A research effort primarily concerned with the understanding of laminated composite plates with cracks subjected to time-dependent extensional loads is reported here. When loads are applied suddenly to a laminate, waves are reflected and refracted through the laminae and give rise to stresses and strains throughout the composite system. The process is three-dimensional in character and presents a formidable problem in the theory of elastodynamics, particularly in the presence of crack-like imperfections.

A number of laminated plate theories have been developed in recent times to analyze the static and dynamic response of composite laminates with or without the presence of stress concentrators such as holes, cracks, etc. Many of the theories tend to quickly become intractable when considering the determination of the state of affairs near the singular crack edges that are present in the laminate, particularly if the loading is time dependent. Additional uncertainties arise due to the lack of information on the mechanical properties of the interface through which load transfer takes place between the adjacent layers. This paper focuses attention on the intensification of stresses near a through crack in the laminate that suddenly undergoes bending. A dynamic plate theory is developed to include many of the essential features of the problem such as material nonhomogeneity in the thickness direction, realistic crack edge stress singularity and distribution while the parameter dependence of various significant quantities is also assessed. Of particular interest is the variation of the dynamic stress intensity factor with time. Numerical results for different geometric and material constants are displayed graphically to show how they can affect the transfer of load to the vicinity of a through crack in the laminate that undergoes sudden bending.

The objective of this study is to model the laminated composite as a multilayered plate each layer being made of a different material. With a crack in the mid-layer of the laminate, the stresses can vary in all three space coordinate directions and the problem is recognized as a three-dimensional one. A laminate plate theory is developed by application of the minimum complementary energy theorem in variational calculus such that the qualitative three-dimensional character of the crack edge stresses is retained while approximations are made in a quantitative sense on the stress intensity factor.

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.

The elastodynamic response of a penny-shaped crack in a cylinder of finite radius is investigated in this study. A step stress is applied to the crack surface resulting in transient behavior. The stress field near the crack front and the dynamic stress intensity factor are determined. Numerical resifits on the dynamic stress intensity factor are obtained to show the influence of inertia, geometry and their interactions on the load transfer to the crack.

The impact response of a crack in a layered composite which is subjected to antiplane shear deformation is considered in this study. The geometry of the composite consists of a finite layer that is sandwiched between two half-planes made of a different material. The finite layer contains a central crack which is oriented normally to the interfaces. Laplace and Fourier transforms are used to reduce the problem to a pair of dual integral equations. The solution to the dual integral equation is expressed in terms of a Fredholm integral equation of the second kind. Dynamic stress intensity factor is obtained as a function of the material properties, the geometry parameters, and time. It is found that the amplitude of the local stresses reaches a peak very quickly and then decreases in amplitude oscillating about the corresponding static value. Depending on the stiffness ratio between the materials, this peak value can be either higher or lower than the value for a homogeneous isotropic material.

The response of a through-the thickness crack with finite dimensions to impact in a finite elastic strip is investigated in this study. The elastic strip is assumed to be subjected to anti-plane shear deformation. Laplace and Fourier transform were used to formulate the mixed boundary value problem. The dynamic stress intensity factor and crack opening displacement are obtained as a function of time and the strip width to crack length ratio, h/a. The results indicate that the intensity of the crack-tip stress field reaches a peak very quickly and then decreases in magnitude oscillating about the static value. In general, the dynamic stress intensity factor is higher for small h/a. Similar behavior has also been found for the crack surface displacement.

The thermal fatigue behavior of a soda-lime-silica glass subjected to water quench and silicon-nitride subjected to thermal environment of a turbine engine was predicted from data of slow (subcritical) crack growth. A numerical integration technique was developed to calculate the extent of slow crack growth for each thermal cycle over the total duration of the transient thermal stress and temperature, as well as the total number of cycles required for catastrophic failure to occur. Good agreement between the predicted and experimental data was found. The results indicate that, for reliable prediction of thermal fatigue resistance, an estimate of critical flaw-depth based on a statistical (such as the Weibull) theory of brittle fracture is necessary.

Scattering of plane harmonic waves by a running crack of finite length is investigated. Fourier transforms were used to formulate the mixed boundary-value problem which reduces to pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The dynamic stress-intensity factors and crack opening displacements are obtained as functions of the incident wavelength, angle of incidence, Poisson’s ratio of the elastic solid and speed of crack propagation. Unlike the semi-infinite running crack problem, which does not have a static limit, the solution for the finite crack problem can be used to compare with its static counterpart, thus showing the effect of dynamic amplification.

The concept of fracture mechanics is introduced to characterize the toughness of fiber-reinforced composites which should be distinguished from tensile strength. A material may have a high tensile strength but a low toughness meaning that it has a low resistance to crack extension. Depending on the analytical model used, the same experimental data may report different fracture toughness values. In general, the combination of crack propagation in directions parallel and perpendicular to the fibers makes the composite problem very difficult to analyze.

The concept of fracture mechanics is applied to analyze the brittle fracture of unidirectional composites. The analytical prediction based on the newly developed S c -theory agrees well with the experimental data on Scotchply 1002 where crack propagation occurs along the fiber direction. The S c -theory represents a departure from the classical stress-intensity factor K c concept in that it is designed to treat the mixed mode fracture problem while the K c -theory is limited to Mode I crack extension.

Steady-state diffraction of stress waves by a semi-infinite running crack is considered in this study. In conjunction with the principle of superposition, an exact solution is obtained by using a method based on the Wiener-Hopf technique. As in the static case, the dynamic stresses possess the familiar inverse square-root singularity at the crack tip. The stress-intensity factors, however, are found to depend on the incident wave length, angle of incidence, Poisson's ratio of the elastic solid and speed of crack propagation. The stress-intensity factor serves as a useful parameter in studying elasto-dynamic crack problems since it can be associated with the rate at which elastic and kinetic energies are released by the crack. Ductile fracture is studied by adapting the Dugdale's hypothesis. The length of the plastic zone is determined and the influence of the speed of crack propagation is displayed graphically.

The problem of a uniformly propagating finite crack in a strip of elastic material is solved using the dynamic equations of elasticity in two-dimensions. Two specific conditions of loading on the strip with finite width are discussed. In the first case, the rigidly clamped edges are pulled apart in the opposite directions. The second case considers equal and opposite tractions applied to the crack surface. By varying the strip width to the crack length ratio, the amplitude of the dynamic stresses ahead of the running crack is determined as a function of the crack velocity. The local dynamic stresses are found to be lower than the corresponding static values for the displacement loading condition and higher for the stress loading condition. This effect becomes increasingly more important as the crack length to strip width ratio is enlarged. Numerical results for the dynamic crack opening displacement are also presented.

The effect of an imperfectly bonded laminar composite is examined in terms of the intensification of the torsional stresses operative near the imperfection which is assumed to be a circular shaped area. The laminar composite is modelled by four layers of different materials with the two outer layers being infinite in height and debonding occurs at the interface of the two inner layers. The analysis based on the application of Hankel transforms and the solution of a pair of dual integral equations can be easily extended to a multilayered system. Depending on the size of the layer thickness relative to the radius of the debonded area, delamination may take place either in a stable or unstable fashion. The analytical results also indicate that the influence of lamination tends to lower the stress intensity around an interface imperfection as compared to the stress state in a homogeneous solid containing the same imperfection. Numerical results are obtained for two special laminate geometries and discussed with reference to the pertinent parameters used in the current theory of fracture mechanics.

This paper is concerned with the anti-plane stress distribution around a semi-infinite crack traveling with constant velocity in an infinitely long strip of finite width. The problem is reduced to the solution of the Riemann-Hilbert problem by application of the Schwarz-Christoffel transformation and the theory of complex functions. Closed-form solutions are obtained for two cases of practical interest: (1) the boundaries of the strip are clamped and displaced in equal and opposite directions causing a tearing motion along the leading edge of the crack and (2) the crack is sheared longitudinally by a pair of concentrated forces moving with the crack while the strip boundaries are free of tractions. In both cases, the effect of strip width on the dynamic stresses is examined.