Fracture analysis of plastically graded material with thermo-mechanical J-integral

In this paper, the influence of plasticity graded property and thermal boundary conditions have been investigated on the fracture parameter, i.e. J-integral using the extended finite element method. A complete computational methodology has been presented to model elasto-plastic fracture problems with geometrical and material nonlinearities. For crack discontinuity modeling, a partition of unity enrichment concept was employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stress–strain relationship of the material is implemented using the Ramberg–Osgood material model and geometric nonlinearity is modeled using an updated Lagrangian approach. The isotropic hardening and von-Mises yield criteria are considered to check the plasticity condition. The elastic predictor–plastic corrector algorithm is employed to capture elasto-plastic stress in a cracked domain. The variation in plasticity properties for plastically graded material is modeled by exponential law. Furthermore, the nonlinear discrete equations are numerically solved using a Newton–Raphson iterative scheme. Various cracked problem geometries subjected to thermal (adiabatic and isothermal conditions) and thermo-mechanical loads are simulated for stress contours and J-integrals using the elasto-plastic fracture mechanics approach. A comparison of the results obtained using extended finite element method with literature and the finite element analysis (FEA) package shows the accuracy and effectiveness of the presented computational approach. A component-based problem, i.e. a Brazilian disc subjected to thermo-mechanical loading, has been solved to show the adaptability of this work.

XFEM Fracture Analysis of 2-D Plastically Graded Domain With Thermo-Mechanical J-Integral

Many engineering components fail in the presence of service loads like thermal residual stresses and thermomechanical loading. An accurate evaluation of the fracture parameter (J-integral) at the crack tip is essential for the safe design of structures. In this work, a novel computational method called the Extended Finite Element Method (XFEM) has been implemented to analyze the plastically graded material (PGM) subjected to thermal and thermo-mechanical loading. For crack discontinuity modeling, a partition of unity enrichment concept can be employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stressstrain relationship of material has been done using the Ramberg-Osgood material model. The isotropic hardening and Von-Mises yield criteria have been considered to check the plasticity condition. The variation in plasticity properties for PGM has been modeled by exponential law. Further, the nonlinear discrete equation has been numerically solved using a Newton-Rhapson iterative scheme.

Dynamic analysis of elastically and plastically graded spherical and cylindrical contact

A dynamic analysis of a hemispherical and cylindrical contact, material properties of which are graded elastically and plastically along the radius, is presented. The static force–displacement behavior of a hemisphere and a semi-cylinder in contact with a rigid flat is obtained using finite element software. The force–displacement is used in a further dynamic analysis for undamped-free as well as for forced-damped vibration of the contact interface. For the undamped free vibration, variation of natural frequency w.r.t. initial displacement is furnished for different values of elastic and plastic gradation parameter. In addition, variation of maximum initial displacement for contact loss is also demonstrated. The forced-damped vibration characteristics of the spherical and cylindrical contact interfaces are presented in the form of frequency response curves with jump up and jump down frequencies. Spherical and cylindrical contact interfaces are found to exhibit softening and hardening type nonlinearity, respectively.