An Inverse Approach For Constructing Residual Stresses Filed And Extracting Plastic Properties Of Ductile Materials

Many significant problems in engineering are well known as inverse problems,including the determination of residual stresses in structure, the identification ofmaterial characteristics and other parameters, and so on. Because the inverseproblems are much difficult to solve than corresponding direct problems, numericalmethods become the main powerful tools to treat them, and sometimes incombination with experimental tests. In this thesis a number of inverse approachesare presented, related to constructing residual stress field in planar and axisymmetricstructures based on fewer testing data, and extracting the plastic properties of ductilematerials from spherical indentation tests.An inverse approach based on the inherent strain method using BEM ispresented for constructing the planar residual stresses field, which meets theself-equilibrium conditions. To enhance the stability of the inverse analysis, theinherent strain field is approximately expressed as a series of smooth basis functions.In order to preserve the advantage of the BEM, the domain integral in integralequation is transformed into boundary integral by means of the dual reciprocityboundary element method (DRBEM). In this way the explicit expression of thesensitivity matrix can be obtained and the distribution of residual stresses can beconstructed efficiently. Numerical examples show the applicability of the presentedscheme.A similar approach is proposed for constructing residual stress field inaxisymmetric structure. After the equilibrium equations with body forces in terms ofGalerkin-Papkovich vectors and the displacement expressions usingGalerkin-Papkovich vectors are deduced, corresponding domain integral can betransformed into boundary integral by means of the DRBEM. The explicit expressionof the sensitivity matrix can be obtained and the distribution of residual stresses canbe constructed efficiently.An energy based inverse approach for extracting plastic properties of ductilematerials from spherical indentation tests is presented, based on dimensional analysisand finite element computations. By defining a representative strain dependent on theenergy, for a given ratio of the indentation depth to indenter radius, a closed-fromexpression of the relationship between the directly measurable quantities and therepresentative stress was obtained. Based on the representative strains and stressescorresponding to two different ratios of the indentation depth to indenter radius, theplastic properties of materials are uniquely determined. Numerical examples andfurther theoretical analysis show that the present method is robust for a wide range ofmaterials, including both highly plastic and highly elastic materials. The existence,uniqueness and especially the stability of the solution of the present algorithm havebeen proved.A similar approach is proposed for extracting plastic properties of ductilematerials by taking the effect of friction into consideration and the key factors indetermining the effect of friction on the indentation response is discussed. It is shownthat the effect of friction is closely related to a directly measurable quantity, i.e., theratio between the reversible work and the total work done by the indenter. The biggerthe ratio of the reversible work to the total work is, the smaller the effect of friction is,and the effect of friction can be neglected provided the ratio of the reversible work tothe total work is bigger than 0.65.