Fatigue crack nucleation in metals

One of the unanswered questions in the study of fatigue is how cracks nucleate at stresses far below the static fracture strength. Previous theories show possible qualitative mechanisms that may operate in a crystal at room and low temperatures but none provides a quantitiative theory of this phenomenon. We show here a quantitative mechanism of fatigue crack initiation.

With a small initial stress field, two closely located thin slices slide in opposite directions under cyclic loading. The increase of the local plastic strain with cycles of loading is calculated. The local plastic shear strain, positive in one slice and negative in the other, reaches 100 per cent at the free surface in a few hundred cycles. These large strains clearly cause the start of an extrusion or intrusion and fatigue crack nucleation.

     

A Fracture Mechanics Model for Cavitation Damage in Mechanical Heart Valve Prostheses

In the 1994 Replacement Heart Valve Guidance of the Food and Drug Administration (FDA), both cavitation and damage tolerance analyses are required for mechanical heart valves (MHV). Cavitation results from a sequence of events. First, vaporous bubbles are generated in the blood flow. They then collapse to form high-speed micro liquid jets, striking against the solid valve boundary, and subsequently causing pits on the surface. Micro cracks may initiate around the pitted areas under repeated jet impacts superimposed with cyclic loading. These events are, of course, closely related to the shape and size of an MHV. The factors specified in the current FDA guidance and considered by many authors for calculating working stresses, including static stresses, dynamic stresses, residual stresses, and stress concentrations, appear to be inadequate. The local high pressure caused by cavitation jets is another important factor which may aggravate crack propagation. The present paper is aimed at quantitatively assessing the influence of cavitation jets on the safe service life of an MHV using a damage tolerance approach. A new fracture mechanics model for estimating service lives of MHV prostheses is proposed, in which bubble dynamics and cavitation phenomenon are incorported. Numerical results show that the local high pressure is dominant, and is large enough to cause a crack to propagate at a greater rate, and resulting in much shorter fatigue life for an MHV.     

Effect of Yield Strength Distribution Welded Joint on Crack Propagation Path and Crack Mechanical Tip Field

Due to the particularity of welding processes, the mechanical properties of welded joint materials, especially the yield strength, are unevenly distributed, and there are also a large number of micro cracks, which seriously affects the safety performance of welded joints. In this study, to analyze the effect of the uneven distribution of yield strength on the crack propagation path of welded joints, other mechanical properties and residual stresses of welded joints are ignored. In the ABAQUS 6.14 finite element software, the user-defined field (USDFLD) subroutine is used to define the unevenly distributed yield strength, and extended finite element (XFEM) is used to simulate crack propagation. In addition, the static crack finite element model of the welded joint model is established according to the crack propagation path, which is given the static crack model constant stress intensity factor load, and the influence of an uneven yield strength distribution on mechanical field is analyzed. The results show that the crack length of welded joints as well as the plastic deformation range of the crack tip in high stress areas can be reduced with the increase of yield strength along the crack propagation direction. Moreover, the crack deflects to the low yield strength side. This study provides an analytical reference for the crack path prediction of welded joints.     

Numerical and Experimental Studies for Fatigue Damage Accumulation of CFRP Cross-Ply Laminates Based on Entropy Failure Criterion

The transverse cracking behavior of a carbon-fiber-reinforced plastic (CFRP) cross-ply laminate is investigated using a fatigue test and an entropy-based failure criterion in this study. The results of fatigue experiments show that the crack accumulation behavior depends on the cyclic number level and frequency, in which two obvious transverse cracks are observed after 10⁴ cyclic loads and 37 transverse cracks occur after 10⁵ cycles. The final numbers of transverse cracks decrease from 29 to 11 when the load frequency increases from 5 Hz to 10 Hz. An entropy-based failure criterion is proposed to predict the long-term lifetime of laminates under cyclic loadings. The transverse strength of 90° ply is approximated by the Weibull distribution for a realistic simulation. Progressive damage and transverse cracking behavior in CFRP ply can be reproduced due to entropy generation and strength degradation. The effects of stress level and load frequency on the transverse cracking behavior are investigated. It is discovered that, at the edge, the stress σ₂₂ + σ₃₃ that is a dominant factor for matrix tensile failure mode is greater than the interior at the first cycle load, and as stress levels rise, a transverse initial crack forms sooner. However, the initial transverse crack initiation is delayed as load frequencies increase. In addition, transverse crack density increases quickly after initial crack formation and then increases slowly with the number of load cycles. The proposed method’s results agree well with those of the existing experimental method qualitatively. In addition, the proposed entropy-based failure criterion can account for the effect of load frequency on transverse crack growth rate, which cannot be addressed by the well-known Paris law.     

Investigation on the Deformation and Failure Characteristics of Concrete in Dynamic Splitting Tests

The dynamic response behavior of concrete is constantly concerned because of seismic, impact and explosion events in the service of constructions. As a classic device for testing the dynamic mechanical properties of materials, the splitting Hopkinson pressure bar was used to carry out dynamic splitting tests on concrete in this paper. The variation of the dynamic tensile strength against the stress rate was fitted by the incubation time criterion. The full-field strain distribution on the observed surface of the specimen at the crack initiation stage was obtained by the digital image correlation (DIC) method. Morphological characteristics of the fragmentized process of concrete specimens in splitting processes were obtained by combining the image processing techniques and the FracPaQ. The size distribution of fragments of concrete specimens was obtained by sieving. The results show that the strain concentration zone and crack initiation appear along the loading direction through the center of the specimen. The secondary cracks initiated occurred at the contact end of the specimen, which expanded along the strain concentration zone and then interacted with the main crack. At the early stage of crack extension, the main crack dominates the normalized length of fracture traces in the horizontal direction. The normalized length of the vertical fracture trace increases with the main cracks opening width and the expansion of the secondary crack. The relationship between the length and angle of fracture traces in the dynamic splitting process of concrete conforms to the Gaussian function. Finally, the fragment sizes decrease with the stress rates of impact loads.     

A Parametric Study of Hertzian Contact Stresses in Pyrolytic Carbon/Graphite Composite

A mechanical heart valve (MHV) prosthesis made of pyrolytic carbon (PyC) coated graphite is a long-term implant that operates continuously for lifetime in patient's body. The ceramic-like PyC coating is brittle and is prone to contact damages. The high-level local contact stress may lead to the initiation of microcracks, as well as accelerated propagation of preexisting cracks. In this paper, the effect of changing coating parameters on Hertzian contact stresses is investigated for a trilayer PyC/graphite laminate undergoing a spherical indentation test, by means of a finite element analysis. It is shown that by suitably changing Young's modulus, Poisson's ratio, and the thickness of the coating material, the stress levels at critical locations can be greatly modified. This can be accomplished effectively within a small range of variations of the coating parameters. Low Young's modulus, large Poisson's ratio, and relatively thick coating are found to be beneficial in general. The results obtained may be useful in the design of MHV components for improving resistance against contact-induced damages by elaborately controlling the deposition process of PyC coating.     

Damage Evolution and Life Prediction of Cross-Ply C/SiC Ceramic-Matrix Composite under Cyclic Fatigue Loading at Room Temperature and 800 °C in Air

The damage evolution and life prediction of cross-ply C/SiC ceramic-matrix composite (CMC) under cyclic-fatigue loading at room temperature and 800 °C in air have been investigated using damage parameters derived from fatigue hysteresis loops, i.e., fatigue hysteresis modulus and fatigue hysteresis loss energy. The experimental fatigue hysteresis modulus and fatigue hysteresis loss energy degrade with increasing applied cycles attributed to transverse cracks in the 90° plies, matrix cracks and fiber/matrix interface debonding in the 0° plies, interface wear at room temperature, and interface and carbon fibers oxidation at 800 °C in air. The relationships between fatigue hysteresis loops, fatigue hysteresis modulus and fatigue hysteresis loss energy have been established. Comparing experimental fatigue hysteresis loss energy with theoretical computational values, the fiber/matrix interface shear stress corresponding to different cycle numbers has been estimated. It was found that the degradation rate at 800 °C in air is much faster than that at room temperature due to serious oxidation in the pyrolytic carbon (PyC) interphase and carbon fibers. Combining the fiber fracture model with the interface shear stress degradation model and the fibers strength degradation model, the fraction of broken fibers versus the cycle number can be determined for different fatigue peak stresses. The fatigue life S-N curves of cross-ply C/SiC composite at room temperature and 800 °C in air have been predicted.     

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 Sandblasting on Static and Fatigue Strength of Flash Butt Welded 75Cr4 Bandsaw Blades

The aim of the research presented in this article is analysis of the effect of the surface treatment method on the static and fatigue strength of flash butt welded bandsaw blades. A 1-mm-thick 75Cr1 cold-work tool steel sheet used for bandsaw blades was used as the test material. Fractographic studies of the fatigue fractures and fractures formed in static tests were also carried out. The static strength tests showed sandblasting the weld surface had no significant effect on the load capacity of the joint. However, the sandblasted specimens showed a higher repeatability of the load capacity (lower standard deviation). In the case of both analyzed sample variants of specimens, sandblasted and non-sandblasted, the number of cycles at which the sample was damaged decreases with the percentage increase of the stress amplitude. When loading the samples with a stress amplitude value in the range between 400 and 690 MPa, sandblasting of the weld surface increased the average value of destructive cycles by about 10–86% (depending on the stress amplitude) compared to non-sandblasted joints. The sandblasting process introduces compressive stresses in the surface layer of the welds, therefore the variable tensile load acting on the sample requires a greater number of cycles before the fatigue cracks initiate and propagate. In the case of all specimens, a ductile fracture was observed. It was also found that, regardless of the variable stress amplitude, sandblasting has a positive effect on reducing the standard deviation of fatigue test results.     

Strain Measurements within Fibre Boards. Part II: Strain Concentrations at the Crack Tip of MDF Specimens Tested by the Wedge Splitting Method

This is the second part of an article series where the mechanical and fracture mechanical properties of medium density fiberboard (MDF) were studied. While the first part of the series focused on internal bond strength and density profiles, this article discusses the fracture mechanical properties of the core layer. Fracture properties were studied with a wedge splitting setup. The critical stress intensity factors as well as the specific fracture energies were determined. Critical stress intensity factors were calculated from maximum splitting force and two-dimensional isotropic finite elements simulations of the specimen geometry. Size and shape of micro crack zone were measured with electronic laser speckle interferometry. The process zone length was approx. 5 mm. The specific fracture energy was determined to be 45.2 ± 14.4 J/m² and the critical stress intensity factor was 0.11 ± 0.02 MPa.     

Characterization on Crack Initiation and Early Propagation Region of Nickel-Based Alloys in Very High Cycle Fatigue

As nickel-based alloys are more and more widely used in engineering fields for bearing cyclic loadings, it is necessary to study their very-high-cycle fatigue (VHCF) properties. In this paper, the fatigue properties of nickel-based alloy 625 were investigated using an ultrasonic fatigue test apparatus. The fracture microscopy shows that around the crack initiation site there are two characteristic zones, a rough area (RA) and a fine granular area (FGA). Inclusions caused the interior fatigue crack initiation, and the coalescence of neighboring micro cracks was strongly influenced by the local microstructure, resulting in the RA morphology. Subsequently, the contact and compressing of the crack surfaces contributed to the formation of the FGA. Finally, the stress intensity factors of the RA and FGA were quantitatively evaluated for further discussion of the crack initiation and propagation processes.     

Cyclic Mechanical Fatigue Lifetime of Bi0.5Na0.5TiO3-Based Eco-Piezoceramics

The mechanical strength and cyclic fatigue behavior of PIC700 commercial eco-piezoceramic disks are investigated under biaxial loading on unpoled and poled samples. The bending strength of unpoled samples was higher than those of poled ones. Fatigue tests were conducted under a load ratio of 10 at a frequency of 20 Hz with a sinusoidal waveform. The curve fitting for the S-N fatigue diagram is used to predict the lifetime of these eco-piezoceramics and describe their fatigue behavior. It was also found that the unpoled samples exhibited higher fatigue resistance than the poled ones. The fatigue limit of maximum load for ten million cycles of unpoled and poled samples was estimated to be 160 and 135 MPa, respectively. The detailed observations of the fatigue fracture surfaces by scanning electron microscopy (SEM) indicated that a wavy surface with a mixture of transgranular and intergranular fractures occurred preferentially in the case of the poled material. On the other hand, transgranular fractures seem to be predominant in the unpoled samples. It appears that the poling process causes the change in failure characteristics due to domain orientation that leaves an anisotropic stress field in the material. The poled ceramics possess a local stress concentration created by the orientation under the electric poling field of the 90° ferroelectric–ferroelastic domains. Under this local stress concentration, a microstructural degeneration is induced by domain switching under the cyclic load that accelerates crack growth, thereby reducing fatigue lifetime.     

Influence of Strain Gradient on Fatigue Life of Carbon Steel for Pressure Vessels in Low-Cycle and High-Cycle Fatigue Regimes

This paper discusses how the strain gradient influences the fatigue life of carbon steel in the low-cycle and high-cycle fatigue regimes. To obtain fatigue data under different strain distributions, cyclic alternating bending tests using specimens with different thicknesses and cyclic tension–compression tests were conducted on carbon steel for pressure vessels (SPV235). The crack initiation life and total failure life were evaluated via the strain-based approach. The experimental results showed that the crack initiation life became short with decreasing strain gradient from 10² to 10⁶ cycles in fatigue life. On the other hand, the influence of the strain gradient on the total failure life was different from that on the crack initiation life: although the total failure life of the specimen subjected to cyclic tension–compression was also the shortest, the strain gradient did not affect the total failure life of the specimen subjected to cyclic bending from 10² to 10⁶ cycles in fatigue life. This was because the crack propagation life became longer in a thicker specimen. Hence, these experimental results implied that the fatigue crack initiation life could be characterized by not only strain but also the strain gradient in the low-cycle and high-cycle fatigue regimes.     

Effect of Underload Cycles on Oxide-Induced Crack Closure Development in Cr-Mo Low-Alloy Steel

Underload cycles with small load amplitudes below the fatigue crack growth threshold are dominantly considered as insignificant cycles without any influence on fatigue lifespan of engineering structural components. However, this paper shows that in some cases these underload cycles can retard the consequent crack propagation quite significantly. This phenomenon is a consequence of oxide-induced crack closure development during cyclic loading below the threshold. The experimentally described effect of fatigue crack growth retardation was supported by measurement of the width and the thickness of the oxide debris layer using the EDS technique and localized FIB cuts, respectively. Both the retardation effect and the amount of oxide debris were larger for higher number and larger amplitudes of the applied underload cycles. Crack closure measurement revealed a gradual increase of the closure level during underload cycling. Specimens tested in low air humidity, as well as specimens left with the crack open for the same time as that needed for application of the underload cycles, revealed no retardation effect. The results can improve our understanding of environmental effects on fatigue crack propagation and understanding the differences between the results of laboratory testing and the fatigue lives of components in service.     

Finite Element Analysis on Initial Crack Site of Porous Structure Fabricated by Electron Beam Additive Manufacturing

Ti6Al4V specimens with porous structures can be fabricated by additive manufacturing to obtain the desired Young’s modulus. Their mechanical strength and deformation behavior can be evaluated using finite element analysis (FEA), with various models and simulation methodologies described in the existing literature. Most studies focused on the evaluation accuracy of the mechanical strength and deformation behavior using complex models. This study presents a simple elastic model for brittle specimens followed by an electron beam additive manufacturing (EBAM) process to predict the initial crack site and threshold of applied stress related to the failure of cubic unit lattice structures. Six cubic lattice specimens with different porosities were fabricated by EBAM, and compression tests were performed and compared to the FEA results. In this study, two different types of deformation behavior were observed in the specimens with low and high porosities. The adopted elastic model and the threshold of applied stress calculated via FEA showed good capabilities for predicting the initial crack sites of these specimens. The methodology presented in this study should provide a simple yet accurate method to predict the fracture initiation of porous structure parts.     

Strain Measurements within Fibreboard. Part III: Analyzing the Process Zone at the Crack Tip of Medium Density Fiberboards (MDF) Double Cantilever I-Beam Specimens

This paper is the third part of a study dealing with the mechanical and fracture mechanical characterization of Medium Density Fiberboards (MDF). In the first part, an analysis of internal bond strength testing was performed and in the second part MDF was analyzed by means of the wedge splitting experiment; this part deals with the double cantilever I beam test, which is designed for measuring the fracture energy as well as stress intensity factor in Mode I. For a comparison of isotropic and orthotropic material behavior, finite element modeling was performed. In addition to the calculation of fracture energy the stress intensity factor was analyzed by means of finite elements simulation and calculation. In order to analyze strain deformations and the process zone, electronic speckle pattern interferometry measurements were performed. The results revealed an elongated process zone and lower results for K_IC if compared to the wedge splitting experiment. The G_f numbers are higher compared to the wedge splitting results and can be explained by the thicker process zone formed during the crack propagation. The process zone width on its part is influenced by the stiff reinforcements and yields a similar crack surface as with the internal bond test.     

Numerical Investigation of the Influence of Ultimate-Strength Heterogeneity on Crack Propagation and Fracture Toughness in Welded Joints

The mechanical properties of dissimilar metal-welded joint materials are heterogeneous, which is an obstacle to the safety evaluation of key welded structures. The variation of stress–strain conditions at the crack tip caused by mismatch of material mechanical properties in dissimilar metal-welded joints is an important factor affecting crack propagation behavior. To understand the influence of uneven distribution of ultimate strength of the base metal and the welded metal on the crack propagation path, fracture toughness, as well as the mechanical field at the crack tip in the small-scale yield range, the user-defined field variable subroutine method is used to express continuous variation characteristics of welded joint ultimate strength in finite element software. In addition, the J-integral during crack propagation is calculated, and the effect of the ultimate strength on the J-integral and the stress field at the crack tip are analyzed. The results show that as the crack propagation direction is perpendicular to the direction of ultimate strength, the gradient of ultimate strength increases from |G_y|= 50 to |G_y|= 100 MPa/mm, the crack deflection angle increases by 0.018%, and the crack length increases by 1.46%. The fracture toughness of the material decreased slightly during crack propagation. Under the condition that the crack propagation direction is the same as the direction of ultimate strength, the crack propagation path is a straight line. As the gradient of ultimate strength increases from G_x = 50 to G_x = 100 MPa/mm, the crack propagation length decreases by 5.17%, and the slope of fracture toughness curve increases by 51.63%. On the contrary, as the crack propagates to the low ultimate strength side, the crack propagation resistance decreases, the ultimate strength gradient increases from G_x = −100 to G_x = −50 MPa/mm, and the slope of the fracture toughness curve decreases by 51.01%. It is suggested to consider the relationship between crack growth behavior and ultimate strength when designing and evaluating the structural integrity of cracks at the material interface of dissimilar metal-welded joints.     

Behavior of Weld to S960MC High Strength Steel from Joining Process at Micro-Jet Cooling with Critical Parameters under Static and Fatigue Loading

The paper is focused on testing the weld of the S960MC steel produced at the micro-jet cooling under static and fatigue loading at critical parameters. This kind of material was in the form of a sheet with a thickness equal to 2 mm. The joint was obtained using three different types of welding wires: EDFK 1000, Union NiMoCr and Union X96 at the same parameters of the process. The joints were examined using non-destructive and destructive tests. The results from non-destructive experiments enable us to assess the quality of the welds directly before the joining process. In contrast, the destructive one allows following welds behavior under different loading conditions with their critical parameters. The bending experiments confirmed the good plastic properties of the weld, expressed by no cracks in the region tested in many variants of the joint manufactured. The results from static tests indicated a significant reduction of mechanical parameters of the weld in comparison to the base metal, expressed by 50% differences. Fatigue data have enabled us to follow the welding behavior at the increasing amplitude of axial stress up to fracture at constant amplitude value covering the following values of stress 650 MPa–100 MPa. Variations of total energy are presented at different values of several cycles up to fracture. Fracture regions are collected for analysis of the joint region features under cyclic loading. They have indicated differences in weld cracking depended on the stress level. Finally, the Wöhler S-N curve of the weld was determined, indicating the value of the fatigue limit of the weld tested, i.e., 100 MPa. The weld at the Union NiMoCr welding wire was indicated as the joint having the highest resistance on static and fatigue loadings.     

Dynamic Initiation and Propagation of Multiple Cracks in Brittle Materials

Brittle materials such as rock and ceramic usually exhibit apparent increases of strength and toughness when subjected to dynamic loading. The reasons for this phenomenon are not yet well understood, although a number of hypotheses have been proposed. Based on dynamic fracture mechanics, the present work offers an alternate insight into the dynamic behaviors of brittle materials. Firstly, a single crack subjected to stress wave excitations is investigated to obtain the dynamic crack-tip stress field and the dynamic stress intensity factor. Second, based on the analysis of dynamic stress intensity factor, the fracture initiation sizes and crack size distribution under different loading rates are obtained, and the power law with the exponent of −2/3 is derived to describe the fracture initiation size. Third, with the help of the energy balance concept, the dynamic increase of material strength is directly derived based on the proposed multiple crack evolving criterion. Finally, the model prediction is compared with the dynamic impact experiments, and the model results agree well with the experimentally measured dynamic increasing factor (DIF).     

Direct Computation of 3-D Stress Intensity Factors of Straight and Curved Planar Cracks with the P-Version Finite Element Method and Contour Integral Method

This paper presents direct computations of 3-D fracture parameters including stress intensity factors (SIFs) and T-stress for straight and curved planar cracks with the p-version finite element method (P-FEM) and contour integral method (CIM). No excessive singular element or enrichment function is required for the computation. To demonstrate the accuracy and efficiency of the proposed approaches, several benchmark numerical models of 3-D planar straight and curved cracks with single and mixed-mode fractures are considered and analyzed: a through thickness edge straight crack in a homogeneous material, a through thickness inclined straight crack, a penny-shaped crack embedded in a cube and a central ellipse shaped crack in a homogeneous cube. Numerical results are analyzed and compared with analytical solutions and those reported by the extended finite element method (XFEM) and the scaled boundary finite element method (SBFEM) in the available literature. Numerical experiments show the accuracy, robustness and effectiveness of the present method.