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System of differential equations that reflects interrelationships of deformation, diffusion, and thermoconductivity used to study stress concentration around holes in elastic body
Stresses were calculated for finite-width orthotropic laminates with a circular hole and remote uniaxial loading using a two-dimensional finite element analysis with both uniform stress and uniform displacement boundary conditions. Five different laminates were analyzed. Computed results are presented for selected combinations of hole diameter/sheet-width ratio d/w and length-to-width ratio L/w. For small L/w values, the stress-concentration factors K sub tn were significantly different for the uniform stress and uniform displacement boundary conditions. Typically, for the uniform stress condition, the K sub tn values were much larger than for the infinite strip reference condition; however, for the uniform displacement condition, they were only slightly smaller than for this reference. The results for long strips are also presented as width correction factors. For d/w less or = 0.33, these width correction factors are nearly equal for all five laminates.
Elastic-plastic deformation theories and elastic solutions method for solving problem of stress concentration around circular hole in spherical shell
The state of stress in a cylindrical shell containing a circular cutout was determined for axial tension, torsion, and internal pressure loading. The solution was obtained for the shallow shell equations by a variational method. The results were expressed in terms of a nondimensional curvature parameter which was a function of shell radius, shell thickness, and hole radius. The function chosen for the solution was such that when the radius of the cylindrical shell approaches infinity, the flat-plate solution was obtained. The results are compared with solutions obtained by more rigorous analytical methods, and with some experimental results. For small values of the curvature parameter, the agreement is good. For higher values of the curvature parameter, the present solutions indicate a limiting value of stress concentration, which is in contrast to previous results.
The stresses in a circular composite plate with a central circular hole in which the material is cylindrically orthotropic and the compliances vary with distance from the center are calculated. A numerical example shows that an arrangement of the fibers at predominantly + or - 45 deg to the radii in the neighborhood of the hole reduces the stress concentrations significantly in an otherwise quasi-isotropic plate.
A computational methodology is described to probabilistically simulate the stress concentration factors (SCF's) in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties, whereas the finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate SCF's, such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using is to simulate the SCF's in three different composite laminates. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the SCF's are influenced by local stiffness variables, by load eccentricities, and by initial stress fields.
This study investigated the Yeh-Stratton Failure Criterion with the stress concentrations on fiber-reinforced composites materials under tensile stresses. The Yeh-Stratton Failure Criterion was developed from the initial yielding of materials based on macromechanics. To investigate this criterion, the influence of the materials anisotropic properties and far field loading on the composite materials with central hole and normal crack were studied. Special emphasis was placed on defining the crack tip stress fields and their applications. The study of Yeh-Stratton criterion for damage zone stress fields on fiber-reinforced composites under tensile loading was compared with several fracture criteria; Tsai-Wu Theory, Hoffman Theory, Fischer Theory, and Cowin Theory. Theoretical predictions from these criteria are examined using experimental results.
An overview of an analytic procedure which can be used to provide comprehensive stress and strength analysis of composite structures with stress concentrations is given. The methodology provides designer/analysts with a user-oriented procedure which, within acceptable engineering accuracy, accounts for the effects of a wide range of application design variables. The procedure permits the strength of arbitrary laminate constructions under general bearing/bypass load conditions to be predicted with only unnotched unidirectional strength and stiffness input data required. Included is a brief discussion of the relevancy of this analysis to the design of primary aircraft structure; an overview of the analytic procedure with theory/test correlations; and an example of the use and interaction of this strength analysis relative to the design of high-load transfer bolted composite joints.
Differential equations and numerical analysis for determining stress concentration and elastic deformation in rubber sheet under axially symmetric stretching
NASTRAN program used to calculate stress concentration caused by surface cavities in plates under biaxial loading
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.
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. 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. 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.
Notched metal crack initiation, determining high cyclic loads effects by prior local plastic behavior at stress concentration
High temperature stress corrosion of titanium and titanium alloys
Because the 2195 aluminum-lithium of the super lightweight external tank (SLWT ET) has a lower toughness than the 2219 aluminum used in previous ET's, careful attention must be paid to stress concentration in the SLWT ET. This report details the initial analysis performed by NASA to determine the material properties required to ensure structural integrity in these critical areas.
Nonlinear boundary value problems of an infinite elastic-plastic plate with a circular hole subjected to pure tension and pure shear at infinity are solved by a method involving Fourier series and finite difference. On the basis of these solutions, the validity of Neuber's relationship between the stress and strain concentration factors for the plane stress problems is examined and a generalized Stowell formula for the stress concentration factor is proposed for problems in which the applied loading may be pure shear as well as pure tension and, furthermore, other stress states. By the same method of solution, the stress distributions around a rigid circular cylindrical inclusion embedded in an infinite rigid-plastic matrix subjected to uniform transverse pure shear and tension are obtained.
The goal of achieving a better understanding of the failure of complex composite structure is sought. This type of structure requires a thorough understanding of the behavior under load both on a macro and micro scale if failure mechanisms are to be understood. The two problems being studied are the failure at a panel/stiffener interface and a generic problem of failure at a stress concentration.
Delamination fracture has limited the use of lightweight Al-Li alloys. Studies of secondary, delamination cracks in alloy 2090, L-T fracture toughness samples showed grain boundary failure between variants of the brass texture component. Although the adjacent texture variants, designated B(sub s1) and B(sub s2), behave similarly during rolling, their plastic responses to mechanical tests can be quite different. EBSD data from through-thickness scans were used to generate Taylor factor maps. When a combined boundary normal and shear tensor was used in the calculation, the delaminating grains showed the greatest Taylor Factor differences of any grain pairs. Kernel Average Misorientation (KAM) maps also showed damage accumulation on one side of the interface. Both of these are consistent with poor slip accommodation from a crystallographically softer grain to a harder one. Transmission electron microscopy was used to confirm the EBSD observations and to show the role of slip bands in the development of large, interfacial stress concentrations. A viewgraph presentation accompanies the provided abstract.