A new alternative approach to fracture problems for materials and structural elements with cracks is set out. It is based on the mechanism of local instability near defects. The approach is used to study the fracture of materials compressed along interacting cracks and the fracture of thin structural members with cracks under tension with allowance for local buckling.Introduction. The main question to answer by linear fracture mechanics, a well-established and widely accepted since, in looking into the possibility of further growth of existing cracks is whether the cumulative elastic energy is sufficient for additional surfaces of the defect to form. In Irwin's interpretation, this question is whether the integral characteristics of the stress-strain state at crack tips (stress intensity factors or crack opening displacement) achieve certain limit (critical) values under given loads.In some cases, however, this approach is a fortiori inapplicable, though intuition suggests that fracture (crack growth or fragmentation) may (and will actually) occur under increasing loads. Among such cases is primarily loads acting along cracks-the stress intensity factors appearing in failure criteria such as the Griffith-Irwin one (linear fracture mechanics) are equal to zero, and, hence, fracture does not occur. The buckling of cracked materials (under compression along near-surface cracks parallel to the free surface) is a widely known and well-described phenomenon (in particular, in laminated composites). The aforementioned pertains equally to parallel cracks along which loads act.It has long been known that local buckling triggers fracture [69]. Moreover, local buckling may strongly affect the classical linear fracture process by preceding it and frequently reducing the threshold levels of applied loads. This is particularly true of thin-walled structural members (plates and shells) where out-of-plane buckling precedes fracture.This paper cites results of solving nonclassical problems of fracture mechanics where local buckling either triggers fracture (loads parallel to crack surfaces) or strongly influences the fracture process by preceding it and altering the geometry of the element (thin-walled plate or shell).When the initial stresses are parallel to crack faces, there may be two classes of problems, depending on whether there is a field of additional stresses that are rather small compared with the initial stresses [8].If there is no such an additional filed, then we deal with fracture under compression along cracks. The approach used to solve such problems is based on the relations of three-dimensional linearized solid mechanics. The concept of fracture is this: local buckling near cracks triggers fracture. The process of fracture is initiated when the initial stresses reach critical levels (values corresponding to local instability). This approach (including the relations of linearized solid mechanics, the corresponding mathematical tool, and failure criteria) is detailed in [8][9][10][11][12]. The formulation of the b...

No abstract

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev-Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Introduction. Fracture mechanics is still one of the most intensively developing branches of solid mechanics, which is primarily due to its great practical importance for the quantitative assessment of critical loads for materials and structures with cracks. However, some problems in this area are yet to be completely resolved. Among them are the effect of initial (residual) stresses on the stress-strain state of materials and compression of cracked bodies. That researchers are interested in such problems is evidenced by the great many recent publications on the subject (see, e.g., [11, 16-18, 23, 26]).Of special interest are cases where prestresses (or compressive forces) act along crack surfaces. According to [5,7,8,16,17], such are nonclassical problems of fracture mechanics because they cannot be solved within the framework of classical linear fracture mechanics. The reason is that according to the linear theory of elasticity, the load components parallel to the crack planes do not appear in the expressions for the stress intensity factors and crack opening displacements and, hence, cannot be allowed for in classical failure criteria such as Griffiths-Irwin or critical crack opening.To solve problems of fracture mechanics for bodies with initial stresses acting along cracks, the papers [2, 4, 5] proposed an approach based on the three-dimensional linearized theory of elasticity and a brittle-failure criterion analogous to the Griffiths-Irwin criterion. This approach made it possible to solve some static and dynamic problems (mainly for single cracks in an unbounded material) and reveal new mechanical effects of prestresses (see [5,6,13,16,20,24] for reviews of relevant studies).In [3,7], local buckling near cracks was considered a failure mechanism in materials compressed by forces parallel to crack planes. Relevant problems were formulated and solved within the framework of the three-dimensional linearized theory of stability of deformable bodies [14,15] (see [7,12,18] for a review of studies based on the approach for homogeneous and composite materials in a continuum formulation). There are also a few recent results obtained using a piecewise-homogeneous medium to model a material containing and compressed along parallel interfacial plane cracks [19].What these two approaches to nonclassical problems of fracture mechanics (fracture of prestressed materials and bodies compressed along cracks) have ...

No abstract