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Surface flaws in structural materials are most likely to be generated during service time. One of the most general shapes of surface flaws is the semi-elliptical surface crack. Frequently, the slow crack growth (SCG) of a crack has been fitted based on the conventional Paris–Erdogan relationship. However, in the case of engineering plastics, which generally reveal a severe unrecoverable damage zone at the crack tip, the conventional Paris–Erdogan relationship is not appropriate to describe the SCG of a crack. Especially, SCG kinetics of some engineering polymers such as high-density polyethylene (HDPE) affect the SCG characteristics, i.e. non-conventional discontinuous SCG behavior, which cannot be simulated by conventional Paris–Erdogan relationship. It is known that the crack layer (CL) theory, which deals with driving forces of crack and process zone (PZ) together, can be a good mathematical model to simulate such SCG behavior. In this study, the discontinuous SCG of a semi-elliptical surface flaw in HDPE plate under cyclic tensile stress was simulated using the CL theory. Although the CL theory has the advantage of simulating the discontinuous SCG of HDPE accurately, until now the applications have been concentrated on one-dimensional slow crack growth. In this paper, the CL model for two-dimensional surface crack growth for axial and bending loading conditions was developed for the first time. The proposed model is validated with actual test results, and the role of some key CL parameters on discontinuous SCG behavior of a semi-elliptical surface flaw is investigated by intensive parametric studies.

The crack layer (CL) model can be used to theoretically simulate unique discontinuous slow crack growth (SCG) and the consequent lifetime of pipe-grade high-density polyethylene (HDPE). However, its application has been limited to several specimen configurations and 1-dimensional (1D) crack growth in pipes. In this study, a 2-dimensional (2D) CL growth model was formulated for a semi-elliptical surface crack in an HDPE pipe, for the first time. The 2D semi-elliptical discontinuous SCG kinetics of the inner surface of the pipe were successfully simulated. In addition, the proposed model was applied to a buried HDPE pipe under the complicated loading condition, e.g., internal pressure, ground pressure induced by structures and traffic loads, as well as the point load due to stones contacting the pipe surface. As the point load exerted by such hard objects within the soil medium can reduce the structural integrity of the buried pipes, this effect is a valid consideration. Various levels of these loading conditions were applied for semi-elliptical CL growth simulations, with different stone sizes in contact with the buried pipe. The results indicate that the diameter of the stone influences semi-elliptical crack propagation behavior and significantly reduces failure time even under the same external loading condition. In addition, it was observed that the lifetime reduction rate depends on the ratio of the internal pressure to ground pressure. This study broadens the applicability of the 2D CL model for buried HDPE pipes to more practical situations and quantifies the effect of stone-embedded soils on SCG kinetics and its lifetime.

The major failure aspect of high-density polyethylene pipes under the service condition is the discontinuous slow crack growth (DSCG) from the initial defects inside the pipe wall. In this study, the DSCG kinetics for an internal eccentric crack is theoretically simulated by developing a crack-layer growth model for an eccentric crack. The present model precisely mimics the experimental DSCG kinetics for the eccentric crack, and it also estimates the final failure time accurately. Furthermore, to investigate the reliability of the DSCG-dominated failure concerning the uncertainties related to the initial crack, a stochastic study on the lifetime distribution due to the probabilistic distribution of the initial crack size is performed. Additionally, lifetime distribution fitting using the Birnbaum–Saunders (B-S) distribution function and the maximum likelihood estimation method is conducted for various initial crack locations, sizes, and applied stresses. The B-S function accurately describes the simulated lifetime distribution, and the equations for estimating the scale and shape parameters of the B-S function with regard to the initial crack distributions at various crack locations and remote stress levels are presented.

Conformability is a property of materials that allows them to conform to the contours of a curved or rough surface. The lack of conformability of a thin plastic film lying on a non-flat substrate is commonly manifested in formation of blisters, wrinkles and other forms of delamination. The delamination is driven by elastic energy of thin film associated with the film deformation required by film application. A simple method of observation and quantitative characterization of delamination and its evolution in time is proposed. The time dependency of delamination is driven by an interplay between the stress relaxation within the film and viscous flow of adhesive. Thus, the conformability of multilayer system is controlled by the stiffness and relaxation characteristics of the film as well as the time dependent strength of adhesive. A methodology of testing the conformability and measurements of delamination growth, as well as quantitative modeling of the process are presented.

A review of empirical equations for slow crack growth under fatigue and creep conditions is presented. The crack propagation rate is commonly expressed as a function of stress intensity factor or energy release rate. A concept of crack driving force and crack stability analysis is employed to predict crack behavior under different loading conditions; the concept of crack growth resistance, such as an effective surface energy, is used. It is shown that for a stable crack propagation (the energy release rate is a decreasing function of crack length) crack growth equation results from the crack equilibrium condition, if the crack resistance is assumed to be constant. Experimental studies demonstrate that crack growth resistance is not constant, but changes with crack propagation. Formation of the so-called process zone appears to be responsible for the changes. Process zone (PZ) is a material reaction to stress concentration at crack tip and it is commonly observed under fatigue and creep conditions in most engineering materials. For an unstable crack growth (the energy release rate is an increasing function of crack length) the effect of PZ even more dramatic; for example, in a perfectly homogeneous elastic solid slow crack growth would be impossible without the stabilizing effect of PZ. A system of a crack and PZ is referred to as crack-layer (CL). CL driving forces that are thermodynamic forces associated with crack and PZ growth are introduced. CL growth equations are employed to explain the observed variations of crack growth resistance commonly known as R-curve behavior. The evolution of the process zone in a complex stress field is illustrated by an experiment demonstrating how process zone accelerates and decelerates crack growth. Modeling of the crack–process zone interaction is a challenging problem; recent advances in computational techniques make it solvable. The CL approach is illustrated on an example of engineering thermoplastics. Applications to lifetime prediction of structural components, as well as toughness and durability of materials are discussed.

The crack-layer model provides a framework for modeling fracture growth and lifetime prediction. In the past two decades, it has been applied to model brittle fracture in a number of engineering materials. This paper demonstrates in-detail procedure of implementation of crack-layer framework, on the example of slow crack growth in a commercial high-density polyethylene under creep conditions. First, we compute crack-layer driving forces by finite element method and determine experimentally the basic material parameters entering constitutive equations of the model. Then, we develop a numerical simulator of fracture growth.

Several standard tests have been widely used for evaluating the pipe grade polyethylene with respect to toughness and lifetime. However, some of these tests turn to be not adequate for new generation of high performance pipe grade polyethylene: the testing takes extremely long time, which makes it impractical. Recently, it has been proposed to use the circular notched specimen (CNS) for studying the crack growth resistance of pipe grade polyethylene. In CNS the stress intensity factor (SIF) increases with crack size much faster than in commonly used test specimens like compact tension (CT) specimen for instance. Thus, CNS may be a good candidate for an accelerated testing as long as it allows reproducing the mechanisms of slow crack growth (SCG) in field conditions. The objectives of the present studies are twofold: (1) to compare pipe grade polyethylene materials with respect to fracture resistance using CNS in order to complete the program in a relatively short time; and (2) to evaluate the applicability of CNS for studies of slow crack growth kinetics. Fatigue crack growth resistance of four PE resins is evaluated in this work. The fracture surfaces after CNS failure, are analyzed by means of optical and scanning electron microscopy (OM and SEM) in order to determine the mechanism of SCG. The effect of load level, stress ratio ( R ) and notch depth is also studied using CNS. In addition, some technical issues associated with CNS testing are discussed.

Rocks and other geomaterials are heterogeneous materials, with a well-recognized hierarchy of defects from micro-heterogeneities on the grain level to a large-scale network of cracks and layering structures. Their nature create a challenge for determining macroscopic properties, particularly for properties that are scale dependent, complicating both the property measurement and its appropriate application in modeling. This paper discusses the concept of a “representative volume”, which is commonly used in modeling microheterogeneous but statistically homogeneous material by an effective homogeneous continuum. The foundation of this concept is presented, along with its limitations in dealing with properties like strength and fracture toughness that exhibit a scale effect. This limitation is illustrated with a study of brittle fracture of a concrete where it is considered a model for statistically homogeneous rock. The study includes determining a scaling rule for the scale effect in fracture toughness, and shows that the fracture of brittle materials like rocks and concrete appears in the form of highly tortuous, stochastic paths. This reflects a complex interaction between a crack and pre-existing as well as newly formed micro-defects controlled by chance, and results in a large scatter of all fracture-related parameters. This behavior suggests a synthesis of fracture mechanics with probability and statistics, and so a brief exposition of statistical fracture mechanics (SFM) that addresses the statistical aspects of fracture is also presented. SFM is a formalism that combines fracture mechanics methods with probability theory and serves as the basis for an adequate modeling of brittle fracture.

Many applications of nanocomposites based on polymeric systems have been developed for some time. However, the mechanisms of failure as well as fracture toughness of nanocomposites are yet to be completely understood. In this study, the clustering of nanoparticles, specifically, the effect of the number of clusters and their sizes on the fracture behavior of polypropylene (PP) and thermoplastic olefin (TPO) nano-composites is investigated. The effect of injection-molding flow profiles is also discussed with respect to the filler morphology and its effect on the tensile fracture toughness. Morphological analysis of the nanoparticle distribution is performed through fractographic analysis, and the contribution of nanoparticle clustering to the micromechanisms of fracture is discussed.

The life expectancy of thermoplastics in durable applications varies from about 10 years to 50 and even 100 years in certain cases. It calls for an accelerated testing of material and structures. The challenges of accelerated testing for lifetime are (a) to reproduce the mechanisms of field failures and (b) to develop a reliable procedure for extrapolation of a relatively short test data into long-term service conditions. Acceleration of fracture by high stress level turns to be inadequate, since the fracture mechanisms change with stress level. Acceleration of testing for lifetime by elevated temperature is the most widely used technique at the present. This paradigm, however, faces a problem associated with the changes in the mechanism and kinetics of slow crack growth (SCG). At a certain combination of load and temperature, a transition from a continuous SCG to discontinuous, stepwise crack propagation has been recorded. Optical and scanning electron microscopy observations suggest that the change of SCG mechanisms is closely related to the material ability to form in front of the growing crack a stable process zone that consists of single or multiple crazes and/or shear bands. The crack acceleration in the continuous growth mode is observed to be significantly higher than that in stepwise propagation. Such changes in the mechanism and kinetics of SCG are associated with a transition from a ductile to brittle behavior of microfibers within the process zone. It is referred to as ductile–brittle transition of the second kind (DBT2) based on a resemblance with well-known ductile–brittle transition in dynamic impact resistance. DBT2 is presented in form of SCG mechanisms map in temperature–stress intensity factor coordinates. SCG mechanism map implies certain limitations for extrapolation of conventional temperature accelerated test data to the service conditions of plastic components. An alternative to conventional accelerated testing approach to evaluate lifetime of plastics structures is proposed in this paper. It consists of three steps. The first is a characterization of the defects population that may be responsible for fracture initiation. Formulation of constitutive equations of fracture process based on specially designed tests is the second step. Numerical simulation of fracture process using constitutive equations developed within the second step and evaluation of the lifetime of plastic structure is the third step. A validation testing of the proposed program is required.

Polymeric foams are widely used in various engineering applications. Understanding and quantitative modeling of foam load-displacement behavior is important for design and development of engineering structures with foams. In this paper we analyze three main micro-mechanisms of foam macroscopic deformation and failure using stress-true- strain diagram of loading cycle. Specifically, connection between 1) large reversible deformation and buckling, 2) large elasto-plastic deformation and 3) brittle fracture of individual cell structural elements on one side and macroscopic foam behavior on the other is discussed. Identification of specific micro-mechanism responsible for macroscopic behavior foam is suggested on the basis of detailed analysis of unloading part of stress-true strain diagram, i.e., strain recovery process.

Stress corrosion cracking (SCC) is a brittle fracture of a ductile material under severe environment. Due to the complexity of mechano-chemical degradation during SCC formation, the scientific community is still far from the complete understanding of this phenomenon. Moreover, it is commonly misunderstood that polymeric materials is ‘SCC-free’, but it should be noticed that SCC is universal phenomenon for all engineering materials including polymers. In this paper, the similarity and differences of SCC in different materials, such as carbon steels and engineering polymers, are observed and reported. The SCC modeling in carbon steels and engineering polymers is also compared and discussed.

Stress corrosion cracking (SCC) is commonly observed to form a colony of closely spaced multiple cracks. Four stages of SCC colony evolution are discussed. The first is the colony initiation stage (CIS), which is associated with formation of corrosion pits randomly distributed over a certain domain of the surface exposed to an aggressive environment. Electrochemical processes play a leading role in CIS. The individual crack growth (ICG) driven by a combination of mechanical stresses and electrochemical processes constitutes the second stage. At the end of the second stage, the individual cracks reach certain proximity of one another resulting in much crack interaction. This becomes a transition to the third, strong crack interaction and clusters formation, stage. Cluster growth and individual crack or a cluster instability leading to the ultimate failure constitute the final, fourth stage of the SCC evolution process. In this article, we present observations and a general approach to modeling the first two stages of SCC, i.e., CIS and ICG, that together constitute the major part of the total lifetime of an engineering structure serving under SCC conditions. A computer simulation of individual SC crack growth is developed and compared with a large set of SCC observation data.

Observations and characterization of brittle fracture initiation in a micro-heterogeneous material (sandstone) are conducted using the standard indirect tensile strength test. Acoustic emissions, optical microscopy and scanning electron microscopy (SEM) are employed for monitoring and characterizing the discrete micro-mechanical events preceding macroscopical fracture. The observations suggest that brittle fracture initiation is the end result of a microscopic damage accumulation process. A simple statistical model of micro damage accumulation leading to brittle fracture in a micro-heterogeneous material is also proposed. The model is calibrated by matching the coefficient of variation of measured ultimate stress with that resulting from the proposed model.

In the case of high density polyethylene (HDPE), the fatigue crack propagates in a discontinuous manner, which can be observed by distinct striations. In this article, fatigue crack growth (FCG) experiments were conducted on two grades of HDPE pipe with compact-tension (CT) and cracked round bar (CRB) specimens. The effects of the stress ratio (R-ratio) which is defined as the ratio of minimum stress and maximum stress of fatigue loadings and the frequency on FCG behavior were experimentally studied. Although FCG rates showed a great dependence on the R-ratio in terms of the range of the stress-intensity factor, the effect of the frequency may be considered to be significant in the low crack growth region. In addition, these experimental data were employed for predicting the lifetime on the basis of the crack layer (CL) theory. Only a few steps of FCG are needed to determine all necessary parameters for CL theory, and the FCG behavior can be reconstructed based on a computer program that has been developed for the application of CL theory. The predictions from this program accord with experimental data. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Degradation of polymers is usually manifested in a reduction of molecular weight, increase of crystallinity in semicrystalline polymers, increase of material density, a subtle increase in yield strength, and a dramatic reduction in toughness. Stress corrosion cracking (SCC) results from strongly coupled thermo-mechano-chemical processes, and is sensitive to material composition and morphology. The individual crack propagation stage is critical in determining the lifetime of pipe. Based on author's previous works, crack layer (CL) theory model is adopted in this study to describe the individual stress corrosion (SC) crack propagation kinetics and the time interval from crack initiation to instability and break through. The effect of localized chemical degradation at the crack tip on SC crack growth kinetics is addressed. Typical SC crack growth is presented and discussed as a step-wise manner based on the proposed model. In addition, scanning electron microscopy (SEM) observation and Fourier transform Infrared spectroscopy (FTIR) analysis of failed samples obtained by accelerated SCC tests are applied to validate the proposed model. SEM is useful to identify the change of fracture mechanisms from chemically driven crack to mechanically driven crack by the formation of visible striations. FTIR analysis enables tracking of the accumulation of chemical degradation by detecting the amount of carbonyls on the crack surface. Carbonyl index is defined to compare the amount of chemical degradation quantitatively. The purpose of this paper is to continue to develop the technical theory and understanding behind SCC phenomena to facilitate all polymer pipe industries and in particular the polyethylene pipe industry to design better resins and piping systems.

Subjected to in-service and environmental loads, even relatively new structural components may reveal signs of microscopic deterioration. Very often, this initial damage further progresses into meso- and macroscales leading to development of one or several macrocracks that cause ultimate structural failure. Although the onset of macroscale cracking can be reliably detected by modern NDE methodologies, there is an increasing need for inspection technologies that may allow for assessing structural damage at a wide range of scales, i.e., from micro to macro. This article explores application of the nonlinear acoustic vibro-modulation technique (VMT) to incipient damage detection and monitoring. The nonlinear acoustic detection of the macroscopic damage is illustrated with examples: inspection of the cast aluminum automotive parts and testing of the aging aircraft fuselage. The microscale damage assessment is realized by real-time monitoring of the acoustic nonlinearity in the strain controlled three-point-be...

Stress corrosion cracking (SCC) in engineering thermoplastics is commonly observed in the form of a microcrack colony within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. A probabilistic modeling of SCC initiation is briefly discussed. A deterministic modeling of slow stress corrosion (SC) crack growth process is developed using Crack Layer (CL) theory. Numerical solution of SC crack growth equations is discussed. Comparison of the kinetics of cracks driven by SC and by stress only is presented. Conventional plot of SC crack growth rate vs. the stress intensity factor is constructed and analyzed. An algorithm for conservative estimation of lifetime of engineering thermoplastic subject to a combination of mechanical stresses and chemically aggressive environment is discussed.

For explaining the SCG behavior of polyethylene, the crack layer theory is applied based on the description of two driving forces: crack and PZ. The relations between the speed of SCG, crack length and elapsed time are the most important characteristics of polyethylene resistance to crack propagation, or long-term brittle fracture. The crack layer model of slow crack growth in polyethylene is designed in such a way that it qualitatively reproduces the main features of the process indicated above and makes it possible to quantitatively match any pattern of step-wise crack growth. In this paper, the behavior of SCG of polyethylene is developed for numerical simulation based on the crack layer theory. Some parametric study and applications are addressed based on the developed simulation program.

The process zone (PZ) that surrounds and precedes a crack is a common feature of fracture in engineering polymers. Depending on the material, the specimen geometry, the temperature, and the loading conditions various types of microdefects such as crazes, shearbands, microcracks, micro-voids, etc, constitute the process zone. The microdefects are formed in response to stress concentration, and shield the crack tip from high stress level. There is a complex crack – damage interaction, which is briefly addressed by means of a semi-empirical method. On a continuum mechanics level, the PZ appears as a domain with effective elastic properties different from that of the original material. The crack and PZ evolve as one system with multiple degrees of freedom. It is regarded as a Crack Layer (CL) in contrast with the conventional image of crack as an ideal cut. There are thermodynamic forces responsible for CL growth, which are defined as derivative of Gibbs free energy with respect to the corresponding CL “coordinates”. The thermodynamic forces can be expressed as integrals of the Energy Momentum Tensor of elasticity. Onsager type relations between CL growth rates and corresponding CL forces constitute a system of constitutive equations for CL propagation. Examples of solution of these equations, and comparison with experimental data as well as with conventional models are presented in accompanying paper.

The 4-dim intrinsic (material) Riemannian metric G of the material 4-D space-time continuum P is utilized as the characteristic of the aging processes developing in the material. Manifested through variation of basic material characteristics such as density, moduli of elasticity, yield stress, strength, and toughness., the aging process is modeled as the evolution of the metric G (most importantly of its time component G00) of the material space-time P embedded into 4-D Newtonian space-time with a Euclidean metric. The evolutional equation for the metric G is derived by the classical variational approach. Construction of the Lagrangian for an aging elastic medium and the derivation of a system of coupled elastostatic and aging equations constitute the central part of the work. The external and internal balance laws associated with symmetries of material and physical space-time geometries are briefly reviewed from a new viewpoint.

The fracture initiation in engineering thermoplastics resulting from chemical degradation is usually observed in the form of a microcrack network within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. Degradation of polymers is usually manifested in a reduction of molecular weight, increase of crystallinity in semi crystalline polymers, increase of material density, a subtle increase in yield strength, and a dramatic reduction in toughness. An increase in material density, i.e., shrinkage of the degraded layer is constrained by adjacent unchanged material results in a buildup of tensile stress within the degraded layer and compressive stress in the adjacent unchanged material due to increasing incompatibility between the two. These stresses are an addition to preexisting manufacturing and service stresses. At a certain level of degradation, a combination of toughness reduction and increase of tensile stress result in fracture initiation. A quantitative model of the described above processes is presented in these work. For specificity, the internally pressurized plastic pipes that transport a fluid containing a chemically aggressive (oxidizing) agent is used as the model of fracture initiation. Experimental observations of material density and toughness dependence on degradation reported elsewhere are employed in the model. An equation for determination of a critical level of degradation corresponding to the offset of fracture is constructed. The critical level of degradation for fracture initiation depends on the rates of toughness deterioration and build-up of the degradation related stresses as well as on the manufacturing and service stresses. A method for evaluation of the time interval prior to fracture initiation is also formulated.

The quantitative description of rough surfaces and interfaces has been an important challenge for many years. This paper addresses the potential application of fractal geometry to characterize the fracture surface and to determine whether there is any correlation between fracture properties and the roughness of the fracture surface. Fractured surfaces of three different size wedge-splitting specimens, dimensions varying from ( width × total depth × thickness ) 420×420×50 mm to 1680×1680×200 mm with four different maximum aggregate sizes of 9.5, 19, 38, and 76 mm, were analyzed using a modified slit-island technique. It was found that fractal dimension, i.e., roughness, increases with an increase in both specimen and maximum aggregate size. A clear correlation exists between roughness (fractal dimension) and fracture toughness: the tougher the material, the higher the fractal dimension.

Necking is a significant part of the yielding process in many thermoplastics. It starts as strain localization associated with microshear banding and/or cavitations and appears as a domain of oriented (drawn) material, i.e., a “neck”, separated from the domain of original (isotropic) material by a narrow transition zone, which appears as a distinct boundary of the neck region. On further increase of displacement, the neck propagates through the test specimen under constant draw stress. Strain localization such as crazing and shear bending is associated with necking on micro- and sub-microscales. As a result material toughness, i.e., resistance to cracking, as well as durability, i.e., service lifetime under various service conditions, are related to the material ability to necking and specific characteristics of necking process. Necking is manifested in significant changes in a characteristic length scale, e.g., the distance between equally spaced marks in the reference state may increases by factor of 2 in amorphous polymers and up to a factor of 10 in some semicrystalline thermoplastics. There is also a characteristic relaxation time change during the necking. Thus from continuum mechanics viewpoint, the changes of intrinsic material space-time metric are the most fundamental manifestation of necking. Therefore we model necking phenomena as space-time scales transformation and introduce a four-dimensional (4D) Riemannian metric tensor of a material space-time imbedded into 4D Newtonian (laboratory) space-time with a Euclidean metric. Kinetic equation of necking, i.e., evolution equation for material metric tensor is derived using extremal action principle. An example of traveling wave solution for neck propagation in a tensile bar is presented. Analysis of the solution and comparison with experimental observations are discussed.

Flexible printed circuitry (FPC) is a patterned array of conductors supported by a flexible dielectric film made of high strength polymer material such as polyimide. The flexibility of FPC provides an opportunity for three dimensional packaging, easy interconnections and dynamic applications. The polymeric core layer is the primary load bearing structure when the substrate is not supported by a rigid plate. In its composite structure, the conductive layers are more vulnerable to failure due to their lower flexibility compared to the core layer. Fatigue data on FPCs are not commonly available in published literature. Presented in this paper is the fatigue resistance and reliability assessment of polyimide based FPCs. Fatigue resistance of a specific material system was analyzed as a function of temperature and frequency through experiments that utilized a specially designed experimental setup consisting of sine servo controller, electrodynamic shaker, continuity monitor and temperature chamber. The fatigue characteristics of the selected material system are summarized in the form of S-N diagrams. Significant decrease in fatigue lifetime has been observed due to higher displacements in high cycle fatigue. Observed temperature effect was however counter-intuitive. Failure mechanisms are discussed and complete fracture analysis is presented. In various FPC systems, it has been found that the changes take place in FPC failure mechanisms from well-developed and aligned single cracks through the width at low temperature to an array of multiple cracks with random sizes and locations at high temperature.

In the present work, the distribution of the random toughness characteristics (i.e. critical energy release rate, G1c) has been evaluated on the basis of experimental observations. Fracture test results from three groups of geometrically similar concrete specimens of size (width×total depth×thickness), 420×420×50–1680×1680×200 mm3, made with different maximum aggregate size of 9.5, 19, 38, and 76 mm were analyzed using a recently proposed distribution of extremes. In applications of probability, it is important to use an appropriate distribution type and adequate techniques for estimating the parameters of distribution. In this study, a new type distribution of minima is employed for probability computations. It was noticed that the entropy of distribution increases with the crack length, i.e. the uncertainty of toughness, G1c, value increases with crack length. A non-linear reduction of the maximum allowable splitting force with the defect size, a, was noticed. For large specimens, the maximum allowable splitting load is more sensitive to the required reliability level than that for small specimens. Reliability increases with aggregate size when all other conditions were constant.

This paper is concerned with an accelerated testing and modeling of stress corrosion cracking (SCC) phenomena in pipe grade steels in near neutral pH environment. In modeling of SCC, the authors adopt the crack layer theory that provides formalism to account for contributions to crack growth rate such processes as electro-chemical corrosion, hydrogen embrittlement and mechanical loading. Special attention is paid to the hydrogen diffusion, a precursor to hydrogen embrittlement. The energy-momentum tensor (Eshelby's tensor) is employed to evaluate the thermodynamic forces responsible for SC crack growth. Griffith' crack equilibrium condition is used to derive a quasi-equilibrial SC crack growth equation. A parametric study and comparison with the experimental results of corrosion fatigue tests for various maximal stress, stress ratio and electric potential are performed to examine the validity of the proposed model.

Crack layer model provides a comprehensive foundation for modeling of fracture growth, failure analysis, and lifetime prediction. During the past two decades, it has been widely applied for modeling various aspects of brittle fracture in general. This paper illustrates in details the procedure of implementation by an example of slow crack growth in a commercialized high-density polyethylene undergoing creep conditions. Firstly, we determine experimentally the basic parameters employed in constitutive equations of crack layer model such as draw ratio λ, the specific energy of transformation γtr, and drawing stress σdr, etc.. Secondly, we implement crack layer model numerically in lab-developed “Simulator”. The paper provides a paradigm for implementation of crack layer model in slow crack growth, and a blueprint for potential software development that can be used in ranking and the lifetime assessment of a large set of engineering polymers.

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76 mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125 mm/min (0.005 in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G 1). There is a well pronounced general trend observed: G 1 increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G 1 increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G 1, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.

Toughness evaluation and durability analysis are two of the critical steps to design a toughened HDPE resin for durability in pipe applications. Durability analysis involves defect characterization, crack initiation and propagation mechanism, and long-term performance prediction. The methodology for durability analysis of high-density polyethylene (HDPE) pipe will be discussed in this paper. Various analytical techniques, such as fractography, hot-stage microscopy, energy-dispersive X-ray (EDX), microtransmittance infrared spectroscopy, scanning electron microscopy (SEM), and transmission electron microscopy (TEM), have been used to characterize the defect properties and size distribution. Crack initiation and propagation mechanisms in HDPE have been analyzed by some accelerated tests and compared with that observed in the long-term hydrostatic pressure test. A new procedure for lifetime prediction of HDPE under creep is discussed based on the crack layer theory (Chudnovsky, A., 1984, NASA Contractor Report 174634). [S0094-9930(00)00802-7]

This paper presents a set of constitutive equations to model cold-drawing (necking) in polycarbonates (PC). The model is based on a representation of cold drawing as a double glass transition, i.e., a transition from a glass into a rubbery state, when a certain yield surface in the stress space is reached, and a transition back to the glassy state upon unloading or when a certain molecular orientation (draw ratio) is achieved. The stretching process in the rubbery state is modeled by a hyperelastic extension of the J2-flow theory to the finite strain range. An appropriate yield surface and an associative flow rule (defined via the Kuhn‐Tucker optimality conditions) are presented to simulate this process in polycarbonates. The isochoric constraint during double glass transition is treated via an exact multiplicative decomposition of the deformation gradient into volume preserving and spherical parts. Numerical constitutive integration algorithm is based on an operator splitting technique where constraint/consistency during inelastic deformation is enforced via return mapping algorithm. Numerical results are presented to demonstrate the correspondence with the experimental data. # 1999 Elsevier Science Ltd. All rights reserved.

The objective of this paper is to present a comprehensive review of an approach which stands aside from the mainstream of statistical modeling of fracture. The approach is essentially based on the concept of an ensemble of macroscopically identical fracture specimens and on averaging over it. Equivalently, an ensemble Ω of virtual crack trajectories is associated with a single specimen; the averaging is then expressed in the form of functional integration over Ω. The approach combines the concepts of weakest link theories with fracture mechanics formalism and models crack propagation through a brittle microheterogeneous solid. The statistics of microheterogeneity, e.g. the population of pre-existing defects, is reflected in a random field of specific fracture energy γ and in the statistical features of Ω. The fracture parameters employed in the approach are: parameters of the pointwise distribution of the γ-field; its correlation distance; and the characteristics of roughness of the fracture surfaces, including their fractal dimension. The probability of crack formation between any two points in a two-dimensional solid (referred to as “crack propagator”) is introduced as the main building block of the approach. It is expressed as a functional integral (over the set Ω) of the probability of crack formation along a particular path. The probability distributions of critical loads, critical crack lengths, G 1c , crack arrest locations, etc., are derived in terms of crack propagator. The dependence of the distributions on the statistical characteristics of the material as well as on the roughness of the crack trajectories is analyzed by both analytical and numerical means.

Most of the crack growth equations proposed so far correlate the crack growth rate (da/dN or da/dt) with crack tip parameters such as the stress intensity factor (SIF) or energy release rate (ERR). In our previous works, an experimental setup was designed to examine the applicability and the boundary of the functional relationship between da/dN and the crack tip parameters, particularly, ERR. In the present paper, the variation of the ERR along the experimentally observed curvilinear crack trajectories is obtained by means of the finite element method. The analysis shows that the Paris-Erdogan type of laws are applicable until the crack tip is located outside the strong crack-defect interaction region (SI region). A functional relationship between da/dN and ERR breaks down within this region. This suggests the existence of additional crack tip parameters that are not accounted for within conventional fracture mechanics. An approach to modeling the observed phenomenon is discussed following the concept of the Crack Layer theory.

A new method for predicting the time to brittle failure of polyethylenes is proposed. The method includes modeling slow crack growth in polyethylenes and the experimental determination of material parameters for the model. The model is based on the concept of the crack layer, i.e., a system consisting of the strongly interacting crack and process zone and the kinetic equations which govern the crack layer growth. The process zone in polyethylenes usually appears to be a thin strip of drawn material extending along the crack line. This permits a characterization of the crack layer by two parameters: the crack and process zone lengths. The two-parameter crack layer kinetic model allows description of slow crack growth as the discontinuous (stepwise) process which is commonly observed in the brittle fracture of polyethylenes. The model also predicts a relationship between time to failure and applied stress, identical to that established experimentally. The material parameters of the kinetic model can be determined by experiments on smooth specimens, i.e., are independent of slow crack growth and require relatively short-term observations. Thus, the combination of the material testing and the mathematical modeling of the crack layer evolution is proposed as a method for lifetime prediction in the brittle fracture of polyethylenes. © 1995 John Wiley & Sons, Inc.

The thermomechanical behavior of poly(bisphenol A carbonate) (PC) undergoing cold-drawing (necking) over a large range of temperature and strain rate has been studied. The cold-drawing of PC has been described from a material particle perspective in terms of true stress and strain relationships. The isothermal draw stress is shown to be a material parameter, and the true stress-strain behavior of necked material above the true drawing stress follows conventional treatment by rubber elasticity. Cold-drawing is described as a double glass transition: first, a transition from an isotropic glass to an isotropic rubber at the yield point, then, on unloading after stretching of a rubbery mesophase, a transition from an oriented rubber to an oriented glass.

The Green's function is constructed for the stress intensity factor due to the unit dipole force applied to the crack surface in the presence of a circular inclusion in front of the crack tip. An explicit functional form of the Green's function is proposed in terms of dipole force location, Young's modulus ratio and the inclusion size and position with respect to the crack tip. This is achieved through a combination of the dimensional analysis and parametric studies by means of the finite element method. The purpose of this paper is to provide the basis for further studies of a crack interaction with an array of microdefects and/or inclusions.

The importance of the process zone (also called the damage zone, plastic zone or active zone) has been recognized since the works of Irwin [1], Orowan [2] and the celebrated models of Dugdale [3] and Barenblatt [4]. Recently, a thermodynamic analysis of the crack and process zone growth as an evolution of one system called the Crack Layer has been advanced [5-9]. The Crack Layer analysis is quite tedious, particularly due to the complexity of the crack tip field resulting from the crack-process zone interaction problem [10]. In the present work the effect of the process zone on the fracture path is analyzed experimentally using a new technique based on controlled exposure of a poly(ethylene-co-carbon monoxide), ECO, to ultraviolet radiation, (UV). UV exposure to ECO results in hardening and embrittlement of the sample [11]. A comparison of the findings in this work with previous studies is also presented [ 12].

The fracture toughness of polycarbonate specimens of 3–9 mm thickness obtained from an actual aircraft canopy, were studied under accelerated weathering conditions and different rates of loading. Although no significant effects of thickness and loading rate on the critical stress intensity factors were observed, two different failure modes, brittle fracture and ductile fracture triggered by “pop-in,” were observed. The mode of failure was a random event and the probability of ductile failure associated with pop-in increases with the weathering time. More insight to material characteristics are gained through analysis of the specific fracture energy (SFE). The average values of SFE decrease monotonically with accelerated weathering time. This effect is ascribed to physical aging of the PC in the weatherometer that was corroborated through increases in density. The values of SFE seem to correlate with the probability for ductile fracture. This information can be used to establish conservative critical stress values for design. © 1994 John Wiley & Sons, Inc.

One of the key requirements for developing tough multiphase blend systems, for example, selecting the type of discrete phases (hard or soft) in a polymer matrix, is the ability to predict the fracture path. Most of these selections rely heavily on prior experience or on intuitive rationale. There are few mathematical guidelines for the materials scientists who are designing new multiphase systems. This article is designed mainly to provide such insight through the development of a theoretical model and through experimental observation. A finite element model has been used to predict the crack velocity and the crack path for a crack that approaches and penetrates a hard or a soft inclusion. A novel experimental approach is then utilized to verify these predictions by introducing hard and soft circular domains in poly(ethylene-co-carbon monoxide) specimens by selective photodegradation. © 1993 John Wiley & Sons, Inc.

This paper gives an energy analysis of an elastic solid with a crack which penetrates an elastic inclusion. The purpose of our work is to evaluate the energy release rates (ERR) associated with crack tip extension while the inclusion is stationary, and to evaluate the ERR due to inclusion translation, rotation and expansion with respect to the crack tip. Reduction and increase in the crack ERR caused by an inclusion (shielding and amplification effects of the inclusion) are expressed in terms of the inclusion elastic properties normalized by Young's modulus of the bulk material. The variation in ERR as a crack approaches and passes through a circular inclusion is also examined.

A thermodynamic model for the equilibrial process zone ahead of a crack in polycarbonate is developed from the recently proposed Chudnovsky model and experimental characterization of the process zone. Based on the model, the force for evolution of the process zone is proposed from the consideration of irreversible thermodynamics and chemical reaction theories. The experimental data reported in our previous paper are well described by the equilibrial process zone model and a new kinetic equation. © 1993 John Wiley & Sons, Inc.

The service lifetime for several linear polyethylene copolymers was studied by fatigue-type accelerated tests. The material morphology and crystallization behavior were correlated with the lifetime and the failure modes. The correlation is based on the rate constant of material degradation (RCMD) recently introduced by the authors within a mathematical model for crack layer growth kinetics. RCMD is found to depend on the loading conditions (e.g., creep or fatigue) and on material morphology reflected in crystallization kinetics. The ratio of RCMDs for fatigue and creep is a scaling factor that allows one to correlate fatigue and creep lifetimes. The dependence of the RCMD's ratio on the morphological features associated with the primary and secondary crystallization kinetics is also reported in this paper.