Uncertain Fracture Analysis Methods For Structures

Structural fracture is one of the main reason which leads to the break of engineering equipment,such as the airframe cracking,the rupture of pressure pipelines,the fatigue fracture of rails and axles.Due to the errors of manufacture and service environment,there are generally many uncertain parameters in cracked structures,such as material properties,geometrical sizes of cracks and external loads.With the complication of operation conditions and the promotion of reliability requirements of the equipment,the deterministic fracture analysis can no longer meet design demands of the structural service stability,therefore,the uncertain fracture analysis theory arises at the historic moment.Although the uncertain fracture analysis has received attentions and developments for a long time,it still needs to be developed and perfected as a whole,especially for complex fracture problems.For examples,in the fracture reliability analysis with multi-source uncertainties,the fracture analysis under random heterogeneous materials and the uncertainty analysis of complex three-dimensional damage tolerance,a series of technical problems still remain to be solved.This dissertation conducts a systematical research for the uncertain fracture analysis of structures,and aims at developing some uncertainty modeling and analysis methods of fracture.The research content is started from the probabilistic fracture analysis of structures.Then through considering the multi-sources,spatial and time features of uncertain parameters or responses,four key uncertain fracture problems including the probabilistic fracture with epistemic uncertainties.random field fracture,stochastic crack propagation path and uncertainty analysis of damage tolerances are further studied.We hope this dissertation can provide guidance and reference for the fracture reliability analysis,the stochastic crack propagation behavior analysis and the residual life interval estimation,and can be applied to the fracture and damage tolerance reliability analysis of planes,high-speed rails,nuclear power equipment,bridges and large aging equipment in the future.The following studies are carried out in this dissertation:(1)A probabilistic fracture moment analysis method of structures is proposed to calculate the probability density function(PDFs)of the stress intensity factors(SIFs)and the failure probability of fracture.Based on the Taylor expansion.the first four moments of the SIFs propagated from uncertain parameters are calculated.The four moments are transformed into the normal space for the purpose of solution stability.By using the maximum entropy theory and taking the first four moments as constraints,the PDFs of the SIFs in the normal space are estimated on the base of the Lagrange multiplier method,and then it will be transformed back to the origin space.Combining the stress-strength interference theory,the fracture probability of the cracked structures can be calculated.Since the loop iteration is not required,the fracture reliability analysis can be completed with a few calculations of the SIFs.In addition,this paper developed a semi-analytical method to solve the sensitivity analysis of the SIFs,which greatly improves the efficiency of the stochastic fracture analysis of structures.(2)A hybrid probability-interval uncertain fracture analysis method of structures is proposed to deal with the fracture problems with epistemic uncertainties.For the material properties and loads,their precise PDFs can be obtained by a large number of samples and thereby they are quantified by the probability model,while for the crack lengths and orientations,they are difficult to be measured by conventional means so that their precise PDFs are generally difficult to be obtained and they are quantified by the interval model.Based on the classical first-order reliability method(FORM),a probability-interval hybrid reliability analysis method with a double nested structure composed of an inner interval optimization and an outer probability optimization is developed and the solution to the nested optimization is calculated by means of the improved HL-RF method.The response surface with mixed probability and interval variables is established by the axial experimental sampling method.The response surface model is then substituted into the probability-interval hybrid model.After a series of loop iterations,an efficient probability-interval hybrid reliability analysis method based on the response surface is developed and the interval of failure probability is obtained.(3)A random field fracture analysis method of structures with random non-homogeneous material is developed to effectively analyze the statistical features of fracture performances with stochastic material spatial variability.The Karhunen-Loeve(KL)expansion is employed to describe the random field and quantify the uncertain characteristics of non-homogeneous materials.The polygon mesh is used to discretize the cracked domain and then its stiffness matrix is established by using the shape function of the scaled boundary finite element method(SBFEM).The random field is then inserted into the constitutive equations in order to establish the stochastic equilibrium equation,and thereby the SIFs with the random spatial distributed materials can be calculated.With the perturbation method,the statistical moments of the responses can be obtained.A semi-analytical sensitivity analysis method of the SIFs with random fields is presented.The effects of the material spatial distribution feature on the fracture properties are studied and the statistical analysis of the fracture properties with random field property is carried out.(4)A stochastic crack propagation path analysis method of structures using dimension reduction integration is proposed to efficiently calculate the random spatial distribution feature of the crack propagation paths with parametric uncertainties.The cracked domain is divided into several subdomains consisting of cracked subdomain and normal subdomain.The SBFEM is employed to calculate the element stiffness matrix and the element load matrix that are then respectively assembled into the global stiffness matrix and the global load matrix for the calculation of the SIFs.Combing the crack propagation criterion of crack angle and the re-meshing technique,the crack propagation paths are simulated.Through the introduction of Hadamard product operator,an improved dimension reduction integration method,which can deal with problems with vector responses,is proposed to transform the high-dimensional integration problem of the crack propagation path into an one-dimensional integration problem,and then efficiently calculate the PDFs and spatial distribution feature of the stochastic crack propagation paths.(5)A fatigue damage tolerance uncertainty analysis method with interval parameters and its experimental verification technique are studied.Considering the strong nonlinear relationship between the fatigue crack propagation life and parameters,an enhanced subinterval analysis method and its adaptive convergence mechanism are presented to predict the upper and lower bounds of the fatigue crack propagation life.In this method,a novel multidimensional parallelepiped convex model is introduced to transform the correlated parameters into the independent standard space,and on the base of this independent space,two expansion paths of subinterval analysis are constructed to efficiently solve the crack propagation life with interval parameters.The proposed method is successfully applied to the interval analysis of the crack propagation life of automotive engine rotors,mechanical gears and turbine blades.Finally,the crack propagation experiments are carried out to verify the validity of the proposed method.