Recent application of caustics on experimental dynamic fracture studies

Combining the caustic method with high‐speed photography is an efficient optical measurement technique to study the dynamic fracture behaviours of homogenous and isotropic material. In the last decade, the main emphasis is extended to study dynamic fracture of anisotropic material and dynamic propagation of multi‐cracks and interface cracks in practical engineering materials. In this paper, the recent advances and applications about the dynamic caustic method in China are reviewed, such as impact response and dynamic fracture of composite materials (fibre composites, functionally gradient materials and nanometre composites), and dynamic interaction and propagation of multi‐cracks and interface cracks. Particularly, some new numerical methods were developed to solve the complicated caustic equations by introducing both the maximum characteristic size and the relevant angles in caustic patterns. Also, some important experimental results in fracture mechanics are described, and the potential research prospects about dynamic caustics are included as well.     

Characterization of engineering ceramics by indentation methods

The induction of indentations in brittle materials and their evaluation result in information useful for the characterization of materials. In addition to the fracture-mechanical evaluation of the indentations, i.e. of the incipient cracks resulting from them, the cracks may be used for determining the fracture toughness,information regarding the hardness, critical size of surface defects, characteristic quantities of crack propagation, durability, as well as existing internal stresses.     

Effect of inclusions on size of surface flaws in glass-crystal composites

Indentation fracture studies were conducted on three sodium borosilicate glasses containing a dispersed phase of alumina inclusions with different degrees of thermal expansion mismatch between the glass matrices and the alumina. The alumina inclusions were found to cause a significant decrease in the size of the indentation cracks compared to those in the glass. This effect was greatest at the higher values of indentation load, which resulted in cracks of dimensions of sufficient size that their propagation was impeded by the tougher alumina dispersions. The fracture toughness for the composite samples calculated from the indentation data showed a significant increase with increasing crack size. For the smallest cracks in these composites, the value for fracture toughness was well below the value obtained in an earlier study by the single-edge notch-beam technique. The fracture toughness for the larger crack sizes which interacted with the alumina dispersions showed excellent agreement with the notch-beam data. The residual stresses due to the thermal expansion mismatch appeared to lead to a slight increase in the mean crack size regardless of the direction of thermal expansion mismatch.     

Komplexe Bewertung von Indentereindrücken zur Charakterisierung von Konstruktionskeramik

The induction of indentations in brittle materials and their evaluation result in information useful for the characterization of materials. In addition to the fracture-mechanical evaluation of the indentations, i.e. of the incipient cracks resulting from them, which cracks are used for determining the fracture toughness. Information regarding the hardness, critical size of surface defects, characteristic quantities of crack propagation, durability as well as existing internal stresses can be derived.     

Fatigue crack growth in welded beams

The fatigue behavior of welded steel beams is evaluated using the fracture mechanics concepts of stable crack growth. A fracture mechanics model for cracks originating from the pores in the web-to-flange fillet weld is developed. Estimates of the stress-intensity factor are made that numerically describe the initial flaw condition. With the final crack size known, a theoretical crack-growth equation was derived from the fatigue test data of the welded beams. The derived relationship compares well with actual crack-growth measurements on a welded beam and available data from crack growth specimens. The regime of crack growth where most of the time is spent growing a fatigue crack in a structural element is shown to correspond to growth rates below 10^?6 in. per cycle. Little experimental crack growth data is available at this level. It is concluded that the fracture mechanics concepts can be used to analyze fatigue behavior and to rationally evaluate the major variables that influence the fatigue life of welded beams.     

BN-SiC层状复合陶瓷的断裂行为研究

以SiC、BN粉为原料,采用热压法制作了BN-SiC层状复合陶瓷,并对层状复合陶瓷的断裂行为进行了研究,发现层状材料通过层间界面优先开裂使横向裂纹扩展路径明显曲折化,断裂从一次性脆断变为对裂纹损伤具有一定容忍能力的逐次多级断裂,裂纹张开位移显著增大,断裂韧性显著提高.     

Intrinsic Notch Effect Leads to Breakdown of Griffith Criterion in Graphene

Due to lack of the third dimension in 3D bulk materials, the crack tip in graphene locates on several atoms implying that its fracture behavior can be closely associated with its lattice structure, i.e., the bond length and angle. As the bond length reflects the discrete nature of the atomic structure, theoretical discussion is focused on the concomitant size effect at the nanoscale with few or no reports about the influence of the bond angle. Through the comparisons between theoretical calculations and experimental data, here it is first demonstrated that the bond angle is essential for understanding the fracture behavior in graphene, serving as an intrinsic notch reducing the stress singularity near the crack tip (the intrinsic notch effect), leading to the breakdown of the Griffith criterion in graphene. The work provides a framework for the studying of the brittle fracture in 2D materials, which gives rise to the more reliable device design based on 2D materials. More importantly, the significance of the intrinsic notch effect is profound and far‐reaching, paving the way to a more comprehensive and deep understanding of the mechanical properties in nano as well as nanostructured materials.     

Pore–crack orientation effects on fracture behavior of brittle porous materials

Mechanical behavior of two-dimensional microstructures containing circular pores were simulated under uniaxial and biaxial loading using the finite element method. Resulting stress distributions were combined with classical fracture mechanics to investigate fracture behavior of brittle porous materials assuming that randomly oriented cracks are present along pore surfaces. Multiple crack orientations were found to introduce a variability in Weibull modulus even for the same set of microstructures containing equal number and size of cracks. Also, the variability increases with increasing crack size to pore size ratio. Under uniaxial loading, angular distribution of fracture origin widens with increasing porosity.     

Grain size effect on high-speed deformation of Hadfield steel

The influence of the microstructure on the tensile properties and fracture behavior of Hadfield steel at high strain rate were studied. Hadfield steel samples with different mean grain sizes and carbon phases were prepared by rolling at medium temperatures and subsequent annealing. A sample with an average grain size larger than 10 μm, and a small number of carbides shows ductility with local elongation (post uniform elongation) at a high-speed tensile deformation rate of 10³ s⁻¹. In addition, the fracture surface changes from brittle to ductile with increasing strain rate. In contrast, a fine-grained sample with carbides undergoes brittle fracture at any strain rate. The grain size dependence is discussed by considering the dynamic strain aging as well as the emission of dislocation from cracks. The accelerated diffusion of carbon due to grain refinement is considered as one of the important reason for brittle fracture in the fine-grained Hadfield steel.     

Fracture toughness behavior of weldments with mis-matched properties at elevated temperature

High temperature fracture toughness tests were performed on welded specimens of 1Cr-1Mo-14 V steel with different levels of mismatch between the base metal and the weld metal and the cracks lying along the fusion line. A wide range of fracture toughness values were obtained for weldments, as opposed to a unique value of J_IC and a unique J-R curve typically obtained for homogeneous materials. Detailed observations of the crack path within the weldments were made to understand the wide scatter in the fracture toughness behavior. The yield strength mismatch between the base metal and the weld metal was found to directly influence the stable crack path, and hence the fracture toughness behavior. The denomination of ‘apparent fracture toughness’ was used to describe the variability of the fracture toughness in the weld region due to microstructure and mechanical property gradients. The apparent fracture toughness exhibited a minima at a fixed distance from the fusion line for a specific weld. The relative position of the fatigue precrack with respect to the fusion line and the region of low fracture toughness was also shown to influence the measured fracture toughness behavior of the specimen. A frame-work is provided for representing the weld fracture toughness behavior and the associated variability due to microstructural gradients. This revised version was published online in August 2006 with corrections to the Cover Date.     

FRACTURE MECHANICS APPLICATIONS TO DRILLING AND BLASTING

Abstract— This paper gives a brief review of research in rock fracture mechanics as conducted at the Fracture and Photo-Mechanics Laboratory (FPML) at Vienna University of Technology. The mechanisms pertaining to percussion drilling and blasting are investigated, with specific reference to the application of fracture mechanics. In order to gain an improved understanding of the mechanisms controlling rock fragmentation, a multidisciplinary approach is followed which includes laboratory experiments conducted in plexiglass and rock, in-situ field experiments and analytical/numerical modelling techniques.
Field experiments revealed that percussively drilled holes exhibit a very shallow region of damaged rock. An analytical model to simulate damage accumulation and crack initiation due to elastic waves generated by impacting drill bits was developed. This model, based on damage and fracture mechanics, was incorporated into a numerical finite difference code. Fracture and damage mechanics parameters are related to the moment tensor which is determined experimentally by means of acoustic emission. Small scale model blasts were used to investigate the blast-induced fractures in the near-borehole zone as well as in the far field. Analytical and numerical investigations give insight into stress wave and gas driven fracturing. The applicability of the dynamic finite difference program SWIFD to the interaction between stress waves and cracks is illustrated.     

Fracture statistic of torsion and flexure in glass rectangular bars

Fracture statistics in rectangular bars subjected to torsion and to three-point bending are studied and the cumulative probabilities of fracture using Weibull's functions for materials that exhibit volume brittleness are determined. Diagrams of the cumulative probability fracture for commercial glass samples are plotted. The parameters of Weibull's functions regarding torsion and bending are appraised by employing lineal regression and nomograms, respectively. For torsion, dispersion of the parameters is determined by resorting to Fisher's information matrix. The size effect experimentally determined becomes half of the same theoretically determined. The different forms of the statistical functions followed by the same material in the two tests, are due to form and size influences of the cracks originating at the fracture, as well as to the finish of the sample sides.     

Delamination cracking in advanced aluminum-lithium alloys - Experimental and computational studies

Delamination cracking in advanced aluminum-lithium (Al-Li) alloys plays a dominant role in the fracture process. With the introduction of these materials into components of aerospace structures, a quantitative understanding of the interplay between delamination cracking and macroscopic fracture must be established as a precursor to reliable design and defect assessment. Delamination cracking represents a complex fracture mechanism with the formation of transverse cracks initially on the order of the grain size. In this work, interrupted fracture toughness tests of C(T) specimens, followed by incremental polishing, reveal the locations, sizes and shapes of delamination cracks and extensions of the primary macrocrack. These observations suggest that delamination crack sizes scale with loading of the primary crack front expressed in terms of J/σ₀. Using a 3-D, small-scale yielding framework for Mode I loading, a companion finite element study quantifies the effects of prescribed delamination cracks on local loading along the macroscopic (primary) crack and ahead of the delamination cracks. An isotropic hardening model with an anisotropic yield surface describes the constitutive behavior for the 2099-T87 Al-Li alloy plate examined in this study. The computational results characterize the plastic zone size, the variation of local J ahead of the macrocrack front and the stress state that serves to drive growth of the macrocrack and delamination crack. The computational studies provide new, quantitative insights on the observed increase in toughness that has been observed during fracture experiments caused by delamination cracks that divide the primary crack front.     

Bruchmechanische Charakterisierung des Ermüdungsverhaltens von SiSiC

Fracture Mechanics Characterization of Fatigue in SiSiC The behaviour of microscopic “natural” cracks and of artificial sharp cracks was investigated on a fracture mechanics base for extruded and slip casted SiSiC. The resulting strength and crack propagation data were used to calculate relations between loading time and probability of fracture and thus provide a base for the practical application of the investigated materials in structures. Examples of calculated life times and probabilities of failure as well as results of experiments performed to check the calculations are discussed.     

Indentation-induced subsurface damage in silicon particles of Al–Si alloys

Damage microstructures generated beneath the Vickers indentation applied to the silicon particles in an Al–18.5 wt.%Si alloys were studied. Plastic deformation at low loads and volume expansion due to subsurface crack formation at high loads (>650 mN) were responsible for pile-up formations around the indentations. The probability of lateral cracks reaching the surface and causing particle fracture was shown to obey Weibull statistics with a low modulus. The indentation pressure estimated as 19.3 GPa induced the transformation of diamond cubic Si-I to bcc Si-III and rhombohedral Si-XII, as observed by Raman microspectroscopy. Cross-sectional FIB and TEM revealed a semi-circular plastic core and subsurface lateral crack pattern below the residual indents and a localized amorphous zone at the median crack boundary immediately below the plastic core.     

An experimental study of the interaction of internal cracks in PMMA

Internal cracks in polymethyl methacrylate (PMMA) specimens were generated by pulsed laser light. The interactions of coplanar cracks, parallel cracks, and cracks in T and H configurations were investigated. The tensile strength of specimens with a single internal crack decreased with increasing crack size, and the strength correlated well with the initial crack and unstable crack size in the Griffith relationship. For specimens with coplanar and parallel cracks, the strength increased and decreased with the crack distance, respectively. For the T and H crack configurations, the presence of delamination cracks decreased the strength, and the reduction in strength became more significant when the crack distance was small. All fracture surfaces showed similar fracture morphology in the sequence of laser-generated crack, smooth fracture mirror, mist with hyperbolic markings, and rough hackle region with rib markings. Examination of the fracture surfaces revealed crack arrest by the delamination cracks in both T and H configurations, and crack bowing between delamination cracks in the H configuration. The propagating crack was eventually able to circumvent the delamination cracks. The experimental results are compared with the available theoretical analyses, and the relevance of the present study to the toughening of brittle materials is discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Microstructure and stray electric fields at surface cracks in ferroelectrics

Ferroelectric perovskites are widely used in transducer, memory and optical applications due to their attractive electromechanical and optical properties. In these brittle materials, reliability and failure of devices is dominated by the behavior of cracks. The electromechanical coupling causes cracks to interact strongly with both mechanical as well as electrical fields. Additionally, cracks and domain patterns interact strongly with each other. Hence, an understanding of the electromechanics of cracks requires an accounting of all these interactions. In this work, we apply a real-space phase-field method to compute the stresses, domain patterns, and stray electric fields in the vicinity of a stationary crack, defined here as a geometric feature that causes large but bounded stress. We investigate the effects of charge compensation on the crack face, crack orientation with respect to the crystal lattice, and applied far-field stress and electric fields.     

Investigation of failure behavior of two different types of Zircaloy clad tubes used as nuclear reactor fuel pins

Nuclear reactor fuel pins act as barriers to the release of radioactive fission products to the coolant flowing around these thin-walled tubes and hence they prevent the leakage of radioactivity to the surroundings of reactor core. These tubes are of small thickness in order to have less resistance in the path of heat flow from the fuel to the coolant. Investigation of failure behavior of these fuel clad tubes is of utmost importance to the designers and plant operators in order to ensure the maximum residence time of the fuel bundles inside the reactor core as well as to ensure minimal activity during operation and refueling activities. Various types of zirconium based alloys are used to manufacture these pins. The focus is to obtain better strength, ductility, corrosion resistance, oxidation resistance, and minimal creep including those due to irradiation-assisted damage and deformation processes. Two number of such types of alloys, namely, re-crystallization annealed Zircaloy-2 and stress-relief annealed Zircaloy-4, have been investigated in this work for their fracture behavior. As standard fracture mechanics specimens cannot be machined from these thin-walled tubes, non-standard specimens with axial cracks have been used in this work. Load normalization technique has been used to evaluate crack growth during loading of these specimens. It was observed that the re-crystallization annealed Zircaloy-2 specimens have higher initiation fracture toughness as well as higher resistance to crack growth compared to the other type of specimens. In order to understand the micro-structural aspects of the fracture resistance behavior of these materials, further investigation incorporating optical and transmission electron microscopy have also been carried out. It was concluded that the higher fracture resistance behavior of the re-crystallization annealed Zircaloy-2 specimens can be attributed to the presence of finer grain and sub-grain micro-structure, very low dislocation density and other defects in the material.     

A multiscale-indentation study of deformation and fracture in 6H polycrystalline silicon carbide

ABSTRACT

The mechanical behaviour of a polycrystalline silicon carbide across length scales was studied using Vickers indentation, focusing on the hardness, fracture toughness and failure mechanism of the material. For macroscopic and microscopic indentations, the hardness decreased with an increase in load, which was associated with the well-known indentation size effect as well as the internal flaws. For nanoindentation, severe plastic deformation was discovered beneath the imprints on the basal plane (0001) which is the most favourable crystallographic plane for dislocation movement. Alternative sources of plastic deformation, including deformation twinning and stacking faults, were found for nanoindentations with an increased load. Also, cracking was observed for indents made at 100 mN and above, which was used to study the fracture toughness.     

Degeneration of mechanical characteristics and performances with Zr nanoparticles inserted in Bi-2223 superconducting matrix and increment in dislocation movement and cracks propagation

This study explains the role of Zr concentration level on mechanical characteristics and performance belonging to the bulk Bi-2223 superconducting materials by means of standard Vickers microhardness (H _v ) measurements at different applied loads in the range of 0.245–2.940 N and evaluated theoretical calculations. The experimental measurement results obtained display that the mechanical performances regress with the increment of the Zr addition level due to the increased artificial disorders/damages/breaks/voids/cracks and irregular grain orientation distribution. In other words, the Zr addition accelerates both the dislocation movement and especially the cracks/voids propagation of as a consequence of the decrement in the Griffith critical crack length, being one of the most striking points deduced from this work. These vital findings are also favored by the extracted parameters of Young’s modulus, yield strength, fracture toughness and brittleness index. Nevertheless, it is found that every sample studied exhibit typical indentation size effect (ISE) behavior due to the production of the elastic and plastic deformations simultaneously in the system. Moreover, the load dependent microhardness values are theoretically analyzed with the aid of six available models such as six available approaches: Meyer’s law, proportional sample resistance model, modified proportional sample resistance model, elastic/plastic deformation, Hays–Kendall (HK) and indentation-induced cracking model for the first time. The results obtained show that the HK approach exhibits perfectly performance on the analysis of the mechanical characteristics of the superconducting materials exhibiting ISE behavior whereas the other models are inadequate to explain the load independent mechanical characteristics of the Bi-2223 system added by the Zr nanoparticles.