Equivalent Stress Intensity Factor Research Articles

Mechanics of crack initiation, propagation and crack grain boundary interaction in bicrystal silicon using near-tip localized stress calculation

Crack propagation and arrest are important phenomena in polycrystalline silicon. This phenomenon considerably affects the effectiveness of solar cells made up of polycrystalline silicon. To understand the crack propagation in polycrystalline silicon, it is essential to study the bicrystal first. Earlier, crack propagation has been studied in bicrystal materials primarily from the perspective of material behaviour. However, the mechanics part is largely missing. In the present work, crack propagation of bicrystal silicon during uniaxial tension has been studied at the atomistic scale. The silicon bicrystal was formed by joining two single crystals: crystal 1 and crystal 2 of different orientations. Various states like crack initiation, propagation, arrest, re-initiation and crack grain boundary (GB) interaction have been analysed using Stress Intensity Factor (SIF), calculated from the local crack tip virial stress field. Considering the effect of crack tip velocity, the dynamic SIFs at crack propagation state have been converted to the SIF of an equivalent static crack using the generalized expression for anisotropic material. It has been found that for the propagation state, crack propagation continues as long as the equivalent static SIF is greater than the critical SIF (CSIF). In crystal 1, crack propagation is along the low CSIF direction. Therefore, the crack did not change its path and propagated along a straight line. On the other hand, when the crack enters to crystal 2, it follows a zigzag path. Both of these observations have been justified in terms of near-tip calculated SIFs.

Numerical Analysis of Crack Propagation in an Aluminum Alloy under Random Load Spectra

This study develops a rapid algorithm coupled with the finite element method to predict the fatigue crack propagation process and select the enhancement factor for the equivalent random load spectrum of accelerated fatigue tests. The proposed algorithm is validated by several fatigue tests of an aluminum alloy under the accelerated random load spectra. In the validation process, two kinds of panels with different geometries and sizes are used to calculate the stress intensity factor, critical crack length, and crack propagation life. The simulated and experimental findings indicate that when the aluminum alloy is in a low plasticity state, the crack propagation life exhibits a linear relationship with the acceleration factor. When the aluminum alloy is in a high plasticity state, this study proposes an empirical formula to calculate the equivalent stress intensity factor and crack propagation life. The normalized empirical formula is independent of the geometry and size of different samples, although the fracture processes are different in the two kinds of panels used in our study. Overall, the numerical method proposed in this paper can be applied to predict the fatigue crack propagation life for the random spectrum of large samples based on the results of the simulated accelerated crack propagation process and the accelerated fatigue tests of small samples to reduce the cost and time of the testing.

Experimental and Numerical Evaluation of Equivalent Stress Intensity Factor Models under Mixed-Mode (I+II) Loading

This study determines the equivalent stress intensity factor (SIF) model that best fits the experimental behavior of low-carbon steel under mixed modes (I and II). The study assessed Tanaka, Richard, and Pook’s equivalent SIF models. The theoretical values used for comparison correspond to the experimental results in a modified C(T) geometry by machining a hole ahead of the crack tip subjected to fatigue loads with a load ratio of R = 0.1. The comparison involved the SIF for six experimental points and the values computed through the numerical simulation. The Paris, Klesnil, and Modified Forman–Newman crack growth models were used with each equivalent SIF to analyze the prediction in the estimated number of cycles. The Klesnil model showed the closest prediction since the error between the calculated and experimentally recorded number of cycles is the lowest. However, the material behavior reflects a reduced crack propagation rate attributed to plasticity in the crack tip. The results suggest that Asaro equivalent SIF conservatively estimates the element lifespan with increasing errors from 2.3% at the start of growth to 27% at the end of the calculation. This study sheds light on the accuracy and limitations of different equivalent SIF models, providing valuable insights for structural integrity assessments in engineering applications.

Propeller blade structural reliability analysis considering mixed-mode fatigue crack growth

Legacy propeller blades made of aluminum alloy are susceptible to fatigue cracking. Once the crack nucleated, it propagates rapidly because of the high rotational speed of the blade. This study uses mixed-mode fatigue crack analysis to understand the out-of-plane interaction of intergranular crack (IGC) and fatigue crack revealed in a U.S. Marine Corp. C-130 crash in 2017. The cracking mechanism is sequential: IGC followed by fatigue cracking, which eventually causes the liberation of the blade. A finite-element-method-based stress analysis elucidates the transition from IGC to fatigue crack. The result showed that the IGC provided enough driving force for the fatigue crack nucleation. A Monte-Carlo-simulation-based risk analysis is performed using the stress and crack growth analyses. The critical plane approach is utilized to determine the equivalent stress intensity factor for the crack growth analysis. The risk analysis results support the rapid liberation of the blade with consideration of large variation in initial crack size. The results also clearly show the necessity of structural risk analysis for planning inspection and maintenance.

Experimental investigation on I-II mixed mode fracture of hot mix asphalt using double-edge notched Brazilian disk test

The I-II mixed mode fracture is a typical failure pattern observed in asphalt pavement. In this study, the fracture behavior under I-II mixed mode of three diverse asphalt mixtures was scrutinized. The investigation involved performing double-edge notched Brazilian disk (DNBD) tests at two different temperatures: −10 °C and 25 °C. DNBD specimens were prepared with two notch lengths (10 mm and 20 mm) and seven notch angles, including 0°, 15°, 30°, 45°, 60°, 75°, and 90°. Stress intensity factor (KIC and KIIC), equivalent stress intensity factor (K*IC and K*IIC), and fracture energy were used to characterize the fracture behaviors. The findings suggest that the generation of mixed-mode fractures can be manipulated through variations in notch length and angle. An increase in notch angle shifted the fracture behavior towards a more mode I-dominant pattern, while elongating the notch length amplified the significance of mode II fracture contributions to the overall fracture process. The influence of reclaimed asphalt pavement (RAP) on the fracture performance of asphalt mixtures exhibited variation across the temperatures ranging from −10 °C to 25 °C. At −10 °C, mixture C, which contained an SBS-modified binder, demonstrated the most robust fracture performance, as evidenced by higher values of KIC and KIIC. This was succeeded by mixture B that used a #70 binder, with mixture A incorporating RAP trailing behind. Conversely, at 25 °C, the presence of RAP contributed to achieving the highest indices of K*IC and K*IIC, surpassing even the performance of mixture C with its SBS-modified binder, followed by mixture B with its #70 binder. For specimens with identical notch lengths and angles, the stress intensity factors recorded at −10 °C were substantially higher compared to those at 25 °C. This observation suggests that fracture resistance diminishes as temperature rises. Furthermore, an increase in notch angle correlated with a reduction in fracture energy at −10 °C, whereas at 25 °C, the notch angle’s influence on fracture energy appeared to be negligible. When examining the performance at −10 °C, mixture C exhibited the highest fracture energy, with mixtures B and A following in descending order. In contrast, at 25 °C, mixture A outperformed mixtures C and B in terms of fracture resistance, as gauged by fracture energy. Notably, the effect of mixture type on fracture energy was consistent with the effect of mixture type on stress intensity factor.

Numerical prediction of fretting fatigue crack growth in scaled railway axles considering fretting wear evolution

To predict the fretting fatigue crack growth (FFCG) life of railway axles, a series of interrupted fatigue experiments were conducted on scaled railway axles. Subsequently, the evolutions of fretting wear and fatigue cracks in the press-fitted region were analyzed. Based on the test results, finite element models incorporating fretting wear evolution were established, and the FFCG was investigated using the maximum tangential stress criterion, cyclic resistance curve, and the modified NASGRO equation. The analysis revealed that the fretting wear evolution leads to stress redistribution at the press-fitted region, thereby promoting FFCG. When considering fretting wear evolution, the equivalent stress intensity factor (SIF) range of the crack remains above the threshold value throughout the short crack stage. However, neglecting fretting wear evolution results in the SIF range being below the threshold value for cracks shallower than 0.30 mm. This implies that considering fretting wear evolution enables life prediction throughout the short crack stage. As the crack length increases, the influence of fretting wear evolution on crack growth gradually diminishes. By accounting for fretting wear, a more accurate stress distribution in the press-fitted region can be obtained, leading to a more precise and conservative prediction of crack growth life.

On the mixed mode fracture of DLP manufactured SCB specimens

The scope of this study is to investigate the mixed mode fracture of components manufactured from photo-polymerized resin using the Digital Light Processing (DLP) additive manufacturing technology.The mixed mode tests were performed on Semi Circular Bend (SCB) specimens loaded under symmetric Mode I, asymmetric mixed mode and mode II loading, respectively. The specimens manufactured via DLP have a crack introduced during the manufacturing process. Tests were performed at room temperature using a universal testing machine with three point bending grips at a constant loading speed. Four tests were carried on for each supports position.The experimental results expressed as KII/KIC versus KI/KIC are plotted by adopting four fracture criteria, namely the Maximum Tensile Stress (MTS), the Strain Energy Density (SED), the Maximum Energy Release Rate (Gmax), and the Equivalent Stress Intensity Factor (ESIF). Most of the experimental results fall in the range of fracture envelope curves.

Stress Intensity Factor equations for incipient transverse external annular eccentric cracks contained in a shaft under bending

One of the most common failures in rotating machines is the apparition and propagation of fatigue cracks in one of its main elements: the shafts. These cracks can cause catastrophic failures and lead to costly maintenance or repair processes. Most of the studies in relation to cracks contained in shafts have focused on straight or elliptical transverse cracks. However, although it is less common, the shaft breaks also occur with cracks whose fronts are approximately circumferential, that are more difficult to analyze. These cracks are transverse with circular shape that extend over a complete circumference and that have a certain eccentricity. This work presents the equations that provide the value of the Stress Intensity Factor (SIF) of an incipient crack with circumferential shape contained in a shaft subjected to bending, along the front, as a function of the characteristics of the crack, size and eccentricity. For this, an exhaustive numerical study has been carried out, using the Finite Element Method (FEM), to determine the SIF value along the circumferential front for different sizes and eccentricities of the annular crack.

Hot cracks in camshaft casting: initiation and propagation

ABSTRACT In this paper, a numerical simulation method based on the camshaft casting process and crack expansion was proposed to study the propagation characteristics of casting hot cracks. The dynamic visualisation process of hot crack growth indicates that the formation of hot tear is dominated by opening mode cracks. And during the propagation process, the equivalent stress intensity factor at the crack front first decreases and then increases. Furthermore, the propagation characteristics of the crack under different hot tear initiation conditions were studied by this method. The results reveal that the expansion ability of a hot crack is affected by the equilibrium solidification scale, solidification sequence, and solidification path of the casting. Finally, using the microscopic morphology of the cracks, the semi-quantitative analysis of the elements illustrates that the carbon content decreases sharply at the crack formation site, while manganese and sulphur are relatively rich.

Effect of mixed-mode loading on surface crack propagation in steels

To understand the effect of mixed-mode loading on surface crack propagation in structural alloy steels, fatigue crack growth tests were performed on surface crack tension (SCT) specimens with initial semi-elliptical surface cracks. SCT specimens with cracks normal to the load axis were used for the mode I tests. Experiments with mixed-mode loading were conducted on SCT specimens with inclined surface cracks. A specific feature of the surface crack propagation, in the segmentation of the crack front, the occurrence of «factory roof» patterns, and deviations in the crack front from a planar shape were established under mixed-mode loading. A reverse engineering technique was applied in a numerical study to reproduce a complex fracture surface under mixed-mode loading. The equivalent stress intensity factor (SIF) formulation was used to interpret the fatigue-crack growth rate. A significant reduction in the fatigue crack growth rate was established for mixed-mode loading compared with pure mode I conditions. Several fracture mechanisms were identified along the surface crack front under mixed-mode loading. The areas corresponding to changes in the dominant fracture mechanism were identified using detailed fractography of the fracture surfaces.

Fatigue Life Assessment in the Typical Structure of Large Container Vessels Based on Fracture Mechanics

Welding defects are known to cause crack propagation and reduce structural fatigue performance. Based on the Paris theory of fracture mechanics, research is conducted on evaluation methods for analyzing fatigue crack propagation by adopting random loads with long-term distribution that follows the Weibull distribution for the stress ranges of fatigue loads. This approach is combined with the corrective stress intensity factor (SIF) equation and the method for calculating the reference stress and failure criterion. A large container ship is selected for a simulation, and fatigue crack propagation analysis is conducted on typical critical locations. A detailed comparison of the forecasted fatigue life is carried out between fracture mechanics theory and the S-N curve. The results indicate that the fatigue life values obtained using the two methods are of the same magnitude. In general, for the welded structure, the fatigue life value obtained via the fracture mechanics method is shorter than that obtained via the S-N curve method, while, for the free edge of the structure and the unwelded structure, the predicted fatigue life value is closer than that predicted via the S-N curve method. Moreover, the influence of initial crack defects on the fatigue life is investigated, and the results show that the depth of the initial crack will greatly affect the fatigue life of the target ship in typical locations, but the influence of the shape ratio on the fatigue life is limited. Therefore, in the actual ship construction process, controlling the initial crack depth of components is effective for limiting crack propagation and improving fatigue life. The above conclusions and suggestions can serve as a reference for the structural design and fatigue life evaluation of large container ships.

The effect of material defect orientation on rolling contact fatigue of a ball bearing

In this study, finite element method (FEM) is applied to investigate the effect of material defect orientation on subsurface crack initiation in rolling bearings. First, the history of stress intensity factors (SIFs) of a subsurface cubic material defect is calculated. SIFs calculation is conducted when it is parallel to the rolling surface of a bearing ring (varphi = 0^circ) under a ball rolling on the ring. Then, the effect of defect orientation, varying from varphi = 0^circ to varphi ; = ;30,; 45; {text{and}} ;60^circ, on the history of SIFs is investigated. It is deduced that changing the defect orientation results in a threefold increase in the equivalent SIF range compared to parallel orientation.

Experimental and Numerical Prediction of Surface Crack Growth in Fatigue in a Finite Width Plate

In the thick components such as gas turbine disks, the cracks usually manifest in the form of part-through or embedded elliptical cracks. The shape of surface crack varies during the crack propagation and significantly affects the fatigue life predictions of the surface cracked components. In present work, crack propagation of semi-elliptical cracks in a finite width specimen of a gas turbine material subjected to fatigue load has been studied experimentally and numerically. The numerical simulation was accomplished by first extending the applicability of available stress intensity factor empirical equation for semi-elliptical cracks to finite width solid. Using this empirical equation for stress intensity factor, the effect of change in the crack shape on the crack propagation life is simulated by numerical models. Also, in order to include the effect of crack closure in the numerical prediction of growth of surface cracks, a ratio of crack closure factor between depth and surface locations of a semi-elliptical crack was obtained by experiments. The experimental observations were used in correlating the numerical predictions for crack shape progression and crack propagation life.

Fatigue strength of self-piercing riveted joints of carbon fiber reinforced composite and Al5052 alloy plates

Self-piercing riveting (SPR) is an alternative to the conventional spot-welding method when joining sheets of dissimilar materials. In this study, the static and fatigue strengths of the SPR joints of carbon fiber composite laminate and an Al5052 aluminum alloy plate under various loading conditions were evaluated. Fatigue test results show that the load amplitudes, corresponding to the fatigue endurance limit, based on a lifetime of one million cycles, were 680 N, 323 N, and 305 N for loading angles of 0°, 45° and 90°, respectively, with corresponding fatigue ratios of the joints of 33%, 23% and 24%. The fatigue strengths at the loading angles of 45°, and 90° in terms of the equivalent stress intensity factor were found to be much higher than those at a loading angle of 0°. This is partially due to the difference in the fatigue failure modes. Regarding the fatigue strength designs of SPR joints consisting of composite laminate and aluminum alloy plates under various loads, it can be suggested that the tensile-shear strengths dominate the SPR fatigue strengths of the joints because they are highly vulnerable to tensile-shear loading.

The influenced zones of stress intensity factor and plasticity at multi-crack tips

The influence range of crack interaction is studied using the distribution dislocation technique, and is defined as the influenced zone. For elastic materials with cracks, the equivalent stress intensity factor influenced zone is obtained, while for plastic materials with cracks, the plasticity influenced zone is determined. The interaction between multiple cracks can be analyzed by introducing the concept of the influenced zone, which simplifies the analysis. The results indicate that if a crack is located outside the influenced zone of another crack, the effect of the former on the latter can be ignored within an acceptable range of error. The influenced zone for elastic materials depends on the length and inclined angle of a crack, whereas for plastic materials, the plastic influenced zone is affected by the crack length, inclined angle, and material yield limit simultaneously. In the case of plastic materials with multiple cracks, fusion of plastic zones between two cracks may occur at certain positions under the influence of other cracks. These theoretical findings can simplify the analysis of the fatigue fracture behavior of materials with multiple cracks, whether they are elastic or plastic.

Theoretical and experimental investigations of crack propagation behavior and delamination in GLARE specimens affected by non-proportional fatigue loadings

In actual operation conditions, the structural parts of automotive, aerospace and other significant industrial applications undergo the multi axial fatigue loading with non-proportionality states. Fiber metal laminates (known as FML) are the best options to manufacture these structural parts. The current study examines the effects of a specific condition of multi-axial fatigue loadings (repeated tension with static shear stresses) on the behaviors of crack growth and delamination in GLARE specimens (abbreviated of glass laminates aluminum reinforced epoxy). Analytical model with idea of maximum tangential stress criterion modification has been adopted to represent the non-proportionality state of fatigue loading. Paris equation, equivalent stress intensity factor range, fiber-bridging effects and delamination shape were included in this model. The current idea was compared with a previous idea that depends on the principal stresses in representation of non-proportional multi-axial fatigue loadings. Specimens have coding GLARE_2A 2/1 were fabricated by VARTM technique (vacuum assisted resin transfer molding technique). Special treatments have been done on the aluminum surfaces before specimen fabrication to increasing delamination resistance. Novel fatigue apparatus was manufactured to guarantee apply the under study conditions for multi axial fatigue loading and to introduce experimental investigation of crack and delamination growths in GLARE specimens. The obtained results of the current idea were in a considerable agreement with that of the previous idea of the principal stresses. The maximum deviations between analytically extracted results were less than 1% for crack growth, 5.4% for bridging stress, 4.8% for crack opening and 6.3% for delamination growth. Experimentally, the measured results have been compared with analytical results for the purpose of validation. Acceptable matching between results with maximum difference of 7.65% was the important outcome of this study.

Numerical Analysis on Fatigue Crack Growth at Negative and Positive Stress Ratios.

The finite element method was used to investigate the effect of the stress ratio on fatigue crack propagation behavior within the framework of the linear elastic fracture mechanics theory. The numerical analysis was carried out using ANSYS Mechanical R19.2 with the unstructured mesh method-based separating, morphing, and adaptive remeshing technologies (SMART). Mixed mode fatigue simulations were performed on a modified four-point bending specimen with a non-central hole. A diverse set of stress ratios (R = 0.1, 0.2, 0.3, 0.4, 0.5, -0.1, -0.2, -0.3, -0.4, -0.5), including positive and negative values, is employed to examine the influence of the load ratio on the behavior of the fatigue crack propagation, with particular emphasis on negative R loadings that involve compressive excursions. A consistent decrease in the value of the equivalent stress intensity factor (ΔKeq) is observed as the stress ratio increases. The observation was made that the stress ratio significantly affects both the fatigue life and the distribution of von Mises stress. The results demonstrated a significant correlation between von Mises stress, ΔKeq, and fatigue life cycles. With an increase in the stress ratio, there was a significant decrease in the von Mises stress, accompanied by a rapid increase in the number of fatigue life cycles. The results obtained in this study have been validated by previously published literature on crack growth experiments and numerical simulations.

Equivalent Stress Intensity Factor: The Consequences of the Lack of a Unique Definition

The concept of an equivalent stress intensity factor Keq is used in the study of fatigue crack growth in mixed-mode situations. A problem seldom discussed in the research literature are the consequences of the coexistence of several alternative definitions of mixed mode Keq, leading to rather different results associated with the alternative Keq definitions. This note highlights the problem, considering several Keq definitions hitherto not analyzed simultaneously. Values of Keq calculated according to several criteria were compared through the determination of Keq/KI over a wide range of values of KI/KII or KII/KI. In earlier work on Al alloy AA6082 T6, the fatigue crack path and growth rate were measured in 4-point bend specimens subjected to asymmetrical loading and in compact tension specimens modified with holes. The presentation of the fatigue crack growth data was made using a Paris law based on Keq. Important differences are found in the Paris laws, corresponding to the alternative definitions of Keq considered, and the requirements for candidate Keq definitions are discussed. A perspective for overcoming the shortcomings may consist in developing a data-driven modelling methodology, supported by material characterization and structure monitoring during its life cycle.

The sloshing effects on the crack instability of the spherical tank under the simultaneous effect of internal pressure and earthquake

Spherical tanks have an important function in the industry due to the internal pressure of their contents. Also, the supporting structure of the spherical tank controls stability and damage to the tank One of the damages that can lead to a critical situation is an unstable crack in the column-vessel joint. In this study, the sloshing effects on the instability of 10 mm and 20 mm long semi-elliptical cracks with three aspect ratios in the connection zones of the supporting structure under the effect of internal pressure and eleven earthquakes have been investigated. Furthermore, using the finite element sub-modeling method around the crack area and part of the structure, the effect of fluid–structure interaction has been considered for three liquid levels to calculate the stress intensity factors along the crack front. Since the tank is under the simultaneous effect of internal pressure, earthquake, and sloshing motion, a three-dimensional mixed-mode stress intensity factor needed to be considered to study the crack instability. The results show that earthquakes and sloshing motions can have various effects on the equivalent stress intensity factors. For almost two-thirds of the studied cases, the equivalent stress intensity factor for the 50% filled vessel was 10%–70% greater than the 98% filled vessel. This finding shows that the crack located in the connection zones of the supporting structure under the simultaneous effect of internal pressure, earthquake, and sloshing motion, could lead to failure.

The onset of unstable fracture and crack deflection of AA7085 in mixed mode I + II loading

The current study focuses on the planar mixed mode fracture of AA7085. A loading device based on the concept given by Richard et al. has been developed for inducing planar mode-mixity in compact tension and shear (CTS) specimens. The CTS specimens extracted from the AA 7085 plate were subjected to mixed mode quasi-static loading after pre-cracking the specimens by fatigue loading under mode-I conditions. The desired pre-cracking length was achieved after performing an extended finite element method (XFEM) based fatigue crack growth simulation. Different mode-mixity has been introduced in the specimens by changing the orientation of the loading device with respect to the loading axis of the machine. Experimentally observed crack deflection was compared with the angles predicted by different planar mixed mode fracture criteria, namely MTS, Richards, and strain energy density. Equivalent stress intensity factors proposed at the onset of unstable fracture have been determined using different criteria and compared with each other. A new equivalent stress intensity factor for mixed mode has been proposed from Shah's equation of fracture locus. It has been found that the equivalent stress intensity factor based on Shah's equation of fracture locus is suitable for the alloy being investigated. The fracture morphology of the fractured specimen was inspected in a field emission scanning electron microscope. Both inter-granular and dimpled ductile fracture was observed in the specimens irrespective of the mode-mixity. Extended finite element simulation was performed to determine tangential stress distribution at a distance around the crack tip.