Probability of cleavage fracture for a crack propagating by fatigue

Standard fracture toughness tests use fatigue pre-cracked specimens loaded monotonically from zero to failure. Scatter in toughness (cleavage) occurs because steel is metallurgically inhomogeneous, and because each specimen has its crack tip in a different local microstructure. A probability of fracture toughness distribution can be obtained by conducting multiple repeat tests on the same steel. This is often used to make probabilistic structural fracture predictions for combinations of crack length and applied load. However, it is likely the true structural situation involves gradual extension of a fatigue crack under a cyclic load. The question then arises as to how often the probability of fracture for the structure needs to be re-calculated. It could be argued that each fatigue load cycle moves the crack tip to a new position and gives a different instantaneous probability of fracture. But if this were the case, the predicted cumulative probability of fracture would quickly tend to unity. This paper describes cold temperature, wide plate fatigue tests designed to investigate this apparent contradiction. The steel is 15 mm thick, grade A, ship plate and the tests involve propagation of a fatigue crack from 300 mm to 650 mm length under a constant amplitude fatigue cycle of 10-100 MPa at −50 °C. The cold temperature fatigue tests do not show an obviously increased probability of fracture compared with the standard monotonic load tests. Nevertheless, in view of uncertainties surrounding the issue, a cumulative probability of fracture determined at 5 mm intervals through the steel is recommended for safe structural predictions.     

Probabilistic optimization of welded joints maintenance versus fatigue and fracture

This paper presents a probabilistic maintenance optimization procedure for welded joints damaged by fatigue. The linear elastic fracture mechanics stands as a basis for fatigue crack growth while the crack depth at failure is determined according to brittle or ductile fracture. The first order reliability method being applied, the assessment is then based on reliability indices. At an inspection instant, different events can occur: no crack detection, crack detection, and repair. All these events are uncertain and are expressed in terms of probabilities. As they are cost-dependent, the total expected cost of maintenance could be obtained. The inspection instant is therefore searched by minimizing that total expected cost. Such an approach appears as a good compromise between reliability and costs. The paper provides some sensitivity studies and an application on a real case.     

An accumulation damage model for fatigue fracture of ferroelectric ceramics

The accumulated plastic displacement criterion for crack propagation in traditional materials is extended to develop equations to predict the fatigue crack growth of ferroelectric ceramics subjected to combined electromechanical loads. The crack-line is perpendicular to the poling direction of the medium. An electric saturation zone and a stress saturation zone are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. This assumption makes it possible to obtain the accumulated plastic deformation in closed form. A fatigue crack growth law, which is a fourth-power function of the effective stress intensity factor, similar to the well-known Paris law, is derived. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided.     

Preparation temperature effect on the synthesis of various carbon nanostructures

Various carbon nanostructures (CNs) have been prepared by a simple deposition technique based on the pyrolysis of a new carbon source material tetrahydrofuran (THF) mixed with ferrocene using quartz tube reactor in the temperature range 700–1100 °C. A detailed study of how the synthesis parameter such as growth temperature affects the morphology of the carbon nanostructures is presented. The obtained CNs are investigated by scanning electron microscope (SEM), X-ray diffraction (XRD), electron dispersive scattering (EDS), thermogravimetry analysis (TGA), Raman and transmission electron microscope (TEM). It is observed that at 700 °C, normal CNTs are formed. Iron filled multi-walled carbon nanotubes (MWCNTs) and carbon nanoribbons (CNRs) are formed at 950 °C. Magnetic characterization of iron filled MWCNTs and CNRs studied at 300 K by superconducting quantum interference device (SQUID) reveals that these nanostructures have an enhanced coercivity (Hc = 1049 Oe) higher than that of bulk Fe. The large shape anisotropy of MWCNTs, which act on the encapsulated material (Fe), is attributed for the contribution of the higher coercivity. Coiled carbon nanotubes (CCNTs) were obtained as main products in large quantities at temperature 1100 °C.     

A practical randomization approach of deterministic equation to determine probabilistic fatigue and fracture behaviours based on small experimental data sets

This paper outlines a new technique to address the paucity of data in determining fatigue and fracture performances based on reliability concepts. Two new randomized models of time-dependent processes are presented for estimating the P–a–t and P–S–N curves, by using a randomization approach of deterministic equations, dealing with small sample numbers of data. The confidence level formulations for these curves are also given. The concepts are then applied for the determination of the P–a–t and P–S–N curves. Two sets of fatigue and fracture tests for these curves are conducted to validate the presented method, demonstrating the practical use of the proposed technique.     

Fracture toughness and fatigue life of MWCNT/epoxy composites

The present work experimentally characterizes the mode-I fracture toughness and stress–life curve of multi-walled carbon nanotube-(MWCNT-)reinforced epoxy-matrix composites. The effects of carbon nanotube weight fraction and voids on the composite fracture toughness are studied. The average fracture toughness of 1 wt%- and 3 wt%-MWCNT/epoxy composites is 1.29 and 1.62 times of that of pure epoxy, respectively. The 0.5 wt%-MWCNT/epoxy composites’ fatigue lives are 10.5 and 9.3 times of the average fatigue life of neat epoxy, when they are subjected to cyclic loadings with stress amplitudes of 8.67 MPa and 11.56 MPa, respectively. The micrographs indicate that the separation and uniform distribution of MWCNTs in the matrix and the formation of voids significantly affect the fracture and fatigue behavior of MWCNT-reinforced composites.     

A progressive fracture model for carbon nanotubes

An atomistic-based progressive fracture model for simulating the mechanical performance of carbon nanotubes by taking into account initial topological and vacancy defects is proposed. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space-frame structures. The finite element method is used to analyze the nanotube structure and the modified Morse interatomic potential to simulate the non-linear force field of the C–C bonds. The model has been applied to defected single-walled zigzag, armchair and chiral nanotubes subjected to axial tension. The defects considered were: 10% weakening of a single bond and one missing atom at the middle of the nanotube. The predicted fracture evolution, failure stresses and failure strains of the nanotubes correlate very well with molecular mechanics simulations from the literature.     

Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

Critical review on the assessment of fatigue and fracture in composite materials and structures

This paper provides a critical review of common approaches to assess fatigue and fracture in composite materials and structures. It explains how fatigue in composite materials and structures should be understood based on the observed fatigue phenomena and mechanisms. In relation to these phenomena, the selection of proper similitude conditions for predictions is discussed and it is explained how mechanistic models can be developed that describe fatigue damage growth in its sequence from first initiation to final failure. An explanation is given for the fact that these mechanistic damage growth approaches have not yet led to suitable prediction models. In addition, this paper illustrates that in-depth understanding of individual damage mechanics may pave the road towards further material optimization with respect to fatigue and durability.     

Proposed fatigue damage measurement parameter for shot-peened carbon steel based on fatigue crack growth behavior

A new technique for evaluating fatigue-damage accumulation in shot-peened (SP) carbon steel based on variations in residual stress is proposed. Using findings from previous studies, a fatigue damage parameter for a material treated with SP based on the change in induced compressive residual stress (CRS) is examined. A plastic replica method with the focused ion beam (FIB) technique is used to assess the relationship between the residual stress state and the fatigue crack growth (FCG) behavior of SP specimens over the fatigue lifespan. It is found that the residual stress relaxation phenomenon can be used as an effective parameter for determining the fatigue damage growth, provided the residual stress relaxation rate of each mechanical load and the critical threshold relaxation boundary of each material is known.     

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered.     

Synthesis of carbon nanostructures by graphite deformation during mechanical milling in air

Abstract

In this investigation, time-dependent carbon nanostructures were prepared by high-energy ball milling in the air from elemental graphite powders. Scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectroscopy (RS), and high-resolution transmission electron microscopy (HRTEM) characterized the ball-milled powders. XRD analysis showed that the crystal size decreased with the milling time. Raman spectra confirmed the presence of carbon nanostructures with sp² hybridization. Meanwhile, HRTEM images revealed different carbon morphologies during the milling time. During the different stages, it appears distortion of layers, large tapes, polyhedral morphologies, nanocapsules, and nano-onions. These carbon nanostructures occur in regions where there is carbon accumulation. In this way, the ball milling process in air conditions can promote distorted carbon and different morphologies.     

Carbon nanofibers enhance the fracture toughness and fatigue performance of a structural epoxy system

This study investigates the monotonic and dynamic fracture characteristics of a discontinuous fiber reinforced polymer matrix. Specifically, small amounts (0-1 wt.%) of a helical-ribbon carbon nanofiber (CNF) were added to an amine cured epoxy system. The resulting nanocomposites were tested to failure in two modes of testing; Mode I fracture toughness and constant amplitude of stress tension-tension fatigue. Fracture toughness testing revealed that adding 0.5 and 1.0 wt.% CNFs to the epoxy matrix enhanced the resistance to fracture by 66% and 78%, respectively. Fatigue testing at 20 MPa peak stress showed a median increase in fatigue life of 180% and 365% over the control by the addition of 0.5 and 1.0 wt.% CNF, respectively. These results clearly demonstrate the addition of small weight fractions of CNFs to significantly enhance the monotonic fracture behavior and long-term fatigue performance of this polymer. A discussion is presented linking the two behaviors indicating their interdependence and reliance upon the stress intensity factor, K.     

Microscopic characterization of hydrogen-induced quasi-brittle fatigue fracture in low-strength carbon steel

The microscopic feature of hydrogen-induced quasi-brittle fatigue fracture in low-strength carbon steel was investigated by transmission electron microscopy and electron backscatter diffraction. These analyses, aided also by fractography, explicitly revealed the following points; i) brittle striation is formed by extensive slip at the crack tip, ii) quasi-brittle facet is not crystallographically related to the {100} cleavage plane, and iii) crack growth process is stable. These results may suggest that the crack growth, despite its brittle appearance, is essentially a combined process of extensive slip and significantly localized ductile cracking, which is distinct from the normal slip-off growth mechanism.     

A plastic fracture mechanics model for characterization of multiaxial low-cycle fatigue

The near-tip stress and strain fields of small cracks in power-law hardening materials are investigated under plane-stress, general yielding, and mixed mode I and II conditions by finite element analyses. The characteristics of the near-tip strain fields suggest that the experimental observations of shallow surface cracks (Case A cracks) propagating in the maximum shear strain direction can be explained by a fracture mechanics crack growth criterion based on the maximum effective strain of the near-tip fields for small cracks under general yielding conditions. The constant effective stress contours representing the intense straining zones near the tip are also presented. The results of the J integral from finite element analyses are used to correlate to a fatigue crack growth criterion for Case A cracks. Based on the concept of the characterization of fatigue crack growth by the cyclic J integral, the trend of constant J contours on the Γ-plane for Case A cracks compares well with those of constant fatigue life and constant crack growth rate obtained from experiments.     

Effect of fiber bridging on the fatigue crack propagation in carbon fiber-reinforced aluminum laminates

A superior crack propagation resistance was observed on various carbon fiber-reinforced aluminum laminates (CARALL) under tension-tension fatigue. It might be attributed to the restraint on the crack opening imposed by intact fibers in the crack wake. These fibers bridging the crack could reduce the effective stress intensity factor actually experienced by the crack tip. Based on the measurement of crack length and delamination size, the effective stress intensity range, ΔK_eff, of fatigue-damaged CARALL laminate was calculated by using a simplified analytical model. It was shown that the fatigue crack propagation rate in CARALL could be expressed as a unique function of the calculated ΔK_eff, which agree well with the Paris equation for the unreinforced aluminum alloy. This result confirmed the applicability of this simplified analytical model in CARALL laminates.     

Effect of matrix sub-layer interfacial fracture on residual strength improvement of the fatigued carbon/carbon composites

In the present study, flexural behavior of carbon fiber reinforced pyrolytic carbon matrix composites (C/C composites) before and after fatigue tests had been studied. The results showed that the residual flexural strengths of the samples had been improved after fatigue tests, and the fracture mechanisms of the original and post-fatigue specimens had some differences. Fracture mechanism of the original specimens could be described as fiber/matrix interfacial de-bonding, and the dominant damage of the post-fatigue specimens could be regarded as pyrolytic carbon sub-layers’ step-delamination. The degradation of matrix sub-layer interfacial bonding strength was beneficial to improve the mechanical properties of C/C composites.     

Estimating probabilistic fatigue of Nitinol with scarce samples

Current work estimates probabilistic fatigue life efficiently with scarce samples. The underlying idea of the estimation is to approximate the cumulative distribution function of the fatigue life in a transformed space using a third order polynomial subject to monotonicity constraint. The variations associated with the estimated quantiles are quantified using bootstrap. The proposed approach is validated on a data obtained from literature. It is observed that the life quantiles with reasonable accuracy can be estimated even with 10 samples. Finally, the probabilistic fatigue of Nitinol in austenitic condition is obtained with limited experiments.