Fatigue Crack Growth Analysis under Constant Amplitude Loading Using Finite Element Method

Damage tolerant design relies on accurately predicting the growth rate and path of fatigue cracks under constant and variable amplitude loading. ANSYS Mechanical R19.2 was used to perform a numerical analysis of fatigue crack growth assuming a linear elastic and isotropic material subjected to constant amplitude loading. A novel feature termed Separating Morphing and Adaptive Remeshing Technology (SMART) was used in conjunction with the Unstructured Mesh Method (UMM) to accomplish this goal. For the modified compact tension specimen with a varied pre-crack location, the crack propagation path, stress intensity factors, and fatigue life cycles were predicted for various stress ratio values. The influence of stress ratio on fatigue life cycles and equivalent stress intensity factor was investigated for stress ratios ranging from 0 to 0.8. It was found that fatigue life and von Mises stress distribution are substantially influenced by the stress ratio. The von Mises stress decreased as the stress ratio increased, and the number of fatigue life cycles increased rapidly with the increasing stress ratio. Depending on the pre-crack position, the hole is the primary attraction for the propagation of fatigue cracks, and the crack may either curve its direction and grow towards it, or it might bypass the hole and propagate elsewhere. Experimental and numerical crack growth studies reported in the literature have validated the findings of this simulation in terms of crack propagation paths.     

Effect of Rod-like Structure on Fatigue Life,Short Surface Crack Initiation and Growth Characteristics of Extruded Aluminum Alloy A2024 (Analysis via Modified Linear Elastic Fracture Mechanics)

In the Al alloy A2024-T3 extruded material, a rod-like structure is generated parallel to the extrusion direction. In this study, the effects of rod-like structures on fatigue crack initiation and growth behavior were comprehensively investigated. Two types of specimens were used in a fatigue experiment, in which the direction of the load stress amplitude was parallel (specimen P) and perpendicular (specimen V) to the rod-like structure. Based on the experimental and analytical results, the following findings were obtained regarding the fatigue life, location of crack initiation, and fatigue crack growth behavior. Because the fatigue life of specimen P was longer than that of specimen V, it is inferred that the rod-like structure significantly affects the fatigue life. In specimen P, fatigue cracks were generated from the grain boundaries of the Al matrix. By contrast, in specimen V, cracks were generated from the Cu–Mg-based intermetallic compound in the Al matrix. In specimen P, fatigue cracks were more likely to propagate across the rod-like structure, which decreased the fatigue crack growth rate. In specimen V, fatigue cracks did not propagate across the rod-like structure; instead, they propagated through the Al matrix. Therefore, the fatigue crack growth resistance of specimen V was lower than that of specimen P. The relationship between the fatigue crack growth rate and the modified linear elastic fracture mechanics parameter could be used to predict the S–N curve (stress amplitude vs. fatigue life) and fatigue crack growth behavior. The predicted results agreed well with the experimental results.     

Effect of Residual Stress Induced by Different Cooling Methods in Heat Treatment on the Fatigue Crack Propagation Behaviour of GH4169 Disc

In this study, the effects of residual stress induced by three different cooling methods during heat treatment on the crack propagation behaviour of the GH4169 disc were investigated. Different levels of stress fields were induced to the specially designed discs by using air cooling (AC), air jetting cooling (AJC) and water quenching (WQ) methods and were quantitated by numerical simulation. These discs were then subjected to prefabricated cracking, and crack propagation tests were conducted on a spin tester with two load spectrums. Crack growth behaviour was depicted via the surface replica technique and fracture morphology. Regarding the linear superposition of residual stress and centrifugal force, the crack propagation behaviour of different discs was simulated using the FRANC3D software. AJC and WQ introduced compressive residual stress (−259 MPa and −109 MPa, respectively) into the disc compared with the AC method (about −1.5 MPa). The AJC method increases the crack propagation life of the disc by introducing residual compressive stress into the area near the surface of the central hole to inhibit the opening of the crack surface. When the fatigue load was low, this inhibition effect was more significant.     

Effects of the Ultrasonic Assisted Surface Rolling Process on the Fatigue Crack Initiation Position Distribution and Fatigue Life of 51CrV4 Spring Steel

In this paper, the effects of the fatigue crack initiation position (FCIP) on fatigue life are discussed. Different modified gradient fields (MGFs) are prepared on the surface of 51CrV4 spring steel components by an ultrasonic assisted surface rolling process (USRP). Subsequently, the fatigue behaviour of steels with different FCIPs is systematically studied. The results show that the fatigue life of steels first exhibits an increasing tendency and then a decreasing tendency with increasing distance between an FCIP and the surface. When an FCIP shifts from the surface of the sample to the interior, the fatigue crack initiation resistance on the interior is greater than that on the surface, which leads to an increase in fatigue life. However, when the FCIP further shifts towards the centre of the specimen, the stress triaxiality experienced by the fatigue source gradually increases, which results in a peak in the curve of FCIP versus fatigue life. The magnitude of this peak fatigue life is related to the change in the stress triaxiality. Moreover, according to focused ion beam-high-resolution transmission electron microscopy (FIB-HRTEM) microstructural analysis near FCIPs, under a higher stress triaxiality, the crack tip area is subject to greater stress constraints, making the multiplication and movement of dislocations in this area more difficult, resulting in the decrease in movable dislocation density. This decrease in dislocation density leads to an increase in the stress concentration and accelerates the crack growth rate, decreasing the fatigue life. Therefore, the significant change in fatigue life is controlled by the MGF and stress triaxiality.     

Linear Elastic Fracture Mechanics Assessment of a Gas Turbine Vane

This work assesses the crack propagation at the most critical point of a second stage of a gas turbine blade by means of linear elastic fracture mechanics (LEFM). The most critical zone where the crack may nucleate, due to a combination of thermo-mechanical loads, is detected with an uncracked finite element (FE) model pre-analysis. Then the sub-modelling technique is used to obtain more precise results in terms of stresses within the area of interest. Simulations of the state of stress at the crack apex are performed through an FE model, using the Fracture Tool within ANSYS Workbench, and the stress intensity factors (SIFs) are determined accordingly. The Fracture Tool was previously verified on a simple model, and the results were compared with its analytical solution. Finally, the evaluation of the crack growth due to fatigue stress, creep, and oxidation is performed through in-house software called Propagangui. The crack behavior is estimated along with the component life. Results show an unexpected decrease in KI with increasing crack length and slowing of the crack growth rate with crack propagation. A detailed analysis of this behavior emphasizes that the redistribution of the stresses at the crack apex means that unstable propagation is not expected.     

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors K_I and K_II for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.     

Finite Element Simulation of a Crack Growth in the Presence of a Hole in the Vicinity of the Crack Trajectory

The aim of this paper was to present a numerical simulation of a crack growth path and associated stress intensity factors (SIFs) for linear elastic material. The influence of the holes’ position and pre-crack locations in the crack growth direction were investigated. For this purpose, ANSYS Mechanical R19.2 was introduced with the use of a new feature known as Separating Morphing and Adaptive Remeshing Technology (SMART) dependent on the Unstructured Mesh Method (UMM), which can reduce the meshing time from up to several days to a few minutes, eliminating long preprocessing sessions. The presence of a hole near a propagating crack causes a deviation in the crack path. If the hole is close enough to the crack path, the crack may stop at the edge of the hole, resulting in crack arrest. The present study was carried out for two geometries, namely a cracked plate with four holes and a plate with a circular hole, and an edge crack with different pre-crack locations. Under linear elastic fracture mechanics (LEFM), the maximum circumferential stress criterion is applied as a direction criterion. Depending on the position of the hole, the results reveal that the crack propagates in the direction of the hole due to the uneven stresses at the crack tip, which are consequences of the hole’s influence. The results of this modeling are validated in terms of crack growth trajectories and SIFs by several crack growth studies reported in the literature that show trustworthy results.     

Effect of Loading Frequency Ratio on Multiaxial Asynchronous Fatigue Failure of 30CrMnSiA Steel

Multiaxial asynchronous fatigue experiments were carried out on 30CrMnSiA steel to investigate the influence of frequency ratio on fatigue crack initiation and propagation. Test results show that the surface cracks initiate on the maximum shear stress amplitude planes with larger normal stress, propagate approximately tens of microns, and then propagate along the maximum normal stress planes. The frequency ratio has an obvious effect on the fatigue life. The variation of normal and shear stress amplitudes on the maximum normal stress plane induces the crack retardation, and results in that the crack growth length is longer for the constant amplitude loading than that for the asynchronous loading under the same fatigue life ratio. A few fatigue life prediction models were employed and compared. Results show that the fatigue life predicted by the model of Bannantine-Socie cycle counting method, section critical plane criterion and Palmgren-Miner’s cumulative damage rule were more applicable.     

Fatigue Failure from Inner Surfaces of Additive Manufactured Ti-6Al-4V Components

Selective laser melting (SLM) is an additive manufacturing process for producing metallic components with complex geometries. A drawback of this process is the process-inherent poor surface finish, which is highly detrimental in materials submitted to fatigue loading situations. The goal of this work is to analyze the fatigue behavior of Ti-6Al-4V specimens with internal axial channels under the following different conditions: hole drilled, hole as manufactured, and hole threaded M4 × 0.7. All the cases studied showed a lower fatigue performance as compared with solid samples due to the surface roughness and geometry effect that produced a surface stress concentration leading to a reduction in fatigue strength. The fractography revealed that crack initiation occurred from the internal surface in all specimens with internal channel mostly from defects as unfused particles and lack of fusion zones, while for the solid specimens crack initiation was observed from the external surface due to insufficient fusion defect. The application of the Smith-Watson-Topper energy-based parameter was revealed to be a good tool for fatigue life prediction of the different series studied.     

Very High Cycle Fatigue Failure Analysis and Life Prediction of Cr-Ni-W Gear Steel Based on Crack Initiation and Growth Behaviors

The unexpected failures of structural materials in very high cycle fatigue (VHCF) regime have been a critical issue in modern engineering design. In this study, the VHCF property of a Cr-Ni-W gear steel was experimentally investigated under axial loading with the stress ratio of R = −1, and a life prediction model associated with crack initiation and growth behaviors was proposed. Results show that the Cr-Ni-W gear steel exhibits the constantly decreasing S-N property without traditional fatigue limit, and the fatigue strength corresponding to 10⁹ cycles is around 485 MPa. The inclusion-fine granular area (FGA)-fisheye induced failure becomes the main failure mechanism in the VHCF regime, and the local stress around the inclusion play a key role. By using the finite element analysis of representative volume element, the local stress tends to increase with the increase of elastic modulus difference between inclusion and matrix. The predicted crack initiation life occupies the majority of total fatigue life, while the predicted crack growth life is only accounts for a tiny fraction. In view of the good agreement between the predicted and experimental results, the proposed VHCF life prediction model involving crack initiation and growth can be acceptable for inclusion-FGA-fisheye induced failure.     

The Numerical Analysis of the In-Plane Constraint Influence on the Behavior of the Crack Subjected to Cyclic Loading

The paper presents the influence of in-plane constraints defined by T-stress on the behavior of a crack subjected to cyclic loading. In the analysis, a modified boundary layer model approach was used in which the cohesive model was introduced. In the simulations, the constant maximum value of the stress intensity factor and four levels of T-stress were defined. The model was subjected to ten repeated stress cycles. Based on the results obtained, an analysis of the effect of the in-plane constraint on selected aspects of crack behavior was made. The strong influence of in-plane constraint applied in the model on the crack closure and the fatigue crack growth rate was proven. Since the in-plane constraint described the influence of geometry on the stress field surrounding the fatigue crack tip in real geometry, the results suggested that it is possible to create precise formulae connecting the level of the in-plane constraint with the effective stress intensity factor range and to incorporate the T-stress or Q-stress level in the Paris law.     

Numerical Study of the Effects of Residual Stress on Fretting Fatigue Using XFEM

Residual compressive stress can improve fretting fatigue strength. In this paper, the effects of residual stress on fretting fatigue of Al 2024-T351 alloy specimens are studied using a numerical approach. The extended finite element method combined with the cyclic cohesive zone model is adopted to model fretting fatigue crack growth behavior. It is shown that residual stress changes the fretting fatigue crack growth path and enhances fretting fatigue life. Crack initiation angle, depth of knee point, crack initiation life, crack propagation life and total life are greater for specimens with residual stress compared to specimens without residual stress. The effects of residual stress are more remarkable for specimens with a high intensity of residual stress. However, the effects of residual stress reduce at a high bulk load level.     

Low Cycle Fatigue Characteristics of Oxygen-Free Copper for Electric Power Equipment

The effect of heat treatment on tensile and low cycle fatigue properties of the oxygen-free copper for electric power equipment was investigated. The heat treatment at 850 °C for 20 min, which corresponds to the vacuum brazing process, caused the grain growth and relaxation of strain by recrystallization, and thus, the residual stress in the oxygen-free copper was reduced. The tensile strength and 0.2% proof stress were decreased, and elongation was increased by the heat treatment accompanying recrystallization. The plastic strain in the heat-treated specimen was increased compared with that in the untreated specimen under the same stress amplitude condition, and thus, the low cycle fatigue life of the oxygen-free copper was degraded by the heat treatment. Striation was observed in the crack initiation area of the fractured surface in the case of the stress amplitude less than 100 MPa regardless of the presence of the heat treatment. With an increase in the stress amplitude, the river pattern and the quasicleavage fracture were mainly observed in the fracture surfaces of the untreated specimens, and they were observed with striations in the fracture surfaces of the heat-treated ones. The result of the electron backscattered diffraction (EBSD) analysis showed that the grain reference orientation deviation (GROD) map was confirmed to be effective to investigate the fatigue damage degree in the grain by low cycle fatigue. In addition, the EBSD analysis revealed that the grains were deformed, and the GROD value reached approximately 28° in the fractured areas of heat-treated specimens after the low cycle fatigue test.     

Fatigue Failure Analyses on a Ti-45Al-8Nb-0.2W-0.2B-0.1Y Alloy at Different Temperatures

The fatigue micro crack initiation and propagation tests of a TiAl alloy with 8% Nb content were carried out by using scanning electron microscopy in situ technology at room temperature and at 750 °C. These results indicated that the fatigue micro crack initiation was mainly caused by the stress concentration at room temperature, but at an elevated temperature (750 °C) the multi-cracks were caused by the coupled factors of both lamellar microstructure and stress concentration. Therefore, fatigue micro crack initiation behavior is much more dependent on the lamellar structure at an elevated temperature. One of the reasons is that the elevated temperature degrades the interface strength between the lamellar of the TiAl alloy with 8% Nb content. Therefore, the small fatigue crack propagation behavior of the alloy exhibited a mixture damage model of interlamellar and translamellar at a micro scale. The crack growth path and fracture characteristics provided a proof of crack deflection, branching and/or bridging induced either by interlamellar or by translamellar failure mode.     

Effect of Residual Stresses on Fatigue Crack Growth: A Numerical Study Based on Cumulative Plastic Strain at the Crack Tip

Residual stresses affect the fatigue behavior, given that compressive stresses delay the phenomenon, while tensile stresses accelerate it. However, the mechanisms behind the effect of residual stresses are not totally understood. A numerical study is developed here to understand the effect of thermal residual stresses (TRSs) on fatigue crack growth (FCG). The crack driving force was assumed to be the cumulative plastic strain at the crack tip. The heating of a region ahead of the crack tip produced elastic compressive TRS, which were 69% of material’s yield stress. Alternatively, plastic deformation was produced by severe cooling followed by heating to generate compressive residual stresses. The crack propagation in the compressive residual stress field produced a decrease in the FCG rate. On the other hand, without the contact of crack flanks, the TRS showed no effect on FCG. Therefore, the TRSs only affect FCG by changing the crack closure level.     

Stress Intensity Factor Assessment for the Reinforcement of Cracked Steel Plates Using Prestressed or Non-Prestressed Adhesively Bonded CFRP

The use of adhesively bonded carbon fiber reinforced polymer (CFRP) materials to reinforce cracked steel elements has gained widespread acceptance in order to extend the lifespan of metallic structures. This allows an important reduction of the stress intensity factor (SIF) at the crack tip and thus a significant increase of the fatigue life. This paper deals with the assessment of the SIF for repaired cracked steel plates, using semi-empirical analysis and finite element analysis. Metallic plates with only one crack originating from a center hole were investigated. Virtual crack closure technique (VCCT) was used to define and evaluate the stress intensity factor at crack tip. The obtained modeling results are compared with experimental investigations led by the authors for different reinforcement configurations including symmetrical and non-symmetrical reinforcement, normal modulus and ultra-high-modulus CFRP plates, and pre-stressed CFRP plates. Results show that finite element model (FEM) analysis can obviously simulate the fatigue performance of the CFRP bonded steel plates with different reinforcement configurations. Moreover, a parametric analysis of the influence of the pre-stressing level was also conducted. The results show that an increase of the pre-stressing level results in an increase of the fatigue life of the element.     

Comparison of Fatigue Properties and Fatigue Crack Growth Rates of Various Implantable Metals

The fatigue strength, effects of a notch on the fatigue strength, and fatigue crack growth rate of Ti-15Zr-4Nb-4Ta alloy were compared with those of other implantable metals. Zr, Nb, and Ta are important alloying elements for Ti alloys for attaining superior long-term corrosion resistance and biocompatibility. The highly biocompatible Ti-15Zr-4Nb-4Ta alloy exhibited an excellent balance between strength and ductility. Its notched tensile strength was much higher than that of a smooth specimen. The strength of 20% cold-worked commercially pure (C.P.) grade 4 Ti was close to that of Ti alloy. The tension-to-tension fatigue strength of an annealed Ti-15Zr-4Nb-4Ta rod at 10⁷ cycles was approximately 740 MPa. The fatigue strength of this alloy was much improved by aging treatment after solution treatment. The fatigue strengths of C.P. grade 4 Ti and stainless steel were markedly improved by 20% cold working. The fatigue strength of Co-Cr-Mo alloy was markedly increased by hot forging. The notch fatigue strengths of 20% cold-worked C.P. grade 4 Ti, and annealed and aged Ti-15Zr-4Nb-4Ta, and annealed Ti-6Al-4V alloys were less than those of the smooth specimens. The fatigue crack growth rate of Ti-15Zr-4Nb-4Ta was the same as that of Ti-6Al-4V. The fatigue crack growth rate in 0.9% NaCl was the same as that in air. Stainless steel and Co-Cr-Mo-Ni-Fe alloy had a larger stress-intensity factor range (ΔK) than Ti alloy.     

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris’ law. The application examples demonstrate the developed program’s capability and performance.     

Effect of the Crack Tip Bifurcation on the Plasticity-Induced Fatigue Propagation in Metallic Materials

This article deals with the influence of the crack path branching (at the micro level) on the plasticity-induced fatigue crack growth. With regard to this, a modeling by means of the finite element method was performed considering a cracked panel subjected to tension with different symmetric and asymmetric configurations of the bifurcated crack tip. The results show the appearance of a retardation effect in the growth rate of the bifurcated crack in relation to the growth rate of the fully straight crack in different cases studied, namely: (i) if the two branches of the bifurcation have different initial projected length, the propagation rate is greater at the crack tip corresponding to the long-branch than that of the short-branch, and the long-branch growth rate increases with the decrease of the initial branch angle and of the initial projected short-branch length and with the increase of the intensity of fatigue; (ii) if the two branches of the bifurcation have identical initial projected length, the retardation effect depends on the initial distance between the two bifurcated crack tips, the growth rate going up with the decrease of such a distance and with the increase of the fatigue intensity.     

Effect of Bond-Line Thickness on Fatigue Crack Growth of Structural Acrylic Adhesive Joints

With an increasing demand for adhesives, the durability of joints has become highly important. The fatigue resistance of adhesives has been investigated mainly for epoxies, but in recent years many other resins have been adopted for structural adhesives. Therefore, understanding the fatigue characteristics of these resins is also important. In this study, the cyclic fatigue behavior of a two-part acrylic-based adhesive used for structural bonding was investigated using a fracture-mechanics approach. Fatigue tests for mode I loading were conducted under displacement control using double cantilever beam specimens with varying bond-line thicknesses. When the fatigue crack growth rate per cycle, da/dN, reached 10⁻⁵ mm/cycle, the fatigue toughness reduced to 1/10 of the critical fracture energy. In addition, significant changes in the characteristics of fatigue crack growth were observed varying the bond-line thickness and loading conditions. However, the predominance of the adhesive thickness on the fatigue crack growth resistance was confirmed regardless of the initial loading conditions. The thicker the adhesive bond line, the greater the fatigue toughness.