A method to determine fracture toughness using cube-corner indentation

For the cube-corner indenter, an approximate linear relationship between the ratio of hardness (H) to reduced modulus (E-r) and the ratio of unloading work (W-u) to total loading work (W-t) is confirmed by finite-element calculations and by experiments. Based on this relationship a convenient method to determine the fracture toughness (K-IC) of brittle materials, especially for those at small scale, using cube-corner indentations is proposed. Finally, the method is calibrated by indentation experiments on a set of brittle materials. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a gamma-Ni(Al)/alpha-Al2O3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacernent curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45 degrees. The shear calculations are conducted for displacements along < 110 > and < 112 > of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a gamma-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.

First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a gamma-Ni(Al)/alpha-Al2O3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacernent curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45 degrees. The shear calculations are conducted for displacements along < 110 > and < 112 > of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a gamma-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.

The influence of core-shell structured modifiers on the toughness of poly (vinyl chloride)

The core-shell structured grafted copolymer particles of polybutadiene grafted polymethyl methacrylate (PB-g-PMMA, MB) were prepared by emulsion polymerization. The MB particles were used to modify poly (vinyl chloride) (PVC) by melt blending. The mechanical properties of the PVC blends were investigated. The micro-morphology of the PVC blends was observed by scanning electron microscopy (SEM). The results indicated that the samples with the best impact strength could be obtained when the core-shell weight ratio of PB to PMMA is lower than 93:7, the mechanical properties correlated well with SEM morphologies, the addition of modifier with the ratio core to shell of 93:7 could reduce the domain size of the dispersed phase. Furthermore, the compatibility and properties of the blends were greatly enhanced and improved. The modifier particles could be well dispersed in the PVC matrix.

Effects of rubber content and temperature on dynamic fracture toughness of ABS materials

The effects of rubber content and temperature on dynamic fracture toughness of ABS materials have been investigated based on the J-integral and crack opening displacement (COD, delta) concepts by an instrumented Charpy impact test. A multiple specimens R-curve method and stop block technique are used. It is shown that the materials exhibit a different toughness behavior, depending on rubber content and temperature. The resistance against stable crack initiation (J(0.2) or delta(0.2)) increases with increasing rubber content. However, J(0.2) first increased with increasing temperature until reaching the maximum value; after that, it decreases with further increasing the temperature. (C) 2000 John Wiley & Sons, Inc.

TEMPERATURE AND STRAIN-RATE DEPENDENCE OF FRACTURE-TOUGHNESS OF PHENOLPHTHALEIN POLYETHER KETONE

A strong strain-rate and temperature dependence was observed for the fracture toughness of phenolphthalein polyether ketone (PEK-C). Two separate crack-blunting mechanisms have been proposed to account for the fracture-toughness data. The first mechanism involves thermal blunting due to adiabatic heating at the crack tip for the high temperatures studied. In the high-temperature range, thermal blunting increases the fracture toughness corresponding to an effectively higher test temperature. However, in the low-temperature range, the adiabatic temperature rise is insufficient to cause softening and Jic increases with increasing temperature owing to viscoelastic losses associated with the p-relaxation there. The second mechanism involves plastic blunting due to shear yield/flow processes at the crack tip and this takes place at slow strain testing of the single-edge notched bending (SENB) samples. The temperature and strain-rate dependence of the plastic zone size may also be responsible for the temperature and strain-rate dependence of fracture toughness.

FRACTURE-TOUGHNESS OF PHENOLPHTHALEIN POLYETHER KETONE

The static and impact fracture toughness of phenolphthalein polyether ketone (PEK-C) were studied at different temperatures. The static fracture toughness of PEK-C was evaluated via the linear elastic fracture mechanics (LEFM) and the J-integral analysis. Impact fracture toughness was also analyzed using the LEFM approach. Temperature and strain rate effects on the fracture toughness were also studied. The enhancement in static fracture toughness at 70 degrees C was thought to be caused by plastic crack tip blunting. The increase in impact fracture toughness with temperature was attributed two different mechanisms, namely, the relaxation process in a relatively low temperature and thermal blunting of the crack tip at higher temperature. The temperature-dependent fracture toughness data obtained in static tests could be horizontally shifted to match roughly the data for impact tests, indicating the existence of a time-temperature equivalence relationship. (C) 1995 John Wiley & Sons, Inc.

MECHANICAL-PROPERTIES OF PHENOLPHTHALEIN POLYETHER KETONE - YIELD STRESS, YOUNGS MODULUS, AND FRACTURE-TOUGHNESS

A series of tensile and three-point bending studies was conducted at various temperatures and loading rates using phenolphthalein polyether ketone (PEK-C). Yield stress, Young's modulus, fracture toughness, and crack opening displacement data were obtained for various conditions. In general, both yield stress and Young's modulus increase with decreasing temperature. However, the relationships between fracture toughness, loading rate, and temperature are very complex. This behavior is due to the simultaneous intersection of viscoelasticity and localized plastic deformation. The increased yield stress is the main factor contributing to the reduction in fracture toughness and crack opening displacement. The relationship between fracture toughness and yield stress are discussed. (C) 1995 John Wiley and Sons, Inc.

TEMPERATURE EFFECT ON IMPACT FRACTURE-TOUGHNESS AND FRACTURE MECHANISM OF PHENOLPHTHALEIN POLY(ETHER KETONE)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K-c and critical strain energy release rate G(c). Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.

COMPARISON OF THE CRACK-GROWTH METHOD AND THE CRACK STRESS WHITENING ZONE METHOD FOR THE FRACTURE-TOUGHNESS DETERMINATION OF PHENOLPHTHALEIN POLY(ETHER KETONE)

Fracture toughness values of phenolphthalein poly(ether ketone) (PEK-C) at 190 degrees C were determined by two different methods, i. e. the conventional crack growth method and the crack stress whitening zone method, which show consistent results. This indicates that the crack stress whitening zone method can be used to determine the crack initiation of some polymers for which the blunting line concept is unsuitable.

FRACTURE-TOUGHNESS AND MORPHOLOGY OF PHENOLPHTHALEIN POLY(ETHER SULFONE) THERMOTROPIC LIQUID-CRYSTALLINE POLYMER BLENDS

Blends of a new phenolphthalein poly (ether sulfone) (PES-C) and a thermotropic liquid crystalline polymer (LCP) were prepared by melt-blending in a twin-screw extruder. Rheological properties, fracture toughness, K(IC), and morphology of the blends were

ON THE ANALYSIS OF THE END-NOTCHED FLEXURE SPECIMEN FOR MEASURING MODE-II FRACTURE-TOUGHNESS OF COMPOSITE-MATERIALS

This paper deals with the correction of mode II strain energy release rate, G(II), of composite laminates measured with the end-notched flexure (ENF) specimen. A derivation is given of the expressions for compliance and strain energy release rate, in whic

DETERMINATION OF INITIATION VALUE OF MODE-I INTERLAMINAR FRACTURE-TOUGHNESS OF UNIDIRECTIONAL POLYMER COMPOSITES

The use of interlaminar fracture tests to measure the delamination resistance of unidirectional composite laminates is now widespread. However, because of the frequent occurrence of fiber bridging and multiple cracking during the tests, it leads to artificially high values of delamination resistance, which will not represent the behavior of the laminates. Initiation fracture from the crack starter, on the other hand, does not involve bridging, and should be more representative of the delamination resistance of the composite laminates. Since there is some uncertainty involved in determining the initiation value of delamination resistance in mode I tests in the literature, a power law of the form G(IC) = A.DELTA alpha(b) (where G(IC) is mode I interlaminar fracture toughness and DELTA alpha is delamination growth) is presented in this paper to determine initiation value of mode I interlaminar fracture toughness. It is found that initiation values of the mode I interlaminar fracture toughness, G(IC)(ini), can be defined as the G(IC) value at which 1 mm of delamination from the crack starter has occurred. Examples of initiation values determined by this method are given for both carbon fiber reinforced thermoplastic and thermosetting polymers.

The use of acoustic emission monitoring to rank paper materials with respect to their fracture toughness

In this study, a simplified Acoustic Emission (AE) equipment, in essence an AE signal conditioner and a USB (Universal Serial Bus) data acquisition system, is used to study what happens in paper structures during mechanical loading. By the use of such equipment, some parameters that can be extracted are e.g. the stress and strain at onset of AE, the stress and strain at the onset of rapid AE defined as some numerical factor (larger then one) times the initial emission rate, the emission rate at the first stage of loading and the stress and strain at final failure i.e. when the specimen loses its load carrying ability.In this study however, the interest is focused on one particular parameter i.e. the elastic strain energy density W c at onset of AE. This is a parameter with a clear physical meaning and in this study, the correlation between this parameter and a fracture toughness measure, is investigated.The conclusion is that when nine different paper materials (with a large span regarding properties) are considered, there is a correlation (however not linear) between these two parameters.