Deformation and fracture behaviour of a rubber-toughened epoxy: 2. Failure criteria

In part 1 the microstructure and fracture characteristics of a rubber-modified epoxy, and for comparison that of the unmodified epoxy, were examined in detail. Based on this analysis a qualitative mechanism involving cavitation, shear yielding and plastic flow was proposed. As an extension of this work, the present paper considers the yield behaviour of the epoxy material and uses the data determined, together with the previously reported fracture results, to calculate values of the crack opening displacement. The rate/temperature dependence of the crack opening displacement and the correlations established between stress intensity factor, K_Ic, yield stress and type of crack growth suggest that the extent of crack tip blunting largely governs the relative toughness of the epoxy materials and induces transitions in the types of crack growth observed. A quantitative expression is then presented which successfully describes the fracture toughness values over a wide range of temperatures and rates. The two parameters in this expression are shown to be material constants and therefore provide a unique failure criterion. They can be viewed simply as curve-fitting parameters but they may also have some significance in terms of a critical stress that must act over a critical distance ahead of the crack tip to produce crack growth.     

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.     

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.     

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.     

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     

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.     

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.     

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.     

Improving the fracture toughness and the cyclic-fatigue resistance of epoxy-polymer blends

Relatively tough epoxy-blend polymers are now commercially available for use as adhesives and as the matrices for fibre composites. Nevertheless, another failure property which may be of equal, or even of greater, importance in some applications is the resistance of the epoxy polymer to cyclic-fatigue loading. However, the cyclic-fatigue behaviour of epoxy polymers has not been studied in great detail, especially for epoxy polymers where the material has been modified by forming a polymer blend in order to increase its toughness under quasi-static test rates or impact test rates. Therefore, a major aim of the present work has been to undertake a novel investigation of a range of rubber and thermoplastic materials to modify an epoxy polymer to study whether both a relatively high toughness and a significantly improved cyclic-fatigue behaviour can be simultaneously achieved in a given formulation. The unmodified epoxy-polymer possessed a value of the fracture energy, G_Ic, of 495 J/m² and a value for the threshold value of the maximum strain-energy release rate in a fatigue cycle, G_th, (below which no significant crack growth occurs) of 155 J/m². Several epoxy-polymer blends have been identified which do show major increases in these values and probably the best combination of such properties were for the epoxy-polymers modified with a poly(polypropylene-glycol)-based polyurethane (PU) modifier: either when used by itself or as a ‘hybrid’ polymer-blend in combination with core–shell rubber (CSii) particles, based upon a styrene-butadiene rubber core. For these PU-based epoxy polymers the values of G_Ic and G_th were found to increase to values of about 2475 J/m² and 445 J/m², respectively. The mechanisms of toughening that were induced by the addition of the polymer-blend modifier revealed that the presence of a multiphase in the epoxy-blend polymer was a critical requirement in achieving relatively high values of G_Ic and G_th. This was due to the second-phase particles initiating plastic deformation of the epoxy-matrix phase, which was the major source of energy dissipation and toughening. In turn, the extent of energy dissipated by the plastic deformation of the epoxy-matrix phase is clearly greatly influenced by the degree of ductility exhibited by this phase of the epoxy-blend polymer. Thus, another important feature of the degree of toughening observed is the effect that the modifier has upon the yield stress and plastic failure strain of the epoxy-matrix phase.     

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.     

The Use of Time-Temperature Superpositioning in Studying the Fracture Properties of Rubber-Toughened Epoxy Polymers

The fracture energies, G_Ic, of an unmodified and a rubber-modified have been ascertained as a function of test temperature and rate. A time-temperature superpositioning technique has been adopted in order to produce a master curve of the fracture energy, G_Ic versus the reduced rate of test, t_f/a_T where t_f is the time-to-failure and a_T is the time-temperature shift factor. The value of shift factor, a_T, as a function of test temperature has been determined from time-temperature shifting the yield stress and the modulus data for the materials. The master curve of G_Ic versus has been t_f/a_T and the values of the constants employed in the model have been deduced The value of the constants so determined are discussed with respect to the microstructures of the epoxy polymers.     

Kinetics of crack tip craze zone before and during fracture

Irreversible deformations form the main energy consumption routes for absorbing supplied energy and thus determine the resistance of materials to fracture. In many polymeric materials under mode-I loading conditions three regions of irreversible deformation behavior can be distinguished as a function of the stress intensity factor K_I or strain energy release rate G_I, respectively:

• no crack growth for K_i < K_Io
• slow crack growth for K_Io < K_I < K_Ic
• rapid crack propagation for K_I < K_Ic

In the three regions the amount and geometrical extent of irreversible deformations may be different and the influence of time, crack speed, and temperature may generate different results. In this paper the influences of time and crack speed on the kinetics of the craze zone at the crack tip will be considered in some detail, with respect to results mainly obtained for poly(methyl methacrylate), PMMA, of high molecular weight under quasi-static loading conditions.     

Rubber-Modified epoxies. IV. Influence of morphology on mechanical properties

The mechanical properties of a system consisting of a bisphenol A diglycidylether (DGEBA) expoxy, cured with a cycloaliphatic diamine (4,4′-diamino-3,3 dimethyldicyclohexyl-methane, 3DCM), in the presence of an epoxy-terminated butadiene-acrylonitrile random copolymer (ETBN), was studied as a function of the cure schedule and the initial rubber concentration. Fracture toughness (K_Ic) and fracture energy (G_Ic) were increased, while Young's modulus and yield strength decreased slightly with increasing volume fraction of the dispersed phase. We show that there is no significant influence of the precure schedule and of the various observed particle diameters on the mechanical properties for a constant rubber volume fraction. In our case, the main deformation process in the rubber-modified epoxy networks is shear yielding while cavitation is negligible.     

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 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.     

Toughness of syndiotactic polystyrene/epoxy polymer blends: microstructure and toughening mechanisms

Thermoplastic/epoxy blends were formed using an amine-cured epoxy polymer and a semi-crystalline thermoplastic: syndiotactic polystyrene (sPS). Complete phase-separation of the initially soluble sPS from the epoxy occurred via ‘reaction-induced phase-separation’ (RIPS) or via ‘crystallisation-induced phase-separation’ (CIPS), depending upon the thermal processing history employed. Dynamic mechanical thermal analysis showed that no sPS was retained dissolved in the epoxy polymer. For RIPS, at concentrations of sPS of up to 8 wt%, the sPS is present solely as spherical particles. However, macro phase-separation, giving a co-continuous microstructure, accompanied by local phase-inversion, dominates the RIPS blends containing more than 8 wt% sPS. In the CIPS blends, the sPS is present as spherulitic particles, and this microstructure does not change over the range of sPS concentrations employed, i.e. from 1 to 12 wt% sPS. The pure epoxy polymer was very brittle with a value of fracture energy, G_Ic, of about 175 J/m². However, the addition of the sPS significantly increases the value of G_Ic, though the toughness of the RIPS and CIPS blends differs markedly. For the RIPS blends, there is a steady increase in the toughness with increasing content of sPS and an apparent maximum value of G_Ic of about 810 J/m² is obtained for 8-10 wt% sPS. On the other hand, the measured toughness of the CIPS blends increases relatively slowly with the concentration of sPS, and a maximum plateau value of only about 350 J/m² was measured in the range of 8-12 wt% sPS. The relationships between the microstructure of the RIPS and CIPS sPS/epoxy blends and the measured fracture energies are discussed. Further, from scanning electron microscopy studies of the fracture surfaces and optical microscopy of the damage zone around the crack tip, the nature of the micromechanisms responsible for the increases in toughness of the blends are identified. For the RIPS blends, (i) debonding of the sPS particles, followed by (ii) plastic void growth of the epoxy matrix are the major toughening micromechanisms. The increase in toughness due to such micromechanisms is successfully predicted theoretically using an analytical model. In the case of the CIPS blends, the increase in the value of G_Ic results from (i) crack deflection and (ii) microcracking and crack bifurcation.     

Toughness measurement on ball specimens. Part II: Experimental procedure and measurement uncertainties

The “Surface Crack in Flexure” method is widely used for fracture toughness (K_Ic) determination of ceramics. In part I of the paper we developed the theoretical fundamentals to apply this procedure to ceramic balls by using the stress application as developed for the so-called “Notched ball test”. The new test (SCF-NB) can be used to test spherical components without the need to cut out special specimens such as bending bars. In this work the practical part is presented including suggestions for crack introduction and specimen preparation and possible measurement errors are discussed. It is concluded that a measurement error less than ±5% is possible.Experiments on balls and bars made from the same silicon nitride ceramic indicate that SCF-NB delivers the same K_Ic-values as standardised measurements on bars. Additionally, K_Ic-values obtained for silicon carbide, alumina and zirconia ceramics are presented. They coincide with K_Ic-data from the literature.     

Oxidation effects on toughness and slow crack growth in polycrystalline graphites

The fracture toughness (K_Ic) and slow crack growth behavior of four fine-grained polycrystalline graphites, oxidized to 5, 10 and 20% weight losses, were measured in air at room temperature. Exponential decreases in the elastic moduli as well as decreases in the fracture surface energy contributed to lowering K_Ic. Oxidation generally shifted the stress intensity-crack velocity (K_I-V_I) diagram to lower stress intensity values, and decreased the slope, or N-value. Scanning electron microscope fractography revealed that a combination of filler particle and binder phase degradation with increasing oxidation was responsible for the decreased toughness and changes in the (K_I-V_I) characteristics. Oxidation conditions were shown to significantly affect the magnitude of decreases in the physical, elastic and mechanical properties of these graphites.     

Crack initiation in PVC for subsequent linear elastic fracture mechanics analysis

Reproducible starter-cracks for subsequent linear elastic fracture mechanics analysis have been grown in PVC by fatigue cycling at 80 Hz. The crack growth rate has been related to the fracture surface markings and to the opening mode stress intensity factor (K_I) of the fatigue cycle. Termination of the fatigue crack growth when crack growth rate is constant ensures a smooth mirror fracture surface and a sharp crack tip.     

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.