*3.3.4 Stress calculation*

In the final step of CM, the residual stress normal to a plane of interest can be obtained by linear elastic finite element analysis. In this step, the negative processed

**Figure 6.** *The processed data of contour: (a) raw data after average; (b) after processing.*

**Figure 7.** *Finite element model for linear elastic analysis.*

to ensure the raw data on a regular rigid and at the same location. It can be seen from **Figure 5** that during surface contour measurement, several measuring sequence may occur. With the starting point and measuring direction marked, the data in surface B will be the same in surface A by data transposed in Excel or Matlab. Since the presence of noise and outliers is inevitable within the measured raw data, leading to the significant errors in the calculated stresses, the noise and outliers have to be smoothed prior to being applied as the nodal displacement condition in the linear elastic finite element analysis. The averaging of the two data sets can cancel out the shear stress effects and other errors. Fitting of the two data

*Data alignment according to the measurement data sequence.*

**Figure 4.**

**Figure 5.**

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*Hexagon coordinate measuring machine.*

*New Challenges in Residual Stress Measurements and Evaluation*

data is applied as the nodal displacement condition of the finite element model which is often created according to the half of the whole welded specimen by using ABAQUS or ANSYS code. **Figure 7** displayed the finite element model of half welded joint, and red arrows representing boundary condition prevented the movement of rigid body. The inverse of the measured contour has been applied to the cut surface (deformation in this figure has been magnified �185). A fine element size (1 mm) is that faces the cutting surface in addition to a fine mesh density around the cutting plane are used in the present FE model.
