Predicting laser weld reliability with stochastic reduced‐order models

Abstract

Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack-like features with a high degree of variability in the geometry and material properties of the welded structure. Accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. Traditional modeling approaches cannot be efficiently employed. To this end, a method is presented for constructing a surrogate model, based on stochastic reduced-order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking -and thus peak load -plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results.

Rapid Uncertainty Propagation for High-Fidelity Prognostics Using SROMPy and Python

“…Then, the outputs Y are estimated using local piecewise-constant or piecewise-linear approximations of the model M. These two steps are elaborated on in the following sections. As many details were omitted for the sake of brevity, consult the relevant references (Grigoriu, 2009;Warner et al, 2013;Emery et al, 2015) for further explanation.…”

“…The stochastic reduced order model (SROM) approach (Grigoriu, 2009;Warner, Grigoriu, & Aquino, 2013;Grigoriu, 2011) was developed as an effective alternative to spectral methods, and has since been successfully applied to a range of stochastic problems (Sarkar, Warner, Aquino, & Grigoriu, 2014;Warner, Aquino, & Grigoriu, 2015;Emery, Field, Foulk, Karlson, & Grigoriu, 2015). This work, however, represents the first application of the approach in the field of prognostics and health management.…”

Bayesian methods for characterizing unknown parameters of material models

“…We assume the elastic properties are fixed with modulus of elasticity = 180 GPa and Poisson's ratio = 0.27. Details about numerical convergence and treatment of the weld geometry can be found in [7].…”

Post optimization for accurate and efficient reliability‐based design optimization using second‐order reliability method based on importance sampling and its stochastic sensitivity analysis

“…g.X/ D OEexp .0:8X 1 1:2/ C exp .0:7X 2 0:6/ 5 =10; (24) where X 1 N.4; 0:8 2 /, and X 2 N.4; 0:8 2 / Figure 2 illustrates the original and approximated performance functions at MPP in X-space. The approximated performance function of ASORM is obtained using the Hessian approximated by SR1 update.…”

“…In spite of the fact that SORM is obviously more accurate than FORM, SORM is limitedly used in engineering problems due to the calculation of the second‐order derivatives of the performance function, which might require huge computational cost. Sampling methods such as the Monte Carlo simulation (MCS) and the importance sampling estimate readily the probability of failure using the stochastic sampling because the complex analytical formulation is not required in the sampling method. In addition to the calculation of the probability of failure, stochastic sensitivity analysis is also readily performed without additional function calls in the sampling method .…”