Abstract Our investigation into the effects of load biaxiality thus far, has produced several findings which, in our opinion, are deemed to be important. 1. (a) The standard expressions for elastic stress and displacement in the crack-tip region, i.e. the so-called “singular-solution’, cannot be considered to be approximations that are acceptable in a completely general sense. 2. (b) This conclusion is best illustrated in the instance of a biaxially loaded infinite sheet with a flat (horizontal) central crack, wherein the effect of the load applied parallel to the plane of the crack appears entirely in the second terms of the series representations for local stress and displacement. Omission of these contributions, which is the usual practice, is tantamount therefore to denial of the physical presence of the horizontal load. Thus, in calculations of stress, displacement and related quantities of interest in the crack border region by means of the standard expressions, no biaxial load effects will appear, leading thereby to the erroneous impression that load applied parallel to the plane of the crack can have no influence with regard to the fracture problem. 3. (c) For the infinite sheet problem with a horizontal central crack, our analytical analysis shows significant biaxial load effect on crack border region and crack edge displacement, on local maximum shear stress, on the pattern of maximum shear isostats, on the angle of initial crack extension, and on local elastic strain energy density and strain energy rate. On the other hand, both the elastic stress intensity factor (as to be expected) and the J -integral show no sensitivity whatsoever to the presence of the horizontal load. 4. (d) The analytical results referred to above for the infinite sheet are also seen in the results obtained for a finite sheet using finite element numerical analysis. 5. (e) A nonlinear finite element analysis of the same biaxially loaded finite specimen geometry, designed to simulate elastic-plastic material behavior under conditions of no unloading, shows that the global energy rate, the J -integral, the plastic stress and strain intensity factors (in the sense of Hilton and Hutchinson), and the size of the crack border region plastic yield, all have pronounced biaxial load dependency.
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