.

A new domain-independent interaction integral for three-dimensional non-homogeneous thermoelastic materials

This work establishes a new domain-independent interaction integral for the evaluation of mixed-mode stress intensity factors (SIFs) in three-dimensional non-homogeneous materials with complex thermo-mechanical interfaces subjected to thermo-mechanical loadings. A new auxiliary field called Zero-Mean stress field is developed to deal with the mismatch of thermoelastic properties across the material interfaces. An area integral along with the material interfaces, which is indispensable to keep domain-independence of the conventional interaction integral using Williams’ auxiliary fields, is eliminated by using this new auxiliary. A crack-face integral is added to maintain the domain-independence of this new method. The expression of this new domain-independent interaction integral contains no thermal property parameters. Because of this feature, the new interaction integral holds domain-independent for both discontinuous mechanical properties and discontinuous thermal properties. Since tracking crack-planes is much easier than tracking a material interface in numerical implementations, it brings convenience to the practical applications to analyze three-dimensional non-homogeneous materials with discontinuous thermoelastic material properties. The new interaction integral, combined with the finite element method, is applied to investigate several representative examples, which demonstrates that the new interaction integral has good accuracy and domain-independence for thermo-mechanical interfaces.

Experimental evaluation of effective stress intensity factor using thermoelastic stress analysis and digital image correlation

During the last decades, the debate over the mechanisms governing fatigue crack shielding has been mainly focused on demonstrating the existence of fatigue crack closure and the difficulties on quantifying the induced stress during crack propagation. Hence, most adopted experimental methods have been based on the direct or indirect measurement of contact loads between crack surfaces as the crack starts closing. Nevertheless, these methods depend on many factors sometime difficult to control, which has contributed to question their reliability by many authors. For this reason, two modern well established, full-field, non-contact experimental techniques, namely Thermoelastic Stress Analysis (TSA) and 2D Digital Image Correlation (2D-DIC), have been analysed to evaluate the influence of crack shielding during fatigue experiments conducted on two aluminium alloys (Al2024-T3 and Al7050) tested at different stress ratios. In the particular case of TSA, the technique appears to have a great potential in the evaluation of fatigue crack shielding since crack tip events are inferred directly from the temperature changes occurring at the crack tip rather than from remote data. Experimental data from both techniques have been employed in combination with two different mathematical models based on Muskhelishvili’s complex potentials to infer the effective range of stress intensity factor. Results from both techniques agree quite well, showing a variation in the stress intensity factor range as the R-ratio changes from 0.1 to 0.5 and illustrating the potential ability of both techniques to account for the shielding effect due to crack closure.

Evaluation of SIFs for cracks under thermal impact based on Green-Naghdi theory

This paper presents a study on the crack behavior under a thermal shock in a wide range of applications. The Stress Intensity Factors (SIFs) for a stationary crack under a non-Fourier thermal shock according to the Green-Naghdi (GN) theory is computed. The crack is considered as an adiabatic line in the framework of the eXtended Finite Element Method. The interaction integral is employed to extract the SIFs for three types of the Green-Naghdi theory. The differences in the time history of SIFs due to the thermal shock based on all types of the GN theory is studied. Also, the effect of damping coefficient on the SIFs and the temperature field is investigated. Finally, the role of inclined cracks, which disturb the time history of SIFs, displacement and temperature distributions for type II and III of the GN theory are discussed.

Stress intensity factor evaluation for central oriented cracks by stress dead‐zone concept

Stress intensity factor evaluation for central oriented cracks by stress dead‐zone concept

A hybrid DIC–EFG method for strain field characterization and stress intensity factor evaluation of a fatigue crack

A Hybrid DIC–EFG Method combining Digital Image Correlation (DIC) and Element-free Galerkin (EFG) method is proposed to characterize the strain field and study the fracture performance of a crack by evaluating the stress intensity factor (SIF). The full-field displacement data is measured by DIC. The meshless calculation model is developed by using the speckle image coordinate. Then the displacement data is imported into the model and strain is calculated by the EFG method. The SIF is obtained based on the J-integral method. A static tensile test with a quasi-static cyclic load is conducted on a Compact Tensile specimen (CT specimen) to experimentally validate the accuracy and stability of proposed method. The proposed method can effectively predict the strain at the crack tip, which is a great challenge for the DIC measurement. Compared with the reference ASTM standard, the proposed method can obtain the SIF accurately without knowing the geometry, load and boundary condition of the structure.

Subsurface Facet-fisheye Induced Failure of Titanium Alloy under Very High Cycle Fatigue

Very high cycle fatigue test under pulsating tension was performed to investigate the subsurface failure mechanism of a titanium alloy. A peculiar region, called “facets cluster zone (FCZ)”, is located at the center of fisheye. The slip-like patterns on facet surface, coalescence of nanoscale cracks and growth of microcracks in the maximum shear stress plane are observable. Combined with the evaluation of stress intensity factors at crack tips, the subsurface failure processes are summarized as: (a) localization of plastic strain, (b) occurrence of slip lines, (c) nucleation of microcracks, (d) coalescence and growth of microcracks, (f) occurrence of the FCZ, (g) formation of fisheye and (i) unstable crack growth until final fracture.

Effect of constraints on stress intensity factor for dissimilar metal plate with centre crack under uniform tension

Dissimilar metal joints (DMJs) are more common in the coolant systems of most of the engineering applications and are subjected to variety of loadings. To understand the constraint effect of the dissimilar metal welded joints (DMJs), fracture studies have been carried out on dissimilar metal plate (DMP) with center crack made up of ferritic steel (SA 508 Gr.3 Cl.1), austenitic steel (SA312 Type 304LN) and Inconel – 182 alloy (ENiCrFe-3). 2-D and 3-D finite element analysis (FEA) is carried out on the DMP with centre crack (length = 250 mm, width = 150 mm) for various crack lengths (15, 20, 30 and 50 mm) and various dissimilar metal welded joint widths (DMJWs) (5, 10, 20, 30, 40 and 50 mm) to evaluate stress intensity factor (SIF). SIF has been evaluated by employing domain integral method. It is observed from the studies that, (i) SIF increases with increase of crack length and DMJW, (ii) 3-D finite element analysis yields realistic SIF (iii) SIF of DMP reduces compared to homogenous plate, (iv) constraint effect is found to be significant if DMJW is less than the initial crack length, resulted in reduction of SIF (iv) constraint effect is found to be insignificant if DMJW is more than 20 mm and the ratio of crack length to DMJW is greater than 0.75. The study will be useful for damage tolerant analysis of structures/components which in turn will be helpful for repair, retrofitting of components and in-service inspection.

Accurate evaluation of stress intensity factors using dual interpolation boundary face method

Accurate computation of stress intensity factors for two-dimensional cracks by a dual interpolation boundary face method (DiBFM) is presented in this paper. Dual interpolation method combines traditional element polynomial interpolation and moving least-squares approximation. Dual interpolation elements are obtained by adding virtual nodes on the boundary of traditional discontinuous elements, and they unify traditional continuous and discontinuous elements. With the dual interpolation elements, both the continuous and discontinuous fields can be approximated, and the accuracy of interpolation increases by two orders compared with the corresponding discontinuous elements. In addition, a new singular element based on the dual interpolation method for modeling displacement fields around the crack tip is proposed in this paper. The stress intensity factors are extracted from the relative displacements between the crack surfaces. Using the DiBFM combined with the proposed singular element, accurate results of the stress intensity factors can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.

Notch stress intensity factor and C-integral evaluation for sharp V-notch in power-law creeping solids

The characterization of the stress intensity for a sharp V-notch in creeping solids is an important topic as it is a preliminary to evaluate and assess the notch contained structure at elevated temperature, however, it is not investigated in-depth in available literatures. In this paper, the C-integral evaluation for the sharp V-notch in power-law creeping solids is studied and the concept of notch stress intensity factor (NSIF) is extended to the sharp V-notch in creeping materials based on asymptotic solution of sharp V-notch tip field. C-integral of a sharp V-notch tip is demonstrated to be dependent on the integration path away from notch tip regardless of creep extents. A novel path-independent CV-integral is proposed based on the derivation of C-integral and the concept of NSIF for sharp V-notch. A numerical method to determine NSIF as well as CV-integral for sharp V-notch is presented and verified. Typical solutions of NSIF and CV-integral for single edged sharp V-notch specimen are also discussed in this paper. The concept of NSIF and CV-integral presented in this paper is very promising to be extended to characterize fatigue issues in further investigations.

A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

Calibrating thermoelastic stress analysis with integrated digital image correlation: Application to fatigue cracks

This article discusses the dual use of digital image correlation and thermoelastic stress analyses for the study of propagating cracks. It is shown that a few critical parameters such as emissivity and the thermoelastic constant required for the latter can be calibrated with the former. A unified framework is introduced, which treats both experimental techniques equally to locate crack tips, and then evaluate stress intensity factors. This framework allows for a detailed and quantitative comparison between both methods. It is found that, for the case at hand, the thermoelastic stress analyses outputs were less noise sensitive while the digital image correlation method was less dependent on calibration. The proposed procedure was very robust for finding the crack tip location for both experimental methods.

Fracture Mechanics Approach to Splitting in Low Spring Index Cold Coiling Process.

This paper is an attempt to understand the coil splitting phenomena by means of fracture mechanics. The methods used combine the residual stress measurement with neutron and finite element analysis. The support of the metallurgical evaluation is used as evidence to justify the use of the fracture mechanics concept. Comparing coil springs manufactured at two different manufacturing lines, namely N1 and N6, residual stress distributions in three main directions were measured using neutron diffraction. The results of the residual stress measurement were then converted into the stress intensity factor to enable the analysis in fracture mechanics. The mixed-mode analysis of opening, Mode I, and in-plane shearing, Mode II, is used to solve the splitting problem. The discrepancy between the coil made at N1 and N6 was identified and taken into account in terms of the profile difference. Based on this difference, an FEA simulation was conducted. The results support the experimental finding, which is that the shape of the coil manufactured influences the pattern of the residual stress, which leads to different splitting behaviors. This simple analysis helps practitioners understand why, and how, some cold coiled products split after manufacturing. It is concluded that this very basic concept of fracture mechanics can be used to establish the limit of the cold coiling process by evaluation of the mixed-mode stress intensity factor to the fracture toughness of the material.

A two-scale generalized FEM for the evaluation of stress intensity factors at spot welds subjected to thermomechanical loads

This paper presents a two-scale Generalized Finite Element Method with global-local enrichments (GFEMgl) for the evaluation of stress intensity factors (SIFs) at spot welds subjected to thermomechanical loads. The method uses the solution of local boundary value problems as enrichment functions for the global/structural model and can provide accurate solutions on coarse meshes adopted at the structural scale. The faying surface and spot welds are represented by special enrichment functions instead of meshes fitting the weld geometry. This greatly simplifies the model generation process in comparison with a Direct Finite Element Analysis DFEA. Numerical experiments show that the proposed GFEMgl is able to capture the strong gradients and singularities near the spot weld edge. It can provide accurate solutions and SIFs comparable to a 3-D DFEA while requiring significantly less computational resources and user time. The robustness of the method is demonstrated through examples involving spot welds with irregular shapes and built-up panels subjected to sharp thermal fluxes.

Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor

This paper is concerned with evaluating stress intensity factors (SIFs), for a cracked curved beam of rectangular cross section, applying an approach which allows us to estimate the strain energy release rate. The beam is located on an elastic foundation. The out-of-plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach, namely differential quadrature element method (DQEM), to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam.

Evaluation of stress intensity factors in functionally graded materials by natural element method

This paper is concerned with the numerical evaluation of the stress intensity factors (SIFs) of 2-D isotropic functionally graded materials (FGMs) by the natural element method (more exactly, Petrov-Galerkin NEM). The spatial variation of elastic modulus in inhomogeneous FGMs is reflected into the modified interaction integral $${\tilde M^{(1,2)}}$$ . The local NEM grid near the crack tip is refined, and the strain and stress fields that were directly approximated by PG-NEM were enhanced and smoothened by the patch recovery technique. Numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The stress intensity factors are parametrically evaluated with respect to the exponent index in the elastic modulus and the crack length, and those were compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately evaluates the stress intensity factors of 2-D inhomogeneous functionally graded materials.

A Numerical Study of Creep Crack Growth in an Aero-engine Turbine Disc using XFEM

In this paper, a turbine disc of an aero-engine having a macro crack under creep loading is studied to predict the creep crack growth. Extended finite element method (XFEM) is used as it does not require conformal meshing and remeshing due to change in the topology during crack growth. The elasto-plastic behavior of the material is modelled by Ramberg-Osgood model and von-Mises yield criterion. The creep behavior is modelled by coupling of spatial and temporal dimensions to capture the effect of stress relaxation and redistribution due to creep strain. The creep crack growth rate is computed by the C(t)-integral which includes small-scale creep, transition creep and extensive creep. The crack growth direction is estimated by the maximum principal stress criterion using mode-I and mode-II stress intensity factors (SIFs). The interaction integral approach is implemented for the evaluation of stress intensity factors of different modes. The history fields of plasticity and creep are transferred properly from the old configuration to new configuration after the crack growth which is the main challenge in this analysis. This proposed numerical scheme is then utilized to obtain the creep crack growth in the component made of elasto-plastic-creeping material. The creep crack growth variation with time is estimated by the XFEM to evaluate the life of an aero-engine turbine disc under creep conditions.