A comprehensive experimental and numerical study on redistribution of residual stresses by shot peening

Performances of conventional fiber reinforced composites are challenged in thermomechanical loading, when development of interlaminar stresses at the interface becomes the weakest link of the components. Development of functionally graded materials (FGMs) could lead to the reduction of such interlaminar failures, especially at high temperature applications. Therefore, these FGMs have a huge potential for use in many structural applications, particularly under thermomechanical loading. There has been a large number of works already reported on FGM components, starting from manufacturing to stress analysis of such components. Cracks in such FGM components may develop due to variety of reasons during service and need to be addressed while analyzing the performances of such components. This paper reviews the progress made till date on the analysis of structural components made of FGMs with a special emphasis on the analysis of cracked FGM components. In view of the potential use of components made of FGMs in a wide range of applications, it is important to understand the state of the art in this area. This paper thus provides a critical review of works reported in this area with an objective of providing the key challenges and future scopes of development in the direction of analysis of such structure for assessing safety in the presence of cracks.

Static and dynamic analyses of cracked functionally graded structural components: A review

A smoothed inverse eigenstrain method for reconstruction of the regularized residual fields

A modified stress function approach is developed for reconstruction of residual stress and eigenstrain fields from limited experimental measurements. The modified approach is successfully applied to three experimental case studies where residual stresses are introduced by surface peening. The smooth reconstructed residual fields not only minimize the deviation of measurements from its approximation but also satisfy all continuum mechanics requirements. Furthermore, a comprehensive discussion is performed on regularity of the solution in Tikhonov scheme and the regularization parameter is then determined utilizing Morozov discrepancy principle. Newton iterative method is also shown to have an excellent fast convergence to the regularization parameter while effectively reduces the computational cost.

http://journals.sagepub.com/doi/pdf/10.1177/0309324714558326

Inverse determination of the regularized residual stress and eigenstrain fields due to surface peening

The unified gradient elasticity theory with applications to nano-mechanics of torsion is examined. The Reissner stationary variational principle is invoked to detect the differential and boundary conditions of equilibrium along with the consistent form of the constitutive laws. An efficient meshless numerical approach is established by making recourse to the Reissner variational functional wherein independent series solution of the kinematic and kinetic field variables are proposed. Suitable forms of the coordinate functions, in terms of the Chebyshev polynomials, are introduced to fulfill a set of kinematic and higher-order boundary conditions in the elastic torsion of nano-bars with practical kinematic constraints. Torsional behavior of the unified gradient elastic bar is studied for structural schemes of applicative interest. An excellent agreement between the torsional responses of the nano-bar detected based on the established meshless method and obtained exact analytical solution is realized. The proposed meshless numerical approach is confirmed to have a fast convergence rate and an admissible convergence region in determination of the torsional rotation field with high accuracy. The introduced meshless method is demonstrated to be highly efficacious in characterizing both the softening and stiffening structural behaviors at nano-scale. The presented numerical approach therefore paves the way ahead in mechanics of nano-structures.

Analytical and meshless numerical approaches to unified gradient elasticity theory

Residual stresses, created in a steel beam by elastic–plastic bending, are predicted using an approximate analysis and the finite element method. The predictions are compared to experimental measur...

Measurement, analysis and reconstruction of residual stresses:

A complete investigation on the free vibration and stability analysis of beams made of functionally graded materials (FGMs) containing open edge cracks utilizing four beam theories, Euler-Bernoulli, Rayleigh, shear and Timoshenko, is performed here. It is assumed that the material properties vary along the beam thickness exponentially and the cracked beam is modeled as two segments connected by two mass-less springs, extensional and rotational spring. Afterward the equations of motion for the free vibrations and buckling analysis are established and solved analytically for clamped-free boundary conditions. A detailed parametric study is also performed to examine the influences of the location and depth of the crack, material properties and slenderness ratio of the beam on the free vibration and buckling characteristics of cracked FGM beams for each of the four engineering beam theories.

https://www.ije.ir/article_72331_7a2a66e9081466f403433b77af0a25b0.pdf

Analytic approach to free vibration and buckling analysis of functionally graded beams with edge cracks using four engineering beam theories

A thin layer on the component surface can be found with high tensile residual stresses, due to turning operations, which can dangerously affect the fatigue performance of the component. In this paper an analytical approach is presented to reconstruct the residual stress field from a limited incomplete set of measurements. Airy stress function is used as the primary unknown to directly solve the equilibrium equations and satisfying the boundary conditions. In this new method there exists the flexibility to impose the physical conditions that govern the behavior of residual stress to achieve a meaningful complete stress field. The analysis is also coupled to a least squares approximation and a regularization method to provide stability of the inverse problem. The power of this new method is then demonstrated by analyzing some experimental measurements and achieving a good agreement between the model prediction and the results obtained from residual stress measurement. Keywords—Residual stress, Limited measurements, Inverse problems, Turning process.

A New Analytical Approach to Reconstruct Residual Stresses Due to Turning Process

An analytical solution is presented that reconstructs residual stress field from limited and incomplete data. The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function. This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon. The analytical solution is demonstrated by developing a reference solution from which selected “measurement” points are used. An artificial error is then randomly added to “measurement” points for studying the stability of the reconstruction method utilizing TikhonovMorozov regularization technique. It is found that there is an excellent agreement between the model prediction and limited set of residual stress data in the sense of least-square approximation. © 2012 IAU, Arak Branch. All rights reserved.

http://jsm.iau-arak.ac.ir/article_514471_9d7d9b9e247563c7080261461794184e.pdf

S A Faghidian

Papers

Measurement, analysis and reconstruction of residual stresses:

Analytic approach to free vibration and buckling analysis of functionally graded beams with edge cracks using four engineering beam theories

A New Analytical Approach to Reconstruct Residual Stresses Due to Turning Process

An analytical solution for inverse determination of residual stress field