A New Approach to the Determination of the Macrocrack Nucleation Period Near a Stress Concentrator

Abstract

The stress-strain state of a rectangular plate with a central circular hole and a disc with an edge notch is analyzed both for elastic and elastic-plastic behaviour when cracks emanate from the contours of these concentrators. Stress intensity factors are determined as well as the value of the inelastic deformation at stress concentration zones. The parameters describing the process of crack nucleation are established. The computational results are compared with experimental data when evaluating the period of macrocrack nucleation. NOMENCLATURE a,b = plate length and width d* = the material constant E = Young's modulus G = elastic shear modulus h = thickness of a plate or a disc K, = stress intensity factor (SIF) for the opening mode crack K,$ = SIF for the opening mode of a crack emanating from the concentrator L, = concentrator contour (K = 0); plate or disc contour ( K = I); crack contour ( K = 2.3) I = crack length 1, = length of equivalent crack f , = length of plastic zone 1, = length of a crack emanating from the concentrator N, = number of loading cycles before crack nucleation N ( t K ) , T(tK) = stress components on the L, contour R = disc radius or hole radius in the plate t , = current coordinate of the contour L, u(t,), o(t,) = displacement vector components S , , 86, = notch tip opening displacement (NTOD) and NTOD range (in point A) p = Poisson ratio p = notch radius in the disc uys = yield stress of the material u : , Au:= normal stress and normal stress range at the characteristic distance d* from the concentrator tip uyvmax = maximum stress at the concentrator tip uy(x) = normal stress component along the concentrator axis O(z), Y ( 2 ) = Kolosov-Muskhelishvili complex stress function

Unified model of nucleation and growth of fatigue cracks. Part 1. Use of force parameters of fracture mechanics of materials in the stage of crack nucleation

“…5). This distribution calculated by methods of the theory of elasticity has the form [29] A~y(x, 0, p)=A~y(0)f/~ ),…”

“…5b for x = 0 and y = 0) relax to the value of local stresses cy~, and their maximum lies at a characteristic distance d* from the tip of the notch [ 14,29]. We assume that, under cyclic loading, the local stress range A(Yy is determined [14,29] as the stress range Aov(x, 0) at the point x = d*, y = 0 (Fig.…”

“…If the parameter d* of the material is known, then, by relation (1), for given loading range A P, we can easily calculate the local stress range A~y in an arbitrary structural element with a structural stress concentrator [29]. Under these conditions, we performed experiments on specimens (see Fig.…”

“…where A~y(0) is the maximum stress range at the tip of the concentrator (x = 0, y = 0), which can be calculated by using the theoretical stress concentration factor K t and the nominal stress range AS n or the stress intensity factor range AK for an equivalent crack (for details, see [29]),…”

Tension of an elastoplastic disk. Part 1. Central crack

“…The lengths and orientations of these lines are determined in the process of numerical solution of the problem by the method of singular integral equations. The values of the crack tip opening displacement are also determined.Disk specimens with notches or cracks are used in the investigation of the processes of initiation and development of cracks under static and cyclic loading [1][2][3][4]. The level of local strains near a concentrator characterized by the jump of normal displacements (opening displacement) at its tip 6 can be regarded as a parameter that controls these processes in elastoplastic materials.…”