Linear Elastic Fracture Mechanics Parameter Research Articles

Stress Intensity Factors for Pressurized Pipes with an Internal Crack: The Prediction Model Based on an Artificial Neural Network

During pipeline operation, internal cracks may occur. The severity around the crack tip can be quantified by the stress intensity factor (KI), which is a linear–elastic fracture mechanics parameter. For pressurized pipes featuring infinitely long internal surface cracks, KI can be interpolated from a function considering pressure, geometry, and crack size, as presented in API 579-1/ASME FFS-1. To enhance KI prediction accuracy, an artificial neural network (ANN) model was developed for such pressurized pipes. Predictions from the ANN model and API 579-1/ASME FFS-1 were compared with precise finite element analysis (FEA). The ANN model with an eight-neuron sub-layer outperformed others, displaying the lowest mean squared error (MSE) and minimal validation discrepancies. Nonlinear validation data improved both MSE and testing performance compared to uniform validation. The ANN model accurately predicted normalized KI, with differences of 2.2% or lower when compared to FEA results. Conversely, API 579-1/ASME FFS-1′s bilinear interpolation predicted inaccurately, exhibiting disparities of up to 4.3% within the linear zone and 24% within the nonlinearity zone. Additionally, the ANN model effectively forecasted the critical crack size (aC), differing by 0.59% from FEA, while API 579-1/ASME FFS-1′s bilinear interpolation underestimated aC by 4.13%. In summary, the developed ANN model offers accurate forecasts of normalized KI and critical crack size for pressurized pipes, providing valuable insights for structural assessments in critical engineering applications.

Monotonic crack propagation in a notched polymer matrix composite reinforced with continuous fiber and printed by material extrusion

The study presents the crack mouth opening and propagation of cracks in a composite material printed by material extrusion subjected to monotonic loading. The composite material is made out of a nylon matrix (with embedded short carbon fiber—called Onyx®) and reinforced with continuous Kevlar fibers. Three-point bending tests were performed on notched specimens built according to ASTM-E399. Tests were digitally recorded to extract crack opening displacement (COD) and crack length data through image treatment techniques (using ImageJ), and results were analyzed using linear elastic fracture mechanics parameters through the use of COD. Therefore, the crack mouth opening was established, and fracture toughness was found to be 46 MPa√m. Additionally, microscopy analysis identified fracture zones, crack initiation, transition, and final rupture. The observed failure mechanisms were matrix cracking, fiber pull-out, fiber breakage, and defects such as non-proper fiber-matrix bonding.

Assessment of mechanical and fatigue crack growth properties of wire + arc additively manufactured mild steel components

AbstractA study has been conducted to evaluate the mechanical and fatigue crack propagation properties of wire + arc additively manufactured ER70S‐6 components. A parallel‐built deposition strategy was employed to fabricate the additively manufactured wall. The hardness values were slightly higher at the bottom and top of the wall due to the presence of Widmanstätten ferrite and carbides. The characterization of mechanical properties in both orientations; parallel and perpendicular to the deposition direction showed a marginal difference in yield strength and ultimate tensile strength. The crack growth rates were correlated with linear elastic fracture mechanics parameter ΔK and compared with an oscillation‐built deposition strategy from the literature. The crack growth rates of both deposition strategies were found to be very similar to each other. Furthermore, it has been demonstrated that the variability in the crack growth histories can be reasonably well captured by using the NASGRO crack growth equation.

Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion and their evaluation through molecular dynamics simulations

Molecular dynamics method and finite element analysis are applied for the analysis of the stress field in the neighborhood of the crack tip in a copper plate with a single edge notch. The molecular dynamics simulations implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) are aimed at evaluating classical continuum linear elastic fracture mechanics parameters such as stress intensity factors, T-stresses and higher order coefficients of the Williams power series expansion of the near crack stress field for Mode I, Mode II and Mixed Mode (Mode I + Mode II) loadings of the cracked specimen in isotropic linear elastic materials. The key objective of the study is the comparison of continuum and atomistic approaches for the estimation of the near crack tip fields using the example of one of the most common cracked configurations. Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion for a copper plate with the single edge notch under Mode I and Mixed Mode loadings are evaluated by atomistic modeling and by finite element method. The wide class of the computations in LAMMPS is performed. The atomistic values of stress intensity factors and higher order terms of the Williams series expansion are compared with the values obtained from the numerical solutions given by finite element method. It is shown that the continuum fracture theory successfully describes fracture and the near crack tip fields even at extremely confined singular stress field of only several nanometers. The angular distributions of the stress components from atomistic modeling are retrieved and compared with the angular distributions of the stresses from continuum linear elastic fracture mechanics. The comparison shows good agreement between two approaches.

Coefficients of the williams power expansion of the near crack tip stress field in continuum linear elastic fracture mechanics at the nanoscale

The paper presents the analysis of the stress field in the neighborhood of the crack tip by molecular dynamics method implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The molecular dynamics simulations are aimed at computing continuum linear elastic fracture mechanics parameters such as stress intensity factors, T-stresses and higher order coefficients of the Williams power series of the stress field in an isotropic linear elastic material. The overwhelming objective of the study is the comparison of continuum and atomistic approaches for the estimation of the near crack tip fields. Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion for a copper plate with a central crack under Mode I and Mixed Mode loadings are evaluated by atomistic modelling. The wide class of the computational experiments in LAMMPS is realized. The atomistic values of stress intensity factors and higher order terms of the Williams series expansion are compared with the values obtained from the classical solutions of continuum linear elastic fracture mechanics. It is shown that the continuum fracture theory successfully describes fracture and the near crack tip fields even at extremely confined singular stress field of only several nanometers. The circumferential distributions of the stress tensor components from atomistic modeling are retrieved and compared with the angular distributions of the stresses from linear elastic fracture mechanics. The comparison shows good agreement between two approaches.

Experimental study on the interaction between two cracks by digital photoelasticity method: construction of the Williams series expansion

The multi-point Williams series expansions for the near-crack-tip fields in the vicinity of two interacting cracks in an isotropic linear elastic material are experimentally and numerically determined. The experimental method used to study the interaction of two cracks is the digital photoelasticity method which is applied for determination of coefficients of the higher-order terms of the Williams series expansion for a plate of finite width with two interacting cracks. The digital image processing tool for handling of the entire set of experimental data isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is relied on the classical Ramesh technique but enables to scan the experimental image in any direction and to analyse the image after any number of logical operations. The realized digital image analysis allows us to extract photoelastic data from the entire field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns in the vicinity of the crack tips are converted into text file and then the points of isochromatic fringes with minimum light intensity are used for estimating linear elastic fracture mechanics parameters. The multi-parameter stress field description with the first fifteen terms is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two interacting cracks using 1) the classical over-deterministic method in the form based on the stress field and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is demonstrated that the BFGS method has indisputable advantages over the classical over-deterministic method. The significance of higher-order terms in the Williams expansion is proved for the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement. This verifies the experimental analysis

Development of fracture evaluation of a flat plate with multiple flaws

Stress corrosion cracking (SCC) has been detected in the welded components of nuclear power plants. The components of nuclear power plants consist of highly ductile materials such as austenitic stainless steels, and their failure mode is expected to be plastic collapse due to ductile fracture. The limit load analysis, which is applied to fracture assessment for ductile materials, is employed in the fitness-for-service (FFS) codes such as JSME Code “Rules on Fitness-for-Service for Nuclear Power Plants”. The FFS codes provide flaw characterization rules for multiple flaws, and the technical basis seems to be based on interaction of stress intensity factors which are linear elastic fracture mechanics parameters based on small scale yielding. Thus, the applicability of current flaw characterization rules for multiple flaws to limit load analysis is unclear. The limit load analysis for non-aligned multiple flaws was developed based on the net-section approach and the test results of flat plates with two flaws in the past studies. The test results can be represented by using the defined net-section of non-aligned multiple flaws. Finite element analyses were conducted to interpolate the test conditions. The effect of flaw positions on collapse load was estimated by the test and analysis results.

Computational and experimental identification of coefficients of the Williams series expansion by considering higher order terms in the cracked specimens through digital image analysis

In the study, digital photoelasticity method is used for finding of the linear elastic fracture mechanics parameters for a plate of finite width with two inclined interacting cracks. The digital image processing tool for the whole set of experimental data namely isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is based on the well-known Ramesh technique but allows us to scan the image in any direction and to analyse the image after any number of logical operations. The performed digital image analysis allows us to extract photoelastic data from the whole field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns near the crack tips were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-point stress field description is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two inclined interacting cracks using 1) the algorithm based on the classical over-deterministic method and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is shown that the latter method has undeniable advantages over the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement.

Effect of Rod-like Structure on Fatigue Life, Short Surface Crack Initiation and Growth Characteristics of Extruded Aluminum Alloy A2024 (Analysis via Modified Linear Elastic Fracture Mechanics).

In the Al alloy A2024-T3 extruded material, a rod-like structure is generated parallel to the extrusion direction. In this study, the effects of rod-like structures on fatigue crack initiation and growth behavior were comprehensively investigated. Two types of specimens were used in a fatigue experiment, in which the direction of the load stress amplitude was parallel (specimen P) and perpendicular (specimen V) to the rod-like structure. Based on the experimental and analytical results, the following findings were obtained regarding the fatigue life, location of crack initiation, and fatigue crack growth behavior. Because the fatigue life of specimen P was longer than that of specimen V, it is inferred that the rod-like structure significantly affects the fatigue life. In specimen P, fatigue cracks were generated from the grain boundaries of the Al matrix. By contrast, in specimen V, cracks were generated from the Cu–Mg-based intermetallic compound in the Al matrix. In specimen P, fatigue cracks were more likely to propagate across the rod-like structure, which decreased the fatigue crack growth rate. In specimen V, fatigue cracks did not propagate across the rod-like structure; instead, they propagated through the Al matrix. Therefore, the fatigue crack growth resistance of specimen V was lower than that of specimen P. The relationship between the fatigue crack growth rate and the modified linear elastic fracture mechanics parameter could be used to predict the S–N curve (stress amplitude vs. fatigue life) and fatigue crack growth behavior. The predicted results agreed well with the experimental results.

Fatigue crack growth behaviour of wire and arc additively manufactured ER70S-6 low carbon steel components

The new emerging Wire and Arc Additive Manufacturing (WAAM) technology has significant potential to improve material design and efficiency for structural components as well as reducing manufacturing costs. Due to repeated and periodic melting, solidification and reheating of the layers, the WAAM deposition technique results in some elastic, plastic and viscous deformations that can affect material degradation and crack propagation behaviour in additively manufactured components. Therefore, it is crucial to characterise the cracking behaviour in WAAM built components for structural design and integrity assessment purposes. In this work, fatigue crack growth tests have been conducted on compact tension specimens extracted from ER70S-6 steel WAAM built components. The crack propagation behaviour of the specimens extracted with different orientations (i.e. horizontal and vertical with respect to the deposition direction) has been characterised under two different cyclic load levels. The obtained fatigue crack growth rate data have been correlated with the linear elastic fracture mechanics parameter varDelta K and the results are compared with the literature data available for corresponding wrought structural steels and the recommended fatigue crack growth trends in the BS7910 standard. The obtained results have been found to fall below the recommended trends in the BS7910 standard and above the data points obtained from S355 wrought material. The obtained fatigue growth trends and Paris law constants from this study contribute to the overall understanding of the design requirements for the new optimised functionally graded structures fabricated using the WAAM technique.

Notch effect on the linear elastic fracture mechanics values of a polysulfone thermoplastic polymer

Users of the most popular procedures for determining the linear elastic fracture mechanics parameters on polymers have noted that the repeatability and reproducibility of the results depend strongly on the quality of the notches generated. In an attempt to provide a better understanding, polysulfone specimens were pre-cracked using classical razor blade methods (tapping and sliding), and also by the femtosecond pulsed laser ablation technique. These specimens were analyzed, and the critical stress intensity factor was determined. The ablated specimens showed very good notch quality, the sharpest crack tip radii, displayed neither mechanical nor thermal damage in front of the crack tip, and were very consistent, providing both a lesser scatter and a statistically significant lower critical stress intensity factor than the razor blade pre-cracked specimens. Finally, some consideration and advice for suitable generation of notches are also given.

Risk assessment based on analytical evaluation of structural integrity and life of drilling rig pipe

Risk assessment procedure based on structural integrity evaluation has been applied to oil drilling rig pipe. The new concept based on application of structural integrity evaluation to assess risk level according to probability and consequence of failure was used. Analytical expressions for surface cracks are used to calculate stress intensity factors for different crack geometries. Oil drilling rig welded pipe integrity has been evaluated analytically by simple application of the Failure Assessment Diagramme (FAD), i.e. by using the ratio of linear elastic fracture mechanics parameter, KI, and its critical value, KIc, in relation with the ratio of applied stress and its critical value, to define the point in FAD. Probability of failure is then taken according to the position of the point in the FAD, corresponding to oil drilling rig welded pipe data. The same logic is employed in the case of cyclic loading, i.e. fatigue crack growth. In that case, structural life is estimated by using Paris law to calculate crack length vs. number of cycles, to be used in risk assessment procedure and by managers to make decision about further use of damaged pipes, based on data provided by engineers.

Comparison of experimental, numerical and analytical risk assessment of oil drilling rig welded pipe based on fracture mechanics parameters

Fracture mechanics parameters are used for experimental, numerical and analytical risk assessment of structural integrity and life of oil drilling rig welded pipe with a crack. As a simple analytical tool, the Failure Assessment Diagramme (FAD) has been applied to assess probability of pipe failure, using the ratio of linear elastic fracture mechanics parameter, KI, and its critical value, KIc, in relation to the ratio of applied stress and its critical value. Alternatively, the ratio of J integral, evaluated experimentally and numerically, and its critical value, JIc, has been used to estimate probability of failure. Risk was then assessed for all three approaches, in combination with the estimated consequence. Results are given in the form of risk matrix, indicating the effects of the most (analytical) and the least (experimental) conservative estimates. In the case of risk based structural life assessment, number of cycles, obtained analytically and numerically, are related to the number of cycles to the critical crack length, to assess risk due to fatigue.

Risk assessment of oil drilling rig welded pipe based on structural integrity and life estimation

Risk assessment procedure based on structural integrity and life estimation has been introduced and applied to oil drilling rig welded pipe. The new concept based on application of structural integrity and life estimation to assess risk level according to probability and consequence of failure was used. Oil drilling rig welded pipe integrity has been assessed by simple application of the Failure Assessment Diagramme (FAD), i.e. by using the ratio of linear elastic fracture mechanics parameter, KI, and its critical value, KIc, in relation with the ratio of applied stress and its critical value, to define the point in FAD. Probability of failure is then taken according to the position of the point in the FAD, corresponding to oil drilling rig welded pipe data. Then, the FEM has been applied to calculate more precisely the strain and stress state and to get another, less conservative, risk assessment. Oil drilling rig welded pipe life has been estimated by simple integration of the Paris law, as well as by more complex simulation of fatigue crack growth, using the extended Finite Element Method (xFEM). Probability of failure is then taken as the ratio of the number of cycles for a given crack length and the number of cycles for the critical crack length. These analyses are useful for managers to make decision about further use of damaged pipes, based on data provided by engineers. Also, the procedure introduced here for risk assessment is not limited to oil drilling rig pipes, but it is rather a general one, applicable to any component with known geometry, material properties and loading data.

Study on Fatigue Lifetimes and Their Variation of Mg Alloy AZ61 at Various Stress Ratios

In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was investigated using a scanning electron microscope to study the size of the intermetallic compounds from which the pioneer fatigue crack initiated and led to the final failure of the specimen. To determine the maximum size of the intermetallic compounds existing within the cross section of the specimen at higher risk, Gumbel’s extreme-value statistics were utilized. In the present study, the intermetallic compounds contained within the specimen were assumed to be the initial cracks existing in the material before the fatigue tests. A modified linear elastic fracture-mechanics parameter, M, proposed by McEvily et al., was used to analyze the short FCG behavior under different stress ratios, R. The relation between the rate of FCG and M parameter was found to be useful and appropriate for predicting the fatigue lifetimes under different R ratios. Moreover, the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios could be predicted with this method, which utilizes both the FCG law and a statistical distribution of sizes of the most dangerous intermetallic compounds. The evaluated results were in good agreement with the experimental ones. This correspondence indicates that the estimation method proposed in the present study is effective for evaluation of the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios.

Analysis of fatigue crack propagation in laser sintering metal

Laser sintering metal has recently been used in the manufacture of components for different applications like aerospace or medicine. The approach to engineering design based on the cracks propagation assumption applying the concepts of linear elastic fracture mechanics (LEFM) is commonly used for aerospace engineering. However, fatigue crack propagation is linked to irreversible and non-linear mechanisms at the crack tip, therefore LEFM parameters can be successfully replaced by non-linear crack parameters, namely the plastic CTOD. A model linking da/dN with plastic CTOD is proposed here to characterize fatigue crack propagation. A comparison is made with other materials showing that for the same plastic CTOD the laser sintering material has a relatively large crack growth rate.

Fracture Assessment of Strengthened Cracked Metallic Components Using FRP Stiffeners

The present study focuses on applying the fracture mechanics approach to the fracture assessment of a cracked member/component strengthened with fiber-reinforced polymer composite stiffeners. The parameters of linear elastic fracture mechanics (LEFM) — the stress intensity factor and the crack opening displacement — are estimated using a finite-element analysis. A metallic plate with an edge crack repaired with fiber-reinforced polymer composite stiffeners is considered in the study. The effects of crack length, debonding length, and adhesive stiffness on the LEFM parameters are examined. Two different loading conditions are considered — axial tension and bending. The results obtained show that fiber-reinforced polymer composite stiffeners are very useful in repairing cracked metallic components.

Stress intensity factors for multiple cracks in thick-walled cylinder

The stress intensity factor (SIF) is the linear elastic fracture mechanics parameter that relates remote load, crack size and structural geometry. It predicts very accurately the stress state. In this work, cylinders with multiple cracks are considered. The following parameters are varied during the analysis of the cylinders: the number of cracks, (the variation in number of cracks ultimately led to a variation in the inter-crack spacing), the crack length to cylinder thickness ratio (a/t), the diameter ratio of the cylinders. Very good agreement between the finite element stresses and the theoretical stresses is seen.

Identification of interlaminar fracture properties of a composite laminate using local full-field kinematic measurements and finite element simulations

The paper is devoted to the identification of interlaminar properties by analyzing three tests with different mode mixities on a unidirectional thermoset composite material. It is shown that by coupling digital image correlation with finite element simulations, it is possible to locally extract energy release rates whose standard uncertainty is at most equal to 50J/m2. This performance is achieved with a standard finite element code by optimizing the location of the crack tip, which is the key information needed to evaluate (linear elastic) fracture mechanics parameters of these materials. The level of stress intensity factors and the experimental mode mixity can be identified in all configurations with an acceptable uncertainty.

Fatigue crack growth behavior and mechanism of closed-cell PVC foam

The applicability of linear-elastic fracture mechanics parameters (DK and Kmax), elastic–plastic fracture mechanics parameter (DJ), and time-dependent fracture mechanics parameter (C*) to characterize fatigue crack growth (FCG) rate of closed-cell polyvinyl chloride foam was investigated in the present work. The effect of stress ratios (R ¼ 0.1 and 0.4) on FCGs was observed when the DK, Kmax and DJ were used as fracture mechanics parameters. As a fracture mechanics parameter that combines DK and Kmax, the K* successfully characterized FCGs (da/dN )a tR ¼ 0.1 and 0.4. While, a time-dependent fracture mechanics parameter (C*) successfully correlated da/dt of creep crack growth (CCG) test, but it failed to correlate da/dt of FCG tests. The FCGs at both R ¼ 0.1 and 0.4 were cyclic dependent, while the CCG was time dependent. For cyclic-dependent crack growth, the interaction between polymer-chain scission and small scale cracktip blunting was the main mechanism, whereas the interaction between polymer-chain pullout and large scale crack-tip blunting dominated fracture process for time-dependent crack growth. POLYM. ENG. SCI., 53:1719–1727, 2013. a 2012 Society of Plastics Engineers