Initial Crack Distribution Research Articles

Numerical methods for the strain-softening response of concrete in uniaxial compression

In the present paper the mechanical comprcssive behaviour of quasi-brittle materials is analyzed by means of an ad hoc boundary element algorithm. The analysis is carried out by taking into account the initial crack distribution, which cannot be neglected if the experimental reality (developing over three scale levels, micro-, meso- and macro-scale) is to be modelled. The algorithm permits to follow the evolution of the crack geometry during the loading process, which is characterized, at each step, by the propagation of the most critical meso- or macro-crack. Moreover, in order to take into account the micro-crack effect causing the progressive decay of the material, a decreasing variation of the elastic modulus is assumed, depending on the strain energy density absorbed during the loading process. Different geometries, with different slcnderness and size-scale, are considered by the proposed model, with and without friction between specimen and loading platens. The numerical simulations represent the experimental results consistently.

Transport treatment of crack population in finite medium. Part II—Damage behavior in different zones

Extensive graphical results are given of a non-linear transport equation approach (derived and described in part I of this work) for crack population in a spherical medium surrounding a charged borehole. The central quantity numerically computed by time integration is the “damage” or the total volume associated with the cracks. Typically, intensive cracking (large damage) appears near the borehole and close to the surface (spalling), where the detonation pulse becomes (upon reflection) tensile. The extents and quantities of damage in these two zones are given as functions of the sample size, initial crack distribution, attenuation length and the form of the pulse. An interesting result arising from this non-linear method is the disappearance of the spall zone in spite of the relatively strong tensile part of the wave. This phenomenon is caused by the increased attenuation of the tensile pulse (on its way to the surface) due to the large number of cracks (either iniatially present or formed later).

Matrix cracking of cross-ply ceramic composites

A micromechanics study is presented of the matrix cracking behavior of laminated, fiber-reinforced ceramic cross-ply composites when subject to tensile stressing parallel to fibers in the 0° plies. Cracks extending across the 90° plies are assumed to exist, having developed at relatively low tensile stresses by the tunnel cracking mechanism. The problem addressed in this study is the subsequent extension of these initial cracks into and across the 0° plies. Of special interest is the relation between the stress level at which matrix cracks are able to extend all the way through the 0° plies and the well known matrix cracking stress for steady-state crack extension through a uni-directional fiber-reinforced composite. Depending on the initial crack distribution in the 90° plies, this stress level can be as large as the uni-directional matrix cracking stress or it can be as low as about one half that value. The cracking process involves a competition between crack bridging by the fibers in the 0° plies and interaction among multiple cracks. Crack bridging is modeled by a line-spring formulation where the nonlinear springs characterize the sliding resistance between fibers and matrix. Crack interaction is modeled by two representative doubly periodic crack patterns, one with collinear arrays and the other with staggered arrays. Material heterogeneity and anisotropy are addressed, and it is shown that a homogeneous, isotropic average approximation can be employed. In addition to conditions for matrix cracking, the study provides results which enable the tensile stress-strain behavior of the cross-ply to be predicted, and it provides estimates of the maximum stress concentration in the bridging fibers. Residual stress effects are included.

Probabilistic Fracture Evaluation of a Fast Breeder Reactor Cover

The structural reliability of a fast breeder reactor cover was evaluated using probabilistic fracture mechanics. The effects of important factors (initial crack distribution, crack detection level, crack growth rate, incidence of events such as earthquakes, in-service inspection for cracks, weld toughness, residual stresses, and environmental effects) on the reliability of structures were estimated, and methods for maintaining proper reliability were studied. It was found that the probability of the reactor losing its function is --10/sup -8/ in the terminal stage of the plant lifetime, even when the most conservative initial crack distribution and crack detection level are assumed. However, the prerequisite of such a condition is the use of appropriate leak monitors or proper atmospheric control. It was also confirmed that the degree of improvement in reliability through in-service crack detection, which was considered to be important, is not necessarily significant for the reactor cover.

Shock‐induced microfractures in six terrestrial igneous rocks characterized with differential strain analysis

Samples from a suite of 10 low porosity igneous rocks were shock loaded to low pressures (5 to 10 kbar). The specimens were recovered and analyzed with differential strain analysis (DSA) in order to characterize the microcracks and thus determine the influence of initial sample properties and shock pulse characteristics on shock‐induced microcracks. The DSA results reveal the following: The duration of a shock pulse is an important parameter; those samples that had been subjected to a shock of longer duration had a higher postshock crack porosity. If a sample initially contains a high concentration of cracks closing at a particular pressure, then such a concentration is also present in the postshock sample in addition to a concentration of cracks closing between 100 and 300 bars which is generally produced by the shock process. The shock‐induced cracks in samples with low initial crack porosity close over a wider range of pressures than those in samples with higher preshock crack porosity. Neither the grain size nor the high pressure (2 kbar) compressibility of the samples exerted any influence on the postshock crack distributions. Thus, the distribution of crack porosity with closure pressure of shock‐induced cracks reflects only the shock history and the initial crack distribution of a rock.