Crack Layer Theory Research Articles

Crack layer modeling of butt-fusion joints induced slow crack growth in high-density polyethylene pipes

The design and reliability of high-density polyethylene (HDPE) pipes can be dictated by the damage tolerance of their butt-fusion joints. A slow crack growth (SCG) model based on the crack layer theory for HDPE pipes internal and external circumferential and butt-fusion joints cracks is developed to investigate the discontinuous SCG behavior and lifetime tf variations. Using the developed model, the discontinuous SCG patterns, jump lengths and lifetime tf can be accurately simulated. In addition, the effects of pipes standard dimension ratio, internal pressure, and temperature on the SCG behavior and tf are investigated. Compared to pipe cracks, it was found that butt-fusion induced SCG can reduce the pipe tf > 60 %. Unlike longitudinal cracks, tf of external circumferential cracks, were found shorter than the internal ones, mandating an earlier evaluation. The new SCG model shows good accuracy with the experimental results. The same substitute geometry approach used can be followed for othercomplex designs, which aids in establishing a fundamental methodology for more realistic lifetime predictions.

Effect of the crack layer theory parameters on the discontinuous slow crack growth of high density polyethylene under fatigue loading

For engineering thermoplastics, particularly high density polyethylene (HDPE), the crack layer (CL) theory is an effective proposition for modeling slow crack growth and predicting their lifetime. Nevertheless, the associated excessive input parameters needed in its implementation sets a difficulty for its use. Therefore, an understanding of the role of each parameter and how they affect the CL growth is needed. The effect of the parameters has been studied in the past, however, under creep conditions only. Their effects under other loading conditions, e.g., fatigue, and geometries, e.g., compact tension (CT) specimen, is still unclear. For instance, increasing the natural drawing ratio λ was found to non-linearly reduce failure time tf, whereas a rise in the drawing stress σdr increased tf which correlates logarithmically with the loading frequency f. Furthermore, tf was found to increase with the transformation energy γtr, specimen thickness B, plane stain elastic modulus E′, drawing stress σdr, characteristic time t∗, and the specific fracture energy γ0. Therefore, outcomes of this work extend the applicability of the CL theory in the design and lifetime prediction of various industrial products within oil and gas, nuclear, automotive, and aerospace.

Stochastic Study on Discontinuous Slow Crack Growth Kinetics from an Arbitrarily Located Defect of Polyethylene Based on the Crack Layer Theory

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.

Modeling and application of discontinuous slow crack growth behaviors of high-density polyethylene pipe with various geometries and loading conditions

A slow crack growth model based on the crack layer theory for various geometries of a high-density polyethylene (HDPE) pipe is developed to investigate the discontinuous slow crack growth (SCG) behavior of HDPE pipes. Discontinuous SCG patterns, jump lengths, and periods can be accurately simulated using the proposed model. In addition, effects of soil embedding height, internal pressure, and ground pressure on the discontinuous SCG behavior and consequent lifetime are investigated. It is confirmed that the additional ground pressure increased the discontinuous SCG rates of the buried HDPE pipes, thereby reducing the final lifetime considerably.

Stochastic study on effects of material and physical parameters on slow crack growth behaviors of HDPE using the crack layer theory

High-density polyethylene exhibits discontinuous slow crack growth (SCG) mode in fatigue and creep conditions. To simulate the unique SCG mode, the crack layer (CL) theory can be adopted as an alternative method. However, the stochastic approach is also required for reliability-related problems. In this study, the current deterministic CL model was modified to describe the stochastic discontinuous SCG. First, the influence of the normally distributed nine input parameters in CL simulation on discontinuous SCG kinetics and the resulting lifetime distributions were thoroughly investigated. Second, important CL parameters that affect discontinuous SCG kinetics and the final lifetimes were identified. Then, the 2- and 3-parameter Weibull function and the Birnbaum–Saunders (B–S) function were compared to determine the function that correctly fits the lifetime distribution from discontinuous SCG. Finally, appropriate equations of the scale and shape parameters of the B–S function were developed with regard to the identified parameters.

Discontinuous slow crack growth modeling of semi-elliptical surface crack in high density polyethylene using crack layer theory

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.

Specific crack enthalpy as material characterization parameter

Abstract In this study, the specific crack enthalpy (damage), considered a material characterization parameter according to crack layer theory, is discussed. The crack region and its accompanying damage become a crack layer. Fatigue crack propagation experiments were conducted on HT60 and HT80 steel. The specific enthalpy γ* of fracture due to ductile crack propagation in steel HT60 and HT80 has been calculated. The energy release rate and damage coefficients were determined at different stress ratios varying from R = 0.04 to 0.8. The crack layer translational resistance moment R1 has been determined. Because interpreting the data of crack propagation on two types of steel in the light of this theory reveals reasonable similarity, the need to set up experiments specifying the limitations and applicability of the theory is essential.

Impact of material and physical parameters of the crack layer theory on slow crack growth behavior of high density polyethylene

The crack layer theory, proposed by A. Chudnovsky many years ago, can be a very effective tool to quantitatively model slow crack growth in engineering thermoplastics. However, the large number of input parameters required by this theory has been a technical hurdle for its use in industrial and research applications. Thus, in order to achieve a practical applicability of the crack layer theory, a clear understanding of the effect of each parameter on slow crack growth is quite important. In this study, simulations of slow crack growth in high density polyethylene are performed using the crack layer theory for various key parameters, and the effect of each parameter on crack growth behavior in high density polyethylene is investigated.

Prediction of discontinuous fatigue crack growth in high density polyethylene based on the crack layer theory with variable crack layer parameters

Crack layer (CL) theory has the advantage of capturing the physics of slow crack growth (SCG) and simulating various scenarios of SCG in thermoplastics. However, lack of knowledge regarding the dependency of CL input parameters on loading conditions and time limits the use of CL theory in predicting the lifespan of materials subject to brittle fracture. In this study, CL theory with variable average process zone (PZ) boundary traction (σclose) and characteristic time for PZ degradation (t∗) is applied to fatigue tests with various loading conditions in order to observe discontinuous SCG. Using simulations, experimental results are achieved by changing two CL parameters, thereby establishing these two parameters as the key factors affecting SCG for various types of applied loads. In addition, the specific relationships between these two parameters and fatigue loading conditions are obtained. These obtained relationships may be beneficial for practical use of CL theory to estimate the SCG processes as well as their lifespan under various fatigue conditions.

Modeling of axisymmetric slow crack growth of high-density polyethylene with circular notched bar specimen using crack layer theory

Because of the characteristic of high triaxial stress of a circular notched bar (CNB) specimen under tensile loads, it is a promising candidate for accelerated durability testing of high-density polyethylene (HDPE). To understand the slow crack growth (SCG) behavior of HDPE using a CNB specimen, it is practically important to base the evaluation of the SCG model using a CNB specimen on the concept of fracture mechanics. In this study, the SCG kinetics of HDPE with a CNB specimen is modeled on the basis of the concept of an axisymmetric crack layer (CL) system. CL theory is applied to the modeling of the axisymmetric SCG considering the geometry of the CNB specimen. Green's functions of the stress intensity factor and crack opening displacement of the CNB specimen are calculated in order to simulate the CL kinetics. The obtained Green's functions are also utilized to compute the thermodynamic forces for both the crack growth and the CL growth, and a generalized CL growth algorithm is developed. A parametric study of several key input parameters is conducted for validation of the developed CL model. In addition, actual SCG generated experimentally is simulated using the developed model, and it is found that the actual test results can be successfully simulated using the developed CL model.

The use of crack layer theory to predict the lifetime of the fatigue crack growth of high density polyethylene

AbstractIn 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

Experimental and theoretical investigation of stress corrosion crack (SCC) growth of polyethylene pipes

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.

Development and Application of Slow Crack Propagation of Polyethylene Based on Crack Layer Theory

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.

Stress Corrosion Cracking in Plastic Pipes: Observation and Modeling

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.

Fatigue Fracture Resistance Analysis of Polymer Composites Based on the Energy Expended on Damage Formation

Analysis of the fatigue crack propagation behavior of filled polytetrafluoroethylene (PTFE) composites using the energy expended on damage formation was performed. A 25% chopped glass fiber filled PTFE with a commercial name of Rulon LR and a 25% polymer particle filled PTFE (Rulon J) were chosen as candidate materials for the study. Fatigue crack propagation (FCP) tests were performed using both unnotched and single edge notched (SEN) specimens under tension-tension load control condition. The notched specimens were prepared with the same notch length to sample width ratio (a/w) of 0.09. The applied frequency was 3 Hz. The maximum stress was 6 MPa, and the ratio of minimum stress to maximum stress was kept at 0.10. FCP data such as the crack length and the number of cycles were used to calculate the crack speed. The hysteresis energies for both notched and unnotched specimens during cyclic loading were obtained. The energy release rate was determined as the first derivative of the relationship between the potential energy and the crack length. The potential energy was calculated as the area above the unloading curve from the hysteresis loops at various crack lengths. The cyclic rate of energy dissipation on damage formation was calculated based on the hysteresis energies for both notched and unnotched specimens. It was found that the fatigue kinetics are related to the cyclic rate of energy dissipation into the active zone evolution. The specific energy of damage (γ) a material parameter characteristic of the fatigue fracture resistance was evaluated using the Modified Crack Layer (MCL) theory. It was found that the value of γ for the particle filled PTFE is 3200 kJ/m3, which is about three times higher than that for the fiber filled PTFE (750 kJ/m3). This indicates that the particle filled PTFE has higher fracture resistance than the fiber filled PTFE. The fracture surface of the second region for both materials was examined using scanning electron microscopy (SEM). Interfacial debonding, drawn ligaments and large voids were associated with the fatigue fracture of the fiber filled PTFE. The particle filled PTFE displayed more fibrillation than that of the fiber filled PTFE, which indicates a higher energy consuming process related to the fatigue crack growth in the particle filled PTFE.

Stress Corrosion Crack Growth in Pipe Grade Steels in Near Neutral pH Environment

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.

Fatigue crack growth analysis of a premium rail steel

The fatigue crack growth behavior of a premium rail steel was studied using the Modified Crack Layer (MCL) theory. The rate of energy expended on damage formation and evolution within the active zone was evaluated from the hysteresis energy of unnotched and notched specimens. Due to head hardening of the rail, there is a vertical microstructure gradient inside the rail. In this work, the fatigue test specimens were sliced longitudinally from the head of a new rail near the web which represents the microstructure of the base material. The notch length to sample width ratio (a/w) was 0.1. Fatigue tests were performed on both unnotched and single edge notched (SEN) specimens under tension-tension load control condition at 5 Hz. The maximum fatigue stress was 200 MPa, which is about 40% of the yield strength of the material. The minimum to maximum stress ratio was 0.1. The crack length, number of cycles, and hysteresis loops were recorded during the tests from which the crack speed, the energy release rate, and the hysteresis energy for both notched and unnotched specimens were determined. The rate of energy dissipation on damage formation was evaluated based on the difference between the hysteresis energy for the notched and the unnotched specimens. These data were used in the MCL theory to extract the specific energy of damage, γ′; a material parameter characteristic of the fatigue crack growth resistance of the rail steel. It was found that the value of γ′ is 1300 kJ/m3. Three distinctive stages of crack growth kinetics were observed; crack initiation, stable crack growth and unstable crack growth. Microscopic examination of the active zone revealed damage species in the form of microcracks, inter-granular separation, and plastic deformed material. It is these damages that have led to the crack deceleration in the second stage. The fracture surface was also examined. The initiation region showed drawn-out lamellar pearlite. Ductile tearing and coarse ridges with intensive lamellar formation as well as microcracks were observed in the second region. The formation of these damage species has also contributed to the crack deceleration in the second stage of fatigue crack growth kinetics. The unstable crack growth region displayed cleavage facets initiated from the grain boundaries.

Methodology for Durability Analysis of HDPE Pipe

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]

Fatigue failure analysis of V–4Ti–4Cr alloy

In the present work, the fatigue fracture and failure behavior of a V–4Ti–4Cr has been studied. Static tests were conducted to study the overloading behavior and to select the magnitude of the stress level for the fatigue studies. Fatigue tests were performed using single edge notched (SEN) specimens under tension–tension load control conditions. Fatigue crack propagation (FCP) data such as the crack length, number of cycles, and hysteresis loops were recorded to calculate the crack speed, the energy release rate, and the change in work expended on damage formation and dissipative processes within the material. Parameters characterizing the fatigue fracture resistance of V–4Ti–4Cr alloy, namely the specific energy of damage ( γ ′), and the dissipative coefficient ( β ′), were determined from the fatigue data using the modified crack layer (MCL) theory. Fracture surface examination using scanning electron microscopy (SEM) revealed ductile failure mechanisms under tensile overloading conditions. The fatigue fracture surface of the V–4Ti–4Cr consists of three distinct regions, corresponding to the threshold, stable and unstable crack propagation stages.

Fatigue Crack Growth Analysis of Polymonochlorotrifluoroethylene (CTFE)

Fatigue crack growth behavior of a polymonochlorotrifluoroethylene (CTFE) was investigated. Tension-tension fatigue propagation tests on geometrically identical specimens were performed at different frequencies. Specimens with different notch to width ratios ( a/w) were also tested. The applied stress level in all tests was kept the same. The maximum stress was 16.0 MPa and the ratio of minimum stress to maximum stress was kept at 25%. Fatigue test data such as the number of loading cycles, the crack length, and the hysteresis loops were recorded. The Modified Crack Layer (MCL) theory was employed to analyze the FCP behavior of this CTFE material. Also the results were analyzed using the Paris equation for comparison. It has been found that the fatigue crack growth behavior of this material cannot be described by the Paris power law due to the three distinct stages of the FCP kinetics. The MCL model was successfully used for extracting material parameters; γ', the specific energy of damage, and β', the coefficient of energy dissipation. The specific energy of damage for this CTFE was 855 kJ/m3 and the value of the coefficient of energy dissipation was 6.2 x 10-6. It was found that the values of γ' and β' are independent of a/w and the frequency ( f), though the FCP kinetics and life-time were dependent on a/w and f The variation in γ' and β' when aiw changed from 0.04 to 0.1 were only ±0.9% and +6.8%, respectively. For different frequencies (from 0.5 Hz to 5 Hz), the variation of these two parameters were ± 0.6% and ± 1.4%, respectively. In situ and post failure analysis of the fatigue fractured samples revealed a clear damage zone adjacent to the main crack. The larger the volume of the damage zone, the longer the fatigue life-time. It was also found that a higher micro-crack density associated with a larger damage zone. A larger damage zone with higher micro-crack density consumes more energy and thus reduces the portion of energy required to fuel the main crack growth.