Model For Crack Arrest Research Articles

A two-curve model for crack arrest prediction of high-grade pipeline based on Crack Tip Opening Angle

The core of arrest control for natural gas pipelines is the prediction of crack arrest toughness. Relevant studies have shown that the Battelle two-curve model (BTCM) which is based on Charpy impact toughness is no longer applicable for high-grade pipelines with high strength and toughness. Thus, it is urgent to establish a new prediction model for crack arrest based on a more appropriate fracture parameter. In view of this, the Crack Tip Opening Angle (CTOA), which has a wide application prospect, is selected as the arrest toughness parameter to modify the BTCM. Firstly, based on the previous work, an analytical model of crack arrest pressure based on CTOAC is established with the energy balance theory. Then, the relationship between crack tip pressure and crack velocity under different conditions is explored with the help of the numerical simulation method for dynamic crack propagation in pipelines. Finally, based on the above results, the BTCM is modified to form a novel two-curve model taking CTOAC as the parameter to characterize the crack arrest toughness. The results for the proposed CTOA-based two-curve method (CBTCM) are discussed and compared with those obtained by well-established methods such as BTCM, HLP and HLP-Sumitomo models. The work in this paper provides a new reference for fracture control of the high-grade pipeline.

Mathematical model for crack arrest of an infinite plate weakened by a finite and two semi-infinite cracks

The problem of an unbounded plate weakened by three quasi-static coplanar and collinear straight cracks: two semi-infinite cracks and a finite crack situated symmetrically between two semi-infinite cracks, is investigated. The plate is subjected to uniform unidirectional in-plane tension at infinite boundary. Developed plastic zones are arrested by distributing cohesive yield point stress over their rims. The solution is obtained using complex variable technique. Closed form analytic expressions are derived for load bearing capacity and crack-tip-opening displacement (CTOD). A case study is presented for CTOD and load bearing capacity versus crack length, plastic zone length and inter-crack distance etc. Results are presented graphically and analyzed.

Mathematical model for crack arrest of a transversely cracked piezoelectromagnetic strip – Part I

A magnetic, electric and mechanical yield model is proposed for a cracked piezoelectromagnetic ceramic narrow strip. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic loads, consequently the crack opens in self-similar fashion forming a magnetic, a saturation and a slide zone ahead each tip. These in turn are arrested by prescribing a magnetic, electric and mechanical load, respectively. Employing Fourier integral transform the problem reduces to the solution of three dual integral equations. The solution of dual integral equations is then expressed in terms of Fredholm integral equation of second kind. Expressions are derived for yield induction zone, slide-yield zone and saturation zone lengths, energy release rate. A case study is carried for BaTiO3–CoFe2O4 and results are presented graphically. It is shown that proposed model is capable of crack opening arrest under small-scale-yielding.

Crack Arrest Model for Transversely Cracked Piezoceramic Strip under Mechanical and Electrical Yielding

Crack arrest model is proposed for a poled piezoceramic strip under four different mechanical and electrical yield conditions. It is assumed that developed slide zone is bigger than that of developed saturation zone. Expressions are derived for energy release rate and load required to arrest developed zones. Results obtained are applied to predict the crack arrest of strip made of PZT-4, PZT-5H and BaTiO3. Results are presented graphically.

Dynamic modeling of cleavage crack propagation and arrest with a local approach

The assessment of reactor pressure vessels, usually based on crack initiation, could be completed using the crack arrest concept. The methodology classically recommended in safety codes and standards does not take into account the dynamic effects which are very important in crack arrest phenomena. To overcome this difficulty, a local crack arrest criterion has been recently proposed by some of the authors, for cleavage crack propagating in a low alloy bainitic steel: the crack propagates since the largest principal stress reaches a critical stress that depends on temperature. This study deals with the modeling of crack arrest experiments performed on A533-C1.B type steel with this criterion. Crack arrest was obtained on CT under isothermal conditions at –150°C and –125°C. The crack arrest criterion was identified with 2D computations. The application of this criterion shows that the crack propagation versus time leads to a good prediction of the crack speed and of the crack length.

The Dugdale solution for two unequal straight cracks weakening in an infinite plate

A crack arrest model is proposed for an infinite elastic perfectlyplastic plate weakened by two unequal, quasi-static, collinear straight cracks. The Dugdale model solution is obtained for the above problem when the developed plastic zones are subjected to normal cohesive quadratically varying yield point stress. Employing complex variable technique and the superposition principle the desired solution is obtained. A qualitative study of load required to arrest the plastic zones opening with respect to affecting parameters viz. inter-crack distance, plastic zone and crack length is carried out. The results obtained are presented graphically.

Crack arrest model for a piezoelectric plate — A generalised Dugdale model

The constant search for new materials has provided impetus to research in piezoelectric materials. An anti-plane problem for a cracked unbounded two-dimensional poled piezoelectric plate has been investigated. The crack rims open on account of shear mechanical forces applied at the remote boundary and in-plane electric displacement field prescribed at the infinite boundary. Thus the crack yields both mechanically and electrically. Consequently, a plastic zone and a saturation zone protrude ahead of each tip of the crack. These developed zones are in turn closed by applying yield point shear stress at the rims of plastic zone and normal closing saturation limit displacement on the rims of saturation zones. Two cases are investigated when (i) the developed saturation zone length exceeds that of the developed plastic zone, and (ii) saturation zone length is smaller than that of the plastic zone. Fourier integral transform method is used in each case to obtain the length of plastic zone and saturation zone. Closed form analytic expressions are obtained in each case. Crack opening displacement and potential drop across the rims of the crack are also obtained. The effect of mechanical loads on crack closure in the presence of electric field is investigated and vice-versa. Also energy release rate expressions are obtained for both the cases.

Solution for a cracked piezoelectric plate subjected to variable load on plastic zones under mode-I deformation

A model for crack arrest is proposed for a poled piezoelectric plate weakened by a finite, hairline and straight crack. Remotely applied uniform, constant tension and electric field acting in the direction perpendicular to the rims of the crack opens the crack rims in mode-I type deformations. The plate is assumed to be mechanically brittle and electrically ductile. Under this assumption the plate will encounter mechanical singularity first. In this situation a plastic zone protrudes ahead of each tip of the crack. To arrest the crack from further opening, the rims of the developed plastic zones are subjected to normal cohesive quadratically varying yield point stress. Two cases investigated are: (i) when crack lie perpendicular to poling axis and (ii) crack lie parallel to poling axis. Each case is solved employing complex variable technique. Closed form analytic expressions are obtained for complex potentials, determining elastic and electric fields in the plate. A non-linear transcendental equation is obtained to determine plastic zone length, using Dugdale hypothesis.

Theoretical modeling of crack arrest by inserting interference fit fasteners

The repair technology under consideration involves drilling a number of holes along a crack in a metal part and inserting fasteners (bolts, rivets, or pins) into the holes with a predetermined interference fit. A fracture mechanics-based model is proposed to study the decrease in the crack growth rate after repair. A parametric analysis is performed to discover the effect of geometry and materials on crack retardation. Elastic-plastic contact stress distributions in the specimens during cyclic loading are determined by the finite element method. The results show that a significant enhancement of fatigue life until crack re-initiation can be achieved through an optimal set of parameters: number of fasteners, their material, and interference fit. The model is validated using a comparison of fatigue tests of the specimens.

On crack arrest in ceramic / metal assemblies

Brittle parts of ceramic/metal assemblies are subjected to a residual stress field generated by the fabrication. During that process, cracks are initiated and the key question is whether they propagate through the whole brittle part. The use of classical probabilistic fracture models applied to the ceramic (i.e., based on a weakest link hypothesis), allow one to conclude that cracks are likely to initiate after the manufacturing process. Consequently, a crack arrest model is proposed, based on a random toughness distribution. Applied to micro-hardness experiments, the statistical parameters are identified, and the predictive capacity of the model is analyzed. The model is then used to study the reliability of ceramic/metal assemblies during the fabrication stage.

Crack arrest model for a plate weakened by internal and external cracks: A modified dugdale approach

A modified Dugdale model solution is obtained for an elastic-perfectly-plastic plate weakened by one internal and two external straight collinear hairline cracks. The tension applied to the infinite boundary of the plate opens the rims of cracks with forming a plastic zone ahead of each tip of the internal crack and also at each finitely distant tip of the two external cracks. The developed plastic zones are closed by normal cohesive linearly varying yield-point stress distributions applied to their rims. The problem is solved using the complex-variable technique. A case study is carried out to find the load required to prevent the cracks from further growing with respect to affecting parameters. The results obtained are reported graphically and analyzed.

Decrepitation and crack healing of fluid inclusions in San Carlos olivine

Fluid inclusions break, or decrepitate, when the fluid pressure exceeds the least principal lithostatic stress by a critical amount. After decrepitation, excess fluid pressure is relaxed, resulting in crack arrest; subsequently, crack healing may occur. Existing models of decrepitation do not adequately explain several experimentally observed phenomena. We developed a linear elastic fracture mechanics model to analyze new data on decrepitation and crack arrest in San Carlos olivine, compared the model with previous fluid inclusion investigations, and used it to interpret some natural decrepitation microstructures. The common experimental observation that smaller inclusions may sustain higher internal fluid pressures without decrepitating may be rationalized by assuming that flaws associated with the inclusion scale with the inclusion size. According to the model, the length of the crack formed by decrepitation depends on the lithostatic pressure at the initiation of cracking, the initial sizes of the flaw and the inclusion, and the critical stress intensity factor. Further experiments show that microcracks in San Carlos olivine heal within several days at 1280 to 1400°C; healing rates depend on the crack geometry, temperature, and chemistry of the buffering gas. The regression distance of the crack tip during healing can be related to time through a power law with exponent n = 0.6. Chemical changes which become apparent after extremely long heat‐treatments significantly affect the healing rates. Many of the inclusions in the San Carlos xenoliths stretched, decrepitated, and finally healed during uplift. The crack arrest model indicates that completely healed cracks had an initial fluid pressure of the order of 1 GPa. Using the crack arrest model and the healing kinetics, we estimate the ascent rate of these xenoliths to be between 0.001 and 0.1 m/s.

An inclusion model for crack arrest in a composite reinforced by sliding fibers

The inclusion model of Mori and Mura for crack arrest in fiber reinforced materials is extended. The analysis is restricted to short fibers. The sliding of fibers is allowed along fiber-matrix interfaces. Analytical expressions for energy release rate and extra energy dissipation during crack extension are obtained. Sliding fibers result in a larger energy release rate than non-sliding and perfectly bridging fibers. However, the energy dissipation accompanied by sliding offers additional resistance to the extension of a crack. Fibers of smaller radius decrease the energy release rate and raise the energy dissipation more efficiently.

An inclusion model for crack arrest in fiber reinforced materials

A tensile crack bridged by strong and tough fibers is modeled in such a manner that it can be analyzed based on concepts from the mechanics of inclusion. Analytical expressions for the energy release rate, stress intensity factor and crack opening are derived. It is shown that the presence of the supporting fibers reduces the values of those quantities which saturate at a certain level determined by the size and spacing of the fibers.

A combined ligament rupture-cleavage model for crack arrest in thick-section steel plate

In the transition regime, plane strain crack propagation in ferritic steels proceeds by a combination of cleavage and ductile rupture processes, the latter being confined to ligaments that are parallel to the direction of macroscopic crack propagation. The paper models crack propagation, and particularly the limiting case of crack arrest, when fracture proceeds via these two modes. An important theoretical result is that, because of the unfractured ligaments which remain behind the crack tip, the plastic zone size is much smaller than when it is predicted for the operative K values and assuming that there are no ligaments. Linear elastic fracture mechanics procedures may therefore be used to describe the arrest phenomenon at K values that exceed the normally accepted limits for their validity. The theoretical results are also used to speculate upon the effect of neutron irradiation on the arrest toughness.