Plane strain fracture toughness testing of high density polyethylene

The concepts of linear elastic fracture mechanics (LEFM) are applied to three grades of high density polyethylene in an attempt to determine their fracture behavior in terms of a linear elastic fracture toughness, K_c. The effect of specimen size (thickness and width), crack length and the mode of loading on K_c has been investigated in order to determine the plane strain fracture toughness, K_Ic, of these materials. The effect of temperature (between +23 and ?180°C) on their fracture behavior has also been investigated and compared in terms of their plane strain fracture toughness values.     

Fracture mechanics studies on concrete compounds

An experimental and analytical investigation was conducted to determine fracture mechanics characteristics of hardened cement paste, aggregates and aggregate-cement paste interfaces. For this the fracture toughness K_Ic was determined on wedge loaded CT-specimens. It was found that hardened cement paste, aggregates and interfaces exhibit unique K_Ic values which are independent of the initial crack length. In additional test series the ductility of various model concretes tested in flexure was determined. The ductility depends primarily on the fracture toughness toughness of the aggregate-hardened cement paste interfaces and is less affected by the fracture toughness of the hardened cement paste.     

Deformation and fracture behaviour of a rubber-toughened epoxy: 1. Microstructure and fracture studies

The microstructure and fracture behaviour of an unmodified and a rubber-modified epoxy have been studied. Values of the stress intensity factor, K_Ic, at the onset of crack growth, the type of crack growth, and the detailed nature of the associated fracture surfaces have been ascertained. Both materials exhibit essentially the same types of crack growth but the values of K_Ic for the rubber-modified material were usually significantly higher than those for the nmodified epoxy. The mechanisms for this increased toughness have been considered and a mechanism that accounts for all the observed characteristics has been proposed.     

Fracture toughness of glasses as measured by the SCF and SEPB methods

The fracture toughness, K_Ic, of six glasses was measured by the surface crack in flexure (SCF) and single-edged precracked beam (SEPB) methods. Results depended upon the loading rate as well as the test environment. Environmentally-assisted slow crack growth affects the results for tests done in air. Dry nitrogen testing is preferred. Crack healing may be a severe complicating factor with precracked flexure bar type specimens if the specimens are unloaded between the precracking and final fracture test. Success in K_Ic testing depends to a large degree on upon the ability to make good precracks.     

Elastic properties and fracture toughness of SiOC-based glass-ceramic nanocomposites

Four different SiOC glass ceramics were synthesized and their fracture toughness (K_Ic) and fracture surface energy (γ) were assessed by means of the single-edge precracked beam (SEPB) method. In addition, the elastic moduli were measured and the Vickers indentation behavior (hardness and microcracking) was characterized. In particular, the dependence of K_Ic on the free carbon content and on the fraction of crystallized nanoparticles (SiC, ZrO₂, HfO₂) was investigated. An increase in K_Ic, from about 0.73 to 0.99 MPa √m is observed as the free carbon content is increased from less than 1 to 12 vol%. The addition of Hf and Zr (resulting in 4.5 to 7.8 vol% HfO₂ and ZrO₂ nanoparticles) was found to increase K_Ic to an extent similar to the free carbon content. Moreover, predicted K_Ic values, assuming that the crack travels through all phases accounting for their respective volume fractions, disrupting the weakest links within the structural units, are in agreement with the experimental values.     

Fracture toughness of glass fiber-reinforced acetal polymer

The critical stress field intensity factor for crack propagation, K_Ic, was determined for a large number of glass fiber-reinforced acetal copolymer compositions and for the unfilled resin. The results were interpreted in terms of a model previously proposed for the tensile behavior of these materials. The K_Ic could be regarded as a linear function of the contribution of the fiber reinforcement to the tensile strength, but was otherwise substantially independent of the amount and length of the fibers and the nature of the fiber finish. From this relationship it was estimated that the inherent flaw size of these materials was of the order of magnitude of the fiber length. The observed variation of K_Ic with loading rate was also consistent with the model. The notched Izod impact strength of these same materials was shown to be roughly equivalent to G_Ic, the critical strain energy release rate, or fracture energy per unit area, which can be computed from K_Ic by the methods of fracture mechanics. The behavior of these crack propagation parameters is consistent with the previous hypothesis that failure is initiated by loss of adhesion between the matrix and those fibers which lie transverse to the applied load.     

Fracture Toughness of Advanced Structural Ceramics: Applying ASTM C1421

The three methods of determining the quasi‐static Mode I fracture toughness (K_Ic) (surface crack in flexure—SC, single‐edge precracked beam—PB, and chevron‐notched beam—VB) found in ASTM C1421 were applied to a variety of advanced ceramic materials. All three methods produced valid and comparable K_Ic values for the Al₂O₃, SiC, Si₃N₄, and SiAlON ceramics examined. However, not all methods could successfully be applied to B₄C, ZrO₂, and WC ceramics due to a variety of material factors. The coarse‐grained microstructure of one B₄C hindered the ability to observe and measure the precracks generated in the SC and PB methods while the transformation toughening in the ZrO₂ prevented the formation of the SC and PB precracks and thus made it impossible to use either method on this ceramic. The high strength and elastic modulus of the WC made it impossible to achieve stable crack growth using the VB method because the specimen stored a tremendous amount of energy prior to fracture. Even though these methods have passed the rigors of the standardization process there are still some issues to be resolved when the methods are applied to certain classes of ceramics. It is recommended that, when appropriate, at least two of these methods be employed to determine the K_Ic, especially when a new or unfamiliar ceramic is being evaluated.     

Festigkeitsuntersuchungen and rißbehafteten Polyolefinen

The importance of fracture mechanics parameters are discussed in comparison with conventional failure criteria. As an example for conventional failure criteria the yield stress and elongation at fracture of unnotched and notched samples of polyethylene, polypropylene, and polybutene-1 are investigated as a function of strain rate and temperature. As suitable parameter describing the crack resistance of a material the fracture toughness values K_Ic and K_IQ are chosen and studied for polyethylene and polybutene-1 as a function of strain rate.     

Plane stress and plane strain fractures in polypropylene

The concepts of Linear Elastic Fracture Mechanics (LEFM) are applied to polypropylene, a homopolymer and two copolymers, with a view to characterizing their brittle behavior at slow rates (0.5 cm/min) in terms of a fracture toughness, K_Ic. The effect of thickness, notch sharpness, and the mode of loading on K_Ic have been investigated in order to determine the plane strain toughness values, K_cI for the materials. The two types of material are compared in terms of their toughness values over a range of temperatures between +30 and ?160°C. Evidently, the small amounts of ethylene added to the copolymers show plasticizing effects, suppressing the yield stress and the ductile-brittle transition temperature. In addition, the copolymers exhibit a ductile-brittle region between ?100 and ?45°C where notch strengthening is apparent in the tension mode and a slow crack growth region between ?45 and ?30°C where slow growth precedes unstable fracture. The homopolymer, however, shows no clear evidence of such intermediate regions, except for slight amounts of slow growth above 0°C, and becomes ductile around 30°C.     

Fracture toughness characterization of a PC/ABS blend under different strain rates by various J-integral methods

A published, nonconventional J-integral method, based on the hysteresis energy and the ASTM E813 methods, has been employed to test the fracture toughness of a polycarbonate (PC)/acrylonitrile-butadiene-styrene (ABS) blend. The critical J values (J_Ic) at crosshead speeds ranging from 0.5 to 20 mm/min obtained from the hysteresis energy method are ∼10 to 20% higher than those obtained from the E813–81 method and ∼50 to 70% lower than those obtained from the E813–87 method. However, the hysteresis energy method results in comparable J_Ic values with a modified ASTM E813–87 method when the 0.2 mm offset line is replaced with a 0.1 mm offset line. The critical displacements in terms of the onset of crack initiation, determined from the plots of hysteresis energy vs. displacement, hysteresis ratio vs. displacement, and the true crack growth length vs. displacement, are fairly close in value. This indicates the critical crack initiation and the corresponding J_Ic obtained from this hysteresis energy method indeed represent the actual physical event of the onset of crack initiation.     

Acoustic emission behavior of epoxies during tensile loading

The acoustic emission behavior during tensile loading of two common epoxy systems of different ductility was investigated at different loading rates. At low threshold voltage, it was possible to register acoustic emissions before the final failure. Only very few emissions were recorded compared with the amount commonly recorded for metals and composite materials. The acoustic emissions detected were of burst-type, revealing a brittle damage accumulation process. They originated from the initiation and incremental growth of microcracks of stochastic nature. The events occurred before gross yielding and during the final “brittle” failure process. Basically no events were detected between gross yielding and the final failure during which large scale yielding, necking, and stable crack growth took place. The occurrence of events at the different loading rates was strongly influenced by the yielding behavior and fracture toughness, characterized by the yield stress σ_y and the plane-strain fracture toughness K_Ic respectively. K_Ic was inversely dependent on the total number of events up to gross yielding. The event distribution normalized with respect to the conditions at gross yielding was hardly affected by the loading rate.     

Fracture toughness testing of biomedical ceramic-based materials using beams,plates and discs

The testing of fracture toughness becomes problematic when only limited amount of material is available that hinders the production of typical beam specimens to be tested in bending. Here we explore fracture toughness testing methodologies that allow for small discs and plates having surface cracks to be tested in biaxial flexure using the Ball-on-3-balls (B3B) set-up, or sawed notches as in the Compact Tension geometry. The B3B-K_Ic test has shown to be versatile and account for a very small overestimation of the K_Ic-value in the order of 0.8–1.25% due to in-plane crack mispositioning, and a maximum of 4% if a worst-case scenario of additional out-of-plane mispositioning is assumed. The geometrical factor in the standard SCF method, derived by Newman and Raju, resulted in an overestimation of ～8% of the K_Ic-value compared to the new calculation by Strobl et al. for materials with Poisson’s ratio <0.3.     

Plane-strain fracture toughness of epoxies at different loading rates

The plane-strain fracture toughness of two common epoxy systems of different ductility were determined at different loading rates, according to ASTM E 399 for metallic materials. The ASTM standard was applicable, but underestimated slightly the specimen thickness required for K_Ic. K_Ic decreased with an increasing loading rate and with an increasing yield stress. The fracture surfaces were all very smooth as long as plane-strain conditions prevailed.     

The fracture toughness of natural fibre- and glass fibre-reinforced SMC

The fracture toughness properties, in terms of stress intensity factor K_Ic and strain energy release rate G_Ic, of hemp fibre mat-reinforced sheet moulding compound (H-SMC) are measured using the compact tension (CT) method and compared with those of glass fibre-reinforced SMC (G-SMC). Three material parameters were considered for composite optimisation: fibre volume fraction, CaCO₃ filler content and hemp fibre surface treatments using either alkaline, silane or a combination of these two treatments. The highest fracture toughness for H-SMC composites was obtained at a fibre loading of around 30?vol.-%, while it was also shown that the fracture toughness properties of H-SMC are sensitive to mineral filler content. Surface treatment of the hemp fibres using a combined alkaline-silane treatment resulted in a significant improvement in fracture toughness of H-SMC composites. Optimised H-SMC composites exhibited fracture toughness properties similar to those of G-SMC at fibre contents of 20?vol.-%, with K_Ic values of around 6?MPa.m^?1/2.     

Fracture properties of a rigid polyurethane foam over a range of densities

Single edge notch fracture tests have been carried out on rigid polyurethane foam in the density range 32 to 360 kg/m³. Fracture properties were characterized in terms of the fracture toughness parameter (K_Ic), the critical strain energy release rate (G_Ic) and crack opening displacement (c.o.d.). The values of crack opening displacement lead to a proposed mechanism of crack propagation in foams of density greater than about 140 kg/m³.     

Comparison of fracture resistance as measured by the indentation fracture method and fracture toughness determined by the single-edge-precracked beam technique using silicon nitrides with different microstructures

Because of the industrial need for an assessment of fracture resistance, K_R from small ceramic parts, K_R of Si₃N₄ ceramics has been measured by the indentation fracture (IF) method using representative formulae to evaluate the compatibility with the fracture toughness, K_Ic determined from the single-edge-precracked beam (SEPB) technique. K_R of the fine Si₃N₄ showed little dependence on the crack length, whereas the samples with coarse microstructures exhibited a rising R-curve behavior. The IF equation which gave the nearest value to K_Ic from SEPB was different depending on the microstructures. The assessment of fracture resistance with Miyoshi's equation was considered to be preferable for the flat R-curve behavior. By contrast, in the case of the rising R-curve behavior, it was revealed that the relationship between the IF and SEPB values was difficult to explain unless the effective crack extension against K_Ic for SEPB was clarified.     

On the mode I delamination test and the importance of laminate lay-ups

The aim of this work has been the study of mode I delamination of multiply double cantilever beam specimens of glass fiber/epoxy. The results show an important influence of laminate lay-ups on delamination resistance. The value of G_Ic at the initiation of delamination varies with laminate curvature coupling K_y/K_x and K_xy/K_x. An empirical model describing this variation has been proposed. In addition, it is seen that the values of G_Ic at the initiation of delamination and at stable crack growth will be very different. The delamination resistance can be characterized by two constants: G_Ic corresponds to the initiation of delamination, and G^S_Ip corresponds to the plateau of stable crack propagation. The correlation between experimental measurement and analysis of compliance and energy release rate results reveals significant three-dimensional effects.     

Double cantilever beam fracture toughness measurement method for glass

A simple method of measuring Mode I fracture toughness, K_IC, of glass using the double cantilever beam (DCB) geometry is presented. An inert atmosphere is created at the crack tip to prevent subcritical crack growth and enable “pinning” the crack while the specimen is loaded to failure. This was achieved experimentally using liquid toluene or a glovebox with dry argon. K_IC values measured by this method showed good agreement with published literature values for selected glasses. Applicability of the analytical stress intensity factor solution based on crack length, crack front curvature, and the height of the crack guiding groove are confirmed through experimental data and finite element analysis. The experimentally observed crack front curvature, which leads near the edges for small groove heights and leads in the center for larger groove heights, is predicted from the geometry of the DCB specimen for a linear elastic solid through finite element modeling.     

Relationship between fracture toughness determined by surface crack in flexure and fracture resistance measured by indentation fracture for silicon nitride ceramics with various microstructures

The reliability of the Vickers indentation fracture (IF) method for various types of silicon nitride (Si₃N₄) ceramics was assessed by comparing the fracture resistance, K_R obtained from the IF test with the fracture toughness, K_Ic from the surface crack in flexure (SCF) technique in the same crack depth region. The K_R of a fine-grained and equiaxed Si₃N₄ matched with the K_Ic from the SCF test when Miyoshi's equation was used, while the K_Ic of a bearing-grade Si₃N₄ was found to lie between K_R values calculated with Niihara's equation (higher side) and Miyoshi's equations (lower side). In the case of coarse Si₃N₄ with elongated grains, the K_R determined using Niihara's equation gave the best fit with K_Ic. The inconsistent outcomes were explained by the probable mechanisms, indicating that the K_R from the IF test cannot be correlated directly with the K_Ic unless the effective crack length for the IF test was clarified.     

Elasticity,hardness, and fracture toughness of sodium aluminoborosilicate glasses

Due to an increasing demand for oxide glasses with a better mechanical performance, there is a need to improve our understanding of the composition-structure-mechanical property relations in these brittle materials. At present, some properties such as Young's modulus can to a large extent be predicted based on the chemical composition, while others—in particular fracture-related properties—are typically optimized based on a trial-and-error approach. In this work, we study the mechanical properties of a series of 20 glasses in the quartenary Na₂O–Al₂O₃–B₂O₃–SiO₂ system with fixed soda content, thus accessing different structural domains. Ultrasonic echography is used to determine the elastic moduli and Poisson's ratio, while Vickers indentation is used to determine hardness. Furthermore, the single-edge precracked beam method is used to estimate the fracture toughness (K_Ic) for some compositions of interest. The compositional evolutions of Vickers hardness and Young's modulus are in good agreement with those predicted from models based on bond constraint density and strength. Although there is a larger deviation, the overall compositional trend in K_Ic can also be predicted by a model based on the strength of the bonds assumed to be involved in the fracture process.