Crack Growth In Polyethylene Research Articles

Cohesive crack growth in polyethylene considering Schapery equation using XFEM

A nonlinear rate-dependent cohesive rule based on a novel incorporation by Schapery nonlinear coefficients is suggested to model crack growth in the case of polyethylene which is well-defined through the Schapery nonlinear constitutive equation. As the matter between the crack faces in a polymeric medium like polyethylene may tolerate large strain ranges during crazing and before complete separation, it may involve stress-dependent factors as same as bulk material. A useful damage-creeping cohesive rule is selected and its creeping part is extended in a way to incorporate the nonlinear Shapery parameters. The augmented relation is fitted to both high and low constraint results and applied to an experimented medium using Extended Finite Element Method (XFEM) to evaluate its ability to properly predict cohesive crack propagation. The results are in tight agreement with the existing experimental outputs. The suggested framework may illuminate a way of expressing the damage zone in polymers using nonlinear specifications of the bulk material.

Applying the crack-layer concept to modeling of slow crack growth in polyethylene

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.

Improvement of Hardening Stiffness Test as an Indicator of Environmental Stress Cracking Resistance of Polyethylene

Long term mechanical behavior of polyethylene (PE) is of great importance especially in cases where structural integrity is required. In order to predict characteristics of the mechanical behavior of PE, it is necessary to fully understand the molecular structure of the employed resins. In this study, evaluation of several micromolecular properties of PE is conducted. These properties influence an important performance indicator of PE for structural applications, namely, the environmental stress cracking resistance (ESCR). ESCR in PE resins occurs through a slow crack growth mechanism under low applied stresses and long periods of time. This property is usually assessed by unreliable and time consuming testing methods such as the notch constant load test (NCLT) on notched PE specimens in the presence of an aggressive fluid at elevated temperatures. In the work presented herein, relationships between molecular structure and material response characteristics, mainly between molecular weight properties and short chain branching content in relation to strain hardening behavior of PE resins, were investigated based on results from tensile experiments. Inter-lamellar entanglements are believed to be the main feature controlling slow crack growth of PE. Extent of entanglements and entanglement efficiency has been investigated by monitoring the strain hardening behavior of PE resins in solid state through a uniaxial tensile test. The hardening stiffness (HS) test for prediction of ESCR was refined and improved to cover a broader range of PE resins, along with easier sample preparation, and faster testing. The improved test offers a more reliable and consistent ESCR picture without the drawbacks of the subjective notching process and ad-hoc presence of aggressive fluids.

Constraint effect on the slow crack growth in polyethylene

PurposeFrom the practical point of view, most relevant damage to high density polyethylene (HDPE) structures is caused by slow crack growth. Therefore, detailed information about this type of damage is necessary. Experimental results transfer from specimens to real structure can be influenced by structure geometry (constraint). Therefore, the purpose of this paper is to investigate and discuss the effect of the constraint and relation between crack mouth opening displacement (CMOD) and crack length.Design/methodology/approachThe constraint effect is mainly effect of the structure geometry and can be quantified by T‐stress. Two different test specimens with different constraint level (T‐stress) were prepared: single edge notched specimen and modified single edge notch (SEN) specimen. The crack mouth opening displacement, crack tip opening displacement and crack length was measured.FindingsThe main conclusions of this work can be summarized as: the slow crack growth rate in HDPE materials corresponds to velocity of CMOD; the influence of the presented specimen geometry on slow crack growth rate can be considered as negligible; and for transfer of the experimental results from specimens to real structure the influence of the structure geometry (constraint) is not critical.Originality/valueExperimental results obtained from different specimens with different constraint level are rare and can lead to better data transfer from experimental specimens to the real structures.

Micromechanisms of slow crack growth in polyethylene under constant tensile loading

Circumferentially notched specimens of a first generation and a third generation pipe-grade of high density polyethylene with similar weight average molar masses have been subjected to constant tensile loads at 80°C. A transition from full ligament yielding to failure by stable sub-critical crack growth was observed as the applied load was decreased. The specimen lifetimes in this latter regime were dependent on the initial stress intensity factor, K i, and failure was associated with slow crack propagation preceded by formation of a wedge-shaped cavitational deformation zone at the notch tip. The fibril diameters in the deformation zones decreased with stress intensity factor near the transition, the limiting behaviour of a relatively slow crack growth resistant third generation grade at the lowest K i being inferred from testing in Igepal™ to be the breakdown of diffuse zones of interlamellar voiding. This regime was not directly accessible to testing in air within the allotted experimental times. However, comparison with the results of accelerated testing in cyclic fatigue has indicated stable interlamellar voiding in the third generation grade not to necessitate the presence of Igepal. Moreover, in both grades, very similar modes of deformation were observed in air and in Igepal at relatively high K i. Igepal was therefore inferred not to lead to qualitative changes in the range of mechanisms that are characteristic of slow crack growth in polyethylene.

Creep crack growth in polyethylene under combined mode I and mode II loading

Creep crack growth characteristics under various combined mode I and mode II loadings were studied using the compact tension shear (CTS) specimens of polyethylene. Creep crack growth rates da/dtunder combined mode I and mode II loading can be correlated with a single effective stress intensity factor KIeffderived from the combined — mode fracture toughness envelope. The steady state or constant crack growth rates which occupy the significant part of creep failure life increase with the increasing initial effective stress intensity factor.

Cohesive zone modelling of crack growth in polymers Part 1 –Experimental measurement of cohesive law

The initiation, evolution, and breakdown of the craze ahead of the crack tip is known to control the onset of slow crack growth in polyethylene. Extensive craze zones and large specimen deformations in tough polymers render conventional fracture mechanics approaches incapable of achieving a valid toughness characterisation for these materials. This paper describes a novel experimental method for measuring the local work of separation in tough polyethylene, using tensile specimens with deep circumferential notches, which provide a high level of constraint. The traction–separation behaviour of the material within the constrained ligament is measured directly in situ, yielding a rate dependent cohesive law, which is believed to provide a physically based material description of the damage zone that precedes crack growth. Measurements indicate that both the local work of separation and the cohesive strength are strongly rate dependent, allowing quantification of the fracture behaviour over a wide range of test speeds and discrimination between the stress crack performances of different grades of polyethylene.

Measurement of cohesive zone parameters in tough polyethylene

AbstractThe initiation, growth and final failure of the craze ahead of a crack tip generally controls the onset of crack growth in polyethylene, particularly in slow crack growth. In this research, circumferentially deep notched tensile specimens are used to analyze the evolution and failure of crazes in polyethylene under plane strain conditions. An experimental method is used wherein the traction‐separation behavior of the craze structure is measured directly in‐situ. Results yield a cohesive zone type analysis in which a two parameter traction curve, containing within it all information pertaining to local decohesion, fully describes the separation of the interface. Experimentally measured rate dependent trends in the work of separation (I) provide good discrimination between different grades of tough polyethylene at both high and quasi‐static test speeds, and highlight the exceptional long term behavior of one particular grade. The method also allows for the quantification of the long term behavior of each grade by more traditional stress‐time analysis.

Application of the crack layer theory to modeling of slow crack growth in polyethylene

A crack and a domain of highly fibrillated and stretched material ahead of the crack (process zone), commonly observed in polyethylene, are considered as a system called the crack layer. Slow crack layer growth is assumed to be a result of interactions between the crack, process zone and the rest of the body, as well as of degradation of the process zone material. The energy balance for process zone formation and crack layer advance is presented. The equations governing crack layer propagation are formulated and numerically solved. The proposed mechanism of fracture process models the discontinuous crack growth often observed in polyethylene, and predicts the relationship between the crack growth rate and the stress intensity factor consistent with the experimental one. The dependence of the lifetime on load is discussed.

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.

A sensitive mechanical test for slow crack growth in polyethylene

AbstractSlow crack growth (SCG) in a wide variety of polyethylenes has been investigated by a constant tensile load test (the PENT test) for a single edge notched specimen. The PENT test is very sensitive to the changes in molecular structure and morphology of polyethylene. The resistance to SCG depends on the density of the tie molecules and the strength of the crystals.

Abnormal slow crack growth in polyethylene

The normal slow crack growth behaviour of polyethylenes consists of a ductile-brittle transition where the transition to brittle fracture occurs below a critical stress and after a critical time. The curves of stress vs. failure time depend on temperature, but all curves can be shifted vertically and horizontally by well established shift functions. It has been observed that there are some polyethylenes whose stress vs. time to failure curves do not shift in the normal way and in some cases the time for brittle fracture does not change with temperature. SEM micrographs do not reveal any difference between the fibrillated fractured surfaces from the normal and abnormal specimens. Whereas the normal slow crack growth behaviour has been attributed to the disentanglement of the molecules by sliding without chain scission, it is proposed that the abnormal fracture behaviour may involve a disentanglement mechanism that consists of a combination of chain sliding and scission.

A new automated method for recording and predicting failure by slow crack growth in polyethylene

The PENT test (ASTM F1473) which measures the resistance to slow crack growth (SCG) has been modified so that the crack opening displacement (COD) can be automatically recorded through a computer. From the curve of COD rate versus time, fine details of the fracture processes can be observed and a very early stage of fracture initiation can be determined. Consequently, the time for complete failure can be predicted from the initiation time sooner than has been possible by previous techniques.

The effect of γ‐irradiation on slow crack growth in polyethylene

AbstractHDPE was γ‐irradiated at room temperature. The resistance to slow crack growth (SCG) was measured in single edge notched tensile specimens under constant load as a function of the dose. The resistance to SCG initially decreased to a minimum value at a dose between 0.05 and 0.10 Mrd. The minimum value was 45% less than for the undosed state. For doses greater than 0.10 Mrd, the resistance to SCG increased up to a dose of 50 Mrd, where its value had increased by a factor of 102. The gel point occurred at 1–3 Mrd. MI and the crack opening displacement exhibited maximum values at a dose of 0.1 Mrd. The behaviors of SCG, MI and crack opening displacement were consistent with the explanation that chain scission dominated for doses less than 0.1 Mrd, and cross‐linking dominated at the higher doses. For doses beyond 50 Mrd, the resin became so brittle that it cracked during the loading of the specimen. Beyond the gel point the density increased from 0.9694 to 0.9716 g/cm3 at a dose of 160 Mrd. ©1995 John Wiley & Sons, Inc.

A fundamental theory for slow crack growth in polyethylene

The following theoretical equation has been obtained for measuring the rate of slow crack growth in polyethylene in terms of the crack opening displacement rate δ: δ ̇ = α y(1−y 2) 2 ηd oE 2α 2 c K 4 Here δ y is the yield point, K is the stress intensity, η is the intrinsic viscosity of the fibrils in the craze, E is Young's modulus, δ c is the stress to produce a craze, d 0 is the primordial thickness from which the craze originates and γ is Poisson's ratio. The theoretical equation agrees with the experimental observation: δCK 4 e- −Q/RT Thus, for the first time, the dependence of δ on stress and notch depth have been derived in fundamental terms and the physical parameters that constitute the factor C have been identified. The intrinsic viscosity η can be calculated from the theory using specific experimental data. For example at 42°C, the fibrils in a craze in a homopolymer have an intrinsic viscosity of 3 × 10 11 Pas. This is much larger than the melt viscosity of the amorphous region, which is about 10 5–10 6 Pas. Thus, the resistance of polyethylene to slow crack growth is governed by the crystals and not by the amorphous region.

The fracture mechanics of slow crack growth in polyethylene

The following theoretical equation was obtained for the rate of initiation fx- of slow crack growth in polyethylene:

Slow crack growth in polyethylene: A novel predictive model based on the creep of craze fibrils

AbstractAn extensive series of homopolymers and copolymers has been investigated to test earlier indications of a possible link between resistance to slow crack growth and creep of macroscopic oriented samples. It was found that in the majority of cases a good correlation exists between a single creep parameter and slow crack growth. The existence of such a correlation supports the model presented, in which crack growth is primarily controlled by the creep of fibrils spanning the craze zone. The limit of improvement achievable by increasing molecular weight and the greater effectiveness of short‐chain branching to improve fibril creep have been highlighted. © 1994 John Wiley & Sons, Inc.

Slow crack growth in polyethylene ‐ a review

AbstractSlow crack growth in a wide variety of polyethylenes have been investigated. The quantitative relationship between: (1) the external variables such as stress, temperature, stress intensity and J‐integral; (2) the morphological variable such as density and crystal size and (3) molecular variables such as molecular weight, branch density and branch distribution and the rate and time to failure for slow crack growth will be presented. The kinetics of slow crack growth is correlated with the microstructural changes. A fundamental description of slow crack growth is given in terms of tie molecules and the stress field on the boundary of the craze from which fracture initiates.

The mechanism of slow crack growth in polyethylene by an environmental stress cracking agent

Using single edge notch tensile specimens under plane strain conditions, the time to fail by slow crack growth was accurately measured in an ethylene-octene copolymer in Igepal and air. The primary result was the observation of a critical time for failure called the ‘Igepal transition’. Only for failure times greater than the ‘Igepal transition’ did Igepal accelerate fracture. For failure times shorter than the ‘Igepal transition’ the temperature dependence and stress dependence of the failure times in air and Igepal were the same and secondary crazes were observed in Igepal but not in air. By relaxing the local stress the secondary crazes made the failure time in Igepal longer than in air. For times longer than the ‘Igepal transition time’ the Igepal accelerated fracture. The activation energy in Igepal was reduced to 69 kJ mol −1 as compared to 118 kJ mol −1 in air and the dependence of failure time on stress was changed by the Igepal. The Igepal has two distinct effects: it enhances crazing by plasticizing the amorphous region of the bulk polymer; and it enhances fracture of the craze by plasticizing the crystalline region of the fibrils. The ‘Igepal transition time’ was related to the difference between the diffusion coefficients in the crystalline and amorphous regions.

Dependence of slow crack growth in polyethylene on butyl branch density: Morphology and theory

AbstractA theoretical equation has been developed to described the rate of slow crack growth in an ethylene‐hexene copolymer in terms of the basic morphological parameters. These parameters are spacing of the butyl branches, number of tie molecules, and the thickness of the lamellar crystal. Experimentally, the thickness of the lamellae and the long period were determined as functions of the branch density. The calculation of the number of tie molecules is based on the values of the molecular weight and the long period. The model of slow crack growth is based on the rate of disentanglement of the tie molecules. The rate of disentanglement varies inversely with the number of tie molecules and directly with the number of tie molecules that are not pinned by the branches.