Normalized Stress Intensity Factor Research Articles

Compact-tension-shear specimen for orthotropic materials in fracture toughness testing

Conducting Compact-Tension-Shear (CTS) tests emerges as a promising research methodology to determine the fracture toughness of orthotropic materials in mixed-mode I&II. However, the absence of pertinent fracture parameter solutions incorporating material orthotropy impedes the further application and standardization of CTS testing. Therefore, this study performed a systematic two-dimensional finite element analysis (FEA) on orthotropic CTS specimens to evaluate critical fracture parameters, including the normalized stress intensity factors (YI, YII) and compliance (u). First, the impacts of three commonly cited boundary conditions (BCs) of CTS models were investigated, revealing that the simplified or equivalent methods developed for isotropic CTS models are no longer applicable. Subsequently, the suitable CTS models were used to analysis the coupling effects of material orthotropy (λ, ρ), crack length ratios (a/W), and loading angles (β). Findings indicated that YI or u no longer exhibit a monotonic relationship with respect to a/W or β under strong orthotropy. The impact of λ and ρ on fracture parameters is equally significant across different geometries and loading conditions. Further, the impact of orthotropy on YII is relatively small, while the more affected YI may have a difference compared to isotropic results of over 80%. Finally, CTS tests were carried out on the unidirectional carbon fiber-reinforced epoxy resin composite measuring the fracture toughness in mixed-modes I&II. The obtained fracture parameter solutions were applied and validated during the process. The acquired results are poised to contribute to the advancement of fracture toughness testing standardization for orthotropic materials under mixed-mode loading.

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

This paper contains the solution to the problem of a semi-infinite moving crack situated in an orthotropic strip bonded between two identical strips. The crack moves with a constant velocity, and the surface is under shear wave disturbance. We first examine the equations of elasticity, which include equilibrium equations and stress and displacement constitutive relations with the model-specific continuity and boundary conditions. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W-H) equation is obtained, which is solved using the W-H method. The analytical expressions for the considered crack problem have been obtained for stress intensity factor (SIF), normalized stress intensity factor (NSIF), and stress magnification factor (SMF). The behavior of NSIF has been graphically presented for particular cases of composite materials for different crack propagation velocities and various depth ratios of the strips. The novelty of this paper lies in the analytic solutions using the W-H method for the semi-infinite moving crack problem under the influence of anti-plane shear waves. The pictorial presentations of normalized SIF clearly show their dependency on strip depths, crack propagation velocities and elastic constants.

Stress intensity factor analysis for mixed-mode fracture behavior of inclined semi-elliptical surface crack in stiffened plate under tension load

This study aims to investigate the mixed-mode fracture behavior of stiffened plates with inclined semi-elliptical surface cracks (ISSCs). For this purpose, a new numerical model is developed for the fracture analysis using FRANC 3D in combination with ABAQUS. Normalized stress intensity factors (SIFs) are used to analyze the fracture behavior at the surface and deepest points of the surface crack. Additionally, an arrest parameter ψ is proposed to quantify the level of crack arrest under mixed-mode conditions. Then, a thorough investigation is conducted to examine the fracture behavior of stiffened plates with ISSCs, focusing on the effects of aspect ratio, relative depth, spacing ratio, stiffness coefficient, crack angle, and loading mode. The findings indicate that the restraint effect of stiffeners on the fracture of large surface cracks is significantly stronger compared to small surface cracks. It is also identified that the restraint effect is more pronounced at the surface point than at the deepest point. Finally, a set of novel formulas is derived to evaluate the mixed-mode SIFs in stiffened plates through statistical analysis of the results.

Numerical study and experimental validation of the size effect of smooth and mode I cracked semi-circular bend specimens

The edge-cracked semi-circular bend (SCB) specimen subjected to three-point bending loading is used in many applications to measure the fracture behavior of quasi-brittle materials. The main objective of the present work was to study the effect of the crack length to SCB specimen radius ratio (a/R), span to specimen diameter ratio (S/D), and specimen size on its flexural and mode I crack growth behavior. The contour integral method was implemented using the 3-D finite element method to determine the mode I stress intensity factor. In addition, high-strength concrete specimens were experimentally studied to validate the numerical results. The results show that the maximum compression stress is not sensitive to the S/D value, while the tensile stress is very sensitive. The value of S/D is the main parameter controlling the crack driving force (i.e., the crack mouth opening displacement (CMOD) and the normalized stress intensity factor, YI). For the same S/D, the SCB specimen diameter value change has a marginal effect on CMOD and YI. The specimen with S/D = 0.8 showed that it is the most compatible specimen with three-point bending test conditions, regardless of the SCB specimen size. A good agreement between the numerical and experimental results was achieved.

Dynamic fracture behavior and fracture toughness analysis of rock-concrete bi-material with interface crack at different impact angles

The crack initiation and propagation behavior of interface crack under impact are of great significance for evaluating the stability of rock-concrete system and other layered structures. Dynamic test using split-Hopkinson pressure bar (SHPB) system was performed on bi-material cracked straight-through Brazilian disc (CSTBD) specimens, and the fracture processes of specimens were monitored by means of a high-speed camera. The effects of the impact angle, concrete strength and strain rate on the dynamic fracture behavior were investigated. The results show that three typical fracture types can be identified: interface fracture, combined fracture (interface/shear and tension fracture) and tensile fracture. The interface fracture appears under small impact angle, while the combined fracture occurs with the further increase of impact angle. The crack initiation time of wing cracks and the number of secondary cracks are mainly affected by the strength of concrete in the bi-material specimen. Crack initiates earlier and more secondary cracks are generated in concrete material (weak material), and the number of secondary cracks increases with increasing strain rate. The dissipated energy increases gradually as the impact angle increases from 0° to 75°, while it decreases when the impact angle exceeds 75°. As the concrete strength increases, the difference in dissipated energy for different impact angles decreases. Furthermore, the effects of impact angle, concrete strength and loading rate on the dynamic fracture toughness for different loading modes are also discussed. The results indicate that the normalized stress intensity factors (SIFs) at the two tips of the interface crack are distinct and the difference increases with increasing crack length-to-diameter ratio. The impact angle, concrete strength and loading rate influence the dynamic fracture toughness significantly.

Damage Prediction of Pre-cracked High-Pressure Pipelines

Due to the increasing need to transport fluids, the use of industrial pipes and their sustainability is a crucial aspect to address. The motive of this work is to predict the behaviour of a pre-cracked pipeline under internal and external pressure using Finite element simulation. An intermediate range of pressure conditions has been selected to analyse the dispersal of normalized stress intensity factor along a semi elliptical crack front for a predefined crack geometry. This work also presents a comparative study of various piping material behaviour to address a relatively better choice for industrial use. Among the various alloys considered in the analysis Inconel 625 was found to be most appropriate for the pressure range.

Exploiting fractal features to determine fatigue crack growth rates of metallic materials

An alternative approach to the classical fracture mechanics equation to quantify the fatigue crack growth rate is proposed and examined. The method exploits the fractal features of the propagating fatigue crack. The reference crack growth response of AISI 410 martensitic stainless steel is established using compact tension C(T) specimens. Fractal analysis of microscopic images along the edge length of the crack establishes the fractal dimensions, dF of the fatigue crack. The box-counting algorithm is developed for the fractal analysis based on optical images of the crack at 100X magnification and the resolution of 1090 pixels/mm. Results show that the crack initially exhibits a Euclidean nature (dF ≈ 1). The fractal dimension increases steadily with increasing crack length in the Paris crack growth rate region with 1.05 < dF < 1.24. The corresponding stress intensity factor range varies between 18 ≤ ΔKI ≤ 40 MPa√m. The fractal dimension, dF correlates linearly with the normalized stress intensity factor range, ΔKKIC within the Paris crack growth region. This enables the multifractal fatigue crack growth rate equation to be established in terms of the fractal dimension, Paris coefficient and exponent, and fatigue fracture properties of the material. The fatigue crack growth rate of the material could then be determined using the multifractal fatigue crack growth rate model without requiring the geometry factor of the crack.

Fracture behavior of an interface crack in a magnetoelectric sandwich structure under electric field: Effects of the poling directions

Magnetoelectric (ME) sandwich structure is a common form in device applications. Poling directions of component materials are essential for the improvement of ME device properties. In this paper, the effects of the electric and magnetic poling directions on the interface fracture of a ME sandwich structure are investigated by integral transform and singular integral equation techniques. The expressions of the normalized stress intensity factors (NSIFs) are derived, and some numerical examples are presented. It is found that the poling direction of active layer can greatly affect the interface cracking mode. And the crack propagation can be promoted or impeded by adjusting the applied field. The structure with a larger volume fraction of active material will be more likely to crack.

A generalized 2D Bézier-based solution for stress analysis of notched epoxy resin plates reinforced with graphene nanoplatelets

In this study, a robust Bezier-based multi-step method is extended to accurately solve the governing fourth-order complex partial differential equation (PDE) in linear elastic fracture mechanics (LEFM) problems. The Bezier technique was first introduced by the authors to solve initial value problems in one dimension. Now, the method is further extended to simultaneously solve Boundary Value Problems (BVPs) in orthogonal directions. To examine the accuracy and performance of the present method, the first-mode normalized stress intensity factor (SIF) of a 2D epoxy resin plate having an initial edge crack and reinforced with randomly oriented graphene nanoplatelets (GnP) is determined and compared with the associated exact analytical solution using the Bayesian statistical analysis. Besides, the impact of GnP aspect ratio on the normalized crack opening displacement (COD) of the reinforced matrix is elaborated for the first time in the literature. Results of the present study suggest that GnPs with maximum aspect ratio are most effective to enhance elastic properties of the plate and potentially limit the edge crack propagation. Specifically, inclusion of 0.5 and 1.0% of needle-shaped GnPs in a notched epoxy resin plate decrease the maximum normalized COD by 33 and 50%, respectively, while for square-shaped GnPs, these reductions are limited to 20 and 37%, respectively.

Numerical investigation of bimaterial interfacial crack with interaction of voids and inclusions using XFEM

This article is presented to investigate the influence of several discontinuity like interfacial-crack, void and inclusion in the bimaterial plate, to analyze the normalized mixed-mode stress intensity factor (NMMSIFs) using XFEM under the uniaxial tensile load with considering the several numerical problems. It is investigated the normalized stress intensity factors (NSIFs) for an isotropic bimaterial plate and NMMSIFs for an isotropic-orthotropic bimaterial plate through varying the single-multi voids/inclusions position while its above, aligned and away from the interfacial edge crack and center crack of the bimaterial plate. It is also analyzed the void/inclusion several shape influence in the bimaterial plate. It is observed higher and fluctuating SIFs obtained with more number of voids/inclusions, influence of elliptical and diamond shape of void/inclusion is higher.

Effects of infilling materials on mechanical behaviors and cracking process of pre-cracked rock: Insights from a hybrid continuum-discontinuum method

The process of crack nucleation, initiation and propagation are of great significance in rock engineering such as hydrofracturing, underground excavation and gas or petroleum industry. In this study, the fracturing process of rock models with filled-flaws are mimicked by the hybrid continuum-discontinuum method. The effects both on mechanical response and cracking behaviors induced by the frictional properties including cohesion and friction coefficients of infilling materials are investigated. The results indicated that the minimum crack initiation stress of infilled flawed specimens lie in the inclination angle of 45–75° with different cohesions. When the friction angle changes, the minimum crack initiation stress appears when the inclination angle is in the range of 15–60°. The inclination angles are in accordance with that value when the normalized stress intensity factor of K1 acquired by changing cohesion and friction angle reaches maximum in the sliding crack model. Besides, with the increasing of cohesion and friction angle, the transition from wing crack to secondary crack appeared. The crack initiation sequence and pattern are comparable with the laboratory test.

Interaction of multiple straight cracks and elliptical inclusions in a finite plate due to mismatched thermal expansion

The purpose of this paper is to study the interaction between multiple elliptical inclusions and straight cracks in a finite plate due to a uniform temperature change. In this solution, Eshelby’s equivalent inclusion method involving both interior Eshelby’s tensor and exterior Eshelby’s tensor is applied to calculate the thermal stress fields of an infinite plate containing multiple elliptical inclusions under a uniform temperature change first. Then the multiple cracks and the boundary are modeled by continuous distributions of dislocation densities in an infinite plate. Based on the stress boundary conditions of the cracks and boundary, a system of singular integral equations with Cauchy kernels are obtained. After solving the singular integral equations with Gauss–Chebyshev numerical quadrature, the stress intensity factor of each crack can be calculated. Besides, the finite element method is employed to examine the accuracy and efficiency of the presented method. Finally, the effects of the material and geometric parameters on the normalized stress intensity factors of the cracks are studied.

The Effect of the Size and Position of the Crack on the Normalized Stress Intensity Factor

In this work, finite element method was used to determine the normalized stress intensity factors for different configurations. For this, a 2-D numerical analysis with elastic behavior was undertaken in pure I mode. This simulation was carried out using a numerical calculation code. On the basis of the numerical results obtained from the different models treated, there is a good correlation between the nodal displacement extrapolation method (DEM) and the energy method based on the Rice integral (J) to evaluate the normalized stress intensity factors and this for different crack lengths. For each configuration, the increase in the crack size causes an amplification of normalized intensity stresses fators.

SIF determination in finite double-edge cracked orthotropic composite using J-integral and digital image correlation

This paper demonstrates ability to evaluate the stress intensity factor in a double-edge cracked finite [013/905/013] graphite-epoxy orthotropic tensile composite from J-integral and a single digital image correlation recorded displacement field. Relevant stress/strain/displacement information is obtained by processing the measured displacement data with stress functions, conformal mapping and analytical continuation method. A normalized stress intensity factor of 2.05 is determined experimentally for the present geometry, loading and material. Plane-stress is assumed. The technique is not restricted to a laboratory environment and concepts are applicable to other structural shapes, loads and crack configurations. Unlike purely numerical or theoretical approaches, the present method does not require knowing the external loading. This is significant as loads are often unknown in practice. Results are verified independently.

Damage Assessment and Fracture Resistance of Functionally Graded Advanced Thermal Barrier Coating Systems: Experimental and Analytical Modeling Approach

Enhancement of stability, durability, and performance of thermal barrier coating (TBC) systems providing thermal insulation to aero-propulsion hot-section components is a pressing industrial need. An experimental program was undertaken with thermally cycled eight wt.% yttria stabilized zirconia (YSZ) TBC to examine the progressive and sequential physical damage and coating failure. A linear relation for parameterized thermally grown oxide (TGO) growth rate and crack length was evident when plotted against parameterized thermal cycling up to 430 cycles. An exponential function thereafter with the thermal cycling observed irrespective of coating processing. A phenomenological model for the TBC delamination is proposed based on TGO initiation, growth, and profile changes. An isostrain-based simplistic fracture mechanical model is presented and simulations carried out for functionally graded (FG) TBC systems to analyze the cracking instability and fracture resistance. A few realistic FG TBCs architectures were considered, exploiting the compositional, dimensional, and other parameters for simulations using the model. Normalized stress intensity factor, K1/K0 as an effective design parameter in evaluating the fracture resistance of the interfaces is proposed. The elastic modulus difference between adjacent FG layers showed stronger influence on K1/K0 than the layer thickness. Two advanced and promising TBC materials were also taken into consideration, namely gadolinium zirconate and lanthanum zirconate. Fracture resistance of both double layer and trilayer hybrid architectures were also simulated and analyzed.

Effect of Prestrain on Hydrogen-Induced Delayed Cracking for Medium Mn Steels

Medium Mn steels are a class of the new-generation ultra-high-strength materials used in automotives. However, despite excellent ductility, they may suffer from delayed cracking and thus cause serious concerns. In this study, several medium Mn steels were tested with different prestrain and hydrogen charging conditions. The interaction and synergistic effects of prestrain and hydrogen content on hydrogen-induced delayed cracking behavior are investigated. The threshold stress of hydrogen-induced cracking (HIC) decreased during dynamic hydrogen charging under a constant load. In the process of dynamic hydrogen charging, for M7B and M10B steels, the normalized stress intensity factor σ/σb and the corresponding threshold stress σHIC decreased sharply as prestrain increased. This is because the volume fraction of retained austenite decreased with an increase in prestrain. Similarly, σHIC was reduced and the critical hydrogen content dropped drastically with increasing prestrain. For M7C, the influence of prestrain on threshold stress and hydrogen concentration was less than that of M7B. This is because the different treatment processes leads to a different stability of the retained austenite. By observing the SEM fractographs, the fracture surface of medium Mn steels showed different fracture characteristics, such as dimple fractures and intergranular and transgranular modes.

A predictive failure framework for brittle porous materials via machine learning and geometric matching methods

Brittle porous materials are used in many applications, such as molten metal filter, battery, fuel cell, catalyst, membrane, and insulator. The porous structure of these materials causes variations in their fracture strength that is known as the mechanical reliability problem. Despite the importance of brittle porous materials, the origin of the strength variations is still unclear. The current study presents a machine learning approach to characterize the stochastic fracture of porous ceramics and glasses. A combined finite element modeling and fracture mechanics approach was used to generate a unique empirical data set consisting of normalized stress intensity factors (nSIFs, KI/σ∞ = Y$$ \sqrt {\pi a} $$) that define fracture strength of brittle systems under uniaxial tensile loading and biaxial tensile loading. These empirical data sets were used to generate prediction functions and validate their accuracy. Monte Carlo simulations with two machine learning algorithms, random forests (RF) and artificial neural networks (ANN), were used to simultaneously determine the optimum percentages for the training and test data set split and the prediction function validation. The constraint was taken to be the mean absolute percentage error (MAPE) during the process. In the implementation step, new porous media with uniformly distributed pores were created and the prediction functions were used to obtain nSIFs and characterize the media. As a novelty of this approach, which ensures the predictive characterization of the generated media, a geometric matching method by means of the Euclidean bipartite matching between the empirical and the generated media was presented and the nSIFs were compared by means of MAPE. As a result of the study, MAPE ranges are 3.4–17.93% (uniaxial load) and 2.83–19.42% (biaxial load) for RF, 3.79–17.43% and 3.39–21.43 for ANN at the validation step; 3.54–18.20% (uniaxial load) and 3.06–21.60% (biaxial load) for RF, 3.57–18.26% and 3.43–21.76% for ANN at the implementation step. The proposed approach can be thus used as a predictive characterization tool, especially for the analysis and Weibull statistics of porous media subjected to brittle failure.

Investigation of fatigue damage accumulation by measurements of deformation response to narrow notch increment

A new destructive method of damage accumulation quantifying in the stress concentration zone has been proposed and verified. Damage accumulation in the vicinity of the hole was created by means of preliminary low-cycle fatigue loading of specimens with holes. The damage accumulation functions for different stress ratio and stress range are expressed in an explicit form proceeding from distributions of the normalized stress intensity factor as a function of number of cycles.

The edge-notched clamped beam bend specimen as a fracture toughness test geometry

Edge-notched clamped beam bend fracture specimens provide the required geometric stability for controlled crack growth in brittle materials, enabling the measurement of R-curves and cyclic crack growth. In this paper, finite element simulations were carried out on this test geometry to extract the normalized stress intensity factor KI solutions for different useful specimen dimensions, loading tip radius and loads. Based on these results, geometric factors have been proposed that can fit various beam aspect and crack depth ratios. Crack stability analysis is carried out in terms of the R locus for various beam aspect ratios for the clamped beam geometry and compared to other fracture toughness tests. Experimental verification of the same has been carried out at the macro-scale using poly-methyl methacrylate (PMMA) and WC-Co as model materials.

Hygro-thermally induced stress intensity factor of an edge crack piezo laminated composite plate

Purpose The purpose of this paper is to evaluate hygro-thermo-mechanically induced normalized stress intensity factor (NSIF) of an edge crack symmetric angle-ply piezo laminated composite plate (PLCP) using displacement correlation method. Design/methodology/approach In the present work, the governing equations are solved through conventional finite element method combined with higher order shear deformation plate theory utilizing the micromechanical approach. Findings The effects of crack length, the thickness of the plate and piezoelectric layer, stacking sequences, fiber volume fraction, position of piezoelectric layer, change in moisture and temperature, and voltage on the NSIF are examined. The numerical results are presented in the form of a table for the better understanding and accuracy. The present outlined approach is validated with results available in the literature. These results can become a benchmark for future studies. Research limitations/implications The mathematical models theoretically have been developed by considering different parameters. The results are generated using MATLAB 2015 software developed by the authors’ side. Originality/value The fracture analysis of a single edge crack PLCP with the effect of a piezoelectric layer at the different location of cracked structures, plate thickness, and actuator voltage and hygro-thermo loading is the novelty of research for health monitoring and high-performance analysis.