Characterization of the fatigue crack behavior of pipe grade polyethylene using circular notched specimens

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.     

Some considerations of fracture mechanics applications in ships design,construction and operation

The structural performance demands placed on present day high performance ships and some types of shipboard liquid natural gas (LNG) cargo containment systems requires the use of new materials which can perform under higher loadings and severe service environments. Such critical designs must be accomplished while maintaining a high structural reliability and decreased life-cycle costs. For high performance ships these critical designs can be accomplished with damage-tolerant design procedures which provide for redundant load paths and/or crack arrest capabilities. The ship construction and maintenance requirements must also be included in the design because of their effect on the structural life performance of the high performance ship. For shipboard LNG cargo containment systems modified LEFM (linear elastic fracture mechanics) is used in the design phase.The paper discusses the philosophy of a fatigue and fracture control plan for high performance ships and the use of modified LEFM for shipboard LNG cargo containment systems. Current applications of a fatigue and fracture control plan are discussed. The types of shipboard cargo containment systems designed using the modified LNG approach are described.The paper addresses the need for an integrated life time quality assurance program. Such a program is shown to require a synthesis of materials characterization, structural analysis and nondestructive testing. A service performance feedback loop will assist the designers in continually improving the then governing design criteria. In addition, areas requiring further work and possible future applications for fatigue and fracture analysis will be discussed.     

Analysis of a Failure in a Polyethylene Gas Pipe Caused by Squeeze off Resulting in an Explosion

A failure caused by squeezing off a polyethylene (PE) gas pipe was investigated. The failure mechanisms were analyzed. Two modes of fracture were found: brittle and slow crack growth (SCG). The formation of the brittle fracture was particularly interesting because its origin was not produced by a defect in the material, but by the compressive stress fields produced by squeezing and enhanced by the visco-elastic behavior of PE. The micro deformation, which was associated with the nucleation of brittle fracture, was analyzed. The time for the SCG was predicted based on the size of the brittle fracture. It is most likely that the failure would not have occurred if the squeeze and release rates had been controlled.     

A fracture mechanics concept for the accelerated characterization of creep crack growth in PE-HD pipe grades

For the lifetime prediction of pressurized polyethylene (PE) pipes based on methods of the linear elastic fracture mechanics the knowledge of the crack resistance and the kinetics of creep crack growth (CCG) is essential. In the present work a rather brittle nonpipe material was used to develop a methodology for an accelerated measurement of crack kinetics in fatigue tests on cracked round bar (CRB) specimens at ambient temperatures of 23 °C. A material and specimen specific compliance calibration curve was generated to detect the crack kinetics with only one single CRB test. Based on an already proposed concept the kinetics at different R-ratios (minimum/maximum load) was measured and extrapolated to the case of CCG. To demonstrate the transferability of this concept to pipe materials a PE 80 pipe grade was used. Although the necessary testing time increased considerably the concept still has the potential to reduce the overall testing time for new pipe materials to be certified significantly. With the presented procedure a characterization of CCG in modern PE pipe grades at room temperature and without the use of stress cracking liquids is possible within a few months.     

Critical review of the fatigue growth of short cracks

Retirement for cause (RFC) has become a popular design/analysis philosophy because it facilitates continued use of components which would otherwise be retired based on a safe life philosophy. RFC permits this continued service on the basis that service-induced damage tracked by periodic inspections will not develop to a critical size within a future operating interval. Successful implementation of RFC requires fracture mechanics technology to predict in-service growth behavior. Recent observations suggest that nonconservative estimates of crack growth rate (and therefore inspection interval) and critical flaw size arise when conventional linear elastic fracture mechanics (LEFM) is applied to predict the growth of physically small cracks. This paper summarizes the results of an extensive limited-circulation critical review of the phenomenology and mechanics of short crack growth with a view to identifying when this anomalous growth makes RFC analyses untenable in terms of LEFM. Factors which control the growth of short cracks are enumerated. It is shown for unnotched samples that the apparent effect may be traced to microcrack closure and the metallurgical, mechanical, and environmental transients which develop in the transition from initiation to steady-state growth. For notch samples the anomalous growth of cracks is traced to the inelastic action that develops a displacement-controlled notch field, which, contrary to LEFM analysis, dominates crack extension. Mechanics analyses relevant to characterizing the growth of short cracks are discussed. A crack tip opening displacement criterion is indicated to be appropriate.     

Craze testing for tough polyethylene

It has been generally accepted that all the modes of fracture, including rapid crack growth, quasi-static fracture and slow crack growth in polyethylene are associated with the behaviour of the craze ahead of the crack tip. For recently developed tough pipe grade polyethylene materials, the need for knowledge of the craze behaviour seems particularly important in understanding the fracture behaviour of various modes since, with the low Young's moduli and low yield stresses, large craze zones tend to make it difficult to interpret the test data using a fracture mechanics approach. A novel test method is described in this paper which is designed for craze generation and craze behaviour analysis under plane strain conditions. The test method has been proved to be suitable both for quasi-static fractures and for long term fractures, and hopefully for rapid fractures, in tough polyethylene materials. The test data of yield stress against time to yielding show a clear brittle ductile transition which implies different fracture mechanisms in short term fracture and in long term fracture.     

Fracture characterization of random short fiber reinforced thermoset resin composites

The fracture toughness characterization of random fiber reinforced polymer composites has been investigated by several research groups in recent years. This paper discusses the methods and results of some of these investigations with regard to the applicability of classical linear elastic fracture mechanics approaches to such materials. In polymers randomly reinforced with short fibers (0.5 mm) the region of inelastic behavior ahead of crack tips is sufficiently small that LEFM toughness tests are valid with standard specimen sizes. However, calculations suggest that during fracture of composites with “long” fibers (24 or 50 mm), inelasticities occur to such an extent that the small scale yielding requirements of LEFM are not satisfied. An alternative approach based on the material tension-softening curve may be more appropriate to characterize fracture toughness in fiber reinforced composites.     

A discrete cohesive model for fractal cracks

The fractal crack model described here incorporates the essential features of the fractal view of fracture, the basic concepts of the LEFM model, the concepts contained within the Barenblatt-Dugdale cohesive crack model and the quantized (discrete or finite) fracture mechanics assumptions proposed by Pugno and Ruoff [Pugno N, Ruoff RS. Quantized fracture mechanics. Philos Mag 2004;84(27):2829-45] and extended by Wnuk and Yavari [Wnuk MP, Yavari A. Discrete fractal fracture mechanics. Engng Fract Mech 2008;75(5):1127-42]. The well-known entities such as the stress intensity factor and the Barenblatt cohesion modulus, which is a measure of material toughness, have been re-defined to accommodate the fractal view of fracture.For very small cracks or as the degree of fractality increases, the characteristic length constant, related to the size of the cohesive zone is shown to substantially increase compared to the conventional solutions obtained from the cohesive crack model. In order to understand fracture occurring in real materials, whether brittle or ductile, it seems necessary to account for the enhancement of fracture energy, and therefore of material toughness, due to fractal and discrete nature of crack growth. These two features of any real material appear to be inherent defense mechanisms provided by Nature.     

Seismic crack propagation analysis of concrete structures using boundary elements

The time-domain boundary element method is applied to study the propagation of discrete cracks under dynamic loadings. The principles of linear elastic fracture mechanics are employed to accurately represent the stress singularity in front of the crack tip. A fracture criterion suitable for brittle materials is employed to determine the time and direction of the propagating crack. Discrete crack closure under dynamic loadings is modelled and the response of a 2-D cracked body is obtained by direct integration of the equations of motion. Results are presented for three test problems wherein the accuracy and usefulness of the proposed formulation is established through comparisons with available data. 'It is expected that this formulation can be used to study the seismic cracking of mass concrete structures such as gravity dams.     

纤维增强PE材料增韧效果的研究

以聚乙烯(PE)材料为基体,应用玻璃纤维随机或定向分布,增加材料的强度、刚度和断裂韧性,是发展高压大口径复合材料天然气管道的需要。本文基于PFRAC程序的动态断裂分析能力[1],增加了各向异性材料的本构条件,发展了对纤维增强复合材料未开裂和开裂管道的计算功能。由力学性能的试验结果,提供了材料的本构关系,对未开裂和开裂的管道进行了计算分析。结果表明,PE管道经纤维增强之后,与纯PE材料的管道相比,其环向位移下降到53%(纤维随机分布)~5%(纤维沿管道轴向80度分布);裂纹驱动力相应下降到50%~17%,充分反映了纤维对PE材料的增强和增韧效果。     

The nitrogen gas tension test. Part 2: failure mechanism

In this study, the mechanism of concrete failure in the nitrogen gas tension test was investigated through a series of experiments. First, the nitrogen gas tension test was carried out two types of specimens: solid cylinders and hollow cylinders. The test results clearly showed that there was no significant difference in the gas pressure at failure between the solid specimen and the hollow specimen. Since a tension crack occurring on the surface of the concrete specimen at a gas pressure almost equal to the tensile strength of the concrete might play a key role in understanding the failure mechanism, a failure criterion based on linear elastic fracture mechanics (LEFM) was consequently developed. The nitrogen gas tension test was newly carried out on cylindrical specimens with circumferential notches of various depths. Though LEFM was found to be useful in developing an understanding of the mechanism of concrete failure, the experimental results indicated that it was not really valid for specimens with notch depths deeper than some critical size (critical notch depth). However, based on the experimental observation that the concrete specimen failed at its tensile strength at notch depths smaller than the critical notch depth, a modified LEFM based failure mechanism was proposed taking into account the notch sensitivity of the concrete.     

The role of thermal and residual stresses in linear elastic and post yield fracture mechanics

The general role played by thermal and residual (TR) stresses in fracture mechanics is still unclear. It is sometimes argued (a) that in the linear elastic fracture mechanics (LEFM) regime TR stresses are secondary (rather than primary) i.e. that the overall loading is relaxed (rather than maintained) as well as redistributed as the crack grows, and (b) that because TR stresses do not influence the plastic limit load of a structure they have little influence on the post yield fracture mechanics (PYFM) regime. This paper demonstrates the dangers of these views. Examples are given of TR stresses behaving in either primary or secondary manner in both the LEFM and PYFM regimes. The danger of drawing general conclusions in fracture mechanics from the nearness of a structure to its plastic limit load is demonstrated, and it is shown that local rather than global (limit-analysis) collapse parameters must be used in empirical formulae that interpolate between LEFM and plastic-collapse regimes. In LEFM it is shown that the standard Green's function (weight or influence function) method can be applied to TR stress calculations. The method also applies in the PYFM regime if the Dugdale-type strip yield model is assumed. A general method of analysing fixed-grip loadings in the plastic regime, based on Rice's J contour integral is also given.     

Investigation of Progressive Damage and Fracture in Laminated Composites Using the Smeared Crack Approach

The smeared crack approach (SCA) is revisited to describe post-peak softening in laminated composite materials. First, predictions of the SCA are compared against linear elastic fracture mechanics (LEFM) based predictions for the debonding of an adhesively bonded double cantilever beam. A sensitivity analysis is performed to establish the influence of element size and cohesive strength on the load-deflection response. The SCA is further validated by studying the in-plane fracture of a laminated composite in a single edge bend test configuration. In doing so, issues related to mesh size and their effects (or non-effects) are discussed and compared against other predictive computational techniques. Finally, the SCA is specialized to orthotropic materials. The application of the SCA is demonstrated for failure mechanics of the open hole tension test, where fiber/matrix fracture is predominant and predicted well by the present approach.     

Efficient prediction of deterministic size effects using the scaled boundary finite element method

This paper develops an efficient numerical approach to predict deterministic size effects in structures made of quasi-brittle materials using the scaled boundary finite element method (SBFEM). Depending on the structure’s size, two different SBFEM-based crack propagation modelling methodologies are used for fracture analyses. When the length of the fracture process zone (FPZ) in a structure is of the order of its characteristic dimension, nonlinear fracture analyses are carried out using the finite element-SBFEM coupled method. In large-sized structures, a linear elastic fracture mechanics (LEFM)-based SBFEM is used to reduce computing time due to small crack propagation length required to represent the FPZ in an equivalent nonlinear analysis. Remeshing is used in both methods to model crack propagation with crack paths unknown a priori. The resulting peak loads are used to establish the size effect laws. Three concrete structures were modelled to validate the approach. The predicted size effect is in good agreement with experimental data. The developed approach was found more efficient than the finite element method, at least in modelling LEFM problems and is thus an attractive tool for predicting size effect.     

PROPAGATION BEHAVIOUR OF SHORT FATIGUE CRACKS IN Q2N STEEL

Abstract— The work described in this paper characterizes short fatigue crack growth behaviour of Q2N steel having a complex microstructure and designated for pressure vessel and offshore structure applications. Short and long fatigue crack growth tests for this steel were conducted under three point bend loading conditions. It was found that, in the initial stages of growth, short cracks propagate much faster than those of long cracks when correlated with the linear elastic fracture mechanics (LEFM) parameter Δ K. A period of crack growth retardation was observed at crack lengths of approx 50 μm. The theory of the interaction between short cracks and grain boundaries fails to predict the occurrence of this deceleration minima. A new short crack deceleration mechanism is proposed based on experimental observation. Observation of the characteristic behaviour of short cracks allowed the development of a short crack growth model based on microstructural fracture mechanics analyses.     

Estimation of dynamic fatigue strengths in brittle materials under a wide range of stress rates

This paper aims to statistically estimate the dynamic fatigue strength in brittle materials under a wide range of stress rates. First, two probabilistic models were derived on the basis of the slow crack growth (SCG) concept in conjunction with two-parameter Weibull distribution. The first model, Model I, is a conventional probabilistic delayed-fracture model based on a concept wherein the length of the critical crack growth due to SCG is enough larger than the initial crack length. For the second model, Model II, a new probabilistic model is derived on the basis of a concept wherein the critical cracks have widely ranging lengths. Next, a four-point bending test using a wide range of stress rates was performed for soda glass and alumina ceramics. We constructed fracture probability–strength–time diagrams (F–S–T diagrams) with the experimental results of both materials using both models. The F–S–T diagrams described using Model II were in good agreement with plots of the fracture strength and the fracture time of both materials more so than Model I.     

Basic issues in the mechanics of high cycle metal fatigue

Mechanics issues related to the formation and growth of cracks ranging from subgrain dimension to up to the order of one mm are considered under high cycle fatigue (HCF) conditions for metallic materials. Further efforts to improve the accuracy of life estimation in the HCF regime must consider various factors that are not presently addressed by traditional linear elastic fracture mechanics (LEFM) approaches, nor by conventional HCF design tools such as the S-N curve, modified Goodman diagram and fatigue limit. A fundamental consideration is that a threshold level for ΔK for small/short cracks may be considerably lower than that for long cracks, leading to non-conservative life predictions using the traditional LEFM approach. Extension of damage tolerance concepts to lower length scales and small cracks relies critically on deeper understanding of (a) small crack behavior including interactions with microstructure, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) development of reliable small crack monitoring techniques. The basic technology is not yet sufficiently advanced in any of these areas to implement damage tolerant design for HCF. The lack of consistency of existing crack initiation and fracture mechanics approaches for HCF leads to significant reservations concerning application of existing technology to damage tolerant design of aircraft gas turbine engines, for example. The intent of this paper is to focus on various aspects of the propagation of small cracks which merit further research to enhance the accuracy of HCF life prediction. Predominant concern will rest with polycrystalline metals, and most of the issues pertain to wide classes of alloys.     

Strength size effects and fracture mechanics: What does the physical evidence say?

Being able to predict the strength of geometrically-similar cracked specimens of different sizes or scales is a fundamental requirement for success for linear elastic fracture mechanics (LEFM). The prediction contained in LEFM is that the strength reduces as the inverse square-root of the scale factor in the plane of the crack: here we review how well this prediction actually agrees with the physical evidence. In particular we examine agreement for materials and configurations exhibiting brittle responses—the situations complying best with the underlying linear elastic assumptions in the theory. The data show that the agreement is not good, even in the most brittle of instances.     

Evaluation of the amount of crack growth in 2D LEFM problems

This work proposes an algorithm for the evaluation of the amount of crack growth in two-dimensional problems of linear elastic fracture mechanics. The method is based on the energetic formulation of the coupled displacement–crack propagation problem defined by Nguyen et al. in 1990 in order to study the stability of crack growth in elastic fracture. To avoid the remeshing usually needed for modelling crack growth, a PUFEM model is utilized. The proposed algorithm is valid for stable rectilinear crack growth in LEFM but it can be extended to evaluate stable curvilinear crack growth in materials showing dissipative deformations.