Flaw Tip Research Articles

Crack Initiation Behaviors of Granite Specimens Containing Crossing‐Double‐Flaws with Different Lengths under Uniaxial Loading

Crack initiation is an important stage in the failure process of rock masses. In this paper, crack initiation behaviors (crack initiation model, crack initiation location, crack initiation angle, and crack initiation stress) of granite specimens containing crossing‐double‐flaws with different lengths were investigated using PFC2D software. Crack initiation models were all tensile wing cracks, which did not exactly initiate from the main flaw with a length of 30 mm. They can initiate from the secondary flaw with a length 20 mm at α of 30° (included angle between main flaw and horizontal direction) and β of 90° (included angle between main and secondary flaws) and from main and secondary flaws at α of 30° and β of 60°. These were mainly induced by the superposition of stress fields around the main and secondary flaws as β varied from 0° to 90°, especially the tensile force concentration zones superposition. The tensile forces concentration zone around flaw shrank towards flaw tips with the increase of flaw’s inclinations measured horizontally. Under stress field superposition effects, the crack initiation stress decreased firstly and then increased with β at α of 30° and 45°. Crack initiation locations were close to flaw tips but not restricted to them. The distances between crack initiation locations and flaw tips, and the crack initiation angles depended on the flaw where first macrocracks initiated from. Microdisplacement field distributions of granite specimens to reveal the mesomechanism of crack initiation behaviors were discussed.

The Influence of Infilling Conditions on Flaw Surface Relative Displacement Induced Cracking Behavior in Hard Rock

The relative tangential displacement (or slip) and relative normal displacement of flaw surfaces are two of the main factors driving crack initiation and propagation of rocks. In this study, uniaxial compression experiments are performed in flawed marble under different cases, i.e., open flaw and flaw filled by gypsum, cement and resin, and different flaw inclinations, to study the influence of infilling conditions on the flaw surface relative displacement (i.e., relative tangential and normal displacement) and the induced cracking behaviors, such as crack initiation, propagation and crack patterns. The digital image correlation (DIC) technique is used to trace the evolution of relative deformation across the flaw surface and cracking process of flawed specimens. The results reveal that the difference in flaw surface relative displacement, at a given load, is introduced by different infilling materials. Among the four types of flaws, the filled flaw with smaller relative displacement is less likely to initiate cracks than the unfilled flaw with larger relative displacement. Moreover, the crack initiation position, angle, and types are also dependent on the relative deformation between the flaw surfaces. With the increase of the stiffness of the filler or flaw inclination angle, the effect of relative normal displacement on the cracking behavior is weakened, while the effect of relative tangential displacement increasingly dominates. As a result, the filled flaw with smaller relative normal displacement makes wing crack initiation points closer to flaw tips. Moreover, the filler with higher stiffness makes the wing crack initiation angle smaller, improves the possibility of the quasi-coplanar crack initiation, and suppresses the initiation of anti-wing cracks from the flaw tips in hard rock.

Strengthening and toughening mechanisms in refilled friction stir spot welding of AA2014 aluminum alloy reinforced by graphene nanosheets

Refilled friction stir spot welding is proposed to replace friction stir spot welding to solve the problem of keyhole in joining of light metals. However, it is rather challenging to ensure the mechanical property of refilled friction stir spot welding joints because of hook defect. In this study, a novel method was proposed to use graphene nanosheets to strengthen the tip of hook defect and improve overall mechanical properties of joint. The joints of AA2014 aluminum alloy with 0.6%wt graphene nanosheets were fabricated by refilled friction stir spot welding. The results show that the tensile/shear strength of joint increases by 31% and the fracture toughness also is improved by nearly 20% with graphene nanosheets. Extension in fatigue life was achieved on joint with graphene nanosheets. Microstructural observations, fracture characteristics and electron back scattered diffraction analysis were systematically investigated to clarify the mechanism for improvement of strength and toughness. The synergetic effect including grain refinement, load transfer, dislocation strengthening and crack bridging, caused by graphene nanosheets, leads to hardening behavior of graphene nanosheets pinned zone and a significant crack deflection during fracture process, which contributes greatly to improving strength and toughness of joint.

Modeling and estimation of hole-type flaws on cracking mechanism of SiC ceramics under uniaxial compression: A 2D DEM simulation

Ceramic materials usually contain a large number of hole-type flaws or defects with different characteristics. These flaws are closely related to the fracture failure of materials. Based on the discrete-element method (DEM), three different hole-type flaws were constructed by the super-ellipse equation for SiC ceramics in 2 dimensions. The relationship between the flaw with different characteristics and the failure of SiC ceramic specimens was studied. Further, the crack evolution and the two important parameters (distance from the tip of flaw d and the initiation angle α) to describe the crack initiation position were investigated. Lastly, the stress fields around the hole-type flaw were analyzed. The results show that with the increase of inclination angle of the flaws, the crack initiation position moves from the center position to the flaw tips and the crack initiation angle α increases. Moreover, when the aspect ratio is large and the inclination angle is small, the maximal-tensile stress region around the hole-type flaw is large. Moreover, as the inclination angle increases, the maximal-tensile-stress region moves clockwise around flaws. Finally, the critical dimension of the hole-type flaw affecting the material strength is discussed.

Experimental and numerical study of granite blocks containing two side flaws and a tunnel-shaped opening

In this study, uniaxial compression tests were conducted on granite specimens containing two side flaws. Based on the experimental results, the numerical models containing two side flaws and a tunnel-shaped opening were created to investigate the peak stress, cracking process and stress distribution under uniaxial compression. It is found that the flaw inclination angle strongly affects the strength, cracking process and stress distribution, while the slight change of the opening shape has little influence. The cracks initiate from the flaw tips and the top and bottom of openings. Unlike the case of a circular opening, in addition to arch waists, large compressive stress occurs at the arch foots of the tunnel-shaped opening.

Computer assisted data analysis for predicting the protective potential of hull structures of ships and floating facilities

Nowadays, stress corrosion fracturing of hull structures of ships and floating facilities is a matter of concern. Considering the presence of the juvenile surface at the tips of local defects, some adjustment is required for parameters governing protection in the existing methods of protecting against stress corrosion damages. However experimental determination of the juvenile surface for all steels is impossible. This article deals with solving a problem of predicting the protective potential to prevent hull structures of ships and floating facilities against stress corrosion fracturing. The solving is performed by use of a computer assisted data analysis with intermediate prediction of reference parameters such as potential of steel with an oxide film on, and that of steel without any oxide film, for different steel grades and sea water salinities. The suggested approach allows improving quality of protective means of hull structures of ships and floating facilities against stress corrosion damages by stabilizing the cathodic polarization process, providing appropriate potential of the uncharged surface.

Determination of the stress field and crack initiation angle of an open flaw tip under uniaxial compression

In the uniaxial compression test of rock containing pre-existing flaws, the flaws are generally open, and the corresponding theoretical calculations are mostly based on the closed flaws. The suitable theoretical solution is needed for the crack initiation and extension of open flaws (Flaw: Prefabricated, inherent defects. Crack: Defects generated during the loading process). In this paper, first, the corresponding stress field formulae under compression are established by comparing and analyzing the stress field at the flaw tip under tensile condition. Then, ANSYS is used to simulate and confirm the stress field at the flaw tip under compression and shear conditions. Thus, the difference between the open flaw and the closed one is explained, and the stress field formulae of the open flaw tip under compression are determined without considering the flaw thickness. Second, based on the determined stress field formulae at the flaw tip, the relationship between the crack initiation angle of the open flaw tip and the inclination angle of the prefabricated flaw is derived. Finally, laboratory test and PFC simulation are conducted to verify the resulting crack initiation angle formulae. The experimental and simulation results are basically consistent with the theoretical formula.

Asymptotic Analysis of the Crack Tip Stress Field (Consideration of Higher Order Terms)

This paper presents multi-parameter asymptotic description of the stress field near the tip of a central crack in a linear-elastic plate under: (1) normal tensile stress; (2) transverse shear; (3) mixed mode deformation in the full range of mixed modes of loading, from the opening mode fracture to antiplane shear. A multi-parameter expansion of the stress tensor components including higher order terms has been constructed. All the scale (amplitude) factors—coefficients of the complete Williams asymptotic expansion—have been determined as functions of the crack length and parameters of loading. The expansion constructed and formulas obtained for the expansion coefficients can be used for keeping any preassigned number of terms in asymptotic representations of mechanical fields at a crack tip in a plate. The number of components to keep at different distances from the tip of defect was subjected to analysis. The angles of crack propagation under conditions of mixed-mode loading were calculated using a multi-parameter expansion of stress field by means of (1) the maximum tangential stress criterion and (2) the criterion of minimum elastic strain energy density.

The effect of flaw filling material on the compressive behaviour of 3D printed rock-like discs

The effect of flaw filling material on the deformation and failure behaviour of 3D printed rock-like Brazilian discs with pre-existing flaws is investigated by quasi-static compressive loading test combined with digital image correlation (DIC) technique. In particular, a number of specimens with various flaw and bridge inclination angles and overlapping features are designed by computer aided design (CAD) and 3D printed. Crack initiation and propagation in the loaded specimens are studied and coalescence types of these flaws are identified by DIC analysis. The results indicate that filling material imposes strong impacts on the deformation behaviour of specimens and the resulting crack patterns are different from those with open flaws. It is revealed that filling the flaws with gypsum and clay mixture improves the strength characteristics of the specimens with significantly enhanced peak loads. Furthermore, DIC results indicate that in the single filled flaws inclined at 45°, 60° and 75° normal to the loading direction, the shear cracking first develops in the filling and then tensile cracks appear from the flaw tips. It is observed that the filled specimens develop much larger fracture process zone prior to the peak load. Moreover, when the specimens develop a crack inside the fillings, the enhancement of the peak load is remarkably larger than that of the filled specimens without cracking in the fillings. Overall this study has demonstrated not only the advantages of 3D printing combined with DIC method in rock deformation and crack study, but also the significant impacts of the flaw filling on the deformation and mechanical behaviour of rock-like material.

Temperature and thermal stress around an elliptic functional defect in a thermoelectric material

Functional defect leads to high temperature as well as considerable thermal stress in thermoelectric materials, which is one of the major reliability failure mechanisms of thermoelectric devices. In this perspective, the thermal-electric-elastic fields around an elliptic functional defect in a two-dimension thermoelectric plate is analyzed based on the complex variable method, and the field distributions have been obtained in closed-form. The results show that the temperature at the defect tip increases with the defect size, and can surpass the temperature at the hot end and even exceed the material melt point. Besides, both the von Mises stresses within the matrix and defect can exceed the yield stresses of many materials. These results can be used for the fracture study and reliability analysis of thermoelectric materials.

A micromechanical Sliding-Damage Model Under Dynamic Compressive Loading

For most rock materials, there exists a strong coupling between plastic flow caused by sliding along micro-crack faces and damage evolution due to nucleation and growth of wing-cracks. The aim of this article is to develop the self-consistent based micromechanical model by taking into account the coupling between frictional sliding and damage process under dynamic compressive loading. The developed model algorithm was programmed in the commercial finite difference software environment for numerical simulation of rock material to investigate the relationship between the mechanical behaviour and microstructure. Eventually while the stress intensity factor at flaw tips exceeds the material fracture toughness, the wing-cracks are sprouted and damage evolution occurs. For frictional closed cracks, an appropriate criterion for the onset of frictional sliding along micro-cracks was proposed in this paper. Also, plastic strain increments were determined by the flow rule, consistency condition and normality rule within the thermodynamic framework. The simulation results demonstrate that the developed micromechanical model can adequately reproduce many features of the rock behaviour such as hardening prior to the peak strength, softening in post-peak region, damage induced by wing-cracks and irreversible deformations caused by frictional sliding along micro-cracks. Furthermore, the softening behaviour of material in post-peak region is affected and the material undergoes higher values of strains and damage up to the residual strength. Therefore, the rock sample simulation with the coupled frictional sliding-damage model could increase plasticity and ductility of the rock in post-peak region because of regarding plastic strains caused by the frictional sliding along micro-cracks.

Assessment of Delayed Hydride Cracking at volumetric flaws formed due to bearing pad fretting

Pressurized Heavy water reactor is a horizontal channel type reactor where fuel bundles are inside pressure tubes (PT) and supported at bearing pad locations. Bearing pad (BP) fretting results in formation of volumetric flaws at PT inner surface which may lead to delayed hydride cracking (DHC). In this paper, safety assessment of pressure tube was carried out against DHC initiation at volumetric flaws using CSA N285.8 procedures. Bounding envelop was developed for threshold bulk Heq and volumetric flaw depth for DHC initiation. Several flaw root radius (r) were assumed to arrive at bounding flaw sizes and threshold bulk Heq in the PT. Peak stress was calculated considering hydride ratcheting condition at flaw tip considering sustained hot condition. Four locations, rolled joint inlet/ outlet and PT main body inlet/outlet were selected to assess DHC initiation for volumetric flaws. Residual tensile stress was considered for the assessment at rolled joint location

Згин зосередженою силою тонкої пластини, розташованої на пружній основі та послабленої контактною тріщиною

The paper considers the two-dimensional formulation of the problem of the contact interaction of the crack edges in a plate bent by the concentrated force on the elastic Winkler foundation. The crack closure is described using the model of contact along a line in one of the plate surfaces. Within the framework of this model, the boundary value problem is formulated for the equations of the classical theories of plate bending on the elastic foundation and a plane stress state with interrelated tension and bending conditions on the crack line. The obtained boundary value problem has been solved using singular integral equations method. Based on numerical solutions of the integral equation the dependences of forces and moments intensity factors in the vicinity of the defect tips and distribution of contact forces along the crack line on the parameters of elastic foundation stiffness and the coordinate of the application point of the load have been investigated. The effect of crack closure and influence of the elastic foundation stiffness on the limit equilibrium of the plate, depending on the coordinate of the point of application of the concentrated force, has been evaluated. The area of the correctness of the problem statement when the crack closure occurs throughout its length has been established. It was found that the crack closure leads to the appearance of nonzero forces intensity factor, reduction of the moments intensity factor and increase of the limit load. The dependences of the forces and moments intensity factors and the limit load on the dimensionless coordinate of the point of application of the concentrated force are nonmonotonic. Numerical analysis showed that increasing the elastic foundation stiffness, as well as the displacement of the point of application of the force from the center of the cut, increase the limit load and weaken the contact reaction.

Dynamic Mechanical Properties and Fracturing Behavior of Marble Specimens Containing Single and Double Flaws in SHPB Tests

Dynamic impact tests were conducted on rectangular marble specimens with flaws to investigate the effect of the flaw angles and ligament angles on the rock dynamic mechanical properties, fracturing behavior, and energy evolution characteristics. A 75-mm diameter split Hopkinson pressure bar (SHPB) device was used in the tests. The experimental results show that the flaw geometries have a strong effect on the dynamic mechanical properties and fracturing behavior of rocks. In general, the effects of the flaw angle and flaw number on the dynamic strength are more significant than the effect of the ligament angle. A high-speed camera was used to monitor and record the crack initiation and coalescence and the failure processes of the marble specimens in real-time. The crack propagation can be divided into two major stages, i.e., the formation of white patches and the generation of macrocracks. The white patches usually appear prior to the peak stress of the specimen. The shear cracks usually initiate at or near the flaw tips and propagate to form X or half-X shear belts that dominate the macroscopic failure under impact loading. Nine types of crack coalescence behaviors are identified for the marble specimens with double flaws, and the macro failure modes of the specimens is usually combined by some of them. The energy absorption properties of the marble specimen are also significantly affected by the pre-existing flaws. The energy absorption ratio can be maximized by setting a certain number of pre-existing flaws with an appropriate inclination angle and a proper ligament angle to effectively improve the fragmentation efficiency of rocks.

Stress Intensity Factor Interaction for Subsurface to Surface Flaw Transformations Under Stress Concentration Fields

If a single subsurface flaw is detected that is close to a component's free surface, a flaw-to-surface proximity rule is used to determine whether the flaw should be treated as a subsurface flaw, or transformed to a surface flaw. The transformation from subsurface to surface flaw is adopted as flaw-to-surface proximity rules in all fitness-for-service (FFS) codes. These proximity rules are applicable when the component's free surface is without a stress concentration. On the other hand, subsurface flaws have been found under notches, such as roots of bolts, toes in welded joints, or geometrical discontinuities of components. The stress intensity factors of the subsurface flaws are affected by the stress concentrations caused by the notches. The stress intensity factor of the subsurface flaw increases with increasing stress concentration factor of the notch and decreasing ligament distance between tip of the subsurface flaws and the notch, for a given notch width. Such subsurface flaws are transformed to surface flaws at a distance from the notch tip for conservative evaluations. This paper shows the interactions of stress intensity factors of subsurface flaws under stress concentration fields. Based on the interaction, a flaw-to-surface proximity criterion is proposed for a circular flaw under the stress concentration field induced by a notch.

Corrosion effects on fatigue behavior of dissimilar friction stir welding of high-strength aluminum alloys

This paper examines the effects of corrosion defects on the low-cycle fatigue performance of dissimilar friction stir welded AA6061-to-AA7050 aluminum alloys. Corrosion defects were produced on the crown surface of the weld by static immersion in 3.5% NaCl for various exposure times. Results revealed localized corrosion damage in the thermo-mechanically affected and heat-affected zones. The corrosion damage featured general pitting, pit clustering, and exfoliation that revealed increasing depth with increasing exposure time. The higher corrosion attack was measured in the AA7050 compared to the AA6061. Results demonstrated a decrease in the fatigue life with evidence of crack initiation at the corrosion defects; however, the fatigue life was nearly independent of the exposure time. This can be attributed to total fatigue life dominated by incubation time. Furthermore, two types of failure were observed: crack propagation in the AA6061 side at high-strain amplitudes (> 0.3%) and crack propagation in the AA7050 side at low-strain amplitudes (< 0.2%). This can be attributed to the cyclic strain hardening evolution and the localized high-stress field at the tip of the corrosion defect. Lastly, a microstructure-sensitive fatigue model was employed to capture the effect of corrosion defects for the life prediction of the dissimilar friction stir welded AA6061-to-AA7050.

Dynamic Fracture Evolution and Mechanical Behavior of Sandstone Containing Noncoplanar Elliptical Flaws under Impact Loading

To investigate the effects of preexisting flaws with different geometries, including flaw inclination angle and ligament angle on dynamic strength, deformation properties, and fracture evolution of rock materials, a series of dynamic impact tests were conducted on green sandstone specimens containing double elliptical flaws using a 75 mm diameter split Hopkinson pressure bar (SHPB) testing device with a high-speed camera recording in real time. The experimental results show that dynamic strength of specimens with different flaw angles is reduced between 5.91% and 39.92% but from 18.50% to 28.44% for specimens with different ligament angles, indicating that the effect of the flaw angle on the dynamic strength is more significant than that of the ligament angle. However, the dynamic deformation properties are influenced greatly by the ligament angle. Macroscale cracks mostly initiate at or near the flaw tips and then propagate in different paths with varying flaw geometries, leading to the ultimate failure in five typical modes based on the crack coalescence. Shear crack coalescence and tensile crack coalescence are identified through both macroscopic fracturing photos taken by the high-speed camera and microscopic surface morphology obtained by the scanning electron microscope (SEM).

A Three-Dimensional Numerical Investigation of Dynamic Fracture Characteristics of Rock Specimens with Preexisting Surface Flaws

FEM-based numerical investigation was conducted to investigate the fracture characteristics of heterogeneous rocks with preexisting surface flaws under dynamic loadings. Different types of cracks from initiation to coalescence of the specimen with a single flaw were reproduced in numerical tests, which were very highly agreed with experimental results. Numerical testing on specimens with a single flaw demonstrated that the crack behaviors, including its path, length, and cracking velocity, were significantly different on the surface of and inside the rock specimen. In addition, the higher the incident pressure level applied, the longer the cracking distance propagated; the more the AE count is, the larger the AE energy released and the greater the fragmentized. Furthermore, the cutting depth of flaw could significantly affect crack propagation patterns and AE characteristics. When the cutting depth of flaw is equal to the thickness of the specimen, there would be no shell-like crack emerged. Subsequently, testing results of the multi-preexisting flaws indicated that the surface flaws on the specimen made the crack initiation and coalescence behaviors more complicated. The coalescence between flaw tips is not easy, and the coalescence of preexisting flaws needs two or multiple cracks to achieve. The coalescence points occurred not only in the preexisting flaw but also in the trajectory of the wing cracks and antiwing cracks. The accumulative AE energy and AE counts are positively correlated with the amounts of preexisting flaws. Finally, crack evolution under dynamic and static loading was compared. Short tensile cracks are found to be the most common crack type, which are responsible for specimen failure. These findings could give a better explanation on the crack initiation and propagation of rock specimen with preexisting flaw, which is the phenomenon that has not been observed in many dynamic experiments.

Affected depth approach to determine the fatigue strength of materials containing surface defects

This paper explains a novel methodology to determine the High Cycle Fatigue (HCF) reliability of materials with defects. A defect was represented by a semi-spherical void situated at a specimen surface subjected to periodic loading. Then, the Finite Element (FE) method was carried out to find out the stress distribution near the defects for diverse sizes and diverse loadings. The Crossland stress change is studied and interpolated by a mathematical function depending on fatigue limits, defect radius, and profundity from the defect tip. The HCF strength of defect material is computed by the “stress strength” approach via the Monte Carlo sampling. This approach leads to determine Kitagawa–Takahashi diagrams, for a definite reliability, of materials with defects. The calculated HCF reliabilities agree well with fatigue tests. Obtaining Kitagawa–Takahashi diagrams with reliability level permits the engineer to be engaged in an endurance problem to compute the defective fatigue lives in safe and efficient process. As a final point, we discuss the sensitivity effects of defect size, defect free fatigue limits, affected depth, and load amplitude to envisage the fatigue reliability of materials with defects.

Fracture Analysis of ARB-Processed CP-Ti Sheets Under Unidirectional Tensile Loading

The fracture behavior of commercially pure titanium (CP-Ti) processed by accumulative roll bonding (ARB) was investigated in this study. Monolithic and Ti-SiC composite samples were first produced by ARB process and then subjected to uniaxial tensile testing at room temperature. Two different ductile fracture mechanisms including shear dimple rupture and equiaxed dimple rupture were observed in the initial and final ARB cycles, respectively. The difference in the rupture mechanism was attributed to different stress states at the crack tip and different densities of metallurgical defects. A non-uniform distribution of dimple size was obtained for fracture surfaces of the samples processed by a low number of ARB cycles. This was attributed to the heterogeneity of microstructure in the primary ARB cycles. The fracture surface of the samples processed by high ARB cycles represented more uniform dimples. This was attributed to more homogenous microstructure in the final cycles. Moreover, SiC particles showed a major role in fracture of samples, so that they affected the size and depth of the dimples, as well as the number of ARB cycles in which the transmission of the fracture mechanism occurred.