Crack Initiation Toughness Research Articles

Contact damage initiation in silicon nitride in Hertzian indentation: role of microstructure

A bearing-grade silicon nitride with fine microstructure and a turbine-grade silicon nitride with coarse microstructure were studied with respect to the influence of their microstructures on (a) crack-growth-resistance behavior, (b) strength degradation due to Vickers indentation, and (c) crack initiation in quasi-static indentation with WC spheres. The turbine grade exhibited strong rising crack-growth resistance and less strength degradation due to Vickers indentation as compared to the bearing grade. Partial-ring or C cracks initiated in Hertzian indentation and the critical loads exhibited linear (Auerbach) variation with indenter radius above a critical value. For smaller radius, indentation plasticity preceded C-crack initiation. The bearing grade exhibited higher critical loads for C-crack initiation, but showed greater extension toward a ring crack than the turbine grade. These differences in crack initiation and growth were consistent with the differences in crack initiation and propagation toughness of the two grades. A ball-on-ball impact analysis was used to predict the critical velocities for initiating C cracks in the impact of silicon nitride surfaces with WC spheres.

Fracture, aging, and disease in bone

From a public health perspective, developing a detailed mechanistic understanding of the well-known increase with age in fracture risk of human bone is essential. This also represents a challenge from materials science and fracture mechanics viewpoints. Bone has a complex, hierarchical structure with characteristic features ranging from nanometer to macroscopic dimensions; it is therefore significantly more complex than most engineering materials. Nevertheless, by examining the micro-/nanostructural changes accompanying the process of aging using appropriate multiscale experimental methods and relating them to fracture mechanics data, it is possible to obtain a quantitative picture of how bone resists fracture. As human cortical bone exhibits rising ex vivo crack-growth resistance with crack extension, its fracture toughness must be evaluated in terms of resistance-curve (R-curve) behavior. While the crack initiation toughness declines with age, the more striking finding is that the crack-growth toughness declines even more significantly and is essentially absent in bone from donors exceeding 85 years in age. To explain such an age-induced deterioration in the toughness of bone, we evaluate its fracture properties at multiple length scales, specifically at the molecular and nano dimensions using vibrational spectroscopies, at the microscale using electron microscopy and hard/soft x-ray computed tomography, and at the macroscale using R-curve measurements. We show that the reduction in crack-growth toughness is associated primarily with a degradation in the degree of extrinsic toughening, in particular involving crack bridging, and that this occurs at relatively coarse size scales in the range of tens to hundreds of micrometers. Finally, we briefly describe how specific clinical treatments, e.g., with steroid hormones to treat various inflammatory conditions, can prematurely damage bone, thereby reducing its fracture resistance, whereas regulating the level of the cytokine Transforming Growth Factor-β can offer significant improvements in the stiffness, strength, and toughness of bone and as such may be considered a therapeutic target to treat increased bone fragility induced by aging, drugs, and disease.

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK I , the crack tip biaxiality parameter\(\beta = T\sqrt {{{\pi a} \mathord{\left/ {\vphantom {{\pi a} K}} \right. \kern-\nulldelimiterspace} K}} \) is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.

Application of ductile fracture assessment methods for the assessment of pressure vessels from high strength steels (HSS)

The economical and safe design of pressure vessels requires, besides others, also a detailed knowledge of the vessel failure behaviour in the case of existing imperfections or cracks. The behaviour of a cracked component under a given loading situation depends on material toughness. For ferritic steels, the material toughness is varying with temperature. At low temperature dominantly brittle fracture behaviour is observed, at high temperature the failure mode is dominantly ductile fracture. The transition between these two extremes is floating. In the case of existing or postulated cracks, the safety analysis has to be performed using fracture mechanics methods. In the lower shelf of toughness, K Ic as of ASTM E 399 is the characterising value for crack initiation and immediate unstable crack extension (cleavage). In the upper shelf level the characterising value is the ‘actual crack initiation toughness’ J i acc. to ISO 12135, characterising the onset of slow stable crack extension. For the transition regime in ASTM E 1921 the instability values K Jc are defined, characterising cleavage failure after more or less extended ductile crack growth. The safety analysis of a component operated in the upper shelf of the material toughness, has to consider initiation as well as stable crack extension following initiation. The inclusion of any crack extension into this consideration needs to consider the influence of the constraint in front of a crack tip, leading to multiaxial stress conditions and decreasing the material crack resistance significantly. Thus, the exclusion of crack initiation needs to be proven in a first step of each safety analysis. Assessing the component in a uniform way over the relevant temperature range is possible by using initiation characteristics, which also have the advantage of transferability. A change of criterion considering initiation at the lower shelf, instability in the transition range and again initiation in the upper shelf can be avoided. Depending on the aim of the analysis, the fracture mechanics safety analysis procedures can be used to determine the critical load, the critical crack size or the required material characteristic.

Mechanistic aspects of fracture and R-curve behavior in human cortical bone

An understanding of the evolution of toughness is essential for the mechanistic interpretation of the fracture of cortical bone. In the present study, in vitro fracture experiments were conducted on human cortical bone in order to identify and quantitatively assess the salient toughening mechanisms. The fracture toughness was found to rise linearly with crack extension (i.e., rising resistance- or R-curve behavior) with a mean crack-initiation toughness, K 0 of ∼2 MPa√m for crack growth in the proximal–distal direction. Uncracked ligament bridging, which was observed in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed R-curve behavior. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging zone length and estimate the bridging stress distribution. Additionally, time-dependent cracking behavior was observed at stress intensities well below those required for overload fracture; specifically, slow crack growth occurred at growth rates of ∼2×10 −9 m/s at stress intensities ∼35% below the crack-initiation toughness. In an attempt to measure slower growth rates, it was found that the behavior switched to a regime dominated by time-dependent crack blunting, similar to that reported for dentin; however, such blunting was apparent over much slower time scales in bone, which permitted subcritical crack growth to readily take place at higher stress intensities.

Mechanical and fracture behavior of an artificially ultraviolet-irradiated poly(ethylene-carbon monoxide) copolymer

In this work, 1 wt % carbon monoxide (CO) poly(ethylene-carbon monoxide) (ECO) copolymer sheets were artificially exposed to ultraviolet (UV) light with a power density of 3 mW/cm2 for up to 130 h. A thorough mechanical characterization of the irradiated material was conducted, in which both the stress–strain data and the values of the quasistatic crack initiation and growth toughness were measured and correlated with companion uniaxial tensile tests and single-edge-notched fracture tests. Average values of the elastic modulus, failure strain, and failure stress were determined from the tensile tests. The full-field optical technique of digital image correlation was used to quantify in-plane deformation (displacements and displacement gradients) during the fracture experiments and to extract values of the crack initiation and growth fracture toughness. The elastic modulus increased monotonically with UV irradiation for the exposure times used in this investigation. In addition, for low irradiation times of less than 5 h, both the failure strain and failure stress of ECO decreased, and this caused a corresponding decrease in the crack initiation and growth toughness. However, for longer irradiation times, the failure strain remained almost invariable, whereas the failure stress increased by about 25% over that of unirradiated ECO. As a result, for longer irradiation times (>5 h), 1 wt % CO ECO became not only stiffer but also stronger and tougher, as quantified by companion fracture experiments. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 139–148, 2004

Effects of Aging on the Toughness of Human Cortical Bone: A Study from Nano to Macro Size-Scales

ABSTRACTAge-related deterioration of both the fracture properties and the architecture of bone, coupled with increased life expectancy, are factors leading to the increasing incidence of bone fracture in the elderly. In order to facilitate the development of treatments which counter this increased fracture risk, a thorough understanding of how fracture properties degrade with age is required. The present study describes ex vivo fracture experiments to quantitatively assess the effects of aging on the fracture toughness of human cortical bone in the longitudinal direction. Because cortical bone exhibits rising crack-growth resistance with crack extension, we depart from most previous studies by evaluating the toughness in terms of resistance-curve (R-curve) behavior, measured for bone taken from donors 34 to 99 years old. Using this approach, both the crack-initiation and crack-growth toughness are determined and are found to deteriorate with age; the initiation toughness decreases ∼40% from 40 to 100 years, while the growth toughness is effectively eliminated over the same age range. Evidence from x-ray synchrotron tomography is provided to support the hypothesis that the reduction in crack-growth toughness is associated primarily with a degradation in the degree of extrinsic toughening, in particular involving crack bridging at the microstructural level in the wake of the crack. Atomic force microscope-based nanoidentation of individual collagen fibers revealed changes at the collagen fibrillar level and deep-ultraviolet Raman spectroscopy showed that the cross-linking at the nanostructural level also changes with age. These results should provide for a better mechanistic understanding of the increased propensity for bone fracture with age.

Mechanistic Aspects of Fracture of Human Cortical Bone

AbstractThere has been growing interest of late in the fracture properties of human bone. As understanding such properties in the context of the hierarchical microstructure of bone is of obvious importance, this study addresses the evolution of the in vitro fracture toughness with crack extension (Resistance-curve behavior) in terms of the salient mechanisms involved. Fracture-mechanics based measurements were performed on compact-tension specimens hydrated in Hanks' Balanced Salt Solution using cortical bone from mid-diaphyses of 34-41 year-old human humeri. Post-test observations of the crack path were made by optical microscopy and three-dimensional X-ray computed tomography. The fracture toughness was found to rise linearly with crack extension with a mean crack-initiation toughness of Ko ∼ 2.0 MPa√m for crack growth in the proximal-distal direction. The increasing cracking resistance had its origins in several toughening mechanisms, most notably crack bridging by uncracked ligaments. Uncracked-ligament bridging, which was observed by tomography in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed Rcurve behavior through compliance-based experiments. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging stress distribution. The results obtained in this study provide an improved understanding of the mechanisms associated with the failure of cortical bone, and as such are of importance from the perspective of developing a realistic framework for fracture risk assessment, and for determining how the increasing propensity for fracture with age can be prevented.

Modeling of crack growth in ductile solids: a three-dimensional analysis

A population of several spherical voids is included in a three-dimensional, small scale yielding model. Two distinct void growth mechanisms, put forth by [Int. J. Solids Struct. 39 (2002) 3581] for the case of a two-dimensional model containing cylindrical voids, are well contained in the model developed in this study for spherical voids. A material failure criterion, based on the occurrence of void coalescence in the unit cell model, is established. The critical ligament reduction ratio, which varies with stress triaxiality and initial porosity, is used to determine ligament failure between the crack tip and the nearest void. A comparison of crack initiation toughness of the model containing cylindrical voids with the model containing spherical voids reveals that the material having a sizeable fraction of spherical voids is tougher than the material having cylindrical voids. The proposed material failure determination method is then used to establish the fracture resistance curve ( J– R curve) of the material. For a ductile material containing a small volume fraction of microscopic voids initially, the void by void growth mechanism prevails, which results in a J– R curve having steep slope. On the other hand, for a ductile material containing a large volume fraction of initial voids, the multiple voids interaction mechanism prevails, which results in a flat J– R curve. Next, the effect of T-stress on fracture resistance is examined. Finally, nucleation and growth of secondary microvoids and their effects on void coalescence are briefly discussed.

Application of Acoustic Emission for Measuring Crack Initiation Toughness in Instrumented Charpy Impact Testing

AbstractAcoustic Emission (AE) has been used to detect onset of ductile tearing in instrumented Charpy impact tests to enable determination of dynamic ductile tearing initiation toughness using a single specimen method. An AE based method was developed whereby a conventional instrumented impact tester is instrumented with a commercial broadband acoustic emission sensor mounted on the anvil. The results obtained using the new AE based method were compared to the results obtained by other researchers using specially developed AE sensors located inside the tup. Tests using both AE and direct measurement of the load-line displacement during the instrumented Charpy testing were conducted simultaneously on a conventional ship grade steel. V-notched and fatigue precracked test pieces were tested in the temperature range +23°C to −80°C.The results obtained with AE monitoring were compared to those obtained using the optical Direct Displacement Interferometric Strip (DDIS) method developed by the authors. Good correlation was found between the initiation fracture toughness determined at 0.2 mm blunting and crack extension, J0.2, by the multispecimen Ductile-Brittle Transition (DBT) method and those derived from single specimens applying AE and the new interferometric method to detect ductile fracture initiation. Fast Fourier Transformation (FFT) was applied to analyze the AE signals. The results showed that the different phases of AE and fracture modes could be distinguished based on characteristic frequency and time variance.

Transformation zones, crack shielding, and crack-growth resistance of Ce-TZP/alumina composite in mode II and combined mode II and mode I loading

Crack-tip transformation zones, crack shielding and crack-growth-resistance ( R-curve) behaviors of a transformation-toughened ceria-partially stabilized zirconia–alumina (Ce-TZP/alumina) composite were studied in mode II and combined mode I and mode II loading using compact-tension-shear (CTS) specimens. The mode II and mode I stress intensities for both the initial straight cracks and the subsequent kinked cracks were assessed by the method of caustics using geometrically equivalent specimens of polymethyl methacrylate (PMMA). The angle of formation of the transformation zones as well as of extension of the cracks increased systematically with increasing ratio of the mode II and the mode I stress intensities and approached a value of θ ∗=−72 ° in pure mode II loading. This angle was close to the angle for maximum hoop tension in the stress field of a mode II crack ( θ ∗=−70.5 °). A crack-initiation toughness envelope was constructed on a K I– K II diagram using the critical loads for incremental crack extension. The crack-initiation toughness in pure mode II loading was less than the corresponding toughness in mode I loading. This result was consistent with calculations that indicated no shielding from the asymmetric and elongated zones developed in mode II loading. The fracture toughness measured for the kinked cracks at long kink lengths approached the maximum fracture toughness measured for a mode I crack.

Experimental analysis of the practical LBZ effects on the brittle fracture performance of cryogenic steel HAZs with respect to crack arrest toughness near fusion line

Focusing on crack arrest behavior, this study investigates the practical influence of local brittle zones (LBZs) on the brittle fracture resistance of heat-affected zones (HAZs) in advanced 9% Ni cryogenic steel welds, and discusses whether the LBZs of this steel in practice have potentially deleterious effects as previously thought, or not. By analyzing the variations in brittle crack arrest toughness ( K a) and brittle crack initiation toughness ( K c) within actual HAZ, it is found that LBZs of this steel may not be harmful in consideration of crack arrest toughness near fusion line.

Crack-initiation toughness and crack-arrest toughness in advanced 9 pct Ni steel welds containing local brittle zones

The present study investigates the influence of local brittle zones (LBZs) on the fracture resistance of the heat-affected zones (HAZs) in quenched, lamellarized, and tempered (QLT) 9 pct Ni steel weld joints. The results of Charpy impact tests using simulated coarse-grained, heat-affected zone (CGHAZ) specimens show that the intercritically reheated (IC) CGHAZ and unaltered (UA) CGHAZ are the primary and secondary LBZs, respectively, of the steel at cryogenic temperature. Compact crack arrest (CCA) tests and crack-tip opening displacement (CTOD) tests were conducted at a liquefied natural gas (LNG) temperature to measure the variations in crack-arrest toughness and crack-initiation toughness along the distance from the fusion line (FL) within the actual HAZ. While CTOD tests show a decrease in toughness when approaching the FL, i.e., the regions containing LBZs, the crack-arrest-toughness values are found to be higher than those in the regions near the base materials. This is due to the fact that the crack-arrest toughness is governed by the fraction of microstructures surrounding LBZs instead of the LBZs themselves. By direct comparison of the brittle-crack-arrest toughness (Ka) with the brittle-crack-initiation toughness (Kc), this investigation has determined that, with regard to crack-arrest behavior, the LBZs of QLT-9 pct Ni steel do not limit the practical safety performance of the weld joints in LNG storage tanks.

Dynamic fracture behavior of syntactic epoxy foams: optical measurements using coherent gradient sensing

Dynamic fracture behavior of syntactic foams made of thin-walled microballoons dispersed in epoxy matrix is studied. Monotonically decreasing dynamic Young's modulus with increasing volume fraction of microballoons is observed using ultrasonic pulse-echo and density measurements. The results are also in good agreement with the Hashin–Shtrikman lower-bound predictions for elastic porous solids. Dynamic crack initiation toughness and crack growth behaviors are examined using instrumented drop-tower tests and optical measurements. Crack initiation toughness shows a linear relationship with Young's modulus over the entire range of volume fraction of microballoons studied. A proposed model based on simple extension of micromechanics prediction agrees well with the measurements. The optical method of coherent gradient sensing (CGS) has been used along with high-speed photography to record crack tip deformation histories in syntactic foam samples subjected to impact loading. Pre- and post-crack initiation events have been successfully captured and apparent dynamic stress intensity factor histories are extracted from the interferograms. Results suggest increasing crack speeds with volume fraction of microballoons. No significant dependence of dynamic fracture toughness on crack speed in any of the volume fractions is observed.

Simulation of porosity by microballoon dispersion in epoxy and urethane: mechanical measurements and models

Effective mechanical properties of microballoon-dispersed epoxy and urethane are studied under quasi-static and dynamic loading conditions. Elastic modulus measurements of these mixtures over a volume fraction range of 0–0.45 are in good agreement with Hashin-Shtrikman lower-bound predictions for two-phase mixtures comprising of randomly distributed spherical pores in an elastic matrix. The measurements have also been predicted accurately by a LEFM based pore-flaw model for a selected flaw size to pore size ratio. These imply that the microballoons offer negligible reinforcement due to extremely small wall thickness to diameter ratio. Accordingly, feasibility of using these materials to simulate controlled porosity for tensile strength and fracture toughness modeling is explored. Measured tensile strength and fracture toughness values decrease monotonically similar to the Young's modulus variation with volume fraction of microballoons. Guided by the measurements linear elastic models for porous materials that predict tensile strength and fracture toughness of these mixtures are proposed and validated. The tensile strength predictions are in very good agreement with measurements for both epoxy and urethane compositions. The quasi-static crack initiation toughness prediction captures the measurement trends rather well in both cases. The agreement between the measurements and predictions are modest for epoxy matrix while they are good for urethane compositions. Based on fracture surface micrography, an empirical corrective procedure is advanced to improve the agreement between the measurements and the model. The dynamic crack initiation toughness measurements for epoxy, on the other hand, are in excellent agreement with the predictions.

Fracture Toughness of a 6061Al Matrix Composite Reinforced with Fine SiC Particles

The fracture toughness of 6061 Al alloy metal matrix composite reinforced with 15 vol% fine SiC particles of 600 nm, in size under a high temperature over-aged condition was studied. And the toughness of the 6061 Al matrix alloy and the same matrix alloy reinforced with coarse SiC particles of 9.5 mum were also measured for comparison. Fracture toughness tests were conducted on a servo-hydraulic testing machine by using three point bending specimens. The results showed that the toughness of the fine particle reinforced composite was obviously higher than that of the coarse particle reinforced composite in terms of crack initiation toughness, crack propagation energy and total absorbed energy. The mechanisms controlling the fracture toughness of the two composites reinforced with fine and coarse SiC particles were discussed based upon the measured toughness data and microstructure examinations by means of an optical microscope and a scanning electron microscope.

Evaluation of crack tip fields and stress intensity factors in functionally graded elastic materials: Cracks parallel to elastic gradient

Particulate functionally graded materials (FGM) made of glass-filled epoxy with edge cracks parallel to the direction of the elastic gradient and subjected to pure bending have been studied. Crack tip measurements are used to examine continuum models for FGMs by treating the material as isotropic and nonhomogeneous at macroscales. Situations where cracks are located on the compliant and the stiff sides of the beams are separately examined by mapping crack tip deformations using optical interferometry. Comparative experiments on homogeneous compositions corresponding to identical elastic properties of the crack tip region in the FGM are also undertaken. A methodology for extracting fracture parameters in FGMs based on locally homogeneous material descriptions is advanced. Companion finite element models are used to aid the development of fringe analysis procedures and to provide a direct comparison to the optical measurements. Stress intensity factors in FGMs are compared to each other and to their homogeneous counterparts. Optical measurements near quasi-statically growing cracks in FGMs have been undertaken, and crack growth resistance behavior is explained using crack initiation toughness variation as a function of filler volume fraction in homogeneous sheets.

Dynamic fracture toughness of 6061Al composites reinforced with SiC particulates

Dynamic fracture toughness experiments were conducted at room temperature on 6061Al alloy reinforced with 15 and 25% volume fractions of 9.5μm SiC particulates. The fracture properties were evaluated in terms of crack initiation toughness, crack propagation energy and total absorbed energy. The dynamic fracture of the unreinforced 6061Al alloy was also studied as a comparison. The results of dynamic tests for both composites and matrix alloy are compared with their respective quasi-static cases. It is found that addition of SiC particles can drastically decrease fracture toughness of 6061Al alloy at both quasi-static and dynamic loading rates. 15%SiC P composite shows a considerable increase in crack initiation toughness and a much greater increment of crack propagation energy in dynamic loading case compared with static loading case, whereas 25%SiC P composite exhibits a negligible increment of crack propagation energy and a reduced increase of crack initiation energy in dynamic case in contrast to 15%SiC P composite. Detailed SEM examination of the fracture surfaces and optical observation of microstructures beneath the fracture surfaces of both composites, combined with an in-situ SEM observation, were made to investigate the fracture processes of the composites.

Conservatism of ASME KIR-reference curve with respect to crack arrest

The conservatism of the RT NDT temperature indexing parameter and the ASME K IR-reference curve with respect to crack arrest toughness, has been evaluated. Based on an analysis of the original ASME K Ia data, it was established that inherently, the ASME K IR-reference curve corresponds to an overall 5% lower bound curve with respect to crack arrest. It was shown that the scatter of crack arrest toughness is essentially material independent and has a standard deviation (S.D.) of 18% and the temperature dependence of K Ia has the same form as predicted by the master curve for crack initiation toughness. The ‘built in’ offset between the mean 100 MPa√m crack arrest temperature, TK Ia, and RT NDT is 38°C (TK Ia=RT NDT+38°C) and the experimental relation between TK Ia and NDT is, TK Ia=NDT+28°C. The K IR-reference curve using NDT as reference temperature will be conservative with respect to the general 5% lower bound K Ia(5%)-curve, with a 75% confidence. The use of RT NDT, instead of NDT, will generally increase the degree of conservatism, both for non-irradiated as well as irradiated materials, close to a 95% confidence level. This trend is pronounced for materials with Charpy-V upper shelf energies below 100 J. It is shown that the K IR-curve effectively constitutes a deterministic lower bound curve for crack arrest The findings are valid both for nuclear pressure vessel plates, forgings and welds.

展伸用アルミニウム合金中の粗大な金属間化合物粒子の損傷によって誘発される破壊の計算機シミュレーション

Coarse inclusion materials have shown evidence of inclusion cracking ahead of a crack-tip by in-situ SEM observations, which degrades the fracture toughness. In-situ strengths of various inclusions have also been estimated in the preliminary analysis. The present work is aimed at numerical analyses of toughness degradation due to the existence of damaged inclusions with an A2091 alloy as its model material. Especially, microstructural control for toughness enhancement is discussed in the lights of the results.The investigation employs a combination of HRR singularity and an Eshelby model, which considers both elastic mismatches between a matrix and inclusions and back stresses due to rigidity of the inclusions, to conduct an estimation of internal stresses in the inclusions. The essential feature of the model is to predict crack initiation toughness and crack path morphologies using a mixed-mode fracture criterion. An appropriate criterion for the damage initiation, effects of a deflected crack-tip and shielding/antishielding effects due to the damaged inclusions are taken into consideration.The toughness is found to be degraded in the case of large matrix grains, high volume fraction of inclusions, and low fracture strength of the inclusions. When the spatial distribution of the inclusions is homogeneous, these effects are predicted less than 10%. However, the effect is remarkably pronounced when the inclusions are agglomerated. Some of these results are consistent with those by in-situ SEM observations reported elsewhere. The estimated lower boundary values of the fracture strengths are 2520 and 2440 MPa respectively for Al3Zr and Al3Ti particles. These values are of particular interests, because they are several times larger than the measured in-situ strengths of CuAl2 and Al2CuMg particles. Aligned weak inclusions on grain boundaries act to deflect the crack along the grain boundaries even when inferior crack propagation resistance within grain boundary PFZs is not considered.