Mixed-mode Fatigue Research Articles

Computational modeling of three-dimensional mixed mode-I/II/III fatigue crack growth problems and experiments

Mixed mode-I/II/III fatigue crack growth experiments and their simulations are performed using a system permitting all possible combinations of three-dimensional mixed mode loading conditions. The so-called Compact Tension-Shearing and Tearing (CTST) specimens used in the experiments are made of 7075-T651 aluminum alloy. Different mixed mode loading conditions are considered and the applicability of a previously developed new 3-D fracture criterion on 3-D mixed mode fatigue problems is evaluated. Crack growth surfaces obtained from numerical simulations and experiments are compared using existing criteria in the literature and the developed criterion. Especially for highly mixed mode conditions, the developed criterion predicts the crack growth surface better than the MTS criterion by reducing nearly half of the latter’s deviation from the experimental surface. Based on the computed mixed mode stress intensity factors, comparisons of lives show that most mixed mode fracture criteria underpredict fatigue crack propagation lives. Numerical analyses are also performed on a cylindrical steel bar under combined tension–torsion fatigue load to further validate the method presented. The predicted results showed good agreement with experimental data from the literature.

Fatigue crack growth behavior of rib-to-deck double-sided welded joints of orthotropic steel decks

Innovative double-sided welding is expected to improve the fatigue resistance of rib-to-deck welded joints of orthotropic steel decks (OSDs). Welding crack-like defects are the crucial issue affecting the fatigue performance of rib-to-deck double-sided welded joints. This study presents a numerical simulation of three-dimensional (3D) mixed mode fatigue crack growth behavior of rib-to-deck double-sided welded joints of OSDs. Maximum tensile stress theory and equivalent stress intensity factor (SIF) were used to simulate mixed mode fatigue cracks growth. The Paris law model was employed to predict the fatigue life. Fatigue cracks of rib-to-deck double-sided welded joints were characterized by the presence of mixed mode cracks of modes I (open), mode II (shear), and mode III (tear), which was dominated by mode I. The equivalent SIF was found to be complex at the growth stage with the maximum value at the two ends of the crack front and the minimum value at the midpoint of the crack front. The crack shape became flatter in the later phase of the crack growth. The fatigue crack surface underwent deflections during crack growth, making the final crack shape exhibiting the characteristic of a spatial curved surface. The initial crack geometry showed a significant impact on the fatigue life.

Adaptive Finite Element Prediction of Fatigue Life and Crack Path in 2D Structural Components

The existence of a hole near a growing fatigue crack can cause the crack trajectory to deviate. Unless the hole is too close to the crack, the crack is arrested at the edge of the hole and does not progress further. The purpose of this paper was to predict the crack propagation and lifetime of two-dimension geometries for linear elastic materials in mixed-mode loading using a finite element source code program written in Visual Fortran language. The finite element mesh is generated using the advancing front method. The onset criterion of crack propagation was based on the equivalent stress intensity factor which provides the most important parameter that must be accurately estimated for the mixed-mode loading condition. The maximum circumferential stress theory was used as a direction criterion. The modified compact tension (MCTS) was studied to demonstrate the influence of the hole’s presence on the direction of crack growth and fatigue life for different configurations. The Paris’ law model has been employed to evaluate the mixed-mode fatigue life for MCTS in different configurations under the linear elastic fracture mechanics (LEFMs) assumption. The framework involves a progressive crack extension study of stress intensity factors (SIFs), crack growth direction, and fatigue life estimation. The results show that the fatigue growth was attracted to the hole either changes its direction to reach the hole or floats by the hole and grows as the hole is missed. The results of the study agree with several crack propagation experiments in the literature revealing similar crack propagation trajectory observations.

Mixed-mode fatigue crack growth using cohesive zone modeling

In order to capture nonlinear crack tip behavior and account for mixed-mode fatigue crack growth, a cohesive zone based fatigue crack growth model is proposed in conjunction with the Park-Paulino-Roesler (PPR) traction-separation relationship. The model clearly defines five stages during arbitrary fatigue loading: softening, unloading, reloading, contact, and complete failure. The cohesive traction-separation relationship is based on the PPR fracture potential, while the fatigue damage is accumulated by introducing two conjugate damage measures. One damage measure is associated with the rate of separation, while the other is related to the rate of traction (or local stress). Additionally, two model constants are introduced to control the normal contact condition, which may be associated with physical conditions such as crack closure, crack face roughness, and oxidation of fracture surface. Furthermore, computational simulations of the proposed fatigue crack growth model are performed for a simple mode-I test, double cantilever beam test, modified mixed-mode bending test, and three-point bending test. The observed computational results lead to stable and consistent fatigue crack growth.

Numerical Analysis of Fatigue Crack Growth Path and Life Predictions for Linear Elastic Material.

The main objective of this work was to present a numerical modelling of crack growth path in linear elastic materials under mixed-mode loadings, as well as to study the effect of presence of a hole on fatigue crack propagation and fatigue life in a modified compact tension specimen under constant amplitude loading condition. The ANSYS Mechanical APDL 19.2 is implemented for accurate prediction of the crack propagation paths and the associated fatigue life under constant amplitude loading conditions using a new feature in ANSYS which is the smart crack growth technique. The Paris law model has been employed for the evaluation of the mixed-mode fatigue life for the modified compact tension specimen (MCTS) with different configuration of MCTS under the linear elastic fracture mechanics (LEFM) assumption. The approach involves accurate evaluation of stress intensity factors (SIFs), path of crack growth and a fatigue life evaluation through an incremental crack extension analysis. Fatigue crack growth results indicate that the fatigue crack has always been attracted to the hole, so either it can only curve its path and propagate towards the hole, or it can only float from the hole and grow further once the hole has been lost. In terms of trajectories of crack propagation under mixed-mode load conditions, the results of this study are validated with several crack propagation experiments published in literature showing the similar observations. Accurate results of the predicted fatigue life were achieved compared to the two-dimensional data performed by other researchers.

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.

Experimental and numerical investigation on fatigue crack growth behavior of commercial pure titanium under I-II mixed mode loading at negative load ratios

With the increase of design and application parameters for pressurized structures, the mixed mode fatigue crack growth (FCG) behavior has become a concerned problem in the field of structural integrity. In order to understand FCG behavior of I-II mixed mode crack growth at negative load ratios, an improved compact tensile shear (CTS) specimen of commercial pure titanium is taken to study the effects of load ratio and loading angle on I-II mixed mode FCG behavior through experiments and finite element method (FEM), which mechanism is discussed in depth as well. The contribution of mode I and mode II crack growth driving forces to I-II mixed mode FCG is analyzed. The changes of crack fracture criterion and the mechanism of crack growth in I-II mixed mode FCG process are revealed, and the competition relationship between two crack closure mechanisms of I-II mixed mode crack at negative load ratios is explained. An improved fatigue crack growth rate (FCGR) model that can make I-II mixed mode FCGR normalized is proposed by considering both the crack closure and the crack fracture criterion eventually.

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.

Numerical analysis of mixed-mode fatigue crack growth of adhesive joints using CZM

With the increased use of adhesive joints in industrial environments, the need for improvement of this bonding technology arises. Namely, a reliable fatigue life estimation is essential to prevent catastrophic failure in adhesively bonded structural components. The cohesive zone model (CZM) approach has been used in numerical models to assess degradation by fatigue under pure mode conditions. However, in real life, components are subjected to multiaxial loads, the aim of this paper is to perform a numerical estimation of the fatigue behavior of an epoxy-based adhesive subjected to mixed mode loading conditions. To achieve this, the mixed mode was split into the corresponding components of mode I and mode II. For each mode, the adhesive’s cohesive properties were degraded by fatigue, according to a relation previously published for pure mode I and which has also been validated for pure mode II. Fatigue tests were performed on DCB specimens to calibrate the degradation model which, along with a triangular shaped CZM, was included in an Abaqus user material subroutine (UMAT) to perform a simulation of the fatigue behavior. Results showed that such approach can be applied to estimate the fatigue life of adhesive joints under mixed mode loading conditions.

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.

Assessment of mixed mode fatigue crack growth under biaxial loading using an iterative technique

Crack growth is investigated numerically in a cruciform specimen with an inclined center crack subjected to biaxial fatigue loading. The mixed-mode fatigue crack growth was examined using a parametric study both on the biaxial stress ratio and the initial crack angle. A fatigue crack growth code for two-dimensional problems was developed to investigate the mixed-mode behavior of fatigue crack growth under biaxial loading. The effects of initial crack angle and the biaxial stress ratio on the specimen fatigue life are explored using finite element analysis and the results are discussed.

T-Stress on a cruciform specimen: A preliminary study for a new crack propagation model

Mixed mode fatigue crack growth (FCG) can occur due to complex loading or specimen geometry. Fatigue crack paths can be determined using propagation criteria like the Maximum Tangential Stress (MTS) criterion, or the Maximum Shear Stress (MSS) criterion, for mode I and II dominated propagation respectively. These criteria only consider mode I and II Stress Intensity Factors (SIF), neglecting the T-Stress effects. In order to develop a new fatigue crack propagation model, that takes this fracture mechanics parameter into account, T-Stress values on a cruciform specimen were calculated for different loading conditions. Using a previously developed Finite Element Analysis (FEA) automatic propagation algorithm, cracks with two different initial orientations, were allowed to grow under different biaxial loading ratios and phases. Also, two holes were simulated on the specimen, in order to assess their influence on FCG. The resulting T-Stress values were determined as a function of the loading conditions and compared with the crack paths. It was possible to correlate the T-stress values with crack propagation direction stability and loading parameters, enabling the future development of a new crack propagation model, considering the influence of this fracture mechanics parameter.

Application of Response Surface Method in Probabilistic Fatigue Crack Propagation Life Assessment using 3D FEA

Fatigue crack growth life assessment is an important task in damage tolerant design practices. Being able to assess variability of crack propagation path and remaining useful life requires both deterministic and probabilistic modeling capabilities. Three-dimensional fatigue crack growth finite element modeling and Radial Basis Function based Response Surface modeling is shown to be an accurate and efficient route to predict crack propagation path in uncertainty quantification studies. A mixed-mode fatigue crack growth experimental measurement from literature is used for validation purposes and for quantifying crack path sensitivity due to off-nominal specimen geometry. Two sets of deterministic 3D crack propagation simulations are performed to relate geometric deviations to crack path predictions: first set is used to calibrate the response surface model while the second for verification purposes. Once verification requirements are satisfied, the response surface model can be employed in Monte Carlo type probabilistic simulations.

Study of the Fatigue Crack Growth in Long-Term Operated Mild Steel under Mixed-Mode (I + II, I + III) Loading Conditions.

The paper presents an analysis of mixed-mode fatigue crack growth in bridge steel after 100-years operating time. Experiments were carried out under mode I + II configuration on Compact Tension Shear (CTS) specimens and mode I + III on rectangular specimens with lateral stress concentrator under bending and torsion loading type. Due to the lack of accurate Stress Intensity Factor (SIF) solutions, the crack path was modelled with the finite element method according to its experimental observation. As a result, the Kinetic Fatigue Fracture Diagrams (KFFD) were constructed. Due to the change in the tendency of higher fatigue crack growth rates from KI towards KIII dominance for the samples subjected to bending and torsion, it was decided to analyze this phenomenon in detail using electron-scanning microscopy. The fractographic analysis was carried out for specimens subjected to I + III crack loading mode. The mechanism of crack growth in old bridge steel at complex loads was determined and analyzed.

The effect of anisotropic microstructure on the crack growth and fatigue overload behaviour of ultrafine-grained nickel

Changes in crack growth rate associated with overload events during fatigue are poorly understood, especially for materials with anisotropic microstructures. Here overload fatigue tests are reported for compact tension samples cut in two different orientations from high pressure torsion disc samples. During growth the crack planes reoriented either slightly, or significantly, to align with the elongated grain structure leading to low, and high, levels of mixed mode fatigue loading respectively. In both cases the ultrafine grained microstructure led to macroscopically flat crack faces. The fatigue crack growth rate was around 2.4 times slower for the case with the high mode II component than for the low. A 100% overload was then introduced and synchrotron X-ray diffraction and digital image correlation (DIC) were applied in-situ to map the bulk crack-tip elastic strain field (plane strain) and surface displacement field (plane stress) respectively prior to, during and after overload. The high mode II case displayed a larger degree of retardation after overload. Residual stress and plasticity-induced crack closure were found to be the primary causes for the retardation as the crack grows into the overload plastic zone. Significant crack face contact was observed for the high mode II case along with significant levels of compressive stress transferred across the crack faces at minimum load. Compared with conventional (coarse) grain Ni, the ultrafine grained Ni is less retarded by overload, because of its relatively flatter crack path and higher yield stress and thus less plasticity and residual stress induced closure.

Mixed mode fatigue crack growth studies in AISI 316 stainless steel

Damage tolerance assessment requires the accurate prediction of fatigue crack growth lives. Numerical simulation techniques using mixed mode Paris' law and various equivalent stress intensity factor models (ΔKeq) are widely employed for fatigue life prediction. In the present work, mixed mode (I/II) fatigue crack growth experiments are performed using the compact tension shear specimens made of AISI 316 austenitic stainless steel for various loading angles. Finite element fatigue crack growth simulations are carried out, and the effect of ΔKeq model in fatigue life prediction is studied. To achieve this, a three parameter double exponential type best fit is proposed for fitting the experimental mixed mode crack length vs fatigue life. The performance and capability of various selected models are assessed by comparing the predicted life with the experimental results. Fractographic studies at different stages of crack propagation for different loading angles are also presented to aid the above assessments. Based on the overall consistent performance, Irwin's and Tanaka models are predicting life close to the experimental data and Richard's and Yan's models provide conservative solutions.

Experimental and numerical investigation of mixed mode fatigue crack growth models in aluminum 6061-T6

Damage tolerance philosophy and safe life design principles are widely used for critical structural components, and in such cases, fatigue life prediction using the numerical techniques is essential. In the present work, mixed mode fatigue crack growth experiments are performed using the compact tension shear specimens made of Al 6061-T6 alloy for mode mixity angles of 30°, 45°, and 60°. These experimental studies are supported by numerical and fractographic studies on the selected specimens. A three-parameter double exponential model for fitting the fatigue crack growth curves (crack length vs. the number of fatigue life cycles) is also proposed for both the mode I and mixed mode (I/II) loading conditions. Numerical prediction of mixed mode (I/II) fatigue life is carried out using the Paris’ law in combination with various ΔKeq models. The results of the present investigation show that highly satisfactory best fits to the scattered experimental data can be obtained with the help of the proposed double exponential model. The predicted life is compared with the experimental fatigue life using various measures of error. Based on the overall performance of the models during the entire crack growth regime, the results of the present investigation clearly show that Irwin’s model and one of the Tanaka’s model are consistently found to predict the mixed mode fatigue life close to the experimental data. Whereas, Richard’s and Yan’s models, again based on the overall performance, are found to be conservative models consistently for the prediction of the mixed mode fatigue life. These conclusions are verified with the published results.

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.

Effects of Mixed Mode Loading Conditions on Fatigue Crack Growth Rate

The fatigue crack growth rate is the most important factor in predicting the life of a product when applying the damage tolerance design concept. Studies related to pure mode I for structures under fatigue loading have been actively conducted, while not many studies are conducted on the mixed mode. In this study, therefore, mixed mode fatigue crack growth experiments were designed using the Compact-Tension-Shear (CTS) specimens and the loading devices, proposed by Richard. Furthermore, the finite element analysis was used in determining the stress intensity factors of CTS specimen. As the results, the fatigue crack growth rate using the equivalent stress intensity factors proposed by previous researchers was lower than that of pure mode I at the initial stage of crack growth when the load angle increases.

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.