Energy Release Rates for a Plane Crack Subjected to General Loading and their Relation to Stress-Intensity Factors

The well-known J integral of elastic fracture mechanics has been related to potential energy-release rate associated with crack extension and has proved to be of great value in fracture testing. In particular, the path-independence of the J integral has been used to an advantage in performing acoustoelastic measurements along a closed contour surrounding a crack tip. In Mode I (opening mode) for example, the J integral depends essentially only on the corresponding stress intensity factor KIwhich can thus be determined. Actually, J is the component of a vector in the plane of the crack and there exists a component of this vector normal to the crack plane, which, however, has not been interpreted properly in the past. It is one aim of this paper to supply a valid interpretation of this path-independent integral and to relate it to still another integral, also path-independent, which has been termed the L integral. It will be further shown explicitly that for a crack under mixed-mode loading this latter integral represents the energy release rate for rotation which can be used to determine both KI and KII

Theoretical Determination of Lifetime of Compressed Plates at Elevated Temperatures

A method for the theoretical determination of the lifetime of com- pressed plates at elevated temperatures is presented. In this approach, linearized equations are used throughout with the assumption that the plate material is a standard linear solid. The critical time (lifetime) is determined by reducing the time-dependent behavior to the time- independent response of purely elastic buckling. Theoretically predicted lifetimes of 2024-T3 (formerly 24S-T3) aluminum-alloy plates at 450 F are compared with experimental values obtained in previous work

Acoustic Nondestructive Evaluation of Energy Release Rates in Plane Cracked Solids

Acoustic measurements, using longitudinal waves in plane specimens, based on the theory of acoustoelasticity, permit the determination of the sum of the principal stresses (σl + σ2). By automatic scanning, we are able to make such measurements throughout a region of interest. In this paper we shall be concerned with the application of this acoustoelastic stress analysis to fracture mechanics. Specifically, the energy release rates for extension and rotation of a crack will be determined experimentally (J integral for extension, L integral for rotation) followed by a numerical adjustment procedure which may be called the rescaling technique. If desired the stress intensity factors at a crack tip may also be evaluated. This procedure was applied to three different specimen configuratlons, and the results compare favorably with purely theoretical predictions

A versatile algorithm for two-dimensional symmetric noncausal modeling

In this paper a novel algorithm is presented for the efficient two-dimensional (2-D) symmetric noncausal finite impulse response (FIR) filtering and autoregressive (AR) modeling. Symmetric filter masks of general boundaries are allowed. The proposed algorithm offers the greatest maneuverability in the 2-D index space in a computational efficient way. This flexibility can be taken into advantage if the shape of the 2-D mask is not a priori known and has to be dynamically configured

THE INFLUENCE OF THE USE OF RECYCLED GYPSUM ON THE PROPERTIES OF GYPSUM PRODUCTS IN LABOR CONDITIONS

The article presents the first results from research, which is deal with recycling of plaster boards and use of the resulting material. The research is carried out within the project MPO Trio c. FV30359 “Recyklace sádrokartonových desek a nová materiálová využití s pridanou hodnotou – GIPSRec”. The plasterboards are produced of stucco, which is calcinated of Flue Gas Desulfurization Gypsum (FGD Gypsum). There is possibility to replace a part of this stucco with recycled material. There is opportunity for saving costs for production. The question how this utilization can change the properties of the products is very important and it is necessary to find the possible improvement or deterioration. This is the objective of this research. The effect on properties was monitored on the samples which was prepared of only pure stucco and of stucco with part of recycled material. There was observed water ratio (splash test), setting times, volume changes, flexural strength, compressive strength and elasticity module

Induced Fubini-Study metrics on strictly pseudoconvex CR manifolds and zeros of random CR functions

Let $X$ be a compact strictly pseudoconvex embeddable Cauchy-Riemann manifold and let $T_P$ be the Toeplitz operator on $X$ associated with a first-order pseudodifferential operator $P$. In our previous work we established the asymptotic expansion for $k$ large of the kernel of the operators $\chi(k^{-1}T_P)$, where $\chi$ is a smooth cut-off function supported in the positive real line. By using these asymptotics, we show in this paper that $X$ can be projectively embedded by maps with components of the form $\chi(k^{-1}\lambda)f_\lambda$, where $\lambda$ is an eigenvalue of $T_P$ and $f_\lambda$ is a corresponding eigenfunction. We establish the asymptotics of the pull-back of the Fubini-Study metric by these maps and we obtain the distribution of the zero divisors of random Cauchy-Riemann functions. We then establish a version of the Lelong-Poincar\'e formula for domains with boundary and obtain the distribution of the zero divisors of random holomorphic functions on strictly pseudoconvex domains.Comment: 63 page