*3.3.2 Surface contour measurement*

**3.2 CM measuring principle**

**3.3 CM measurement procedure**

*3.3.1 Welded specimen cutting*

**Figure 2.**

**110**

**Figure 1.**

*Weld groove and dimensions.*

*Schematic diagram of the CM.*

On the basis of the Bueckner's superposition principle, the CM is applied for evaluating residual stress existing in metallic parts or structures. The ideal theoretical implementation of CM used for weld is displayed in **Figure 2**. Step A in **Figure 2** is the undisturbed welded joint and the residual stress that one wishes to determine. In step B, the part was cut in two on the plane x = 0 and the cutting plane deformed due to the near-surface residual stress fully released by the cut; therefore stress in the plane x = 0 was zero. Step C is an analytical step, in which the deformed cut surface is forced back to its original shape; the resulting change in stress is determined. Superimposing the stress state in B with the change in stress from C gives the original residual stress throughout the part. And for arbitrary plane in weld, its

residual stress can be determined by the following general expression:

ð Þ *<sup>x</sup>*,*y*,*<sup>z</sup>* <sup>¼</sup> *<sup>σ</sup><sup>B</sup>*

ð Þ *<sup>x</sup>*,*y*,*<sup>z</sup>* <sup>þ</sup> *<sup>σ</sup><sup>C</sup>*

Welded specimen cutting is the first and most important step during the CM procedure as the subsequent steps of surface measurement, data processing, and stress calculation rely on the cutting quality of surface contour. It assumes that the

ð Þ *<sup>x</sup>*,*y*,*<sup>z</sup>* (3)

*σA*

*New Challenges in Residual Stress Measurements and Evaluation*

After the welded specimen cutting, the out-of-plane displacement can be implemented through contact measurement and non-contact measurement. Optical machines such as triangulating laser probes, confocal microscopes, et al. are useful for surface measurement. However, handling the large data sets, these systems produced can be problematic, usually requiring some sort of data reduction process. Comparing to non-contact measurement by optical machine, the coordinate measuring machine (CMM) with the uniform measured data is extensively employed for the contour measurement because the regular measured point can be obtained. In this study, the Hexagon micro plus is equipped with a 5-mm diameter touch probe, as is illustrated in **Figure 4**. And each cut surface was sampled with a measurement point spacing of 1 1 mm.

#### *3.3.3 Data processing*

The procedure of measured data processing is data alignment, data smoothing, averaging of the two data sets, and fitting of the two data sets. The data alignment is

**Figure 3.**

*Schematic drawing of contour cut configuration for welded specimens: (a) conventional contour cut configuration; (b) embedded cut.*

sets can be conducted by spline, Fourier, or polynomial. In this study, the "sgolay" method was used to remove noise and outliers and also fit the measured data

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

through Matlab: the processed data was displayed in **Figure 6**.

*DOI: http://dx.doi.org/10.5772/intechopen.90409*

*Residual Stress Evaluation with Contour Method for Thick Butt Welded Joint*

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

*3.3.4 Stress calculation*

**Figure 6.**

**Figure 7.**

**113**

*Finite element model for linear elastic analysis.*

**Figure 4.** *Hexagon coordinate measuring machine.*

#### **Figure 5.**

*Data alignment according to the measurement data sequence.*

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

*Residual Stress Evaluation with Contour Method for Thick Butt Welded Joint DOI: http://dx.doi.org/10.5772/intechopen.90409*

sets can be conducted by spline, Fourier, or polynomial. In this study, the "sgolay" method was used to remove noise and outliers and also fit the measured data through Matlab: the processed data was displayed in **Figure 6**.
