Variational eigenstrain analysis of residual stresses in a welded plate

Abstract

We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stressstrain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice, complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.

Fourier basis for the engineering assessment of cracks in residual stress fields

“…A number of different families of basis functions have been used by other researchers. For example Korsunsky et al [18] have used Chebyshev polynomials and Kartal et al [19] employed Legendre polynomials in eigenstrain analyses. Here we adopt a classical Fourier approach because the basis functions have a well defined wavelength that is inversely proportional to the order of the term and because the terms are separated into even and odd functions which is convenient for determining stress intensity factor contributions.…”

“…Tada and Paris [28] analysed the same data and proposed a different analytical stress function meeting the same boundary conditions (an even function having a maximum value at x/c=0 and crossing the axis at x=c with the residual stress vanishing far from the weld as x/c → ∞). (18) A similar analytic stress function representing the same problem is given by [29]: (19) The three analytic stress functions, Eq. (8), Eq.…”

A Note on the Inverse Reconstruction of Residual Fields in Surface Peened Plates

“…One such method known as variational eigenstrain method is based on the theory of eigenstrains. The variational eigenstrain method utilized a combination of finite element analysis and distributed basis eigenstrains that combines experimental characterization in terms of residual elastic strains (Korsunsky et al, 2007;Korsunsky, 2009;Jun and Korsunsky, 2010). A smoothed inverse eigenstrain method is also developed for reconstruction of residual field from limited strain measurements that allows suppressing fluctuations that are contrary to the physics of the problem (Faghidian, 2014).…”

Numerical Reconstruction of Residual Stress Fields from Limited Measurements

“…After residual stress basis functions have been generated, both the stress function based and eigenstrain based methods proceed in a similar fashion (this can be seen in references: [15], [16]). A weighted sum of the stress basis functions is constructed, and (some function of) the difference between any available measured residual stress values and the corresponding values from the weighted sum is minimised.…”