Treatment of singularities in cracked bodies

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems

Association and path coefficient analysis among yield attributes and berry yield in black pepper (Piper nigrum L.)

Eighty two germplasm accessions of black pepper aggregated from pepper cultivating tracts of Karnataka, Kerala, Goa and Maharashtra were characterized for 17 quantitative traits as per the IPGRI descriptors during 2018-19 at the field gene bank of ICAR-Indian Institute of Spices Research, Experimental Farm, Kozhikode. Wide range and high coefficient of variation (CV) were recorded for dry berry weight, fresh berry weight and number of spikes vine-1 whereas, lower CV was observed for berry size. Fresh berry weight showed significant positive correlation with dry berry weight followed by number of spikes vine-1 whereas, number of immature berries spike-1 and berry size showed significant negative association with setting percentage. High positive direct effect of fresh berry weight on dry berry weight was observed during path analysis. Both fresh rachis weight and number of spike vine-1 had indirect positive effects on dry berry weight through fresh berry weight. Residual effect was meagre suggesting that the 17 quantitative traits explained 99% variability. Traits like number of spikes vine-1 and fresh berry weight are the important traits that need to be augmented during improvement of black pepper for yield

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method

Impact of nontariff measures on the exports of the beverage sector in India

In the recent past, agricultural exports, especially plantation crops, which are the backbone of India, have been subjected to many nontariff measures. Since the liberalisation of trade has led to the integration of global commodity markets, developing countries are significantly affected by these trade barriers, which indirectly hurt millions of plantation community. Traditionally, India is well known for its exports of beverages and stringent maximum residual limits, traceability issues, and food safety standards are complex issues surmounting trade in the plantation sector around the world. Hence, the present research study attempts to find the shock of nontariff measures on the prices of both export and domestic beverages and the hammering in returns to the Indian beverage industry by the partial equilibrium method. This model directly measures the simulation effect of nontariff measures by imposing NTM on tea and coffee sector.  It is obvious that as the NTM percent increases from 10 percent to 25 percent on tea sector, the loss in export quantity was more from 22.24 million kg to 55.61 million kg and loss of revenue was from Rs. 2997 million to Rs. 7492 million for the corresponding NTMs. Likewise the loss in export quantity (62.85 million kg) and loss in revenue (Rs. 9412 million) were high in 25 per cent of NTM. The present study shows how to allow for market imperfections and trade facilitating effects of nontariff measures in the beverage sector.

Multiplier Based On Add And Shift Method By Passing Zero

In this paper, a low-power structure for shift-and-add multipliers is proposed. The architec-ture considerably lowers the switching activity of conventional multipliers. The modification to the multiplier which multiplies A by B include the removal of the shifting register, direct feeding of A to the adder, bypassing the adder whenever possible, using a ring counter instead of a binary counter and removal of the partial product shift. The architecture makes use of a low-power ring counter proposed in this work . The proposed multiplier can be used for low-power applications where the speed is not a primary design parameter

Characterisation and Liberation of Graphite Schist

This paper deals with the characterisation and liberation studies of graphite schist from Shivaganga, Tamilnadu. The graphite flakes are interbanded with quartz and calcite. Secondary calcite veins often traverses graphite flakes and quartz grains. Based on grain counting, frequency curves , comminution followed by flotation tests , the liberation size of graphite is estimated between 150to 90 microns. Therougher concentrate achieved at d&, passing of 145 micron size product contain 35 % FC with 99% recovery.The SFM study reveals the presence of minute inclusions of calcite and quartz within graphite flakes

A fiber-resin micromechanics analysis of the delamination front in a DCB specimen

A 3-D finite element model was developed to analyze the fiber-resin behavior near the delamination front in a graphite-epoxy double cantilever beam (DCB) specimen. The specimen interior was analyzed using a typical one-fiber slice, represented by a local 3-D fiber-resin model. The resin stresses were computed for the resin-rich layer at the ply interface as well as for the regions between the fibers close to the delamination front. However, the computed strain energy release rate G sub I along the delamination front varied by less than two percent, and was within about four percent of the plane-strain value. The von Mises yield criterion was used to estimate the extent of yielding near the delamination front. The yielding extended ahead of the delamination and also developed between the fibers. Although the fibers had only a negligible effect on G sub I, they caused yielding within the ply and therefore could influence delamination fracture toughness. The normal and shear stresses at the fiber-resin interface were computed near the delamination front. These results suggest that multi-axial stress criteria may be required to analyze fiber-resin interfaces

Factors influencing elastic stresses in double cantilever beam specimens

An elastic stress analysis was conducted for a double cantilever beam (DCB) specimen using finite-element methods. The purpose of this study was to identify the important parameters that influence stresses ahead of the delamination front. The study focused on an aluminum DCB specimen, typical of adhesively-bonded joints, and on a graphite/epoxy specimen representing a cocured composite. Opening mode sigma sub y stresses ahead of the crack tip were calculated and compared with those for a monolithic reference specimen. Beyond the singularity-dominated region very near the crack tip, the sigma sub y distribution was elevated compared to the monolithic case. Both the adhesive thickness and the adherend transverse (thickness-direction) stiffness were found to influence the elevation of sigma sub y. In contrast, adherend thickness and longitudinal stiffness has very little effect on this stress distribution. Estimates for adhesive yielding beyond the aluminum DCB crack tip showed that both the area and height of the plastic zone increased to a peak value for increasing adhesive thicknesses. Results from this study would provide insight for comparing data from different DCB specimens and for designing new DCB specimens