Linear Elastic Fracture Mechanics Analysis Research Articles

Comparison of Mode I fracture toughness of an elastic and an elastoplastic methyl methacrylate polymer as measured by SENB and DCDC tests

An elastic and an elastoplastic methyl methacrylate polymer, both in the glassy state, have been submitted to mode I fracture characterization with two different tests, the single edge notch bending (SENB) and the double cleavage drilled compression (DCDC) tests. The elastic material toughness was simply assessed by the linear elastic fracture mechanics analysis. For the elastoplastic material, the J-integral was computed when the strain fields were available. Moreover, numerical analyses were carried out using finite element simulations with a phase-field damage approach, providing comparison when the J-integral had been calculated and estimate otherwise, of the critical energy release rate. For each material, as well as for each test, the values of the critical energy release rate that have been estimated here, are in good agreement with the literature. More interestingly, for the same material, both tests provide with very different estimates of this material parameter, leaving engineers uncertain on which test to choose to assess the material toughness in crack opening mode.

Structural integrity analysis with crack propagation for reactor pressure vessel nozzles based on XFEM

Structural integrity analysis for reactor pressure vessel (RPV) nozzles has been a vital issue due to the irradiation embrittlement and especially the discontinuity of geometry in RPV nozzles, which may cause a higher stress concentration and influence the structural integrity of RPV nozzles. For the linear elastic fracture mechanics (LEFM) analysis of the RPV nozzle, a postulated crack with a specific crack depth is presumed to evaluate the stress intensity factors (SIFs) whose crack depth does not grow during LEFM analysis. Thus, this paper would discuss the crack propagation for the postulated crack with a specific crack depth under the different reference temperature of nil-ductility transition (RTNDT), and the SIFs on the specific crack depth are also calculated. In recent research, the extended finite element method (XFEM) was developed, which is based on the enrichment solution space to simplify the computational fracture mechanics with the crack propagation of various discontinuities, and can be used to evaluate the crack propagation of RPV nozzle with a specific crack depth under RTNDT of −23.89, −10.89, 0.89, 2.69, and 2.89 °C. To investigate the crack propagation and structural integrity of RPV nozzles, the finite element analysis of Taiwan domestic boiling water reactor (BWR) nozzles containing the postulated circular corner crack with depths of one-fourth and one-tenth thickness along the 45° path from the tip of the nozzle corner is engaged. The present result shows that the crack was growing when the RTNDT was 0.89 °C and. In addition, the XFEM calculation of the SIFs for the specific crack depth is similar to the LEFM results.

New Plastic Crack-Tip Opening Displacement Tool Based on Digital Image Correlation for Estimating the Fatigue-Crack-Growth Law on 316L Stainless Steel.

This work presents a new approach for studying crack growth resulting from fatigue, which utilizes the plastic contribution of crack-tip opening displacement (CTODp). CTODp is used to predict austenitic stainless-steel crack propagation. Unlike linear elastic fracture mechanics analysis, the method presented here is also helpful for tasks other than small-scale yielding. The approach was based on correlating full-field displacement information with post-processing digital images. This work describes a detailed post-processing protocol that can be used to calculate CTODp. The results for steel compact-tension specimens were especially promising. Of note, there was a linear relationship between the propagation rate of fatigue cracks and the CTODp range.

Fatigue strength assessment of welded joints in the marine environment

Welding is a commonly applied joining method in many applications in arctic and marine conditions, e.g., in ship and offshore structures, and energy production equipment. Such applications are usually subjected to fluctuating load conditions, and during a decades-long service, they may experience millions of load cycles. Consequently, fatigue strength design and acceptable flaw sizes in the welded details of these structures are among the most important design criteria. Multiple fatigue strength assessment approaches exist for assessing the fatigue strength of a welded detail. The present study introduces a numerical and analytical fatigue strength assessment, conducted on a non-load-carrying X-joint, which is a representative joint type used in many steel constructions. Fatigue analyses are carried out following the DNVGL-RP-C203 and BS7910:2013 fatigue design guidelines for offshore steel structures. The stress intensity factors (SIFs) for linear elastic fracture mechanics (LEFM) analyses were obtained using three different methods: the weight function approach, the analytical equations provided in the IIW Recommendations, and by conducting numerical crack propagation analysis using the Franc2D software. All three methods had a good agreement particularly for short crack depths, indicating the applicability of the analytical approaches for the fatigue analyses. The results showed that the consideration of degree of bending at the welded detail is crucial due to the distinguishing notch stress factors of membrane and bending loading, and different stress distributions in the through-thickness direction. In addition, it was found that the LEFM-based fatigue life assessments are significantly more conservative than the life predictions obtained using the structural hot-spot and effective notch stress approaches.

Investigation of the tensile-shear failure of asphalt concrete base (ACB) construction materials using a non-linear cohesive crack model and critical crack threshold analysis

The American Society for Testing and Materials (ASTM) has recommended ASTM D8044, an international standard test using Semi-Circular Disc Bend (SCB) specimens, to test only the tensile fracture toughness (mod I) of Asphalt Composite (AC) materials. However, AC materials are exposed to not only tensile stresses but also both compressive and shear stresses under wheel load. Thus, one of the main objectives of this study is to develop a new approach for the mixed mode I-II (tension and shear) testing of AC materials by using the SCB geometry. This study deals with a comparative assessment of the fracture toughness of AC materials by using the results of experimental, analytical, and Linear Elastic Fracture Mechanics (LEFM) and Non-LEFM (NEFM) numerical analyses done on the SCB specimens. The numerical analyses of the stress distribution and the cohesive crack growth were performed using the fracture mechanics program FRANC2D. Experimental results showed that the notched cracks opened at a 30° inclination angle (β) and kept opening up to β of 45°. The mode I fracture toughness (KIC) value of Asphalt Concrete Base (ACB) specimens was found at 0.37 MPa√m. On the other hand, the KC value was found to be 0.44 MPa√m for the 30° inclined crack and 0.40 MPa√m for the β = 45° inclined notch crack.The critical crack length for the mode-I loading was found to be 2–2.5 mm using the experimental and Critical Crack Threshold (CCT) analytical analysis, and it was found to be 2.5–3 mm using the NEFM-based cohesive crack analysis. Moreover, the NEFM-based cohesive crack analyses showed the critical crack length was between 3 mm and 7 mm for the mixed mode (I-II) condition, in which the notch cracks are inclined at 30° and 45°. The feasibility of the SCB test proposed by ASTM and AASHTO standards in determining the mixed mode I-II (tensile-shear) fracture toughness value of ACB specimens, which is an important parameter in determining the strength of materials, was verified by comparing the experimental results with LEFM and NEFM numerical analyses. As a result, experimental and numerical analysis results showed that the SCB test could be an appropriate geometry to determine the mixed mode I-II fracture toughness of AC materials when the crack is inclined at 30°. It is believed that this study would be evaluated as initial research on the use of SCB geometry for AC materials not only for mode I test but also for mixed mode loading tests and for the establishment of an international standard test.

Stress intensity factor assessment for reactor pressure vessel nozzles containing postulated corner cracks

Due to the structural discontinuity of geometry having higher stress concentration, the nozzles may dominate the structural integrity of reactor pressure vessel (RPV) system, even the material radiation embrittlement is insignificant. The nonmandatory Appendix G in Section XI of the ASME Boiler and Pressure Vessel code provides a fracture mechanics-based methodology using magnification factors to calculate the stress intensity factor of reference crack tips as long as the stress distribution through the nozzle section is available. This paper establishes various three-dimensional finite element models of Taiwan domestic RPV nozzles to conduct a series of stress and linear elastic fracture mechanics analyses to estimate the stress intensity factors. The circular and elliptical reference corner cracks with depths of one-fourth and one-tenth thickness of the vessel wall along the 45° path are considered. Two evaluation results using the ASME method and the finite element linear elastic fracture mechanics analysis are compared. It is found that the ASME method produces conservative values of stress intensity factor at crack tips of circular corner cracks but underestimates the elliptical corner cracks. Finally, an adjusted magnification factor formula is proposed to obtain more accurate stress intensity factors for elliptical-shaped nozzle corner cracks.

On the effect of microplasticity on crack initiation from subsurface defects in rolling contact fatigue

This work demonstrates numerically how microplasticity, i.e. the yielding behavior below the conventional 0.2% plastic strain threshold, can lead to initiation of cracks at subsurface defects, in rolling contact applications operating under realistic loads. A 3D elasto-plastic finite element model is employed to perform shakedown analysis of the bearing steel around a small spherical void with two different approximations of the steel constitutive behavior at the plastic micro-strain regime. When non-linear kinematic hardening is used to model a fast but smooth onset of plasticity, the fields of plastic strains and micro-residual stresses around the void evolve very distinctly to the case where a sharp transition is assumed. To further investigate the role of the tensile micro-residual stresses occurring in the former case on crack initiation, a planar circular crack is inserted at the equator of the void and an entire overrolling cycle is investigated by means of linear elastic fracture mechanics (LEFM). This analysis is repeated for different crack sizes and the respective stress intensity factors and their amplitudes, relevant for crack growth, are reported. The work also reports implementation details for the coupling of a 3D elasto-plastic model for shakedown analysis to a subsequent LEFM analysis model.

Singular patch method for linear elastic fracture mechanics analysis using isogeometric analysis

Singular patch method for linear elastic fracture mechanics analysis using isogeometric analysis

Fatigue crack propagation studies based on the plastic component of the CTOD evaluated from Digital Image Correlation data

This work presents a new approach based on the Crack Tip Opening Displacement (CTOD) for studying the fatigue crack growth. The plastic component of the CTOD is employed for predicting the crack propagation on austenitic stainless steel. This is in contrast to Linear Elastic Fracture Mechanics analysis based on the Stress Intensity Factor (SIF) (Ewalds and Wanhill 1984). The current method is also valid beyond Small Scale Yielding (Antunes et al. 2016)(Antunes et al. 2017a)(Borges et al. 2020) as it incorporates naturally the plasticity effects taking place at the crack tip (Lopez-Crespo et al. 2018). The approach is based on post-processing the full-field displacement information generated by Digital Image Correlation technique (Chernyatin et al. 2018). Such technique is used to monitor the crack advance throughout the test (Cruces et al. 2020). The post-processing procedure employed for extracting the plastic component of the CTOD is described in detail. The results on steel CT specimens appear very promising.

Constraint-corrected fracture mechanics analysis of nozzle crotch corners in pressurized water reactors

This paper presents fracture mechanics analysis results for various cracks located at pressurized water reactor pressure vessel nozzle crotch corners taking into consideration constraint effect. Technical documents such as the ASME B&PV Code, Sec.XI were reviewed and then a fracture mechanics analysis procedure was proposed for structural integrity assessment of various nozzle crotch corner cracks under normal operation conditions considering the constraint effect. Linear elastic fracture mechanics analysis was performed by conducting finite element analysis with the proposed analysis procedure. Based on the evaluation results, elastic-plastic fracture mechanics analysis taking into account the constraint effect was performed only for the axial surface crack of the reactor pressure vessel outlet nozzle with cladding. The fracture mechanics analysis result shows that only the axial surface crack in the reactor pressure vessel outlet nozzle has the stress intensity factor exceeding the low bound of upper-shelf fracture toughness irrespectively of considering the constraint effect. It is confirmed that the J-integral for the axial crack of the outlet nozzle does not exceed the ductile crack initiation toughness. Hence, it can be ensured that the structural integrity of all the cracks is maintained during the normal operation.

A Linear Elastic Fracture Mechanics Analysis of the Pre-Cracked Concrete Failure Mechanism Under Modes I, II, III, and IV Loading Conditions

A Linear Elastic Fracture Mechanics Analysis of the Pre-Cracked Concrete Failure Mechanism Under Modes I, II, III, and IV Loading Conditions

The Application of Linear Elastic Fracture Mechanics Analysis to Bluntly Notched Round Bar Specimens.(Dept.M)

A technique has been presented which allows the use of small notched round-bar specimens without fallgue pre-cracking for the determination of the plane strain fracture toughness of engineering materials. The technique is based on the linear elastic fracture mechanics analysis and the principle of stress concentration factors at the tip of the notch. The error inherent in the fracture toughness calculations, i.e. due to the absence of very sharp crack, can be corrected from an error correction factor which is a function of the normalized notch-tip radius, r/d. The technique has been applied to two metallic alloys (bronze and steel) and the plane strain fracture toughness for the two materials were obtained. Small round-bar specimens having V-notches with different angles and tip-radii have been tested in tension. A comparison of the KIc values calculated using the present technique and those calculated in the literature indicated reasonable agreement with a difference between the two values ranging from 0 to ±5 %. It is recommended that the normalized notch-tip ratio, r/d, should not exceed about 0.14 for this difference to stay within acceptable limits. The present technique may be considered relatively fast and economic and indicating a level of accuracy adequate for many practical purposes.

A computationally efficient approach for predicting toughness enhancement in ceramic composites with tailored inclusion arrangements

Advanced manufacturing techniques such as extrusion-based methods have enabled the fabrication of ceramic composites with ordered inclusion phases (i.e. the size and position of the inclusion can be precisely controlled) to improve their overall strength and toughness. Conventional theories, simulation approaches, and experimental methods for analyzing fracture in composites with randomly dispersed inclusion phases (resulting in homogeneous, isotropic effective properties) become inadequate at understanding and designing composites with ordered inclusions for enhancing effective properties such as toughness. In addition, existing methods for analyzing fracture in composites can be computationally expensive and pose challenges in accurately capturing experimentally observed fracture growth. For example, extended finite element and phase-field methods are computationally expensive in evaluating the large design space of possible inclusion arrangements enabled by the new manufacturing techniques. In this work, a closed-form analytical model for the mixed-mode stress intensity factor in a composite with selected inclusion arrangements is presented, which expedites the analysis for various composite designs. Moreover, the fracture initiation calculation is adapted to approximate crack propagation with computational efficiency. The accuracy of this model for predicting fracture initiation is validated by linear elastic fracture mechanics analysis using the finite element method. The prediction of fracture propagation is validated using a phase-field model, as well as a 4-point bending experiment. Finally, the model is applied to analyze three different composite inclusion arrangements to study the effect of various material combinations and geometries on the overall toughness of the composite; a complete sampling of (and optimization) over the entire design space, however, is beyond the scope of this work. The relative increase in crack length (compared to a homogeneous material) is used as a metric to compare the relative toughness of three different composite designs. Within these designs, using the fast-running approximate method, the effect of the ratio of inclusion radius to inclusion spacing, and the elastic mismatch on the resulting crack length are compared to determine the composite arrangements that result in the greatest toughness enhancement for selected material properties. In particular, a multi-phase cubic array resulted in the greatest toughness enhancement of the designs considered.

Fatigue strength capacity of load-carrying fillet welds on ultra-high-strength steel plates subjected to out-of-plane bending

Weld root fatigue strength capacity is an important design criterion in load-carrying (LC) fillet welded joints subjected to cyclic loads. This paper elaborates on the weld root fatigue strength capacity of fillet welded LC joints made of ultra-high-strength steel (UHSS) and subjected to out-of-plane bending. Experimental fatigue tests are carried out using constant amplitude loading with an applied stress ratio of R = 0.1 with both pure axial, i.e. DOB = 0 (degree of bending, bending stress divided by total stress) and bending, i.e. DOB = 1.0, load conditions. The applicability of different approaches – nominal weld stress, effective notch stress concepts, and 2D linear elastic fracture mechanics (LEFM) – for the fatigue strength assessment of weld root capacity is evaluated. Furthermore, a parametric LEFM analysis is used to evaluate the effect of weld penetration on the root fatigue strength capacity in axial and bending loading. The results indicate that in the case of bending, nominal weld stress can be calculated using the linear stress distribution over the joint section and FAT36 as a reference curve. In the bending loading, for the joints failing from the weld toe, a mean fatigue strength of up to 185 MPa in the nominal stress system was achieved, indicating that the reference curve FAT63 is overly conservative. The ENS concept with FAT225 seemed to be slightly unconservative for assessing the root fatigue strength capacity. LEFM analyses revealed that in the case of increasing weld penetration and bending loading, weld root fatigue strength capacity seemed to correlate with the nominal weld stress calculated using effective weld throat thickness, while in axial loading, weld stress should be calculated using external throat thickness summed with penetration length.

In Situ Mechanical Characterization of the Mixed-Mode Fracture Strength of the Cu/Si Interface for TSV Structures.

In situ nanoindentation experiments have been widely adopted to characterize material behaviors of microelectronic devices. This work introduces the latest developments of nanoindentation experiments in the characterization of nonlinear material properties of 3D integrated microelectronic devices using the through-silicon via (TSV) technique. The elastic, plastic, and interfacial fracture behavior of the copper via and matrix via interface were characterized using small-scale specimens prepared with a focused ion beam (FIB) and nanoindentation experiments. A brittle interfacial fracture was found at the Cu/Si interface under mixed-mode loading with a phase angle ranging from 16.7° to 83.7°. The mixed-mode fracture strengths were extracted using the linear elastic fracture mechanics (LEFM) analysis and a fracture criterion was obtained by fitting the extracted data with the power-law function. The vectorial interfacial strength and toughness were found to be independent with the mode-mix.

Meshless fracture analysis of 3D planar cracks with generalized thermo-mechanical stress intensity factors

This paper implements three dimensional meshless local Petrov–Galerkin method in the linear elastic fracture mechanics analyses of isotropic functionally graded and homogeneous materials under different thermo-mechanical loads. Energy equation based on Lord–Shulman non-Fourier heat conduction law coupled with equation of motion is applied to evaluate the effect of theoretical and realistic relaxation times on transient thermal stress intensity factors along 3D thorough or semielliptical cracks under thermo-mechanical shock. A new coordinate transform method with linear weight function is introduced to evaluate stress intensity factors by generalized interaction integral method based on incompatibility formulation. Simple linear test function is introduced, which is approximated via compatible radial basis functions and leads in eliminating internal boundary integrals of meshless method and reducing computational time. Shape functions are constructed in every Gauss point by determining the closest domain point method in preprocessing. Parametric studies are carried out in order to determine suitable radial basis functions shape parameters and penalty method parameter. Reasonable accuracy and the small number of used points are the main advantages of this method over finite element method.

Reconciling fracture toughness parameter contradictions in thin ductile metal sheets

AbstractThe well‐known trade‐off between strength and fracture toughness in bulk specimens is often used to explain the low fracture toughness of very thin ductile face‐centred cubic metal specimens, but this interpretation contradicts the relative length scales of thickness‐dependent strength and thickness‐dependent fracture toughness. This study uses the concept of similitude to demonstrate that linear elastic fracture mechanics analysis of 25.4 μm thick annealed aluminium is invalid, although the resulting fracture toughness measurements fit well with the existing literature and idea of a strength/fracture toughness trade‐off. Similarly, an elastic plastic fracture mechanics analysis is sensitive to out‐of‐plane deformation that cannot be practically eliminated or corrected for with a model. However, a plastic collapse analysis using a critical net section stress criterion is demonstrably valid by the concept of similitude, is insensitive to out of plane deformation, and agrees with the evidence of extensive plasticity in the fracture surfaces.

Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks

The in-plane classical dislocation-based linear elastic fracture mechanics analysis is extended to the case of strain gradient elasticity. Nonsingular stress and smooth-closure crack profiles are derived. As in the classical treatment, the crack is represented by a distribution of climb edge dislocations (for Mode I) or glide edge dislocations (for mode II). These distributions are determined through the solution of corresponding integral equations based on variationally consistent boundary conditions. An incompatible framework is used and the nonsingular full-field plastic distortion tensor components are calculated. Numerical results and related graphs are provided illustrating the nonsingular behaviour of the stress/strain components and the smooth cusp-like closure of the crack faces at the crack tip. The work provides an alternative approach to celebrated “Barenblatt’s treatment” of cracks, without the introduction of a cohesive zone and related to intermolecular forces ahead of the physical crack tip. It also supplements a recent paper by the authors in which the mode III crack, represented by an array of screw dislocations, was solved within the present gradient elasticity framework.

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment 'Wendelstein 7-X'

At the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7-X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non-planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub-modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment ‘Wendelstein 7‐X’

AbstractAt the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7‐X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non‐planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub‐modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.