Predicting Fatigue Crack Initiation Lives Of Compenents By Using Damage Mechanics

Fatigue failure is an important consideration in the design of most of the engineering compenents, a fatigue failure consists of two steps: crack initiation and crack propagation. in general terms, there are two methods in analyzing crack initiation. The methods based on test obtain key fatigue data by carrying out some tests which conditions are the same as practical conditions, or similar to practical conditions. Although the data are creditable derived from the tests, costs are more expensive and hinder its implementation. Based on some empirical equivalent principles and modified methods, another method combines tests with statistics analysis, which evaluates fatigue index of practical conditions by use of existing test data. Unforturnately, numerous statistical tests must be completed in order to gain perfect modifications for various practical conditions. Obviously, the study on crack initiation lives is much important in theoretical exploration and practical application. This dissertation is mainly devoted to evaluate fatigue crack initiation lives of engineering compenents with large range damage by use of damage mechanics. Focal points focus on establishing the variational principles of coupled systems and its applications for evaluating fatigue crack initiation lives of engineering compenents with large range damage, a set of new system is developed for this problem.The closed form solutions are derived to evaluate fatigue crack initiation lives for a pole subjected to a stretch or compression loading, and a beam subjected to a pure bending load. Applying least squares technique, the method to determine material constants in damage evolution equations is established. This part of work is fundamental and much important in damage mechanics analysis.Applying direct method, the closed form solutions are obtained for evaluating crack initiation lives of a circular shaft subjected to twist loading, a rectangular section beam subjected to pure bending load, and a beam subjected to transverse bending load. Applying virtual work principle, the closed form solution is obtained for evaluating crack initiation lives of a plane compenent under plane stress. The methods of evaluating fatigue crack initiation lives and determining working stress under assigned fatigue crack initiation lives are given for those compenents mentioned above. Applying variational principles, fatigue crack initiation lives is evaluated for a plane compenents with large range damage. Coupled system is defined firstly, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of a plane compenent under plane stress.For three dimensional compenents with large range damage, coupled system is defined for solving the problem of fatigue crack initiation, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of three dimensional compenents with large range damage. The closed form solutions are obtained for evaluating crack initiation lives of a circular shaft subjected to a twist loading, a beam subjected to a pure bending load or a transverse bending load, and a pole subjected to a stretch or compression loading.As an application, fatigue crack initiation lives of the backup roll of cool rolling mill is evaluated, the method is given for evaluating its fatigue crack initiation lives. An example is presented to demonstrate the application of new method developed by this dissertation in evaluating fatigue crack initiation lives of back-up roll.