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.     

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.     

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.     

Slow Crack Growth in Cement Paste

The dependence of crack velocity on stress intensity was measured in hardened cement paste. Fracture toughness, modulus of rupture, and dynamic elastic modulus were also measured to permit calculation of the time-to-failure (life expectancy) of stressed cement paste. The double torsion method was used for slow crack growth studies and fracture toughness measurements. Fracture toughness was also measured by a notched-beam method; the agreement between the two methods was excellent. The crack-velocity-stress-intensity curve for cement paste resembles that of glass in water. The slope of the log V -log K _I curve is ∼35.     

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.     

The effect of amine/epoxy ratio on the fracture toughness of tetrafunctional epoxy resin

Summary. The effect of amine/epoxy ratio on the fracture toughness (K_Ic) of tetrafunctional epoxy resin was investigated. K_Ic value was measured by single-edge notch-bend test. The K_Ic value of the tetrafunctional epoxy resin increased with increasing the amount of amine curing agent. This result was explained with the structural viewpoint of the epoxy network. The network structure of the tetrafunctional epoxy was analyzed with dynamic thermomechanical measurement and in-situ near IR technique. Received: 19 June 1997/Accepted: 17 Juli 1997     

Fracture energy and strength of polymer impregnated cement

The fracture energy, or effective surface energy of hardened cement paste and polymer-impregnated hardened cement paste, was measured by an analytical method. The fracture energy of polymer impregnated hardened cement paste is considerably higher than the unimpregnated past (7.5 × 10⁴ to 0.91 × 10⁴ ergs/cm²). The increase appears to be entirely due to the polymer contribution. The results predict a factor of 5 improvement in the fracture strength of hardened cement paste upon polymer impregnation.     

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.     

Simulation of crack propagation in fiber-reinforced concrete by fracture mechanics

Mode I crack propagation in fiber-reinforced concrete (FRC) is simulated by a fracture mechanics approach. A superposition method is applied to calculate the crack tip stress intensity factor. The model relies on the fracture toughness of hardened cement paste (K_IC) and the crack bridging law, so-called stress-crack width (σ-δ) relationship of the material, as the fundamental material parameters for model input. As two examples, experimental data from steel FRC beams under three-point bending load are analyzed with the present fracture mechanics model. A good agreement has been found between model predictions and experimental results in terms of flexural stress-crack mouth opening displacement (CMOD) diagrams. These analyses and comparisons confirm that the structural performance of concrete and FRC elements, such as beams in bending, can be predicted by the simple fracture mechanics model as long as the related material properties, K_IC and (σ-δ) relationship, are known.     

A model law for the notch sensitivity of brittle materials

In this paper a model law for the notch sensitivity of brittle materials, for instance hardened cement paste, mortar or concrete is presented. This model law shows that notch sensitivity is a necessary however not a sufficient condition for the applicability of linear elastic fracture mechanics. The model law indicates that notch sensitivity of a brittle material decreases with increasing fracture toughness, decreasing tensile strength and decreasing specimen size. The model law explains the increase of the net failure stress of notched specimens with increasing notch depth after passing through a minimum. Such behavior frequently has been observed in experiments on hardened cement paste, mortar and concrete specimens. Results of flexure tests on notched and unnotched hardened cement paste specimens and concretes of various sizes are in accord with the model law.     

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.     

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 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.     

A new method for the preparation of ultra-sharp V-notches to measure fracture toughness in ceramics

The preparation of an ultra-sharp V-notch on structural ceramics is a prerequisite for reliable fracture toughness assessment. Femtosecond lasers are used to cut ultra-sharp V-notch on the Si₃N₄ and Al₂O₃ ceramics for fracture toughness testing by single-edge V-notched beam method. The radius of the V-notch tip is smaller than 0.5 μm. The K_Ic of Si₃N₄ and Al₂O₃ ceramics determined by this method is much close to the actual fracture toughness. This method exhibits obvious advantage in good reproducibility, high accuracy and precision for reliable fracture toughness testing of structural ceramics.     

The fracture toughness of inorganic glasses

Measuring the fracture toughness (K_Ic) of glasses still remains a difficult task, raising experimental and theoretical problems as well. The available methods to estimate K_Ic are reviewed, with emphasis on their respective advantages and drawbacks. In view of our current understanding, this analysis gives precedence to the SEPB method. The ultimate glass strength, the critical flaw size, and the indentation load for the onset of crack initiation are discussed, in the light of the fundamentals of fracture mechanics and classical background regarding the mechanics of brittle materials. Analytical expressions were further proposed to predict the fracture energy and fracture toughness of glasses from different chemical systems from their nominal compositions. The theoretical values were compared with the experimental ones, as obtained by self‐consistent methods when available. The agreement observed in most cases suggests that measured K_Ic values correspond to the crack propagation regime (as opposed to the crack initiation threshold), and supports previous investigations in glasses and ceramics, which showed that a crack tip is nearly atomically sharp in these materials (but for metallic glasses). Some ideas to design tougher glasses are finally presented.     

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.     

The fracture toughness and stress corrosion cracking characteristics of an anhydride-hardened epoxy adhesive

The toughness and stress corrosion cracking characteristics of an epoxy resin (DER 332) hardened with hexahydrophthalic anhydride (HHPA) were investigated. The epoxy was studied in both the bulk and bond form, and its properties were compared with an amine-hardened (tetraethylene pentamine, TEPA) system. The toughness, ??_Ic, of the anhydride system varied less as a function of ratio of hardener-to-resin content and postcure temperature than it did in the TEPA-hardened system. Like the latter, however, its toughness in the bulk and bond forms could not be correlated, but ??_Ic of the joints was dependent on tensile modulus and/or yield strength of the bulk epoxy. Both systems were also toughened in the vicinity of the crack tip by water for short-time loading, but their long-time load carrying capability was reduced by a water environment. The anhydride hardened system was more sensitive to strength loss in water than the amine system. The fracture morphology for the two systems was the same, i.e., fast cracking occurred cohesively near the center of the bond, and slow cracking occurred at the interface.     

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.     

Experimental chemo-mechanics of early-age fracture properties of cement paste

The risk of early-age fracture of cementitious materials in ever more challenging environments provides a unique opportunity to employ an experimental chemo-mechanical platform to develop functional relations between hydration degree, fracture and strength properties, assessed by isothermal calorimetry, micro-scratching, splitting and microindentation on white cement paste at various curing ages from 7 h to 28 days. We show that the modulus, tensile strength, fracture toughness and energy all evolve with a natural logarithmic dependence on the hydration degree. These trends are linked to the densification of the material during the hydration process, explained by compaction mechanics and free volume theory. We show that while the fracture process zone size is essentially constant during the hydration process, the ductility of the material, quantified by M/H, decreases, and is consistent with the evolution of K_c/H. Both quantities provide a convenient way to experimentally assess the fracture sensitivity of early-age cement-based materials.     

Effect of boiling water aging on strength and fracture properties of chopped strand mat–polyester laminates

Four types of unsaturated polyesters and chopped strand mat laminates prepared from these resins were examined for their durability after immersion in boiling water. The boiling water aging of fiber-reinforced plastics (FRP) by use of a pressure cooker was found to be 3–4 times faster than boiling water immersion at atmospheric pressure. The weight gain of neat resins increased, and their tensile strength decreased with an increase in immersion time. No variation in the plane strain fracture toughness, K_Ic of the neat resins was observed after boiling water immersion. The elastic–plastic fracture toughness J_Ic of the immersed FRP was measured by a partial unloading procedure. Although J_Ic showed considerable scatter, on the whole, J_Ic of FRP was found to be independent of the four types of matrix resins and also was not effected by immersion in boiling water at 116°C for 24 h.