Mixed-mode Crack Propagation Research Articles

Fatigue behavior of corroded non-load-carrying bridge weathering steel Q345qDNH fillet welded joints

Fatigue behavior of corroded non-load-carrying fillet welded joints exposed to atmosphere in Nanjing for 1-year which were made of bridge weathering steel Q345qNH was explored in this paper. Fatigue tests were conducted on 8 specimens which were under 8 stress ranges, fitted S-N curve and lower bound of 95% survival probability were established. It was found that fatigue strength dropped by 26.2% after 1-year exposure compared to uncorroded specimens, the design S-N curve for non-load-carrying fillet welded joint in Eurocode 3 is still satisfactory for fatigue assessment of this batch of specimens. Fractography analysis revealed that fatigue cracks always originated from multiple corrosion pits, geometries of corrosion pits were quantified by surface morphology analysis. Numerical simulation of mixed-mode fatigue crack propagation was conducted, it is found that taking the geometry of the deepest pit as the equivalent initial crack and orienting the crack in the direction normal to the maximum tensile stress plane could predict fatigue lives safely and satisfactorily. The research provides reference for design and fatigue assessment of uncoated weathering steel bridges.

XFEM simulation of a mixed-mode fracture experiment in PMMA

The eXtended Finite Element Method (XFEM) has become a popular framework for the simulation of fracture phenomena. There has been substantial work to verify the method and expand its formulation for new applications such as hydraulic fracturing; however, there have been limited reports to date which validate XFEM with experimental data. The aim of this paper is to summarize recent efforts to validate a cohesive zone XFEM model with a mixed mode fracture experiment in PMMA. In the experiment, a thin rectangular specimen of PMMA was subjected to axial splitting along its major axis. In order to induce mixed mode crack propagation in the specimen, an initial angled crack was machined into the specimen. The experiment was simulated using an XFEM model with a mixed-mode cohesive traction. Two XFEM models were investigated: one in which the initial crack is idealized with zero initial width; and a second in which the initial crack geometry is explicitly modeled. With these two models, the impacts of the support conditions, geometry, and model parameters were all investigated. The fitted model parameters all fell within the expected range for PMMA. The simulated crack growth was able to capture all of the qualitative behaviour of the experimental crack growth. The simulated and experimental curved crack paths showed excellent agreement throughout the entire loading. Explicitly modeling the initial crack geometry was found to have negligible effects during crack propagation, but exhibited delayed crack initiation compared to the idealized crack. The simulated and experimental force-displacement curves showed excellent agreement in the elastic region, which provides confidence that the support conditions are prescribed correctly. After crack propagation began, the simulated specimen was noticeably stiffer than the experimental specimen. We are able to conclude that the difference in stiffness is not due to differences in the crack path, the crack length, or the model parameters, but we are unable to draw any further conclusions about the root cause of the difference in stiffnesses.

Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel

Bridge weathering steel produced in China has been employed in bridges worldwide, among them Q345qNH is the most commonly used steel grade. Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qNH was explored in this paper. Fatigue tests were conducted on 13 specimens involving 9 stress ranges, S-N curve and its lower bound of 95% survival probability were established. It was observed that the design S-N curve for butt welded joint in Eurocode 3 is suitable for fatigue assessment of this batch of specimens and provides a considerable safety margin. Numerical simulation of mixed-mode fatigue crack propagation and analytical investigation of fatigue crack propagation were conducted, it was found that numerical simulation is preferred since it considers the variation in stress due to crack propagation. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were investigated, the expression between fatigue life and initial crack size was derived. Additionally, it is recommended that a semi-elliptical crack with initial crack depth of 0.2 mm and initial aspect ratio of 1/4 to be adopted when information on initial crack is unavailable. The fatigue test results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control for analysis of deterioration of fatigue behavior due to corrosion for corroded butt welded joints made of uncoated weathering steel.

Material Configurational Forces applied to mixed-mode fatigue crack propagation and life prediction in elastic-plastic material

Within the framework of material configurational mechanics, an innovative fatigue model based on configurational force is proposed to predict the mixed-mode fatigue crack propagation in elastic-plastic material. This fatigue mode can provide the estimation of crack initiation, crack deflection, and residual fatigue lifetime simultaneously. The configurational-force fatigue model has the following basic stipulations: (a) the onset of crack growth occurs when the resultant of configurational forces reaches a critical value; (b) the crack growth takes place along the direction of resultant configurational force vector; and (c) the growth rate of mixed-mode fatigue crack is correlated to the equivalent range of material configurational forces. In order to validate the accuracy of the newly proposed fatigue model, a series of experiments are constructed by the compact tension shear specimen. The mixed-mode fatigue crack growth path and rate are obtained under different mixed-mode loading conditions. In addition, numerical implementation of configurational-force fatigue model is performed in elastic-plastic material. The results show that the mixed-model fatigue crack deflections predicted by the configurational-force fatigue model are in good agreement with experimental observations. Meanwhile the fatigue crack growth rate in elastic-plastic material has the power law relation with the equivalent range of material configurational forces, which is regardless of mixed-mode loading. It is demonstrated that the configurational-force fatigue model is able to provide a more convenient and accurate procedure to predict the mixed mode elastic-plastic fatigue crack propagation and lifetime.

Mixed-mode crack propagation in a semi-circular disc under bending made of an environmental-friendly concrete

The paper is devoted to investigations on the crack deflection angle under mixed-mode loading conditions. Several semi-circular disc configurations with an inclined crack under three-point bending are suggested and its fracture behavior is analyzed experimentally as well numerically. Various mixed-mode levels are obtained via varying basic parameters, such as crack length and/or crack inclination angle. Williams power expansion is applied for approximation of the crack-tip stress field to generalize the common strain energy density criterion. This procedure of estimation of the crack deflection angle is tested because it can bring more accurate results when materials with specific fracture response is used. Experimental and numerical results are compared and discussed to formulate recommendations on using classical or generalized fracture criterion.

Experimental database of mixed-mode crack propagation tests performed on mortar specimens with a hexapod and full-field measurements. Part II: interactive loading

This second paper presents a series of 4 crack propagation tests with the same experimental protocol as in a companion paper, but with some significant loading modifications. The first difference is that the loading is composed of in-plane rotation in addition to tension and shear translations. The second difference is that the loading is manually changed during the tests, depending on the crack tip location. This leads to tests with several bifurcations, and/or different loading ratios during the same test. One of them leads to mode I+II, and then mode I+III crack propagation. Some tests end with instabilities while others are controlled to be stable up to the complete failure of the specimen. In some cases, crack closure and friction between the crack faces occur.

Simulation of fatigue cracks growth processes of two parallel cracks in thin plate pulled by the constant amplitude cyclic loading

In the paper, the propagation processes of two parallel cracks in 2-mm-thick plate pulled by the cyclic loading were investigated by numerical simulation and experiment. The codes Abaqus and Franc3D were implemented jointly to predict the crack growth path, the stress distribution around the cracks tip and the fatigue life. The corresponding fatigue experiment was carried out on a servo-hydraulic fatigue testing machine. The investigation indicates that the predicted crack paths agree well with the experimental results at the crack propagation early stage, and the predicted crack growth rate is consistent with the findings in experiment, which validate the prediction of the mixed mode crack propagation processes.

An improved computational framework based on the dual boundary element method for three-dimensional mixed-mode crack propagation analyses

This study presents an improved computational framework based on the Dual Boundary Element Method (DBEM) for modelling three-dimensional mixed-mode fatigue crack propagation in geometrically complex structural components. The improvements are: (i) an input data scheme based on an alternative collocation strategy, which enables the discretization of each Non-Uniform Rational B-splines (NURBS) surfaces of geometrical models without any concerning about conform meshes at the surface´s intersections. (ii) a variational formulation defined over the crack front, which accounts for both kinking and twisting angles of the during the crack propagation. (iii) a linear approximation for the Stress Intensity Factors (SIF) range, which was applied in the three-dimensional fatigue analysis and enables the discrete solution of the Paris law in accurate form. The SIF are assessed by the displacement correlation or extrapolation techniques. The maximum energy release rate or the Schöllmann's criteria are adopted for driving the propagation process. Four numerical examples are presented in order to validate the proposed computation framework and investigate its accuracy and robustness.

Mixed mode fracture: numerical evaluation and experimental validation using PMMA specimens

Mixed mode crack propagation analysis has been more accessible with the development of new numerical tools, allowing to evaluate the influence of non-mode I loadings in the crack path and in the growth rate. The aim of this work is to analyse the propagation of pre-existing cracks under pure mode I, pure mode II and unstable mixed mode I-II loading conditions. Numerical simulations with two-dimensional models created in Abaqus software were performed, and the results obtained were compared with the analytical and experimental results. To determine T-stress and stress intensity factors, the conventional finite element method was used, post-processed with the modified virtual crack closure technique (mVCCT) and / or the J-integral. The extended finite element method (XFEM) is also used to predict the crack trajectory under different loading conditions. The experimental procedures were performed in three and four-point bending tests on single edge notch specimens of PMMA, in which a natural pre-crack was created by small impacts with a hammer on a blade located over the pre-existing machined notch. The four-point bending test was performed with an asymmetrical configuration. Varying the locations of supports and loading points with respect to the crack plane, this configuration allows to create pure mode II and mixed-mode I-II situations. The three-point bending test was performed in the conventional manner, with only the distance from the load line to the crack plane being varied.

Quasi-static analysis of mixed-mode crack propagation using the meshless local Petrov–Galerkin method

The efficiency of classical truly meshless local Petrov–Galerkin method with linear test function approximation in the crack growth problems of complex configurations is investigated in this article. Several unique and multiple (two) cracks are examined to show the accuracy of the proposed meshfree method by comparing the crack path with boundary element, finite element, element-free Galerkin and experimental results. Crack propagation under both mechanical and thermal loads and also mode I and mixed-mode conditions are evaluated. Effect of the functionality of material properties on crack paths and sensitivity of crack growth to boundary conditions are investigated. Classical maximum circumferential stress criterion is employed into the formulation of the MLPG method to predict crack growth direction. Despite the common numerical studies, a simple and straightforward automatic increment size determination method is introduced and implemented in the MLPG method. Besides, regular domain point distribution in the vicinity of the crack tip without the increased density of points is used. Various test problems show the computational accuracy and applicability of this method to linear elastic fracture mechanics problems.

Cohesive Model for the Simulation of Crack Initiation and Propagation in Mixed-Mode I/II in Composite Materials

A cohesive element able to connect and simulate crack growth between independently modeled finite element subdomains with non-matching meshes is proposed and validated. The approach is based on penalty constraints and has several advantages over conventional FE techniques in disconnecting two regions of a model during crack growth. The most important is the ability to release portion of the interface that are smaller than the local finite element length. Thus, the growth of delamination is not limited to advancing by releasing nodes of the FE model, which is a limitation common to the methods found in the literature. Furthermore, it is possible to vary the penalty parameter within the cohesive element, allowing to apply the damage model to a chosen fraction of the interface between the two meshes. A novel approach for modeling the crack growth in mixed mode I + II conditions has been developed. This formulation leads to a very efficient computational approach that is completely compatible with existing commercial software. In order to investigate the accuracy and to validate the proposed methodology, the growth of the delamination is simulated for the DCB, ENF and MMB tests and the results are compared with the experimental data.

Simulation of uniaxial tensile behavior of quasi-brittle materials using softening contact models in DEM

This study proposes new contact models to be incorporated into discrete element method (DEM) to more accurately simulate the tensile softening in quasi-brittle materials, such as plain concrete and masonry with emphasis on fracture mechanism and post-peak response. For this purpose, a plain concrete specimen (double notched) and stack bonded masonry prism under direct tensile test are modeled. Furthermore, mixed mode crack propagation is investigated in concrete and brickwork assemblages. Two modeling approaches are proposed, the simplified and detailed meso modeling, both based on DEM. In the simplified meso-model, a smooth contact surface is considered between two separate blocks, whereas the internal structure of the material is explicitly represented as a tessellation into random polyhedral blocks in the detailed meso-model. Furthermore, recently developed tensile softening contact constitutive models implemented into a commercial discrete element code (3DEC) are used to simulate the softening behavior of concrete and masonry. As an important novel contribution, it is indicated that the proposed computational models successfully capture the complete (pre- and post-peak) material behavior and realistically replicate the cracking mechanism. Additionally, a sensitivity analysis demonstrates the influence of the various micro-contact parameters on the overall response of the examined materials.

Effect of temperature on the probability and cost analysis of mixed-mode fatigue crack propagation in patched aluminium plate

By the present paper, a numerical model for cost and probability analysis of mixed mode fatigue crack propagation in a patched 2024-T3Aluminium plate is developed. The finite element method is used to analyse the temperature effect on the bonded composite repair performance of the Aluminium plate. Using a fine mesh, mid-plane finite element results are in good experimental results given by literature. Different patch shapes are proposed like; circle, rectangle, square, ellipse, regular octagon, and prolonged octagon. The stress intensity factors at the crack tip are chosen as fracture criteria in order to estimate the repair performance. According to the temperature variation, the lifespan of the repaired fatigue crack growth is estimated using Paris law. The repair done on a central inclined crack with a single-side composite patch show that, best results are given by prolonged octagon and patch is damaged under at elevated temperature. The life-cycle of the patched Aluminium plate is obtained by Monte Carlo simulation, and the probability of failure is quantified according to various geometrical and mechanical parameters. At elevated temperature, the most dominant input parameters are thicknesses of adhesive and patch. In sensitivity analysis effect of thickness of the adhesive layer reaches 35%.Finally, a code source has been developed and implanted in ANSYS software, to consider the manufacturing process and optimal maintenance costs to prove the performance of patch operation from both safety and economical point of view.

Numerical simulation of fatigue crack propagation in mixed-mode (I+II) using the program BemCracker2D

PurposeThe purpose of this paper is to present the application of the boundary element method (BEM) in linear elastic fracture mechanics for analysis of fatigue crack propagation problems in mixed-mode (I+II) using a robust academic software named BemCracker2D and its graphical interface BemLab2D.Design/methodology/approachThe methodology consists in calculating elastic stress by conventional BEM and to carry out an incremental analysis of the crack extension employing the dual BEM (DBEM). For each increment of the analysis, the stress intensity factors (SIFs) are computed by the J-Integral technique, the crack growth direction is evaluated by the maximum circumferential stress criterion and the crack growth rate is computed by a modified Paris equation, which takes into account an equivalent SIF to obtain the fracture Modes I and II. The numerical results are compared with the experimental and/or BEM values extracted from the open literature, aiming to demonstrate the accuracy and efficiency of the adopted methodology, as well as to validate the robustness of the programs.FindingsThe paper addresses the numerical simulation of fatigue crack growth. The main contribution of the paper is the introduction of a software for simulating two-dimensional fatigue crack growth problems in mixed-mode (I+II) via the DBEM. The software BemCracker2D coupled to the BemLab2D graphical user interface (GUI), for pre/post-processing, are very complete, efficient and versatile and its does make relevant contributions in the field of fracture mechanics.Originality/valueThe main contribution of the manuscript is the development of a GUI for pre/post-processing of 2D fracture mechanics problems, as well as the object oriented programming implementation. Finally, the main merit is of educational nature.

Algorithm for automatic fatigue crack growth simulation on welded high strength steels

Nowadays the demand for high strength steels is increasing. In order to design and develop high performance products, it is essential to understand the fatigue behavior of these materials. When considering welded components, the fatigue behavior is even more complex. The material parameters may change along the crack growth and mixed mode crack propagation may also occur. To assess welded high strength steel fatigue behavior, different welded CT specimens were tested. The Paris law material constants were obtained for the heat affected zone material. Fatigue crack growth life predictions were made using the obtained parameters and different automatic techniques. Previous work showed that the ABAQUS extended finite element method can predict fatigue crack growth, but as the implementation of the Paris law is not straight forward, to many conversions must be made and the results are too computer intensive. A simpler and more intuitive Python algorithm was developed, to enable the use of the experimental material parameters, to predict the crack propagation path. The obtain results show a good agreement with both the experimental Paris curves, and the analytical solution.

Effect of stop holes on structural integrity of offshore structures: a numerical model

As offshore structures are reaching their original design life, effective repair and life-extension techniques are required, in order to ensure continued safe operation. A stop hole may be drilled at the end of a crack, in order to delay further fatigue crack propagation. To compare the stop hole technique with other relevant repair techniques, its effect needs to be modelled. Here, a procedure for modelling the stop hole-induced fatigue crack growth delay for a crack propagating under mixed-mode I + II conditions is presented. The procedure combines the S–N curve for fatigue crack initiation and the Paris law for fatigue crack propagation, with models for mixed-mode crack propagation and finite-element analysis of the cracked geometry. The failure criterion inherent in the S–N curves is used to define the transition between initiation and propagation. The procedure is implemented on an example, and the importance of considering the mixed-mode conditions is indicated.

An adapting cohesive approach for crack-healing analysis in SMA fiber-reinforced composites

In this study, a varying/adapting cohesive approach is developed to model crack-healing procedure in reinforced shape memory composites. To this aim, the stress–strain behavior of SMA fiber in thermo-mechanical condition is converted into a traction–separation response between crack faces. The extended finite element formulation is employed to model crack in reinforced composites and to avoid remeshing while maintaining the required accuracy of results. Combination of XFEM to model arbitrary crack and traction–separation formulation enables the model to simulate mixed-mode crack propagation and crack-healing with different fiber orientations. Examining the results shows that the proposed model maintains the precision of direct modeling of SMA fibers while decreasing the computational costs and complexity of modeling significantly.

Phase field method for simulating the brittle fracture of fiber reinforced composites

We implemented a three-dimensional phase field model to simulate crack initiation and propagation in fiber reinforced composites. An efficient and robust staggered scheme is adopted by decoupling the fracturing phase field and displacement field. With this approach, the mixed-mode crack propagation in composite materials as well as the fracture process of fiber reinforced composites can be precisely captured. Our results revealed that the mechanical properties and crack propagation are influenced by the direction of inside imperfection with respect to load, interactive effects of the imperfections and damageable layer impact. We observed that accurate post-peak displacements and sharper crack evolution can be obtained by employing smaller displacement increments. The present model precisely captured the physical-consistent phenomena that crack initiates from a damageable layer, followed by matrix cracking, crack branches when it encounters a stiffer material and propagates along the interface, and interactive crack growth.

Combined static-cyclic multi-axial crack propagation in cruciform specimens

Two cracks, initiated from the opposite tips of a 45° inclined central notch, were considered in cruciform specimens made of Ti6246. A static load was applied along one arm of the specimen and a cyclic load (R = −1) was applied along the other arm. Crack propagation was carefully monitored by optical means for different ratios of static to cyclic load. The observed crack propagation was simulated using two numerical tools, involving two different mixed-mode crack propagation prediction methods. The experimental evidence shows that there is a switch in crack propagation direction from orthogonal to the cyclic load at low static load levels to orthogonal to the static load for high static load levels. Both numerical procedures were able to predict this switch, albeit at slightly different static to cyclic load ratios.

Novel engineered high performance sugar beetroot 2D nanoplatelet-cementitious composites

In this paper, we show for the first time that environmentally friendly nanoplatelets synthesized from sugar beetroot waste with surface area and hydroxyl functional groups similar to those of graphene oxide (GO) can be used to significantly enhance the performance of cementitious composites. A comprehensive experimental and numerical simulation study was carried out to examine the performance of the bio waste-derived 2D nanoplatelets (BNP) in cementitious composites. The experimental results revealed that the addition of BNPs decreased the workability of the cement pastes due to their high surface area and dominant hydrophilic functional groups. The experimental results also revealed that the BNP sheets altered the morphology of the hydration phases of the cementitious composites. At 0.20-wt%, the BNP sheets increased the content of the C-S-H gels. At higher concentrations (i.e., 0.40-wt% and 0.60-wt%), however, the BNP sheets increased the content of the calcium hydroxide (Ca(OH)2) products and altered their sizes and morphologies.The flexural results demonstrated that the 0.20-wt% BNPs produced the highest flexural strength and modulus elasticity and they were increased by 75% and 200%, respectively. The numerical simulations were in good agreement with the fracture test results. Both results showed that the 0.20-wt% BNPs optimal concentration significantly enhanced the fracture properties of the cementitious composite and produced mixed mode crack propagation as a failure mode compared to Mode I crack propagation for the plain cementitious composite due to combined crack bridging and crack deflection toughening mechanisms. Because of this, the fracture energy and the fracture toughness were increased by about 88% and 106%, respectively.