The propagation of a surface flaw in a cylindrical shaft subjected to rotary bending is analysed using a two‐parameter theoretical model. The stress‐intensity factor distribution along the crack front is numerically determined for any position of the flaw with respect to the bending moment axis. The crack front is assumed to present an elliptical‐arc shape with aspect ratio α = a/b (a, b = ellipse semi‐axes), whereas the relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a, and the bar diameter, D. The results for rotary bending are compared to those for reversed cyclic bending.

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The abundant literature on tensile strength size effects would appear to indicate the need for a dramatic change in our conceptual framework, in order to consider and measure material constants. For a large class of problems, it is well known that the phenomenon of the dependence of material behavior on the specimen dimensions can be interpreted by using Griffith's theory. This paper illustrates an effort to compare the results of Griffith's theory and gradient elasticity in the interpretation of size effect. A short review of both approaches is first presented. Then, a more detailed study of the stress concentration factor is provided for the normalized failure stress of a hole contained in an elastic plate. This problem has been solved analytically, by using a simple form of gradient elasticity. The minimum and maximum values of the dimensionless hole radius are found, for which the gradient effect has an influence on the mechanical behavior of the material. It is shown that both (Griffith's and gradient elasticity) lead to analogous results, and similar size effect predictions. Gradient elasticity shows a trend similar to the Griffith's one for small scales. When the hole radius is comparable with the square root of the gradient coefficient, , the stress concentration effect vanishes.Otherwise, for large values of the hole radius, gradient elasticity coincides with classical elasticity and the stress concentration effect is maximum. In gradient elasticity the size effect illustrated by the bilogarithmic diagram (lnc^vs. ΙηΛ), is nonlinear and shows an upward concavity, whereas Griffith's theory presents a linear variation. The former predicts an asymptotic value different from zero for the tensile strength, whereas for the latter the asymptotic value is unrealistically equal to zero. On the other hand, for small structural sizes both theories present similar results.

In stress analysis of cracked plates, alongside the stress intensity factor which quantifies the singular stress component perpendicular to the crack plane, the role played in crack growth by the constant term parallel to the crack plane, called the T-stress, has been widely investigated by many researchers. There are, however, cases of practical interest where the influence on the stress field of the higher order terms in the series expansion for the crack tip stress field, is not negligible. The main aim of the present investigation is to present and apply a set of equations able to describe more accurately the stress components for those cases where the mode I and mode II stress intensity factors used in combination with the T-stress are unable to characterise with sufficient precision the complete stress field ahead the crack tip. The starting point is represented by the Williams' solution (Williams, 1957) where stresses as expressed in terms of a power series. An example is investigated of a thin-thickness welded lap joint characterized by various joint width to thickness ratios, in the range of d/t ranging from 0.5 to 5. The present paper indicates that the local stresses as well as the strain energy averaged over a control volume which embraces the slip tip, can be evaluated with satisfactory precision only by taking into account a further four terms besides KI, KII and T-stress.

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