Critical Crack Length Research Articles

Critical crack lengths of concrete gravity dam by using fracture mechanics

Concrete gravity dams are generally designed based on the principle that the tension does not occur in any portion of the dam, as concrete is weak in tension. Cracks will occur if concrete is subjected to undesirable tensile stresses. The modeling of crack propagation is of high importance in simulation of dam failure. Koyna concrete gravity dam was chosen for the present study. A seismic study of the dam – reservoir – foundation structure is conducted first by using ANSYS. On the basis of the results obtained, critical zones are identified within which the tensile strength of the concrete exceeds the allowable limits. In these zones cracks have been initiated and are modeled using the Extended Finite Element Method (XFEM). The stress intensity factor (SIF) has been chosen to estimate critical crack length. Further critical crack lengths of each initiated individual cracks are determined to know the structural stability. From the present analysis it was observed that SIF rises with an increase in the length of the crack and it was also observed that the structural failure occurs at the critical crack length of the crack after the fracture toughness of the dam material has been achieved.

Analytical model for assessing fatigue limit of welded joints of ferritic-pearlitic steels

Introduction. Microdefects and zones with stress concentration in welded joints cause fatigue macrocracks. Such damage is potentially dangerous, especially if the fatigue life of the structure is almost exhausted. In this case, the crack size is close to the critical value, and it is crucial to determine its length. The paper considers the development of an engineering analytical model for assessing the critical crack length and endurance limit of welded joints with the formed grain in the structure of ferrite-pearlitic steels after welding. Materials and Methods. The theory and methods of fracture mechanics at the mesoscale are used. A simple analytical dependence is obtained, which provides determining the critical dimensions of a macrocrack for ferrite-pearlite steels without using the Griffiths formula. . The calculation results of the critical crack lengths of various steels depending on their yield strength are presented. An analytical dependence of the endurance limit calculation for the most dangerous symmetric loading cycle, according to the standard set of mechanical characteristics and the average grain diameter of ferrite-pearlite steel, is presented. Results. Structural deformation analysis of the crack propagation process has been performed. On its basis, an engineering technique for assessing the endurance limit is developed. A mathematical model that enables to calculate the endurance limit and the critical crack length in the components of welded assemblies of large-sized facilities, considering periodic loads of a symmetrical cycle, is developed. Using this model, it is possible to estimate the degree of metal sensitivity to the original characteristics (yield stress, Poisson's ratio, grain diameter, relative constriction, Young's modulus, power-law hardening coefficient, etc.). Discussion and Conclusion. Under stresses corresponding to the steel endurance limit, the critical crack opening rates of the tip and edges approach each other. Energetically, this moment approximately corresponds to the transition of the crack to an unstable state. The accumulation of one-sided plastic deformations causes the limiting state of plasticity of the region adjacent to the crack tip and its avalanche-like or sharply accelerated motion. This critical area is interrelated with the grain diameter of the material, the characteristic of critical plasticity and the critical opening at the crack tip at the fatigue limit. The proposed analytical dependences can be used to assess the residual life and the fatigue limit of welded structures, the influence of various factors on the fatigue limit of welded joints of ferrite-pearlitic steels used in mechanical engineering, shipbuilding, pipeline transport, etc

Evaluation of TBM Cutterhead’s Comprehensive Performance Under Complicated Conditions

A comprehensive performance evaluation method for the tunnel boring machine(TBM) cutterhead is proposed in this paper. The evaluation system is established on strength and vibration. Based on fracture mechanics theory, fatigue strength evaluation indices are determined under critical crack length. The concept of crack regions division is proposed to evaluate fatigue strength more accurately and specifically. In addition, the velocities in three directions of critical locations are obtained with dynamics equations. Then, the root-mean-square values of velocities are taken as the vibration severity indices. Taking the cutterhead of Jilin diversion engineering as an example, the evaluations of each index are completed; then, the vibration of the TBM cutterhead is measured and compared with the theoretical calculation results. There are similar change laws between the theoretical calculation results and the testing results of the cutterhead acceleration, which proves that the method of calculation of the vibration index is effective, the reliability of the cutter saddle welding should be paid attention to when the TBM is working, and the condition of vibration severity of the TBM cutterhead meets the requirements but needs to be improved.

Stick-slip failure in heterogeneous sheared fault with a variety of fault roughness

Stick-slip failure, as a possible mechanism for destructive shallow focus earthquakes, often occurs in heterogeneous faults. To investigate the physical processes of stick-slip failure in heterogeneous faults, direct shear tests are performed in the laboratory, combined with the use of multi-channel high-speed dynamic strain acquisition system, on the bimaterial samples. The bimaterial samples consist of PMMA (poly methyl methacrylate) and PC (poly carbonate). This experimental study is concerned with the effects of fault roughness on the stick-slip behaviors along the heterogeneous faults. The metallographic microscope is used to quantitatively measure the surface morphology of the heterogeneous faults. The stress distribution along the simulated fault is highly non-uniform, which dictates the initiation locations of stick-slip failure. The nucleation starts at a firstly-yielded material point, and as the energy accumulates in the heterogeneous fault, the nucleation zone is progressively formed. The crack tip propagates at an increasing velocity until the entire fault is penetrated. It is found that a rougher fault is corresponding to a slower rupture velocity, a smaller local stress drop, a larger critical slip-weakening displacement, and a larger critical crack length.

Investigating the Crack Initiation and Propagation of Asphalt Binder in Linear Amplitude Sweep Test

The linear amplitude sweep (LAS) test has been widely accepted for estimating the fatigue resistance of asphalt binders in the last 10 years. This paper proposes a fracture mechanics–based analytical approach for crack initiation and propagation characterization in the LAS test, aiming to more precisely explore the binder crack growth and failure mechanism. Seven unmodified neat asphalt binders and one styrene-butadiene-styrene (SBS) polymer-modified binder are selected in this study. The crack length (a), rate of cracking (da/dN), stress intensity factor (K), and energy release rate (G) are the fundamental parameters for the data interpretation approach proposed in this paper. Experimental and analysis results demonstrate that the energy-based failure definition (either from continuum damage mechanics or fracture mechanics) should be utilized to detect the material-dependent failure occurrence in LAS test. The fracture behavior of asphalt binder in the LAS test follows the two-phase crack growth (TPCG) model in terms of the crack initiation and crack propagation. The crack propagation phase further consists of stable crack growth and unstable crack growth. It is found that the fatigue performance of asphalt binder is intrinsically governed and dominated by its resistance to the crack propagation. The SBS binder in this study clearly displays slower crack propagation behavior than other neat binders. Additionally, the traditional fatigue life can also be divided into the crack initiation life and crack propagation life, which is promising to clarify the specific modification contribution to binder fatigue resistance. The two critical crack lengths of initiated crack and propagated crack for a given asphalt binder are found to be correlated to each other, indicating the potential links between the binder crack initiation and propagation behaviors.

Investigation on impact absorbed energy index of drill pipe

Drill pipe is one of the most important tools for petroleum and natural gas drilling exploitation. The application of S135 drill pipe can significantly increase drilling depth, reduce drilling cost and improve drilling quality. Impact absorbed energy is the most important toughness index, which has a decisive influence on the service safety of drill pipe. The statistical results of 91 drill pipe failure cases show that the piercing is the main failure mode of S135 drill pipe, including oval-shaped piercing and slot piercing. The length of oval-shaped piercing hole is mainly distributed in 20–50 mm, and the impact absorbed energy of failed drill pipe is dispersed in 42–156 J. The length of slot piercing hole is mainly distributed in 60–90 mm, and impact absorbed energy of failed drill pipe is concentrated in 76–150 J. Analysis results show that there is certain correlation between the length of piercing hole and impact absorbed energy values of drill pipes. In this work, the impact absorbed energy index calculation formula of “leakage before fracture” failure mode for drill pipe is proposed. The results show that the impact absorbed energy value increases with the increasing of critical crack length, square of stress strength coefficient and strength level. The impact absorbed energy value of S135 drill pipe should be greater than 80 J to ensure the service safety.

Finite element analysis on the factors affecting die crack propagation in BGA under thermo-mechanical loading

Ball grid array (BGA) is one of the most innovative semiconductor packaging technologies which is capable of high input-output capacities while addressing handling and coplanarity compared with other packages. However, the BGA package is subjected to thermo-mechanical load which makes it susceptible to quality and reliability issues such as die crack. The occurrence of die crack is difficult to monitor as it is considered as an internal package issue and can be catastrophic to the electronic device which may lead to its failure. This study aims to investigate the various factors affecting die crack propagation using finite element analysis (FEA) model under thermo-mechanical loads. The energy release rate in the silicon die was used to quantify the propagation of die crack in the BGA package. The influence of the various factors on the propagation of die crack was determined through a design of experiment approach consisting of the definitive screening for initial factor screening, and response surface method through the central composite design. The results have shown that the die thickness, the glass transition temperature, the in-plane CTE of the substrate, and the initial crack length are the factors significantly affecting the die crack propagation in a BGA package. Moreover, at critical parameter conditions, the results have identified a critical crack length of 0.02236 mm. The study is aimed to benefit the research, design, development, assembly, and material engineers in the semiconductor industry providing insight to the die crack propagation of a BGA package.

Fracture behavior of fibrous network materials: Crack insensitivity and toughening mechanism

A 3D numerical model is established to characterize the fibrous network materials and the fracture behavior is investigated through the finite element method (FEM) analysis. The numerical results show that fibrous network material is insensitive to the crack when the crack length is less than a critical value, which is three times as much as the average length of fiber segments in the fibrous network. In addition, the toughening mechanism of the fibrous network material is revealed based on the FEM simulations. Due to the damage accumulation of bonds near the crack tip, the fibers around the crack tip are reoriented and become perpendicular to the crack path, which can further inhibit the crack propagation, and the deformation mode changes from bending-dominated deformation to tensile-dominated deformation, with the loading capacity of the fibrous network materials enhanced. The results in this paper demonstrate that the fibrous network materials show damage-tolerance to the small crack under the critical crack length, and the fibrous network formed by brittle fibers can exhibit ductile behaviors by controlling the microstructure and relative density, which is useful for the design and optimization of fibrous network materials.

The RHOSSA campaign: multi-resolution monitoring of the seasonal evolution of the structure and mechanical stability of an alpine snowpack

Abstract. The necessity of characterizing snow through objective, physically motivated parameters has led to new model formulations and new measurement techniques. Consequently, essential structural parameters such as density and specific surface area (for basic characterization) or mechanical parameters such as the critical crack length (for avalanche stability characterization) gradually replace the semiempirical indices acquired from traditional stratigraphy. These advances come along with new demands and potentials for validation. To this end, we conducted the RHOSSA field campaign, in reference to density (ρ) and specific surface area (SSA), at the Weissfluhjoch research site in the Swiss Alps to provide a multi-instrument, multi-resolution dataset of density, SSA and critical crack length over the complete winter season of 2015–2016. In this paper, we present the design of the campaign and a basic analysis of the measurements alongside predictions from the model SNOWPACK. To bridge between traditional and new methods, the campaign comprises traditional profiles, density cutter, IceCube, SnowMicroPen (SMP), micro-computed-tomography, propagation saw tests and compression tests. To bridge between different temporal resolutions, the traditional weekly to biweekly (every 2 weeks, used in this sense throughout the paper) snow pits were complemented by daily SMP measurements. From the latter, we derived a recalibration of the statistical retrieval of density and SSA for SMP version 4 that yields an unprecedented spatiotemporal picture of the seasonal evolution of density and SSA in a snowpack. Finally, we provide an intercomparison of measured and modeled estimates of density and SSA for four characteristic layers over the entire season to demonstrate the potential of high-temporal-resolution monitoring for snowpack model validation.

Effect of Nano TiO2 on Static Fracture Toughness of Fiberglass/Epoxy Composite Materials in Hot Climate regions

This work is an experimental and numerical approach to analyze the effect of Nano powder additives and temperature on the critical crack length in fiber reinforced composite materials (FRC) exposed to uniaxial tensile load. Fiberglass/Epoxy compact tension test samples (CT) are prepared according to ASTM standard E399 . Tio2 Nano powder is added by 2% wt to the resin to other samples. The static tensile test is applied to the samples and the results for crack length/time are discussed. ABAQUS/CAE software is used to simulate the case. The numerical and experimental results were close. The experimental results showed that the addition of 2%wt Tio2 Nano powder increased the critical crack length by 32.4%. The effect of ambient temperature is studied too by applying the experimental test on the fiberglass/Epoxy samples in room temperature (30°C) once and at outdoor (60°C) temperature. The results showed that the effect of the temperature increase decreased the critical crack length by 51%. The numerical results determined the fracture toughness (KIC) for the fiberglass/Epoxy samples to be 491 pa.mm0.5 and 517 pa.mm0.5 for the fiberglass/Epoxy-Nano powder samples.

Determining the tensile strength of concrete for wedge splitting specimens based on the fracture extreme theory

Two theoretical methods were developed to determine the tensile strength ft of concrete using wedge splitting specimens based on nil-stress intensity factor (nil-SIF) criterion and force equilibrium theory, respectively. With the fracture extreme theory (FET), only experimental peak load of one specimen was needed and did not require the measurement of critical crack mouth opening displacement CMODc for calculation. The existing experimental data were utilized to verify the two methods. Results show that the values of ft were insensitive to the initial notched ratios a0/D and agreed well with the experiment data. The influence of the size of the specimen was analyzed, ft was affected by the specimen size when the nil-SIF criterion was adopted. Nevertheless, ft calculated by the force equilibrium theory appeared to be kept a constant when the height of the specimen varied from 200 mm to 600 mm. Finally, the critical effective crack length ac and critical crack tip opening displacement CTODc were obtained and compared using the two methods.

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.

Plastic Limit Pressure Solutions for Elbows With Slant Through-Wall Cracks

Abstract For leak-before-break (LBB) assessment, an idealized through-wall crack (TWC) is typically postulated to determine the critical crack length of cracked piping. However, such an idealization in terms of crack shape can lead to underestimations of plastic limit pressure. Although many studies have been performed to obtain accurate limit load solutions for cracked straight pipes by considering realistic crack geometries, there is still a lack of information regarding slant TWC at elbow. Therefore, three-dimensional finite element (FE) models of an elbow considering the effects of slant TWC on plastic limit pressure are developed. The proposed FE model and analysis procedure were verified through comparisons to the existing solutions for idealized TWCs in elbow. On this basis, the effect of slant TWC on the plastic limit pressure is analyzed, and a closed-form solution of the plastic limit pressure is proposed, for an elbow containing a longitudinal or a circumferential through-wall crack.

Mechanical properties and prediction of fracture parameters of geopolymer/alkali-activated mortar modified with PVA fiber and nano-SiO2

Properties of fly ash (FA) and metakaolin (MK) based geopolymer/alkali-activated mortar modified with polyvinyl alcohol (PVA) fiber and nano-SiO2, including workability, compressive strength, flexural performance, elastic modulus and fracture property were tested in this study. PVA fiber content varies from 0 to 1.2%. Nano-SiO2 content is 0 and 1%. Adaptive neuro-fuzzy interfacial systems (ANFIS) method was used to establish the artificial intelligence (AI) model to predict the fracture parameters of geopolymer/alkali-activated mortars. The inputs of ANFIS models include PVA fiber content, nano-SiO2 content, compressive strength, flexural strength, elastic modulus, critical crack mouth opening displacement, crack load and peak load. The outputs of ANFIS model include critical effective crack length, initiation fracture toughness, unstable fracture toughness, and fracture energy. Experiment results showed that PVA fiber addition enhanced the mechanical properties especially the compressive strength and fracture performance, but decreased the workability. 0.8%–1.0% was considered as the optimal content of PVA fiber. Addition of 1% nano-SiO2 shows a slight improvement on both workability and mechanical properties of the mortar no matter how much fiber is added. Based on the ANFIS algorithm and 42 sets of experimental data, the trained models were proved to have high accuracy with root mean square error (RMSE) under 0.15, mean absolute error (MAE) under 0.01, and coefficient of determination (R2) over 0.85. The ANFIS model established in this study combined the fracture properties with the basic mechanical properties of geopolymer/alkali-activated composites, which can provide a new method to assess the fracture performance of geopolymer/alkali-activated mortars modified with PVA fiber and nano-SiO2 in the future.

Fracture of rocks in the mountains of Southeast Tibet under hydrothermal conditions at different elevations

Significant changes in the hydrothermal conditions in the mountains of Southeast Tibet result in frequent propagation of cracks and disintegration of rock masses. The mechanism that drives this fracturing process might vary considerably depending on elevation. In this work, we employed computational fracture mechanics to study three different fracture mechanisms in which ice or water drives crack propagation. These case studies were corroborated by field observations at low, intermediate, and high elevations. We employed a novel extended finite element method (XFEM), which could be used to propagate cracks without remeshing, to study the effects of the driving forces, crack geometry, and characteristics of perilous rocks. It was found that stress intensity factors induced by freezing of water or by thermal expansion of ice were much higher than induced by hydrostatic pressure, and they resulted in smaller critical crack lengths and tinier collapses at intermediate or high elevations. Moreover, the effects of crack inclination and propagation could have considerable impact on rock collapse. In particular, long cracks with large outward inclination located near the free surface of perilous rocks would tend to fracture easily.

K-S Test for Crack Increment in Probabilistic Fracture Mechanics Analysis

Crack increment is a phenomenon in fracture mechanics. It is occurred due to the stress concentration at the imperfection material. Thus, it leads a crack to growth. Then, the crack will reach to a critical crack length before catastrophic failure could occur. Before the catastrophic failure occur, the cracked structure can be fully utilised until the crack reach to the critical crack length. Thus, it is crucial to investigate the behaviour of the crack increment in fracture mechanics. The main purpose of this paper is to model the crack increment in fracture mechanics analysis via Kolmogorov-Smirnov test. The modelling requires a collection of crack data through experimental work. Then, the data was evaluated based on Kolmogorov-Smirnov test. The results show that the crack increment can be modelled as a Gaussian distribution.

Prediction of Crack Propagation Rate and Stress Intensity Factor of Fatigue and Welded Specimen with a Two-Dimensional Finite Element Method

This paper presents the fundamental investigation on crack propagation rate (CPR) and Stress Intensity Factor (SIF) for a typical fatigue and welded specimens which are Compact Tension (CT) and Single Edge Notch Tension (SENT) as well as Butt and longitudinal T-joint. The material data of austenitic stainless steel SS316L was used to observe crack propagation rate with different initial crack length and different tensile load was used for the fracture mechanics investigation. The geometry of the specimens was modelled by using open source software CASCA while Franc 2D was used for post processing based on Paris Erdogan Law with different crack increment steps. The analysis of crack propagation using fracture mechanics technique requires an accurate calculation of the stress intensity factor SIF and comparison of the critical strength of the material (KIC) was used to determine the critical crack length of the specimens. it can be concluded that open source finite element method software can be used for predicting of fatigue life on simplified geometry.

An experimental investigation on FPZ evolution of concrete at different low temperatures by means of 3D-DIC

The three-point bending tests of concrete specimens at different temperature levels (20 ℃, 0 ℃, −20 ℃, and −40 ℃) were performed using a low-temperature fracture test system. The 3D digital image correlation (3D-DIC) technique was employed to measure the surface deformations of the beams during fracture process. Combined with the displacement fields obtained from 3D-DIC, the crack propagation lengths and crack widths at different loading points were determined, providing information for the fracture process zone (FPZ) evolution in concrete at different temperatures. The results revealed that temperature has significant effect on the crack propagation, i.e. the average FPZ length in the later stage of unloading and the critical crack length ac decrease with decreasing temperature. In addition, the FPZ length for specimens at 0 ℃, −20 ℃ and −40 ℃ decreases slowly in the initial stage and then decreases significantly when the crack extends to the specimen boundary.

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.

Fundamental criterion Ktrans for failure analysis of hydrogen-assisted cracks in notched specimens of pure Ni

The effects of short notches on crack initiation and extension were studied under electrochemical hydrogen charging in pure nickel. In the hydrogen-charged smooth specimen, multiple cracks were initiated on grain boundaries after significant plastic deformation and were subsequently arrested by crack blunting in the interior of neighboring grains. With the assistance of sub-cracks on specimen surface, quasi-cleavage crack propagation occurred soon after, causing the final failure. The introduction of a notch did not change the crack initiation site (grain boundary). However, crack propagation exhibited significant initial notch-length dependence. A 2.5 mm notch caused quasi-cleavage crack propagation without sub-critical cracks (intergranular cracks) initiation and growth, because the notch root acted as a strongly preferential site for crack extension. However, with a smaller notch, sub-critical cracks initiation and growth were necessary to extend intergranular fracture depth and reach a critical crack length to supply adequate plasticity. This plasticity could not be met in the initial stage from the notch root with hydrogen charging. The relation between maximum remote stress and critical crack length among different notch lengths was shown to be a geometry-independent parameter of pure nickel, which can predict tensile strength under various notch configurations.