Obtaining S–N curves from crack growth curves: an alternative to self-similarity

A crack growth model that allows us to obtain the S–N curves from the crack growth rate curves is presented in an attempt to harmonize the stress based and fracture mechanics approaches in lifetime prediction of long cracks propagation. First, using the Buckingham theorem, the crack growth rate curve $\frac{da}{dN}-\varDelta K$ is defined over all its range as a cumulative distribution function based on a normalized dimensionless stress intensity factor range $\varDelta K^+$ . Then, a relevant theorem is derived that provides an alternative to self-similarity allowing significant reduction of experimental planning. In this way, different $a-N$ crack growth curves for different stress ranges $\varDelta \sigma $ and initial crack lengths $a_0$ can be obtained from a particular crack growth curve under some conditions. The S–N field is obtained from the crack growth curves, showing the close relation between the fracture mechanics and stress approaches. Finally, the model is applied to a particular set of experimental data to obtain the crack growth rate curve and the S–N curves of a certain material for a subsequent fatigue lifetime assessment     

Probabilistic model of fatigue crack propagation and estimation of probability-confidence bounded a–N curves

The fatigue crack growth model is expressed as a function of mechanical properties. The uncertainties associated with the crack growth process are incorporated assuming them as random variable following a statistical distribution. The effect of material nonhomogeneity is included in the model through a random process parameter of Gaussian type. Assuming fatigue life as a random variable, probability-confidence bounded mean crack growth relation is developed and an algorithm is presented. The model is validated through the experimental and predicted results from several data sets.     

Size effect in S–N curves: A fractal approach to finite-life fatigue strength

It has experimentally been observed that the finite-life fatigue strength of metallic materials in the high-cycle regime decreases with increasing the specimen size. In the present paper, such a decrease is explained by considering the fractal nature of the reacting cross-sections of structures. Accordingly, the so-called fractal (or renormalized) fatigue strength is represented by a force amplitude acting on a surface with a fractal dimension lower than 2, where such a dimensional decrement depends on the presence of heterogeneity, cracks, defects, voids, etc. in the material ligament. Moreover, it is shown that this decrement tends to progressively diminish with increasing the structure size. Two scaling laws (monofractal and multifractal, respectively) for the finite-life fatigue strength of metals are proposed, and some experimental results are examined to show how to apply such a theoretical fractal approach.     

A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys

A numerical analysis using cohesive zone model under cyclic loading is proposed to develop a coupled predictive approach of crack growth in single crystal. The process of material damage during fatigue crack growth is described using an irreversible cohesive zone model, which governs the separation of the crack flanks and eventually leads to the formation of free surfaces. The cohesive zone element is modeled to accumulate fatigue damage during loadings and no damage during unloadings. This paper presents the damage model and its application in the study of the crack growth for precracked specimens. The use of cohesive zone approach is validated through a convergence study. Then, a general procedure of parameters calibration is presented in pure fatigue crack growth. In the last section, an extension of the cohesive zone model is presented in the case of creep–fatigue regime at high temperature. The model showed its capability to predict with a good agreement the crack growth in the case of complex loading and complex specimen geometries.     

A dislocation barrier model for fatigue limit – as determined by crack non-initiation and crack non-propagation

Fatigue damage is caused by cyclic slip, and cyclic slip is driven by dislocation glide force. In order to cause fatigue damage, the cyclic glide force has to overcome the resistance of the primary and secondary dislocation barriers. Based on this cyclic damage process, the following diverse fatigue phenomena are synthesized into an integral and self-consistent analysis: Fatigue damage occurs in persistent slip bands (Hempel, 1956; Smith, 1957; Forsyth, 1957, 1961, 1963), and a nucleated fatigue micro crack is a shear crack (Forsyth, 1961). Pre-cracking fatigue damage is confined to the surface layer of a stressed metal (Wood et al., 1963). Fatigue limit is inversely related to grain size as shown in brass (Sinclair and Craig, 1952), in mild steels (Klesnil, Holzmann, Lukáš and P. Ryš 1965; Yoshikawa and Sugeno, 1965; and Taira, Tanaka, and Hoshina, 1979), and in ferritic-martensitic steel, (Kunio, Shimizu, and Yamada, 1969). Forrest and Tate (1964) found fatigue cracks in fine-grained brass at an alternating stress even below the fatigue limit. The cracks were within the boundaries of single grains. But they found no cracks in coarse-grained brass below the fatigue limit. The analysis synthesizes all of these experimental observations. The analysis is based on a realistic physical model. With a better understanding of the model and an improved calculation of the glide force, quantitative evaluations of the resistance of the dislocation barriers would eventually be possible. The needs for additional research are pointed out. A number of means of improving fatigue strength, based on the analysis, are suggested or explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimating S–N curves and their scatter using a differential ant-stigmergy algorithm

We present an alternative approach to the rapid estimation of S–N curves and their scatter. A simultaneous estimation of the S–N curve and its scatter is achieved by applying a two-parametric Weibull distribution to describe the scatter of a number of load cycles to failure at an arbitrary amplitude stress level. The shape of the S–N curve is generally modelled as a linear dependence between the logarithmic value of the number of load cycles to failure and the logarithmic value of the amplitude stress level. This dependence is described by two parameters: a constant term and a scale coefficient of the S–N curve in a log-log scale. Therefore, the same formulation was applied to model the dependence between a scale parameter of the Weibull distribution and the logarithmic value of the amplitude stress level. In this manner the S–N curve and its scatter are described by three parameters: the constant term, the scale coefficient and the shape parameter of the Weibull distribution. The three parameters are estimated with a differential ant-stigmergy algorithm from the experimental data. In the article a mathematical background of the approach is presented and applied to three cases of experimentally obtained durability data. The results are analysed and discussed.     

A graphic approach to draw the S‐curves for the symbol synchronizers

Abstract

The characteristics of the S‐curve in a symbol (bit) synchronizer are important in evaluating the timing‐variance performance. However, the calculation of S‐curve is so tedious and complicated that almost all the S‐curves in the literature are drawn by computer simulations. A simple and quick graphic approach to draw the S‐curve for a symbol synchronizer is proposed in this paper, which can provide exactly the same S‐curve as that with the conventional method for high SNR case.     

Investigating environmental effects on small fatigue crack growth in Ti–6242S using combined ultrasonic fatigue and scanning electron microscopy

In situ ultrasonic fatigue with a cyclic frequency of 20 kHz was employed in an environmental scanning electron microscope (ESEM) to characterize fatigue crack formation and growth in the near alpha titanium alloy Ti–6242S. The role of environment on small fatigue crack initiation and growth was investigated in vacuum and in variable pressures of saturated water vapor, as well as in laboratory air. Small crack growth behavior from cracks initiated at FIB-produced micro-notches indicated a significant environmental dependence, with fatigue crack growth rates increasing with increasing partial pressures of water vapor. Environment also influenced crack initiation lifetime in that cracks initiated earlier in laboratory air than in vacuum or saturated water vapor environments. Transgranular, crystallographic crack growth was observed in each environment, with the crack path in primary α grains producing facets parallel to basal planes when crack size was small. Small crack growth resistance had a marked sensitivity to microstructural features, such as α/α grain boundaries with high misorientation and α/α + β boundaries. These initial investigations demonstrate the usefulness of in situ ultrasonic fatigue instrumentation (UF-SEM) as a new tool for the characterization of environmental and microstructural influences on very high cycle fatigue (VHCF) behavior.     

Experimental investigation of surface crack initiation, propagation and tension stiffening in self-compacting steel–fibre-reinforced concrete

To investigate crack initiation and propagation in reinforced, self-compacting, steel?Cfibre-reinforced concrete (SCSFRC) members, tie elements were tested in tension. Strain and surface crack formation were monitored with an optical strain measurement system based on digital image correlation. In addition, to capture the softening behaviour (???Cw) of the material, uni-axial tension testing was performed on SCSFRC cylinders. The results show that, with the optical strain measurement system, it was possible to detect different cracking modes and to follow the crack growth. It was especially of interest to recognize that high fibre amounts tend to change a sudden opening of a crack (as in non-fibrous concrete) into a more stable procedure. It was found that, for a given crack width, the SCSFRC specimens exhibited a noticeably higher tension stiffening than the specimens without fibres. Moreover, at a given load, the crack widths decreased by as much as 65% for the SCSFRC specimens with a nominal fibre content of 1%. For the uni-axial tension tests the results showed that with higher fibre content, for this type of fibre and concrete, both the peak stress and the residual tensile stress were increased. Additionally, it was noted for both specimen types that the scatter in fibre distribution decreased with increasing fibre content.     

Deterministic surface tractions in rough contact under stick–slip condition: Application to fretting fatigue crack initiation

A robust approach for the deterministic prediction of pressure distribution in dry rough-line contact configuration considering the elastic-fully plastic asperity effects is presented. Adopting Civarella–Jager approach, a procedure for calculation of the tangential traction distribution for cyclic loading condition in stick–slip regime is also described in detail. The effect of surface roughness on the pressure and tangential traction distribution and sub-surface stress field is evaluated. To illustrate the utility of the approach, the crack initiation risk in a stick–slip (fretting) contact is investigated for different surface roughness values. The methodology is conceptually simple and can be easily implemented in a computer code.     

A design model and a production–distribution and inventory planning model in multi-product supply chain networks

Supply chain network (SCN) design implicates decision-making at a strategic level. That includes selecting the right suppliers and determining the number and the location of plants, distribution centres and retailers. An apt design model of the supply chain is imperative for the proper function of the supply chain and consequently for making better operational decisions in an attempt of a continuous improvement. In this paper, we propose two models. The first model is a mixed-integer linear programming model which is concerned with the SCN design problem, whereas the second operational model is a mixed-integer non-linear programming model in respect to the production–distribution and inventory planning problem in a supply chain network. The number of customers and suppliers as well as their demand and capacities are assumed to be known in both models. Two steady-state genetic algorithms were implemented in MATLAB in order to solve both the design and the operational model. The results were compared with GAMS. Some examples were devised in order to demonstrate potential ways of use for the designer of the supply chain network, as well as for the supply chain manager.     

A modified Zerilli–Armstrong constitutive model to predict hot deformation behavior of 20CrMo alloy steel

True stress and true strain values were obtained from isothermal hot compression tests conducted on a Gleeble thermal simulation machine, in a wide range of temperatures (1173–1373 K) and strain rates (1.5 × 10⁻³–1.5 × 10⁻² s⁻¹). The experimental data were used to develop a modified Zerilli–Armstrong constitutive model. The predicted flow stresses using the developed model were compared with experimental values. A correlation coefficient (R) of 0.989 and an average absolute relative error (AARE) of 7.71% between the measured and calculated flow stresses have been obtained. Comparing with a modified Johnson–Cook model developed in the authors’ previous study, the accuracy, the number of material constants involved and the computational time required of the model were evaluated.     

A mediated model on the adoption of social media and SMEs’ performance in developing countries

PurposeSmall and medium-sized enterprises (SMEs) can adopt and use social media (SM) for communicating information with stakeholders with minimal cost. The ability to access and share information influences the SMEs' performance, but there is little scholarship on the association between the adoption of social media and SMEs' performance. This research aims to investigate the effects of technology-organizational-environmental (TOE) factors on the adoption of SM and SMEs’ performance in developing countries.Design/methodology/approachThis study employed the TOE framework as determinants affecting the adoption of social media and SMEs' performance. The paper used a closed-ended questionnaire to gather data, through an online survey, from randomly selected respondents from SMEs operating in Pakistan. Partial-least-squares-structural-equation-modeling (PLS-SEM) was used for the path analysis of 423 responses from SMEs' owners, executives, and managers. The present study also explores the mediating role of SM between TOE characteristics and SMEs’ performance.FindingsThe findings revealed a direct positive relationship between TOE constructs, the adoption of SM, and SMEs' performance. Full mediation was found between technological factors and SMEs performance, and partial mediation was found between organizational and environmental factors and SMEs’ performance. Complementary mediation among the variables was also examined.Originality/valueThis paper has implications for practitioners and researchers interested in investigating social media adoption in SMEs. It builds an empirical, multi-dimensional hypothesized model, including several determinants that may influence the adoption of social media.     

Comparison of a linear and a non-linear model for using sensory–motor,cognitive, personality,and demographic data to predict driving ability in healthy older adults

This study compared the ability of binary logistic regression (BLR) and non-linear causal resource analysis (NCRA) to utilize a range of cognitive, sensory–motor, personality and demographic measures to predict driving ability in a sample of cognitively healthy older drivers.Participants were sixty drivers aged 70 and above (mean = 76.7 years, 50% men) with no diagnosed neurological disorder. Test data was used to build classification models for a Pass or Fail score on an on-road driving assessment. The generalizability of the models was estimated using leave-one-out cross-validation.Sixteen participants (27%) received an on-road Fail score. Area under the ROC curve values were .76 for BLR and .88 for NCRA (no significant difference, z = 1.488, p = .137). The ROC curve was used to select three different cut-points for each model and to compare classification. At the cut-point corresponding to the maximum average of sensitivity and specificity, the BLR model had a sensitivity of 68.8% and specificity of 75.0% while NCRA had a sensitivity of 75.0% and specificity of 95.5%. However, leave-one-out cross-validation reduced sensitivity in both models and particularly reduced specificity for NCRA.Neither model is accurate enough to be relied on solely for determination of driving ability. The lowered accuracy of the models following leave-one-out cross-validation highlights the importance of investigating models beyond classification alone in order to determine a model's ability to generalize to new cases.     

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.     

A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

The most commonly used dose–response models implicitly assume that accumulation of dose is a time-independent process where each pathogen has a fixed risk of initiating infection. Immune particle neutralization of pathogens, however, may create strong time dependence; i.e. temporally clustered pathogens have a better chance of overwhelming the immune particles than pathogen exposures that occur at lower levels for longer periods of time. In environmental transmission systems, we expect different routes of transmission to elicit different dose–timing patterns and thus potentially different realizations of risk. We present a dose–response model that captures time dependence in a manner that incorporates the dynamics of initial immune response. We then demonstrate the parameter estimation of our model in a dose–response survival analysis using empirical time-series data of inhalational anthrax in monkeys in which we find slight dose–timing effects. Future dose–response experiments should include varying the time pattern of exposure in addition to varying the total doses delivered. Ultimately, the dynamic dose–response paradigm presented here will improve modelling of environmental transmission systems where different systems have different time patterns of exposure.     

Magnetite particle surface attrition model in dense phase gas–solid fluidized bed for dry coal beneficiation

Dense-phase high-density fluidized bed has received considerable attention worldwide due to the urgent need for an efficient dry separation technology. This study on magnetite particle attrition model and size distribution change rule in a dense-phase gas–solid fluidized bed for dry beneficiation analyzes the complex process of magnetite particle attrition and fine particle generation. A model of magnetite particle attrition rate is established, with the particle attrition rate leveling off gradually with the attrition time in the dense-phase gas–solid fluidized bed. Magnetite particle attrition in the dense-phase gas–solid fluidized bed is consistent with Rittinger’s surface theory, where the change in surface area of magnetite particles is proportional to the total excess kinetic energy consumed and the total attrition time. An attrition experiment of magnetite particles is conducted in a laboratory-scale dense-phase gas–solid fluidized bed for dry beneficiation.     

Evaluation of crack growth behavior and probabilistic S–N characteristics of carburized Cr–Mn–Si steel with multiple failure modes

The unexpected failures of case-hardened steels in long life regime have been a critical issue in modern engineering design. In this study, the failure behavior of a carburized Cr–Mn–Si steel under very high cycle fatigue (VHCF) was investigated, and a model for evaluating the probabilistic S–N curve associated with multiple failure modes was developed. Results show that the carburized Cr–Mn–Si steel exhibits three failure modes including the surface flaw-induced failure, the interior inclusion-induced failure without the fine granular area (FGA) and the interior inclusion-induced failure with the FGA. As the predominant failure mode in the VHCF regime, the interior failure process can be divided into four stages: (i) the small crack growth around the inclusion, (ii) the stable macroscopic crack growth outside the FGA, (iii) the unstable crack growth outside the fish-eye and (iv) the momentary fracture outside the final crack growth zone. The threshold values are successively evaluated to be 2.33 MPa m^1/2, 4.13 MPa m^1/2, 18.51 MPa m^1/2 and 29.26 MPa m^1/2. The distribution characteristics of the test data in transition failure region can be well characterized by the mixed two-parameter Weibull distribution function. The developed probabilistic S–N curve model is in good agreement with the test data with multiple failure modes. Although the result is somewhat conservative in the VHCF regime, it is acceptable for safety considerations.     

A Gauss–Newton full-waveform inversion for material profile reconstruction in viscoelastic semi-infinite solid media

An inversion framework employing a Gauss–Newton method is developed to reconstruct material profiles in heterogeneous, viscoelastic, semi-infinite domains. In particular, a full-waveform inversion approach is investigated to image the elastic and attenuating parameters of a layered media. To account for the viscoelasticity of the medium, a Generalized Maxwell Body with one spring and two Maxwell elements in parallel (GMB2) is adopted in the forward and inverse wave propagation problems. Perfectly-matched-layers were introduced as wave absorbing buffers to simulate the semi-infinite extent of the domain. Using transient wave equations endowed with the GMB2 constitutive relation and the PML, a partial-differential-equations-constrained optimization scheme was implemented that lead to classic KKT (Karush–Kuhn–Tucker) conditions including time-dependent state, adjoint, and time-invariant control problems. An optimal solution of the viscoelastic parameters was obtained using a reduced-space approach based on a line search algorithm where the search direction was computed by the Gauss–Newton method. Considerable improvements on the accuracy and convergence rate of solutions were made by the developed Gauss–Newton inversion procedure compared to previous research using the Fletcher–Reeves method.