**3. Experimental observations and numerical analysis**

#### **3.1 Carbon steel and cemented carbide dissimilar welding**

As an example of dissimilar welding, we discuss here a previous analysis [26] on butt-brazing of a carbon steel (skh51) and cemented carbide (V30). **Figure 5a** illustrates the arrangement of the brazing. An skh51 plate of 18.5 mm wide, 50 mm long, and 3.37 mm thick was placed on a mount with the 18.5 mm side contacting a V30 plate of the same dimension. For approximately 30 mm in length around the contacting area, an induction coil was arranged to heat the specimen for brazing. On brazing, Ag braze paste (Ag-Cu-Zn-Ni alloy, ISO Ag450) was put on the contact surface, and a braze temperature of 800<sup>∘</sup> C was applied for 10 s. After this 10 s period, the brazed specimen was air-cooled. The noncontacting 18.5 mm sides of the respective plates were clamped to the steel blocks as shown in **Figure 5a**. The two steel blocks were connected via slide guides for free vertical slide. This means that the only constrain on the plates during the brazing operation was gravity. **Table 1** shows the material constants of skh51 and V30.

A contact acoustic transducer and a scanning acoustic microscope (SAM) were used for the analysis. The acoustic signal from the contact acoustic transducer travels through the entire thickness of the specimen. Thus, the measured acoustic velocity indicates the elastic property averaged over the specimen thickness. On the other hand, the acoustic signal emitted from the transducer head of the SAM is focused in a subsurface area of the specimen. Therefore, it detects the elastic property of the subsurface region. Hence, through a comparison of data from the contact acoustic transducer and the SAM, we can obtain information regarding the

*Acoustic velocities relative to nominal value. (a) Line a, (b) line b, and (c) line c.*

**Material Steel (skh51) Cemented carbide (V30)**

Elastic modulus (GPa) 219 580 Thermal expansion (10<sup>6</sup> K1) 11.9 5.3 Thermal conductivity (W m <sup>1</sup> K1) 23.0 67.0

**Figure 5b** shows the butt-brazed specimen and the coordinate points where the acoustic measurements were conducted. The shear wave and longitudinal wave velocities were measured with contact acoustic transducers (Olympus V156-RM and M110- RM, respectively), driven commonly by a square wave pulser/receiver (Model 5077PR). The surface acoustic wave velocity was measured with a SAM (Olympus UH3) with 200 and 400 MHz transducer heads in the burst mode for V(z) curve analysis [22, 23].

**Figure 6** plots the acoustic velocities relative to the nominal values (measured before the brazing). Here the three graphs are for reference line a, line b, and line c (labeled in **Figure 5b**) from top to bottom. The following observations can be made.

The longitudinal wave (*z*-wave) velocity shows the following features. On the

V30 side, it is lower than the nominal value for the entire horizontal span

depth of the residual stress.

**Table 1.**

**Figure 6.**

*Material constants of the brazed plates.*

*Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*

*3.2.1 Observation 1*

**19**

**3.2 Transverse residual stress profile**

*(a) Setup for skh-cc welding (brazing). (b) Butt-brazed specimen and coordinate points for acoustic measurements.*

#### *Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*


#### **Table 1.**

By substituting Eqs. (19)–(21) into Eqs. (13)–(18), we can find the third-order

To compare with acoustoelastic measurement, it is necessary to express the effect of the inclusion of the third-order elastic coefficient in the corresponding acoustic velocity. Assuming that the density is unaffected by the inclusion of the third-order effect, the relative acoustic velocity can be expressed as follows:

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *cij* þ Δ*Cij* � �*=ρ*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð*cij*þΔ*Cij*Þ *Cij*

C was applied for 10 s. After this 10 s

(22)

s

*ij* denote the acoustic velocity of the

ffiffiffiffiffiffiffiffiffiffi *Cij=<sup>ρ</sup>* <sup>p</sup> <sup>¼</sup>

As an example of dissimilar welding, we discuss here a previous analysis [26] on

period, the brazed specimen was air-cooled. The noncontacting 18.5 mm sides of the respective plates were clamped to the steel blocks as shown in **Figure 5a**. The two steel blocks were connected via slide guides for free vertical slide. This means that the only constrain on the plates during the brazing operation was gravity. **Table 1**

A contact acoustic transducer and a scanning acoustic microscope (SAM) were

*(a) Setup for skh-cc welding (brazing). (b) Butt-brazed specimen and coordinate points for acoustic measurements.*

used for the analysis. The acoustic signal from the contact acoustic transducer travels through the entire thickness of the specimen. Thus, the measured acoustic velocity indicates the elastic property averaged over the specimen thickness. On the

butt-brazing of a carbon steel (skh51) and cemented carbide (V30). **Figure 5a** illustrates the arrangement of the brazing. An skh51 plate of 18.5 mm wide, 50 mm long, and 3.37 mm thick was placed on a mount with the 18.5 mm side contacting a V30 plate of the same dimension. For approximately 30 mm in length around the contacting area, an induction coil was arranged to heat the specimen for brazing. On brazing, Ag braze paste (Ag-Cu-Zn-Ni alloy, ISO Ag450) was put on the contact

ð Þ2

effect for each stress tensor component.

Here *i*, *j* ¼ 1 … 6, and *v*

surface, and a braze temperature of 800<sup>∘</sup>

**Figure 5.**

**18**

shows the material constants of skh51 and V30.

*v* ð Þ3 *ij v* ð Þ2 *ij* ¼

> ð Þ3 *ij* and *v*

*New Challenges in Residual Stress Measurements and Evaluation*

q

corresponding mode with and without the third-order effect.

**3. Experimental observations and numerical analysis**

**3.1 Carbon steel and cemented carbide dissimilar welding**

*Material constants of the brazed plates.*

#### **Figure 6.** *Acoustic velocities relative to nominal value. (a) Line a, (b) line b, and (c) line c.*

other hand, the acoustic signal emitted from the transducer head of the SAM is focused in a subsurface area of the specimen. Therefore, it detects the elastic property of the subsurface region. Hence, through a comparison of data from the contact acoustic transducer and the SAM, we can obtain information regarding the depth of the residual stress.

**Figure 5b** shows the butt-brazed specimen and the coordinate points where the acoustic measurements were conducted. The shear wave and longitudinal wave velocities were measured with contact acoustic transducers (Olympus V156-RM and M110- RM, respectively), driven commonly by a square wave pulser/receiver (Model 5077PR). The surface acoustic wave velocity was measured with a SAM (Olympus UH3) with 200 and 400 MHz transducer heads in the burst mode for V(z) curve analysis [22, 23].

#### **3.2 Transverse residual stress profile**

**Figure 6** plots the acoustic velocities relative to the nominal values (measured before the brazing). Here the three graphs are for reference line a, line b, and line c (labeled in **Figure 5b**) from top to bottom. The following observations can be made.

### *3.2.1 Observation 1*

The longitudinal wave (*z*-wave) velocity shows the following features. On the V30 side, it is lower than the nominal value for the entire horizontal span

(0 <*x*< 50 mm). On the skh51 side, the velocity is clearly higher than the nominal value in the near-joint region (20<*x*<0 mm) and slightly lower than the nominal value toward the cold end (*x*< 20 mm). These features can be translated into the following characteristics in the residual stress in the *z*-direction. The V30 side experiences tensile stress uniformly over the entire horizontal span. The skh51 side experiences compressive residual stress near the joint and very slight tensile stress for the rest of the horizontal span. Along reference line a, the situation toward the cold end on the skh51 side is slightly different. The material experiences clearer tensile residual stress.

> the phase transformation does not take place. The V30 side experiences uniform thermal expansion with the cool end constrained by the table of the welding setup. The gravity acts in favor of this compression experienced by the HAZ. The greater elastic modulus of V30 also helps this compressing mechanism. In the cooling phase, the HAZ of skh51 shrinks less than the other regions (the non-HAZ of skh51 and the V30 side). This makes the HAZ of skh51 tend to be stretched by the other regions. However, this time the stretching force is against the gravity. Consequently, the compressive stress

*Deformation induced by thermal load due to brazing and other constraints. Inward arrows represent compressive residual stress and outward arrows tensile residual stress. Sizes of arrows represent the magnitude of*

*Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*

formed in the heating phase remains in the HAZ on the skh51 side.

at the boundary.

**Figure 7.**

*residual stress.*

than unity in these directions on the V30 side.

reference line a side of the specimen.

**4. Depth of residual stress**

**21**

4.The events along the *y*- and *z*-axes are slightly different. At the boundary (the joint), the higher thermal conductivity makes the expansion (in the heating phase) and shrinkage (in the cooling phase) faster on the V30 side than the skh51 side. Consequently, when the skh51 side is still shrinking, the V30 side has already completed the shrinkage, preventing the skh51 side from further shrinkage. Consequently, the skh51 side is compressed along the *y*- and *z*-axes

5.The residual stress on the V30 side results from the above events. As the reaction to the compressive stress on the skh51 in the cooling phase, the V30 side experiences tensile stress in the *y* and *z*-directions at the boundary. Between these two directions, the material is less constrained in the *z*-direction due to the shorter span of the joint. Along the *x*-axis, the V30 side is constrained by the skh51 at the joint and by the table at the cool end. Consequently, it is likely that the tensile deformation occurs preferably in the *z*-direction. By Poisson's effect, the material on the V30 side undergoes compressive deformation in the *x* and *y*directions. This explains the observation of relative acoustic velocity greater

6.The different behavior observed on the skh51 side along reference line a from reference lines b and c is due to the involvement of rotational displacement at the boundary. When the V30 side exerts compressive force in the *x*-direction on the skh51 side at the joint, the force induces counterclockwise rotation around the *z*-axis (in **Figure 5b**). This causes the compressive stress on the

**Figure 7** illustrates this observation schematically with some exaggeration.

Another important factor in residual stress analysis in general is the information

regarding the depth of residual stresses. The capability to detect the depth of
