G.A. Papadopoulos

Elastodynamic forms of caustics for running cracks under constant velocity

Abstract For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K d I , which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating under Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K d I , evaluated.

The stationary value of the third stress invariant as a local fracture parameter (Det.-criterion)

Abstract In this paper the stationary value of the third stress invariant as a local fracture parameter is studied. The third stress invariant [ Det (σ ij ) ] is calculated along a circle around the crack-tip. This circle, which defines the core-region around the crack-tip, is the initial curve of the caustics. This distribution of the Det (σ ij ) presents a positive maximum. The crack propagates in the direction of the maximum value of the Det (σ ij ) and the fracture will initiate when the Det (σ ij ) on the core-region boundary reaches a critical maximum value which is a material property. This condition of initiation of the crack is proposed as Det.-criterion of fracture.

Crack initiation from blunt notches under biaxial loading

Abstract In this paper the crack initiation from blunt notches under biaxial loading is studied. The crack extension angle and the critical fracture stress are determined for notches with finite notch tip radii and for various angles of loading and for various biaxiality factors. The Det.-criterion, developed by the first author, is used. According to Det.-criterion, the crack propagates in the direction of the maximum value of the determinant of the stress tensor. The Det.-criterion is simpler and more flexible and applicable than the other fracture criteria up to now.

The Effect of Filler-Volume Fraction on Crack-Propagation Behavior of Particulate Composites

In the present investigation high-speed photography along with the well-known method of caustics were used for the determination of the crack-propagation velocity and the K I-stress intensity factor in iron-epoxy particulate composites. Specimens with three different low percentage filler-volume fractions were used; namely, 3%, 5% and 7%. It was found that the mean crack-propagation velocity decreases linearly with increasing filler-volume fraction. In addition, by using the method of caustics, the KI-stress intensity factor was calculated for each one of the composite specimens separately. It was found that the KI-S.I.F. increases by steps with increasing crack-length.

CRACK INITIATION UNDER BIAXIAL LOADING

Abstract In this paper the crack initiation under biaxial loading is studied. The crack extension angle and the critical stress of fracture are determined for various values of the crack inclination angle and for various values of the biaxial factor k . The Det.-criterion, developed by the author, was used. According to the Det.-criterion, the crack propagates in the direction of the maximum value of the determinant of the stress tensor. The Det.-criterion is simpler and more power than other fracture criteria used up to now.

Crack propagation and bifurcation in fiber-composite models. I: Soft-hard-soft sequence of phases

The influence of the hard fiber and the mesophase layers in a soft-hard-soft com bination of a biphase plate subjected to a dynamic tensile load, on the fracture mode and bifurcation process in both phases was investigated. It was assumed that the soft matrix envelops the hard-fiber layer of the plate, so that this plate constitutes a merid ianal section of a representative volume element of a unidirectional fiber com posite.

Stress intensity factors from reflected caustics in birefringent plates with cracks

Abstract In the present paper the method of reflected caustics is used for the evaluation of stress intensity factors in plates made of birefringent materials with a crack submitted to the opening mode of loading. It has already been established that due to the optical anisotropy of the material the rays reflected from the rear face of the plate form a double caustic. In this paper the influence of the optical anisotropy factor ξ of the material on the relative position and sizes of the two constituent branches of the caustic is studied. Nomograms are given for the accurate evaluation of mode I stress intensity factors from the geometrical characteristics of the two branches of the caustic. A series of tests, undertaken on plates made of polycarbonate of bisphenol A with ξr = 0.153, showed that the accuracy of evaluation of κI is the same as with the same method applied to optically inert materials.

Crack Propagation and Bifurcation in Fiber-Composite Models-II: Hard-Soft-Hard Sequence of Phases

An experimental study of the influence of a soft-fiber inclusion and the mesophase layer surrounding it in a hard-soft-hard bi-phase representative volume element (RVE), on the fracture and bifurcation processes in both phases was undertaken. The influence of the mechanical properties of each phase and the effect of the external loading-rate on the crack propagation velocity and the initiation of the crack bifurcation was studied by using high speed photography and dynamic caustics. It was shown that the propagating crack tended to bifurcate either in the hard or in the mesophase layer, and the bifurcation of the crack depended strongly on the strain rate, the elastic modulus and the Poisson ratio of the phases, as well as on the extent of the mesophase layer, which relies upon the degree of adhesion between phases.

CRACK INITIATION UNDER BIAXIAL LOADING WITH HIGHER-ORDER APPROXIMATION

Abstract In this paper the crack initiation under biaxial loading is examined by giving the expressions for stresses in a series form, which are equally valid near and far from the crack tip. Based on these expressions, the crack extension angle and the critical stress of fracture are determined by use the Det.-criterion. According to Det.-criterion, developed by the first author, the crack propagates in the direction of the maximum value of the determinant of the stress tensor. The Det.-criterion is simpler and more powerful than the other fracture criteria up to now.

THE INFLUENCE OF GEOMETRY OF EDGE-CRACKED PLATES ON CRACK INITIATION

Abstract In this paper the influence of geometry of edge-cracked plates on crack propagate under mixed mode loading conditions is studied. The edge-cracked plates under tension are examined. The crack extension angle and the critical stress of fracture are determined for various values of the crack inclination angle and the ratio of the crack length to specimens width. The Det.-criterion developed by the author is used.