Engineering topics

Raju, I. S.

Publications and source records attributed to Raju, I. S..

At least 55 records · Page 3

NASA NTRS1991

Strain energy release rate distributions for double cantilever beam specimens

A 24-ply composite double cantilever-beam specimen under mode I (opening) loading has been analyzed by a 3D FEM code that calculated along a straight delamination starter for several different specimen materials. An isotropic specimen was found to have a strain-energy release rate distribution which varied along its delamination front due to the boundary-layer effect and another effect associated with the anticlastic curvature of the bent specimen arms. A 0-deg graphite-reinforced epoxy specimen had a nearly-uniform strain-energy release rate distribution which dropped only near the edge, due to the boundary-layer effect, and a +/- 45-deg graphite/epoxy specimen exhibited a pronounced strain-energy release rate variation across the specimen width.

Crews, J. H., Jr.↗

NASA NTRS1991

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.

Shivakumar, K. N.↗

NASA NTRS1991

A three-dimensional equivalent domain integral method for cracked solids

Three-dimensional FEM analysis is presently undertaken via the general formulation of the equivalent-domain integral method for mixed-mode fracture problems in general anisotropic and nonlinear materials. In mixed-mode integrals, the total J-integral is split into three separate modes of fracture; direct and decomposition methods are effective in this separation of the modes, as presently demonstrated by their application to several pure and mixed-mode fracture problems. The results are found to agree well with those reported in the literature, and suggest the usefulness of the method as a FEM-program postprocessing subroutines.

Shivakumar, K. N.↗

NASA NTRS1990

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 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.

Shivakumar, K. N.↗

NASA NTRS1990

Strain energy release rate analysis of delamination in a tapered laminate subjected to tension load

A tapered composite laminate subjected to tension load was analyzed using the finite-element method. The glass/epoxy laminate has a (+ or - 45)sub 3 group of plies dropped in three distinct steps, each 20 ply-thicknesses apart, thus forming a taper angle of 5.71 degrees. Steep gradients of interlaminar normal and shear stress on a potential delamination interface suggest the existence of stress singularities at the points of material and geometric discontinuities created by the internal plydrops. The delamination was assumed to initiate at the thin end of the taper on a -45/+45 interface and the delamination growth was simulated in both directions, i.e., along the taper and into the thin region. The strain-energy-release rate for a delamination growing into the thin laminate consisted predominantly of mode I (opening) component. For a delamination growing along the tapered region, the strain-energy-release rate was initially all mode I, but the proportion of mode I decreased with increase in delamination size until eventually total G was all mode II. The total G for both delamination tips increased with increase in delamination size, indicating that a delamination initiating at the end of the taper will grow unstably along the taper and into the thin laminate simultaneously.

Salpekar, S. A.↗

NASA NTRS1990

Crack-face displacements for an embedded elliptic crack in an infinite solid subjected to arbitrary tractions

Analytical expression for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary traction are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

Raju, I. S.↗

NASA NTRS1990

Evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

Tan, P. W.↗

NASA NTRS1990

Treatment of singularities in a middle-crack tension specimen

A three-dimensional finite-element analysis of a middle-crack tension specimen subjected to mode I loading was performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed nonsingular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities, by a log-log regression analysis, along the crack front. Analyses showed that finite-sized cracked bodies have two singular stress fields. Because of two singular stress fields near the free surface and the classical square root singularity elsewhere, the strain energy release rate appears to be an appropriate parameter all along the crack front.

Shivakumar, K. N.↗

NASA NTRS1990

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

An equivalent domain integral (EDI) method for calculating J-integrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. 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.

Raju, I. S.↗

NASA NTRS1989

Crack-face displacements for embedded elliptic and semi-elliptical surface cracks

Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

Raju, I. S.↗

NASA NTRS1989

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.

Shivakumar, K. N.↗

NASA NTRS1989

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.

Raju, I. S.↗

NASA NTRS1989

An equivalent domain integral for analysis of two-dimensional mixed mode problems

An equivalent domain integral (EDI) method for calculating J-integrals for two-dimensional cracked elastic bodies subjected to mixed mode loading is presented. The total and product integrals consist of the sum of an area or domain integral and line integrals on the crack faces. 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 the problems analyzed.

Raju, I. S.↗

NASA NTRS1989

A finite-element alternating method for two dimensional mode I crack configurations

A finite-element alternating method is presented for two-dimensional Mode-1 crack problems. An analytical solution for an arbitrary polynomial normal pressure distribution applied to the crack faces is obtained and used as the basic solution in the method. The method is applied to several crack problems to study its efficiency and the results are compared to accurate stress-intensity factor solutions in the literature. The method gave reasonably accurate stress-intensity factors and crack opening displacements with minimal computing effort. Because the method must model only the uncracked body, finite-element models with many degrees of freedom are not warranted and therefore, the method has been implemented on personal computers.

Raju, I. S.↗

NASA NTRS1988

Three-dimensional elastic analysis of a composite double cantilever beam specimen

Attention is given to the stresses and the strain energy release rate along the delamination front in the present three-dimensional elastic analysis of a 24-ply, cocured double-cantilever beam specimen by means of 20-noded parabolic-isoparametric finite elements. At the free surface, the strain energy release rate was found to be substantially smaller than the plane strain value; this is suggested to be due to the free-surface effect that exists where the delamination meets the surface edge.

Raju, I. S.↗

NASA NTRS1988

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.

Tan, P. W.↗

NASA NTRS1988

A finite-element alternating method for two-dimensional Mode-1 crack configurations

A finite-element alternating method is presented for 2-D Mode-1 crack problems. An analytical solution for an arbitrary polynomial normal pressure distribution applied to the crack faces is obtained and used as the basic solution in the method. The method is applied to several crack problems to study its efficiency and the results are compared to accurate stress-intensity factor solutions in the literature. The method gave reasonably accurate stress-intensity factors and crack opening displacements with minimal computing effort. Because the method must model only the uncracked body, finite-element models with many degrees of freedom are not warranted and therefore, the method has been implemented on personal computers.

Raju, I. S.↗

NASA NTRS1988

Stress-intensity factors for small surface and corner cracks in plates

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

Raju, I. S.↗