Analytical Model for Distortion Prediction in Wire + Arc Additive Manufacturing

Abstract

An analytical model was developed to predict bending distortion of the base-plate caused by residual stresses in additively manufactured metal deposits. This avoids timeconsuming numerical simulations for a fast estimation of the expected distortion. Distortion is the product of the geometry factor K, which is determined by the cross-section of substrate and deposit, and the material and process factor S, which is the quotient of residual stress and the Young's Modulus. A critical wall height can be calculated for which the structure distorts the most. This critical height is typically less than 2.5 times the thickness of the substrate. Higher walls increase the stiffness of the cross-section and reduce the distortion with increasing height.

Digital Image Correlation for Measuring Full-Field Residual Stresses in Wire and Arc Additive Manufactured Components

“…Figure 3 illustrates the distribution of the longitudinal component of residual stress in a WAAM part. If the substrate is clamped rigidly during printing, the residual stress is the summation of the initial stress field before unclamping and the deformation-induced stress field resulting from unclamping , which can be expressed by Equation (1) [ 5 , 13 , 57 , 58 ], where the term can be assumed or measured experimentally; can be obtained by DIC-monitored unclamping. Equation (1) is schematically represented in Figure 3 .…”

“…Based on experimental observations reported in the literature [ 5 , 13 , 57 , 58 , 59 ], assumptions made to simplify residual stresses analysis using the DIC technique are as follows:…”

“…The magnitude of this stress depends on the thermal properties, and for steel, this can be as high as the material’s yield strength at room temperature [ 58 ]. This assumption also provides a safety margin, as equalizing to yield strength represents the worst-case scenario [ 5 , 13 , 59 ].…”

“…Analytical method: The stress field caused during unclamping could be calculated using the principles of solid mechanics, as proposed by Hönnige et al [ 13 ]. Stress caused by unclamping was calculated using Equation (3), and then residual stresses were calculated using Equation (1) assuming the initial stress field in deposited walls equalled the tensile yield strength of the material, i.e., 502 MPa.…”

“…Localised heating and uneven cooling during the WAAM process introduce large thermal gradients causing distortion and residual stresses, which can affect the topology and global integrity of a WAAM component [ 3 ]. In the last decade, WAAM induced residual stresses have been experimentally investigated for various alloys, such as steel [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ], aluminium [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ], titanium [ 3 , 13 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], nickel [ 13 , 29 , 31 , 32 , 33 ], intermetallics [ 21 , 34 , 35 ], etc. The aforementioned literature has focused on quite a few areas including but not limited to the effect of process and geometrical variables on residual stresses, the effect of interpass and side rolling on controlling/reducing residual stresses, and the effect of pre-and post-processing on residual stresses, etc.…”