A periodic inspection of a reactor pressure vessel in refinery was scheduled. Prior to that inspection, criteria need to be established to determine what flaw indication would be tolerable so that the vessel can safely be put back in to service in a timely manner, or in the worst case, identify what flaw indication would create a very strong case for repair or replacement criteria for the vessel. A flaw tolerance criterion that can be applied to the refinery inspection process was developed for numerous potential flaw locations in this vessel. The finite element alternating method was used to determine the appropriate fracture parameters to assist in this flaw assessment procedure. These computational efforts involved examining the fracture response of the system in preparation for planned inspections. Stress intensity factors were evaluated for a total of ten (10) cracks inserted into the refinery pressure vessel at several locations and crack orientations. Most of the cracks had depth to thickness ratios of 0.25 and a half width 3 times this depth. The crack sizes are chosen based on the assumed maximum initial flaw sizes expected to be found from NDI. The stress intensity factor for residual stress loading was conservatively estimated by placing a unit tensile pressure on the crack face for all 10 cracks. The approximation of crack face pressure loading to simulate residual stress is also shown to be accurate. Therefore, one can estimate the contribution to stress intensity factor by multiplying the residual stress value of K by the estimated residual stress ratio. The final estimate of crack driving force for a crack, K I , is obtained by adding the contributions of the pressure loading with the residual stress contribution. Internal pressure loading of this vessel is the only significant source of loading in this vessel.

The pressure surge in pipes due to change in operating conditions exerts an axial load on elbows proportional to the change in momentum of fluid and unbalanced pressure forces. The response of piping structure to such load needs the full time history analysis in three dimensional spaces which is cumbersome process due to high computing memory requirements and long simulation time. In present work it has been shown that using Rayleigh energy balance for each elbow-load configuration, the system can be reduced to equivalent 1D spring mass system and the response can be estimated by solving 1D equation of motion. Then it has been recommended to simulate the response of each elbow which gives good approximation of dynamic amplification of displacement also called as Dynamic Load Factor (DLF). These dynamic load factors for each elbow can be used for the interaction of forces using static equivalent response in 3D space. This approach is pseudo static equivalent analysis where the load amplifications factors DLF are estimated from the dynamic force profile and system response in one-dimensional space. An algorithm is developed for the above explained process. Most of the engineers are using the DLF = 2 for the load estimation due to absence of method to estimate the dynamic load factor. The approach was proposed by Goodling in 1989 and still widely followed in the industry. The present paper discusses uncertainty and inaccuracy involved in performing approximate analysis and shows the significance and need of performing full force time history analysis. The proposed method shows very good agreement with the time consuming 3D full force time history results. There are also limitations for the proposed method. As the spring mass system is simulated with dimensional reduction to single frequency domain, the pipe supports and guides should be properly placed before applying the present approach. It has been shown that with proper support configuration, this simplified approach yields very good approximation of surge load on pipes with reduced time.

The Bree solution to the problem of a ratcheting cylinder under constant pressure and cyclic thermal load is a fundamental result in nuclear engineering and widely used as the technical basis for the ASME Boiler and Pressure Vessel Code and other design methods. However, because the loading conditions in the Bree problem are difficult to achieve experimentally there have been relatively few works experimentally examining the problem and extending it to other relevant design situations, for example cladded components. In contrast, 2-bar problems are widely studied experimentally and are relatively easy to setup. These 2-bar problems are thought to be representative of Bree-type geometries, but a formal connection has not been demonstrated. This work formally establishes the connection between the Bree cylinder and an n -bar problem — a coupled bar experiment with, in general, more than two bars linked in parallel. The connection suggests that n -bar experiments using a fairly limited number of bars might be an experimentally-accessible setup that better represents ratcheting phenomenon in actual nuclear pressurized components. Such experiments could test surrogate cladded or multi-material components by using bars of different materials. Finally, this work suggests control schemes that yield optimally efficient n -bar experiments — experiments that best replicates a Bree cylinder with a limited number of bars.

The Joukowsky equation has been used as a first approximation for more than a century to estimate water hammer pressure surges. However, this practice may provide incorrect, non-conservative, pressure calculations under several conditions. These conditions are typically described throughout fluid transient text books, but a consolidation of these issues in a brief paper seems warranted to prevent calculation errors in practice and to also provide a brief understanding of the limits and complexities of water hammer equations. To this end, various issues are discussed here that result in the calculation of pressures greater than those predicted by the Joukowsky equation. These conditions include reflected waves at tees, changes in piping diameter, and changes in pipe wall material, as well as frictional effects referred to as line pack, and the effects due to the collapse of vapor pockets. In short, the fundamental goal here is to alert practicing engineers of the cautions that should be applied when using the Joukowsky equation as a first approximation of fluid transient pressures.

Being capable in predicting the removal of material from a surface subjected to the impingements of solid particles within a carrier liquid is of considerable industrial interest. This phenomenon, called impact erosion, is of concern in many applications due to its severe technical and economic consequences. The use of Computational Fluid Dynamics (CFD) techniques for impact erosion prediction is a challenging approach to avoid the cost and complexity of laboratory testing. A well-established methodology exists for CFD-based erosion estimation, consisting in the simulation of the slurry flow by an Eulerian–Lagrangian two-phase model followed by the application of an empirical erosion correlation to estimate the loss of material produced by each particle-wall impact. One of the main assumptions of this approach is that the solids are treated as massive point particles, even if, from a theoretical point of view, this approximation may be too simplistic, as it requires the particle size to be infinitesimal. The objective of the present study was, primarily, to assess how the point–particle treatment of the dispersed phase may affect the accuracy of CFD-based erosion prediction models. Based on these findings, numerical strategies were proposed in order to correct for the induced error without the need of resorting to a fully-resolved description of the slurry flow, which would not be affordable in practical applications due to its excessive computational burden. As a first step, reference was made to the benchmark case of slurry abrasive jet impingement test. The obtained results will open the way for addressing more complex flows in future research.

Shorter development design schedules and increasingly dense product designs create difficult challenges in predicting structural performance of a mainframe computer’s structure. To meet certain certification benchmarks such as the Telcordia Technologies Generic Requirements GR-63-CORE seismic zone 4 test profile, a physical test is conducted. This test will occur at an external location at the end of design cycle on a fully functional and loaded mainframe system. The ability to accurately predict the structural performance of a mainframe computer early in the design cycle is critical in shortening its development time. This paper discusses an improved method to verify the finite element analysis results predicting the performance of the mainframe computer’s structure long before the physical test is conducted. Sine sweep and random vibration tests were conducted on the frame structure but due to a limitation of the in-house test capability, only a lightly loaded structure can be tested. Evaluating a structure’s modal stiffness is key to achieving good correlation between a finite element (FE) model and the physical system. This is typically achieved by running an implicit modal analysis in a finite element solver and comparing it to the peak frequencies obtained during physical testing using a sine sweep input. However, a linear, implicit analysis has its limitations. Namely, the inability to assess the internal, nonlinear contact between parts. Thus, a linear implicit analysis may be a good approximation for a single body but not accurate when examining an assembly of bodies where the interaction (nonlinear contact) between the bodies is of significance. In the case of a nonlinear assembly of bodies, one cannot effectively correlate between the test and a linear, implicit finite element model. This paper explores a nonlinear, explicit analysis method of evaluating a structure’s modal stiffness by subjecting the finite element model to a vibration waveform and thereafter post processing its resultant acceleration using Fast Fourier Transformation (FFT) to derive the peak frequencies. This result, which takes into account the nonlinear internal contact between the various parts of the assembly, is in line with the way physical test values are obtained. This is an improved method of verification for comparing sine sweep test data and finite element analysis results. The final verification of the finite element model will be a successful physical seismic test. The tests involve extensive sequential, uniaxial earthquake testing in both raised floor and non-raised floor environments in all three directions. Time domain acceleration at the top of the frame structure will be recorded and compared to the finite element model. Matching the frequency content of these accelerations will be proof of the accuracy of the finite element model. Comparative analysis of the physical test and the modeling results will be used to refine the mainframe’s structural elements for improved dynamic response in the final physical certification test.

Engineering Critical Assessment (ECA) of welds is the process of predicting the structural integrity of a structure in the presence of a weld defect under specified loading conditions. Standardized ECA techniques consider the weld to be equal in properties when compared with base metal or use the concept of ‘strength mismatch’ to distinguish the weld from the base metal. In both cases, the weld region is homogeneous. This is a severe approximation from reality, as welds show complex strength heterogeneity patterns. The authors are concerned with techniques to simplify welds in such way that the structural response of the weld is similar to that of the idealized, homogeneous weld. Two approaches are considered: (a) integrating properties along assumed slip lines originating from the defect tip, and (b) assigning All Weld Metal Tensile Tests (AWMTT) to the entire weld region. A plastic analysis procedure suggested by the ASME BP&V code (‘Twice Elastic Slope method’) is adopted to estimate Plastic Load, whose values are compared for the heterogeneous and equivalent homogeneous welds. Finite Element (FE) simulations were performed for Single Edge notched Tensile (SE(T)) specimens. The results put forward the possibilities of weld homogenization while showing its limitations. This will assist in further improvement of weld ECA.

Polyethylene (PE) pipe, particularly high-density polyethylene (HDPE) pipe, has been successfully utilized to transport cooling water for both non-safety-related applications and safety-related applications in nuclear power plant (NPP). However, concerns of a lack of non-destructive examination (NDE) procedures and qualifications specialized for HDPE pipe impede its broader application. Traditional approximation without considering effects of acoustic dispersion could work for PE pipe with a small inspection depth. But for PE pipe of large size used in nuclear power plant, effects of acoustic attenuation and dispersion accumulate with depth, and have influence on waveforms of target pules, which brings great challenges to the energy concentration when performing ultrasonic phased-array inspection for PE pipe in NPP. In this paper, a theoretical method applying Szabo’s causal convolutional propagation operator based on causality theory was presented to obtain wave equations of ultrasound in PE considering both attenuation and dispersion, in which attenuation coefficient and phase velocity were used to separately characterize acoustic attenuation and dispersion. Then, an experimental method using ultrasonic spectroscopy technology was proposed to confirm the proposed model, and a good agreement was obtained. The results indicated that attenuation coefficient of PE had an approximately linear relation with frequency and that phase velocity rose logarithmically with frequency. Finally, effects of attenuation and dispersion on amplitude spectrum and waveform in time domain of the target signal were investigated. Frequency downshift and time delay shift had an influence on image resolution and focus capability, and were believed to be a restriction of current inspection technology. This work also theoretically proved that lower testing frequencies (less than 2.5MHz) could improve the inspection effectiveness of the applied inspecting systems for HDPE pipes in NPP applications.

In ASME Section VIII, Division 1, rules are provided for calculating the thickness of 2:1 ellipsoidal heads in UG-32. UG-32(c) also states that “an acceptable approximation of a 2:1 ellipsoidal head is a torispherical head with a spherical radius of 0.9D and a knuckle radius of 0.17D”. However, calculating the thickness of a torispherical head with those “equivalent” dimensions results in a thicker head. This result is inherently inconsistent, which starts to bring into question the so-called equivalency. Code Case 2260 further perpetuates this equivalency by providing alternative rules for calculating the thickness of torispherical heads, and then permitting the engineer to calculate 2:1 ellipsoidal heads implementing this 90-17 equivalency. Additionally, the calculation methodology for a 2:1 ellipsoidal head in ASME Section VIII, Division 2 uses the torispherical head calculation methodologies and directly implements this 90-17 equivalency. However, this calculation method results, for the same allowable stress basis, in a completely different thickness from the above three methods. This paper reviews the past 90+ years of work on this topic, and presents some theoretical treatment of the different head geometries. A review of the current Code rules is presented, with a comparison of results for several sizes. A survey of head fabricators is presented to show the actual geometries produced for use in ASME pressure vessels. Finally, conclusions regarding whether or not the 2:1 ellipsoidal head is in fact equivalent to the 90-17 torispherical head are presented, and recommendations for future revisions to both ASME Section VIII, Division1 and Division 2 are provided.

Vibrations of piping systems and structures pose significant operational and commercial risks. Due to their inherently low mechanical damping, these systems exhibit resonance frequencies with high dynamic amplification factor. When subject to external forces from flow turbulences, pressure pulsation or mechanical equipment, these systems can respond with large amplitude vibration. Tuned mass dampers (TMD) provide effective means of controlling resonant vibration and offer two major advantages compared to other vibration control means: Firstly, the vibration reduction can be accurately predicted even if the forcing function remains unknown, leading to increased reliability of the proposed solution. Secondly, the need for hot work during installation can be avoided, resulting in reduced safety risks and less disruption to plant operations. Although TMDs are widely used in civil and mechanical engineering, they are not commonly considered when controlling vibrations in the piping industry. One reason for this may be the absence of industry design guidelines. This paper provides simple mathematical models for the design and analysis of TMDs using Microsoft Excel spreadsheet calculations. A method for the approximation of mechanical systems’ dynamic behavior based on site measurements or finite element analyses is described, and practical guidance for the TMD design process provided. A series of examples shows how TMDs can be optimized to provide robust control of resonant vibrations.

It is recognized that piping systems used in nuclear power plants have a significant amount of the safety margin, up to the point of boundary failure, even when the input seismic load exceeds the allowable design level. The reason is attributed to the large strength capacity of the piping systems in the plastic region. In order to establish an evaluation procedure, in which the inelastic behavior of piping systems is considered in a rational way, a task group activity under the Japan Society of Mechanical Engineers (JSME) has been conducted. As a deliverable of this activity, a Code Case in the framework of the JSME Nuclear Codes and Standards is now being developed. The Code Case provides the strain-based criteria, an evaluation procedure using the response-spectrum based inelastic analysis, and detailed inelastic response analysis based on a finite element model. For developing the Code Case, inelastic benchmark and parametric analyses of the tests of a pipe element and piping system made of carbon steel were conducted to investigate the variation of the elastic-plastic analyses results. Based on these analytical results, it is assumed that setting the yield stress has a significant influence on the inelastic analytical results, while the work hardening modulus in the bi-linear approximation of the stress-strain curve has little influence. From the results of the parametric analyses, it is confirmed that the variation in the analytical results among the analysts would be reduced by having a unifying analysis procedure. In this paper, the results of the parametric analyses and the variation in the elastic-plastic analysis are discussed.

The purpose of this work is to establish a method for safety assessment with respect to plastic collapse, which is consistent for design assessment in accordance with Section III of the ASME Boiler and Pressure Vessel Code and assessment of in-service defects. In the Swedish nuclear power industry, a procedure is used for assessment of in-service defects that is based on failure assessment diagrams according to the R6-method combined with a safety evaluation system corresponding to Section III and XI of the ASME Code. The Swedish procedure was originally based on R6 Revision 3 combined with the 1995 edition of the ASME Code. In recent years the procedure has been updated to correspond to current versions of R6 and ASME. These updates include a transition to the updated definition of flow stress as well as structural factors against plastic collapse that was included in the 2002 Addenda of ASME 2001 Section XI. Following these updates, discrepancies were found between plastic collapse analyses made in accordance with Section III and assessments of in-service defects. Due to this, a project was initiated to make the procedure for assessment of in-service defects consistent with Section III analyses. An in-depth study of the flow stress definitions and structural factors in Section XI was initiated. This study found that the structural factors are based on approximations to get material independence. These approximations uses mean values based on a number of materials which was found to be quite inaccurate for many materials used in the Swedish nuclear power industry and can differ up to about 15 % compared to Section III analyses. A method has been developed to calculate material specific structural factors that gives a near perfect match between plastic collapse according to Section III and the Swedish procedure for assessment of cracks. The method is based on the methodology for structural factors in Section XI, but excludes the assumptions made to get material independent structural factors. The method is presented and comparisons show the agreement to Section III and highlight cases of large discrepancies in Section XI.

The effect of uncertainty is critical in the design of complex engineered systems, components, and structural materials subjected to fatigue. Uncertainty in fatigue life prediction is a combination of several factors. In fact, it cannot be eliminated from experimentation due to material and loading variability, manufacturing processing, and imprecise scientific modeling. Consequently, uncertainty must be characterized and managed. The impact of uncertainty is exacerbated especially when high reliability must be assured. One of the ways to estimate the effect of uncertainty is to consider confidence bounds for fatigue life prediction, specifically, for cumulative distribution functions associated with life. The purpose of this paper is to investigate the statistical variability and appropriately model that variability for life in fatigue using appropriate cumulative distribution functions, and subsequently, evaluate a variety of statistical methods to estimate confidence bounds. Specifically, the confidence bounds will be estimated using mean square error, Dvoretzky-Kiefer-Wolfowitz, and pointwise Normal approximation methods. Since high reliability and long life is typically desired, extra emphasis will be placed on estimation in the lower tails of the distribution functions. The ensuing analyses are based on data for a cold-rolled, low carbon, extra deep drawing steel, ASTM A969, and creep strengthened 9Cr-1Mo steel.

Steel pipelines are subjected to a variety of complex, and sometimes difficult to predict, loading schemes during the fabrication, installation and operation phases of their lifecycles. Consequently, the mechanical behavior of steel pipelines is not only influenced by the steel grade but also by the loading history of the pipe segments. Due to the resultant intricacies of the nonlinear load-deformation behavior of pipelines, adequate numerical analysis techniques are usually required for simulation of pipelines under different loading schemes. The validity of such numerical simulations is largely influenced by the accuracy of the true stress-true strain characterization of the pipeline steels. However, existing stress-strain mathematical expressions, developed for the characterization of metallic materials over the full-range of the stress-strain relationship, have been observed to either loose predictive accuracy beyond a limited strain range or, for the more accurate full-range models, are cumbersome due to their requirement of a large number of constituent parameters. This paper presents a relatively accurate and simple true stress-true strain model which is capable of accurately predicting the stress-strain behavior of pipeline steels over the full range of strains. The proposed stress-strain model is characteristically unlike existing stress-strain models as it is essentially defined by a Product-Log function using two proposed parameters, and is capable of capturing a reasonable approximation of the yield plateau in the stress-strain curve. To validate the proposed model, curve-fitting techniques are employed for comparison to experimental data of the stress-strain behavior of different pipeline steel grades (X52 – X100). Excellent agreements are observed between the proposed model and the different pipeline steels over the full-range of the true stress-true strain relationship. Furthermore, the applicability of the proposed model is validated by means of a proposed parametric procedure for predicting the ultimate compressive strength of shell elements.

Structural integrity assessment codes such as R6 [1] and BS7910 [2] provide guidance on the assessment of flaws that are assumed to be infinitely sharp using the Failure Assessment Diagram (FAD). In many cases, such as fatigue cracks, this assumption is appropriate, however it can be pessimistic for flaws that do not have sharp tips such as lack of fusion, porosity or mechanical damage. Several Notch Failure Assessment Diagram (NFAD) methods have been proposed in the literature to quantify the additional margins that may be present for non-sharp defects compared to the margins that would be calculated if the defect were assumed to be a sharp crack. This paper presents the second stage of validation work, using 3D Finite Element (FE) Analyses and a wide range of test data on non-sharp defects, to validate an NFAD method proposed for inclusion in R6 and to quantify the errors caused by various approximations in the method.

A finite element method (FEM)-based solution of an industry-grade problem with complex geometry, partially-validated material property databases, incomplete knowledge of prior loading histories, and an increasingly user-friendly human-computer interface, is extremely difficult to verify because of at least five major sources of errors or solution uncertainty (SU), namely, (SU-1) numerical algorithm of approximation for solving a system of partial differential equations with initial and boundary conditions; (SU-2) the choice of the element type in the design of a finite element mesh; (SU-3) the choice of a mesh density; (SU-4) the quality measures of a finite element mesh such as the mean aspect ratio.; and (SU-5) the uncertainty in the geometric parameters, the physical and material property parameters, the loading parameters, and the boundary constraints. To address this problem, a super-parametric approach to FEM is developed, where the uncertainties in all of the known factors are estimated using three classical tools, namely, (a) a nonlinear least squares logistic fit algorithm, (b) a relative error convergence plot, and (c) a sensitivity analysis based on a fractional factorial orthogonal design of experiments approach. To illustrate our approach, with emphasis on addressing the mesh quality issue, we present a numerical example on the elastic deformation of a cylindrical pipe with a surface crack and subjected to a uniform load along the axis of the pipe.

The commonly accepted approach to dealing with material damage as the cause of structural failure is to treat the most highly distressed location in the structure as an equivalent simple test and to define failure of the structure as a whole as being failure at that point location. The exception to this rule is plastic deformation. Yielding at a point was recognized several decades ago as being an excessively conservative definition of component failure and it is now standard design practice to accept failure as being the limit load, which is only reached, sometimes after extensive propagation of a plastic zone. Other material failure mechanisms also occur after a finite period of damage propagation, but this additional strength, or life, is not usually taken into account, partly because the damage mechanisms themselves are not always well defined, and partly because of the computational difficulty involved in assessing the propagation of damage. Creep rupture falls into the category of a mechanism which can enjoy an extensive period of damage propagation before structural failure occurs, but the difficulty of evaluating it quantitatively has meant that it continues to be dealt with as essentially a point failure phenomenon. Relatively recently, many of the problems associated with assessing creep damage have been resolved, on the material side by increased use of so-called “continuum damage mechanics” based models such as Kachanov and Omega and, on the computational side, by the exponential growth in the capabilities of advanced Finite Element Analysis. It is now possible in principle to trace the entire life of a complex component, down to final disintegration. However, this capability still comes at a significant cost, and there is still room for simplification in order to bring this capability to a wider range of potential users. This paper describes a process for evaluating the propagation of creep damage, down to the point of total disintegration, using approximations which exist within the standard capabilities of a typical FE design package. This innovation does not do anything that cannot be done today using the full repertoire of computational tools that exist, notably user subroutines, but provides a simpler platform which can be used to push damage evaluation further into the activities of day-to-day design with a significant reduction in the resource allocation currently required to do the job. Results are compared with creep experiments on notched bars.

This work is about evaluating the behavior facing HIC of high strength steels by means of the Small Punch Test (SPT). It can be considered as a quasi-non-destructive test in comparison to structural integrity analysis of large components. It was developed during the 80’s with the purpose of estimating the embrittlement grade of nuclear components reducing the amount of material employed. During the last years it has been successfully employed in the evaluation of mechanical properties of different materials and creep behavior. Also approximations for the fracture properties estimations have been carried out using this method. Although a reference standard that includes the tensile and fracture parameters estimations by SPT does not exist, a European Code of Practice (CWA 15627:2008) was recently developed. In addition a European standard is in preparation, including the ultimate research and the backup of the most relevant groups. In this work, high strength steels behavior facing stress corrosion cracking (SCC) or hydrogen Embrittlement (HE) processes are analyzed by means of the Small Punch Test (SPT). The evaluation of the response of materials facing environmental damage processes requires a different consideration if cracks are present on the material or not. In a first stage the study carried out tries to analyze the behavior without cracks, using the threshold stress (σscc) parameter. The aforementioned parameter is obtained from slow strain rate tensile tests (SSRT), which involves its own particular disadvantages. Thus the aptitude of the SPT to obtain the threshold stress is studied, evaluating the influence of variables such as the solicitation rate. In the second part of the work, specimen geometry and test conditions are proposed for the SPT, in order to evaluate the susceptibility facing SCC and HE in presence of cracks for the materials studied. In this case, the fracture toughness parameter that describes the crack initiation process ( Khe ) will be evaluated and validated by conventional tests based on fracture mechanics. The influence of variables, such as test solicitation rate on the results, is analyzed in order to obtain a qualitative methodology to evaluate mechanical-environmental damage processes by SPT means. For the SPT tests carried out, common Small Punch specimens of 10×10 mm of section and 0,5 mm of thickness are used for σscc determination.

For assessing possible failure of piping structures under excessive seismic loading, dynamic structural analysis methods employing advanced constitutive models need to be established. The multilayer kinematic hardening model for cyclic plasticity, which is applicable up to large strain, was proposed in the previous paper by the authors for carbon steel STS410 (JIS, Japanese Industrial Standard) to represent precisely nonlinear stress-strain relation as well as cyclic hardening, and was validated through its application to quasi-static cyclic bending tests of an elbow. In this paper, the applicability of the model to dynamic analysis of piping systems under earthquake loading is evaluated. An existing simulated earthquake excitation test of a piping system made of carbon steel STPT370 (JIS) is dealt with for validation of the finite element nonlinear dynamic analysis method using the presented model. To emphasize the advantage of this model, analyses using the conventional linear kinematic hardening model are also conducted. The results by the latter model are shown to be highly variable depending on the method of bilinear approximation of stress-strain curves. It is shown that the multilayer kinematic hardening model can predict well inelastic strains in piping systems under excessive earthquakes, which is important for the failure assessment.

The general approach of numerical treatment of integro-differential equation of the flat crack problem is considered. It consists in presenting the crack surface loading as the set of the polynomial functions of two Cartesian coordinates while the corresponding crack surface displacements are chosen as the similar polynomials multiplied by the function of form (FoF) which reflects the required singularity of their behavior. To find the relations matrixes between these two sets a new effective numerical procedure for the integration over the area of arbitrary shape crack is developed. In based on the classical hyper-singular method, i.e. Laplace operator is initially analytically applied to the integral part of equation and the resulting hyper singular equation is subsequently considered. The presented approach can be implemented with any variant of FoF, but Oore-Burns FoF, which was earlier suggested in their famous 3D weight function method, is supposed to be the most accurate and universal. It takes into account all points of crack contour, which provides perfect physical conditionality of the solution, but such FoF is relatively heavy in implementation and of low computational speed. The special procedure is developed for the approximation of the crack contour of arbitrary shape by the circular and straight segments. It allows to easily obtain analytical expression for Oore-Burns FoF, which greatly increases the calculation speed and accuracy. The accuracy of the considered method is confirmed by the examples of the circular, elliptic, semicircular and square cracks at different polynomial laws of loading. The developed methods are used in the implemented procedure for crack growth simulation. It allows to model growth of crack of arbitrary shape at arbitrary polynomial loading, at that all contour points are taken into account and can expand with their own speeds each. Procedure has high accuracy and don’t need complex and high-cost re-meshing process between the iterations unlike FEM or other numerical methods. At that usage of Oore-Burns FoF provides high flexibility of the presented approach: unlike similar theoretical methods, where FoF calculation procedure is rigidly connected with the crack shape, which complicates the adequate crack growth modeling, the used FoF automatically takes into account all points of crack contour, even if its shape became complex during the growth. Presented crack growth procedure can be effectively used to test accuracy and correctness of correspondent numerical methods, including the newest XFEM approach.