C. C. Hsiao

Theory of Mechanical Breakdown and Molecular Orientation of a Model Linear High‐Polymer Solid

A phenomenological theory of the molecular orientation dependence of mechanical breakdown phenomena is presented for a model linear high‐polymer solid. Taking into account the variation of the volume a general microscopic molecular model is first introduced. After simplification an approximation is considered. For one‐directional orientation the result indicates a rapid increase in the fracture strength as the degree of molecular orientation increases. The maximum fracture strength is found to increase to nearly six times the unoriented strength.

Influence of Reforming Processes on the Fracture Strength of Solids

The macroscopic strength of an oriented medium is investigated under the assumption that processes of breaking and reforming of microscopic components in the medium may occur. The differential equation governing the time‐dependent variation of the number of load‐carrying components is considered. Emphasis is placed on the study of the effect of the reformation processes on the stress‐time‐to‐fracture behavior. It is suggested that under small loads these processes may be responsible for the frequently observed phenomena of the deviation from linearity of the strength and logarithm of time‐to‐fracture relationship. An attempt is also made to compare theoretical results with some reported experimental data.

Behavior of Elastic Networks of Various Degrees of Orientation in the Kinetic Theory of Fracture

This paper describes a kinetic theory of fracture initiation using a linear elastic network as an approach to represent the strength and elastic properties of oriented materials. Emphasis has been placed on the questions as to whether the assumptions of small strains and invariant molecular orientational distribution are valid for the whole period of fracture initiation. The decrease of the modulus of elasticity resulting from the breakage of molecular elements during this period was found to be less than 1%. For brittle materials with high velocities of crack tip propagation the initiation period covers most of the lifetime of a sample. The logarithms of time to break calculated accordingly for network systems of different degrees of orientation are linear functions of applied stress over a wide range of stress. The slopes of these linear curves are inversely proportional to the modulus of elasticity of the network at zero time. Therefore, if the calculated curves of the logarithm of time are plotted ver...

Time‐Dependent Mechanical Strength of Oriented Media

For a homogeneous oriented and stressed medium, a theory of strength behavior is formulated and analyzed on the basis of considering the kinetic breaking and forming processes present in the microscopic molecular structure. The solution to this formulation gives not only reasonable results comparable to available experimental findings, but also yields new information which may not be possible to be verified experimentally at present. In general, it is found that under either fairly large or moderate stresses, the fracture strength is almost linearly related with logarithm of time. For small stresses, the kinetic nature of molecular reformation is found to be quite influential and thus the time required for fracture becomes larger and larger and finally approaches to infinity. The analysis is also extended to a partially oriented molecular system under more general loading conditions.

Anisotropy of Oriented Polymers

For a large deformation, the deformation‐dependent anisotropic elastic characteristics are illustrated through the analysis of a model medium. The variations of the elastic constants of an oriented polymer are then analyzed and correlated. The analytical results compare favorably with some available experimental data reported from dynamic measurements.

Nonlinear quasi‐fracture behavior of polymers

This paper deals with the nonlinear quasi‐fracture behavior of polymers. Using the finite element method, the quasi‐fracture model composed of an isolated craze opening with a nonlinear boundary envelope forces represented by oriented fibril domains is analyzed in simply‐stressed rectangular plate. The stress distribution, the displacement profile, as well as the yield or plastic or flow zone adjacent to the craze tips are obtained. It is found that the variation of the stress distribution near the craze tip is not as sharp as that for an elastic crack. The initial load required for yielding or flowing is greater for the quasifracture as compared with that for a classical fracture. Under the same load the yeild or flow zone is somewhat smaller as compared with that obtained on the basis of linear elastic‐plastic fracture mechanics theory.

A time dependent theory of crazing behavior in polymers

The development of crazing is not only a function of stress, but also a function of time. Under a simple state of tension, a craze opening displacement is closely associated with the viscoelastic behavior of the original bulk polymer medium in which individual crazes initiate and develop. Within each craze region, molecular orientation takes place when conditions permit, and a new phase of rearranged molecules governs its local behavior. Based upon a time‐dependent viscoelastic two‐dimensional model, using a computer program the craze opening displacement field has been calculated, time‐dependent craze length was also computed by taking into consideration the molecular orientation mechanism and large deformations in the craze region. Examples are given for simple viscoelastic media with simplified stress distributions. It is interesting to find out that the occurrence of crazing may be interpreted in terms of the stability or instability of the constitutive behavior of the bulk polymer.

Propagation of crazing in viscoelastic media

Up to now, the growth rate of a craze has been considered either constant or inversely proportional to time. By taking into consideration the effect of the surrounding population of crazes, it is found that the craze growth rate is affected by the local effective stress acting in the vicinity of the craze. Measured data of craze length as a function of time are found to be greatly affected by local interactions.

Mechanics of polymer craze

A new model consisting of symmetrical membranes with an enclosed elastic foundation is considered for studying the nature of a polymer craze in a tensile stress field. Both local displacement and stress distribution have been calculated for a linear craze under simple tension.

Laser microspeckle technique in displacement measurement near a crack tip

The laser speckle method has been found quite useful in obtaining in‐plane displacement measurements. It is especially useful if the displacement field in a small region can be effectively determined. By obtaining directly the speckle patterns at higher magnifications, a better distinction of the displacements in the vicinity of a crack tip is possible. In this short report some results are obtained and compared with those calculated from linear fracture mechanics and the finite element method for an aluminum crack.