An improved model for predicting fatigue S–N (stress–number of cycles to fail) behavior of glass fiber reinforced plastics

In a previous study a model to predict the fatigue S–N behavior of glass fiber reinforced thermoplastics by using a fracture mechanics approach was presented. Using a single flaw size model, some degree of success was observed, particularly for a reinforced polyamide. The model was not successful in predicting the S–N behavior of a reinforced polyester. The earlier study also employed flexural fatigue rather than tensile fatigue data in the calculations because the calculated flaw sizes were more nearly constant as a function of stress level. Subsequently it was shown that the flexural fatigue stress calculations were in error for these types of short glass fiber reinforced plastics owing to the nonlinearity of their stress–strain behavior. In this report we reexamine the utility of the fracture mechanics approach to predict fatigue S–N behavior for both materials using an improved model. Whereas previously a single initial surface flaw was assumed, here we assume multiple flaws growing simultaneously across the sample thickness. The new model is applied to both flexural and tensile fatigue loading. Results demonstrate that this new approach provides accurate predictions of the S–N behavior for both materials under both loading conditions. This reflects the fact that the calculated initial flaw sizes are relatively independent of stress level. No additional adjustable parameters are required if one uses the initial breaking strength of the material as part of the model calculations.     

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

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

Cohesive Fracture Model Based on Necking

A linear hardening model together with a linear elastic background material is first used to discuss some aspects of the mathematical and physical limitations and constraints on cohesive laws. Using an integral equation approach together with the cohesive crack assumption, it is found that in order to remove the stress singularity at the tip of the cohesive zone, the cohesive law must have a nonzero traction at the initial zero opening displacement. A cohesive zone model for ductile metals is then derived based on necking in thin cracked sheets. With this model, the cohesive behavior including peak cohesive traction, cohesive energy density and shape of the cohesive traction–separation curve is discussed. The peak cohesive traction is found to vary from 1.15 times the yield stress for perfectly plastic materials to about 2.5 times the yield stress for modest hardening materials (power hardening exponent of 0.2). The cohesive energy density depends on the critical relative plate thickness reduction at the root of the neck at crack initiation, which needs to be determined by experiments. Finally, an elastic background medium with a center crack is employed to re-examine the shape effect of cohesive traction–separation curve, and the relation between the linear elastic fracture mechanics (LEFM) and cohesive zone models by considering the cohesive zone development and crack growth in the infinite elastic medium. It is shown that the shape of the cohesive curve does affect the cohesive zone size and the apparent energy release rate of LEFM for the crack growth in the elastic background material. The apparent energy release rate of LEFM approaches the cohesive energy density when the crack extends significantly longer than the characteristic length of the cohesive zone.     

Fracture mechanics modelling of constant and variable amplitude fatigue behaviour of field corroded 7075‐T6511 aluminium

For ageing airframe structures, a critical challenge for next generation linear elastic fracture mechanics (LEFM) modelling is to predict the effect of corrosion damage on the remaining fatigue life and structural integrity of components. This effort aims to extend a previously developed LEFM modelling approach to field corroded specimens and variable amplitude loading. Iterations of LEFM modelling were performed with different initial flaw sizes and crack growth rate laws and compared to detailed experimental measurements of crack formation and small crack growth. Conservative LEFM‐based lifetime predictions of corroded components were achieved using a corrosion modified‐equivalent initial flaw size along with crack growth rates from a constant K_max‐decreasing ΔK protocol. The source of the error in each of the LEFM iterations is critiqued to identify the bounds for engineering application.     

Cohesive zone modelling of interface fracture near flaws in adhesive joints

A cohesive zone model is suggested for modelling of interface fracture near flaws in adhesive joints. A shear-loaded adhesive joint bonded with a planar circular bond region is modelled using both the cohesive zone model and a fracture mechanical model. Results from the models show good agreement of crack propagation on the location and shape of the crack front and on the initial joint strength. Subsequently, the cohesive zone model is used to model interface fracture through a planar adhesive layer containing a periodic array of elliptical flaws. The effects of flaw shape are investigated, as well as the significance of fracture process parameters. The results from simulations of fracture in a bond containing circular flaws show that localization of crack propagation in the vicinity of a flaw has significant effect on the joint strength and crack front shape. The localization effects are highly dependent on the fracture process zone width relative to the flaw dimensions. It is also seen that with increasing fracture process zone width, the strength variation with the flaw shape decreases, however, the strength is effected over a wider range of propagation.     

Transverse fracture in multilayers from tension and line-wedge indentation

Crack propagation across laminated brittle solids from uniaxial tension or line-wedge loading is studied in real time using a model glass/epoxy architecture. The fracture progresses from one layer to the next via reinitiation from pre-existing flaws on the glass surfaces ahead of the primary crack in a process accompanied by some penetration through the interlayer but generally little or no delamination or deflection along the glass/epoxy interface. Depending on the system parameters, the material behind the crack front may be fully or intermittently severed. A 2D brittle fracture analysis is developed with the aid of the FEM technique taking into consideration stress gradients over flaws and flexure from contact loading. The analysis identified the flaw size and misfit in modulus, toughness and thickness between the layer and interlayer as the prime system variables. The results generally collaborate well with the experiments. Thick and compliant interlayers are generally advantageous except for contact loading, where they may promote crack reinitiation from the back surface of a layer. The explicit relations for crack penetration and reinitiation presented in this work facilitate convenient means for optimal design. Herzl Chai—on leave, School of Mechanical Engineering, Tel Aviv University, Israel.     

Evaluation of the mechanical performance of zirconia bioceramic based on the size of incipient flaw

The mechanical performance of ceramic materials is highly dependent on the existence of incipient flaws. This paper investigates the relationship between the size of the pre-existing flaw and failure stress for disc-shaped specimens of zirconia bioceramic subjected to an equibiaxial stress field. As the size of initiating flaw increased, the stress under which discs failed decreased, sensibly allowing the fracture toughness of the material to be calculated. The value obtained, 8 MPam^1/2, is in reasonable agreement with previous experience, giving confidence in the validation procedure used and the data obtained. For cyclic loading, periods of stable fatigue crack growth occurred with initial defects extending to reach critical values. Based on data for discs that failed under monotonic loading conditions, it was possible to determine the critical flaw size and hence degree of crack growth necessary for discs to fail from fatigue at a given peak cyclic stress. Predictive constant flaw size fatigue curves showed reasonable accuracy in that the estimated incipient flaw size at a given fatigue life was equivalent to the true flaw size, measured from the fracture surface of failed disc specimens.     

Stress intensity in the vicinity of a surface flaw in the linear part of a pipeline

Real sharp-edted surface and subsurface flaws detected in a gas pipeline body are modeled by surface semi-elliptical mathematical cracks (cuts) in a closed cylindrical shell. A relationship is proposed that relates the geometrical dimensions of the flaws to the crack aspect ratio. Based on the line spring model, the problem of stress state and boundary equilibrium conditions of a closed cylindrical shell with a surface semi-elliptical crack is reduced to a system of singular integral equations. An algorithm was developed for computational solution of the problem, and numerical analysis was made for the dependence of stress intensity factors on loading conditions and geometrical parameters of shell and crack. For a shell subjected to internal pressure and weakened by a surface longitudinal semi-elliptical crack, a closed approximation formula is proposed that interrelates pressure level, shell/crack dimensions, and material mechanical properties in boundary equilibrium conditions. The maximal error value is indicated for the results obtained using this formula. Lvov Polytechnic State University, Lvov, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 38–47, July–August, 1999.     

Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference

With the increasing wide use of hydraulic fractures in the petroleum industry, it is essential to accurately predict the behavior of fractures based on the understanding of fundamental mechanisms governing the process. For effective reservoir exploration and development, hydraulic fracture pattern, geometry and associated dimensions are critical in determining well stimulation efficiency. In shale formations, non-planar, complex hydraulic fractures are often observed, due to the activation of preexisting natural fractures and the interaction between multiple, simultaneously propagating hydraulic fractures. The propagation of turning non-planar fractures due to the interference of nearby producing wells has also been reported. Current numerical simulation of hydraulic fracturing generally assumes planar crack geometry and weak coupling behavior, which severely limits the applicability of these methods in predicting fracture propagation under complex subsurface conditions. In addition, the prevailing approach for hydraulic fracture modeling also relies on linear elastic fracture mechanics (LEFM) by assuming the rock behaves purely elastically until complete failure. LEFM can predict hard rock hydraulic fracturing processes reasonably, but often fails to give accurate predictions of fracture geometry and propagation pressure in ductile and quasi-brittle rocks, such as poorly consolidated/unconsolidated sands and ductile shales, even in the form of simple planar geometry. In this study, we present a fully coupled poro-elasto-plastic model for hydraulic fracture propagation based on the theories of extend finite element, cohesive zone method and Mohr–Coulomb plasticity, which is able to capture complex hydraulic fracture geometry and plastic deformations in reservoir rocks explicitly. To illustrate the capabilities of the model, example simulations are presented including ones involving simultaneously propagating multiple hydraulic fractures and producing well interference. The results indicate that both stress shadow effects and producing well interference can alter hydraulic fracture propagation behavior substantially, and shear failure in ductile reservoir rocks can indeed make a significant difference in fracturing pressure and final fracture geometry.     

Distributed damage creates flaw tolerance

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

Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.     

On crack tip stress fields in pseudoelastic shape memory alloys

In a domain of reasonable accuracy around the crack tip, asymptotic equations can provide closed form expressions that can be used in formulation of crack problem. In some studies on shape memory alloys (SMAs), although the pseudoelastic behavior results in a nonlinear stress–strain relation, stress distribution in the vicinity of the crack tip is evaluated using asymptotic equations of linear elastic fracture mechanics (LEFM). In pseudoelastic (SMAs), upon loading, stress increases around the crack tip and martensitic phase transformation occurs in early stages. In this paper, using the similarity in the loading paths of a pseudoelastic SMA and a strain hardening material, the stress–strain relation is represented by nonlinear Ramberg–Osgood equation which is originally proposed for strain hardening materials, and the stress distribution around the crack tip of a pseudoelastic SMA plate is reworked using the Hutchinson, Rice and Rosengren (HRR) solution, first studied by Hutchinson. The size of the transformation region around the crack tip is calculated in closed form using a thermodynamic force that governs the martensitic transformation together with the asymptotic equations of HRR. A UMAT is written to separately describe the thermo-mechanical behavior of pseudoelastic SMAs. The results of the present study are compared to the results of LEFM, computational results from ABAQUS, and experimental results for the case of an edge cracked NiTi plate. Both set of asymptotic equations are shown to have different dominant zones around the crack tip with HRR equations representing the martensitic transformation zone more accurately.     

New insights into crack analysis: general solution vs LEFM

This paper examines the behaviour under tensile load of an elastic plate with a crack. Significance of the general solution of the problem is investigated. It is found that the crack opening parameters can be used as fracture parameters. It is shown that the first term in the power series expansion for any stress component of the general solution is the same as the expression for the stress of one term linear elastic fracture mechanics (LEFM) analysis.     

Failure of amorphous polystyrene

The failure behaviour of amorphous polystyrene was studied in methanol and ambient air under constant load and strain rate conditions. The good correlation found between fracture mechanics theory and the test results of both crazing and fracture indicates that fracture mechanics theory can be used in predicting failure of amorphous polystyrene. From the fracture mechanics analysis of the results it is inferred that the kinetics associated with craze initiation and crack propagation are similar and that the inherent flaw responsible for failure first initiates the craze in which a crack is then formed. Both the distribution of inherent flaws and the kinetics of crazing and fracture are dependent on the test environment.     

Bruchmechanik und zerstörungsfreie Werkstoffprüfung

Requirements by Fracture Mechanics on Nondestructive Testing Methods Fracture mechanics is a tool in evaluating the magnitude of critical flaws in structures. By means of Material properties such as fracture toughness, subcritical flaw growth, and existing primary and secondary stress it becomes possible to evaluate critical values for given flaw configurations. In Section XI, Appendix A of the ASME-Nuclear Pressure Vessel Code allowable flaw dephts are usually determined as a function of flaw configuration and localisation and wall thickness. Thus one wants to enable a fracture mechanical assessment of detected defects and of the safety of a component against brittle and tough fracture. Besides, it shall be possible to get an idea about the subcritical flaw growth. Therefore Practical application of fracture mechanics is based on progress in nondestructive surveillance methods. In the presented work the guidelines for integrity assessment of flawed structures based on Appendix A are described and the problems relating with fracture mechanical approaches are outlined. Up to this day it is not possible to get quantitative statements about the configuration, localisation and magnitude of flaws in structures by means of non destructive testing. Therefore factors of safety are introduced with the goal of assuring the integrity of flawed structures.     

The control of crack arrays in thin films

Thin-film fracture can be used as a nano-fabrication technique, but generally, it is a stochastic process that results in nonuniform patterns. Crack spacings depend on the interaction between intrinsic flaw populations and the fracture mechanics of crack channeling. Geometrical features can be used to trigger cracks at specific locations to generate controlled crack patterns. However, while this basic idea is intuitive, it is not so obvious how to realize the concept in practice, nor what the limitations are. The control of crack arrays depends on the nature of the intrinsic flaw population. If there is a relatively large density of long flaws, as commonly assumed in fracture mechanics analyses, reliable crack patterns can be obtained fairly robustly using relatively blunt geometrical features to initiate cracks, provided the applied strain is carefully matched to the properties of the system and the desired crack spacing. This process is analyzed both for cracks confined to the thickness of a film and for cracks growing into a substrate. The latter analysis is complicated by the fact that increases in strain can either drive cracks deeper into the substrate or generate new cracks at shallower depths. If the intrinsic flaws are all very short, the geometrical features need to be very sharp to achieve the desired patterns. While careful control of the applied strain is not required, the strain needs to be relatively large compared to that which would be required to propagate a large flaw across the film. This results in an approach that is not robust against the introduction of accidental damage or a few large flaws.     

A study of fracture criteria for ductile materials

In order to establish a ductile fracture criterion, several potential fracture parameters were investigated by comparing numerical simulations of crack extension with available experimental data. Based on the comparison, a fracture criterion, the Global-Local Fracture Criterion (GLFC), was proposed. The J-integral is employed as a global parameter to characterize the initial stage of crack extension. In the subsequent steady state crack growth, the fracture criterion is switched to a local parameter characterizing the crack tip stress or strain. The accuracy of the proposed fracture criterion in predicting ductile fracture behavior was verified.     

Splitting failure in brittle rocks containing pre-existing flaws under uniaxial compression

Splitting failure of rock specimen containing pre-existing crack-like flaws under compression is numerically investigated using Rock Failure Process Analysis (RFPA^2D). Crack growth from single, triple and multi-crack-like flaws contained in numerical specimens are studied. The analysis of parameters, such as angle and length of the flaws, specimen width and the arrangement of flaw locations, is conducted to examine its influence on the growth and coalescence behaviour. Flaw length, flaw location and stress interaction between the nearby flaws are found to be important factors affecting the behaviour of crack initiation, propagation and coalescence.     

Crack initiation under far-field cyclic compression and the study of short fatigue cracks

A procedure involving crack initiation under far-field cyclic compression is used to study the fatigue behavior of small flaws which are ˜0.3–0.5 mm in length and are amenable to linear elastic fracture mechanics (LEFM) characterization. This technique enables the determination of the threshold stress intensity range at which crack growth begins for small flaws and provides insight into some closure characteristics. Cracks were propagated in notched specimens of a bainitic steel subjected to fully compressive remote cyclic loads, until complete crack arrest occurred after growth over a distance of only a fraction of a mm at a progressively decreasing velocity. Following this, physically small flaws were obtained by machining away the notch. For the loads examined, the results indicate that the extent of damage left at the tip of the crack grown (and arrested) under remote compression is not large enough to affect subsequent tensile fatigue crack growth, when closure effects are not significant (e.g. at high load ratios). At high load ratios, the growth of small linear elastic cracks is identical to that of corresponding long flaws subjected to the same stress intensity range, which corroborates the similitude concept implicit in the nominal use of LEFM. At low load ratios, however, short tensile cracks propagate substantially faster than the longer flaws and exhibit lower threshold stress intensity range levels. Such apparent differences in their growth rates seem to arise, to a large extent, from the differences in their closure behavior, as indicated clearly from various aspects of the compression method. Global measurements of closure, with their inherent uncertainties, however, cannot account completely for the anomalous behavior of short flaws and for the effect of load ratio on short crack growth. Closure of short flaws begins to develop after growth over a minimum distance of about 0.5 mm in this steel. The significance and limitations of the compression technique are discussed and possible mechanisms responsible for the differences between long and short fatigue cracks are outlined.