Micromechanics Of Fatigue Crack-Growth At Low Stress Intensities In A High-Strength Steel

An attempt to systematically investigate the effects of microstructural parameters in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels has been made for a high strength low alloy steel to observe in general, widely different trends in the dependence of both the total threshold stress intensity range, DELTA-K(th) and the intrinsic or effective threshold stress intensity range, DELTA-K(eff-th) on the prior austenitic grain size (PAGS). While a low strain hardening microstructure obtained by tempering at high temperatures exhibited strong dependence of DELTA-K(th) on the PAGS by virtue of strong interactions of crack tip slip with the grain boundary, a high strength, high strain hardening microstructure as a result of tempering at low temperature exhibited a weak dependence. The lack of a systematic variation of the near-threshold parameters with respect to grain size in temper embrittled structures appears to be related to the wide variations in the amount of intergranular fracture near threshold. Crack closure, to some extent provides a basis on which the increases in DELTA-K(th) at larger grain sizes can be rationalised. This study, in addition, provides a wide perspective on the relative roles of slip behaviour embrittlement and environment that result in the different trends observed in the grain size dependence of near-threshold fatigue parameters, based on which the inconsistency in the results reported in the literature can be clearly understood. Assessment of fracture modes through extensive fractography revealed that prior austenitic grain boundaries are effective barriers to cyclic crack growth compared to martensitic packet boundaries, especially at low stress intensities. Fracture morphologies comprising of low energy flat transgranular fracture can occur close to threshold depending on the combinations of strain hardening behaviour, yield strength and embrittlement effects. A detailed consideration is given to the discussion of cyclic stress strain behaviour, embrittlement and environmental effects and the implications of these phenomena on the crack growth behaviour near threshold.

Learning Challenges in Biogas Production for Sustainability : An activity theoretical study of a network from a swine industry chain

This study is about the challenges of learning in the creation and implementation of new sustainable technologies. The system of biogas production in the Programme of Sustainable Swine Production (3S Programme) conducted by the Sadia food processing company in Santa Catarina State, Brazil, is used as a case example for exploring the challenges, possibilities and obstacles of learning in the use of biogas production as a way to increase the environmental sustainability of swine production. The aim is to contribute to the discussion about the possibilities of developing systems of biogas production for sustainability (BPfS). In the study I develop hypotheses concerning the central challenges and possibilities for developing systems of BPfS in three phases. First, I construct a model of the network of activities involved in the BP for sustainability in the case study. Next, I construct a) an idealised model of the historically evolved concepts of BPfS through an analysis of the development of forms of BP and b) a hypothesis of the current central contradictions within and between the activity systems involved in BP for sustainability in the case study. This hypothesis is further developed through two actual empirical analyses: an analysis of the actors senses in taking part in the system, and an analysis of the disturbance processes in the implementation and operation of the BP system in the 3S Programme. The historical analysis shows that BP for sustainability in the 3S Programme emerged as a feasible solution for the contradiction between environmental protection and concentration, intensification and specialisation in swine production. This contradiction created a threat to the supply of swine to the food processing company. In the food production activity, the contradiction was expressed as a contradiction between the desire of the company to become a sustainable company and the situation in the outsourced farms. For the swine producers the contradiction was expressed between the contradictory rules in which the market exerted pressure which pushed for continual increases in scale, specialisation and concentration to keep the production economically viable, while the environmental rules imposed a limit to this expansion. Although the observed disturbances in the biogas system seemed to be merely technical and localised within the farms, the analysis proposed that these disturbances were formed in and between the activity systems involved in the network of BPfS during the implementation. The disturbances observed could be explained by four contradictions: a) contradictions between the new, more expanded activity of sustainable swine production and the old activity, b) a contradiction between the concept of BP for carbon credits and BP for local use in the BPfS that was implemented, c) contradictions between the new UNFCCC1 methodology for applying for carbon credits and the small size of the farms, and d) between the technologies of biogas use and burning available in the market and the small size of the farms. The main finding of this study relates to the zone of proximal development (ZPD) of the BPfS in Sadia food production chain. The model is first developed as a general model of concepts of BPfS and further developed here to the specific case of the BPfS in the 3S Programme. The model is composed of two developmental dimensions: societal and functional integration. The dimension of societal integration refers to the level of integration with other activities outside the farm. At one extreme, biogas production is self-sufficient and highly independent and the products of BP are consumed within the farm, while at the other extreme BP is highly integrated in markets and networks of collaboration, and BP products are exchanged within the markets. The dimension of functional integration refers to the level of integration between products and production processes so that economies of scope can be achieved by combining several functions using the same utility. At one extreme, BP is specialised in only one product, which allows achieving economies of scale, while at the other extreme there is an integrated production in which several biogas products are produced in order to maximise the outcomes from the BP system. The analysis suggests that BP is moving towards a societal integration, towards the market and towards a functional integration in which several biogas products are combined. The model is a hypothesis to be further tested through interventions by collectively constructing the new proposed concept of BPfS. Another important contribution of this study refers to the concept of the learning challenge. Three central learning challenges for developing a sustainable system of BP in the 3S Programme were identified: 1) the development of cheaper and more practical technologies of burning and measuring the gas, as well as the reduction of costs of the process of certification, 2) the development of new ways of using biogas within farms, and 3) the creation of new local markets and networks for selling BP products. One general learning challenge is to find more varied and synergic ways of using BP products than solely for the production of carbon credits. Both the model of the ZPD of BPfS and the identified learning challenges could be used as learning tools to facilitate the development of biogas production systems. The proposed model of the ZPD could be used to analyse different types of agricultural activities that face a similar contradiction. The findings could be used in interventions to help actors to find their own expansive actions and developmental projects for change. Rather than proposing a standardised best concept of BPfS, the idea of these learning tools is to facilitate the analysis of local situations and to help actors to make their activities more sustainable.

Differentiation of embryoids and plantlets from shoot callus of sandalwood

Callus cultures of sandalwood (Santalum album L.) were established from shoot segments and shoot tips of trees over 20 years old. Shoots were induced directly from shoot tip callus, while in shoot segments embryoids developed from the callus within 4 weeks after subculturing on to a medium supplemented with gibberellic acid (GA). Embryoids of 4–5 mm were transferred to basal medium or basal medium supplemented with low concentrations of auxin showed plantlet development.

Breakup of drops around the edges of Rushton turbine

A detailed experimental and simulation study has been carried out in the present work to understand drop breakup in regions around the edge of the Rushton turbine in agitated vessels. The effect of impeller speed, impeller size, interfacial tension, and the viscosities of the two phases is studied on drop breakup through their effect on dmax, the size of the largest drop in the system, and the whole size distribution. The measurements were carried out using Galai particle size analyser and optical microscope. Experimental analysis shows that the dmax, maximum stable drop diameter varies with impeller tip velocity to the power -1. The variation of dmax with interfacial tension is studied using different surfactants. The effect of viscosity ratio, achieved by changing the dispersed phase viscosity, on dmax is captured. For the same dmax values obtained from two different dispersed phases show that the wider drop size distribution is observed for higher dispersed phase viscosity.

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.

Influence of strain softening on the fracture of plain concrete beams

Fracture behaviour of notched and un-notched plain concrete slender beams subjected to three-point or four-point bending is analyzed through a one-dimensional model, also called Softening Beam Model. Fundamental equations of equilibrium are used to develop the model. The influence of structural size in altering the fracture mode from brittle fracture to plastic collapse is explained through the stress distribution across the uncracked ligament obtained by varying the strain softening modulus. It is found that at the onset of fracture instability, stress at the crack tip is equal to zero. The maximum load and fracture load are found to be different and a unique value for the fracture load is obtained. It is shown that the length of the fracture process zone depends on the value of the strain softening modulus. Theoretical limits for fracture process zone length are also calculated. Several nonlinear fracture parameters, such as, crack tip opening displacement, crack mouth opening displacement and fracture energy are computed for a wide variety of beam specimens reported in the literature and are found to compare very well with experimental and theoretical results. It is demonstrated that by following a simple procedure, both pre-peak and post-peak portions of load versus crack mouth opening displacement curve can be obtained quite accurately. Further, a simple procedure to calculate the maximum load is also developed. The predicted values of maximum load are found to agree well with the experimental values. The Softening Beam Model (SBM), proposed in this investigation is very simple and is based on rational considerations. It can completely describe the fracture process from the beginning of formation of the fracture process zone till the onset of fracture instability.A l'aide d'un modèle unidimensionnel dit ldquoSoftening Beam Modelrdquo (SBM), on analyse le comportement à rupture de poutres élancées pleines entaillées ou non, soumises en flexion en trois ou quatre points. Des équations fondamentales d'équilibre sont utilisées pour développer le modèle. On explique l'influence de la taille du composant sur l'altération du mode de rupture en rupture fragile et en effondrement plastique par la distribution par la distribution des contraintes sur le ligament non fissuré lorsque varie le module d'adoucissement. On trouve que la contrainte à l'extrémité de la fissure est nulle est nulle au début de l'instabilité de la rupture. La charge maximum et la charge à la rupture sont trouvées différentes, et on obtient une valeur unique de la charge à la rupture. On montre que la longueur de la zone concernée par le processus de rupture d'pend de la valeur du module d'adoucissement. On calcule également les limites théoriques de longueur de cette zone. Divers paramètres de rupture non linéaire sont calculés pour une large gamme d'éprouvettes en poutres reprises dans la littérature; on trouve qu'il existe une bonne concordance avec les résultats expérimentaux et théoriques. On démontre qu'en suivant une procédure simple on peut obtenir avec une bonne précision la courbe reliant les portions avant et après le pic de sollicitation en fonction du COD de la fissure. En outre, on développe une procédure simple pour calculer la charge maximum. Les valeurs prédites sont en bon accord avec les valeurs expérimentales. Le modèle SBM proposé est très simple et est basé sur des considérations rationnelles. Il est susceptible de décrire complètement le processus de rupture depuis le début de la formation de la zone intéressée jusqu'à l'amorçage de la rupture instable.

Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK th , and the intrinsic threshold stress intensity range, ΔK eff, th , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK th and ΔK eff, th on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK th and ΔK eff, th on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔKth and ΔKeff, th with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure.

A new model for coalescence efficiency of drops in stirred dispersions

A model for coalescence efficiency of two drops embedded in an eddy has been developed. Unlike the other models which consider only head-on collisions, the model considers the droplets to approach at an arbitrary angle. The drop pair is permitted to undergo rotation while they approach each other. For coalescence to occur, the drops are assumed to approach each other under a squeezing force acting over the life time of eddy but which can vary with time depending upon the angle of approach. The model accounts for the deformation of tip regions of the approaching drops and, describes the rupture of the intervening film, based on stability considerations while film drainage is continuing under the combined influence of the hydrodynamic and van der Waals forces. The coalescence efficiency is defined as the ratio of the range of angles resulting in coalescence to the total range of all possible approach angles. The model not only reconciles the contradictory predictions made by the earlier models based on similar framework but also brings out the important role of dispersed-phase viscosity. It further predicts that the dispersions involving pure phases can be stabilized at high rps values. Apart from explaining the hitherto unexplained experimental data of Konno et al. qualitatively, the model also offers an alternate explanation for the interesting observations of Shinnar.

Fracture Properties of Concrete-Concrete Interfaces Using Digital Image Correlation

The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete-concrete jointed interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement, crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis matches well with those measured experimentally.

A general procedure for modified crack closure integral in 3D problems with cracks

In linear elastic fracture mechanics (LEFM), Irwin's crack closure integral (CCI) is one of the signficant concepts for the estimation of strain energy release rates (SERR) G, in individual as well as mixed-mode configurations. For effective utilization of this concept in conjunction with the finite element method (FEM), Rybicki and Kanninen [Engng Fracture Mech. 9, 931 938 (1977)] have proposed simple and direct estimations of the CCI in terms of nodal forces and displacements in the elements forming the crack tip from a single finite element analysis instead of the conventional two configuration analyses. These modified CCI (MCCI) expressions are basically element dependent. A systematic derivation of these expressions using element stress and displacement distributions is required. In the present work, a general procedure is given for the derivation of MCCI expressions in 3D problems with cracks. Further, a concept of sub-area integration is proposed which facilitates evaluation of SERR at a large number of points along the crack front without refining the finite element mesh. Numerical data are presented for two standard problems, a thick centre-cracked tension specimen and a semi-elliptical surface crack in a thick slab. Estimates for the stress intensity factor based on MCCI expressions corresponding to eight-noded brick elements are obtained and compared with available results in the literature.

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

Cracks emanating from pin-loaded lugs

Pin-loaded lugs were analysed in the presence of cracks emanating from circular holes. The analysis presents a unified treatment of interference, push or clearance fit pins. Both metallic (isotropic) and composite (orthotropic) plates were dealt with. The finite element model used special singular six-noded quadrilateral elements at the crack tip. The non-linear load contact behaviour at the pin-hole interface was dealt with by an inverse technique. A modified crack closure integral (MCCI) technique was used to evaluate the strain energy release rates (SERRs) and stress intensity factors (SIFs) at the crack tips. Numerical results are presented showing the non-linear variation of SIF with applied stress, and the influence of the amount of interference or clearance and the interfacial friction on SIF.

Modified Crack Closure Integral (MCCI) For 3-D Problems Using 20-Noded Brick Elements

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

Modified crack closure integral (MCCI) for 3-d problems using 20 noded brick elememnts

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.