Short Crack Lengths Research Articles

A model of failure in ideal elastoplastic media

1. The constructed model describes in sufficient detail the deformation mechanism and takes into account the thickness reduction of the material in the plastic zone in the vicinity of the crack tip. As in the CCO model, the physically trivial result was obtained: when the crack length approaches zero, the strength of the defect-free material is obtained. 2. The results calculated from the constructed model and the CCO model (Fig. 2) are sufficiently similar, firstly, at low levels of applied stress at which the plastic zone is highly localized, and, secondly, at short crack lengths, i.e., at higher. 3. With a reduction in the value of the small parameter (this characterizes the transition to more ductile materials), the results calculated from the two models also converge (see Fig. 3).

Yet another finite width correction for the center cracked tension specimen

The c e n t e r c r a c k e d tension specimen is the mainstay configuration in linear ealstic fracture mechanics for the determination of toughness values and for the collection of crack growth rate data. Its widespread acceptance relates to three rather significant advantages over alternative configurations: a closed form analytical solution exists for short crack lengths; it may be gripped in clamps without ambiguous bending; and cracks tend to grow in a straight line to significant lengths. A concise and reliable assessment of the finite width effect on near-tip stresses as characterized by the stress intensity factor K I is necessary to conveniently exploit the latter feature.

Low cycle fatigue of as-HIP and HIP+forged rené 95

The continuous cycling and hold time low cycle fatigue properties of the Ni base superalloy Rene 95 were studied at 649°C using powder products (−60 mesh) in the as-HIP and HIP + forged conditions. It was shown that cracks were initiated by pores, by ceramic particles and by a classical stage I mechanism for both materials and for both cycle characters. For the continuously cycled as-HIP material, deformation was restricted to well defined bands at low strains and became homogeneous as the strain level increased. The total energy to fracture increased abruptly in the low strain regime and this was also reflected by a break in the Coffin-Manson plot. In all cases cracks initiated at pores. The hold time specimens exhibited an extremely high dislocation density and surface connected initiation yet without a significant life reduction. The observations were essentially similar for the HIP + forged material except that deformation tended to be confined to well defined slip bands even at high strains and to some extent even for the hold time tests. This behavior was attributed to the fact that theγ′ were smaller, more coherent and more readily sheared by dislocations which were strongly paired. There was a marked tendency for crack propagation to change from transgranular to intergranular (also observed for the as-HIP material) at a unique combination of crack length and plastic strain. The transition occurred at shorter crack lengths for the HIP + forged material except when crack initiation was subsurface. In this case the transition was delayed and the life was greatly enhanced, indicating that the environment plays a major role in determining the fatigue life.

Fatigue Crack Propagation of Short Cracks

Previous studies have shown that both threshold stress intensity factors and fatigue crack growth rates are dependent on crack size. The average growth rates for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data. Elastic and elastic plastic fracture mechanics solutions are modified to predict this behavior of short cracks by introducing an effective crack length l0 into the solutions for intensity factors and the J integral method of analysis. The threshold stress at a very short crack length approaches the fatigue limit of the material, and therefore the value of l0 can be obtained once the threshold stress intensity factor and the fatigue limit are known. The accuracy of the term l0 in predicting crack growth rates for short cracks is found to be independent of the applied strain level. It varies linearly with the grain size of the material and can be considered at the surface as a measure of the reduced flow resistance of surface grains due to their lack of constraint.

A post yield fracture mechanics analysis of three-point bend specimens and its implications to fracture toughness testing

A Post Yield Fracture Mechanics analysis of three point bend specimens of a low strength, high toughness alloy steel, was performed on two series of tests. In the first the specimen dimensions were fixed and the crack length varied. In the second geometrically similar sub-standard specimens were tested. The smallest specimen tested was one-eighth valid size. The results were analysed using three post yield theories; the J-integral, the Bilby, Cottrell and Swinden (BCS) model and the Witt equivalent energy method. In the short crack length series the results were adequately described by the J-integral, the BCS model or by standard linear elastic fracture mechanics within the observed experimental scatter. In the geometrically similar series the Witt equivalent energy method consistently predicted toughness values within the scatter band of the valid tests. The BCS and J-integral methods underestimated the toughness for the two smallest sizes tested. This phenomenon is explained in terms of the relaxation of the plane strain plastic constraints towards the unconstrained plane stress state. The results of other workers on bend specimens are reproduced and retreated.

Notes on further experiments on crack propagation in tensioned plates subjected to high intensity noise

Sonically induced vibrations of structures, especially at high noise intensity levels, can initiate cracks in skins and ribs, or can propagate existing cracks which were caused by mechanical damage or other structural loads. Tests on simple stressed plates, with existing cracks, indicated that the propagation depends on noise intensity and spectrum, stress in the panel, geometrical parameters of the plate and the crack length. Assuming all parameters constant except for the intensity, the indications are that the rate of crack propagation is proportional to square of pressure (straight line relationship when crack propagation rate is plotted on a log scale against intensity in decibels) and the rate of crack propagation is approximately doubled for each 3 dB increase in noise intensity—the ratio varies from just below 2 for pre-buckling short cracks to almost 4 for postbuckling crack lengths, near the failing point. Tests also indicated that for very short crack lengths there was no propagation at all, even at high noise intensities. Increasing the thickness of the plate while keeping other parameters constant resulted in a slower rate of crack propagation below buckling crack length and then much faster crack propagation rates above this crack length.

Unified Theory of Thermal Shock Fracture Initiation and Crack Propagation in Brittle Ceramics

A fracture‐mechanical theory is presented for crack propagation in brittle ceramics subjected to thermal shock. The criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries. Thermal stress crack instability occurs between two values of critical crack length. For short initial crack length, crack propagation occurs kinetically, with the total area of crack propagation proportional to the factor St2 (1‐2v)/EG, where St is tensile strength, v is Poisson's ratio, E is Young's modulus, and G is surface fracture energy. Under these conditions the newly formed crack is subcritical and requires a finite increase in temperature difference before propagation will proceed. For long initial crack length, crack propagation occurs in a quasi‐static manner and can be minimized by maximizing the thermal stress crack stability parameter Rst= [G/α2E]1/2, where α is the coefficient of thermal expansion. For heterogeneous brittle solids, such as porous refractories, the concept of an “effective flaw length” is introduced and illustrated on the basis of experimental data in the literature. The relative change in strength of a brittle solid as a function of increasing severity of thermal shock is estimated. Good qualitative agreement with literature data is found.