The most dangerous flaw orientation in brittle materials and structures

In the present paper a sheet of material is considered. It is loaded by uniaxial tensile stress and contains a random distribution of flaw orientations, with the flaws thought of as flat pre-cracks of comparable length, and with all crack planes being oriented perpendicular to the faces of the sheet. Intuition suggests that the most likely flaw to initiate fracture, which will be termed the “most dangerous defect”, lies orthogonally to the major load axis. The purpose of the present paper is to show that such an assumption is incorrect. Neither the most dangerous defect nor the first increments of crack growth will be oriented perpendicularly to the stress direction (nor will they be co-planar with the orientation of the most critical flaw).     

Distributed damage creates flaw tolerance

A qualitative micromechanical fracture mechanics model is presented that shows how a structure that is sensitive to the presence of a single crack or hole can be rendered flaw tolerant by the presence of an interacting distribution of such flaws. The simple model was inspired by the ductile fracture experienced by the under-designed gusset plates recovered from the I-35W Bridge collapse and by the experimentally measured increase in toughness of concrete damaged by fire.     

On flaw tolerance of nacre: a theoretical study

As a natural composite, nacre has an elegant staggered ‘brick-and-mortar’ microstructure consisting of mineral platelets glued by organic macromolecules, which endows the material with superior mechanical properties to achieve its biological functions. In this paper, a microstructure-based crack-bridging model is employed to investigate how the strength of nacre is affected by pre-existing structural defects. Our analysis demonstrates that owing to its special microstructure and the toughening effect of platelets, nacre has a superior flaw-tolerance feature. The maximal crack size that does not evidently reduce the tensile strength of nacre is up to tens of micrometres, about three orders higher than that of pure aragonite. Through dimensional analysis, a non-dimensional parameter is proposed to quantify the flaw-tolerance ability of nacreous materials in a wide range of structural parameters. This study provides us some inspirations for optimal design of advanced biomimetic composites.     

Correlations between flaw tolerance and reliability in zirconia

Interrelations between flaw tolerance and reliability in Y-TZP, Ce-TZP and Mg-PSZ ceramics are investigated. Indentation-strength tests indicate an enhanced flaw tolerance with increasing R-curve behaviour from tetragonal martensite transformation. The Weibull modulus of unindented specimens increases with the enhanced tolerance. However, even the most tolerant zirconias show persistent scatter in strength, implying that variability in material microstructure may be as important a factor in reliability evaluation in these materials as variability in flaw size.     

The effect of flaw shape on fracture initiation at a blunt flaw

The author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. The approach is based on the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture. An earlier paper has derived a blunt flaw fracture initiation relation which gives the critical elastic flaw-tip peak stress σ_pcr (a “signifier” of a critical condition in the process zone) in terms of the process zone material parameters, subject to the proviso that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius ρ. The relation has been derived using a “two-extremes” procedure, whereby the separate σ_pcr solutions for small and large s/ρ are blended together to give an all-embracing relation that is valid for all s/ρ. A key feature of the relation is that σ_pcr essentially depends on only one geometrical parameter: the flaw root radius ρ. Though the relation has evolved from a consideration of the characteristics of one model, i.e. that of an elliptical flaw in an infinite solid that is subjected to an applied tensile stress, it is anticipated that the relation can be applied equally well for a wide range of geometrical configurations involving different flaw shapes. It is against this background that the present paper demonstrates that the relation also applies to the behaviour of an intrusion type flaw in the surface of a semi-infinite solid subjected to an applied tensile stress.     

Fracture toughness determination of brittle materials using small to extremely small specimens

Diametral compression of a grooved, disc shaped specimen is used to determine fracture toughness. This method's most important features are that extremely small specimens can be used and no knowledge of material properties is needed. It is suitable for many brittle materials, e.g. glass, cemented carbides, ceramics, many geological, mining and building materials, perspex-like plastics, etc.     

Non-symmetric extension of a small flaw into a plane crack at a constant rate under polynomial-form loadings

The superposition-related problems which arise from the non-symmetric extension at a constant rate of a plane crack from a small flaw by the removal of normal and shear tractions along the crack plane is treated. It is assumed that these tractions are, or can be approximated by, polynomials in the spatial and time variables in the crack plane. Because any more general polynomial can be obtained by proper combination, attention is focused on polynomials homogeneous of degree $\text{n ? 0}$ which have n + 1 terms with arbitrary constant coefficients. Expressions for the stresses and displacements are readily obtained as single integrals of analytic functions and observations concerning the dynamic intensity factors at the crack edges are made. Certain previously obtained results follow as special cases of the present work.     

An examination of the role of flaw size and material toughness in the brittle fracture of polyethylene pipes

At low temperatures and hoop stresses, polyethylene pipes fail by the time-dependent propagation of a crack. These brittle, fissure-like failures have been observed to initiate from adventitious flaws, and the concepts and methods of fracture mechanics indicate that flaw size should determine stress rupture lifetime. A number of controlled model experiments have therefore been undertaken to assess the influence of flaw size and material toughness on the stress rupture lifetimes of polyethylene pipes. To two different pipe grade polyethylene resins (one shorter, one longer lifetime resin) flaws of varying sizes have been added. For the shorter lifetime resin small flaws were, in addition, purposely excluded by the use of fine melt filtration techniques. Pipes containing added flaws or pipes where flaws were excluded were then stress rupture tested under those conditions designed to induce brittle failure by slow crack growth. The stress rupture lifetimes of the various pipes are then correlated with flaw size. The results of the tests using the shorter lifetime resin show that flaw size does have a significant influence. It is particularly interesting to note that melt filtration, which removes large inherent flaws, substantially improved the stress rupture lifetime. With respect to material toughness, the longer lifetime pipe grade polyethylene resin showed a healthy tolerance to included flaws. In respect of the stress rupture test preferred resins can therefore be identified in terms of their tolerance to included flaws.     

Sample size dependence of flaw distributions for the prediction of brittle solids strength using additive Weibull bimodal distributions

A method to evaluate the mean strength of brittle solids at short gauge length from experiments performed at higher gauge length is proposed for bimodal fracture behavior. The method based on additive Weibull bimodal distributions takes the evolution of the relative proportion of flaws along the gauge length into account via a gauge length dependent mixing parameter. A linear dependence of this parameter vs. the gauge length is proposed. The approach is assessed using experimental results on carbon and E-glass fibers. The new method provides values for the average tensile strength of the fibers at 100 μm up to 27% higher than those calculated using the classical approach. The underestimation of the classical approach can be attributed to the weight of the severe category of flaws at short length that is considered to be the same as that determined at the experimental gauge length, which can be several orders higher. A simplified approach taking into account solely the more severe category of flaw is shown to be applicable for the prediction of the strength at short gauge length independently of the nature of the fiber.     

The effective tensile failure stress of an uncracked brittle structure: failure at a blunt stress concentration

The paper proceeds from the basis that the dominant source of the geometry dependence of the effective tensile failure stress of an uncracked brittle structure is deterministic and is related to the formation of a damage zone at a free surface. The damage is represented by a cohesive zone, and failure, i.e. the attainment of maximum load, is associated with the attainment of an elastically calculated effective tensile failure stress. With regard to failure arising as a result of the formation of a damage zone at the surface of a blunt stress concentration, the paper predicts the extent to which the effective tensile failure stress increases with increasing severity of the stress concentration, i.e. as the root radius decreases.     

The toughness of a composite containing short brittle fibres

A method is presented whereby various potential contributions to the toughness of a polymer containing short brittle fibres can be quantified. It relies on a model for predicting the cumulative probability distribution of fibre pull-out lengths. The method reveals that toughness increases to a maximum value with increasing fibre length. Good agreement between theory and experiment supports the validity of our approach.