Three-dimensional Fracture Analysis Research Articles

Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form

Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form

Three-Dimensional Fracture Analysis of Large Opening Box Girder With Crack Damage Under Bending and Torsion Loads

Abstract This work aims to investigate the complex fracture behavior of a large opening box girder (LOBG) using three-dimensional (3D) finite element method (FEM). A numerical model is developed to simulate the fracture of LOBG under individually or jointly applied torsion and bending loads. The crack damage is introduced into the side plate and bottom plate of LOBG. The influencing factors such as crack angles, crack locations, and load types are emphatically discussed. Additionally, the crack growth angles are also predicted during the analysis. The results present that the large opening can generate significant effects on the crack growth of the side plate crack (SPC) and the bottom plate crack (BPC). Under the condition of torsion or hogging, SPC grows more easily than BPC, while BPC is relatively prone to grow under sagging condition. Compared with the torsion condition, the initial crack angle can significantly reduce the stress intensity factor (SIF) under the bending condition. Furthermore, the cracks that gradually approach transverse frames are also more likely to induce mode I fracture under torsion conditions. These findings from the present study can reveal insights for a better understanding of fracture behavior for LOBG.

Interaction integral approach for the Evaluation of Crack-front Singularities in a Solid Cantilever Beam under Magneto-Electro-Elastic loading using XFEM

In the piezoelectric energy harvesting devices, the most preferred is the cantilever beam orientation that can produce maximum deflection. Therefore, in this paper, three-dimensional fracture analysis of a cracked magneto-electro-elastic cantilever beam is studied using extended finite element methods (XFEM). The crack-front singularities like stress intensity factors (SIFs), electric displacement intensity factor (EDIF), and magnetic induction intensity factor (MIIF) are evaluated using the MEE interaction integral approach. The contour J-integral in domain form is solved with the asymptotic crack front fields as auxiliary fields using the Stroh formalism. The numerical results showed good agreement with the benchmark problem. Few case studies for the crack front singularities are presented using the proposed method. The results provided give useful guidance in the designing and manufacturing of smart devices.

Three-dimensional fracture mapping and analysis of coronal fractures in AO/OTA types 33-B3 and C3

BackgroundAlthough the relatively high incidence of coronal fractures in the supracondylar–intercondylar fractures is well established, little is currently known about the morphology of those fractures. Herein, we characterized the coronal fractures in AO/OTA type 33-C3 and assessed their differences with Busch–Hoffa fractures (33-B3).MethodsWe retrospectively collected 61 cases of AO/OTA type 33-B or C fractures with coronal plane fragments and generated three-dimensional fracture maps of those with coronal fractures based on CT imaging and measured angle α (the angle between the coronal fracture and the posterior condyle axis in the axis plane) and angle β (the angle between the coronal fracture and the posterior femoral cortex in the sagittal plane).ResultsThirty-three cases (32%) of AO/OTA type 33-C fractures contained coronal fragments. Most of them were type 33-C3 fractures. Angles α and β for type 33-C3 were significantly smaller than for type B3 at the lateral condyle, while the angles at the medial condyle were not significantly different. The fracture maps showed that the coronal fractures and the articular comminution area were more anterior in type 33-C3.ConclusionsThe incidence of coronal fractures was 32% and 67% in AO/OTA types 33-C and 33-C3, respectively. Our findings suggest that coronal fractures differed between both types, emphasizing the potential need for different treatment approaches.

Three-dimensional fracture analysis for a thin cracked hardening plate

A semi-analytical method is presented to investigate fracture behavior of a mode-I crack in a thin ductile plate. In the part of theoretical analysis, a total deformation theory of plasticity, in conjunction with a power law hardening stress-strain relation, is employed. Three-dimensional Maxwell stress functions, the minimum complementary potential energy principle and three dimensional J-integrals are used to obtain crack front stress fields. In the part of numerical analysis, three dimensional finite element simulations are carried out to obtain J-integrals, the out-of-plane constraint level and crack front stress fields. Comparison with numerical results of crack front stress fields shows the analytic solutions for crack front stress fields are valid. Numerical and analytic results show that the value of the opening stress ahead of the crack front deceases with increasing z (approaching the free surface) and lies between the corresponding plane strain and plane stress solutions.

Crack kinking and tunneling simulation for the single-fiber composite under transverse tension based on phase-field method

Virtual tests for a single-fiber–reinforced composite model subjecting to transverse tension are carried out based on a phase-field method considering a varying interface toughness parameter. Without pre-treating the crack initiation location and propagation path, the complete fracture process is realized for the first time in a three-dimensional numerical model, including nucleation cracks on the fiber/matrix interface at the free end, tunneling cracks along the fiber axis, and kinked interface cracks deviating from the interface and penetrating into the matrix. The numerically calculated crack propagation process is in good agreement with the in situ observations in the literature, indicating that the present model provides a good real-time quantitative numerical method for three-dimensional fracture analysis of fiber-reinforced composites. Tunneling cracks tend to cause macroscopic interface debonding and fiber pull-out. The interface tunneling crack initiation and the transition to the steady state inside the model are captured and analyzed in the numerical model. Kinked interface cracks can merge with other matrix cracks, forming a macroscopic transverse crack fracture mode. The kinking behaviors affected by the initial crack size and the interface properties are investigated. This study for the detailed crack propagation is helpful in understanding the toughening mechanism of fiber-reinforced composites under transverse tension.

A novel test system for mixed mode-I/II/III fracture tests – Part 2: Experiments and criterion development

In this part of the study, details of mixed mode-I/II/III fracture experiments for the CTST (Compact Tension-Shearing and Tearing) specimen, for which modeling and analyses results are given in Part 1, are presented. Critical fracture loads obtained from the tests are used with knowledge of mixed mode stress intensity factors (SIFs) from three-dimensional fracture analyses (Part 1) to compare with criteria existing in the literature for mixed mode-I/II/III fracture conditions. It is observed that existing criteria start deviating from the experimental measurements for cases in which coupled modes-II and -III are dominant under general mixed mode loading conditions. Similar studies are also performed for the same specimen under different out-of-plane mixed mode-I/III loading cases. Similarly, higher discrepancies are obtained for prediction of unstable fracture load values between fracture criteria and experimental results for highly mode-III conditions. Therefore, an improved empirical mixed mode-I/II/III fracture criterion is developed using all data obtained from numerical and experimental analyses. The results show that the improved criterion gives considerably good congruence with the experimental measurements.

The stress intensity factor calculation for combined sliding wear and fatigue of GH4169 superalloy based on three-dimensional simulation

In this paper, a sliding fatigue-wear methodology based on conventional rotating bending fatigue testing device is proposed. The crack propagation characteristics of GH4169 superalloy under plain fatigue and sliding fatigue-wear conditions are investigated by fatigue tests and SEM. In addition, the crack propagation and wear analysis are carried out with the finite element program ABAQUS and the three-dimensional fracture analysis software FRANC3D. The influence factors of crack growth rate including bending stress, contact stress and wear depth are investigated based on the stress intensity factor calculation and experimental measurements. The results show that the fatigue strength is severely decreased from 780 MPa to 200 MPa due to wear, although both contact stress state and material removal mechanism have positive effects on restraining the crack propagation acceleration. This competition between fatigue and wear is discussed and it is concluded that the fatigue defeats the resisting effect of wear and occupies the dominate position after the nominal crack length reaches a critical value. However, the wear volume and depth would increase the fatigue stress and accelerate crack propagation. Therefore, the positive and negative influence of wear on material fatigue lives also have a competitive mechanism and a correction model is carried out based on the classic Paris law.

Three-Dimensional Mixed Mode Stress Intensity Factors for Inclined Elliptical Surface Cracks in Plates under Uniform Tensile Load

In this study, main results from parametric analyses of three-dimensional inclined elliptical surface cracks using FRAC3D are presented in terms of normalized mixed mode stress intensity factors (SIFs) along crack fronts. FRAC3D is the solver of in-house developed “Fracture and Crack Propagation Analysis System (FCPAS)” and is a finite element-based standalone program employing three-dimensional enriched finite elements. In the analyses, values of the main parameters affecting the problem, which are normalized crack depth with respect to plate thickness (a/t=0.2, 0.4, 0.6, 0.8), crack aspect ratio (a/c=0.25, 0.50, 1.0, 2.0, 4.0) and crack inclination angle (β=0°, 15°, 30°, 45°, 60°, 75°), are changed systematically in their realistic ranges to obtain a wide library of solutions representing the general problem and to develop empirical SIF equations that are valid for all values of the main parameters in their pre-determined ranges. This resulted in a total of 120 three-dimensional fracture analyses. The results show that as the inclination angle of the surface crack increases, mode-I SIF decreases along the crack front, while mode-II and mode-III SIFs increase up to β=45°, which contains the plane with maximum in-plane shear stress. For higher values of β, mode-II and mode-III SIFs start decreasing as expected. As the normalized crack depth increases, the normalized SIFs also increase. When the depth point and the free-surface point are compared with each other, it is seen that the crack aspect ratio also has big effect on the relative values of the normalized SIFs.

Three-dimensional analytical model for exploration of the block cracking phenomenon in asphalt pavements

Block cracking is a common type of distress in asphalt pavements, which can be found in a variety of climatic and geographical locations. The extensive nature of this cracking form often leads to significant maintenance costs and reduces the ride quality and service life of the pavement surface. Although this deterioration mode is covered in many pavement evaluation guides and condition rating systems, the underlying mechanisms of block cracking have not been fully investigated. This is likely because the phenomenon requires a three-dimensional (3D) fracture analysis to be conducted to capture the structural response associated with this complex cracking form. Computational fracture modelling and simulation will ultimately be needed to explore the detailed thermal and material gradients, time dependencies and nonlinearities associated with this 3D cracking phenomenon. However, it is first necessary to develop rigorous closed-form, analytical solutions to serve as benchmarks for the verification of future 3D numerical simulation results. In addition, the reference analytical solutions provide preliminary new insights into the mechanisms of block cracking. This study presents a 3D, analytical elastic model of a two-layer pavement system subjected to constant thermal stresses. Analytical solutions of displacement and stress fields are presented in the equation and graphical form and new insights towards the mechanisms of block cracking are discussed. The use of the model as a tool to verify numerical solutions, such as finite element analyses is also discussed. Illustrative examples a field validation example and a summary of required model extensions are also provided.

Investigation of mixed mode - I/II fracture problems - Part 1: computational and experimental analyses

In this study, to investigate and understand the nature of fracture behavior properly under in-plane mixed mode (Mode-I/II) loading, three-dimensional fracture analyses and experiments of compact tension shear (CTS) specimen are performed under different mixed mode loading conditions. Al 7075-T651 aluminum machined from rolled plates in the L-T rolling direction (crack plane is perpendicular to the rolling direction) is used in this study. Results from finite element analyses and fracture loads, crack deflection angles obtained from the experiments are presented. To simulate the real conditions in the experiments, contacts are defined between the contact surfaces of the loading devices, specimen and loading pins. Modeling, meshing and the solution of the problem involving the whole assembly, i.e., loading devices, pins and the specimen, with contact mechanics are performed using ANSYSTM. Then, CTS specimen is analyzed separately using a submodeling approach, in which three-dimensional enriched finite elements are used in FRAC3D solver to calculate the resulting stress intensity factors along the crack front. Having performed the detailed computational and experimental studies on the CTS specimen, a new specimen type together with its loading device is also proposed that has smaller dimensions compared to the regular CTS specimen. Experimental results for the new specimen are also presented.

Microplane Model for Steel and Application on Static and Dynamic Fracture

AbstractThe behavior of materials and structures is strongly influenced by the loading rate. Compared with quasi-static loading structures loaded by high loading rate and impact acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia effects activated. Both influences are clearly shown in experiments. Although steel does not exhibit significant strain rate sensitivity, the dynamic fracture of steel is highly sensitive on loading rates. In this paper, the static and dynamic fracture of steel is numerically studied on a compact tension specimen (CTS), which is loaded under loading rates up to 100 m/s. First, the proposed microplane model for steel is discussed and verified for monotonic and cyclic quasi-static loading. Subsequently, three-dimensional (3D) finite element dynamic fracture analysis is carried out. It is shown that the resistance of steel (apparent strength and toughness) increases progressively after the critical s...

Three-Dimensional Fracture Analysis of Circumferentially Cracked Boiler Tubes

A comprehensive methodology is developed to understand and characterize the fracture behavior of circumferentially cracked boiler tubes in this study. Weld overlay is applied on the coal-fired boiler tubes in order to prevent the degradation of corrosive and erosive environment that the boiler tubes are exposed to in the power plants. Finite element modeling and analysis are employed for all of the computations including steady-state and transient stress intensity factor (SIF) calculations in this study. Circumferential cracking has been one of the failure modes in waterwall boiler tubes, which results in high maintenance and replacement costs. Thermomechanical stresses and corrosive environment are basically the two remarkable contributors that bring about this failure mode. The former one is investigated and quantified in this study in order to explain the fracture behavior of weld overlay coatings during the power plant operation. Periodic soot blowing operations cause cyclic transient thermomechanical stresses on the weld overlay coating that results in crack propagation and fatigue failure. Three-dimensional fracture analysis of circumferentially cracked boiler tubes is examined using enriched finite element method in this study. Transient temperatures and thermomechanical stresses are computed using ANSYS for five different periodic crack spacing values (h), which are 2, 4, 6, 10, and 20 mm in the axial direction. 3D fracture analysis was performed, and stress intensity factors were computed using FRAC3D, which is Finite Element Analysis (FEA) software developed at Lehigh University. The maximum stress intensity factor is obtained at the deepest penetration of the crack in the model which has the largest periodic axial crack spacing, h = 20 mm. The stress intensity factors due to welding residuals decrease as the axial crack spacing, h, decreases. The FEA methodology developed in this research would provide the engineers with the ability to understand the fracture problem and predict component life and improve the reliability of the weld overlay coated boiler tubes utilized in the power plants.

Three-dimensional fracture analysis using tetrahedral enriched elements and fully unstructured mesh

In the absence of automated and customized methods and tools, some of today’s existing methods for solving three-dimensional fracture problems require comprehensive finite element meshing, labor-intensive analysis and post-processing efforts. In this study, a tetrahedral enriched element method and related applications are presented that demonstrate employment of fully unstructured tetrahedral meshes for general mixed-mode three-dimensional fracture problems. As in the case of hexahedral enriched elements, the tetrahedral enriched elements also alleviate the needs of pre- and post-processing the finite element model, allowing direct computation of stress intensity factors in the solution phase. In addition, when tetrahedral enriched elements are used, the crack front region can also be meshed using unstructured elements allowing direct use of automatic free-meshing programs. The applications presented are plane-strain central crack problem, mode-I surface crack in a plate, inclined penny-shaped crack, edge-cracked bar under constant heat flux and lens-shaped crack embedded in a large elastic body. The results obtained are in good comparative agreement with those available in the literature. Thus, it is concluded that the enriched tetrahedral elements can be applied efficiently and accurately on a general three-dimensional fracture problem allowing usage of fully unstructured finite element meshes.

三次元き裂進展自動解析システムの構築 : 第1報,き裂解析システムの概要と有限要素法モデル生成

Although three-dimensional finite element analysis has become a common tool in the industries to perform their design analyses, there still exist some difficulties in performing three-dimensional fracture analyses. One of them is that although automatic mesh generation techniques are available for tetrahedral finite elements, hexahedral finite elements are commonly used in three-dimensional crack analyses. The other is that the analysis models tend to be large in their scales. Therefore performing a three-dimensional fracture analysis takes much manual labor in the analysis model generation processes and computational time. In present research, the authors have been developing a fracture mechanics analysis system that minimizes the manual labor. The key components in the analysis system are a mesh generation software and the virtual crack closure-integral method (VCCM) for the second-order tetrahedral finite element to evaluate the crack parameters (the energy release rates and the stress intensity factors). Based on them, the software system was carefully designed to handle large scale analysis model. In this paper, as the first report, the outlines of the system and the finite element model procedures are described.

A weakly-singular SGBEM for analysis of cracks in 3D anisotropic media

A weakly-singular, symmetric Galerkin boundary element method (SGBEM) is developed for analysis of fractures in three-dimensional, anisotropic linearly elastic media. The method constitutes a generalization of that by Li et al. [S. Li, M.E. Mear, L. Xiao, Symmetric weak-form integral equation method for three-dimensional fracture analysis, Comput. Methods Appl. Mech. Engrg. 151 (1998) 435–459] for isotropic media, and is based upon a pair of weak-form displacement and traction integral equations recently established by Rungamornrat and Mear [J. Rungamornrat, M.E. Mear, Weakly-singular, weak-form integral equations for cracks in three-dimensional anisotropic media, Int. J. Solids Struct. 45 (2008) 1283–1301]. The formulation involves only weakly-singular kernels and, as a consequence, standard C 0 elements can be employed in the numerical discretization. The kernels possess a relatively simple form (for general anisotropy) which involves an equatorial line integral like that associated with the displacement fundamental solution. Despite their simple form, it is still necessary to evaluate these kernels efficiently in the numerical implementation; to do so, certain symmetry properties associated with the specific material type under consideration are exploited, and a simple yet accurate interpolation strategy is introduced. Another important aspect of the numerical treatment is the use of a special crack-tip element which allows highly accurate mixed-mode stress intensity factor data to be extracted as a function of position along the crack front. This crack-tip element was originally introduced by Li et al. [S. Li, M.E. Mear, L. Xiao, Symmetric weak-form integral equation method for three-dimensional fracture analysis, Comput. Methods Appl. Mech. Engrg. 151 (1998) 435–459] in their treatment of isotropic media, and here it is extended to allow evaluation of the stress intensity factors for generally anisotropic media. The element involves “extra” degrees of freedom associated with the nodes along the crack front (with these quantities being directly related to the stress intensity factors), and it is capable of representing the asymptotic behavior in the vicinity of the crack front to a sufficiently high order that relatively large crack-tip elements can be utilized. Various examples are treated for cracks in an unbounded domain and for both embedded and surface-breaking cracks in a finite domain, and it is demonstrated that very accurate results can be obtained even with relatively coarse meshes.

Different Delamination Cracks during Fracture and Their Influences on the Fracture of X70 Pipeline Steel

Single or multiple of delaminations have been found frequently on the fracture surface of X70 pipeline steel. In this study, the delamination cracks and their influence on the fracture of pipeline are investigated by both experiment and three-dimensional fracture analyses. It is shown that the three-dimensional stress state is prerequisite for delamination crack and the strength distribution of material influences the form and direction of delamination crack. The delamination cracks are produced on the weak interfaces among the material by the tensile stress perpendicular to them before the fracture passes. The direction of delamination crack depends on the three-dimensional stress fields and strength distribution of material near the crack tip or notch root. The delamination cracks of the fracture through thickness of pipe wall make the effective thickness decrease and the delamination cracks of surface crack are perpendicular to the direction of fracture propagation direction. The delamination cracks reduce the stress triaxiality near crack tip and in turn, improve the fracture toughness of X70 pipeline steel.

Quantitative Analysis of Three-dimensional Fatigue Fracture Surface Reconstructed by Stereo Matching Method

Three-dimensional geometry of a fatigue fracture surface in a Cu-Be alloy (the grain diameter is about 24 μm) was reconstructed by the stereo matching method based on the coarse-to-fine method. The fractal dimensions of the contours and of the fracture surface profiles extracted from the reconstructed image were then estimated by the box-counting method in the scale length range smaller than about one grain-boundary length (about 14 μm). The mean value of the fractal dimension of the contours was about 1.238, and was close to that of the actual fracture surface profiles in the plane in parallel with the crack growth direction (about 1.210) (in the parallel direction) and in the plane perpendicular to the crack growth direction (about 1.190) (in the perpendicular direction). Thus, the stereo matching method can reproduce the three-dimensional image of the complex fracture surface. However, the mean value of the fractal dimension of the reconstructed fracture surface profiles (about 1 128 in the parallel direction and about 1.146 in the perpendicular direction) was a little smaller than that of the actual fracture surface profiles, since there were microstructural features such as overhang, debris and microcracks on the fatigue fracture surface, which were only partly reproducible by the stereo matching method. Nevertheless, the geometrical information about a given fracture surface in a wide area can be obtained by the three-dimensional fracture surface reconstruction and analysis. Combination of three-dimensional and two-dimensional analyses may lead to the further understanding of the geometrical features of fracture surfaces and the fracture mechanism in materials. The fractal dimension was found to be a useful index not only for characterizing fracture surfaces but also for comparison of the result of three-dimensional image reconstruction with the actual fracture surface morphology.

Three-Dimensional Fracture Analysis and Experimental Investigation of Model Unidirectional Discontinuous Tow Composite Laminates

The purpose of this work is to perform analytical modeling and experimentally produce idealized composites reinforced with discontinuous fiber tows to evaluate the theoretical upper limits of tensile strength as compared to continuous fiber composites. The idealized composite represents a staggered mosaic of prepreg tape strips of equal width and length. Three-dimensional analysis was performed to evaluate the energy release rate of the possible damage accumulation modes, such as vertical splits and delaminations emanating from tape strip ends. Realistic estimates of the failure strain of the discontinued tow composites was obtained by comparing the calculated energy release rates to the critical Mode II energy release for axial cracking in the material system. The predicted failure strain as a function of the strip geometry was also in good correlation with the experimental results.

Predicting residual strength using fully automatic crack growth

In recent years the need to predict how a product will perform over the life cycles has increased. Aerospace and other industries need to demonstrate the durability of designs and plan effective maintenance schedules. The growth of cracks due to fatigue loads plays an important role in limiting the life of products. In this paper, a new method is presented for the automatic growth of edge cracks in three-dimensional fracture analysis using BEM. The procedure described overcomes the current problems with crack growth analysis that currently has to be performed manually. Applications are presented which demonstrate the effectiveness of the technique.