Crack Front Research Articles

Impact of injection pressure and polyaxial stress on hydraulic fracture propagation and permeability evolution in graywacke: Insights from discrete element models of a laboratory test

Understanding the hydromechanical behavior and permeability stress sensitivity of hydraulic fractures is fundamental for geotechnical applications associated with fluid injection. This paper presents a three-dimensional (3D) benchmark model of a laboratory experiment on graywacke to examine the dynamic hydraulic fracturing process under a polyaxial stress state. In the numerical model, injection pressures after breakdown (postbreakdown) are varied to study the impact on fracture growth. The fluid pressure front and crack front are identified in the numerical model to analyze the dynamic relationship between fluid diffusion and fracture propagation. Following the hydraulic fracturing test, the polyaxial stresses are rotated to investigate the influence of the stress field rotation on the fracture slip behavior and permeability. The results show that fracture propagation guides fluid diffusion under a high postbreakdown injection pressure. The crack front runs ahead of the fluid pressure front. Under a low postbreakdown injection pressure, the fluid pressure front gradually reaches the crack front, and fluid diffusion is the main driving factor of fracture propagation. Under polyaxial stress conditions, fluid injection not only opens tensile fractures but also induces hydroshearing. When the polyaxial stress is rotated, the fracture slip direction of a fully extended fracture is consistent with the shear stress direction. The fracture slip direction of a partly extended fracture is influenced by the increase in shear stress. Normal stress affects the permeability evolution by changing the average mechanical aperture. Shear stress can induce shearing and sliding on the fracture plane, thereby increasing permeability.

Three-Dimensional Singular Stress Fields and Interfacial Crack Path Instability in Bicrystalline Superlattices of Orthorhombic/Tetragonal Symmetries

First, a recently developed eigenfunction expansion technique, based in part on the separation of the thickness variable and partly utilizing a modified Frobenius-type series expansion technique in conjunction with the Eshelby–Stroh formalism, is employed to derive three-dimensional singular stress fields in the vicinity of the front of an interfacial crack weakening an infinite bicrystalline superlattice plate, made of orthorhombic (cubic, hexagonal, and tetragonal serving as special cases) phases of finite thickness and subjected to the far-field extension/bending, in-plane shear/twisting, and anti-plane shear loadings, distributed through the thickness. Crack-face boundary and interface contact conditions as well as those that are prescribed on the top and bottom surfaces of the bicrystalline superlattice plate are exactly satisfied. It also extends a recently developed concept of the lattice crack deflection (LCD) barrier to a superlattice, christened superlattice crack deflection (SCD) energy barrier for studying interfacial crack path instability, which can explain crack deflection from a difficult interface to an easier neighboring cleavage system. Additionally, the relationships of the nature (easy/easy, easy/difficult, or difficult/difficult) interfacial cleavage systems based on the present solutions with the structural chemistry aspects of the component phases (such as orthorhombic, tetragonal, hexagonal, as well as FCC (face-centered cubic) transition metals and perovskites) of the superlattice are also investigated. Finally, results pertaining to the through-thickness variations in mode I/II/III stress intensity factors and energy release rates for symmetric hyperbolic sine-distributed loads and their skew-symmetric counterparts that also satisfy the boundary conditions on the top and bottom surfaces of the bicrystalline superlattice plate under investigation also form an important part of the present investigation.

Nanocomposite fracture analysis: Aligned Fe3O4-GNP nanoplatelets’ effects on KIC, GIC, CTODc, and fracture mechanisms in epoxy matrices

Epoxy nanocomposites are crucial in aerospace, enhancing structural performance, reducing weight, and improving fuel efficiency across various applications. They ensure safety, reliability, and optimal performance in critical aerospace systems. Optimizing fracture properties like crack growth resistance (KIC), critical stress intensity factor (GIC), and critical crack tip opening displacement (CTODc), is vital for safety, durability, and innovation, especially in epoxy nanocomposites under extreme conditions. This study examines how random Graphene Nanoplatelets (GNP) and aligned Fe3O4-GNP nanoplatelets impact the fracture resistance of epoxy nanocomposites. It analyzes various fracture properties and crack propagation mechanisms following ASTM D5045-99 standards for CT specimen toughness tests using a COD gauge, focusing on nanoparticle alignment and wt% loading effects. Neat epoxy has a KIC of 0.94 MPa m1/2, increasing to 1.20 with 0.600 wt% GNP. Aligned Fe3O4-GNP peaks at 1.49. the baseline GIC starts at 209 J/m2 and rises to 301 J/m2 with 0.600 wt% GNP, and notably to 419J/m2 with aligned Fe3O4-GNP. Aligned Fe3O4-GNP significantly enhances fracture properties by modifying stress distribution at primary crack fronts through mechanisms such as deflection, branching, and twisting. These findings offer crucial insights for improving epoxy nanocomposites in aerospace, ensuring increased safety, reliability, and performance in critical components.

How are microstructural defect interactions linked to simultaneous intergranular and transgranular fracture modes in polycrystalline systems?

The major objective of this investigation is to fundamentally understand and predict how intergranular (IG) and transgranular (TG) fracture modes nucleate and propagate in f.c.c. polycrystalline systems due to defects, such as total and partial dislocation densities and grain boundary (GB) structures and misorientations. A dislocation density crystalline plasticity (DCP) formulation based on the evolution and interaction of total and partial dislocation densities was integrated with a recently developed fracture approach to investigate the fracture nucleation and propagation of simultaneous multiple fracture events, including both IG and TG fracture events. The aggregate grains and GB orientations and morphologies are based on EBSD measurements that are representative of polycrystalline copper aggregates with a broad range of random high angle and low angle GBs. The predictions indicate that dislocation density pileups induce IG fracture due to interrelated stress, slip, and total and partial dislocation density accumulations and interactions for both high angle GBs (HAGBs) and low angle GBs (LAGBs). TG fracture nucleation and propagation occurred due to normal stress accumulations, which exceeds the fracture stress, along cleavage planes. Furthermore, it is shown how IG cracks transition from the GB plane to the cleavage planes as cracks nucleate and propagate. Accumulated plastic zones due to different slip system activities can impede and blunt crack propagation and fronts. These plastic zones form due to high Lomer and Shockley partial dislocation densities. These predictions, which are consistent with experimental observations, provide a fundamental understanding of how simultaneous failure modes initiate and propagate for physically representative microstructures.

Measuring crack depth via normalized deformation profiles from digital image correlation based on optimum correlation

This paper proposes a novel method to quantify the crack depth through the normalized deformation profiles measured by digital image correlation (DIC). This study determines the crack depth through an optimum correlation between the DIC extracted deformation profile and numerical dataset for different crack sizes, and demonstrates the robustness of the approach by parametric investigations. The experimental tests of SE(B) and M(T) specimens demonstrate the accuracy of the proposed method in quantifying crack depths with single and dual crack fronts. The proposed DIC method does not require measurement of load or compliance and is thus a convenient and robust approach to measure the crack depth.

Fracture of four semi-regular lattices regulated by T-stress in modified boundary layer models

The development of additive manufacturing technology has promoted the rise of various lattice metamaterials, and evaluating their fracture properties is critical for both application and safety. Here, by conducting finite element simulations on four types of elastic-brittle semi-regular lattices (kagome, snub-trihexagonal, elongated-triangular, and snub-square), we indicate that the fracture toughness of lattice metamaterials is not solely determined by the crack-tip singular term, i.e., the critical stress intensity factor, but is also influenced by the non-singular T-stress term. T-stress regulates fracture toughness by modulating geometrical distortions and force-carrying modes of lattice bars around the crack front. This regulation effect depends on the lattice topology and becomes weaker under mixed-mode loading. As the relative density of lattices decreases, T-stress can force elastic buckling of bars around the crack front, which may deteriorate the fracture toughness. Additionally, positive T-stress tends to promote the crack deflection and negative T-stress tends to inhibit. Our results offer new insights into the structure-property relationships in the presence of T-stress, which may contribute to design the geometry of micro/nano-lattice metamaterials.

Assessment of fatigue crack growth resistance of newly developed LTT alloy composition for the repair of high strength steel structures

Tensile residual stress (TRS) is a well-known factor that deteriorate the integrity of welded joints. Fatigue failure is accelerated by the existence of TRS introduced during the welding process. There have been efforts in the last two decades to develop filler alloys that can reduce TRS by introducing compressive residual stress (CRS) to oppose the TRS in high strength steel welded joints. These works are based on the theory of austenite (γ) to martensite (α’) transformation and the filler is often called a low transformation-temperature (LTT) alloy. Many studies have reported that the fatigue strength (FS) of weld joint made with LTT alloy is many times better than that of the conventional fillers. It is reported to be particularly useful in the repair of high strength steel structures. However, studies on the fatigue crack growth (FCG) behaviour of these LTT alloys is scarce. In this work, we developed Fe-CrNiMo based LTT weld metal composition, assessed its FCG behaviour and compared the results with that of a conventional welding wire (ER70S-6). It is found that ER70S-6 weld metal obtained under relatively fast cooling is extremely tough, but the associated heat affected zone (HAZ) has poor resistance to FCG which obscured the benefit of the tough weld metal. High heat input or condition that results to slow cooling of the ER70S-6 weldment deteriorates its resistance to FCG. Unfortunately, despite its low martensite start temperature of 231±7 and the anticipated beneficial effect of induced CRS, the LTT alloy studied had the lowest FCG resistance. The LTT alloy appears to have an intrinsic microstructural feature or a ‘fault line’ that reduced its resistance to FCG. While the LTT alloy weld metal has poor resistance to FCG, the associated HAZ resisted FCG more than the HAZ associated with ER70S-6 weld metal. It is observed that aligning the ER70S-6 weld metal perpendicular to the crack front produced the highest resistance to fatigue crack initiation and propagation. In the case of ER70S-6, it is believed that the weld metal induced a CRS at the notch tip which resulted to the high fatigue resistance. In the case of the LTT alloy, perpendicular alignment of the weld metal produced slight improvement.

Evaluation of RPV closure head penetration integrity considering fitting and residual stresses

To ensure the structure integrity of the Reactor Pressure Vessel (RPV), the main challenge is the embrittlement of beltline material. However, the stress is more complex for the regions of Closure Head Penetration (CHP). Feedback of leakage at the CHP has been found during in-service inspection. Although the detailed mechanical evaluation of the RPV head and the CHP has been carried out by many international institutions, there are limited studies to concern structure integrity of CHP tube. The systematic analysis of the influence of material strength matching, assemble stress, the Welding Residual (WR) stress and work pressure load on the fracture is also limited. In this paper, the systematic influence of these factors is analyzed, and the distribution characteristics of Stress Intensity Factor (SIF) and the crack propagation characteristics are studied. The 2D model and accurate 3D model are carried out using the finite element method. The results show that the WR stress on the outer surface of the CHP and the area adjacent to the weld is larger than the yield strength of the material. There is a gap between the RPV and the upper part of the CHP. The attenuation rate of the WR stress in the outlet direction of RPV is lower than that in the inlet direction, so cracks are more likely to occur in the out of direction. The influence of WR stress on the circumferential stress distribution and fracture parameters in the wall thickness direction of CHP is bigger than the influence of assemble load and design condition load. However, the overall stress of CHP is low. The SIF values along the crack front have an asymmetric distribution, and the SIF value is very small. As the fatigue crack propagation life is much longer than the assumed limit in the design lifetime, the risk of fracture and crack fatigue propagation caused by mechanical stress is low.

Influence of Shale Mineral Composition and Proppant Filling Patterns on Stress Sensitivity in Shale Reservoirs

Shale reservoirs typically exhibit high density, necessitating the use of horizontal wells and hydraulic fracturing techniques for efficient extraction. Proppants are commonly employed in hydraulic fracturing to prevent crack closure. However, limited research has been conducted on the impact of shale mineral composition and proppant filling patterns on shale stress sensitivity. In this study, shale cylindrical core samples from two different lithologies in Jimusaer, Xinjiang in China were selected. The mineral composition and microscopic structures were tested, and a self-designed stress sensitivity testing system was employed to conduct stress sensitivity tests on natural cores and fractured cores with different proppant filling patterns. The experimental results indicate that the stress sensitivity of natural shale porous cores is weaker, with a stress sensitivity coefficient below 0.03, significantly lower than that of fractured cores. The shale mineral composition has a significant impact on stress sensitivity, with the stress sensitivity of clayey argillaceous shale cores, characterized by higher clay mineral content, being higher than that of sandy argillaceous shale, characterized by higher quartz mineral content. This pattern is also applicable to fractured cores filled with proppants, but the difference gradually diminishes with increased proppant concentration. The choice of large particles and high-concentration proppant bedding can enhance crack conductivity. Within the experimental range, the crack conductivity of 20–40 mesh quartz sand is more than three times that of 70–120 mesh quartz sand. At an effective stress of 60 MPa, the conductivity of cores with a proppant concentration of 2 kg/m2 is 3.61 times that of cores with a proppant concentration of 0.3 kg/m2. Under different particle size combinations of proppant filling patterns, the crack conductivity at the crack front with large-particle proppants is 6.21 times that of mixed bedding. This study provides valuable insights for the hydraulic fracturing design of shale reservoirs and optimization of production system parameters in subsequent stages.

Calculation and Discussion for Crack Driving Force of Dissimilar Metal Welded Joint of Nuclear Power Equipment Nozzle and Safe End

This study investigates the effects of the material mechanical properties heterogeneity and strength mismatch variation on crack driving forces for cracks in a dissimilar metal welded joint (DMW) of a reactor pressure vessel inlet nozzle to the safe end. Linear elastic and elastic-plastic analyses are carried out to calculate the stress intensity factor (SIF) and J-integral for cracks in the DMW. The effects of crack locations, crack depths, and strength mismatch factors on the SIF and J-integral are studied. The SIF results obtained by finite element analysis are compared with those obtained by the influence function method adopted in the nuclear power code. Results show that the effect of crack location on the SIF can be ignored. The SIFs calculated by the influence function method for cracks in the DMW are basically reasonable, although its conservatism is slightly insufficient. Moreover, with moving the crack location from the nozzle through buttering and weld metal to the safe end, the J-integral increases. The effect of the crack location and strength mismatch factors on the J-integral is essentially caused by variation of the plastic zone and the material properties of the crack front. The crack sizes affect the level of influence of the crack location and the strength mismatch factors on the J-integral. The J-integral increases with decrease of the strength mismatch factor.

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

A deep neural network-based method to predict J-integral for surface cracked plates under biaxial loading

As surface cracks may cause potential failure for engineering structures, it is of vital significance to carry out the fracture assessment for cracked structures. The crack driving force in the form of J-integral is an important input parameter in fracture assessment. This paper focuses on the determination of J-integral for surface cracked plates under biaxial loading. A method for predicting the J-integral based on the deep neural network (DNN) is proposed to estimate J-integral efficiently and accurately. Firstly, extensive three-dimensional (3D) elastic–plastic finite element (FE) analysis is conducted to compute the J-integral along the crack front for developing a FE J-integral datasets containing 1600 cases. Various crack aspect ratios, crack depth ratios, strain hardening exponents, ratios of the loading perpendicular to the crack plane to yield stress, and biaxial ratios, are strategically considered. Secondly, DNN models for predicting the J-integral are constructed and trained according to the obtained datasets by FE analysis. Then, the evaluation criteria for DNN models and the grid search method are utilized to determine the optimal DNN model structure. Finally, test cases are employed to verify the feasibility and prediction accuracy of the determined DNN model. Based on validation results, the determined DNN model exhibits sufficiently accurate prediction performance. This research provides an idea for engineering applications, through building software based on continuously optimized DNN models, the J-integral for surface cracked plates under biaxial loading can be accurately and efficiently predicted for performing fracture assessments.

Strategy for simulating high-speed crack propagation in 3D-plate structures based on S-version FEM

Plate structures serve as the fundamental components of many large structures; therefore, dynamic crack propagation in plates is a significant safety concern. This paper proposes a novel strategy based on the s-version finite element method (s-method) for simulating high-speed crack propagation in a 3D plate structure. We employed a combination of the nodal force release technique and local mesh update method to simulate a dynamically propagating crack front. The global mesh was generated based on the entire domain geometry without considering crack propagation, which significantly simplified the mesh generation procedure, whereas the local mesh was generated only in the vicinity of the crack front with fine elements to ensure high accuracy. In the proposed strategy, the local mesh completely covered the crack front beyond the surface of the 3D plate structure. Such an incompatibility between the surface of the target domain and boundaries of the local mesh causes non-negligible errors in the conventional s-method. Hence, we propose an approach based on Heaviside enrichment to eliminate these errors. To investigate the effectiveness of the proposed strategy, numerical examples to analyse the experimental results of high-speed crack propagation in double cantilever beam-type plate specimens made of polymethyl methacrylate are presented. The numerical results demonstrated the effectiveness of the proposed strategy for simulating high-speed crack propagation in 3D plate structures. Therefore, the proposed strategy has the potential to serve as a fundamental numerical framework for simulating dynamic crack propagation in engineering structures.

Study on the effect of three-dimensional crack initiation and propagation and plastic zone of crack front on fracture-splitting quality of connecting rod

Study on the effect of three-dimensional crack initiation and propagation and plastic zone of crack front on fracture-splitting quality of connecting rod

On the determination of the quasi-static evolution of brittle plane cracks via stationarity principle

The crack front evolution in brittle solids is commonly modelled by defining some crack increment criterion, which can be derived from considerations on the stress singularity, from the definition of a dissipative potential, from the introduction of phenomenological concepts such as the crack mobility, and so on. In this work, we faced the problem with no allowance for any crack increment criterion, but using only the elastic properties, the fracture energy, and a stationarity principle. We will show that these ingredients are enough for determining the equilibrium and the quasi-static evolution of generally shaped three-dimensional brittle plane cracks. In doing this, we pointed out some new insight on the crack front motion, a set of new, generalised, domain integrals for measuring the pointwise crack ‘tension’, and a rigorous calculation of the intersection angle between the crack front and the free surface.

Characterization of fatigue crack growth behavior in welded tubular T-joint

This paper focuses on investigating the fatigue crack growth (FCG) characteristics and residual fatigue life of tubular T-joints which are prone to suffer fatigue damage at the brace and chord intersections under multi-axial stress. Static and fatigue loading tests are performed to investigate the FCG behaviors of tubular T-joints, combining beach marking technique. The evolution of FCG characteristics is studied during the crack growth, convergence and wall penetration through an efficient co-simulation system that established using the multi-scale modeling technique. Fracture morphology analysis is conducted to gain insight into the FCG behaviors combining the scanning electron microscope (SEM) observation. Results indicate that multiple cracks initiate at the crown regions and subsequently evolve circumferentially around the weldments in a doubly-curved shape towards wall-thickness. Interaction effects between adjacent cracks extend the fatigue life along the outer surface, attributed to the premature exposure of converged crack front and the induced variation of stress intensify factor (SIF) distribution along the crack front. The dominant failure mode of tubular T-joints is characterized by an opening mode crack, with the contribution of anti-plane shear mode crack gradually increasing as structural symmetry diminishes. The established co-simulation system shows advantage in capturing the FCG behavior, predicting the fatigue life and characterizing the FCG characteristics with a good balancing of simulation efficiency and calculation accuracy.

Complexity of crack front geometry enhances toughness of brittle solids

Brittle solids typically fail by growth and propagation of a crack from a surface flaw. This process is modelled using linear elastic fracture mechanics, which parameterizes the toughness of a material by the critical stress intensity factor, or the prefactor of the singular stress field. This widely used theory applies for cracks that are planar, but cracks typically are not planar, and instead are geometrically complex, violating core tenets of linear elastic fracture mechanics. Here we characterize the crack tip kinematics of complex crack fronts in three dimensions using optical microscopy of several transparent, brittle materials, including hydrogels of four different chemistries and an elastomer. We find that the critical strain energy required to drive the crack is directly proportional to the geodesic length of the crack, which makes the sample effectively tougher. The connection between crack front geometry and toughness has repercussions for the theoretical modelling of three-dimensional cracks, from engineering testing of materials to ab-initio development of novel materials, and highlights an important gap in the current theory for three-dimensional cracks.

Fracture Analysis of Planar Cracks in 3D Thermal Piezoelectric Semiconductors

The study of piezoelectric semiconductor (PSC) materials and devices is experiencing rapid growth, giving rise to a burgeoning research domain known as piezotronics. Understanding the fracture behavior of PSC materials is essential for designing robust devices and ensuring their long-term functionality. A planar crack of arbitrary shape in the isotropic plane of a three-dimensional (3D) transversely isotropic thermal PSC body subjected to combined thermal-electrical-mechanical loadings is studied via the extended displacement discontinuity (EDD) boundary integral equation method. Under the framework of linearized basic equations and one-way thermal coupling, the hypersingular boundary integral equations with the volume integrals containing the temperature and carrier concentration are obtained and expressed by the EDDs which include displacement, electric potential, carrier concentration and temperature discontinuities across the crack surfaces and are the basic variables in analyzing crack problems. Based on the finite part of hypersingular integrals, the EDDs near the crack border are proved to have the classical behavior of O(r). Furthermore, the asymptotic solutions of extended stresses including the stress, electric displacement, current density and heat flux at the crack front are presented and display classical singular behavior of O(1/r). The extended stress intensity factors are defined and given in terms of EDDs. A 3D numerical model of a penny-shaped crack in the thermal PSC cylinder is established and used to verify the presented formulae.

Non-equilibrium nature of fracture determines the crack paths

Local kinetic processes during crack growth are non-equilibrium and discrete and thus cannot be resolved in the framework of continuum thermodynamics. Atomistic modeling using existing empirical or machine-learning force fields also fails to offer satisfactory solutions for the lack of sufficient accuracy in predicting the energetics of strong lattice distortion and edge cleavage during fracture. The problem is addressed here by using a high-fidelity neural network-based force field for fracture (NN-F3) that covers the space of strain states up to material failure and the non-equilibrium, intermediate states at the crack tip. Atomistic simulations using NN-F3 reveal spatial complexities from lattice-scale kinks to sample-scale crack patterns in 2D crystals such as graphene, which evolve along the process of crack growth. The non-uniform lattice distortion and undercoordination of cleaved edges at the crack front play critical roles in the fracture process. The fracture toughness by cleaving specific edges thus cannot be quantified by their energy densities with relaxed atomic-level structures, which, however, have been widely used in the literature. Instead, the fracture patterns, the critical stress intensity factors corresponding to the kinking events, and the energy densities of edges in the intermediate, unrelaxed states offer reasonable measures for the fracture resistance and its anisotropy, which can be determined from experimental or simulation data with the atomic-level resolution. The findings conform well with recent experimental observations.

Microcracks in CVD diamond produced by scaife polishing

We investigate sub-surface damage in a CVD diamond, polished on a (110) plane using the traditional scaife method. The damage lies in tracks that consist of microcracks lying perpendicular to the polishing direction. These cracks have an irregular spacing and are comprised mainly of {111} facets. Their geometry is consistent with a modified Hertzian fracture, caused by a stick-slip movement of relatively large (micron-sized) diamond particles on the scaife. The interior surface of the cracks shows a 1 × 1 CH3 surface reconstruction, consistent with a high hydrogen overpressure that results from ingress of hydrocarbons in the polishing lubricant and a relatively low temperature process. The crack edge is ragged, and voids with sizes of a few nm are found up to hundreds of nm from the crack front, particularly where the crack ends at the polished surface. We propose that these features are evidence of significant healing of the cracks once the applied stress is removed. Luminescence at the crack tips is seen, presumably due to impurities trapped in these voids, which quenches with electron irradiation at 10 keV.