This paper is the second of a two-part series assessing the feasibility of using the J-integral with full-field deformation data from Digital Image Correlation (DIC) to characterize toughness in continuous fiber, SiCf/SiCc ceramic matrix composites (CMCs). In Part I, line and area integral adaptations of the J-integral were validated with analytical and experimental deformation fields. It was f...

In a recently developed approximation technique [1] for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this paper we work with the generic φ3+φ4 model in d = 0 dimensions. We compare the first, and simplest, approximation in the above sequence with the one-loo...

In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Banaś and L. Olszowy, a...

0 u(t, s, x(s)) ds, t ∈ J := [0,+∞), where f : J → R, u : J × [0, T ] × R → R are given functions and A : C(J,R) → C(J,R) is an appropriate operator. Here C(J,R) denotes the space of continuous functions x : J → R. Integral equations arise naturally from many applications in describing numerous real world problems, see, for instance, books by Agarwal et al. [1], Agarwal and O’Regan [2], Cordune...

It is generally accepted that residual stresses present in welded joints alter the conditions for fracture initiation by contributing to the crack-driving force. In this study, it is shown that weld residual stresses also alter crack-tip constraint, affecting fracture in an additional way. The fracture behavior of two crack geometries, a large pressure shell and a small fracture specimen, both ...