Crack Growth Law Research Articles

Coupled FEM-DBEM Simulation of 3D Crack Growth under Fatigue Load Spectrum

Numerical predictions of fatigue crack growth under load spectrum are obtained by coupled FEM-DBEM approach. An initial part-through corner crack, in a pre-notched specimen undergoing a traction fatigue load, propagates becoming through the thickness. A two parameter crack growth law (“Unified Approach”) is calibrated by in house made constant amplitude experimental tests and the crack growth retardation after an overload application is reproduced. The residual stresses responsible for such retardation are calculated by a sequence of elastic-plastic static FEM analysis; such stresses are then applied to the crack faces for the propagation simulation in a DBEM environment. A satisfactory agreement between numerical and experimental crack growth rates are displayed, for both part-through crack and through the thickness crack. This approach provide general modeling capabilities, with allowance for general crack front shape and fully automatic propagation.

Three-dimensional crack growth modelling of a Ni-based superalloy at elevated temperature and sustained loading

High temperature materials subjected to elevated temperature have been shown to be sensitive to dwell times, giving an increased crack growth rate. The interaction between these dwell times and rapid cyclic loads have been shown to constitute a complex problem. Many models have been developed for 1D conditions, but the application to general 3D conditions has seldom been seen, although this is the most common case in most structures. In this paper a model for taking care of the interaction between these load modes in general 3D crack growth has been developed. The model uses 1D results for extension to general 3D, thus providing for local crack front evolution with a minimum of numerical simulations. Consequently, a history dependent crack growth law in 3D is given in this paper, which is capable of tracking the damage from the sustained load, and the interaction with rapid cyclic loading. The model has been implemented for usage with finite element calculations and several different tests are simulated and compared with experimental results for the nickel based superalloy Inconel 718 at 550°C. The simulation results show crack shapes in agreement with experimental fracture surfaces and time to failure.

Fatigue crack growth in functionally graded material using homogenized XIGA

In this work, the effect of defects/flaws (holes, inclusions, cracks) on the fatigue life of functionally graded material (FGM) is analyzed by homogenized extended isogeometric analysis (XIGA). In FGM, the gradation in the material properties is taken along the length of the plate. In XIGA, the crack faces are modeled by discontinuous Heaviside jump function, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. Holes and inclusions are modeled by Heaviside jump function and distance function, respectively. The values of stress intensity factor (SIF) are numerically evaluated using the domain form of interaction integral approach. Paris law of fatigue crack growth is employed for computing the fatigue life. The flaws are modeled in a 30% region near the main crack, while the rest of the region is modeled with an equivalent homogeneous material. Several problems involving discontinuities in 30% region of the domain are solved by XIGA, and the results are compared with those obtained by modeling discontinuities in the entire domain of the plate.

Three-dimensional fracture and fatigue crack propagation analysis in structures with multiple cracks

A methodology is presented for fracture and fatigue crack growth simulations of multiple cracks. Computed stress intensity factors and a crack growth law are used to predict incremented positions of crack front nodes. The procedure is repeated until failure criterion is reached. The cases presented in this study include structures containing two or more cracks which propagate, coalesce or grow as planar and non-planar cracks. Comparisons of results with literature data shows excellent agreement. Therefore, it is concluded that the presented procedure can be used to accurately to assess fatigue crack propagation behavior of structures with multiple three-dimensional cracks.

高強度鋼のギガサイクル疲労強度予測式に関する考察

Predictions of gigacycle fatigue strength in high-strength steel were discussed by using reported fatigue test results. The discussed prediction models were Tanaka-Akiniwa model, Murakami’s equation and a new model. The prediction based on the Tanaka-Akiniwa model overestimated the effects of inclusion sizes, resulting in much lower fatigue strength for a large inclusion than actual. The prediction based on the Murakami’s equation provided us good estimations for the effects of the inclusion sizes. However, estimated ODA sizes, which were necessary in the calculation, were imaginary since the estimated fatigue strength did not agree with the fatigue test results. The new model, proposed in this research, was a modification of the Tanaka-Akiniwa model. The new model used a new fatigue crack growth law instead of conventional Paris law. In this new model, coefficient of determination, R2 value, in the fitting of the fatigue test results was maximized to determine a new constant. The prediction based on the new model provided us much better estimations than that based on the Tanaka-Akiniwa model, and the new fatigue crack growth law showed good agreements with the measured crack growth rates for internal small cracks. Validity of the new model was thus confirmed in this research.

Stress Intensity Coefficients in DCB Sample Under Strain–Force Loading of its Cantilever Beams

The crack-length dependences of the stress intensity coefficients K 1 in a DCB sample in different schemes of strain-force loading of its cantilever beams are analyzed. It is found that the character of the cracklength dependences of the stress intensity coefficients K 1 is fundamentally different for different ratios of the parameters of simultaneous force and strain loading. Greater attention is now being paid to the strength and reliability of the elements of complex technical systems, such as NPP, aerospace systems, and petrochemical enterprises, and to the effect of defects and cracks on their reliability [1‐3]. Great importance is attached to studying the growth of fatigue and corrosion cracks. Experimental studies of the laws of crack growth are needed. In this respect, samples in the form of double cantilever beams (DCB samples) offer attractive possibilities; such samples were proposed as alternatives to Robertson’s samples for determining the fracture toughness K 1C at the start and the stopping (braking) temperature of cracks [4‐9]. The DCB samples were subsequently elaborated and used to study the fracture toughness in a wide temperature range under single static loading, the strength of glued, soldered and welded connections, as well as the laws of propagation of fatigue cracks and the influence of a medium with a constant stress intensity coefficient [10]. Their range of application has also touched medicine [11]. Different methods of joining and loading the cantilever beams of a DCB sample greatly expand the possibilities in studying the laws of crack propagation under cyclic as well as long-duration static loading [11‐14]. The crack resistance of materials is tested using programs where the initial loading conditions are based on the dimensions of the samples and the loads on a sample. The use of DCB samples for crack-resistance tests can greatly change the approach to picking the initial conditions, since their cantilever beams make it possible to use different strain-force loading schemes. For two beams, one independent force factor can be used to set the initial conditions or control the stress intensity coefficient and the other for the actual load. A rigidly loaded DCB sample is simultaneously an object of investigation and a loading arrangement. It does not require servicing during the tests. This feature makes it attractive for use under irradiation, in the presence of hazardous media, and in other locations with limited or impossible access. The aim of the present article is to analyze the stress intensity coefficients as a function of crack length for different schemes of complex strain-force loading of DCB samples. Loading schemes for DCB sample (Fig. 1). Four loading schemes are analyzed. Hinged‐rod systems are not setups for strain loading; they are used for clarity and convenience of indicating dimensions and the directions of movement of the arms. They are considered to be absolutely rigid. Real setups for rigid loading are not proposed, but we think that disjoined

Investigation of the residual tensile behavior of fiber bundles after static fatigue: Implications for the prediction of durability of composites

Several brittle inorganic fibers (including glass, SiC- or alumina- based fibers) are sensitive to slow crack growth activated by environment (water, high temperature air, etc.) in fatigue, so that failure can occur under stresses much smaller than the fracture stress. The delayed fracture of glass fibers has been investigated in a previous paper, on multifilament tows loaded under constant deformation in water. This tow testing technique was shown to be powerful for the estimation of the intrinsic crack growth law and the determination of the statistical distribution of rupture times pertinent to filaments. The present paper focuses on the residual behavior of filaments and tows after static fatigue (under constant deformation). It is aimed at assessing this tow-based approach to slow crack growth in filaments, i.e. demonstrating validity of the model, of the values of slow crack growth constants and of the equation of residual strength. For this purpose, E-glass fiber tows that comprised 2000 single filaments were subjected to interrupted static fatigue tests under constant deformation in water in a first step, and, then to residual tensile tests in inert environment in a second step. The residual behavior of tows was predicted using the slow crack growth constants that have been extracted from the static fatigue tests, and the fast fracture statistical parameters estimated from tensile tests on as-received tows. Validity of the approach was established by comparing experimental and predicted results. Then, the equations of residual strength and residual behavior were used for the investigation of residual behavior of filaments and tows.

A FEM-DBEM investigation of the influence of process parameters on crack growth in aluminum friction stir welded butt joints

This paper deals with a numerical investigation on the influence of FSW process parameters on fatigue crack growth in AA2024-T3 butt joints. The computational approach is based on the sequential usage of Finite Element Method (FEM) and Dual Boundary Element Method (DBEM). The distribution of the process induced residual stresses has been mapped by means of the contour method. The residual stress field has then been superimposed in a DBEM environment to the stress field induced by a remote fatigue traction load. A two-parameter crack growth law has been used for the crack propagation rate assessment. The simulation results corresponding to different combinations of process parameters are presented. The influence of process parameters on the residual stress distribution has also been highlighted.

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based onJ‐integral

ABSTRACTLoad‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJwith stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effectiveJ‐integral range was modified by ΔJpin order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios ofR > 0.

Bi-Linear Fatigue and Fracture Approach for Safety Analysis of an Offshore Structure

The design of welded structures for the fatigue limit state is normally carried out by means of either linear or bilinear S-N curves, which have been found adequate to predict crack initiation only. To properly assess the effects of the design, fabrication, inspection, and repair strategy for structure degradation due to crack growth, fracture mechanics (FM) models need to be applied. In this paper, alternative S-N and FM formulations of fatigue are investigated. The probabilistic fracture mechanics approach predicts the fatigue life of welded steel structures in the presence of cracks under random spectrum loading. It is based on a recently proposed bi-linear relationship to model fatigue crack growth. Uncertainty modeling, especially on fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bilinear crack growth relationship. Results pertaining to the fatigue reliability and fatigue crack size evolution are presented using the Monte Carlo simulation technique and the emphasis is placed on a comparison between the linear and bilinear crack growth models. Variations in the system configuration, service life, and coefficients of crack growth laws have been studied on the parametric basis

Fatigue Lifetime and Crack Growth Behavior of WC-Co Cemented Carbide

It is well known that WC-Co cemented carbides have excellent wear resistance. However, information about their fatigue crack growth behavior and fatigue properties is limited. In the present study, rotating bending fatigue tests were carried out on a fine grained WC-Co cemented carbide to evaluate its fatigue lifetime and crack growth behavior. From observations of the micro-notched specimen surface during the fatigue process, it was revealed that most of the fatigue lifetime of the tested WC-Co cemented carbide is comprised of crack growth cycles. Using the basic equation of fracture mechanics, the relation between the rate of fatigue crack growth da/dN and the maximum stress intensity factor Kmax of the WC-Co cemented carbide was derived. From this relation, both the threshold intensity factor Kth and the fatigue fracture toughness Kfc of the material were determined. Fatigue lifetime of the WC-Co cemented carbide was estimated based on the fatigue crack growth law.

J0560202 流体温度変動による配管熱疲労に関する研究(18) : 微小き裂に対する破壊力学的伝ぱ則の適用性の検討([J056-02]エネルギープラント安全に向けた構造/熱流体/材料の連成問題(2))

J0560202 流体温度変動による配管熱疲労に関する研究(18) : 微小き裂に対する破壊力学的伝ぱ則の適用性の検討([J056-02]エネルギープラント安全に向けた構造/熱流体/材料の連成問題(2))

Prediction of Life and Scatter of Fatigue Failure Originated at Nonmetallic Inclusions

Fatigue failure of high strength steels mostly originates at nonmetallic inclusions. An optically dark area (ODA) beside the inclusion can be observed in specimens fractured at very high cycle fatigue (VHCF) regime. The present paper proposes fatigue life prediction models from low to VHCF regime. The hypothetical cycle-by-cycle fatigue crack growth model inside ODA has been developed in the VHCF regime based on the master curve of ODA where fatigue failure is caused by cyclic loading assisted by hydrogen trapped by inclusion. The fatigue crack growth law is proposed for a small crack outside ODA within the framework of the √area parameter model where the concept of “continuously variable fatigue limit” for small crack is introduced. The life and scatter of fatigue life originated at inclusions can be well evaluated by the proposed models.

Fatigue Resistant Design of Round Bars Weakened by a V-Shaped Circumferential Notch

In the present paper, fatigue crack propagation in V-notched round bars under cyclic eccentric axial loading is numerically evaluated using both a finite element analysis and an automated numerical model proposed by the first author. The stress- intensity factors are computed at a set of points on the crack front by the finite element method. Then, a suitable fatigue crack growth law is applied to the above set of points. By varying the loading eccentricity value and the notch root geometry, several initial semi-elliptical surface crack configurations are analysed.

Statistical distribution and size effect of residual strength of quasibrittle materials after a period of constant load

In preceding studies, the type of cumulative probability distribution functions (cdf) of strength and of static lifetime of quasibrittle structures, including their tails, was mathematically derived from atomistic scale arguments based on nano-scale cracks propagating by many small, activation energy-controlled, random breaks of atomic bonds in the nanostructure. It was shown that a quasibrittle structure (of positive geometry) must be modeled by a finite (rather than infinite) weakest-link model, and that the cdf of structural strength as well as lifetime varies from nearly Gaussian to Weibullian as a function of structure size and shape. Excellent agreement with the observed distributions of structural strength and static lifetime was demonstrated. Based on the same theoretical framework, the present paper formulates the statistics of the residual structural strength, which is the strength after the structure has been subjected to sustained loading. A strength degradation equation is derived based on Evans' law for static crack growth during sustained loading. It is shown that the rate of strength degradation is not constant but continuously increasing. The cdf of residual strength of one RVE is shown to be closely approximated by a graft of Weibull and Gaussian (normal) distributions. In the left tail, the cdf is a three-parameter Weibull distribution consisting of the (n+1)th power of the residual strength, where n is the exponent of the Evans law and the threshold is a function of the applied load and load duration. The finiteness of the threshold, which is typically very small, is a new feature of quasibrittle residual strength statistics, contrasting with the previously established absence of a threshold for strength and lifetime. Its cause is that there is a non-zero probability that some specimens fail during the static preloading, and thus are excluded from the statistics of the overload. The predictions of the theory are validated by available test data on glass–epoxy composites and on borosilicate and soda-lime silicate glasses. The size effect on the cdf of residual strength is also determined. The size effect on the mean residual strength is found to be as strong as the size effect on the mean initial strength.

Fatigue crack growth simulations of homogeneous and bi-material interfacial cracks using element free Galerkin method

In this paper, quasi-static fatigue crack growth simulations of homogeneous and bi-material interfacial cracks have been performed using element free Galerkin method (EFGM) under mechanical as well as thermo-elastic load. The thermo-elastic fracture problem is decoupled into thermal and elastic problems. The temperature distribution obtained by solving heat conduction equation is used as input in the elastic problem to get the displacement and stress fields. Discontinuities in the temperature and displacement fields are captured by extrinsic partition of unity enrichment technique. The values of stress intensity factors have been extracted from the EFGM solution by domain based interaction integral approach. The standard Paris fatigue crack growth law has been implemented for the life estimation of various model problems. The results obtained by EFGM under mechanical and thermo-elastic loads were compared with those obtained by FEM using remeshing approach.

Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading

The design of various engineering structures, such as buildings, infrastructure, aircraft, ships, as well as microelectronic components and medical implants, must ensure an extremely low probability of failure during their service lifetime. Since such a low probability is beyond the means of histogram testing, we must rely on some physically based probabilistic model for the statistics of structural lifetime. Attention is focused on structures consisting of quasibrittle materials. These are brittle materials with inhomogeneities that are not negligible compared with the structure size, as exemplified by concrete, fiber composites, tough ceramics, rocks, sea ice, bone, wood, and many more at the micro- or nano-scale. This paper presents a finite weakest-link model of the fatigue lifetime of quasibrittle structures that fail at the fracture of one representative volume element (RVE). In this model, the probability distribution of critical stress amplitude is first derived by assuming a prescribed number of loading cycles and a fixed stress ratio. The probability distribution of fatigue lifetime is then deduced from the probability distribution of critical stress amplitude through the Paris law for fatigue crack growth. It is shown that the present theory matches well with the experimentally measured lifetime histograms of various engineering and dental ceramics, which systematically deviate from the two-parameter Weibull distribution. The theory indicates that the mean fatigue lifetime of quasibrittle structures must strongly depend on the structure size and geometry. Finally, the present model indicates that the probability distribution of fatigue lifetime can be determined from the mean size effect analysis.

Fatigue crack growth simulations of 3-D problems using XFEM

In this work, a simple and efficient approach based on extended finite element method (XFEM) has been presented to simulate three-dimensional fatigue crack growth simulations. In XFEM, standard displacement based approximation is enriched by additional functions using partition of unity concept. These enrichment functions are derived from the theoretical background of the problem under consideration. In the proposed approach, a crack front has been divided into many piecewise curve crack segments to avoid an iterative solution. Three-dimensional triangulation scheme is adopted for the calculation of level set functions on the crack surface. At the crack front, the level set functions are approximated using the concept of hanging nodes using quadratic finite element shape functions. These level sets are used to accurately define the crack geometry. The fatigue crack growth simulations have been performed using Paris law of fatigue crack growth. Various 3-D planar, non-planar and arbitrary shape crack growth problems are solved to reveal the sturdiness and versatility of the proposed XFEM approach.

Advanced FE model for simulation of pitting crack growth

An advance parametric FEA model for simulation of pitting arise phenomena on the gear teeth is presented in this article. The assumption of the developed computational approach was that pitting (pits on the contact surfaces) is a result of fatigue crack propagation under (rolling) contact loading conditions. Developed crack growth laws (based on the Paris law) allow to perform simulations of pitting crack growth with respect to the non-proportional and non-linear nature of loading of pitting crack tip, which result from specific loading condition. Specific crack tip loading and pitting crack growth was evaluated using the J-integral criterion of fracture mechanics. Advance model of penetration of the fluid lubricant into fatigue (pitting) cracks was designed using special hydrostatic fluid finite elements, which allow to include the closure of pressured lubricant between fracture surfaces during the simulation of gearing meshing. A simplified distribution of residual stresses in the surface layers of teeth is included as well. The simulations were carried out under the commercial code ABAQUS CAE FEM programme which allows to develop in-house codes using the Python scripting language and user subroutines. Mentioned programme codes and user subroutines are the basis of all FEA including the simulation of the specific loading conditions of pitting crack tip and the incremental pitting crack growth. Wide sensitivity study of the influence of selected model parameters was carried out. Achieved results – final pitting crack shapes and time needed for their formation were compared with experimental results.

Analysis on fatigue crack growth laws for crumb rubber modified (CRM) asphalt mixture

In recent years, crumb rubber has been applied widely in asphalt pavement, and many researchers have indicated that crumb rubber modified (CRM) asphalt mixture is an environmentally friendly material. In this study, the notched semi-circular bending (SCB) test was employed to study the fatigue cracking property for CRM asphalt mixture. Then the cracking growth length was obtained by image processing technology, and its correlation with the fatigue number was established and studied in this paper. Concurrently, the influence of gradation type, asphalt content, test temperature, stress ratio, loading frequency, rubber powder concentration and rubber powder size on CRM asphalt mixtures’ fatigue life and crack growth laws were investigated by this method. The results indicated that the gap-graded CRM asphalt mixture had a longer fatigue life and a lower crack growth rate than the continuous graded mixtures Moreover, at the optimum asphalt content, the fatigue life was much longer and the crack growth rate was much lower at smaller loading times with higher loading frequency at the CRM asphalt mixture concentration of 20% using the smaller 80 mesh fine crumb rubber size.