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Methods of determining the margin of cyclic crack resistance of metal structures for hoisting machinery

In the course of manufacturing and operation, there can appear cracks in load-carrying metal structures which are hard to be detected till a definite moment. That is why in the course of designing metal structures, it is necessary to ensure their durability during possible existence of cracks up to the next routine inspection of a structure. For the prognostication of the durability of a structure with a crack, a research of coefficients of stress intensity on end-element models with crack-like defects of different length is carried out. As a result of this, a procedure for the definition of crack-resistance resource allowing the supposition of safe operation of a metal structure with a crack within the limits of recurrent routine works is developed.


Introduction
Both technological and fatigue cracks can appear in parts of load carrying metal structures in hoisting machines during production or operation processes. The resistance of metal to structure crack propagation is called fracture toughness.
The known concept of secure damage is based on the assumption that in any metal structure, even in new, there are always defects that may remain long undetected. Dimensions of detected defects are determined by resolution of applicable testing aids. All defects which are beyond the scope of testing aids remain undetected and, when present in the metal structure, they are potentially dangerous for metal structure operation.
To assess the vitality and the remaining life of metal structures, as well as to assess the impact of technological and operational defects on their load-bearing capacity, we must have a calculation device to predict behavior of metal structures with cracks under operational loads, which includes methods of fracture mechanics using the stress intensity factor (SIF) as the main characteristics of the stress and strain state of the material near the crack tip. The value of SIF may be found, for example, by reference data [1,2] or by numerical methods. However, SIF guides do not contain practically any solutions to the cracks in the spatial objects of box-section typical for parts of metal structures of hoisting machines. In the paper presented this problem is solved on the basis of the end-element modeling of structures with crack defects with the purpose of the assessment of metal structure durability at the stage of designing.

Simulation of the stress and strain state at the tip of the fatigue crack
Many scientists were engaged in the solution of problems concerning cracking and fracture of load carrying metal structures of machinery, with the use of the finite element method as well [3][4][5][6][7]. In this study, finite element models of metal structures with box-section design were built to calculate the stresses in the vicinity of the crack tip and SIF in the automated design system and in the analysis of automated workstations WinMachine. These constructions are typical for the type of bridge cranes, which are the most common means of mechanization of cargo handling, transport and warehousing operations during various types of production and warehouse complexes [8]. In the bearing section models, simulated crack-like defects of different lengths were simulated. When constructing models and studying the stress and strain state, some measures were foreseen. They allowed one to improve the accuracy of the solution, namely, small discretization was carried out during the crack tip partition into small elements; at points located at different distances r from the crack tip, the values of stress intensity coefficient I K were determined by calculation; diagrams of I K dependence on r were built. Required value I K corresponding to the considered crack is defined as a result of extrapolation when 0 r → . When carrying out extrapolation, we exclude values I K , corresponding to the points which are most closely located to a crack.
In the current study, the values of SIF were found for normal separation cracks by extrapolating the graph of function is stress at distance r from the crack tip. The linear extrapolation is carried out within the zone of accumulation of elastic-plastic fractures [9], where the stress partially exceeds yield stress T σ . As a result of numerical experiment, stress values and SIF have been determined under rated stresses in the considered section of the metal structure equal to 50, 75 and 100 MPa, respectively.
The obtained SIF values were approximated by polynomial functional dependencies ) (α   The margin of crack toughness of a metal structure under cyclic loading is characterized by the number of cycles required for the crack growth from initial size 0 a to critical c a . If the cycle of stress changes in the crack location is of constant signs, then modeling and planning of the process, operational load of a metal structure are exercised by the method described in [10].

Forecasting methods of structure durability with a crack
Engineering assessment of the crack toughness margin is performed in the framework of the settlement system at the ultimate limit states, so we must enter the relevant factors that will ensure the reliability of this assessment. The number of crane working cycles up to failure a Z when the crack growth occurs to a critical size is defined by the formula: where dN γ is the coefficient of reliability of calculation methods; m γ is safety factors as an intended design or a part of the structure; m γ is safety factors according to characteristics of the material; ( ) I K α is a function of SIF changes from the relative crack length; 0 a , c a is the initial and relative size of the crack. By results of modeling and calculation, dependence graphs of durability of a metal design from a relative length of a crack are constructed ( figure 3).
where d Z -number of loading cycles for the period between complete technical examinations; c nnumber of cycles per shift; s n -number of shifts per day; d n -number of working days a year; N = 3 years -the period of operation of the crane between complete technical examinations.