A. S. Kobayashi

Stress intensity factor for an elliptical crack under arbitrary normal loading

Abstract Harmonic stress function and the stress intensity factor for an elliptical crack embedded in an elastic solid and subjected to an arbitrary internal pressure are derived in this paper. The internal pressure is assumed to be expressible in terms of a polynomial of x and y as σ zz = − p ( x , y ) where p ( x , y ) = A 00 + A 10 x + A 01 y + A 20 x 2 + A 11 xy + A 30 y 2 + A 30 x 3 + A 21 x 2 y + A 12 xy 2 + A 03 y 3 . The stress intensity factor for the elliptical crack subjected to this polynomial loading reduces to the solutions given by Green and Sneddon when all coefficients A ij except A 00 are zero and by Kassir and Sih when all coefficients except A 10 are zero. The solution is then used to determine the transient stress intensity factor of an elliptical crack embedded in a thick plate, one side of which is subjected to a sudden temperature change. Other possible applications of this solution, such as an elliptical crack in a large beam in pure bending, are also discussed in this paper.

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved.The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poissons ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions.The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.

Reevaluation of Arterial Constitutive Relations: A FINITE-DEFORMATION APPROACH

The purpose of this investigation was to use the finite-deformation theory of elasticity to interpret pressure-diameter data for in situ canine aortas and other arterial response data reported in the literature. A meaningful mechanical property for arterial tissue was identified as ∂W1/∂I, the partial derivative of the strain-energy density function with respect to the first strain invariant. An exponential function was found to characterize the mechanical property ∂W1/∂I for all arteries considered. Thin-walled tube stress approximations were found to result in inaccurate values for arterial stresses and incremental elastic mechanical properties. Wave speeds calculated using ∂W1/∂I for these arterial tissues agreed well with experimental measurements of wave speeds reported in the literature. Elevated values for strain-energy density were found in the inner arterial tissue layers. These high values for strain energy may contribute to atherogenesis in relatively straight arteries (e.g., the abdominal aorta) subjected to hypertension.

Hybrid experimental-numerical stress analysis

The hybrid experimental-numerical stress-analysis technique, which saw limited applications during the 1950s, has been resurrected with the vastly improved numerical techniques of the 1970s. By inputing the experimental results as initial and boundary conditions, modern computer codes are executed in its generation and application modes to yield results which are unobtainable when only one of the two techniques is used. The hybrid technique thus exemplifies the complementary role of the experimental and numerical techniques.

Dynamic fracture toughness of Homalite-100

Dynamic fracture toughness of Homalite-100 determined by T. Kobayashi and Dally are compared with those previously obtained by the authors where similarities in the two results for single-edged-notch specimens of various configurations are noted. Dynamic fracture toughness of Araldite B obtained by Kalthoff, Beinert and Winkler and those of Homalite-100 obtained by the authors are then compared and, again, similarities in the two results and, in particular, the scatters in experimental data for wedge-loaded DCB specimens of different sizes are found. All three teams of investigators used static near-field solution to compute the dynamic stress-intensity factors from recored dynamic isochromatics or dynamic caustics. Errors generated through this use of static near-field solutions, as well as through the use of larger isochromatic lobes, are thus discussed.

CRACK BRANCHING IN HOMALITE-100 SHEETS

Abstract Crack branching in Homalite-100 sheets of 1/8-in. and 3/8-in. thickness was studied by dynamic photoelasticity. Dynamic stress intensity factors, crack velocities and branching angles were measured and corresponding static stress intensity factors were determined by the method of finite element analysis. Dynamic stress intensity factors which preceded the actual branching reached a peak value of approximately three times the fracture toughness. The dynamic stress intensity factor drops prior to branching and then increases again to the maximum stress intensity factor at which point branching could occur again. Roughness of the fracture surface can be related to large dynamic stress intensity factors and crack velocities prior to branching and also after branching. Average branching angle was 26 deg. The results of this series of tests thus suggest that large dynamic stress intensity factors are necessary but not sufficient to cause crack branching.

Fracture dynamics—a photoelastic investigation

Abstract Isochromatic patterns associated with dynamic brittle crack propagation were recorded by means of a modified Schardin multiple-spark-gap, dynamic polariscope for 10 × 10 in. Homalite-100 edge crack panels. With the material properties determined by dynamic calibration, the resulting photoelastic information was used to evaluate the elastic fields surrounding the propagating crack by the semi-inverse technique. This solution was characterized by the dynamic stress intensity factor whose behavior was determined for accelerating, constant velocity, and arresting cracks. For the series of experiments discussed and the evaluation procedure used, the local stress field surrounding the dynamic crack can be characterized by a two-parameter stress function model. With this model, it was found that the change in crack velocity lagged the change in the dynamic stress intensity factor, but that the degree of crack surface roughness correlated closely with the magnitude of the stress intensity factor.

Dynamic crack curving—A photoelastic evaluation

AbstractA dynamic-crack-curving criterion, which is valid under pure Mode I or combined Modes I and II loadings and which is based on either the maximum circumferential stress or minimum strain-energy-density factor at a reference distance ofr0 from the crack tip, is verified with dynamic-photoelastic experiments. Directional stability of a Mode I crack propagation is attained when

A numerical and experimental investigation on the use of J-integral☆

r_o= \frac{1}{{128\pi }}(\frac{{K_r }}{{\sigma _{ox} }})^2 V_o^2 (C,C_1 ,C_2 ) > r_c