International Science Index
Simplified Stress Gradient Method for Stress-Intensity Factor Determination
Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.
Mixed Mode Fracture Analyses Using Finite Element Method of Edge Cracked Heavy Spinning Annulus Pulley
Rotating disk is one of the most indispensable parts of a rotating machine. Rotating disk has found many applications in the diverging field of science and technology. In this paper, we have taken into consideration the problem of a heavy spinning disk mounted on a rotor system acted upon by boundary traction. Finite element modelling is used at various loading condition to determine the mixed mode stress intensity factors. The effect of combined shear and normal traction on the boundary is incorporated in the analysis under the action of gravity. The variation near the crack tip is characterized in terms of the stress intensity factor (SIF) with an aim to find the SIF for a wide range of parameters. The results of the finite element analyses carried out on the compressed disk of a belt pulley arrangement using fracture mechanics concepts are shown. A total of hundred cases of the problem are solved for each of the variations in loading arc parameter and crack orientation using finite element models of the disc under compression. All models were prepared and analyzed for the uncracked disk, disk with a single crack at different orientation emanating from shaft hole as well as for a disc with pair of cracks emerging from the same center hole. Curves are plotted for various loading conditions. Finally, crack propagation paths are determined using kink angle concepts.
Study on Sharp V-Notch Problem under Dynamic Loading Condition Using Symplectic Analytical Singular Element
V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.
Effect of Inclusions on the Shape and Size of Crack Tip Plastic Zones by Element Free Galerkin Method
The present study investigates the effect of inclusions on the shape and size of crack tip plastic zones in engineering materials subjected to static loads by employing the element free Galerkin method (EFGM). The modeling of the discontinuities produced by cracks and inclusions becomes independent of the grid chosen for analysis. The standard displacement approximation is modified by adding additional enrichment functions, which introduce the effects of different discontinuities into the formulation. The level set method has been used to represent different discontinuities present in the domain. The effect of inclusions on the extent of crack tip plastic zones is investigated by solving some numerical problems by the EFGM.
Thermal Fracture Analysis of Fibrous Composites with Variable Fiber Spacing Using Jk-Integral
In this study, fracture analysis of a fibrous composite
laminate with variable fiber spacing is carried out using Jk-integral
method. The laminate is assumed to be under thermal loading.
Jk-integral is formulated by using the constitutive relations of plane
orthotropic thermoelasticity. Developed domain independent form
of the Jk-integral is then integrated into the general purpose finite
element analysis software ANSYS. Numerical results are generated
so as to assess the influence of variable fiber spacing on mode I
and II stress intensity factors, energy release rate, and T-stress. For
verification, some of the results are compared to those obtained
using displacement correlation technique (DCT).
Estimation of Stress Intensity Factors from Near Crack Tip Field
All current experimental methods for determination of
stress intensity factors are based on the assumption that the state of
stress near the crack tip is plane stress. Therefore, these methods rely
on strain and displacement measurements made outside the near
crack tip region affected by the three-dimensional effects or by
process zone. In this paper, we develop and validate an experimental
procedure for the evaluation of stress intensity factors from the
measurements of the out-of-plane displacements in the surface area
controlled by 3D effects. The evaluation of stress intensity factors is
possible when the process zone is sufficiently small, and the
displacement field generated by the 3D effects is fully encapsulated
by K-dominance region.
Numerical Study of Fatigue Crack Growth at a Web Stiffener of Ship Structural Details
It is necessary to manage the fatigue crack growth (FCG) once those cracks are detected during in-service inspections. In this paper, a simulation program (FCG-System) is developed utilizing the commercial software ABAQUS with its object-oriented programming interface to simulate the fatigue crack path and to compute the corresponding fatigue life. In order to apply FCG-System in large-scale marine structures, the substructure modeling technique is integrated in the system under the consideration of structural details and load shedding during crack growth. Based on the nodal forces and nodal displacements obtained from finite element analysis, a formula for shell elements to compute stress intensity factors is proposed in the view of virtual crack closure technique. The cracks initiating from the intersection of flange and the end of the web-stiffener are investigated for fatigue crack paths and growth lives under water pressure loading and axial force loading, separately. It is found that the FCG-System developed by authors could be an efficient tool to perform fatigue crack growth analysis on marine structures.
Obtain the Stress Intensity Factor (SIF) in a Medium Containing a Penny-Shaped Crack by the Ritz Method
In the crack growth analysis, the Stress Intensity
Factor (SIF) is a fundamental prerequisite. In the present study, the
mode I stress intensity factor (SIF) of three-dimensional penny-
Shaped crack is obtained in an isotropic elastic cylindrical medium
with arbitrary dimensions under arbitrary loading at the top of the
cylinder, by the semi-analytical method based on the Rayleigh-Ritz
method. This method that is based on minimizing the potential
energy amount of the whole of the system, gives a very close results
to the previous studies. Defining the displacements (elastic fields) by
hypothetical functions in a defined coordinate system is the base of
this research. So for creating the singularity conditions at the tip of
the crack the appropriate terms should be found.
Stress Intensity Factor for Dynamic Cracking of Composite Material by X-FEM Method
The work involves develops attended by a numerical
execution of the eXtend Finite Element Method premises a
measurement by the fracture process cracked so many cracked plates
an application will be processed for the calculation of the stress
intensity factor SIF. In the first we give in statically part the
distribution of stress, displacement field and strain of composite plate
in two cases uncrack/edge crack, also in dynamical part the first six
modes shape. Secondly, we calculate Stress Intensity Factor SIF for
different orientation angle θ of central crack with length (2a=0.4mm)
in plan strain condition, KI and KII are obtained for mode I and mode
II respectively using X-FEM method. Finally from crack inclined
involving mixed modes results, the comparison we chose dangerous
inclination and the best crack angle when K is minimal.
A Study of Shear Stress Intensity Factor of PP and HDPE by a Modified Experimental Method together with FEM
Shear testing is one of the most complex testing areas where available methods and specimen geometries are different from each other. Therefore, a modified shear test specimen (MSTS) combining the simple uniaxial test with a zone of interest (ZOI) is tested which gives almost the pure shear. In this study, material parameters of polypropylene (PP) and high density polyethylene (HDPE) are first measured by tensile tests with a dogbone shaped specimen. These parameters are then used as an input for the finite element analysis. Secondly, a specially designed specimen (MSTS) is used to perform the shear stress tests in a tensile testing machine to get the results in terms of forces and extension, crack initiation etc. Scanning Electron Microscopy (SEM) is also performed on the shear fracture surface to find material behavior. These experiments are then simulated by finite element method and compared with the experimental results in order to confirm the simulation model. Shear stress state is inspected to find the usability of the proposed shear specimen. Finally, a geometry correction factor can be established for these two materials in this specific loading and geometry with notch using Linear Elastic Fracture Mechanics (LEFM). By these results, strain energy of shear failure and stress intensity factor (SIF) of shear of these two polymers are discussed in the special application of the screw cap opening of the medical or food packages with a temper evidence safety solution.
An Adaptive Dynamic Fracture for 3D Fatigue Crack Growth Using X-FEM
In recent years, a new numerical method has been
developed, the extended finite element method (X-FEM). The
objective of this work is to exploit the (X-FEM) for the treatment of
the fracture mechanics problems on 3D geometries, where we
showed the ability of this method to simulate the fatigue crack
growth into two cases: edge and central crack. In the results we
compared the six first natural frequencies of mode shapes uncracking
with the cracking initiation in the structure, and showed the stress
intensity factor (SIF) evolution function as crack size propagation
into structure, the analytical validation of (SIF) is presented. For to
evidence the aspects of this method, all result is compared between
FEA and X-FEM.
Stress Intensity Factors for Plates with Collinear and Non-Aligned Straight Cracks
Multi-site damage (MSD) has been a challenge to
aircraft, civil and power plant structures. In real life components are subjected to cracking at many vulnerable locations such as the bolt
holes. However, we do not consider for the presence of multiple cracks. Unlike components with a single crack, these components are
difficult to predict. When two cracks approach one another, their
stress fields influence each other and produce enhancing or shielding effect depending on the position of the cracks. In the present study,
numerical studies on fracture analysis have been conducted by using
the developed code based on the modified virtual crack closure integral (MVCCI) technique and finite element analysis (FEA) software ABAQUS for computing SIF of plates with multiple cracks.
Various parametric studies have been carried out and the results have
been compared with literature where ever available and also with the solution, obtained by using ABAQUS. By conducting extensive
numerical studies expressions for SIF have been obtained for collinear cracks and non-aligned cracks.
Numerical Solution for Elliptical Crack with Developing Cusps Subject to Shear Loading
This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.
Probe of Crack Initiate at the Toe of Concrete Gravity Dam using Numerical Analysis
In this survey the process of crack propagation at the
toe of concrete gravity dam is investigated by applying principals
and criteria of linear elastic fracture mechanic. Simulating process of
earthquake conditions for three models of dam with different
geometrical condition, in empty reservoir under plain stress is
calculated through special fracture mechanic software FRANNC2D
 for determining fracture mechanic criteria. The outcomes showed
that in spite of the primary expectations, the simultaneous existence
of fillet in both toe and heel area (model 3), the rate of maximum
principal stress has not been decreased; however, even the maximum
principal stress has increased, so it caused stress intensity factors
increase which is undesirable. On the other hand, the dam with heel
fillet has shown the best attitude and it is because of items like
decreasing the rates of maximum and minimum principal stresses and
also is related to decreasing the rates of stress intensity factors for 1st
& 2nd modes of the model.
Effect of Welding Processes on Fatigue Properties of Ti-6Al-4V Alloy Joints
This paper reports the fatigue crack growth behaviour
of gas tungsten arc, electron beam and laser beam welded Ti-6Al-4V
titanium alloy. Centre cracked tensile specimens were prepared to
evaluate the fatigue crack growth behaviour. A 100kN servo
hydraulic controlled fatigue testing machine was used under constant
amplitude uniaxial tensile load (stress ratio of 0.1 and frequency of
10 Hz). Crack growth curves were plotted and crack growth
parameters (exponent and intercept) were evaluated. Critical and
threshold stress intensity factor ranges were also evaluated. Fatigue
crack growth behaviour of welds was correlated with mechanical
properties and microstructural characteristics of welds. Of the three
joints, the joint fabricated by laser beam welding exhibited higher
fatigue crack growth resistance due to the presence of fine lamellar
microstructure in the weld metal.
Hydrogen Embrittlement in a Coupled Mass Diffusion with Stress near a Blunting Crack Tip for AISI 4135 Pressure Vessel
In pressure vessels contain hydrogen, the role of
hydrogen will be important because of hydrogen cracking problem. It
is difficult to predict what is happened in metallurgical field spite of a
lot of studies have been searched. The main role in controlling the
mass diffusion as driving force is related to stress. In this study, finite
element analysis is implemented to estimate material-s behavior
associated with hydrogen embrittlement. For this purpose, one model
of a pressure vessel is introduced that it has definite boundary and
initial conditions. In fact, finite element is employed to solve the
sequentially coupled mass diffusion with stress near a crack front in a
pressure vessel. Modeling simulation intergrarnular fracture of AISI
4135 steel due to hydrogen is investigated. So, distribution of
hydrogen and stress are obtained and they indicate that their
maximum amounts occur near the crack front. This phenomenon is
happened exactly the region between elastic and plastic field.
Therefore, hydrogen is highly mobile and can diffuse through crystal
lattice so that this zone is potential to trap high volume of hydrogen.
Consequently, crack growth and fast fracture will be happened.
The Investigation of Crack's Parameters on the V-Notch using Photoelasticity Method
The V-notches are most possible case for initiation of cracks in parts. The specifications of cracks on the tip of the notch will be influenced via opening angle, tip radius and depth of V-notch. In this study, the effects of V-notch-s opening angle on stress intensity factor and T-stress of crack on the notch has been investigated. The experiment has been done in different opening angles and various crack length in mode (I) loading using Photoelasticity method. The results illustrate that while angle increases in constant crack-s length, SIF and T-stress will decrease. Beside, the effect of V-notch angle in short crack is more than long crack. These V-notch affects are negligible by increasing the length of crack, and the crack-s behavior can be considered as a single-edge crack specimen. Finally, the results have been evaluated with numerical finite element analysis and good agreement was obvious.
Method of Moments for Analysis of Multiple Crack Interaction in an Isotropic Elastic Solid
The problem of N cracks interaction in an isotropic
elastic solid is decomposed into a subproblem of a homogeneous solid
without crack and N subproblems with each having a single crack
subjected to unknown tractions on the two crack faces. The unknown
tractions, namely pseudo tractions on each crack are expanded into
polynomials with unknown coefficients, which have to be determined
by the consistency condition, i.e. by the equivalence of the original
multiple cracks interaction problem and the superposition of the N+1
subproblems. In this paper, Kachanov-s approach of average tractions
is extended into the method of moments to approximately impose the
consistence condition. Hence Kachanov-s method can be viewed as
the zero-order method of moments. Numerical results of the stress
intensity factors are presented for interactions of two collinear cracks,
three collinear cracks, two parallel cracks, and three parallel cracks.
As the order of moment increases, the accuracy of the method of
Prediction of Fatigue Crack Growth of Aeronautical Aluminum Alloy
In this paper fatigue crack growth behavior of
aeronautical aluminum alloy 2024 T351 was studied. Effects of
various loading and geometrical parameters are studied such as stress
ratio, amplitude loading, etc. The fatigue crack growth with constant
amplitude is studied using the AFGROW code when NASGRO
model is used. The effect of the stress ratio is highlighted, where one
notices a shift of the curves of crack growth. The comparative study
between two orientations L-T and T-L on fatigue behavior are
presented and shows the variation on the fatigue life. L-T orientation
presents a good fatigue crack growth resistance. Effects of crack
closure are shown in Paris domain and that no crack closure
phenomenons are present at high stress intensity factor.
Using Stresses Obtained from a Low Detailed FE Model and Located at a Reference Point to Quickly Calculate the Free-edge Stress Intensity Factors of Bonded Joints
The present study focuses on methods allowing a convenient and quick calculation of the SIFs in order to predict the static adhesive strength of bonded joints. A new SIF calculation method is proposed, based on the stresses obtained from a FE model at a reference point located in the adhesive layer at equal distance of the free-edge and of the two interfaces. It is shown that, even limiting ourselves to the two main modes, i.e. the opening and the shearing modes, and using the values of the stresses resulting from a low detailed FE model, an efficient calculation of the peeling stress at adhesive-substrate corners can be obtained by this way. The proposed method is interesting in that it can be the basis of a prediction tool that will allow the designer to quickly evaluate the SIFs characterizing a particular application without developing a detailed analysis.
Fatigue Analysis of Crack Growing Rate and Stress Intensity Factor for Stress Corrosion Cracking in a Pipeline System
Environment-assisted cracking (EAC) is one of the most serious causes of structural failure over a broad range of industrial applications including offshore structures. In EAC condition there is not a definite relation such as Paris equation in Linear Elastic Fracture Mechanics (LEFM). According to studying and searching a lot what the researchers said either a material has contact with hydrogen or any other corrosive environment, phenomenon of electrical and chemical reactions of material with its environment will be happened. In the literature, there are many different works to consider fatigue crack growing and solve it but they are experimental works. Thus, in this paper, authors have an aim to evaluate mathematically the pervious works in LEFM. Obviously, if an environment is more sour and corrosive, the changes of stress intensity factor is more and the calculation of stress intensity factor is difficult. A mathematical relation to deal with the stress intensity factor during the diffusion of sour environment especially hydrogen in a marine pipeline is presented. By using this relation having and some experimental relation an analytical formulation will be presented which enables the fatigue crack growth and critical crack length under cyclic loading to be predicted. In addition, we can calculate KSCC and stress intensity factor in the pipeline caused by EAC.
The Relationship between Fugacity and Stress Intensity Factor for Corrosive Environment in Presence of Hydrogen Embrittlement
Hydrogen diffusion is the main problem for corrosion fatigue in corrosive environment. In order to analyze the phenomenon, it is needed to understand their behaviors specially the hydrogen behavior during the diffusion. So, Hydrogen embrittlement and prediction its behavior as a main corrosive part of the fractions, needed to solve combinations of different equations mathematically. The main point to obtain the equation, having knowledge about the source of causing diffusion and running the atoms into materials, called driving force. This is produced by either gradient of electrical or chemical potential. In this work, we consider the gradient of chemical potential to obtain the property equation. In diffusion of atoms, some of them may be trapped but, it could be ignorable in some conditions. According to the phenomenon of hydrogen embrittlement, the thermodynamic and chemical properties of hydrogen are considered to justify and relate them to fracture mechanics. It is very important to get a stress intensity factor by using fugacity as a property of hydrogen or other gases. Although, the diffusive behavior and embrittlement event are common and the same for other gases but, for making it more clear, we describe it for hydrogen. This considering on the definite gas and describing it helps us to understand better the importance of this relation.
Study on Damage Tolerance Behavior of Integrally Stiffened Panel and Conventional Stiffened Panel
The damage tolerance behavior of integrally and
conventional stiffened panel is investigated based on the fracture
mechanics and finite element analysis. The load bearing capability
and crack growth characteristic of both types of the stiffened panels
having same configuration subjected to distributed tensile load is
examined in this paper. A fourteen-stringer stiffened panel is
analyzed for a central skin crack propagating towards the adjacent
stringers. Stress intensity factors and fatigue crack propagation rates
of both types of the stiffened panels are then compared. The analysis
results show that integral stiffening causes higher stress intensity
factor than conventional stiffened panel as the crack tip passes
through the stringer and the integrally stiffened panel has less load
bearing capability than the riveted stiffened panel.
Geometry Calibration Factors of Modified Arcan Fracture Test for Welded Joint
In this study the mixed mode fracture mechanics
parameters were investigated for high tensile steel butt welded joint
based on modified Arcan test and finite element analysis was used to
evaluate the effect of crack length on fracture criterion. The nondimensional
stress intensity factors, strain energy release rates and Jintegral
energy on crack tip were obtained for various in-plane
loading combinations on Arcan specimen starting from pure mode-I
to pure mode-II loading conditions. The specimen and apparatus were
modeled by finite element method and analyzed under various
loading angles (between 0 to 90 degrees with 15 degree interval) to
simulate the pure mode-I, II and mixed mode fracture. Since the
analytical results are independent from elasticity modules for
isotropic materials, therefore the results in elastic fields can be used
for Arcan specimens. The main objective of this study was to
evaluate the geometric calibration factors for modified Arcan test
specimen in order to obtain fracture toughness under mixed mode
Numerical Investigation of Delamination in Carbon-Epoxy Composite using Arcan Specimen
In this paper delamination phenomenon in
Carbon-Epoxy laminated composite material is investigated
numerically. Arcan apparatus and specimen is modeled in ABAQUS
finite element software for different loading conditions and crack
geometries. The influence of variation of crack geometry on
interlaminar fracture stress intensity factor and energy release rate for
various mixed mode ratios and pure mode I and II was studied. Also,
correction factors for this specimen for different crack length ratios
were calculated. The finite element results indicate that for loading
angles close to pure mode-II loading, a high ratio of mode-II to
mode-I fracture is dominant and there is an opposite trend for loading
angles close to pure mode-I loading. It confirms that by varying the
loading angle of Arcan specimen pure mode-I, pure mode-II and a
wide range of mixed-mode loading conditions can be created and
tested. Also, numerical results confirm that the increase of the mode-
II loading contribution leads to an increase of fracture resistance in
the CF/PEI composite (i.e., a reduction in the total strain energy
release rate) and the increase of the crack length leads to a reduction
of interlaminar fracture resistance in the CF/PEI composite (i.e., an
increase in the total interlaminar strain energy release rate).
Evaluation of Mixed-Mode Stress Intensity Factor by Digital Image Correlation and Intelligent Hybrid Method
Displacement measurement was conducted on compact normal and shear specimens made of acrylic homogeneous material subjected to mixed-mode loading by digital image correlation. The intelligent hybrid method proposed by Nishioka et al. was applied to the stress-strain analysis near the crack tip. The accuracy of stress-intensity factor at the free surface was discussed from the viewpoint of both the experiment and 3-D finite element analysis. The surface images before and after deformation were taken by a CMOS camera, and we developed the system which enabled the real time stress analysis based on digital image correlation and inverse problem analysis. The great portion of processing time of this system was spent on displacement analysis. Then, we tried improvement in speed of this portion. In the case of cracked body, it is also possible to evaluate fracture mechanics parameters such as the J integral, the strain energy release rate, and the stress-intensity factor of mixed-mode. The 9-points elliptic paraboloid approximation could not analyze the displacement of submicron order with high accuracy. The analysis accuracy of displacement was improved considerably by introducing the Newton-Raphson method in consideration of deformation of a subset. The stress-intensity factor was evaluated with high accuracy of less than 1% of the error.
2D Fracture Analysis of the First Compression Piston Ring
The incidence of mechanical fracture of an
automobile piston rings prompted development of fracture analysis
method on this case. The three rings (two compression rings and one
oil ring) were smashed into several parts during the power-test (after
manufacturing the engine) causing piston and liner to be damaged.
The radial and oblique cracking happened on the failed piston rings.
The aim of the fracture mechanics simulations presented in this paper
was the calculation of particular effective fracture mechanics
parameters, such as J-integrals and stress intensity factors. Crack
propagation angles were calculated as well. Two-dimensional
fracture analysis of the first compression ring has been developed in
this paper using ABAQUS CAE6.5-1 software. Moreover, SEM
fractography was developed on fracture surfaces and is discussed in
this paper. Results of numerical calculations constitute the basis for
further research on real object.