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An approach is described for singularity computations based on a numerical method for elastoplastic flow to delineate radial and angular distribution of field quantities and measure the intensity of the singularity. The method is applicable to problems in solid mechanics and lends itself to certain types of heat flow and fluid motion studies. Its use is not limited to linear, elastic, small strain, or two-dimensional situations.
The inadequacy of a two noded beam-column element with a linear axial and a cubic transverse displacement field for inelastic analysis is demonstrated. For complete equilibrium satisfaction in the linear elastic range a three noded beam-column element is shown to be consistent. Next, the sensitivity of the inelastic response to numerical solutions of the inelastic response of a cantilever beam resulting from approximate integration of strain energy are brought out and finally, consequences of this on the nonlinear transient response of structures are considered.
A two-parameter fracture criterion has been derived which relates the linear-elastic stress-intensity factor at failure, the elastic nominal failure stress, and two material parameters. The fracture criterion was applied to center-crack tension, compact, and notch-bend fracture specimens made of steel, titanium, or aluminum alloy materials tested at room temperature. The fracture data included a wide range of crack lengths, specimen widths, and thicknesses. The materials analyzed had a wide range of tensile properties. Failure stresses calculated using the criterion agreed well (plus or minus 10 percent) with experimental failure stresses. The criterion was also found to correlate fracture data from different specimen types (such as center-crack tension and compact specimens), within plus or minus 10 percent for the same material, thickness, and test temperature.
Thin-gaged or high toughness materials containing cracks usually fail in a ductile manner with nominal failure stresses approaching the ultimate strength of the material. For such materials, a two-parameter fracture criterion was developed. An equation which related the linear elastic stress-intensity factor, elastic nominal stress, and two material parameters has previously been derived and has been used as a fracture criterion for surface- and through-cracked specimens under tensile loading. In the present paper the two-parameter fracture criterion was rederived in a more general form and was extended to compact and notch-bend fracture specimens. A close correlation was found between experimental and calculated failure stresses.
The limitations of linear elastic fracture mechanics in aircraft design and in the study of fatigue crack propagation in aircraft structures are discussed. NASA-Langley research to extend the capabilities of fracture mechanics to predict the maximum load that can be carried by a cracked part and to deal with aircraft design problems are reported. Achievements include: (1) improved stress intensity solutions for laboratory specimens; (2) fracture criterion for practical materials; (3) crack propagation predictions that account for mean stress and high maximum stress effects; (4) crack propagation predictions for variable amplitude loading; and (5) the prediction of crack growth and residual stress in built-up structural assemblies. These capabilities are incorporated into a first generation computerized analysis that allows for damage tolerance and tradeoffs with other disciplines to produce efficient designs that meet current airworthiness requirements.
The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models.
A two-dimensional, linear-elastic, finite element analysis of selected graphite/polyimide rail shear test specimens was made to determine the mechanical loading and the effect of heating the specimen to a uniform temperature. The presence of specimen free edges and their influence on the accuracy of the rail shear test is discussed. Parameters include the length-to-width ratio of the specimen and the ply layup for symmetric, balanced laminates. Results presented include shear and normal stress distributions and the deflection behavior of various specimens caused by the mechanical loading and elevated temperature.
In the vincinity of earthquake focal regions, conditions may not be equal. Crustal rocks stressed to more than approximately 0.6 of their failure strength exhibit material properties over and above that of linear elasticity. Interactions between the earth tide and crustal rocks that are under high tectonic stress are discussed in terms of simple phenomenological models. In particular, the difference between a nonlinear elastic model of dilatancy and a dilatancy model that exhibits hysteresis is noted. It is concluded that the small changes in stress produced by the earth tide act as a probe of the properties of crustal rocks. Observations of earth tide tilts and strains in such high stress zones may, therefore, provide keys to the constitutive properties and the tectonic stress rate tensor of these zones.
A method to determine the displacement and the stress on the crack plane for a three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane is presented. The main idea of the method is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. As a test of the accuracy of the numerical technique, the results are compared with known solutions for two simple cases.
The validation of a proposed fatigue life prediction methodology was sought through the use of aluminum butt and scarf joint and graphite/epoxy butt joint specimens in a constant amplitude fatigue environment. The structural properties of the HYSOL 9313 adhesive system were obtained by mechanical test of molded heat adhesive specimens. Aluminum contoured double cantilever beam specimens were used to generate crack velocity versus stress intensity factor data. The specific objectives were: (1) to ascertain the feasibility of predicting fatigue failure of an adhesive in a primary bonded composite structure by incorporating linear elastic crack growth behavior; and (2) to ascertain if acoustic emission and/or compliance measurement techniques can be used to detect flaws.
Present U.S. Air Force and proposed U.S. civil airworthiness regulations are based on considerations of 'damage tolerance' in aircraft structures. Airworthiness is assured by demonstrating that damage that escapes one in a sequence of periodic inspections will not grow to critical size before the next inspection. The evaluations conducted employ fracture mechanics analyses. Problems arise because the features of fracture mechanics applications related to aircraft structures are more complex than the cases of fracture mechanics which have been mainly investigated. NASA has, therefore, conducted a variety of research tasks to extend the capabilities of fracture mechanics to deal with some of these complexities. The current stage of development of these capabilities is described. Attention is given to the limitations of linear elastic fracture mechanics, a two-parameter fracture criterion, aspects of fatigue crack propagation, and crack propagation and fracture in built-up structures.
Results are presented for a finite element modal analysis of a centrally cracked rectangular plate made of linearly elastic material. The objective is to assess the effect of crack size on the natural vibration frequencies of the cracked plate. Only the in-plane vibration modes are studied. The results presented are finite-element mesh-size dependent. Namely, shrinking the mesh size, especially in the crack tip region, would change the magnitudes of the natural frequencies, and the trends would be the same as shown in the present note.
DESAPI program synthesizes linear elastic structures under static loads. Its design objective is finding element sizes that minimize total weight without changing layout structure. Primary constraints are upper limits on stresses and displacements prescribed as yield and loacl instability criteria. Program is written in FORTRAN IV for batch execution and is implemented on IBM 360 computer.
The yield function for plane stress of a transversely isotropic composite lamina consisting of stiff, linearly elastic fibers and a von Mises matrix material is formulated in terms of Hill's elastic stress concentration factors and a single plastic constraint parameter. The above are subsequently evaluated on the basis of observed average lamina and constituent response for the Avco 5505 boron epoxy system. It is shown that inclusion of residual stresses in the yield function together with the incorporation of Dubey and Hillier's concept of generalized yield stress for anisotropic media in the constitutive equation correctly predicts the trends observed in experiments. The incorporation of the strong axial stress interaction necessary to predict the correct trends in the shear response is directly traced to the high residual axial stresses in the matrix induced during fabrication of the composite.
This report presents the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test. The effects of non-uniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates are shown. A two-dimensional linearly elastic finite element model was used to analytically determine how various geometric parameters influenced the magnitude and distribution of inplane normal and shear stresses in a tensile rail shear specimen. Rail shear tests were conducted at room temperature and 589 K (600 F) on selected graphite-polyimide composite laminates using two titanium rail configurations. The analysis and test methods are discussed, and the results of the effects of the various parameters on shear modulus and ultimate strength are presented.
A detailed study of linear elastic deformation in Ralston basalt during triaxial loading has been made as a function of strain rate (8 x 10 to the -8th per sec to 5 x 10 to the -5th per sec) and moisture content under constant confining pressure (500 bars) and temperature (20 C). Young's modulus was found to be constant and independent of moisture content and strain rate; however, Poisson's ratio decreased 5.7 plus or minus 1.6% and 6.7 plus or minus 1.6% per order of magnitude increase in strain rate for two suites of dry samples and 1.4 plus or minus 1.2% per equivalent change in strain rate for one suite of wet rocks. Lateral expansion in dry rocks is therefore a more sensitive function of strain rate than it is in wet rocks. It is suggested that this strain-rate dependence is related to microcracking.
Linear elastic stress distributions obtained from a refined finite element mesh are used in conjunction with the tensor polynomial failure criterion to predict the initiation of failure in symmetric, finite-width graphite-epoxy laminates under tensile loading. Results are presented for a wide variety of laminates including: (+ and - theta)s angle-ply; cross-ply (0/90)s and (90/0)s; and quasi-isotropic (90/0/+ and - 45)s and (+ and -45/0/90)s. It is shown that the elastic stress distributions generally compare favorably with other published results, but also indicate improved satisfaction of the stress-free boundary conditions and indicate some differences in the singular behavior of selected stress components at the free edge. The tensor polynomial failure criterion is used to predict the location and mode of first failure. Examination of the individual terms of the polynomial indicates different modes of failure depending upon the laminate configuration.
The results of a linear elastic, plane stress finite element investigation of the stress distribution in a double V-notched coupon specimen are presented for an isotropic material (steel) and five graphite/polyimide laminates: (0), (90), (0/90)s, (plus or minus 45)s and (0/90/plus or minus 45)s. Stress contours, stress profiles, and stress concentration factors are presented for specimens loaded through rigid fixtures. It is shown that the finite element analysis predicts a region of essentially uniform pure shear in the central portion of the specimen for all laminates considered. Stress concentrations vary considerably with laminate configuration. The influences of elastic fixtures and thermal stresses on the stress distribution in (0) laminates are also investigated. The (0) laminate is predicted to exhibit maximum pure shear in the center of the test section for both rigid and elastic fixtures. It is concluded that the specimen is a practicable candidate for use as a composite shear specimen.