Engineering topics

Sih, G. C.

Publications and source records attributed to Sih, G. C..

At least 19 records

NASA NTRS1982

Moving cracks in layered composites

A three-layered composite with a crack spreading in the center layer has been analytically examined to evaluate the effect of material nonhomogeneity on a constant velocity crack. Two different loading characteristics are considered. In the first case, crack motion is maintained by uniform tensile stresses. In the other, crack deformation is caused by anti-plane shear stresses. Galilean transformation and Fourier sine and cosine transforms are used to determine dynamic crack tip stress fields. Standard Fredholm integral equations yield the dynamic stress intensity factors. The results show that the intensity of local dynamic stresses increases or decreases with crack length to layer thickness as a function of the relative magnitudes of the adjoining layer's material properties. Crack speed tends to increase the effect of material nonhomogeneity.

Sih, G. C.↗

NASA NTRS1981

Sudden bending of a cracked laminate

The intensification of stresses near a through crack in the laminate that suddenly undergoes bending is investigated. A dynamic plate theory is developed which includes the effects of material inhomogeneity in the thickness direction and realistic crack edge stress singularity and distribution. Numerical examples indicate that (1) the crack moment intensity tends to decrease as the crack length to laminate thickness is increased, and (2) the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers.

Sih, G. C.↗

NASA NTRS1980

Normal and shear impact of layered composite with a crack - Dynamic stress intensification

The dynamic response of a layered composite under normal and shear impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. One of the objectives was to develop an analytical method for determining dynamic stress solutions which should lead to a numerical method which utilizes Fourier transform for the space variable and Laplace transform for the time variable. The time-dependent angle loading is separated into two parts: a symmetric and a skew-symmetric with reference to the crack plane. By superposition, the transient boundary conditions consist of applying normal and shear tractions to a crack embedded in a layered composite; one phase of the composite could represent the fiber while the other could be the matrix. Mathematically, these conditions reduce the problem to a system of dual integral equations solved in the transform plane for the transform of the dynamic stress-intensity factor.

Sih, G. C.↗

NASA NTRS1980

Sudden stretching of a four layered composite plate

An approximate theory of laminated plates is developed by assuming that the extensioral and thickness mode of vibration are coupled. The mixed boundary value crack problem of a four layered composite plate is solved. Dynamic stress intensity factors for a crack subjected to suddenly applied stress are found to vary as a function of time and depend on the material properties of the laminate. Stress intensification in the region near the crack front can be reduced by having the shear modulus of the inner layers to be larger than that of the outer layers.

Sih, G. C.↗

NASA NTRS1980

Sudden bending of cracked laminates

A dynamic approximate laminated plate theory is developed with emphasis placed on obtaining effective solution for the crack configuration where the 1/square root of r stress singularity and the condition of plane strain are preserved. The radial distance r is measured from the crack edge. The results obtained show that the crack moment intensity tends to decrease as the crack length to laminate plate thickness is increased. Hence, a laminated plate has the desirable feature of stabilizing a through crack as it increases its length at constant load. Also, the level of the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers. The present theory, although approximate, is useful for analyzing laminate failure to crack propagation under dynamic load conditions.

Sih, G. C.↗

NASA NTRS1980

Effect of material nonhomogeneity on crack propagation characteristics

The influence of material nonhomogeneity on the behavior of a moving crack is investigated. The model assumes a running crack in a material whose elastic properties may differ from those of the surrounding material. Theoretical calculations showed that the energy stored in elements ahead of the crack can be raised or lowered depending on the crack velocity, the crack length and the degree of material nonhomogeneity which is associated with the ratio of the shear moduli and the distance between the crack and the neighboring material with different elastic properties. Based on the strain energy density theory, predictions are made on how material nonhomogeneity can influence the initiation and/or arrest characteristics of cracks.

Sih, G. C.↗

NASA NTRS1980

Axisymmetric elastodynamic response from normal and radial impact of layered composites with embedded penny-shaped cracks

A method is developed for the dynamic stress analysis of a layered composite containing an embedded penny-shaped crack and subjected to normal and radial impact. Quantitatively, the time-dependent stresses near the crack border can be described by the dynamic stress intensity factors. Their magnitude depends on time, on the material properties of the composite and on the relative size of the crack compared to the composite local geometry. Results obtained show that, for the same material properties and geometry of the composite, the dynamic stress intensity factors for an embedded (penny-shaped) crack reach their peak values within a shorter period of time and with a lower magnitude than the corresponding dynamic stress factors for a through-crack.

Sih, G. C.↗

NASA NTRS1979

Normal and radial impact of composites with embedded penny-shaped cracks

A method is developed for the dynamic stress analysis of a layered composite containing an embedded penny-shaped crack and subjected to normal and radial impact. The material properties of the layers are chosen such that the crack lies in a layer of matrix material while the surrounding material possesses the average elastic properties of a two-phase medium consisting of a large number of fibers embedded in the matrix. Quantitatively, the time-dependent stresses near the crack border can be described by the dynamic stress intensity factors. Their magnitude depends on time, on the material properties of the composite and on the relative size of the crack compared to the composite local geometry. Results obtained show that, for the same material properties and geometry of the composite, the dynamic stress intensity factors for an embedded (penny-shaped) crack reach their peak values within a shorter period of time and with a lower magnitude than the corresponding dynamic stress intensity factors for a through-crack.

Sih, G. C.↗

NASA NTRS1979

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Sih, G. C.↗

NASA NTRS1979

Influence of interface on composite failure

The influence of the interface on the composite system behavior is investigated by analytical modeling. The stress analysis is based on the two-dimensional finite element procedure in which twelve-node isoparametric elements with cubic shape functions are used. The location of possible failure sites is predicted by the strain energy density (SED) failure theory which assumes failure to coincide with locations of minimum SED while the locations of maximum SED correspond to regions of excessive distortion or yielding. The results of the analysis show that the way in which the modulus of elasticity varies within the interface is as important in modeling as the average interface modulus.

Sih, G. C.↗

NASA NTRS1976

Influence of specimen boundary on the dynamic stress intensity factor

The problem to be considered is the sudden appearance of a flaw or crack in a strip of material of finite height subjected to tensile loading. Stress waves are generated within the strip and are reflected from boundary to boundary. Of interest is the maximum value of the dynamic stress intensity factor at a given instance of time as the strip height to crack length ratio is varied.

Chen, E. P.↗

NASA NTRS1974

Three-dimensional growth characteristics of a plane crack subjected to concentrated forces

A combination of longitudinal shear and normal forces acting on a half-plane crack is shown to lead to predictions of crack growth qualitatively similar to those obtained by Knauss (1970) for crack propagation in antiplane shear. The presented results, based on the strain-energy-density fracture criterion, predict the direction of growth and the load which initiates it.

Hartranft, R. J.↗

NASA NTRS1973

Growth characteristics of a plane crack subjected to three-dimensional loading

The closed form expressions for the stress intensity factors due to concentrated forces applied to the surfaces of a half plane crack in an infinite body are used to generate solutions for distributed loads in this geometry. The stress intensity factors for uniformly distributed loads applied over a rectangular portion of the crack surface are given in closed form. An example of non-uniformly distributed loads which can be treated numerically is also included. In particular, combinations of normal and shear stresses on the crack which simulate the case of loading at an angle to the crack front are considered. The resulting stress intensity factors are combined with the strain energy density fracture criterion for the purpose of predicting the most likely direction of crack propagation. The critical value of the energy density factor can then be used for determining the allowable load on a specimen with a crack front not perpendicular to the tensile axis.

Hartranft, R. J.↗

NASA NTRS1973

Strain energy density and surface layer energy for a crack-like ellipse

Some of the fundamental concepts of sharp crack fracture criteria are applied to cracks and narrow ellipses. The strain energy density theory is extended to notch boundaries, where the energy in a surface layer is calculated and the location of failure initiation is determined. The concept of a core region near the notch tip, and its consequences, are examined in detail. The example treated is that of an elliptical cavity loaded uniformly at a large distance from the hole, and at an angle to the hole; the results are shown to approach that of the crack solution for narrow ellipses, and to display quite satisfactory agreement with recently published experimental data under both tensile and compressive loading conditions. Results also indicate that in globally unstable configurations in brittle materials, the original loading and notch geometry are sufficient to predict the subsequent crack trajectory with considerable accuracy.

Kipp, M. E.↗

NASA NTRS1973

Application of Papkovich-Neuber potentials to a crack problem.

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered in this paper. A closed form solution using four harmonic functions is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically.

Kassir, M. K.↗

NASA NTRS1973

Variation of strain energy release rate with plate thickness

An analytical model of a through-thickness crack in a statically stretched plate is presented in which the crack front stress state is permitted to vary in the direction of the plate thickness. The amplitude or intensity of this stress field can be made nearly constant over a major portion of the interior crack front which is in a state of plane strain. The average amount of work available for extending a small segment of the crack across the thickness is associated with an energy release rate quantity in a manner similar to the two-dimensional Griffith crack model. The theoretically calculated energy release rate is shown to increase with increasing plate thickness, indicating that available work for crack extension is higher in a thicker plate.

Sih, G. C.↗

NASA NTRS1973

Alternating method applied to edge and surface crack problems.

The alternating method, which intimately combines analytical results with numerical calculations, as applied to edge crack problems in two dimensions and surface crack problems in three dimensions, is treated. The case of a crack perpendicular to the edge of a semiinfinite material is considered. One of the crack geometries that has received continual interest in fracture mechanics is that of a semielliptical crack whose major axis lies on a stress free surface. In order to demonstrate the sensitivity of the solution to the influence of the free surface the semicircular crack problem is again treated by the alternating method.

Hartranft, R. J.↗

NASA NTRS1972

Slow and fast motion of cracks in inelastic solids. Part 1: Slow growth of cracks in a rate sensitive tresca solid. Part 2: Dynamic crack represented by the Dugdale model

An extension is proposed of the classical theory of fracture to viscoelastic and elastic-plastic materials in which the plasticity effects are confined to a narrow band encompassing the crack front. It is suggested that the Griffith-Irwin criterion of fracture, which requires that the energy release rate computed for a given boundary value problem equals the critical threshold, ought to be replaced by a differential equation governing the slow growth of a crack prior to the onset of rapid propagation. A new term which enters the equation of motion in the dissipative media is proportional to the energy lost within the end sections of the crack, and thus reflects the extent of inelastic behavior of a solid. A concept of apparent surface energy is introduced to account for the geometry dependent and the rate dependent phenomena which influence toughness of an inelastic solid. Three hypotheses regarding the condition for fracture in the subcritical range of load are compared. These are: (1) constant fracture energy (Cherepanov), (2) constant opening displacement at instability (Morozov) and (3) final stretch criterion (Wnuk).

Wnuk, M. P.↗