Stress Intensity Factor Research Articles

Entropy‐based method considering nonlinear hardening effect to predict the crack propagation life of superalloy GH4169 at elevated temperature

AbstractThis paper aims to determine the relationship between thermodynamic entropy generation and fatigue crack propagation life of superalloy GH4169 at 300–650°C. The entire specimen was considered as the thermodynamic system. The plastic energy dissipation in the crack tip was obtained by finite element simulation utilizing the Chaboche nonlinear hardening model. Then the cyclic entropy generation rate (CEGR) and the accumulated entropy generation are calculated by combining simulation and experimental methods. Results show that the CEGR is a power function of the stress intensity factor range, and it is almost a constant at fatigue failure. The fatigue fracture entropy (FFE) increases as fatigue cycles at failure increase at constant temperature, but it first decreases and then increases when temperature increases from 300 to 650°C. A fatigue life prediction model based on the thermodynamic damage parameter is established and verified by comparison with experimental results and available data in the literature.

Investigation of fatigue crack growth behavior and crack tip plastic zone characteristics in welded structures based on local displacement fields

The fatigue crack growth behavior in welds is difficult to evaluate due to complex internal stresses and microstructural differences. This paper uses the CJP model based on displacement field variations to describe the fatigue crack growth behavior and the size of the crack tip plastic zone in welds. First, fatigue crack growth rate tests were conducted on base metal and as-welded specimens. The digital image correlation technique was used to capture the speckle pattern variations on the specimen surface during crack growth, obtaining the crack tip displacement field required by the CJP model. Based on this, by calculating the stress intensity factor ranges ΔK and ΔKCJP, two da/dN–ΔK(ΔKCJP) curves defined by the traditional and CJP models were obtained, proving the model’s applicability for describing fatigue crack growth behavior in welded joints. Finally, the CJP model was used to calculate and compare the crack tip plastic zones of base metal and as-welded specimens. It was found that the maximum error for the as-welded specimen was 37.84%, occurring at the initial stage of crack propagation and gradually decreasing with the fatigue process

Analytical solution of two non‐identical edge cracks in an infinite strip under anti‐plane shear wave

AbstractThis article presents an extensive analytical solution addressing the interaction between two non‐identical edge cracks in an infinite orthotropic strip under anti‐plane shear waves. Most studies assume identical cracks or single edge crack in a strip, but this research breaks new ground by considering cracks of different sizes. By incorporating mixed‐type boundary conditions, the study derives dual integral equations. These equations are then transformed into a singular integral equation of Cauchy type with the aid of a trial solution and contour integration technique. The singular integral equation is further converted into a system of integral equations, which are solved numerically utilizing Jacobi polynomials. The obtained solutions are utilized to derive expressions for the stress intensity factor (SIF) and crack opening displacement (COD) at the crack tip using Krenk's interpolation formulae. The derived results are presented graphically and compared against existing solutions for single edge crack and symmetric edge cracks in static scenario.

A micro-macro mechanism of hydraulic fracturing with initial stress state effect of brittle rock

The external initial stress state seriously affects the hydraulic fracturing process of rocks. However, the external initial stress effect on the mechanical relationship between the hydraulic pressure and the internal microcrack extension in brittle rocks is rarely studied. This paper proposes a micro-macro mechanical model for predicting the hydraulic fracturing process of brittle rock under compressive stress. Based on the correlation of the stress intensity factor at the tip of the extended micro-cracks, the hydraulic pressure, and the force characteristics of the cracks inside the brittle rock, the evolution law of the hydraulic pressure with the wing crack length is determined. The effects of confining pressure, axial pressure, stress difference, initial crack angle, initial crack length, initial crack density and rock fracture toughness on the hydraulic initiation stress and peak stress are discussed. The rationality of hydraulic fracturing models is verified by experimental comparison. With the increase of axial pressure, stress difference, fracture toughness, initial crack length and initial crack density, the hydraulic initiation and peak stress of rock decrease, and with the increase of confining pressure and fracture toughness, the hydraulic initiation stress and peak stress of rock increase. The study results optimize the parameters such as pre-crack angle, pre-crack length, and external loading conditions based on rock characteristics. It helps to grasp the progress of hydraulic fracturing according to the nature of rock and the degree of hydraulic pressure change, improve the efficiency of hydraulic fracturing, and enhance economic benefits.

Mode-III fracture of four cracks emanating from an elliptical hole in one-dimensional orthorhombic quasicrystals with piezoelectric effect

In this study, a new generalized conformal mapping is introduced using the generalized complex variable method, focusing on the investigation of the anti-plane problem of an elliptical hole with four cracks in one-dimensional (1D) orthogonal piezoelectric quasicrystals. Under the consideration of electrically impermeable and electrically permeable boundary conditions, the governing equations of the anti-plane problem in 1D orthogonal piezoelectric quasicrystals are successfully simplified into an eighth-order partial differential equation and a fourth-order partial differential equation by introducing a potential function. Based on this, analytical solutions for the stress field and electric field are obtained, and the exact solution for the stress intensity factor (SIF) is derived. In addition, formulas for the electric displacement intensity factor (EDIF) and energy release rate are provided. Subsequently, the influence of geometric parameters and external loads on the field intensity factors and energy release rate is analyzed through numerical examples, providing a theoretical basis for engineering mechanics analysis.

Data-driven prediction of fracture toughness size effect in ductile-to-brittle transition using Two-Step-Scaling procedure

The fracture properties of ferritic steels in transition temperature region are usually statistically treated by models that presuppose the existence of various forms of quenched disorder (critical cleavage triggers). In this study, the fracture toughness from the Euro fracture toughness dataset (stress intensity factor used in the master curve KJc) for reactor steel 22NiMoCr37 is used with the aim of outlining a methodology for using the recently proposed two-step scaling (2SS) method. Three widely different temperatures (−154 °C, −91 °C, and 0 °C), which cover the entire range from lower shelf to upper shelf fracture, are selected to demonstrate the accuracy of extrapolation and interpolation of the fracture toughness CDF (cumulative distribution function) and the pertinent issues related to the procedure application. The obtained predictions at the two lower temperatures are in good agreement with the experimental results and well within the inherent experimental data scatter, while 2SS method is shown not to be applicable in upper-shelf transition region. Special attention is devoted to the effect of statistical sample size on prediction accuracy/reliability along with the minimum sample size requirement. Moreover, the reduction in random sample size affects the Weibull parameters, which in turn impacts the accuracy of predictions, introducing a degree of uncertainty and highlighting limitations in the method.

Stress intensity factor analysis for multiple cracks in orthotropic steel decks rib-to-floorbeam weld details under vehicles loading

In recent years, it has been found that multiple cracks coexist in the existing steel bridge orthotropic steel decks (OSDs) longitudinal rib-to-floorbeam (RF) details. The synergistic expansion mechanism of multiple cracks in the orthotropic steel bridge deck panel is still unclear. This paper proposes a multiscale extension finite element method based on ABAQUS and FRANC 3D interactive technology to simulate the fatigue crack propagation behavior of steel bridge RF details under dynamic vehicle loading. The effectiveness of this method is verified by comparing experimental data. The crack propagation behavior of longitudinal rib weld toes, transverse diaphragm weld toes, and transverse diaphragm arc notches is studied, and the influence of fatigue crack length and angle on the initial crack stress intensity factor (SIF) of adjacent details is discussed.

Investigating the effect of stress ratio on fatigue crack growth rate behaviour in friction stir welded AA7075-T651 aluminium alloy plates

This study examines the characteristics of Fatigue Crack Growth Rate (FCGR) in AA 7075-T651 Friction Stir Welded (FSW) joints with a thickness of 16 mm. Compact tension (CT) specimens from both the base and the FSW joints were utilized to assess FCGR under various stress ratios (0.2 to 0.5). Additionally, the study involved analyzing the transverse tensile characteristics of both the based and the welded joints. The microstructures of the welds were inspected using optical and transmission electron microscopes. Findings indicate that the FSWjoint critical stress intensity factor range (ΔKcr)is lower than the unwelded base, that can be related to precipitates dissolving in the weld zone when the friction stir welding process. Consequently, in contrast to the unwelded base, the fatigue life of AA 7075-T651 aluminium alloy FSW joints is significantly reduced. A scanning electron microscope carried out microstructural analyses of the fracture surfaces of the FSW and base under various stress ratioconditions. The results showed that, in contrast to the parent material, the FSW joint has ultra-fine grains resulting in intergranular cracks in the propagation zone.

Physical and mechanical properties of ceramics based on ZrN-ZrO2 obtained by spark plasma sintering method

Relevance. Increasing the service life of mining tools is an important task in the development of geology associated with the investigation of new ceramic materials for functional purposes. The ability to reduce wear and thermal and chemical effects of rocks on the working elements of mining equipment determines the vector of development of the use of super-hard, high-strength and refractory ceramics. At the same time, the task is set to increase the fracture toughness of the materials used to solve the problem of maintaining the operability of equipment under conditions of critical deformations. To accomplish this task, it is necessary to study the patterns of consolidation of ceramic materials and search for the optimal combination of consolidation parameters to achieve improved physical and mechanical properties. Aim. To develop a method for producing high-density durable ceramics based on commercially available zirconium nitride powders using spark plasma sintering under vacuum conditions, to study the phase composition and physical and mechanical properties of the resulting samples. Methods. X-ray phase analysis of the studied samples, nanoindentation, microscopic analysis. Results and conclusion. The authors have studied the physical and mechanical properties of zirconium nitride consolidated by spark plasma sintering at 2000℃, a pressure of 30–60 MPa and a holding time at a given temperature of 5–10 minutes. Qualitative and quantitative X-ray phase analysis was carried out, within which the content of the main phase of zirconium nitride and zirconium dioxide phase was determined. It was found that an increase in the pressure applied during consolidation and holding time contributes to better compaction and a decrease in the porosity of the samples from 8.52 to 2.72%. It was found that with a decrease in porosity, the elastic modulus increased in the range from 320 to 378 GPa, and the hardness from 7.3 to 10.4 GPa. At the same time, by extrapolating the data, it was established that non-porous zirconium nitride samples will have an elastic modulus of 394 GPa and a Martens hardness of 11.56 GPa. For the samples under study, critical stress intensity factors were determined. It was established that at a porosity of less than 5%, the critical stress intensity factor of zirconium nitride consolidated by spark plasma sintering has values of at least 4 MPa m1/2.

Employing Williams’ series for the identification of fracture mechanics parameters from phase-field simulations

Fracture mechanics and damage mechanics are two theories that describe the degradation of the bearing capacity of structures. Fracture mechanics is based on a discontinuous description of cracking, while damage mechanics proposes a continuous description of material degradation. These two approaches are often opposed in the literature, from both theoretical and numerical points of view. This work suggests correlating the two approaches by applying Williams’ series, usually dedicated to experimental results, to phase-field computations. Williams’ series are employed to extract equivalent fracture mechanics parameters as a post-processing step. The proposed analysis based on a fracture mechanics description excludes the fracture process zone. Typical fracture mechanics parameters such as energy release rate, stress intensity factors, fracture process zone size, and crack tip position are determined from the phase-field computations. The approach is illustrated on a two-dimensional structure representing a beam whose notch opening displacement is controlled. The dependence on the choice of the internal length of the phase-field model is studied. Similarities and differences between both modeling routes are discussed.

Finite element analysis of characterization parameters the double cracks in linear elastic DCFEM

In fracture mechanics, the lifespan of structures plays an important and effective role in terms of rigidity and resistance to secondary effects linked to direct friction and the effects of the atmosphere, in order to avoid any danger that could end to the life of the work. structure, and among these effects are those linked to internal and external cracks. Sometimes the structure may be exposed to double cracks resulting from external loads and influences, such as our study that we present in this paper. We must also not forget the structures which contain holes, which play an important role in tension with other elements and have an essential function in operation and resistance. We don't forget the basic dimensions between the crack and the other. These days, numerical modeling techniques, such the finite element method which is the most popular approach for determining characterisation parameters at the bottom of a crack are the foundation for fatigue problem analysis. This work aims to investigate the impact of two-dimensional parameters (b, c) and the crack length (a) on crack parameters, including the J-integral and stress intensity factor (SIF), of an aluminum alloy structure with a double starting fracture. The finite element method (DCFEM) has been used to study these characteristics under uniform tensile loading. After that, rupture happens in plane stress under mode I loading, and the modeling is done using 4-node CPS4R quadratic elements. Numerous instances have been provided. The optimal rupture resistance solution for plates with two cracks on each sides will be developed using the results obtained.

SINGULAR INTEGRAL EQUATIONS FOR A CRACK SUBJECTED NORMAL STRESS IN A HEATED PLATE

In this paper, a crack in a heated plate is investigated, subjected to normal stress. Employing the relationship between the uniform and perturbation fields, as well as complex potential functions and stresses, the problems of heat conduction and heat stress are modeled as singular integral equations. The derivatives of the crack opening displacement function and the temperature jump function serve as the unknown functions. Gauss integration rules are applied to solve the obtained equations numerically. Analysis of the stress intensity factors(SIFs) for some particular crack configurations is presented.

Effect of thermal ageing on fatigue crack growth behaviour of forged alloy 617M at elevated temperatures

ABSTRACT Fatigue crack growth (FCG) studies have been conducted on compact tension specimens of alloy 617M for as-received and aged for 1000, 5000 and 10,000 h at 710°C. Effects of thermal ageing on FCG behaviour of alloy 617M forged has been characterised at 27°C, 650°C, 710°C and 750°C. Results reveal that threshold stress intensity factor ( Δ K th ) decreases as temperature increases upto 710°C and then increases at 750°C for all the ageing conditions except for 1000 h aged. The Δ K th value also decreases with an increase in ageing time till 5000 h, but at 10,000 h a reverse trend is observed. The influence of thermal ageing and temperature reflects major deviations for Paris constant (C) and exponent (m). Additionally, thermal ageing and temperature influences on FCG, the effects of dynamic strain ageing, Cr-rich carbides and γ’-phase precipitations have been discussed and corroborated with fractographic and microstructural changes.

Effects of single overloads on fatigue crack propagation behaviour of AZ31B magnesium alloy under different temperatures

An experimental study examined the influence of single overload ratio (OLR) on fatigue crack growth (FCG) behaviour in AZ31B magnesium alloy at different temperatures (300 K, 373 K, and 473 K). The results showed that FCG rates and stress intensity factor ranges (ΔK) vary with temperature and overload ratios. After applying a single overload (OL), the FCG rate initially decreased, then increased rapidly, and stabilized at a value consistent with constant amplitude loading (CAL). The fatigue life increased by 86 % to 143 % at 300 K, 75 % to 132 % at 373 K, and 75 % to 134 % at 473 K for OLRs ranging from 1.75 to 2.25 when compared to the fatigue life at CAL. A single overload accumulates energy at the crack tip, forming an overload region with tearing ridges, secondary cracks, dimples, and fatigue striations under varying temperatures.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Experimental Study on Fracture Behavior of Adhesive-Bonded Structure with V-notch Based on Digital Gradient Sensing Method.

In this paper, a comparative study of the mode-I fracture behaviors of two types of specimens with a V-notch defect under plane stress conditions was performed using the digital gradient sensing (DGS) method. First, two types of specimens (namely one-piece specimen and bonded specimen) with the same V-notch defect were both made of polymethyl methacrylate (PMMA), and three different V-notch angles' defect were considered for each type of specimen. Then, three-point bending tests were performed on both types of specimens. The angular deflection field of light near the V-notch region was recorded using a CCD during the experiments. Finally, by utilizing the relationship between the stress gradient and angular deflection as established by the elasto-optic effect, in conjunction with the principles of linear elastic fracture mechanics theory, the stress intensity factors (SIFs) of two types of specimens under different stress conditions were calculated using the least square method. According to the experimental results, the influence of V-notch angle on fracture load and fracture toughness of two kinds of specimens was discussed. Meanwhile, the experimental results show the significant differences in the fracture behaviors of the two types of specimens under mode-I loading conditions.

Fracture of Epoxy Networks Using Atomistic Simulations.

Predicting fracture properties through all-atomistic simulations poses challenges due to classical force field limitations in breaking covalent bonds and the computational demands of reactive force fields like ReaxFF. In addressing this, we propose a scale-bridging method for forecasting the fracture behavior of highly cross-linked epoxy combining classical force fields, the LAMMPS package REACTER, and for bond breaking a parameter based on experimental distance criterion. In our analysis, we anticipate the macroscopic fracture energy GC of the epoxy network through the application of a continuum fracture mechanics model developed for fibrils. In addition, we extract the value of the stress intensity factor KI. This modeling approach is specifically implemented for a frequently used epoxy system that consists of bisphenol F and DETDA hardener. Notably, our results demonstrate a robust correlation with existing literature and experimental studies. Moreover, our approach boasts a substantial computational time advantage, facilitating calculations that are significantly faster compared to those performed using reactive force fields.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Mechanical properties and insulation damage of PMSG stator end windings with eccentricity considerations

The mechanical properties and insulation damage of stator end windings in permanent magnet synchronous generator (PMSG) are investigated by theoretical analysis, finite element analysis (FEA) and experiment verification. First, a theoretical model of the winding electromagnetic force (EF) and vibration response before and after eccentricity faults are established. Then, the stress/strain distribution of the end windings under different working conditions is analyzed. Finally, the insulation damage behavior of end windings with initial cracks is studied and characterized using the stress intensity factor (SIF). The results indicate that the winding EF and vibration responses vary under different faults. The stress/strain at the joint of the winding is the largest, and the insulation layer has the maximum stress/strain under the same section. Additionally, the SIF amplitude of the crack at the winding joint is the largest. And the SIF amplitude of the crack will increase with the increase of fault degree/crack depth/crack length. The contribution of this paper lies in the comprehensive analysis of the winding EF distribution, vibration response, stress and strain, and insulation damage before and after eccentricity. This analysis can provide valuable reference for the health monitoring of PMSG eccentricity faults and the prevention of winding insulation damage.

Theoretical analysis of the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress

A mathematical model of blasting stress wave scattering at an arc-shaped interface crack is established to theoretically analyze and verify the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress. Based on the continuum mechanics, finite deformation, and incremental stress theories and the geometric and physical characteristics of the arc-shaped interface crack, the mathematical model includes a set of the first class of singular integral equations with Hilbert kernels. The opening and dislocating displacements of the arc-shaped interface crack and the effective stress components of scattered stress waves are numerically calculated and discussed with the variation of the type, frequency, and incident angle of the blasting stress wave; the curvature radius and opening angle of the arc-shaped interface crack. The condition that the dynamic stress intensity factors and energy release rates at the upper and lower tips of the arc-shaped interface crack reach peak are also provided. It is found that when the frequency of the blasting stress wave and the curvature radius of the arc-shaped interface crack increase, the peaks of the above dynamic stress intensity factors will increase further, and the arc-shaped interface crack is more likely to expand or destabilize. Although the order of in-situ stress is much smaller than that of Young’s modulus of the deep rock mass, it increases the effective stress concentration of scattered stress waves and the opening and dislocating displacements of the arc-shaped interface crack. These findings will provide theoretical guidance for analyzing the cracking characteristics of blasting stress waves in deep rock masses with high in-situ stress.