A process-based inherent strain method for prediction of deformation and residual stress for wire-arc directed energy deposition

Abstract

Accurate and efficient prediction of deformation and residual stress in large metal components manufactured through wire-arc directed energy deposition is essential for optimizing the process parameters and ensuring the quality of the components. The finite element method (FEM) together with the inherent strain concept is a promising approach to solve the problems, but its prediction accuracy requires improvement, especially for the prediction of the residual stress. Motivated by this, a process-based inherent strain method (PISM) is proposed, which can better reflect the layer-wise process of wire-arc directed energy deposition. For one thing, an accumulative effect of the plastic strain, which results from multiple remelting during the sequential deposition process, is taken into account when the inherent strain is calculated and loaded. For another, an additional strain is introduced into the total inherent strain, in order to resolve the continuity conflict of deformation and then to dismiss the unrealistic stress oscillation between the equivalent layers, when a layer lumping method is used. In addition, the idea of decomposing plastic strain into a locally-related part and a structure-related part is proposed, which clarifies the theoretical basis of the inherent strain method for metal additive manufacturing. Numerical examples confirm the necessity for the consideration of the effect of multiple remelting, and the introduction of the additional strain. Comparisons with the predictions by the thermo-elastic–plastic model and the conventional inherent strain method, as well as with the experimental results, verify the validity and accuracy of the present PISM.

Appendix A: The calibration process of the heat source model

The Goldak double ellipsoid model is used for the arc heat source in the detailed process simulation. The double ellipsoidal shape enables better fitting to the actual heat source geometry, enhancing the precision of thermal analysis and predictions. A schematic illustration of the model is shown in Fig. 

Fig. 20

Schematic illustration of the Goldak double ellipsoid model

20.

The Goldak double ellipsoid model is expressed as [48]:

$$ Q = \frac{{6\sqrt 3 Pf_{i} }}{{\pi \sqrt \pi a_{i} bc}}{\text{exp}}\left[ { - \left( {\frac{{3x_{1}^{2} }}{{a_{i}^{2} }} + \frac{{3x_{2}^{2} }}{{b^{2} }} + \frac{{3x_{3}^{2} }}{{c^{2} }}} \right)} \right]\,\,\left( {i = 1,2} \right) $$

(A1)

where P is the heat source power, f₁ and f₂ are the energy distribution coefficients of the front and back ellipsoids, respectively, and satisfy f₁ + f₂ = 2. And a₁, a₂, b and c are the heat source shape parameters.

In this paper, f₁ = 0.6, f₂ = 1.4, a₁ = 2 mm, a₂ = 6 mm, b = 2.5 mm and c = 3 mm. The calibration process of the heat source model is proposed by Ding [54]. The parameters b and c are calibrated from the measurement of the cross-section of the metallographic profile, as shown in Figs. 4–10(a) in Ref. [54]. The parameters a₁ and a₂ are calibrated from the measurement of weld pool surface ripple markings, as shown in Figs. 4–10(a) in Ref. [54]. Similar calibration process is adopted by other studies and achieves an acceptable level of accuracy [57, 58].

To further validate the rationality of the adopted parameters, the transient thermal FE simulation is conducted using shape parameters calibrated from the experiments by Ding [54]. The FE simulation results of temperature history are compared with experimental results at the coordinates of point (250, 5, 0) of the model illustrated in Fig. 18. As depicted in Fig. 

Fig. 21

For the temperature history at point (250, 5, 0) of the model illustrated in Fig. 18, comparison of the present FE simulation with the experimental measurement by Ding [54]

21, the temperature history results from the present FE simulation align well with the experimental measurement, which further verifies the accuracy of the calibration process of the heat source model.